Teopuu uuyrtf,tgo4f,

I t[loil PnEr Ta LA EDTTTA lNTlr

Prascnlul volutn esle lrtrd.ucerca ilin li,tnba

Romd,nd 6i tcdinla ilin 14 Noembrie

e olcrci salo sil alafi tn limba sa

D. GER,\IANI

t,r.totlt) la acclc aplicalii,, asttel, cd aolu-lt lald sa poatc consiilcra ca prdna Publ,i-. I horiai 5i idcil,or D-l,u,i Ingincr Gogutllrllrucl*, D-sa a linut astlel ca prdna

attglcrd a lucrdrii D-trud Inginer Gogu Conslan-lJtrtau, lipdrdfd penlru lritna oard-Nn 1918 la

' . Lottilra, tib-un numllr - limi,tat ilc cxemfilare,

kolarato sccrcte ile guvernul Br'itanic, ilii cau-' tt clliceliilor bc cdre lc aaea noua teo e tn: hniriul- anncior gi. nijloacelor ik rdzbod.

f tminologia adoptald este aaea Nntrebuin-pl ht clcclriaitatc, cu care gliinla sonicitatea

:, tt o tnarc analogie,' Lt lincla rccstui aol,um, carc loailil nr. 1,

i',W*|, -atlottrl

ti-a Pro|us a ila-la htealit gi- "-0 al iloiloa aubru ablicatiilor ,inilustrial,e. s-a",3r al iloiloa aupra afl,icaliilor ,inilustriale, s-a{h-jat.1i_taxlul containlci linutll ilc D-sa la

.l'i'tea,

rDlTUnA J\cAD!:Mlr ! I nFpuBr,rctr socrALrsTE ROInANTA

tl 7071?, Euourcf , c.hr vlctort.t r. 126

3. (Gott ) Cowla i*cscu eJost un*tr ilinbc cci mai strdhtcili oamcniaJ a)ocll salo, tobihtll n* inpin* de marc exceblie. A urmql tcfli-$ Nalloaald do Poifuii 9i $oscle" ilin BrcurSii, le carc a tctnl-

ca pl ilc lrorroliei a, Jdctd uconicic din limii ani ilc inginadttoti Anghctr Saligny (co*structontl marclai lod metalic dc feslcC anawild ) sd Elio Railr ( cuttoscut hiihotehniciat ) . Etr lisl,ralC amwill ) 9d Elio Railu ( cunoscut hiilrotehnictan ) . EI linatI lmht malematici, Jizbd 9i tehnicd, penbu mt*icil 9i litoro

O *r.rftd Jtrrd ptogct, documentlnilu-se iacontenit Nn ceca cc ctotfibut n@bocit, cl a ilofind,it dc la htcclut o brcEihirc stiintilicllicutala ailhgtnilu'i-sc intuilia exbaotdi*afiin lnpcleghoe -leno-

t l ti t tchnicii, Cn bosibitritalca dc a asocia lenomene btnd. itancihlln a veni cu idef, noi t* brobleme corrsiitl;ate ifeituciibitre, Chi4rrkll ttttilillor inginerc1ti,ln 1004, el etraboreazil 9i dse tifdrcgtcq hpryh.i armat (carc Juscsc daabia brantat), ilc o ingurioi-

ll ai ailmhalia. $i cam tot ilc alunci lwefuse a Ji prioulal|lgf'ti sorrlcltate - loate fiai tlo tnit, cttttt srtwe cl, datoilil

- , $Uixlil be carc o crccazll si o lurrilarr.arteozil tn h tt-absbhitil. Ini010 bteactl tn Aiplia.'tarlt ccre ai.r)ea una ilbrbebhttil. In 1010 lleacll 8n Anglia, lard carc aua una ilit-c, lndu$ttii ale. tinbufui, undc lace e*bcrienle concludenlaI un marc sutres, 6c o catc nc.;stebtatf ! Iit-adnh. tri-'fscmiu la cowursitl lanbu rcglaria thului la nitrciiirelcadoafic Printrc palcle cllcci, Accastll rcglarc era rcatrirutdlll gt a attul o dfa ntar( importanld 4n lrimul rdzboi motlffil gt d attul o aga mare importanld 4n lrimul rdzboi mot

ta unoi conJcrhgc a lui Georyc Constantinescu la Politehnicatrafri6 | 020 ) , viccmncgah aenlui ili* Anglia, Sir Johnti6 1920), viccrnoc$ah.l aerulai din Anplia, Sir John

,,Sc ilatoltge loarlo huk ilomn*hti Consti&incscu Si ira lc sincrotrildrca mihalictular la aaionrc cil noi (utgletii

tfilt{ ugtcmalia awfra gcrmanilot ln aa, aga utm an atttLo".ll Juiamaialll Thcorv of Sonics a loct bubtricatil tn ant ,tJ h nrlrl I t22 ln Roritlnia. $i ntliti sd rZmarcilm cit, la otrt . ,lnxt-o h $coala Naliowld ila Poihni gi $osatre ilitt Bwt+ro Ia $coala Naliowld da Podurt 9i $osatre din Bwv

,,qlinnalrq cil prcglllhoa sa gtilnldJicd do bazd ,,sc il*gl anolra, alinn rr cil Prcglln a sa gtiintt|icd dc bazil ,,sc d*W". 5i td mai nmardm cll lntr-o disculio tlcspre sonicl-

ttllc tottlclidfii cn muica: ,,ln ow way it could bc saiilllt da*,ghlot oJ rl;rtslcal llatmony, bccduso it is in thal

,rlttt",$J tttl 3n Anjlla, Gcorgo Cowlanlinsct ttll gi-a uilal ai-h' ltQlrrrlli, ,tr.raco, l. ctrt . i(Ul.o dlt, tJ bklnw0t ll |?ilrraa dsegodt h len lril. $l lna l-a.aficcld l*aa ,( a otl Jn lttl, l.o alat nll,hnt ol Ara illl,irr R,S.

\ l t l t l t l l \ , l t t , l1p' , l t t t l i t t , t r t , , l t , , , i , l , i , ' i r t , , t i i ' , ' , , , i , t ,, ' t r ' .1, t ,1, , \ t l t l i iu. t .

I t , . l 'Lr t l t tu. t , t t i l t f 'u j r \ l , r t i r t t r t r , l t l t , , r , ,1,1 ' t t t , , i r . / i l ' r 'o l i l sol l i ( i l i l t i i ,t t t ' t t i t l r t l t t ' t , l r t , r n l tn l i . i i t .u unt)1 , \ l , t , .u . t nt l t t \ l l t t .n i t tor . fq.gi j t i

l ro,. l ' r r ' . , ,1 i

' r r r l r t r l t u l l l i t . t t i . tonfr l r l t l t l r t r t r t l l , , r f , l t , r r l t t t )u l i t l r (& tLr jnerr f l

tJr i l t t r , l t r r t , l t l i i l t t t r . l t r iotr t . l ' t r ' l , t r t r : t i t ) t t | | | t I I ) t I I I t t i t ' t r l r l t t . l t t . i ln l tsor ) [atc il l l , t r t t r r

' ' t r . , D| , . , l l i tcLrt I 'L l t t r . s i t t tX. ( t ) \ l t t l i l t t t , t r f ' tn l r t t , cJort t t r i lLt de-

l ' t t \ , f , i ) t l ) r t t \ t l i :1u' t t t ( r r is l , / / r ) i d i l i i i t t l t r , l r t rur i , r l i l '1, '

t , ' t t ; i t i i .l t tut l t . t i , inLl l rur t r tu. t ; t i int f r tst , t t t . , r ! , l t l ,n*141111p,1 l t t loxt tL lL ld. i t la iLor

Irrt t ,r : ' t r ( o .sl t t l l i tst , u tLurtt i i t tr ' t .r t?nl si t t . : i l t t t t tr t tr t . , ,cl t , o(hi i dL. a-It trr ' r", r i l t tr l t i t td-o ,,r t t , oclt i i dL: Lt: i" . ' . l .otul rslLt J11!,.n1,, clu.r dettnt l ,stret,hutt l t t t tu.t lnl . l r t t : t t l i t t idt i l toi . Deostbit t le i .nlcrr:sunte sint; i asociul i ik pettt tr l r f i t r tut lorul nL t l( l .r iLi t&tco;i cu al, tc;t i inlc; i tchnol.ogi i , sxtgrct i i lc detrt \ t l . t) i l , r trrrt l t l i . Si cr,. l i t t t ios lr incipirr, l ,ui sdu. cd ,,estc 1ff i feyicol, ; t i in!&ld , \ l,, rit'ulr'i" , ( inr!,' Oonsttutlinescu prezintri nuinero&sc aplicalii gi str'-t\"ltt , \fttr iDttttult ftntrtt. tL :f l ica tnria gi ingenioascle x.tt i l izdri frdcticeI't ' 'rt ' l , l ,nftr 'ttt :: i dit (r,rL nnrll,: Iu au, Jost dusc tncd !>tnii la cafdt ; i ut'uitrir ' l l tt, l trsr, rlroslorr l i sr ulLutgti sttgryti i le clin capitolul ,,ApLit:ali i l t sortici-lt l lu ,,t l i l t lr l i?rrst 1i lt i ttttrcvntc, l1t1tltc qtit t le act'ualc 1i da posibilc, cx-

ltu\t' t r 1t.t' i .llilo t dtt |,t L'.fti ci1. hti (,rorgt Constantincst:tt, Noi ttu mai ht.sistelntn\l lttt | | ' t t I i I t t t I t t I t t i , J i iud cotti ' i tr; i t i i o l1lorc l)&rte din tI c binecunoscu't ;ttttt ' t l t l \n lrt l ttcri tfrt1futt. ldl,

l,, l t o rtrlt (rrl1 sr: ailas/f It!. tr l |tt! i [1t, rlLutt int(rcs, dar st ctt ]ttstttnelvttlttr ,1 1111,1r,u',ftnlt lt:nu'lc;i ttt, ulttt irulit l .ercu cvcsttndd. falri dc autor. Denll l '1, n',,t\ lJ ft l |t, iruliL: s- orrital .f !.;t dtr (-)ogtt C or,stantin t sctt ; i la implirt irea

ll l l l t l ' ini lr l i ulrsttt ' t l tL stt, i tL t r,tclntl Oongrcstthti utr XVI-lctt el Utl, it l t l i it tt l , rtt,r lt l ttt lr l t ishtrit:; i JiktsoJit & lt i intt i Diit i : i l dc istoria;ti inld, dcl,r l lu,tuil, l i , l i tt trtt,tr. l 19,\1 ,ci t l oantuti dL: sti inlt i rontdu,i, utglt: i ; i t l irt al 'te

llrr t ,ttr ntl .s iutrr,!: i i dt ctL ur,ai i all. nirt l.l ' ,r ltui,r l i ..\ ' . l iontdn.it t i f irettL: ctt (rctfl iotrahi lrQrtirc acwstti ttortd

tltr a toltr,uttt ltr. i yi lorcstL: si f ioati i. tdita;i ctl de-al dailt:tt aolum (czt' r ' ttt-tttt 'rtttt\, t i tnlt i), r ' .r. is/r 'r l l ; i inci nctifdrit.

l 'rtu tltt 'r ' tt tt(tsltt ' i uolu L, toi ardtdttt, cri. Gogtt Cortstantirtcscu eslet ' t t t t t t t iD| tnt ! inDt l , t l r t t l i l0t , st i i .

, \ca(1. I l l , l l .AN I IALAN

I-ucrarea tle fafi t:rrc aparc sub iuglij irea unui coli:ctiv Iorrurrl rlirrplolr:sor l{atci }Iarinescn, ingincr Mircca Petcu si ingiricr (ionstantil .[iartrr,l.rqfindc rcetlitarea primului volum opcrei capitalc a lui CI.IOI{(il.l( ( )N STAN |INESCLI, volurn carc se rcfcri-r Ia TEORIA SONICII'.\ 'I 'I l silrr.Lc l fost tr-adus rliu limba englcz-ir do prolrsor' I)ionisit: Gcmali, tipiirilirt 1922 si completat cu te\tul Conferirrlei pc care (i. Constantircsr rr ir ti.trttl-o la Acadcmia llorniLltir i lt 1919, prccurn si r:rt uranuscrise.lc pt-. cirrr L'-.rIrrclr:rlintat profcsorului Nlatci \{arinescu cn ocazia ultimei s;r.lc vizit(. fi 'r(.ul:li t t { l r -L i r r 1963.

(iir al 2ira volum a1 accstci operc si cale st' refcrit la aplicalii lr SONI-( l l,\l 't l, voluln c;rrc trrbuia sir aparr'r iub ingrijirea lui G. Corrsiaut int'sc u,trrr rr vizut incir lunin;r tiparului, ca llrmarc a nortii salc in 1964. ,,\ctull-ttrcrrlr', tcxtul acestui aL 2-1ca'r'olum sc girs( $tc srrb {ormir dc ntartuscris ittlri lrl iolr:ca locuirrlei salc din Anglia, la Clouiston Lakc. Pc clc altir partc, rhlli irrrl ci-r la uoi in larir au lost realizatc, sau sint incir in curs tl,. r,',rliz;rr,',rrrrr.lc irplir:tti i alc sorricitirli i iniliatc ca unlart a ideilor cupriusc in volurnul l,s ir considr:rat oportun ca pirriL la cditarca volumului 2, accst{) aplicatii si.l irl (:lrpriusc irt Prcz-cnta Lucrarc. I)cqi in ltunl.il restrins, prin irnpolt:rn{lr ',silu:lrt:rli(att:l lor, clc vor suscita intciesul p(rtrLl ()

"un,r,.it"." cii nrai t,orr-

plr ' l i i r l r r lu lot ' apl icat i i lor sonic i t i r i i .( olcr:tivul i;i propune, ca prin tipiLlirt'rL prczentci lucriLri, s:'r far:i-r crr-

loscll oiuncnilor nostri dc ;tiiri jr 'r, ingiueriLrr-, ccrcctirtorilor dirr institutr.,rlrrrl.n{ilor (lin institutdc dc inviL!iLrnint tchnic supcrior, partcu tr:orrticirrr o1rr.r'r.i r':rpitrlc zr lui (,torgc Clonstanlinr:sr:u prccum ii siL dr:zvirluic lrLrgrrlcirrrp rlr.rrplicafii alc accstei S'|IIN-lE carc cstc SO\ICITATEA. Prin posilril i l,rlr::L rarc li se olcrit acurn dc rt o sturliir, cu complctitrilc uterllionirtc,l;i vor' lrrrlcir dn scarna cir csto vorl)il dc o lrrcrarc tiNl(lA in litcratura nous-ttr' i ;l i inlil i<:iL. Slntcm pcntru prima oariL irl prt:z.cnta unci tti intc c1rc dq5irrpitrtii. in l9llJ, cstt: gi irstiLzi a"ctrrdir, i lnstllncl irr nrxl convingiLtor gcnirilr tr'.rlor rrl popoluhri nostlu. t)perl lui (;. (-onstiurtin{:scu ocup:r ln tt:hnir.ir,lrrr rrl p,. r' irlrr oprrclc ttrrui NIihui linrirlcsr:u, uttui (;(lorflo Iincst:rr, rrnrril i l t r .otgl lc lVlar i t tcsct t i l oc: t tpr ' r in l i tcrrr t r r r : - r , inrnrrz, i , i , r , .spr 'ct iv ln; t i i t r tn. { - i t i ,lofql vir l)ll lcl rrrrrtil i rlt:-r lungrl fi lclor (r. ru-rrrr.:rz,i-r, crrrrt sr: t:rt:cazir. o 5li-l r t l l l , i r t l l r :g r l r rurrrr l 'pc t : r r r t : gcniul t1tna11, l ro l r r i r l r l r lc ' la i tkt t : : r in i ! i lL lh, i t p i r -| ttrl]c lxrnlru r. :rjurtl;t: l ir lr:zrtltrtrtl final, isi ,, ' iL <liL sciurlr cir slrrr: tlcosr:ll irr:r l r , ' l ' l ro l r r : rs . l , l t l isort r :an: i r l ucr:rr t l r l : rs lctr ' ; r r r rc l<xh. i tn l r I r . tuIr I i r ' r : r ' r . r ncvoi tr t lo lor ; i r t t i rx l i r r : r t rPi t i t : t ' t i r t cr l r t { i i l , s : r l , r , r ' : r r , . t , r I i r l r t l s . ' r s l ) l l r l i ! c i ! lx : \ .l l t l iL I i t t r r r t i t t r t t r t { i t : s i t t l o t l t ls t : t l lx ' t i r t ' cs l r : t lc t 'o ic r l r :91)( f , t l i rnslr i r i r l i r r 5 ir r r t r r r r r i l ' ) { , i r rspira{ i r . , ( , r \ r r11r: ( or \s l i r l l i l r :s l r r r r r i r ru i r . f l r crr r r r r r l l i r r5rrr i r r I l i1l l r t l l l l i ls l t r r r t ) ( r l l r l t I I I I I ( ' I | | I | | i | , ( r : t : i t ( r ' i i t l t t 'nt t is r ' i r i r t l r - In l i r r rP ro

t t , t t t t t l t t t l l l -

, , l l t , . l r t l tu) t l , r i tu f l i t t t ru

*

. . .. ftrt lirnr,*jrrl rr*rri:r,riLrii: r,,r,i,ii ,; , iiii i"i,,i'i,:,',:'lfi h,lilli'i:Ttn:'H['".?rtrbllcrrst:lL o irriitlogi r intr.rr r:L.r:Ir.ir.rtri|.. ,;, ,u,,rtitiuiu,'ii,iiiiri,ra prrn ".eu.tantrl l(xrLo sonic(: t lr lDil lnr xlcl rt l:ii;p;;iii;;;;;ilil;;";;ffili":ll.ll'lij;,lJl,iilriil,li:lli,it: ,'i (' i,,r.:a8i serie de

,r.r.,;:i, Yill':l':"'lll"?lt"i?,,,fi,',";i; Illt,";;;11,1;;;.,,,,i;ii,lf;1,,,1,,ffiii.':.#;ltrrn do cuvintc sit trcact din domcniul. clt:,,i",i"l,iii.ii.'iii',fll;;ili"#"ffil;i.

l,cntru cci care au vocatir,,ru.it'a.i"C. AJ;fi#;";li.,i:p.ii$f"i"Jit'*vliiltl:t, nroccsur de creaiie

Adlrs?lln multumirile noastre, prezidiului Academiei R.S. Rominiaf lNlturii Academici pcntru importanta pe care ;-;;il;;_, reediti.rii vo_lumulul I al opcrci lu-i G. Consiantin.i.",i, .""ai"i"

""r"- "_pf" il?J ,tnult rosimtit in litcratura noastri Stiinfifiil

25

2626272t282E2830

333,f1l

-5366E?

l0tt21

!3{111r53r56156t6l!63168169r69t7lrt2t71t16

la2I li3

r83!04[08

I t

prcf. MATEI MARTNESCU,

membru coresponilent al Academiol R.S, Rom.dnda

iOtI DrocnAr|cl

I', ITUIIIU INTNODU(TIV

0,1. Actualitatea ti pelsp€ctivelc sonicittrlii0.2. Ciocane0,3. Motoare rotati.re0,{. Tcrmosonicitatea, . . .0.5. Stocarea energiei0.6. Semnalizdri sr cimouri sonore0. 7. Electrosonicitatea0.E, Aptcatii speciale0.9. Cum a creat Geotge Corttanlinescu gtiir'la sonicitd{ii

trTtATAT Dtr TNANS ISIE SONIC-I A EI\IDNGIEI

t .n.

I .lv.

vI,vt I .v l.tx,

x,xlxll

IntroducerePrincipii lizicc elementareCurenfi sonici in tublri scurte. DeJinitiiEfectele cal)€tcitafi, ine4iei, hicfiunii si perdilaDlei in curenlii so iciCurenti ln conducte lungiCurenji sonici in condlcte lungi, linind seama de fricliune'l coria deplasamentelor. Motoare'Iborie crocanelor mecaniceCurenti de inalte f lecventd.. Considtrarea l ini i lor de transmisie cu secl i tDc varirbilIl,bii lncercate'l'rardormatodApllcsliilo sosicitaliiXll. [. Motoare gr getreratoare sonice sincron"XII.2. Gen€rator de itralte trecvcnltrXIL3. Motoare soaice asif,croneXIl.{. Motoare cu colectorXII.5. Pomp sodce . .

XU.5.l. Pompe cu membran!XII.5.2. Pompe volubettict cu acfronare sonicl .XII.5.3. Pomph JAI, supapeX1I.5.4. Pompe volnmetrici cu debit variabil

XII.6. Gencrator soDic pcltru sistem de tracliuneXII.7. Aperate otilizate in instalatile sonrccXII .E, Ciocarr sonic . ' . . . . 'XlI.9. Sistem sonic dc pompareXIl. l0. Comanda suFlp€lot de admisic l i cva(larc t i airr j tct i t i t lc combostibi l

lo motoarele cu ardere intertfXlLl l . l ' raDsnriterca imptlsuri lor do l{ , t ld Prirr l i (hidlXtI.12, Corlrcr lonl , .

t0

ffi,

\ l l . l . l . l . ( i ' \ tnr( l r , , nr t I l : l r ( , rxr tc\ l l . l . l , :1, l r [ t r r ' . | | r t l t . rn l l t i ( : t t . lcur.nt /u. I\ l l . l . l . l t r , ' r l t t to t tc tpt icdr i i s( ,n i ( . i td l i r t , r o l r l ( : rc l i r , l r t ,ust i t r i t r l ( , r .

\ l l , l { . l ) r .sDrr prcFrgl | r l . r ! r r r r rxr l i lor sonic i pc l i r r i i l r rngi i I ( i t r t i t tc , r t lpt icol ial r r l | | a l f r . l ( \ . l r icc [ t ' r lot tc cctor sonicc . . . . . .

Xl l . lJ . ( i , ' r f ( . r i "1a susl i r r td t . r . Academia t iomani in lg lg

1982022tE226

230

245

217

24E

NOTA Bt(X;ttAtrt(:A

Alurxh

c0llTtiN't'H

lr0ru{r, A ||l| tr

Inginerul C'eorge (Gogu) Constantinescu, unul din marii inrcntatorill lumii cu care se mlndre$te tara noastri, a fost ales ln 1920 mernbru co-UDondent, iar in 1963, Nlembru de Onoare al Academiei R.S. Rominia.ttli-a nlscut la Craiova ln 4 octombrie 1881, ca liu a lui Gheorehe Constan-tlncacu, originar din Ploiegti, strS.lucit prolesor de matematici

"la liceul <tin

Gnlova, al cirui dircctor a fost timp de 30 de ani.Matna sa Ana, nlscutl ltoy, de origine francezi, plecati. din Alsacia

dupl rlzboiul franco-gerrnan din 1870, ajunge printr-o fericiti providentirno mclcagurile tirrii noastre. Plinn de {armec, clnta cu mult talent la pian.' Copil precoce, George Constantinescu ttia si. scrie si si citeasci iniintt:do a sc duce la 5coal[. Liceul il face la Craiova, unde talentul seu pentrumrtemirtici uimegtc pe profesori gi pe tattl siu care tinea totugi ca iiul sirrlb[ o culturi gencrali. solidi. Gcorge Constantinescu devenise rnatemati-clonul clasci lntrecind qi pe profesorii sii prin soluliile ̂ elegante ii simplificatepo cnrc lc gisea pentru rezolvarca problemelor pusc. In afari de matematicill plttceau fizica ;i chimia cirora le dedica timpul liber 9i in cadrul unui michborator improvizat, acasi., repeta cu mijloace proprii experienfele demon-

ftrtiv(! dc la poali gi imagina noi variante.Spiritul siu inventiv ll lndeamni. la constrr.rclia a tot felul de dispo-

,ltlvc iontru uturafea rnuncilor gospodlreqti alc familici. l)entru sortrr m:ri micir, refractarir la asimilarea primelor cunostintc dc m;rtcmatici.conitruicftc o ingcnioasir mapini. de calcul care ii perrnitea sir ob{ini in inotllutonurt rezultatelc opera]iilor aritmetice. In afara prcocupirrilor dc ordintohnir:o.qtiintific, estc atras $i de muzicii, cintind 1a pian cu mult talcnt.Glllint ln scctr$tl pasiunc a sa, originea preocupirrilor salc do m;ri tirziu re-lorltolro lo. claborarca unei teorii a armoniei muzical('carc ll va ducc orin-It.o rcmnrcabili. asocialie de idci la acr.a admirabili opcrir ;ti infi{ic:i.,

-ctrr:

rrto SON ICITATEA, crcatic a gcniului sr'ru.. Picrzlnd pe tatll siu inci de cind era in clasa a 5-a, Grorgc (ixstan-

tlnorcu lgi a*sulna, ca fiu ;i fratc mai mare, sarcirra dr: r;rspundcre dc ir in-|ll l l tlo ftmilia sa. Arninlirca anilor pctrccuti la lit(ul diri (lraiovl, ii va fiBtottlorrtnr scumpr-r. (,alitf,ti lc pedagogicc alt: profcsorilor pc curr: i-t avullOolo, r:it gi ntmtrsfr:nr t:olcgialir rlintru profcsori ;ii clcvi, i-au lis:rt o pro-lUnrlil rrfr,ciirrn,: Pcntru ircci arrr.

lhriorrrln slurlii lor ingincrc;li <k: la $ oala Nir(iorrirlir rl, l lxiuli rii f,o-ftle, rlI lrr ivcill iL r:rrli l i 'Ltilo srh: rltxrscbitr:, ruirr: ifcsl intlrr -sc urirrltr: i.rltck, $ig lntr .o t t tur , , or ig i r t i r l i t i i lc l i ( : l r t { ,z. inr l i r in i rL ' i . . \st i . l , rk. l i prolcsonr l t l i .Fgdurl, cur" r.ra Anglr,' l S.rligny, i-;r rivcrtiz;rt y. r.l.r' i sll ir. ir.r,.;rsr',-r ,lr. rrbnt l r t t l prr l r r r i r l in lx, lorr r r lnr ; r l , nrr l t r i l l ncsigrrr , r ' l r i l r pr . r icrr los, ( i . ( orrllhillnflcrr Proirv lcrru 11 ht lrt, ' l tr.tt riir rlc rliplrttrl, rr ;rrlfr,l rl ' 1xrl, r'cr.;r cr.

, /'l h-l2

._*IT

indispune pe Anghel Sal igny, cart : r r . i r r r r r r t , . i l r . t in.rrrr lu i ; r l rsolvcul rccal_crtrant, recomandarea. ficuti elcvilor s.rt, Ll rrr.., .rtr.rlisrur.nl l:r care G.Constantinescu replici. ci.-aceastl rrrr I r.r irrr1,rr.rlr,.r lotrr;i rlc a conitmirn.canera sa asemenea- podur j . In c, , i f . r \ , . . r r r ,1, . l . r . r l ,solr . i i r . i r l t .o l i i Nat io_r)ale .le f-oduri ti $osele atit cit a aclivirt i l l :.r.rvrr irrl Slrrtrrlrri, pc lingi-r'in_ginerul El ie Radu, c i t g i in cadrul in l r , . t , r i r r r l r . r r r t , , r r t r , r l :ur . (1. construct i i -in asocia{ ie cu inginerul Tibt . r iu bir .nt i : r , . , , l : r l r r i . i . . r r r : r 4, , r r i r r l r r r s lu in ds_meniul construcl i i lor d in beton armat, r r I i r r r r i r r r l r r , r , r r r r rnul r l in cei maircprezentat i ! ' i p ionier i in acest nou dr ' r . r r i r r . r l r r ' l r r r r r r . l r r l i r r i c i t t .va dinaceste construct i i care s int totodat i f i : r r1, , r . i r . r r , . , ,1, , . r , . r | , . r r l i r s i care star lll ast[zi mirturie a marclui slu talcnt ;i crrr.ir.j, irl i o r,1xx;-r in rare betonulrrrmat era.privit cu cea mai mare neincrctl,ri. r[, slrrr:irrli l l i 5i autorili l i,lutit la noi in tarir cit ;i in stririnitate undc ir (lirt lo( l;r t[rrnoro;rs(- accidente:podul_pe_ ioscaua dinspre Doftana, plangccle inrolrilrrhri l l inisttrului Lucrir-nlor Publice, clirdirca Carnerei de Comerl ;i I)alirlrrl l irrst:i (azi MinistcrulComerlului gi respectiv Biblioteca Central'ri 'dc Si:rt). t,,ui,,i .l in Parcrrl Ex-pozifici (azi.larcul Libcrt:r!ii), pod de o rarir frurrrrisr.ir, Si r.L:ganlir arhilcc_lonrc,5, man-lc. poduri. dc la Adjud, Rirciciuni, Itourirn si Ikrihasca (de peSrrct), consolidarea prin lucriri do beton armat a Canrcrli l)r,puta1ilor, plan-;eul. Turnului Moscheii rle 1a Constanfa. 'l 'oate irccstc constructii au fostrcalizate intr-un timp dc numai 6 ani.

Cu toate aceste succese obtinute in lari in tlomeniul rol)structiiloril,j LJgl armat, George Constantinescu $i-a dat soama, ca urrnarc a grdutn-likrr intimpinate..in acest inceput de cari;rir, cir nu vir putca gnsi in !ir[ in-l(:lcge.rea nccesarl pentru punerea in va-loarc a ideilor salc prii,intl traisr4isial)utcnl mec.anice. prin.lichide, idei care l-au urmlrit inci.

-din timprrl anilor(lc l.rceu, cind ciuta legile armoniei muzicale. De aceea, in 1910-pleaciL in

Arlglia, !a-ra cu.-industria cea mai avansati la acea epoci, in spcranla deir"giLsi acolo.sgrijinul ti in{elegerea de carc avea ner,oiie, in scop;l vatrifi_, i 'rrii ac('stor idci. La Londra reu$c$tc se con\-iugi un caDitalisr j^ a Jir:antalnilnelc cercetari in domcniul transmisiei puierii mecaniie orin lichide. _{si_ft,1, ir nasterc primul laborator de SONiCITATE, instala'r foarte nrorlestftrtr-o $urd. peresiti,- pe malurile Tamisei. Aici reu;egte si ob{inir primelerczultate concrete, dar care nu au avut inci. darul de a aducc un venitr:rpitalului investit, urmarea fiind retragerea capitalistului englez din aceastiirfur:cre, cu atlt mai mult cu cit o tev"er."r" i Tamisei inu;de laboratorulintprovizat, George Constantinescu neputind salva. de la inunda{ie decit!jgvr1_din. piesele mai importante ali instalali or sale.

. Intre. tinpr sglicltild brevetarea inventiei ,,Transmisia puterii meca-nir;c prin lichidc'', in S.II.A. i se rcfuzi acci,.sta De motivrrl ci lstc o a'bsur-:!11i,1,'.-A Jost nL.voie de garanfia, sub prcstarc tl-c jrrri 'Lrnint, l lrnor p(,rsona-lilnJi rlin lurnr't tchnici engleziL, cart: iu v:-rz.ut frilt:l ionind rnotoari. soniceir l i rL()r i l I ( )nt I r lc po malur i le ' l 'amisci ,

1.r 'n l r r r a r onvings l ) r . \ l |minir tor i iof ic i r r l r r i < l r . I l rc l ' te din Ncrv York dc i , .a l i t i r t r . rL inv, l l ic i i rcclrr ia p, . r .are:rt.r'sli r.xanrirratori i l taxau rlrept ,,un rtt:lIrn rl0 rorrtitn".

( r r ocrrz i l r l rccsic i l r rurr . l i r i , ( icorgr ' ( l rnslatr l incscrr f : r r . r . i r l ( ) l . l r r r rlo i r r j i t r S. I I .A. r rnrb i l v iz i lcazi pr . I , i r l isorr . lnt i ln i r r . r r cu i l r rs l r r r l i r ) \ , , . r r l , r t { ) ri i I r ' iLt ju i tq i lc un sr.hi tn l r r l ( 'p i r r . r ' i ; rsupr.r , , : r r r r torr i r . i l r r rz i r . . rL." , . r . r r r r , . t r . I r rr 'ohsott i t t l lc ; i r I i sr r r r : r r r I t . , l rsr t l r r . l r r . i r ro l l r ( i 'orAt. ( or ts l i r t t l i t r t ' t , r r r , r r ' , . , r r , l r . il r t t r . l ' r r , r ' iz . r l r . , r l . r r , l r r r ' | r r . r r l r r r L l l i r . . r r , r . . r r r . l . r r r l r i i r rvr . l r l i r : , r . 1 . r , , r r r r , I r , r r r r | .r r . r r r r r . r | r l . r ' ' , r r" l t t t , r r r ' r r r r r . r r l . r lor l t i t r r l ro r1r l , . l | r . i l t t t l ' r r r r r , r , , r r r , r r r r

rnrrtcmaticii. Georgc Constirntinescu nu ne sPune daci cu ocazia acestcihlrcvcderi el a in;f,tat mai mult dc la Edison sau acesta mai mult de lrrrrrlr:rlocutorul rom6,n.

Revcnit la Londra, trebuic si aitepte Primul rizboi mondial pentnt,,r SONICITATEA s[ se irnpunir ca o ;tiint:r gi tehnici nouir, cu aplicalii1'r.r, ticc din cele mai importante. George Constantinescu constatir cu amil-i.i, r,rnc ci aplica{iilc accslci iti inle Ia arme dc distrugere, ln timp dc rizboi,r ,rrr ldus suicesc materialc pe care aplicatiile in scopuri paqnicc nu i le-auprrlrrl aduce. Acest parados'i;i g6sc;tc exirlicalic prin aceia ci invcnliile lnilrrtp tlc pace dcranjeazi pe cci iare au investit iapitaluri intr-o industric,,,r1,ltrrluri care pcntiu a fi disponibile pentru noi pla.samente trebuic si a;-t,.pl,. :rrnortizarc,L primclor ini'esti1ii, i ir industrii i6 deja existcntc. in timlr,l,j l izboi, lnsi, pr;bteml amortiz:rrii capitalului investit nu sc pune, astfcltrtr' l l invcntiile ln m'asura in care dau o supcrioritate uneia din pirtile t,cli-ll.f,rntc sint intotdcauna aplicatc cu operativitirte ii lrioritirtc ln 1911lrr linrp cc armata germanl"! detinea supremalia acri;tni., prin aviatia sa rn:rtrrrrrlr:rorsl gi mai binc pregS"tit:r falir de cea englczi!, Amiralitatea englezir,rl.rltnirt;r de miilc de vieti sacrificatc in rindurilc armatci sale, datorit[ Pu-lr,rii rhr tlistrugerc a avioanelor dc luptit germane, ia iniliativa instituirii unrri|o|lorrrs pcntru gisirea unei solulii de a miri putereli focului de armi dcPonviorrxrls salc, prin realizarca tragcrii printre palele elicci ilvionului, in tin-prrl zlxrrului. L:r acest concurs sc pr€zinti. gi Gogu Consta.ntincscu care, ctlintjlr;rr:r:lc modeste carc i s-au pus la clispozitic -tle cittre Amiralitatea llri-llnir:lt, rcalizeaziL iu nurnri citeva luni primul (lispozitiv sonic de trager(:,ullornrtir prin clicca avionului. Lir dcmonstra{ia acc;tui prin model, iuriul, orrr:rrrsrrlrri constituit din sirvan!i cclcbri, printre t:arc: I-orcl liayleigh 1il, l. l ' lrornson, rirrnine uimit de r:ficacitirtcl dispozitivulrri sonic realizltl

r|r. (lrorgr. Constrntinescu, dc preciz.ia tirului, tlc elcganfrt ;i de simplitrtclrrlrrIici, r:iL fi de posibi]itn!ile- noii ;ti in!c SONICI'1. llstc priml aplicati{lrln rnrrr',: lrnvr:rFiurl-r a accstci ;ti inltr ;i carc r(hlcc invcntirtorttlu i romin irIi{ ||rl tirrtl), t:chrlrritaten.

(h rrrnl l r r r . i r accstui l ) r im slrccrts, grrvcrnt t l cuglcz c l t ; i \ I i t r is t r l r r t l l rv i : r -lh.l nl S.tl.A. ii r:onandiL livrarcir u. 50 000 lrsctni:nc't rlislx>zitivc crlre rtpli-r ' r r l f rv iorni ' l (n ' r lc lupt i r , cuccrci te Pentru t l i l l i suprctr t i r t i i r at : ru l r t i , gr l -L l r i r t r lrrrlft,l rlhlitrrl ri"rzlxriului in favoarcu ac{tstorr. 'Iotorlirtir st:rtrrl t 'nglt'z iiprrrtr, l l rlirpozific fontlurilc neccsaro pcntru inIiinfrLrr.rr rruui lirlxrrrtol tL'-nltlrll I S( ]N l(l WORI(S, pc carc (ic'orgc (lonst:tntiur:scu il ittzt'strcirzir r:ttl l l r l r t l r l iuh' nr . r ( .s iu 'c pcntru t :ont i r rurrrc i r ; i r lcz r 'o l t i t r t ' r r rurc l l i r r i lor srxr icr '{ ld r i l r r r pt i t t l r ' r ' { 'zul t ; r tc s i r r t cr l i t i t t r : , in l t tcr i t r r ' ; t ' l lur ' l lu 'ory oI Sot l ics, r l 'I ' l l t r , A| | l r . r l i l l r l r . ; r l l r i t i r r t i r : iL i r r l r r r r t nrr tnr-rr- r ' r 's i r ins rL ' , xt ' t l lyr l i t t r ' , i i \ i t t l l l ( 'rat , t r . l Pl t l . - r ln l t ) l t i . ( i lor '1grr ( ]onsl i r r t l i r r r .s | r r Is l r ' r ' iz i l r r l i r t l l r lxr t i r . lot- t t l sr ' r t t

r l i l lu l l l i r , .ur l l r l i ( l ( ' r i l i i l t l i r , l ) r in l r r ' t i r r r ' 1 i tL ' r ' i i l t r ' srrv: t t t l t t l t r t ' t l t r r lo lJl l l r l rg l r , , M.rr i r t , ' : , , r t , r r r , : r i r '11isr ' , r i t r r r r ' , r r 'prrc i i r r Anl l l i r r l l i r r t is i t r r t t i : r i t t t tc r t f i

f lhh, r l r t r ' ,1 l r r , 1 i r t t ' r ' t t t r r I rot t l "ur . ( i I t lot1I I rc i \ l ; r t i t t r " , r r t , s lc i t t rpt ls i r r t r r I r l , '

FFl t vnrr t l r . i t t i r l r , ' i l l ; r lxr t r r lor . in l r t t t r r lot t t l t t i t t : r l l l i i r r { r ' i ' ; i l r ' l r r r ic i i , l { i l

t$ t r r r t , , r r . r l r l r . (a.r , r ; i r . ( .orrr . | r r r r I i t r r , , i r r r , I r r t r l r l r r l , ' r r r , r t ru ' t r t r l r ' 1t i i t r { : i 'u '{61{h' l l r .ohl l i r l r r , i l l r r l r l r ' r r ' r urn. i r l ) r , r l r r t r r . r i l i rz i r r | , r ' . I i r ' , r I r r I r . i r l ro i r r l t t i

l l f i r r l r , t r r l , l , r r l t r r"r t t , i r t r r t l t r r ' , r 11l . r r . r r l , r r r" , , t , . ' I ' r t r . ' r r \ , t t t i i l i ' ' . r l ' ';6 1111l l r r gr , r l r t , . t ,1, . r r r r l i r r r , . A, , l I , ,1, l r l r ) l ' , \ ' r t ' , t r ! , r r . r Atr t r ' , l l t r rv i l , r l r l r '

f , l l f l A, , r , l , , r r r r r l i , ' t r l t r , r , l , r r '

, , , r r r r r r , | , r t ' '

, r ! r , '1, , ' r r t l r t r l , l r r ' , ' r / l r , l \ l . r t r r r , , r t .

,_- l l l l ln ' t ' ' ' | | | | 1 | | | | I t , | , ,1,r ,

' , ' r t t , i l r l r ' , r , r t r ' , r , l ! r l l r r t r t t l , r l r ' I r " r l l l r ' l , l r . r l t r ' ,

IF lh r . l t t . t l f lhr t lxr{r l to l lq i l l rnf l l f l l l l l$nr l r to ' Sn ur l l t l l l l l ln r r l l r ' l $ l '

r : t r ' l . r l , , r S()Nl( , \ | r ' t r l r r t r ' : r lorr l i r . r r r . . r rn 1.rr , r . t l r r r . r ' r . l r . lo l r l , . i r r l r .nt i r . l r lcl r t i ( , r 'or1gr ' ( i r rs l r r r r l i r r r .sr ' r r i r r rkrrrr , . r r r r r l , , I r , r r r . . r r r i r . i , . i prr l l l i i r r r l t r r r r icr . p l i r rt r l r r r r { i i i r r l i r l r i rh " . (a,or '6r . ( on, l . r r t r r ( . , r r r , , r . r r . i r r lorrrcr : in Algl ia undt:l rc l ' r r t r r sr i l , r i i r l ) ( r 'c i r ) t r . r ' ( .s( .1r . I r r \ i i rk. 5 l , r l r r l l , , r l lL '2, r ' t l r : in bazl lcgi i pr iv int lrcsl i l r r i t , . i r ( i - r l l ' St i r t i r i r \ ' ( . r i l ( | r ' r r l r . lor . r r . r r r .s i r l t inr lugi l i l de pc urma spc-( l l r l i i l ( , r i r l i r tpr t l r r ' tz l r r i r r lu i , I r r l r r r r r l y i 1x ' ( . r .o lgc Constant inescu inr i t t r l t t l ; r , , 's lor i r , p(ntr l r sunlc l ( : r ' i r r , . i s- l r r r I ) l i ' r t i t in l l rma l ivr i r r i i c l t re Ami-r.rl i l :r l l ir l lglt zr-r ir cclor -50 000 1l: 1111111lq11. SONICE pcntru tragerea prinr.l icr., irr l i trt lrul rirzlroiului. I ividunt ciL cra o intcrpretare abuzivi. a legii,r '(\. ir ( ( ' s :r v;izut in lrrma cil i t igirri i dc cirtrc^ Georgc Constantinescu a pro-rr.srrlrri pc r:arc i I-a intcntat statul Englcz, Intrc timp, in lariL, SocietatcaS()Nl(lA rx'rgcir spre falimcnt datorit l incapacitiLli i Consil iului de -{duri-rri:, l t;r l ir: (: iuc ir clczut cir scopul accstei Socictirt i este simpla incasare cler ir lrr. irr '{ ionirri l divit lcntelor, f irrir ca ninteni s:! sc preocupc dc partea teh-rritr"r crrrr. ccr'{: iL coll lpctcntir i i luncir efcctivir in uziniL si1rc santierc. Georgc(irrrstirntirrr:sr:rr iL rcstituit SocictiLfi i intcgral capitalul invcsti l. In fclul acestalr rr soklat prinlir inccrcare a lui Gcorgc Constantint-.scu dc tr punc in serviciul.l i l i i f-r 'rrr:tt: l t: creafici salc tchnice qi a geniului s.ru cre.rtor.

hr Angli iL t:outinur'r ct 'rcctirri lc salc qi invcnteaziL iaimosul CO\VERTOIil)l ' , ( l( lI ' l ,LI (tor(luc conlcrtcr), cu aplica{ie la tractiuncir iruto. Primclcll lorl(,1)i lc t:chipiLte cu accst con\-crtor sint e\puse atit la cxpozitia indus-trirrl ir rr Inrpt:riului Britanic dc Ia \\ 'cmbler', in 1924, cit gi la Salonul auto-tturlri lrr lrri <k: l ir Paris, in 1926, undc standul Georsc Constarlt inescu facoI ' r ' t tz i t { i r : . ( l t t i tc(r i tst i t ocazic, rcvista cnglezi , ,1|c Griphyc", d in 10.01.1926,lt r l l icolul ,,Lcaders in thc March of Progrcss" (Conducirtori ln mersul sprcprogrcs) rcdir f igurilc a l7 mari inventatori si oameni dt ;t i inl l innrlfrvirlul 1900-1925. Printre acc;tia, alirturi de Albcrt Einstein, Cu-glir. lrrto l l irrconi, I-ord RalLcigh, 'fhomas lldison, \Iaric CuriLr, se a{lI Si(i 'ol l. l(: (:onstirntincscu. ln 1933 facc o nouir tcntati\ '5. de a. punc inlen{ii lesirh, yi cirpircit iLtcit sa i l serviciul l irr i i , inchcind un contr:rct iu Uz-inele IIa-l irxir pcrtlrrr rrplicrrca Convcrtorului la locomotivcle ;i automotoarele fabri-cil lc (lc irr:cs{c rrzinc. Primul arutomotor a fost probat pc l inia l}ucure;ti-Ol-lr,rri{rr, rl irr l rczuLtatc {oartc br.rnc. Cu toatc accstea, sistenul nu a lostirrlrrptit l , r lat l i iud prcsiunile oxclcitate dc citrc {irmele stri inc asupra gu-vr.rnlurl i lor ; i oamcnilor polit ici, pentru introduccrea automotorului de Ia-lrri lrrl i t: strir iniL, Georgc Constantincscu povestc;te cum s-a inccrcat a seprrrrr. l;r clrlt: lcci<lcntarea provocatir a automotorului siu, in cursa Bucure;ti-()l lr.r i1rr, 1x'rrlru discreditarea aplicatiei convcrtorului la automotoare, ac-r ir lr.rrl r: lrrc ir fost cvitat gralic f:rptului ci Gcorgc Constantinescu care con-rlullrr irulotttotorul a observat din timp amplasarca unci trirvcrsc pe l iniak'r;rl i crr ( irr(, sr' lrrlr irrca (lcrai( 'rcir automotonllui ; i zr'rdl 'rrnicirt iL pc aceast:rrr rL.rr r rp l i r ' : r { i t . i crr :a. , t ic i salc. l (crrr l iat l i ( l 'zgustat dc nxrralur i lc pol i t i -l ir.rt i lor rrollr i, (,rrrrgt: (lonst:urtincscrr [ j;-rscltr: totu$i o multumirr suf]c-lr ' ,r:,r,r ir conlirr 'trrl 1xr c:rrc i l lrrc clt s;tviirtr i l nr:rrrolog (i ltcorght' l larinescu,(r lr ir, :r ' inl lr '{ irr: inrlelung in problcmc lcg:Ltc dc aplicar(' ir solticit:!t i i ir lr r r , , r l i r i t t r i . ( i l r r .orglrr . Marincst :u stalr i lcstc o atralogic intrc inf luxul ncrvosr;i lrrrln(i i sorrici, cirrc a dat roltk: mai t irziu lrrin aplicarciL sol)icit:!t i i i ;rI t . r l r r t t r l t t t r t l ( l i l i ' r i te lor a{ecl i r r ) i : r le t , rgunismului r rnran. Scnsibi l l r i nruncirrlc r.r.tr:ct;rrc ;i lctl iziLri le tehnicr: alc tincrciuhti studios l i crltrrzi;rsl , (n:org(l( rrttsl:uttitr.st:rr l irspliLtc;tc cu gcnt:rozitatc strirrlanii lc itccstolir, :L nliul ir l( lu-l i' . ' i r l l grcrr l i r l i l .pr i t r catc l t r r : r ' t r l < i r t in i - r r in\ ' (n l i t t r ) r , in lupl ; r r . r r i r I r . i I '1r l r : -l r I r r l r . I ) r I I r . 1 i i l r l i f t r t r r l t r r l i r lo l i l i i r .orrvxl i l i t i i r r r . , lor . i r r . iu.r ' r r rv, , r posi l , i

l t i

l i t l r t r ' : r r l l r i t r r ' r r r r r i . r . r rcrr : , lh r to l r i l . r l ) . r . i r t t ( . . \s l l (1, r ' ispl i t , , t , r r r r t t l l ) r i t t l l l lth ' 20000 h' i i t r t l t r { i r r r l i r ro-( l i fuz(}nr l l i : t i t tg i t t t t t t l t t i \ l i r l r ' r l l , t r i t l r ' f i r l t , l r r r ls ; r r ,atr lu l r r i ( l l t |o lg l t r l laLi l rcsr:u, inr t ' t t ! i l ' r ' l r t r ' i t l ) l ic i l t i t r r r i r i l i tz i t t l i t r ,gr t l , rtourcl- ' tL ' t i tcul t f i t r a lc C.Ir . I { . -u lu i , 1x ' l in i i r l3uturt l t i - l ' r ' t r ' ; l i , r r r l r r (L l rs s"rl ic i i int l , r r t . r r r t l in , xplol tarr ' .

I l t i intors in -{ngli-, George Constantincscu lucreazir t l in ttou iu st'r 'r i , irrlAmiratit:-rj i i Britanicc qi in 1938, lr iz.lncnirc;r cclui d(-al 2-lt 'a rirzt-roi rtt,,ttr l ial, i l girsim contribuin(l <liu non prin aplicali i le inr-cnti i lor salt ' la r-ir lrrri.rrlrmatclor aliatc asuprn :rrntatt ' lor hit lcristc. Dupl'r, r irzboi, sc rotrit!( l. lvih sa de pe rnaluri l i lacului Coniston la 500 km de l-ondra. '{ ici, t l t 'PrLrl ' 'r l t ' a se odihni, lucrcazir. Icbril la noi invcnli i 1i descopcriri. Ast{c1 irrvtntt irz;ltt ma;in:r <lc intcgrat t 'cua!i i cl i{crcn{ialc, creeazir rnetocla {oraiului :orri,pcntru c\tractia ti lciului dc la marc adincimc 9i deparafirlarct souicir l ! iiciului. l\f irrind {rccvcnt'a vibrati i lor sonicc pinir" Ia 20 000+ 100 000 1Iz. strrrl iazI efcctul :rccstora in medicir.rir prccurn i i aplicali i lc Ia sctrtrrit l izrrt i, Ir|. l tdar c:r ; i la trrrnzu'r: ir aliajclor', la t lcfcctoscopia prin rrlt l i lsnnctt, l l ttrtl izarea tclclonit ' i t i tclcgra{iei srrbmirrinc prin modularL'a und('lor sorri(r. 'ln calitatc dc mcmbru i i, ' nno,,r" al Socictir l i i inginerilor t ivi l i t l in I-onrlt l,cca mai tt:ch,r societ at r dc ingincri din lume, tine in cach trl irccst t i Socit t i ! i(rci Confcrintt ' cl istinst' cu mcdalia dc ;rur a SocietiLri i. l \. i l t l ;r t ir lutrL l lr ' loctombric 19.{ti, arc ca tit lu,,Scicntist Ycrsus Enginccr", l)rl lrc in evi(I, ' lr1rlcorrtri lrulia ingincrilor la progrcsclc ;t i infci. r\ 2-a, la 5 urai l95l fLr (). irrirt

rrnir,crsiLri i ccntcnarului socictirt i i , tratcaziL dcspre 100 tlc lrrri i tr t l t 'zr-ol1lt ltrringincrici lncctnicc". ln a 3-,i Confcrin{ir. { i irutr in irpli l ic l9-59, trprtrrlol)cra s:r i i t i intif iciL SO\ICI|ATE-{.- (icorgc (lonstantincscu urmir.rc;te. cu interes prcf:rcctik' car', ' att l,uitt {rrrir:;a tlc origir.rc, dupir r '\.cnimentelc istctrice de la 23 .\ugust l9'{{, crrlcnll l)utciul sl-L nu rcgiscasciL l ln putcrnic ccou in sullt-tul si-[rt intotd.i l l l l i llr 'grri r lc pirmintul nital. \oul climat crcat in tarar, i l att itgt'. l ; i t-xpritrrirkrl irt{ ir dc l vcni in fariL, {afr'r dc cmulul siru ingincrul )latci }l i tt incsctt, cirrl

l)r 'r 'Ai 'rt ( ' l ;to prin intcrvcn!i i pc l ingiL {oruli lc superioarc d(: slit l , l)f,(rrrrr riptitt or/. l irnizarca clc conft-rin{c in circlrul ASI'I ' ; i al -^ca(h'nli( ' i , (rl l l loi l l t( r( rll ;r lr i lrt i ( i lorgr: Constirntincscu in rindurilc ingincrilor' ; i outrrt ' tr i lor uo;lt ir | r ' ' ; l i i r r { t . Ast l i ' l Gcorgc Llonstant incscu cstc invi tat i t r txtotulrr i r ' l96l r l r ', ' r l r , ' ; \ r r r r ! ' r r i i r I l .S. I lonr in ia s i v inr 'L i r t lar i r pcnlr l t l r l t r t nt l l l i j l r t t i t cot t 'l , r r l r r t t l i r l iz i " r l i lc noi i or( l in i socialc inst i tu i tc in tarr ' t . lutr-ulr voirr j I } , ' . r r 'l l l , r r r ' ; r ; r lcrrrgind 3000 km si v iz i t iut l pr iucipal- l , r or i r i r ' i r l ( ' { iu i i , r 's l r ' i t t tpr"rror.r l r l , . pr t ' faccr i lc adinci rcal iz,at t . i r l t r -un t i l r - tp: t l i t ( l ( 'sc l l r t , ( lc l r l t rsIut t t t , r r l i r ( r i l i i intr-un l i rst i . rnt i ( . r ' a l int l r rs i l ia l izr-u- i i , I ) r rpr"r ct l r - r 'cr ' ; l pt t t tI r iurv i t r , r i r l l r l nrr t l l , dc carc i l lcagl 'L t t i l t ' l r r t t t i t r t i r i , sc i l l t ( ) i r f ( r l iL I lucrtr t ; l i .; \ t r ' t , i t t l t o: , r , r l i r t { iL solcntnir a lnst i tutrr l r r i pol i lc l tn i r ' , l i rst l r i ! o l r l i r \ t ' ! iorr i r l i, l r ' l i r l t r l i ; i $<lst lc, , ,Alnr i r t t r i r t i ' r ' ' r l , ' Lt crLt , ' r t Pt ' t ' l t t : r l ( t t i l t ) i i l l t t t t l t l ' t i l tvr ' t

l i i l t r . t r l ' ' I r : tz i t ; r car i r . r t i s i rL ' , L( .cut tost i r lo l r r t f r t { iL r l , ' t t t l r t i l , ' s | rv ic i i l t r l t ls |p,r t r i l i ; i l r r r r r i i p l iu cr-r 'a{ i i lc : i r lc i r rg i r t l l t l l i , i i tot t l t t i i r r r r l l r r r l is t i r r r : { ic, , lXX:11) l t l lONOll lS ( ; \ [ ;2, \" r r l l 'o l i lc l r r r ic i i < l i r r l l t r r r r r '11i , i t ) l r ( ' i r lt t to ' l t r i i (h ' r ' t t l t tz i r rst t t i i \ |n|rr r{ i , ( l ( n(( l ( s(r is. l ls t , r l t t | . r r r rc|r t s i t l )ar l ( t r l lr t t or , rz i : r i r r rp l i r r i r i i v i ts l r i t lc Sl)rL rrrr i , r l r ' , \ , r r r l r r r i , . i r r l r , r , r ' r l i r r { . r srrLrtr t t . r 'I t t , , r t , i r r . r rorr l l - r l i l l r r l r1, , , \ l , r r r l , t t t r l , ot torr t , ' . r l . r r r ' ,1rr i i r r . r l l l ( ) t ' , l l l ! ll l l i r ' . r l { . i r i i .

l r t l t o yr l i r r ( r i ; r Srr( i l i r l r " , t i i r l l l r ' l t t t i r l r r r \ r , r , l l r r r r , i , r ' r t l r t t t l l t r r r l .r r l l t l | t l t l t t l i r lc r r . l l r r l r ' . r r , r r l r r , r , r l r l r r . r { i l r r . r r r r i r i l . r t i i l , r t to i t t r { . r r i ( l . r ' r l r r lr ( | I | t , r I r ' | | i | | , | | i I r . | | | . t 0 l r ' , r

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l i r . i r tor ' , r i r r . \ r rg l i r r , rhrr . , , , r r . l i r 1,r f , r ; r r I rp l i r , . , r mesiLjul <Iezvol t iLr i it l r t l r lu() . r \ r . . r l l i i r r l r . i ; i cul t r r r . i i ! r . r l r i : , , rL, r l , : or ig i iu: .l t t l ( )0. ] csl( : t l i r r t rou i r rv i t r r l r lc r \car[cruic. ln cursul accster a dou&:;r'rh'r ' i . irr lrtr:-r, I ' iziteaz-i l 'stiturrl ,1,,

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l , : : . .1 i ] : ,1: . i ,1 , l i r r t l i ldrurnir i pr i r . ind clezvolrarca accstora prr ,cum gipcntru

r l t ' l , r t i r l r , | l , r . r r . . r . sul ldclor, pentru in jecl i ; r sonic i ]a motoarclc Dicsct e ic. Lal . , , r r l l r r r t l

Al) , .1( ' r constat i cu pl iccrc apl icarca sonic i t j t i i la pomp.r j r r l sorr i r ,1.1..:rl lrr! 'rr l, i lL' cu irp.i dc adincimc. Dupf, o activit i.tc init.n.,. ' , ciepusl ir ir.rrtJr' ir ir(, i l ttzaull progresului tehnicii sonicit it i i ln tari, facc () sr:urtf escali(r ' | (ntrtrr.r t ir LoDstantl unclc vizitcazir moscheia al ciLrui planpu dc beton

'rltrr.rl i i r(.. luin1e ste de prirnclc snlc lucriri i" aorn"ii-t ' tr"tonului irrnat,i.r I,r0uri.r ' .r l l tcestei tehnici. ftxrinte de. intoarcerc a in -A,nglia, incr,:dinteazilrrolcsolrrlui .\Iatci }larinescu .rn.rnuscrisul cuprinzin.l r:Jinplcti,r i lc aduseItrrlrrlrrl. i t lc ,, ' fcoria sonicit i i i i" ir.L vederea edit. ir i i celei dc a <loua cclit i iir

. i l( ( 'sl( ' i- ()lr)rc

.capitalc a sa. E-stc ult ima vizit ir pc carc o facc i. t-, ;; j ;(trrltrrr '. ln 1961 se stinge din vinJir la vila sa dc pu rnalrrri lc l ircului Conistonlur(t( ' s(' Sils(j itc 5i rnorrnintrrl.

, . . . . , . ( .11. t t l r , t r lca sa, .d isparc unul d in cci-rnai str . i r luci ! i r .cpr.r .zc n tanl i a i

i i l{ l ' l ! . l j1l ronli incsti, ir1\'entator clcrtnit.celcbru prin aplicagii lt, nc,i i Sti intc: iONl( l l j I ) ( ' ( :aro a creir t -o intr . -cr cpoci in."r" . i r "" t , , . ' , . . , ; t i lngi t i . i in 1ar:ull()rslri- l (orrslituia un act rlc croisrn cilra cerr.a sacri{ici i, .., ac,,1,r 1>c carci l_,rfricrrl ( it 'orgc Constirntinescu infruntiutl insin5;urarca r;ia,-, i,r i,t i t i i , pentru arl l l l l , , l l ., l ,,

ourt'niri i . fructul gcniului s.-ru, .rclucind prin acclst:r ur) p."fio, o,n"_l i lu ln l r . r ' l l i r t ionr l t i i r i i s , r l l ' natal , . , i r r l r lc c j re i inst i tut i i , l , . i r rv: .Lt iminr rr pr i_ll l t l . l( 'nx lrlr.r preg:rtirc prof,:sionali '1, f ir i. de carc nu rtr f i putut clicl i im_l , r ' ( sr(nr:r lu l , r l i f ic i r r ; t i in l i f ic c i r r t , cst( . SONICITATE-q..

. _ l r t . l run:r l r r l Socier i - r l i i i r rg i r r r . r i lor d in Angl i . r 1vol . LVl l , r . rnuan,. . rnrr-lr ' l(r(i( i, r l. l), societatc a cirrui ncrnbru de onoarc a fost G. Constanti-t l( 's(f rt g;r, i i tu trrutittorul nccrolog:

,,1)1. (;eorgc Constantincscu, rlespre a carrui noartc s_a scris ln ult imultttttttr 'r"r rrl lcvistei noastrc, s-i l niLscut in l lomiLni a in lggt. I i l a relatat lnttvislrr, srrtict; it i i . noastrr (19.s9, p.70) cum_ tati. l siLu, carc a fost profesor(lr: r*irtr.rl,tt ici-r, i-r I isat mostenirc o bibliotecr"L c' cr-rrt i de matimaticil()irrlc I,urc i i cunt intcrcsul s:!u pcntru armonii le muzicalc l_au determinat5.1 l| sl l lr lr, 'z,.sr.rios l i ^r.. 'r ucunrulcze cunogtinte temcinicc ltr ivind rnccanismull)lol), lg:rri i : n(t( ' lor'. lD lrcecu;i rcvist:! este reamintit iL

^ne scurt inti lnirea

sa.in l9l3 crr l, ldison ,,cri l clrc a invcntat _inregistrarea s6nori"L in ciuda fap-Irrlui cir i lrtocrnti clL Ilectlrovcn r:riL complet siurd,,.

l-rlr:r:rr,ra st ,, ' l 'coriu sonicit ir{i i", pc care cl a consitlcrat_o ulcreu ca() l ) r . r r ( r ' i r r t r i intpr l i ; rnt i i r r s,r , i r fost publ icat i r dc Anr i ra l i tatc in l9 lg, darr ' l ' i r r s l i rs l izr , i l l ) ro i l ln 5() ,1 : i r r r i rn.r i l i r -z i r r .s le f l r r l i ' nrob;rbi l ca 'o i s iLrr l i i r r { r . l .s t . r r : r rk 'v.-rr ; r l l ] r , r i n l r r l l rL,r . i r : r r r r int , .L.s i r ior . i i r l r ; i I i insic in.

. I r rvt ' r r { i i r s l r ct .a rrhi r . r r r roscrr t i t r r fost tu i t l r l i r , r r r s incronizat i cu aju_l . r r r l c i r . i r r p i l . l i i : r ' i .ar .krrr l . l r rPrr i : .1 r)ut l r t r : r r i r r

' i ' rz txr i r r r r l in l9 l ' r -19rg

si i f , iA.r Pr i r r l r r , 1rrr I r .L ' r . I i r . r . i l i r l r . s l r ' ( ) l ( , i r . Ar.r . l rs l : r l l r r rLr l o supcr ior i tatc( : ( t l ) l ( ' l t l ( ) i r r . i r r . r ' Pl i ' r ' ; l r ' Prrr . r ' r ' ; r r l r ' f ,x 1 i r r r r r l { i r l i r r . r . r .1r i l r i l ( ; l i c i r r ( . i r l rr i l t r t . rs i r r y i t r {h rrrr : , ( t i : , ( lo i t l l l . i ( orr : , l t r l l i l lsr . r r srr l r l i r r i i r r r l I i r ' l r . r I i , . r . r , I r l , r t .l r t t l t r r l r r r r . i r r l ' l r r l . .

l t l

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it I' ir' i:*i*-+.;;l ,r '#i * ; m: fiii;xii' i*::l\ili".:t',:l;:'iii*Li:i:il,iili#t:ii:""r':trilJlsl'r'";Ju";i,'T':11";i:llit*i;+ili,'.,t.s**frl'[f j','::::{:i,:"J#?iuirli' l"l"l'l,r,,rti"nl.tl ,,Sonicitatca", eI a prezentat I q"t 1"]:lr-gi""lii 'itl*,]r";,' 'r,,; iillti:,T",T{,L:,S;+jfi.ff*:if :i+iT,iil*i a,i, .m (,c ,, _ir{ :i r ii ilii}1ii:l::#f#i;-i5:i',ffi ;"1iiiffi -;:,-",iliiillllllii'iftrTiti'*:"#h{r:T,':l':'ll*'5lr';iiii,:i *' *. i' ri r i "rui . accst ui irJ.ffi t 1l.l] illil *'t"i*,i"ffi iiliiii, r-il*,r " liii:frij:ti:i:.il:til lllt;l]8T"',.ii"'''t r t l lN\ lANl lNl lS(t l l torr I r 'S I i

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. . , . - , . . , ' . . - . . . , t ; , ,1 , : i . r1 i p l i r r r l l s i r .orr : , l r r r i l i r r r r l i r . r r l r . r lor t lc 2 l iWpr: pr in_

r ' t l ' l r l u lur l r ' . r ls I r lnr lo l r . lcr . t losotr i l r r r r l r r l , l l i l t . ( . ( . \ ,onl i r . , , \ccast i in icm_ttr ' . r r r - r l l ) l ) In ' t io: l r I .sol icr . - |c sccundi t , l r r iut l curt , r r lu l r l r ia rc lcaua normal i( l { ' : r , ln.r ' l r , . r rh.r .Lr . l r i r .c. I .ungirnca dc rr t r t l i r sonic i r va f i aproxirnat iv } , :,, ,:.

rrr: l]r. I r( '( r pr.utru o conduct:r sonici dc o lungime I _-U X 7,-50 metri\^ lL -

/ , ) l ) t ) I ) ]1 'snlncir sonic l l va I i in Iazi i sau ol lozi t iunc, .er , . r ( .c corcs_punrh. i r r r ' r r r r t l i l i ik . cr . l : ml i favorabi lc.

,_ l):rr. r ' lr irrr rlacii lrrngimea deviazi. de la aceste multiplc <1c jumit; 'rJi de

ruttrl i , \ islr.nlul _tot Iuuclioncazir, cu condil ia importanti i" .

",.",, o.ap,,_

r ' t l r r . l , . i rPrr l r i . r t i l . r gcncnrtor (r"z i f iE. 4, p. l0 ' l \ .or i : r Sonir i t i t i i pr t ,c i rntt r l iK. 5. P- l l ) . Dlc i i c iocanul c coni t ru i r i . , un ,cron"tor.

- i t lc l_, i r t l rz iL cu

t( tsr1 l , : r ' Pol t tc asirni l rL cu o rczis l ( ,n l i r s imDlar, iar undt, lo "onicr . in con_(lrt( l i \ i)r corr{ine fundamcnlala harmoniciL plus harrnoniciL. srrpcrioarerIr . r ' . r I : r t , . . , . \ r r , r l iz l r complect i i nu c usoirr i . , insl t in rnod pract ic capaci tatcali l Ar' .r ' .11.'r ir l isoilrbc curentelc dcvatute, iar cur-cntul Iundanrental sc for-l l l f irzi it l lr-() rrndiL progresit-[ 1tt ' cind ciocanul ]ucreazir,

2. I)rcsiuncir soniciL dc irlplitudinc H poatc fi r icl icrLti ' t cit dc mult,tr. l;r l i ' l ir P.t 'sirr..a rnedie.. C' n'tati 'ni lc cl" ir i 1r,,girr,. i tr, 1.. Souicitaticil l l l l { i rsr l |orrvr .nubi l de luat p, , ,1, , , : i -10 l i icmr,

^FI ' : . i0 l0t) l i ( . tu: .

-- r\1rrtl lr, splc cxcrnplu,

-dac'iL adoptirrn H .- S0 lgc! r,onr lua p- ..

55 k,rr ':, 1r,,,,,, . lo5 k/ar. I)cci co'ciuctelt trr: l^rie tlalculart. s,-, ,. i ,zistcirf i,sl( 'r lr lsi l l i rnaxirne, dc as(,l lrcrrcA fi prjrcti i e.rpircit l i t i i t.tc. l)r oLrscr r.att 'slc ci 'r pllsirruca sonicir H cst,. nIai i l .r lt i t cirrd riocrrnrLl nu lur:rcazir,, clccic.J)ir( it irt( ' ir (un cil inth'u de ofcl rle pikl-r) trebuie c.lculalir I. (, l)r(.sirrn(. rnlilrt i r l t i-L tlr. 10.5 l i/ce.

Accirsta, bincin{clcs, sc explic.i cit t imp lLrngimtir (()uductci nu der.iazirl ) r | i r_ mult dc 1. , - \ l i , , /2. Al t fe l s i t r r . r t i r rn i cr i t icc-Pot: i i i i r lor : c i l d( . e: icnl_plu in fig. 23 la p. 58-.59.

, 3. ( -u pr iv i r , . la conductelc f l , 'x ib i l t . , i r r .casl , r , . o Drol , l , . rn i ( i r rc nuir lorl ir)r.r rr.?,olVati 'L complcct ; i sunt inci nec(,sar(. { r.rc(.1:rri f rrndamt.nt a lr..

, 1. . ,(-,t privin{i la-frccrcnla loviiuri lor t lc ciocrn, irceasta va depinrlt.r l r ' ( r . I l ( .h ' l l t ( lustnal( . . l . rccr-cnl l r < le 100 Ior. i tur . i /s , ,cun( l i t lar( , in lcrc. .ant i r; i r ' . lxrsilr i l siL dca bnne rczultatc pcntru {oraje in piatri. St' iu cli amcricaniiirrr irrcclcut.sir aplict ' ciocanr: cu 000 to00 lovituii/sccun<ii i aclionatc prinIrl i l l l lcto-stric!i.n. clcctriciL. Accstea arr fost preconizatt Dentru adin;imiloirltr.rntri, insi 'r rczultalclc au {ost nulc Si pr'oicctr.rl alxrnionat.

.5. - (l iocancle sonicc constrrri l t. . lc mine crau cu 2-5 ;i cu .50 lovituri/sct:ttndir ; i. Iurrr:t ionau pcrfcct crr cficicnti loartc inalti. i3incinlelcs, dacirl r irnslonnit lorul clt:clrosonit: r-a rculi binc, frccr.cnta tie 100 iovituri Lar ' i r r r ' ; t r r t t t t v i r l l r ( . /cnta nic i o r l i f i ru l t ; r i r . . l i m(, l l t i ( ,n;r t . r . 15u. n. ,nf f l r , r , , -rcr i r t ( , r : ( l : r ( . i : rcr . i rst i r r - P.si l r i l . , r , , r i *u, *ni l -" i .1r ," i r i i t i ro. ,u i ,J i i r" ' . r :J i irtt t l t i*i ' l 'n.f ici ' . I)r 'oblt 'rnu

'rr csir. insr-L pi"" n;o"ri pirt i lc oscilantc trc-

lruit ' l lr lrrnsatc, <lt 'ci <lorriL gclt( 'r irtoarc in opozitici r.or trclrui sir lucrczc sin_t'rorr. APoi crrrsa arrn:"rturi lor vl lrtr lrui siL {ic r.uprinsir intr.c l imite binc de_litr i lr ' , f ir. lrr plirrr 'L incirrcart', f ic [;-r r.;-L in, irrtrtr,,. \- im locul siL mcnlioncz aiciI r r r r l r . I t r .nr isr .L ; r l : r r rk.s igrrr . i t l . -a l i l r rat i ' c , 's ic lcrarc. in or icc caz, t r i -t l l r l r . | l ) r , l r . r r r l ; , Pl : rnrr l { r . , . r : r l ( i l s i 1 ' iu l r l tc i s intc l i pc drumrr l ccl bun pcn-I t r r : r r . r ' i l ; r grcrr l i { i r r l ter i<xrrr , .

.6, ( lonl l ) i l r i r l i r r r r i crr r . i r lc l r r I r . I r ' r l . i r l r . r .out l . lL i tn i r l r r r r fost f icrr t t , tk,

s1t . r ' i r r l iSl i ia l ' r ' r ' r r l 1 i s-rr r l ' r ' r ' r l i t . i r . r ' ' r r , r r r i l r r i , , prrrr . r ' , ' r ( .c:rni( . : l

( .sr( .

20

l l r , r t l r ' t t l t lxr t l i t l l l . r . l , l l l ) ,1 ( .1/ , l l r l , 5r ' l )o i l l l . r ' rorr t ' r r r I ' 1""" " ' " ' / r r

, l i i r ' , . , r , . r* i , , r . . r rsrrrrrrr l . i , l , r , , , r r r t l r r ' , .s , , l i r , l , t l t i r t r i l r l . r i . r ' r r r , l ' ( l l i r ( ' r ( ot l l -

, t i i t , , , i , ' i r , t i r t r t t ' r l i r r l , l , . r r ' l ic t | r r l : r i r t l r r l r l i ( t ) r l t ln i r ] l r r l l r t ' t i r r r l { ' r r i ' \ l ) i r r l

L l r r t t , . , , ' r l , ' ( i t l l I 5 : l l ) ' 'u , l r r i r r r l ' l ' l r . lz i lur ru l ln( ' r "L l ) l t l l \ ' l r l t l l t I (x ' t l l { l l -

t ' l / .,r1 r'rt l l t(rrtt l fttrtrtzltt t:otnllrt lsori lor' ( '(ncrittori i sonici (rotrrt ivi) att o cli-

, 'u:tt ir ' , i . ' , :,,t i t qo';;, ..t i ,t,,,tn,' i" (:!r tczorli l tor cttm 909; l i c.t:a ce diL 1'

,; l ;; ; o,; '

0,Ji 811,,. I) lt: ir sL'miti adaugri pierdcri dc 10-200,1 in cort

' l r r ( t r . . l ' l r r l iuo ccl Dut l l I r ; t ( ) ta l i lprox. 60lo Pe- accste l razc' cu un sistc l l

:;, ' ;;,"t;; ' ;: ' ; l l , i l ; i i , 'J."^,i ' i t ' . , esti enormir,"chiar dac't lnotorul elcctrit: r ' i

l , r , r i r t ( l ' ,1, t losonic i ar rnt i scat le c i { ra de 60(}o la 40} 'o.Chiar in ?rccst c i r / ' '

, f,,"it i tt, i i 'r s ,,, i i m'ni trtult ir t:ttcrgic perccsivli Ya putca {i l ivratir LL forrrj ' cortt-

txt t , t l ( . l r ' l t t l comf) l l l l l i l l .'

" " ' ,

' f i ' . , , r1, Si , ; ; ' ; , i 1r , ,1 ' t i ' . , ' i t l , ' j r . ' . r ' ' t t t r t t l r t i . o l )a l lo . { l in

l r r r l i r r ' " 1

rrr l t r r l " r t . r . r l r tDi eutr t t - ' i i t r r r" ' r ' " ' l ' ' ' ' ' l in t r t ' 'mor i t t l a lx \x l l i l ac( i ls l : r i l

t r r i t t ' r r l . r r . . l r r t i , ,du, t i ( ' r ' r l , ) S. ' r t i , ' : i . \P1r l i ' r l Souic< 'r\r 'r" ' l ! l l(rn1ol-lu lornl(: i lziL progLatltul luct' l-tr i lol Prezcntc lt \- l l loi lr( ' l l

,1, , r , , , , , , , , i t i i * , .1, ' , , t in l r i i inqinci i ct ' vor s i - ! sc -spccial izezc

in Sonic iL r t r t

; ; ; i : , t , . , . r ' : rz i r r : i s , 1, l i r r : i c ; r nrr l . r ' : r r t : t ' l '

s t t t l rh ' I t r r ' r t r '

l l i lr la(lrt Inar(' pli-Lt:rt." -t: '

' t f l t ' t l iu scrisoart:n t:r (2t-2-58) cir anr {osl

uf,," ,, i ' ' i". ' i i i , i i i . l , i ,,uJor" al l.acleni.i I l .P.l(. I ' i . iL in - 'rczent

insi 't nu arll

pi 'r"rri f i iyri i ,t i ,, i".L ,1. 1" -\, rr, lcnric l l i-a .f irrrt Pl'- ' t.t]." '--t l l-1*-cnea' sit atr(l

,h,r . r r r , . r ' r . r . l r i r r l nrr .u l )n( l r .n to l r l i r rnu, do. t r r t 'Pr ' , , fcsot l i lncr i tus, i i -< lcspr ' '

, i " , i " i , t i j , i " ; ' , i - l ; ; , f ' t i i t , . r ' , '

" '3 "pr i ' r r i - i inul l i rmir i l ' mel" c i ldr t ror tst '

l l r lrt ir{rr rrr( it ( l( ' sitni-!tatc ;t"t 'ui""rni"ti ci-rtrt l t l insJl carc l lr l ln-iL uitat nici-

r r l , r l ; r ,Itr ltr ' l irrrlr itn prinrit vLlti ; i clc l iL ing l iaz'i;art ' ,ca re. est(: unuldiu c{' i

r r r r l i r r r r ' , , , , , , ,1, ' '1, , , i i r tnr ,s in i , t , i i t i l " ' . t "1 ' i t l r lot t t t l t i t t l Sor l ic Si ( i t r r r : i l r l

' . ra i , t , i . ' t . t l l r i l ' t r i t la pro5'rcstr l t . l rn i tc i t l ' ioraj '

( ' tt trt ivi lc h tincri ingincri, tc rog i ir ' ,(:ontact .cu. (l l sccrctar prim (lL

" , " ,1. ' , ; ; , i i . ' l i l i i r . t ' , i " i , . ' l ' t^ i i "* i " i i l ' ' I l ' c i ' ru iu i -ant scr is in accast ' r

I r lv l t | t l .l 'r 't tttitt rrccastit luni;iL scrisoarc' in carc nm irlccrcirl s[ ating p-uncttrlr'

t r l l t t r l l , r lc r l i r r s, r isor i lc t " f " , ' fu ' iugi i t i i ' i i "* t l " t t ' spr i t r t l r . t t t t l t r t l i lor I r t -

liiiiiil,ii;' t;;;ii,.;;i;:";;i" il"i r,un" r"rrirri l,curru r.r.utir a .l ucririlor ii. r(ntn,,iiiiiii,i"ii,i'r ,,iil ii .u p.iti..' t. ,iptlt^t"n $tlitt1"i sonicc irt tara lLomltrcasci'ti ltrl nllrrr r,'r ttl pcrsc\-crcnlL

-;i ' l:rr Oroiioit" pcntru progrc's \-or lti (:um si

| | r r I r r r r r r , , r , , | ' 'o'.ti 'tclc'

t"or"ii.,, citrt: riplit:irri practi'c, sprc {olosul tuturttr''

tur t ' ,1 l t t , , , ' i , ' i ' , , g int lu l ; i cu l r r r t lc lc 1or"

Allr'\,l l tl it l l ir ;i o copic l talrlotr'lrri "l ' iotrt'crs itr tlrc trIarclt of Itro-

; l r , r ' . " , r l t tP,-r r r l | t t r r i cetut .- Ar,r t i , lc log. sol ie i 5 i Ict i l t ' lor ' l i l l ( 's( 'nt i ln(r l l t ( ' l ( : ccl t ' t rxr i b i t r t ' r 'o i t o l t tc

l | t l l l l r l t , i l l , l l i r l t l i s t tcccs in v i i lor ( l i l l part( 'a l )o i ls t r i t '

( ' r t r lL:r{ostc,

. , l^ ( t lx)Sl l ) l l. , r t r , r , , r . r \ l l | | . i l t ( l ( r r . t l t '

l \ r ' l f i t [ ] , \ l l l \ ls{ l 'l l r l , r r , r l l , r l t r r r N,,

"l ln r , , r l [ l , r '

l l t r ' r ' r "11|

l i i r \ l \ l i l \

1l l

O. STUDIU INMRODUCTIV

O.I. ACTUALII'ATEA SI PERSPECTIItsLE SONICITATII

Stnrliind lucririle inventatorului G. Constantinescu se constati c5. elcllit foarlc l.rinc fundamentate teoretic, iar realizS.rile practice sint ln con-Offdnnln crr {coria gi prczinti avantajele previzute. Ele au fost recunoscutell l last;rlc de pcrsorrilititi rti intil ici de prestisiu international in lumeaitllnlifi ' tr crr loid Raylcigli. Sl. J. J. Thonison 5i Sir Ctrarltis Parsons, con-Il0lporani r:u G. Constantinescu. Ace;tia au vizitat laboratoarele sonice dcb lirrrrln, ;ii tu fost irnprcsionati de reaiizirile tehnice - generatoare gilotorrc sonicc - ln care propagarea undelor ln lichide era folositi pentruI ttansnritc putcri considerabilc de zeci de liW intre un emitltor ii unll0!pt(,r.

'l'rirrlru:crea cirlii ,,Theory of Sonics" in limba romini a fost {lcutinU (:tr o lttr:tarc comandati. ci ca o rnani{cstrre a considcratiei omului deftllntl $i spccirlistului in hidraulicS. prof. I). Gcrmani faliL de ideilc ori-j ' lnrla uh autorului.

llecttno:rstcrc;r r''alorii lucri,rilor lui G. Constantincscu in domcniulFnlcltlttl rr fost fr.cuti dc Amiralitatea Britanici care a linanfat laboratorulda runlcltutt: in carc s-au dczvoltat multe aplicalii in anii 1918-1920.

Utilitetca sistemului de sincronizarc a tragerii cu mitraliera prin palclcdlorl, lrluclnd nvia{iei hritanice suprcmatia in luptclc aeriene ale primuluitfibol nondiul, a cieat invcntrrtorului un prestigiu enorm.

In 1926, intr-o revisti britanicir G. Constantincscu era citat printrclffltlll lumii : Maric Curic, Allxrt Einstcin, 'l'homas Edison, A. G. Bcll,l ltfl lhlmo Mtrconi ctc.

ln rrlthnii ani ai vicfii, proclamarca sa Doctor llonoris Cauza al In-1SU_trrlrrl polilchnic din liucureqti yi l legcrca sa cl Mcmbru dc Onoarc al{h&rrrlol

' lt.S. llomlnia, tromplbteazlt o-srmarf, onumcrarc a recunoirttoriifi tlnrprrl vit:Ii i a valorii opcici r:mirrcntrrlrri ing. Gcorgc Constantincscu... Aoorltfl ro(:unoallcro u {ost cxrnfttcrttir 1i post mortcrn pc pltn inturna-FtUl tn cs(lnrl u:lrri rlr:-rtl XVI{ra ()rngrcs'iritornational tic isioria ql iin(t:i,l l ntnntorirr cmircrtl rtlrti i lvr)ntltor r()lnlhl ir fost or*rgiltiL lit irnulirtircl,p. tSlr t t t r r r l r r i r t r r ; lc l i i s i rk. rk. i l r r ; r l l i orrspr l i s t r i l i t r i r l in" Arrgt i r r , Arnr:r icrr ,llrllr,

lhr l l t r .o l i i I r l r r r r . r l r ,scr i r r r i ( | | | ic i I i I I r ! I r s i r r I r ;orr , r : l r ,r r l l tcr t t i i I r l r r t r . r l r ,scr i r t rot t ic i l i r l r r l r s i r r l r ;orr , r :1r , , i l r r r r l r l i r : rL l i ihr sotr i -pror i t t t t l nvrrnlrr j r t l r . l t t t i r :o.r . r :o l r r r r icr ' , r :ut t l sr , r :xpl ic l [ lpt t t l r : i t r :rdrphrr l l t r , l t r l r r t t tc,r l l lR,1, l r r v l t l l pr i r ' t i l i l ,tnHl l lnvr,r l r i / . l i r l r , r r rh,vr l t , r I r ' i t r r r lnr : lorr l r , l r ,

l l t l l rur l r l l l r l l l t l l r l l i l ln t tuu1,1 1, ,un1'11,11 r l r r ( i , I i r r r r l l r r r t l i r t r , r r : r r 1 i r r r rl | | r I l I I r , | |

' r I t I t | . , r t t !l l l t , I r r t t lo t l t r t t r , , r l r t t r r r l r r t r l I r " r l t , l r t r t t t r ! l t l l

l ; i , r r ' l lu l -u l r t t lntplnlr r r ' l r t l l r r t lo t t to l o l r r r , lor

f l l t l r t l l l t t l r ' r r i t t \ ' r r I l l lhI vI hrr r r r r . ,

l , . , l l r r r r l r r r ru l , , , r r , . r , r l l r . r . l l rotn.ul ( i l l l l l t l to nl i t r i invcnt i i impor l . r t r i t .

:11, i1, , , , , ,1 : l ' , ,1: , l l ' l r r , r r rrr t , r r , . / : t r i . r t , , , r r : r l lo i s i [ ic rc]uatc ; i <krzi .o l tatc. S.t .p ' . rn, , ,

: : : 1, , ,1: l . r l l l r , .5t ' . r l r r . r l l . r i r i r r rcrr l r r tonr l a gindi t ; i a invcntat crr

-n lu l t

"" ' ' ' { i : . , , j ,1 '1. , , ] ' 1r ' . r , r 1 i . r , l ' .1) i - , ) i l .n i \ ' , lu l t l , . in(c lcgcrt . a l ( .o!) tcrnpor,Lni lor .. r l r ' l l r \ , . I l l l l t r r r r l , . r i . r r i t r , , l r l iz : r l r iL. nrrrrrai dupiL int l t . | l in i rna t r r ro lr o r l i l i i srx. i i r lc sar i m:r t I r iaL, .

. lrr conft.r. inta <k'sprt, sonicitatc, t inutir la $coala Na(ionali cle p,:t luri: , t f .s. l ' r l i r l l 'curt . ; t i i ' r9r9, autorur, , o. i t " i - un"t" ' i i i r a i r icul t i r r , in_l i t r t I t t r . r t , . r r t r r r r r . i , inr l i r inccrr : r l s i , . rp l ic , , r rnor e-rpcr! i r r . r t "u; ; ;^ ; ) , , , i t i ; ;r ' ir lr ' . ( r(.(,I-fa() ( 'onstantit lcscu a c.heltuit o cnorrni

"""agi,, p"",au a con\:t l lgc, ] l l l '1. : , l . . r ] :

l l l f h. s inr r .onrpr, . i l , i t , . cu mult , "ui _ul i ( tcf i r s( . i r .cetr l . rdr

;.ll.l.li.l.t,.iilll ',,l,lrf,e\te rsentiali-r in uncle cazuri, ca accl:r at p.np"girii .,:i_Ir l:t l l l lol PrlI l lct[de. Lonstruirt,tr :rparatclor dcmonstrati|c l_iru ̂ co"n<]us lal,r.r 'r, lrrrr:^ u'lo[ rcsorturi

' idr:Lulice,'acumuf.tu"r" t ia., i" i lcc ;r chiar a ..r 'or

Irtttrrl i sonicr:. ,\ga cum s-a afirnrat chiar de la apaiit i . "i l

,onr.it.t"o .,.t"tr ( r )r( 'slxD(lcllt i cu .lcctricit.rtt.a iar transmisii le sonicc sint similarc cuIrrrrrsrnis i i le c lcctr icc dc curent al ternat i r( orrs idcr i r r t l iL:r : r logi i r dc mai sus rLdcr. i rat i i , cornpr imrr, . l l rchi t lc lorr ' r . r , . r ' l l rv l . l |nt : r c l l dem() l )str : r rc l at .untrr l i r i lor dc sarcini e lcctr icc inrr_rrnr'(,r(l(.nsirlor. I)acir consirlcrirm saltul er.olutiv al elcctrotclt; ici i dc la expcri.n_

1r 'L ' r l ' r ' l tc l rostar i ( i p inar la apur i t ia rcor ic i I in i or tungi s i -" srst( .melor t r i -l ; r l : r l r ' ( i l rL. s- i t larcut i t r t l . - n t in l l ) fo l r lc Iunl , dc secolr , , surpr inde rapir l i_lir l(. i ! (u care itrvcutirlorul a parcul-s accirsti cvolutie in dorireniul sc'nici_li1ii. ( lontcmporanii nu l-au futut urmiiri cu aceeigi vitezi.' l ' ir 's'r isi i lc

sonicc se rcil izcazi pri ' r-ibrali i iaria inccputul secorurui,).r ' cor)si(lcra cli cncrgia dc vibralic constituie n ioa-:, a"

""".grc degradatl

j.:,11.. ' l ]] ) l- l". l l Poar c ,trirnsforma decit in c:rldurir. I ira clc nccoiccput'ci din-l l '-urI slsl( ' l lr dL' \ ' tbrati i sc poate obtine lucru rrrccanic ctr randarn6nt ricl icat.

l r { r ) r ( r l | r n l l lc i r r ( . a l tcrnat iv i i r fosl cr , rut in {c l ) ruar i , : l9 l3 ; i sc rcferca lat' lr:rnsr)risir t.r ifaziLti- crr gcncrirtor ; i rnotor sincron, I iLriL nici o relerire lar'()||rpr.slr) ttatcir l luldului siru la propagarca rrnor unde in l inii, de;i feno_rrr.nul plopagiLrii cra studiat ; i inaliza"t t le inventatoi.

( i r , r " r r de I ' rcrct pcnlru stocarci l cn(.rAic i in rcci l r icntc cu l ichi t l subl)r ' i . \ t tut , . ( str . d, . lusir in docemlrr iL. l9 l5 t i i rcr , .ptatr-r in i r . lnuar ic 1917.

,, -\c,."t, t lr-r ala j de ..1 ,,Lrri fulri de primul I, icri,r . . in carc arr ap:rrui l i. r | l i l | r \1. t ) l l r lu ( lonr( 'Dlul sonic i t j , l i i _ s l lgereazi-r faplul c j idt . i le t -s, .nt i tL le.r l ( . s( , r i ( i r i t i i " ( . r ru Srcu i r r !c lcs, . dc spt ,c ' ia l i ; t i i .o i t

"n l pornrr i .

r Dir urrl c.Ulz|lr. c(' lr mll l rrnportantc carc au fircut ca sonicitatca sirr r r r s, r ' . i - rp i r r tL. : rsr i - r i r fost l ipsl t dt . inforrrra! i i tc l rn ico_l t i int i I i t .c . Cartea,, ' l .c_r,rl ir sr'rI( t l i i t " :r lu-st ptrLrl icirt i in _limba (,n;{lczi in t inrprrI primul ft-zboi

I ' ] I I I ' , I ]

, , 1 I ' ]

loirrt(: putlr),. .c\L'mPlarc, lucr0rca i i ind considcratiL iccretiL. Dupil . rZlx)1, l l l ( I i r r r ' ; r Du iL l | l i l l Iost . icr ' rc l : r , ( l iu.nu i I fosl rct i t ) i - r r i t ; r sru di fuzai : ' t .S.rt I l"tr tt l Irtuttai o lratlrrr.r 'rr: irr l irtrIr.r rorrritn.r, intr_un rrUmir foartr: micrh: r ' rc tnpl i r r r : .

Ingiur:r 'ul (irrrstutrtirrcscrr ir fost urr irrvt.ntator car-c a lucr.at pe contl_rr()l, l l l t f l l irrr. r lolr. ir sir r. irrrL-r Ir 'otlrrsrrl ulrrrcii si l le _ inr.cnti i lc _'in con-i l l l " : i l

, , , . , t j rv.rr t . r j r , . r \ , . , l ) r r l r i r l .z . r r ru i l . i i r . i l r : I r rovrx:rr lc tk: prc luarci ! unor

l l t r r ' r r l r t (h ' r i r l t r . r r r r r . l , . i r r I r I I r I i r r r l ( . r ' i i r r r l r rs l r i t r l : f i r r . i r DlrLl i r . iUvr:rr i t . r , c l ar l Iv i r r l l l I t , [ . I t r ' r , r r r l i r r r t ) r r r r r r r i r ; r r r , i r i t rvcrr l i iLrr . : , t i l . , in i r l i r l . i r Pt0lrr_lr t lor , r , otr l , r l r , r I l r r r . r ' r ' t l

ta

I r t r r r ' , 's l , ' r 'ondi l i i republ icarta c i -Lr I i i nt t cta iudicat i r .

l lrr i rrtrrlt, sprc sfirgitui activitrl l i i , in3. (1. (ionstantincscu i; i t ' laborttrrt,rrtt i l si nr.r ' le lrrcveta, dcoarccc sistcmttl t lc brcvetc acorcla autorultt irr rri,.r\ ' :r l rk' l irnp rclativ scurt in carc l lutcir irencficiar dc drepturile de,rrl,, i .\sistauu, tst{t '1, la un fcnomen foartc curios in carc invclltatortl l in-,||1r ,,! l | lr i l)ui(. l:r o cunoa;tcrc foarte sumariL a lealiz,irri lor salc, 1a o pttrzcn-l,rr, ttt,r i tnrrl l r:ome'rci:rl ir 5i mai pu(in ;t i intif ic-t, f:tcut:t cu scoPul dc a atragctr t , r ! . r r l ur)or capi t r l i l t i c . r rc . iL invest.nsc:-r {ont l t t r i pcnttu dezvol tarelLl \ . r I I l t lor .

( orrsirlcl it ir l r:rrrtz,clc t lc tnai stts cir cxplica!i i l lcntru ncploli{erarcalr , r t r , r r is i ik l sonice, sc punc problcma t lc : r evalua :rctr ta l i tatca sonic i t i r ( i i

1 l l , r , . l ) ' . ( l i \ ' ( ' l ( ' c i .

Irr rrl l iutclc dtccnii cltrzvoltarca ;t i infl i ; i tcltnicii au l itcut progrfst'hrtrt lr ' !rrrri, 5i nilclul de t:utro;i intr: l l t ncrlt lt ' al ptrsoualultt i anflrcnitt i l l,ultvrl. i l i I c lttt ic o-intlustrialc a cvoluat sPectaculos ;i prol,rLl ' i l i t l tr- ' lcgcrt- L,,rl l ' r l, i i i i nu ar f i {rinati clc idci cronrttc';a , , incomptcsii ' i l i t : r t ca l ichidtlor' .

\ t t : r r i r lu l matcmat ic ut i l izat in mod olr i lu ' r i t r le tehrr ic icni i u l t int t ' i

1r'tt, r,rl i i lstc fo:rrtt ' putcrnic 5i pcrtnitc o in!t ' lc6Jert: irncdiatr-L ;i o alrordart'I t r , ' r l r , ,u l i r s(nic i t i r ! i i . Act ig i t r ' r t i tc l rn ico- l t i int i f ic , c,)nt tmP()ral)c i tu: l lnn5rll ,r l,orrlt,zr, 1.rrolrlt,nr:r oscilati i lor (lu putrrt in instrrla[i i hirlt 'arrl ice diutr-rtrr

I r t r ' t ' l ' '

t , ' ,1 ' , ' r , ' t r . , , t . Act iv i txtca ohi lnui t r -L r , , ' lcrr l t r l t r i , ' is tctnclor autonlat(intr ' , l , t i ' r ' tn i r tar | i r s la l ) i l i t i r t i i s istcmrt l t r i ; i t lc tcrmini t r t ' r l rcgiurur i lor t rat t -, l l r ' r , I l i l izrr tcr t c l t rmr:ntc lor c le <:rccrt l ic h i i l raul icr ' . - c la: i i r : ' ' - i t r s ist t ' t r t r r

. r t t l r , r t r . r l . r t r lc l l t t l in i r t l i .unlnod sl lc l ia l t l l ' l r t t lu 1x 'ntru t :a lcul t t l l l t occst ' l l r t11,11171r. t i i . i r r i rnal iza s iabi l i t i r l i i , s i . tc:nul ' l t ' ar : t iutr i s ' ' consi t l t r iL c l t 'sc l t is

lt ' !r ' .r l) l i( r sislr 'tttultt i scmnalc altcrnativL' t i, ' frtc\ ':r!c <iift 'r i te car.. st 'pro-jurg. t I , r i r r r . I r . r r r r ' r r t r , I r , h idraul icc dc Prr t i r t . . , \nal iz iL 1r-r 'c is iL i r Icnontt 'Dt lori r r . r , , . , r r r i r r l r ,1 l , , r l t , tcor i i lc sonic i t i r t i i . S, : l in l s l i lmrr d,r cot t tpr ts ib i l i t ; r ic ll l r r l , l r r l r r r , r , , , i r r l l t r . lc <l t , l ichid c;rrc sc i t i - rsrsc i r r instalr{ i r ' , r rustL ' r 'orPtt t i lor

I t t r r t ,1 . r t ' | l i r [ r ' l r :a in tcor i t r sonic i t i t i i ' i t ts i t ct t a l t scr,p. \ l i r i nrul t ' i r rg iDtf i

r r r r lorrr , r t i l l i r r r r introdus ca no! iuni t ro i , p({r t tu c. i lcrr lu l s is lL ' tn l ' lot l t i t lLat t -

lhr , r r I I 1 r r . r I i r r r ( I r lr ir l:.ar.rl icir. (::rpircitntea hitlr;rrrl i t ;-r, lo{iutri cu cttc sottit i-

l r t l r ' r l l l t r ' , r r , ; ' r i t t t t t rx l obi lnr , t i t .

A l , t , , l r l r . r r . i t intrc tehnica actui i l i - r rL, r 'ak.ul i r s is letnului h i rhrrrr l ic 1 il l , r r r l ,

' l r r r i r r , t r r is i t , i soniCc cSt( , at i t ( l ( ' nr ; r r t , i t r r i t S(. In)at t i t f i r l t r i r t i - r sot t i I i -

la l r ' , r , , r l t r r r t r . r r r is i r .< lc putcrt .pr i r osci la l i i i r l t l )otr i ( ( l |1, . ' r 'oLranclor t l t ' l ic l r i r l

I t rp l , t l r l l , i \ l l l r l i r r l s istcmclor l t i t l ratr l ic t ' in rc i i inr atntol t t t lx r l l l : r l l ( 'nt '

l t , r l l t r t ' , l | r ' r ' i i r l i l t i , rcgirnt t l l l rnK)nic l ) l ' r l t ) i rncul (st( t l l l i i lz I ) i t l l i ( - l l l r r l{ l I . r l111l1t l t r r r rz i ls t i r r pr .n l tu ul s is l l t t r r l r r l . 1. . ' rs i t r , l r tccasl i t 1 l ; r t - l i t t t l l t t iz . t t - r 'h t " i I l t t l l l t t ' l i t i i i r rsr :anrni i r , r i l , l ) l i r , r , i l1\ ' ( t ) t i r r t i t sor l i r i t i t i i t l l r ' i . i1 i ' r r

r t l l l r / r ' r | ( l | ' i r l l l .

l t r r r prrrrr . t rh. r ' r . r l r . r r . r r l lxrs i l r i l i l i r { i lor 1r ' l rn icc r I r t i t l izrr tc r t r l is lxrz i t i .

t r , I r r r t t t i r ' Pis lo i t t t r ' , c i l i ' ' t l r i , to l , i r t . . l r ' , i l l ) i l r i l l ( ( l i t l l i - ts l l r l - t sr ' ; l ic r r - l

l t , l r r t r , l ,41t t [ . t tur i l , . t r t , , , t r l rq iu iL.rrrrr . l lc s i t r l i t r pr lzct t l cr t l t t t t l l t t t : l i ptrr l t tc

l l t r 1t r r t r r i pt t { i t r t osl is i l r r l r tc r l l r i l l i r i t t r ' l r r r l r t l s l r o l t r l t t i '

l ' r l r i r r [ ' t ' i i t i r l c i prrx l t t t l i . t r l l t t t l t . ' r : , , r l l : ' r ' r i l t t t r r t r ' ' ; i l ip iz l l lc l t r . l "

l l f l l l r , lor rh ' t r , r r r . , r r I i . , i i ' ,

r , r r I , i r I I , r r r . r | , ( r '1, ' r l r i r r ' . I r i r I t r r t I i r , , I t t I ( I I | | | i t I i | t ,

l l l f i , t | l ! r ' ) , l t t l t t t t i t t t I rcr I i t t | r ' I I | | r r ' t l | | l t l t l i l i r r r t t , t , i ' , I r ' I t t t t I t t i r 'ot t t t t t I ' t t I r l l r t

L,& l | an r t | l l r , , , t l , t l , , t , ,1, , t r I r l l r t , l r , r r r l r r , I l , , r r l ' \ r ' t t t , i , l r ' l l l ,ot l i ( | | l l l l l r l

lEN lP" t , t l l ' r l r , t t r , r l r ' rh ' t r ' , t l t r ' r l r ' r l r l l t r r l l r l l ' r l l ' t l l l ' l ' , ' l i t l l r l l t l t l r l l t ' l l l

-

:rii;"1:l':iii:ll,:ir il;:lll;:'ili,il,:ii"lillll!llrl;ir:lli'll"i'i;l:?ri"d"'i .'p"':l'ill,;:iili',;,lii',,;,l;iiliil:";.lll:'l]..il];,;;lli'llL;,.: ,1"J",'"]ifgi,ll-il.T"" ,, ,llliu;l'::'i l;,ll;il'i:i';l:Tl:-d]l.-oti'':r"-pcntru care ;tiinta sonicitnui,,r,,yiii,,i,.. .,.'i;;,''t'tt.,,',''ii,;;,: LX,:Xj,1J:rt:;,11,,:"n:::,1Jj:i.iljl_

0.2. CI(Xt,u\E

lr:'iiif:?::"f; ::,#jli}:,ii'ililrL"lrT:*:i::::"d':.:il'.'il:f; :r';iu.liu.r: , ripicr,i.. -n;;;;,*ffi1,'i;JJ,,.Tr;j"'"n ,T:;ilT [i

gnuriri .ei presc cu;ll,Jilll,'.lj::,,,nT".:..1,:L:i*:;6'"t,ri"_"i_,#iiil,i:J.il;lTii::"$;*:.,,n,,1,'",'"':?,"#,,',ii[:l],.,t:ili;i'l*;r;.i,,.:ilj:i"u.hT:,::lLruc.rsub

. . [ " r ( . r ' \ ' , nt ;L ]oyi tur i lor u"ir,,''r-r,,:,,i r,,',,,i;;:"lli:;:ili i:1:il1i.:'.iTj'i"oj,il;.t,..fij H ;i:",i.,li;

; ; ;;i1,";,i ili";il.i, l:i:i, ":::i:i :ll'ilT"fi "1.:':T::".!!:i';T,:1".il1. f::i;1,,, ,{[[p1u:'".:';ulil*1i: li,*#",,""i0,i]lili,ll,;*1,,::,:ii:f:,J:,fii;:;,'l;,'lll:.',|J'fl';'.Tl::'.d ff,1'[i:i llt,fl*F;hl:1,nci vizi,,i]i,;,,r a

0.3. lloTo,\ttE It ( ).l,aTtvE( a.trcratoarcle sonicc si

r; r ; l I ;i: ;, iti,*l llt. i, uril :Hiitirfr:il*,il1;;l,l,i I,l I * l$, i ;"t,,ri,,. r,.r ,r,. .rcop,,, i l",i,,l,,"iiil,,'ri,l..ffiil: *:',:..,1",:'",,li:;'\iir$l:;lll,i:i:lili.'r'lill; ii,ll;:liillli;'l:,1.,:,,|'T:,,iiit'illn;*1ru:.1"'.'"i.I 6"," ri ., sim-

Ikr lo i r t r . lc sorr i r : t , s iut . ronc s int , , . ; " , , t , l ' . ,^ , - . , , . ,1. , - - -l l r,: ii :i:ii,*i,, ;, iil,t l,lll,,,'r ilffil :;::::'l:il: :''". trl,,y,#:i;ll;'"i,lX:ll li;il ,:1:;,;i:::iil:i"

trtic 'ritt

c.r('! sc lransr)orti energia soniciL-

;,: ll'ii;l::;li:il,llill ii*lll ;1'ii'll,ll'l*lii'llil"''nliil'il1[::i::lr,iLi'x,17i'1,:;iii':,'i':ii;;;;::l; il;'ili'l"i:lii, illi,]ili,i,lliiliilri;i;illi:lilliriiiil::tl

rl, ' rrr:rri sc pot obline ;i menline nedcfinit de mult timP cu inciLlziri ncgli-l,rl 'r1.. \lotolrcle sonicc au caractcristica dc a se adapta singurc, aut otltat,[1 r.rlr'inr'r, astfel incit motorul primar, dc exernplu un motor Diesel, si-L-;irn.rli l ir cu cuplu constant 5i tulafia neschimbatl atunci cind cuplul ;i tu-r'rti,r nxrtorului sonic variazi-r intr-o gami. foarte largl. Aceasta estc o pro-

Inkrlilt(' \'aloroas' a transmisiei de puterc pentru motoarele dc autornobil'irt,r;irrilc dc tracfiunc, laminoarc, pcntru industria petrolicriL etc. l ' lxistirplrilri l itatea de aplicarc a motoarelor sonice in domeniul important aI_trui-i;tl i lrl dc putcre 1)iesel-sonice care sitrt mai ie{tine, mai u;oare ;i mai cfi-rtltttr fatiL de tclrnica I)icscl-electriciL;i I )iesel-hidraulicir util izatc astiLz.i.

0.4. TIIItMOSONI(llTrtTIlA

0 aplica{ic intercsantir a sonicitirli i cste trausmisia cirldurii la tlis-Innl;i intr-un rnod sirnilar incirlzirii clcctricc. Conducta sonici. coutiltinrllp.i lr,atc transmite energie sonicit <1c la u.n €icncrator la o rezisten(iL sorriti ',r' ltr, sc poatc gf,si Ia mare clistan!i.. .\ccasti cucrgie cste transforrnatiL ittr'[l lrrrir, in timp cc conduct:r de transport rirminc rccc. Rczistenta gcnctcaziIntttpr:raturi mari si se poate extrage apir ficrbintc saru abur de la clemcntrtlr!. lnr;i.lzire. Apa sau fluidul util izat ca mccliu dc transmisie iu levi nrt cit--r'ulll i;rr dacl. sc doregte sc poatc utilizir nutnai o singuri leavit (re(ca soniciLt t tot t r t f . r zrr t i ) .

() aplicalic importautr'L a irccstci tt 'hnici cstc indicatit pcntru inciLlzir,:rtth.ittrilol viscoase in levi sau in rczcrvoarc in anotimpurilc rcci. O cconotnicllltlx)rtanti. a putcrii dc pomparc se poirtc olrtinc astfel in condilii dc sigtr-trrtr(.i rlin punct dc vcdcrc al perir:olrrlui tk. inccntliu iu industria pctroltrlrri,lrt .rt z,itoarclc dc comlrustibil grcrr, lrr incirlzirliL sp:r{ii lor cu malcLiaL'r'x-l t lv , iv l r : tc.

Nlr.lorla poatc fi Iolositir 1'rr.rrlrrr [icrlrclr.ir si distilarca tnir lt 'r ' i:t lcL rt'| | | | I . '

I r | , I I ' i I ( ' , clt:rnentelc th' int:i-rlzirc fiiutl si;{rrr(' t:lrirrr utrurci titrtl sittl cottt -

Plr'l Irrlrsirtc in :rrnt:stcr:uli inflarrurlrilc sarr t:,r|lozivc.I r r rkrnrcniu norr r1c upl ic;rrc lL t t ' r 'uursouic i t i r ( i i cs lc posi l r i l i t : r tcrr r l r '

I rr\. t.,r ;rlrncsul ;i a fj(' l lcrir 1-:u1t.r'r, rlitcct rlinlr<l sttrsiL rh: t:l-uklurl'r.l ',rpllir:nlcle r:fectrratt: pc lrrololiptrli ittrlrt '1tt:"t{cst: ;r lttirnrit ci s-at'

pt t l r ' , r . r j r t r rgc l i r r r :zr t l t i r1r ' r ' r 'pracl ic ut cot t tht t t ' l i t noi solu{ i i r : t : ar i t t l t r t t il t t r l r r r r . l ' ' (u girz.

o.i . s L(x:. l t , : , t t t \ t t( i l l , : r

, \ , r 's l r : r r l l i lo l r r to l tct . - r t t t t t l lc r l l t r r l t r i i r l r tp l i r ' : r t i i i r l cr t t l sc l t l r ' l l l l r '

drr r , | , r , | i r i I i r I r . q i l r r ro l t izr i l i . Ast tc l rL. r ' r 'sot l r r l i : iot t i r ' r ' r I l ot ic l c i t t t r tc i I l t I r '

l t r r l l r l , r losi t r ' ( . r o ! i r l i r r l , i i r r l r r r r t l o(r ' lu l r r i , : r t . r ' t t l t t i r ' , r t t t 1 r t i t t t i I I sr l l r t 's{ t t -

l t t l , ' r r l r . r ' i r r t r i r r r .1| ' r l i r r l r ' l . rs l i r l r , l r r . , i l i r r t , ' 'o t I r t t t I , , , r t r i r , l r i r r , l r r r r l i , l r i , l , , ' l t t l t , . rzr

lg l r 1 ' t , " t r l t t r ' l t | , | | l r ' l r t i | | r ' . lxr ; r l r ' | l r ' l t t , t ' , , r r r t t t i \ , io l | . t l l r ' ; t r ' ' t t t . l ( i i r l ot t r r '

l l l l ln l . , \ i r t l ' r , r i l r , ' l r l r r r , r l . r l r l r r l l l , ' l r l l r ' r l l l r " , r r

, r r r l ror , r ' l t t t t l , t l l t t . r

| | | r r , l , l . r , r l l , . t . l l t t t r \ i r l t t t t t t t l , , , r t l r , r l , l : l ' r r l , r l , . r , , r ro. l r r l ' . i l t l , r l , ' r " , '

[ r ryA .ntr t t r ' t r r r ' r r r r ' I r ' r r r In

l l ; . . \ r , , l r r r n,r l r r l l r " l l l r l l l t / , r l r , l r l r lu l , ,1 ' l l r l l r r ' r r l l t t t . r t l , , t l , t lor | '

Dlvo, r rrllruttfr ilnptntlr,, lttr,t 'rl l lrl l ltr tl lr ',

, . . \ r r r r r r r r l ; r t r r r i r sorr i r i t lc . l t t ,s i l rn( , s( , . i r l ) l i ( . i i l i_r sculc lc dc pcrcut ic, prcsc

r l , . nr , l r - l )u l_r . t r , fo l j r . , l : rnsirr i dr . pr , r iL.r t i l r . , lorpi lc. rachcte etc.l, l [r 'ctrrl <h. arnortizarc al rt, ioirrtelor soniic red.uce sau elimini. vibra_

li i lr. plirr alrsollr irc:r si trans{ormarca lor in cilduriL,

0.6. SDMNAL|ZIRI fI CIMPURI SONOLE

. ,, (. rrlr.rt,rrr(.h. sonice pot produce undc sonore de frecven{e joase sau

| | l , t r ' , lxrrnt l tnr , 1r : rnsmlt( ' rc i r unor s|mnalc putcrnice pentru .omunicat i ir r r l ' . r r ' r ' . r t ic , . , pr in roci sau pr in a, . r : f ie pr in unde dircct t l , f ie pr i "

" i ra. ,"_ll, r ' l ir l( ' si.r r ' ' lractatc. Accst.a sint indicate lxntru detectarei obstacolclor;i plcrlnirr, ir ciocniri lor in ccati! sau intuneric.

Irr contr;rst cu metodr:le clcctrice, sunetele generate sonic pot f ir ' l ir rr.r r ' P.'t rrr (l isr.r n1" scurt o ;i sint ust tt. l irrdica te pe't-ru protcc tia u,, i ianr.loirc z l 'oal i r . i r r aPropi | rea solului , la i l t | r izarr sau la t rcct l rca pcstc in i r l . ! imi ,

(a.ncratoiu'clc infrasonicc sau ultrasonicc sint u;oarc ;i compacte com_pirlrl iv crr <;r' lc clcctricc, sint u;or rl i : fabricat, ugor <Ic inticl inut gi nu sintIrft.r ' l ir lr. dc apl-r sau umiditatc.. Asenenea instalali i sint inclicare pcntru ex_plotl l i gt'otl 'zicc, c:iplorirri sul-,tei.anr: pcntru pctrol sall n)increun, ca o \:a_ti ittt l l i inlocuitoarc a mctodei cxplozii lor subieranc.

in.stl lati i lc sonicc pcntru _gLnrr.rrca impulsurilor. pot f i aplicatc penirur,r 'n|| l l l l izi"rri fcrovialc, undc c]iar trecerca trcnului -generca'ziL

impulsuri,r\r 'r 'slr ' :r -sirrt tran.suli-se prin tcr.i la di{erite distan}e unde pot scmnaliza,prolr . j i r r r l t rcnrr l in f r r t i ; i in spatt . .

Sislt 'nul sonic nu nccesitir rucxlif iciri sau adiuRiri la lor:omotir,c sau lar ' r r l . : r rL ' ru lurc; i cstc indcpcndem r l , ' rctcaua clcctr ic i sau al te sursc dc putcre.

Ac('st sjstrm cstc aplicabil la prot_rlcme similare in cart: sir.rt r.rlcesurcitt l l t lrkxr'rri prin _comenzi dc la distanti. Semnalele sc propagir cu vitczirsttrrctrrlui in l ichidul folosit ca mcdiu d{r transmisie, iar ai:e.sia

-poate fi apa

srrr ulr. iuri co nu iugheat;-L sau sr.rluti i antigel.

0.7. ELD[;l'ROSOItCtTATtsA

A(flsta cstc o nouir t lczvoltar-c intercsanti. in car.c curenti i sonic: sintgr.rrlrr{i t l irr:ct t le curentul:rltcrnativ al rclelci de Dutcre. -,\sernenea tra;,:[or_rrr.rtori rl( 'ctrosouit: i ar putea t:onduce lir soluti i noi fentru lo(.omotive tlci. lr ice,irI itt l( l l t ir1(, r[ ircct dr: la f irrrl dt: calc dc tcnsiune inaftl cu lrrc\.(.ntir inrl.slrialir.

intr-o ascrucne:r scheurii, sit:gurul echipament clcctric pc loconrotivir,irr ' l i lr:rrrsforrnrrl onrl clt 'ctrosonic, tr:rnsmisii puterii la roti l ircintlu-sc cut t to(oir t r . sort icr . r tyralr ' s i robuste.

' l r ' :rrrs[olrrr; ltonrl clct:Irosonic estc l.cvcrsibil, cl putinrl gcncra rncrgicllr.r ' lr ir ' ; i l i i lr l ir l i ln('r l irt r lc lrr rt:tr.arrr sonicir. Ascmcn-ca 1r-aniformatori piotl i lot i r . l iv i sarr s l i r l i t i ( in c:u ' r 'ntr s int p icsr: in miscarc). CcLcctareu va dccide( i r r r . l i l ) ( s l ( , p l t .k ' r ' i r l r i l .

{).li. At'l,l( j,l 'l ' sl'1.:{;lAt,n

Str, l l t t t t t l , ,ot t i r l r . rut i { r . l ' r . l r ' t i l r . i t Ptr .s i r r t r i lor r ' \ l rc l l ( lc r r tar . i dr , or . -

r l i r r t l r t t i lor r l r . . r I I r r r r . . l r . r r . , l r r , , , t . r t i r , l i r ' gr , r r r rs i r ' . srr l ,s l i l r r i r r r l l f i . r l r r l cx.plor. i r l r r r . ; \ r r ' , r . .1,r ' , . l l ' l l r . , t t lo\r r l r n l l 'nt l , r l t i r r r r t i l r . r l . r t r r r i l i , I i . , | , I r r i 1 i ,

, ir r . , , r r l r r , l , l , , l rgr . , r . r , l , l ' , r / , r r l | , r \ r l ( , , r ( . , , , r , r 1rr , r l t r l r r r .

Alti aolicaric importanl :r cstc ir)icctiir combustibilului pcntru .motoJ.-rdc f)icscl '" *r., 1'liczi lir cilrt conducta de alimcnlarc cu conlblrstlDrl

isle totositl ca mediu pcntru transmiterea- puterii la injectoarcle indcpen-

rlcnte, cfe la un gcnerltor ccntral de impulsuri'

Un clomeniu interesilnt clc aplicalic cste dezvoltarca rnalinilor dc cal-

culat ionice capabilc sI' rczolvu ripid Problcmc .dificile legate- de rezonanla

ii"tti"tfl. cari altfel nccesitir luni clc catcule migiloasc sau chiar nu se pot

ioluliona prin mctode obi;nuite'O aolicatie specialir a sonicititi i cstc acecir' a imbunirtlfiri i turniLttt

mctaf ioi"a" -,jri." 'i"i.* Urp..i*"nt.l" .., rlovcdit cir turnitri cu granulaLlii

i;;;;;i;"; f"st oblinute'cu accstc mctode' Nu rurnai mctalelc' dar chiat'

il;i;t;;-il;""" 9i o'ric;'m;ie;ial plastic sau amestecuri p"t Ji 1:l"l:;,:lltirnpul procesului de turnarc cu encrgii sonrcc ntcnse t"tf, 1]1tt.l]]t-,'::']]'

i i , i i fori.re prin matcrial Prodncind ;i mcnfinind ornogerlrtatea rrl lrmptrr

lx ' r ioadci dc 'o l id i f icarcCu acelali tratament aplicat amcstccr'rri lor clc acr cu cornlrustibil ptrl-

\ 'cl ' izat, ardcrca este mult i;buni\t i l t i tr-r ; i aplicarcrL cste irt l icati i trcutrtt

I t r l l ' in , l . de gaz' c:rzan' c lc '

t)n clomeuiu lrltLrrcsant du lrp1i"'rc a inpulstir i lor sonicc dr' l ' l ' l lrrc ( '-

t r , i l l i ' t lar d, 'durdtar scui t i t 's t t e" l la al ' rp lor :L l i i gct ' ' lo; ic ' sru ] r ro 'F\ t inr

zi, l inriutclor cle pctrol sau mincralc, ca laiiantir l irt l"L rle metoda e\l l()rl l l() lj i ,,

i ,,r i .,"rotrui 'gcneru.toar'r ' cornPactr |cl ltru a pi 'ocluce undc soll lct |( 'r '-

r uritvc dc tl i lrc Putere, a,.- t i t" 'pt"1ttgc ltr i l l soi in toatc clirccli i l ' i iru ir l-

ii,, ,iii".ti", puiin<l rrtingc distarrtc ioartJ urari prin piurriut'

l i{cctele {iziologit ' , procltt" ' ' [" genclatoli i sorrici dt' ina'l i i t frr 'cvrnti

ri r, i 'rrzori uot i i loiositc lrurltr11 si trpur-i rnctl icrr] ' . ' \scmt'uc;r culontl fo1

i , . , , ' , , , , i i " ' , ,ar , t ; in 11.:ul r i i ; i . r r . r rLr i r r . i os,rrrsr ' [ i r - i p"r ic,r l i r l (1, . . ] r ( l r , : . r r r

: , , , Arr .stra i r c!)ntr st crr cfcct t . lc ct l ronluhr i c l rctr t t : ctLLc ncl lo l l l 'a / . l l l l l -

, i ir ' ,,, t Prin sist(rmuI rlcr\1)s

[) insuccttr ta( ' l l l l l l - l { ' l . i l1-( ' l r t r r t t l l ip l r . lotal- l l ic l r t i i i r r t l t rstr . i l r l r ' i r l t 'sr , t r i t . i

t l l l i i st: dt'splintl rrrrrl l iplt ' l t ' posilr i) it i i i r ' l t 'schist' 1cn,1.t tt aplicl lcit inr'r ' l l i iLl '

It)t l i I i t i !1ii irr ingirlr,ri ir ttrotl ir-trir 1i ttt 'rt l i t lcrt ;t i in{if icir ' f irt ir r lc trt ' ttxtolr '

t l t ' l r i t t ls t t t is i t : i t l ) t l l r r l l c l l ts ict : l r i r l rarr l i r ' ( " l l l r ( i t l l ic l ' | t r I t t t t r i l t icc s i t t t t ' l t . t t i t r "

A. t v l - rz,u1 rLirr cr l , ' r l t . r11i srrs i rc lu i r l i t i r t r .a qi pt ' r 'splct i r ( l ( ' s(mi( i t i r t i i

I t t lkr t t rcnirr l i rPl i t l r \ i i l r r t t l t t t icr ' , r [ i t t s l t t< l i t r l " t r l t l i r t r r l r l i " tu i t i r t [ r ' r i ' t t i t i lo-

t t t l l t i . lu i l i i t l t 's t l i t l i i i r t ls t : l ls lc i r t t i l t t ; t ' l t l 'P l ls i t t t t l i t t l l tc t iu i i i i i t c t r ' : t { t l t

1| | i r r ( i f ic t ' , ( | (x. i IZi | . I - i l | ' i | t l r . i t l l i t l t ' t t t l r l t . i t t t t t t ' t . i t t r is t t t r t l l ' l ' r ' l r { i t . i l t i i r r { i f icr . ,th, r r ' r r r rn, ' , r . i i r t r r r rx lu l r . , ' l I lur i i r r r l t ' r r l i r ' prrxt 'srr l r r I r 's l t ' i t rc i r { i i t r i i r tsPi t i t t r l t t -s |

t t l l l | t ' i Is i ' | ( | l l t ' i | | l l i l l ( l i . l ' . l I | ' . I l l l ' l i ( l \ | | l l r . r t t i l t t r r t t i t l l t i i r r I i I r r l r is l r l r | r . ( ' r ' t t rgr .l ln l l l l ; r t t l i t t t .s | r t 1rrr : ' I r ' r i I i t i I l r i ' '

r r " r r l "1 l ) ' ' l ' . t t r i r r " l l \ ' \ ' { t l l r i r l l l i r i tc l r l l r

. l | l ( | |u| i |1, . i i . , | , . . r ' . . . , | . ' l . . i r l t i t r r l r i r r ' r I r ' . | . .1r I t t t t l l t t | . I t t t t t l t t I t t t I | ; | l i | | | . , ( l l . ( t l . i t | | | |t , - - t l th"rr l t t l i l t , r r '1. I r r " l r l t ' r r l r r t r

r r r , l i l l r l ' lu l r l r r l ' r ' r l l r r l l | r l r ' l r r '1" '

i r r i

L i f* t | l , I ' r r , ' ru l l , r l t t l l t t r , r l '

-r'

Avind in vedcrc marea simPlitatcricc dc inalti. frecventt, acestea pot {imctalelor, a pietrelor,. sticlei etc.

Tra.nsmisiilc de impulsuri hidrosoniccfost aplicate cu succes li armelc avioanelorrnul rezboi mondial.

si grcutctca rnice l ciocanelor so-

utit i iate pentru tl icrc:r 5i fasonarca

au multe aplicalii Posibile ;i auhr i tanicc in t impul l i duPi Pn-

{) . r ) r : t \ t \ ( : l , t . \ ' I ( iuo ( ; t t ( : ( ) \st ' . \ \ ' l ' t \ l iscl ls'r' Yl'.t so\ t(]t't"\'l'r I

I lr,rrrrrrs I, l l isorr, irccst i lustru iur.enta.tt lr. zicci! c11 mult rrmor, t lcalt-l r '1, , i yr l r r l r r r r r [ r rc l o invt .ut ic s iur o r lescopt ' r i r t : , cstc t rcvoie de numai 1(1ii r r ' ,1r i r . r t i , s i ( )9 ' r j , lntnspirat i t . Cu sigural ta-r i lsr-r t :ar dar: iL I ld ison ar { i cu-roslul nr ; r1( l l i r l i ( i , rh ' r r ruul dc la inspiraf ic l iL lezrr l tatrr l f in:r l er f i {ost par ' -1rr ' \ I l l . r i I r 'P|r l t ; i ILr Drul t rnai put inar t ransl) i rat ic, f i iDt l scut i t de ncnumirr , r l l l , i r rct lc iLr i r . r r t i r i r i t r ' . l lccrsarc at lLrrc i c iut l r ru Ptr tctn incar l ra otr icctul, , r r ' t , , r i r i r I i r r r l , r j r r l r r r . r I , . I 1 I . . I i , .

5plt dt oscl rirt ' clc l:dison, (;( 'ors-r' ( ' .(mstirnt ir)f scrr ninuia lrn:rl izl ma-llrrrrrl ir ' i cu rrtult iL rnirit 'stric, ccea cc i-a prrtnis sil I) lLr( rugir drumrrl dt. larrl, ,r irt i t ialrr l lr rczultirtul f inal intr-riu l iml) r( cor(1. Sr-L ciuliLrn rler:i siL-Ir rnr , i r i r r 1r t ( ; r .or i { ( . ( 'orrstal l t incsclr dr , i ! lungrr l : rccstui r l rum pl in c lc int iL-l.rrrir lr ' , I luri a11:s pcrltrrL cci care se clcrl icr-r ct 'rccti-Lli i ;t i intif icc ;i aspiri:..r ' ,t rrrLuci cotttri lrutia la imbogl-LlirciL pirt l i tuoll irrlui ;t i intif i t: nnivcrsal.lrLlrr rl.c la carc a poruit, sa!-i ziccrn inspiratit ' , ir fost irc('ca c1c ir consirlerrrIrtol)l l lr!r(ir strnctrrhri pri l l undo, studiat in itcuslic:r, (: l i r11r cil l p:rrt icul,ur | r ' l tatrst t r is ic a put l r i i rncclrnicc pr in v i l r r i r t i i rh ' lu nn capiLt l i r c i l iL la l t i r )rtttui trrlr ucusti(. l) lrt( 'rca tisticl transntisiL ltr in tulrrrri lrcusticc ('ste insi ' il r l t lut <[ t 'nr ic iL r l in c l r l rz l rn l r r i i chst ic i t l l i u i t l ' ru lu i . I )e nscrncnca, laampl i -lrrl i tt i rtt.r i nrrrri r lt ' r ' i lrrnti i , tr irnsmisia putcli i cstc practic l imitatar dc fc-rrorrrr.rr,. lr t;r loLicc cirLc o insotcsc, pc l ingi! {irptLrl ciL t 'r:urrti i lc propagiri i scrottrlr l ir ' i t orsirL'r 'nlri l in actst t:az, ncrlaiputintl f i lezoivat.i prin metodclcr l l l l ( ) ( r ' l l l " .

l ' t i t t lr-o lL:ocirrt it ' rLr ir lei, Gcorgt Lionstlntincscrr 5i-ir ltus intrelt irrc;rrlrrr '. i i trt r ' l lnl| ir s-l putca spori putr:rcir rucciutif ir t l lDslnisar prir-r uDclc, {o-losi t t r l c ; r t t rcr l iu r l t ' t l ' r rusni tcrc in Ltcul acrulrr i , lp i i , ( i r rc avin( l o ( ' last ic i -l:r l( lr l l l l t tuai rtt icir t lccil lrt:eca ir ncrulrri, ar i)ut(' iL l l tclrrrr putcri rncc;Lnicclr ' . r r .nr t \ ( r r r rnrr i l nt : r i nrrrr i . L) in rni ' rsur i r to l i lc I rccisc:Ll t lu i l l rn i lc Amagalrr : ' t tpr ; r t ' l r rs l ic i t i r l i i i rp i , ( i torgc Const i rnt incsr r . r iL l l r . lurr t : rcc.stc r latc cal-r ' r t l i r t r l r t t ( l ( l l ) l l t ( ' rea rnu:auic i r . cc s- . r r pLt tL:a t r l r rsnt i tc 1lr - in v i l r rat i i , t le o:rtttttrt i l - lr ntlr l i i url int' in ircr:st lucdiu, ircclstir ncrrlLil i iutL l imitatl 'r dc lrno-I l t l n( i , ( i r lor i (c ol t r ' o i r rsotcsc i t r cazrr l t l iursnt is iL i | r - in a( ' r . I lczul tatul r !l r r r l , r r , l r r Pt r ' : r r - t l - r r i l l r r i t i i r rnurne cl-r l ) l r t ( ' r ( 'a t ransrr l isaL ast f f l pr in i rpar,r t ls t r . rL l r r cci l i f ivrL r t t icror lat i t ransnt i i i p l i l t r r ' t , LL zt .c i ; i sntc dc l i \ \ 'I r ' i t l ) . r ) l r . i Pr- i r r r r1t i .

{arr lg( ' ( .o l l : t iu l t in( scu l l r r s-a mrr l ;uur i t i l lsaL clr i tccst r fzul t i r t t rorct i ( l. r l i l r l , . r r r l ) r iL/ , i l or- , r l i r r I - : r supus uuci r .cr i f i t : l -Lr i ( ] \p( r i rn( nt l r l ( . . ( ,u mi j loacct t t rx l , . l ' , i l t l l ) r ' ( ) \ ' izr l r ' , r l r r l iz ,cazi i Pl i r r t l r inst l l i r t ic souicr"L t l t ' t ransnl ls lc i rl ) l l , , r i i r I r ( ( i rn i ( ( ' , pr i r r v i luat i i in apir , punind i lL joc r : i t i la k\ \ ' . Instalat i iLtr ' . r l izrr t , r i t t l ( )12, t r is tctr t r - r : j i i ts i iz i , const i l ( l int l un gcncr i r tor c le v i i r rat i i| | l ( ( i r r I r r ( . r I r I i I i r t r , I I r r ' r rPir t r r l r rnci con(Iu(: tc r l t : o lc l r r rnqr lutc cu api ' r , la c i rp i r -t r t l r l l r r l r r l l t t t t r l t r sot t tcrr Pr<xhrsi in i r l ) ; - t , l ) l l r l i -L loar( ' rLr . r 'ncrgi t v ibrator i t - ,I t r r r l r orr l l l l i l i r l i r r r rou i r r l r r r l t r - r : mccrLnic iu l ) r intr ' -ur ruoiol sonic rot i r t r \ ' .l ) r ' : . i11rrr r , r 1r 'n l r r r ptrr i r , r ' l r r r ( ; r s i ( l ( . / , \ ' ( ) l l i r r ( , r nnol ls l f , l t ic i r tst i r l i r t i i , Gcorgc( ort , l . r r r l i r t l l t t r r t r ' l r r t i l . i : r l r l icc l lor i r r I roIrg,-rr i i sr t t tc l t t l t t i l ) r i t l tu l )u l i, r i r ' ,1r , , . in lor r r r r r , l r ' , r lo,rrr ' , r l ' , r r . r r l r . l r i lor . , l ; r . , t i r i t r r ( , f i { l { l ls i l r r l ( l ) ( ' t ) t r { t, r i I . t r \ r l , ' r r l , , r , ,1, , r , ' , r l , . r . r r r ' l r l r ' r l r , r . r l ' r . , r . r I r , , r . . ' , l , l . r | t l i r t r r t,1, , , r , l r r r r l r r , r l t . r ( r r r r r ,1, . r t r r r , .1, r l , I ' r , r , r , r r ,1, , , r , l r r r r r l . r r r r r r r l , . r ll t r ' , l , r , \ 1r , l , | | t l , l r r . r r r r r , . r . , r r r r , , ' r . r , l , r r r , l , r r , r r r r , r r r t l r t r r r l , l , , r

'L | , |1| t , I r , | | , , . , r , 1, , l , r , , . r r t r i ,1, , r , r r l i r rLLI a mi i dc atmosferc i i l r - iur l in vLr lcr t

l r l r r r I r i l l r r r i r i l , r i r r l r i r l i r r r t ' , r l l l inc per iculos put ind c lucr la spargcrcrr, , , r r , l r r r l , i . I r r I r . l r r l r r r r ' :1rr l l )utut Gcorgc Conslant incscu sa'r" r 'cr i { icc toai t :, , , r r r l r rz i i l r . l IoI i l ' i I r ' i r rs lu l ; r t i i r sa cxl , r r imental i r , ccea cc i -a dat dcpl iDa

r l l r r r . r r r { i i r r r ' : r I . rL i I i I r r t r . : r ipotezci i rdur isc ; i i r concluz. i i lo l tcorct icc dtr l r rscl , r r r t r i t t r l r l r ' l r r : rcr . r r : r l ; t . l ) lu ' (1. ( 'ot tstant infscr l nu s- ; r opr i l l r r accst p nr rrr -l l l . r l , lo l r r ; i i r i i l ( i l i tn l ) (n i iu l t , i i i r i r o a c lorra ctapi ' r a in\1:st igat i i lor , r '1rr

l r r t l lz i o r t ( ) l l i r 1((Di( i r l r iursr t i ' i , i 1 ' r , t r - i i i t ' , , :Lr t , , , | r i t t l i l r rat i i spcr i l i r : iI t . r r r , r r r r i s : r ' i Iu i t . r i i qr t i t r l i t l r i r i r ' . t l r r r :nr i . ic l l ta i ( r t i r t i r lc t . fcctc terur icr car ' ,I t t r r r l r i rz:-r l r i rnsDri : . i i r pr i l sr ln( t , i r t lLcr- . . \st ic l , iu lor s lL i r<r l l r ' tsc i dc la t , r ur-l | |1, . l3 l ' l i r l ( i IL. Inol) i rsarr i i .ut t i '1ului p( 'n l ru a ajuni{c la ( i i {er i tc l ( , ' f (ct{ '

l , l l r ( u l i r r ( , foLrsi t t t l t t r t t rx l r r lu i I {a, , l t igh, i t r t rLtatul c iasic: 7 l r ,or-r ' t ; l sot tn, l ,t , , , ' t l l r ' ( lot tstrrnt i r t r , ' r 'u rr t r r t tazr-r (Lr-r . lmul i l r lc15: porncst t de i i r i r i t r t icrrLLr, , r ' . . r : r iungir l r r 1tcr , r ' l l . I l r rn i r r r l r lL la-1 t lef in i t i i s i rupkr s i iu lunc: . l i i i l i, r l , r l ( i r . r r i rs i r , l r i I t i r r r r ' ; r s i | tTr l i t l rnta, r lat l i incl r ' l - r r rccstc ln i r r i r ) r i : i l1 lnr lI ' r r , i , r l i l r l rsoirr t r ' r r lc t t i i r Ict i t i , c iLtL int t r \ in iu ol i . r ' t t tatr i ic 'starI l l c i , str i , il . . l r ' . r r r l r i tc rc l l t i i i r t i re t l r ' , r ' t r - i l icate Pl in cr lx l i t ,ntc, constala! ( i i l . ( s l , 't ' l , r1r r , i l l analoge crr i rcclc l r crrr t l t ' r rg l - r int lc c l ( ( i rpa(! t i r tc i r , inr lu i t l r t l r r ,r . , ' r . l ,n l r t ser ic ) i ( lcr i \ r r t i ( , Di i r i l r i r i t i iu i tc in c i lcui tc Llcctr- ict : dr ' , r r r l r l, r l l , t r r . r I i r , .

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l r '1, r t r l ' r r ( l c i r rc ar Pcrnl i tc pistonului sar iu l rc crr lproap(. 26 cm.'r ' \r.(l(., l)rin urDlar(', c:L comprcsiuni':r apoi intr-rul tub tlc f icr crr ri i

r r r , r r , r rn i I r 'onsir l t ' r i r tc, rstc factolul pr incipal in schimlr iu- i le dc rrr lunl c l r , ,, l r r ru l r r l srr l r prcsiuut ; i c iL di latarc:r tubulrr i t 's tc aproapt ' ncgl i jabi l i r .

l ..r :rprirrrarca plesiunii cxr.rcittrte asllpri l pistonulrri apa st' r lcslirrrLl r r , r l r r r r r r r l , i i r i t ia l . int l 'brr int inr l a l tq I ichi( lc sc pol obl inc rczr. l l tatc s in l i ,lrt, \ i lrrtsrrl lnr('nl acunl cr-r tulrul, in loc <lc tr f i in(:his in mocl rigit l l :L rrrr' ' l ' r l . ' .1, i r , I r i : , l , r rn l , is l , rn usor nrolr i l l inut p( ' rmancnt in contacl (u, , ' l " , r r . r I i ( l r i , l , i . , l , r r l i l r r r l r ' : r s, . tn i ;c: t i l l lpr( .uni r r r l ic l r i r lu l : s:r pf( .s l r [ r r r ) , . r1,1",r , . r p i . lorrul l l totor, in loc dc a f i impins incct in tub, L.stc lcgir t c l l ( '| | r r t t | \ r ' l , r i , | | ( . s( ' i ] r \ - i I t ( i t ( : r 'ept .c l t . impr iminr lu- i o misc; t rc armonicl- t s i ln l ) l it ' r 1 ' l i r r l l i i rn l ' r r lsrrr ik pistonului , o pr( 's iun(.p( ' r tnal l ( .nt i i lucrclz iL asrryrr ' . ,

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I t t t r t , , t r t , t t I r r | \ ' i l ( 'z( ' i rna\ i l r ( ' : r p istonulrr i , r ' i t t .z ; r st l r r l r r lu i r l r . l i , l r i , ll t r | , , l l . r ' I r r r r . l l t r f i ur l r i n l r r r ' < l i . t i t t rc l r . l r iL s l t i t t l l r i l ( ) l r r ta i inr ! Pir t ; r1, ,l I l r r l : l , r r t r r t . l i I i l r s l r i t lur i lo l lyr lo l t i l lc t l t ' l l is lo11 s(. \ ' i t t f . r l t5 l t r i l , . . I ' lDrr l r r , r r . rur l r ' (L.rr lurrgul colorurr . i . l l r rc lg i r r c l r r . l t r r i t l 'L rL ' Piston i r r ruts:r, ' r l t r , r l t t r , , l r i r r , i l l r I i r r r l t . r ' r r rsr . i , r ,s lc r .on! i r ru l i r i r r coloan:L l ic l t i< l i r , p l r l t r .srr l ,l , , r r t r I ,1, r ' r r l t l1 i r ' lxr l l t t { i r r l i r l l r t r r l i i i rcr l r rct . r ' i i toI t r t t r r I r I i l ichir l r r l r t i l r r contl ' r l l l l r r , r l | . l l l ( . ( i t r ' t l ( ' t - l . l l i t ( t t t (1t( . i t .

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I . . l l , l l i . l ) ,11, ,1, l l lnb. , , , ' l ) i , r r i , , ,1, .1, . - i r r r r , i i r r , r i r , . , r i , . , , , ,* , l i i j , l i , l l l ' " i1 l ', l)',,,'l l ',i ',l,lll:i,,)'Jil,";11,'1' , ",,"' ' ', ll,,ll .'1,'l ' urr' i 1u'zitii r.",rii, ., .i iu. I - t ! t r i t l )snt i terqu sunr- , tu lu i I , r - in .L l r , i lut \ . izLl1 r : ! u sct- le t lL, r . i l r ; t1 i i.itl r:.r,unicarL, prrrticult:l^'r irerrrliri, lor.tinrl.-1" .;- ." ,r;;l;., .i.] '",,.f,.f., p.,Ji,r l , r r t t , i Poz- i r i i , r l i j l .c i i . , i rL rrr , " i r r l . , r r , .< l , r , i l r u l , i . 1, , , rn i r i , l ,1, . I , , , s1r. , . , , , ,' l . r r ' ( l ( ' l ln( t , . r l , t .n;1t , . d, . i , r l l l l ) r \ , i i I l l r r . i r . r r . , . f . , , r i , . . I ) r r i :1, , : t r . r r r , ] , . . . 1

lilll,,lli,i;;.'lllll,ii''..llll';,,lji,ilil],:i::"ii:'iirl:'rffi'::: ll;rulili.;.gili:. r . t t t lg i t ' i I r l i l r r i icrrr-c.ckr un( l ( , D- i r ( . .11) l ( . ( , . ln mod si l l iLLr, sunelrr l : , l r i rLr : -ru l ( l )nn i ic l r i r l t s i sol idc.

lrr l ichid. Am virzut nai sus cir iau na 5tcr-c o serie <lc zone (le inalti-r pre-tlrtnc;i dc l ichid t:omprirnat, alterninil t:u. zonc <lc joasir prcsirtne;i dc l ichidItt cxpansiurc,5i cir accste zonc sc nti;ci t1e-a lungul tuhthrt.

-in l igura I si prcsupunem cit nranir-ela tl se inlirtell( ' rrnifornr, sil intl

;,| ' , lonul l l dc a sc mi;ca- alterrtativ in !ctr ':r c, plinit cu l ichid. La l iecirreirttrir inainlc a pistonuiui sc forrneazl-r o zoniL de inalti l prcsirtne inr atestt 'rrrtt l de inaltir prcsiunc (arr-rtate prin umbrc) circuli-L de-a lrrngll trrl lului,

l,ottt intl dc'l,L 1ri!1on;lntrc douiL zonc vcciue rlc inaltiL presiunc t 'stc o zonit,1,, ;r l:siuuc joiisir (arirtatr-r in alb pe l igrrrir). I)rt 'siulca in oricc punct rrl lcvii

, l ' , r r t r r r i . r l l l r r r . , .1) t i , l . . , i Pr, .11.1

l ' ' \ , ( , \ { , , t . r r j l t t l t t t , . , , , r r , l i r i i . 1, . , - t , , : r

i ] i , ,1 ' ] l ] ' , " l rc l r r t ic s i 1 i t , r iPl i rL rL

f i apt t i t : . r I rLsPurlr ie Yi l r r .at i i I I - r :ar , . - lr tccpt<;rului catr ' r t r i l r , lz_iL s:L f i ( , l l ls ir i l l 'zr h p ' r r ior l i , i tat( l r l i l ) la l l io: ( , - l

l , ix . l . - ( ; .Derarca f ' pro-

l ! rK:rr ,a r t rx l r lor de prr$unclr l r -o.ot l ( luct : r cu l ichid o

' l ( . l ro! i inre in l in i t l .

bc

\,r l r ' r ' r ' , l l - in uttr\rue , l )r i l l t r-o scrie t lc vnlori t lc l l t r t t t ulari l r luln l l r t t t l l , ' i -

rr trrrrr l ; i t t 'estc valori- st vor lepcttr in motl periodir: . I i i ( ' a)-I l ini i ' . r-enrr

rr . r r t , r t i r - i : r valor i i presiuni i n i i j loci i ; la pozi t ia pistonuiui a: : i .1at r -L in f igrrr i i ,

1,r , , . r r r r i l , ' instanlr t r t t 'c r l in di fer i tc puncto dc- i r l r rngul t t r - i i pot l i r , - i l ' , " r r

i , r t , , 1 ' r ' in rrr lonatcl t ' curht- ' i s inusoidalc c19.. ,k ( ,un tn i ;calc;L dc rot i r l j i i l

r r r , , r r r i , l , . i cst t ' ut t i fotmiL, cste cr- ident c i t ( l is l l l l l tc lc i r l t re ' punctclc su( ' " ' l \ i

, l r l , r , , i r r r r , t r tar i r r t i ' r vor I i egalc. I ) is t i lnt i r r t r l i io l rn i t t lc- lL l r tngt t l tcv i i l i . , , r rc

' , r l i , r r l , . l r I |s iutr i i sc rcpci ," t estc lungi t r l , l i t l r r t t l t l i r l r nt i lcr- t r - i i t ' i i , r r r t r t r r : " ,1 i r r

l r ' l ' | l l .l ) , t ( . - ! i r ( ' j t ( ' r - i t tz l i cu cal( l f r ' '1 , r t t t t i , ' c i t -cul i t t l t -a l l r t rgr t l l t t l ' l : - l : , s t

' , r , , t r , | | l l |Diml t l t r rotaj i i in lu l i ta l . : i t ( i r '1 j1nl) i l n lat l i \ t ' l t ' i r t , sc r t r l , i t t l " r . r l

, t l r r t t l l i t t t r ' : r i , : r utrdci va { i i ' ; l t .' , . r l rcsrr t )u l tc: I a l r rnt t - i . i , ' , t . ' , , , t r , ' , , I i l t lg intr ' i i l l i r i , i i i t l< l i l l r ' i l - l . r

I r r r r r l r r l r , l l o-r l is iarrrr : ( i ' ' l ) is1{) l I l l / t , qal i cr l r t t t t t t t t I I i I I I r t t \ ; lc l l r l l l i l l - " , i i

'1 , r t t t r l . r , ' , , r s i i I ) fcsl iDlr i ' , t ) i c l - i c l lLsi i l l is l r r l t t t l t l i t 's l r ' ln i t i r i l l I ' ' I r I I r ' I I . |1 1l

, r r"rrr , r r r t r r l , . i , i igt : t r r j .

' I r r , l , r ( l l conl i ) l ' ( \ ; iL l r . vr i i t opt i t rL l . i / i i r ' ( l l t r t i r la! : i ; r t t r t r t l , r t ' l : , '

I i t | \ . r r t t , r t l l r i t t , r I r t i , i , :L l t t t lgr t l l r r l , r r lL l i l ) r t t - i I t l r r t t i r t l : r crr l l l l l i r l . l l ' r i .L: i r

' | | r r ' , \ r l , / , r r r r t i i i , r 'nr i , l r tnginrt ' : r t , r ' i i ' i r i t lz , r t l , ro l : r1 i ' l i i r r t l r ' ' ' l ' r ' r ' ' r, | r , r r l , . , r r l t r , r r l i r t r t t t t r r r lc l l r l t is iot t t t l / r l t r I r t t t rLr t l I l i i t l r l t l t t t t l l t l l i | l r r ' r rLr I

. r l l , r r ' r l | r r t t , l , r r r r r l i . t l zr t t t l " r r l , ' pt-r 's i l t r t I t t r : r r l l t l , ' l | i l l ) ( ) l l l l ( l r ' l i t l ) l : i l ( ) r r ' \ , ! { l

l r | | r , , l | r ' r l | | t , i t t , l z , , t l : r r , i l , r ' l , i t . , ' i , l r r r ' : t t t r r r ' l l l l l \ i l l l . 'L \ ,1 l l l l l l l l r ' I r r ' i ' i l

I t l t t t l r l r t l , r , , ,1,r \ ' . l r t , t r ' . t , , t t l l , l . t r | r . . r r r t I r I r I r r r I r t r r ' l r r l ' l , r , r r r ' l ' t r r r r l r ' r l '

t l t t l l l t r l l r ' . t . | | , , r l l r I r t r l r ' . t l r t t t l ' r r l l r r l , r r l r r r l i i ' l . r f r . r I | | | t | . I I | | | | I . r l l l i r t l t \ r ' l r ' l

r ' r , l r ' l l r l l r r r r r , t t r r t r I r I I I r t r I t t r r ' . t t t t t r l I l l t . r t t t t t t ' r ' i t r ' r r" ' l r l ' r | | | , r l l r ' r r I l i

r , r r l i l ' r r , , l r l r r l , , r l l , r r , ' r r , l i ' r r r l l . r l r r l , r t r ' l ' r r r ' r r l r l r r r r ' r r l r r r l r t t r l | r ' r ' l

l l ' " l ' ,

' r r r t r r r | l ' l ,1, 1,r , . r r r r r , , r ' l ' l ' r ' ' l r r r r r l ' 1 ' r r r1 ' r r r ' l l l r " l ' ' l r t r

l l l l l r ' l l ' , ' \ r 1 '1, r r r , l '

l r t r r rz, t r l t t t - t . r ' ] r r ' i sc gi is( ,s( . t i rc( ,1) toar( , I11lLt- t r_. sr , t ts j l r i | , r . . t r . I ( ,z.JLtr . i lz I. : : ] ]

, .1] l , 1r , i : r , l Lpt . r r ,1, , . i , , r i l , l i i lor- r i t . o Pcir ,^Lir i r r r rc t l i lerr l i , iD a:rLr-

l1] l l i , , , : l : ]11 . :1, , l l l . , '1 , ,1t t i r r t l . rotu; i r - t ! t 'u i ru t . r | r<, i , l tmu du i r l , r . i rn i , . . i -

l ] : . , .11t . l , ' , , ' . | | r l r , . , . r . r ' , i rDrcr- , 1 i r r r : r i . r1, . . , i l r t l - , , , i , , . , . , . - . r r . . , r , , . r r r i i . 1. , r . .

' ,1 ' l ] j : , , , . , . j , , ,1: l l i ' , ,u rrJrr tor .u l ucr. l0r . r i l r rat i i , ( .stc r)( ,c( .s iu.crL orgaDul r i ] l i . , . .L--' . r n" r r , , , r j l l t : r . l l , . t c , r s i I i , r . , . - I r r I r ) (L. ,

1".r i , ,d i , i r i r i i .P, . , i . i l . , ,1, . : i , r : r r i .

lil' ,:lll, li"li;ril l;li ir,l'i:'l};i' ,l'll l:i; ll:;::,-;lii,::':;:l;l,,i]l,l:i.l;:l r rnt l t t i r l , . r r r i l r l l la l rn isol r . r r r i l , r ,L l i i | . r , , r1r , . i , r r" t , , - . , , , r , i L, , i1t l , , , , t i . , , t i

l ) , , ; i i r r r r r rc l r , r . i rzrrr i in r . l rc l l l l rs i r r .L i i rs l Pirra , r ( l l l l i l . iut5!r \ i \ i r l r intr l ' r . '1 i i i r r r l . r t , r i , . , l r r . , ( r r r , ,1, . , . , . , , , , ,1, i i , , , . , r , ,1 , i , ; ; ; i , ] i , , r , . , r , , , , t . . , , . r r r , , r s i' r , r ' l ) r t t t ( l . l | l , l r ' l r ' l sol t . , r , . i l l I l r ' i , , u, I lL. l . . ,1, I , r r , ; , r r r . , I r , . . t i r r r r , . r l r r . i r , l r r l r , i,1. v i l r r ; r ( i . i r r . t r '1t I r I r - ' I r r i : r [ .s l lLr i r l i i ' \ r . , r l l l , r , t , , i , , ; r , i , , r , r , i , r r r , , , ) J, i ' i i r ilxr '^r t l r r ' , ' l r l , r r r r l . r rorr l , r l n,r 1, , \ l . r ( l . r l l r r r ; r .ntrr ' r , l r r r r r , r r , . , r r l , . l , r . tu., ' , . : ' l l ' ] :

,1," , . '11", ; r , , r I ,ut , r i i l , r i r r r r r i , . , r , ,1, , r , l , , r r , . , , , ( . . , . . t , . t , r r , , r : . , r , .l l ' r r ' \ . l l , l r , r l ' . . r l t r , r | l 11, , . , . l , r t r . , . r r l , r , r l r r l , . , l r r r l rnr , r ,1, . t r , r , t t l l t , , , . : lln) , r r . r . l ' t I | t l , , . t , , ,1r \ , . r t r t , .1, t , l , , l r , . r l . ,

\ . r r r ' r r , , r r I r ' r . r r r r . r r r r r , | , ,1 , , r , , , r , , . , r , r i ,1, . r r r r r r t r r r r l r r r r r . l , , l ,ru l ' l r r . , , ' r ' r , r , , l , r r r t r \ , ur , r r ; , r t l r r l r , r l , . r t r r l r r r r r r 1,rr i r r r , , r 1,rrr , ,

l r r . l r r r r l o l , , . r \ . r t r I l t l t u rrrrr l . ' r r l . n l i l i l l l l r ( . : r r I r 1 I I i t r r r i i r r t : , pr ls iuni l ( .u l r \ i l l { . s i r l : , lx ' t t l r . t , l r r r l r .zr .L. 1 i rh,Pl i rs i - r r ik . nt i rx intr . a lc l ) i l r . t iculc lor osci-l r r l ( ) i t t r ' s l , ( ) r r 's( rh. , r , r . t I I r . r I r . . | .

Si PlcsuPrrrr . r r r , r ( ur l 1,r i r l rx r l t . r r inclr i< l t . tcrrv i r in motL r ig id la punc-I t t l r , lx l r r . t r r i r r . r r r ' l p l r r r I u l I r is ton , i I ( ' l : : l t cu o nlani \1 ' l i - r l l . , analogir cu. f , | ) t ' r ' ( | | t I I : \ r ' l l l l t l , t i t | t t l i r r r . r L

Sir plcsrrpunr.rr r c i rr irrr ivr. la lr se inr. i l t t :stt : cl t i rcceai i l i tczi unghiularirl l ( l t l rcc(frt i i fazi cir si r I l l i \1.1:t r t . I ) i r t- i ' t < oloanlr l ichidiL ar f i contiDuatd.

l r r . . 1. l11,p:r . i iarea und(-l , , r r l l r r ) c( , ' I luct i inchis: i

r r r r y istou.

,1 i , , , , ,1, , ,o1, .p istouul / r , ( 's tc cvi( lc l l t c i r mi1cal t .u pistonului iu 'produc( ' in i r -ir.trsli coloanir () s('r i(. (h. un(lc (: l!Tc ar f i cxact sirtri larc ;i {) ( ontinuarc arrrrrh lo l r l iutrc D si rz.

l) ist<xlrl rn, Prin urrnalt ', ( lac:t s-ar rnilca sincron cu, \ 'a l i apt <lc a".rlr.,ollr i intlt. irgt onclgi(: ir un(lclor produso (lt: [ 5i calt 'circrLliL dc-a luugul 1cvii.

Sc vit \'(.(lca, tlt. irscmcnt':r, ciL pistonul va {i apt de a absorbi 9i utilizalt lrr ' .r l ir ( ' tt( 'r i. l i(: a un(lclor carr soscsc pinir la <littsrrl, dat' i ar- f i aiczat in

l t r r . l r r r r ( l l r l lc | i i , r :u condi l ia c i r Fr ioada lu i t lL, nr iy i r r . . . i r l tcrnat i f i r s i tltr. ,rrlr. ir l i crt l i t pistonul D;i cu <:oncli,t ia ca Iirza nti;ciLri i lui si l ie astfcl cahir 1rrrlulir o Prclrrngirr ', r l incolo tlc ol, a lrndclor r: lrrc protluc impingrrcir;r rr .r l lr ' , rn ir lt ' crr conclit ia (::t ntifclrca pistonului sit { ic in f:rzr'r cu nli icarc:r' , l r , r l r r l r r i r l r : l i th id iu contact cu Distonul .

Ir lr irttsrtt itcrcir (lc putcrc, din accst cscmphr, prin nri;t:urca <lt ' undc',rr,r\ inl!rl prcsiuuii in {car.iL nu v:r intrcct' in nic:i nn punct ntaxirnul <lc prc-. 'ttttt l r l i tr vcr' irt iLtatca pistonului nlotor, oricit de lungir ar- l i l ini lL ([e trans-rl ir,rr 'tr ' l vrr l i ncela;;i f ic cit l inia arc lunginx: de o un<lir, l ic t lt 'un rlr l l l t iphlrl l rtttr l i . l l ascrncncar, cclc dou:L pistoarrc sc pot uri lca fit in irccla;i scns,l ir. irr sr.nsrrri opusc, i irr mi;ciuil(. lor pot di{t:ri in {azi-r cu oric(' unghi potrivitltt lr ' lrr{irr ( ' irr '( ' o}i istir intrc distan!u dintrc pistoeue ;i lunginrt ' ir dt' uudir.

Irt r:xr.rnplul ([ is(:utat rnai sus, introirgl cnorgie pusi-r ln coloana lichidl-rpritt pislotrlr l I poatc fi absorbitir dc pistonul rr. I)aci! sc introtlucc rnai ntult ircrct gic t[t ' l) istr)nul ,1, rkrclt lrcct.:r absorlrit ir dc pistonuL1,, l)re snpunin(l ci 'r

l rA I Lr l r r t r r r .a l ) f .r t l I I r ' ( : r f l -

,1" , l , ' ' ( ,1, . l , , rAr ' , , ( . ) ' , ' l l l l i -

l , l ! i r l IuIA| l r r r l , . l | l ( l i .

o

r i lt r ' \ isl i l Pic[rlcrr. 1[ir frcr:irrr ', cstc t 'r ' i<l 'nt ci-r s( \ '()r- [onIr ; i rutrLr rr '[ l t ' t :-l ; r l r ' pt i t t iz l r i l l l r rnrk. lo l r l i l r r lc r rsupl l r l ) is l ( )n l r lu i / / r . l t (z l r l t i r lu l v l r f i cr ' rst t r l l l t tsrr l tL ' r ' r rcrgic r ' : r r i r rn i r r r . i r r l ic l r i r l i r r r ' (ot t l i t ) l t r r ( ' l to l r r { ic i t ' l : r r l l - t t tg i ri t t tor t l i r r rnr ct t t ' rg i t , s lxr l i r r r l rur \ i r lu l r l r ' ptr ' . r i r r t r i r r r r lx l i r r r t r ' l i t r i l p i r l -L

cirr l i r r r r .L r l i r r r r l r r l i , ( i r , i i i l ( , r r r l l r r l r r r l r t i i r r l r r r r r l ; r l , t r . i r \ ' . r \Lr I rL \ l r .Si l r r r ' : r rprur l t r r r ' ; r , i t t r , r r r t l t l t r i l r t r l t i . i r ' , r rv i t t r l o l t t t t l l t r t tc r l l t r r . r t t r t r r l l r '

l l t r r l r ' , . , r , \ ' i r , r \ r , l . r . l ' r r ' r 'urrr 'n , r r . r l i i t r l t i ' r r r . r '1, l r r r | | | | t | | t | | r . | | | r r r l t ' . r f , r ' - l

i t l l

li: t ;;l'lril;iil:,';i:il:":\il {i.{ ii*lli,r }:ii *"t.,1'* rui::i[l, l'I r l t .r ,r l r ' r ' r t t-r . ," i i t laintc iL ptstr.

i i;iiiil il :,1;liliili'''ri" "'i:" ri '" lill'il1i Jil,i;ri:iiiii,, ir;'ili1".1i";li,,iii' , I rIl i l ir(( r]r:I lrtirr'(' srrtt mttr m;r-L (i(;' i it i i itt t: 'J,totg," ii]Oilll lttt

sarL in af:ttI

, ; ;;i;,i ii,' ri,i,i,,..,. '.ot"ii,, , ':i:jl'illj:,"ll,iili,',;l:i,l,ll i ',llll,,l,:i,1;1"i", lllli;,;ii;';,'li,:i\l'illi],''ll','ll;i ;';ll:l;;"i".,,,, ",',i",i,,'',., ,,,,,ii'r i'"'"s.,r 'f i 1',

iilill'i r' l,,,lr',,r[, ; ijl;y ;i"l:,: ., *,1'.,6.].l ilii,,ill,.l]iii:lll i, il*il ,lll,'l::l:l' )i",lY.l':ll'\,:':;1il ,''l,li-,11,i]]'il,i'ilili!:''rl'r r(-sort' \i'I ', \

Inr,i r :irr f:iffi i,,,,,,.,',*:rl, iljilIl r*i *i;,1*i*t,i' " 'rlll', liil,,ll'u'Li;',;,l,'li'*.':'l'];i:,'' r',r,s rr,, 1,"]$,rl'1. ,1:.1-":"i: ili,'i,]; ,ll.ll:li l : i;ll;llli'l,,,';lil llt'jii','illjll;.] 1 ''1.'"ii,'li',1':li,l 'lrili'l' 'i'iti'i''"^ ""' i

ill;,ij ,,r, i.li'iiil:1,,1'iiili:,,1i,;:;...,,.'' ': 1i1ii:1," ' l ', : ' ,'^ r"c.'l n'li'': 'l

'\;r , tnr:.i(l('rir'r ,,.''", t"' t"''-itig-,:l,,llili',:":ititil; al.jjjjJlt ljlilil,,li',;i:i"i 'J,:illi:iiil,,i:ll''ll,i'11,,'; ::,;: i'', ii.i i'.r r,, .'

li,ilii;;, i;,,,,ri1r,, ,,i,,r,, '1'.",';i{iil ll.*li*,,;;1,1lll.,,*,iii li ;\":ii:lliiiilliili' ii'l X i l, l ;:t riili;i*il *15ij i|*l*t."ilil'if ";.1"i t, ]t " ii l , ; ; " , , i . , i ; , , , , , j i i , r i ' . iut ' tut i ' l i t " r"" t t / r ' i r I i r rPt t l ' r r r r l 'sor l r i l t t tL.r tgr t I t t ' t

1" i'ltl'i,l;;',.,l, ll,,'itllili;:,,ji,j,l:, ':llll,ll;l'i',liilli,il.'l,,illiil:';,)'ll'l',1't,ii'iri , : ,r - ili ,it,;t]il jll l:lli'll,ij\illil,l; ll ili;,,1''.;,;:, ; lill'\:r Lllilili'l:' r

' ;";; i : ,' i;;:,i''illll;,,',1;,: l,lt'i;l;l'l;' ,{r " .li,: ,',;i i'l'l 'lilll .l'rl' 1 1 , : ,

; ; ; l , , l i i , , , , , , , ,1, ,1 t , ' ' ' I | ' ' ' t ' ' ' i ' t t ' '

t " t " ' l i ' t t r r r r i r r r l s i t l r i r r i t ) r r" ( l i r r l r r r ' l i r \ r i l

,l,, i, i;1, ,,, :, :l"i:lll' il i:' , i; "lll; ,',,lrtll 'li, l' ;l ,tiii i,i,il' ,;;,'',1;l;: ,lr',,;l-Ft ', , - I_ ' r , . . , ' t lr , : , -T or l t , , r j l ,6

I

,,i,1 il,iii,,,,i1 ',';;;:, ;iii1,;;:l;iiiiiriri,rri;jri:lJt{irir.;li jriil,:;,i;l'"Ji;,llt , ;i ,ll;l;;:;,ij]:,,lllli:,: ll,:l;ljliil't: 'l;,,,lT:'it,'t;il;j:1,ii,il ,i;;;i1;;i',ii; 'l:rl:r lil,,i:;;;i,,,itriiljli,j,i il, ;"-,jir ijl],Ti:tg::| ill'il;iiillt;;l|;: li;:iii rir,ri: r'i i:,ir ll'l;iit,^"r'liiil'iill'i:':ll,*illl];',,l;;:;:;l:,ti;'i;.1l;l;:iiij:;j:::;i ;iliul,l,i'i'ii:;,,,'ti,;',:t: ',:,tu;:i?"lili,ii j: i il [ ililji'r ", r* :*.ir,i,i--i, ;-,i, i, :

- li','l,i,,ffi it-

i,:i*I:i,it*i-q.1ri1.,;, iHiir:l}lil;,;l*,,rdrkl.1,,,, ;:r ;;1i'l6f lri;f:{i':"ffi ill*rli:ft;' " Ill ll:;"'1,'ll';;l;,ll';;',]:;'"*,il ,,.;::l,,Lm i';l;1,,I'':l ll,,';l;lil,lil:'.1' . ,'ii:i,ili1i:t11, l;,','*1,:1,*:-';"x,;;,;;,;i,T+iXif,lnersir,,r,ccan,ciL :,sr{cr,, ,,,:,:i:li::',Iijili:,:"li"l:;,il;.i:{t:,*"tj;r;:'H.ll"',1'r,a,rs,nisi,, r,,

CAPI'T 'OL1' I - TI I

curtEvfr so-ufl iN TL,BUITT sflrnrE. DEI'tNrrlI

Cu.rtnli Jltr.i:i ,rlltnt it ' i sau. curcnli sorr.icr. Pentru oricc mi;carc dc'ilrrii iItt tul-ruri plinc, dc lungimc scurti, dacir: <,.r - tstc suprafala sccliunii trrbului,In cmz, z-- viteza Jluldrrlui lntr-un monent oarec"ie, ln'cm/s, i - rlel' itrrlht ( rn:r/s, il 'r.m:

j . i.c,+,.

. Sir prcsupunent ci curentul este produs dc un piston carc sc uti;ciL inrr-.rtrr ll ltulrrr rlc () cm3 scctiunt, cu o miparc armonicit simplir. Fie: r -- lunginrcirrrr ltiv;rlrntir a manivelei motrice, in cm, s - r' iteza unghiularil a manivtlcixrtt fulsafia, in radiani pe secundi, rr - numirrul dc rotalii al manivlti;to rlcrtrxlr'r-

Atrrnci dcbitul ce trcce din cilindru in tub, in fiecarc montcnr va rr

i : Is in ( .?t +\r) , i r )

||hdtt I zao cste debitul alternativ maxim, in cm3/s, sau amplitudint:aill lt[tuhri sonic, / : timpul, in secunde, { - unghiul dc faziL, li dacil 7'lrh prrirntl:r unci alternanle complcte egalir cu timpul rrnci rotalii compl lt'I hrftf vr:fci, rvem: d - |rtt., n . ll7'.

lill rh:finim curentul eficace .I", prin ecualia

t7 1213' :T\ i 'd ' : :z ' ( r )

ht v l l , . ' I ' l ' tcc u"t l , . , i r , r .

Vrrltttttrrl I ul crrrsci pistonrrlrri vt fi <lirt rh' rcla{iir

D , 2/(l 2tlt.

Al,r t t i l r r lorr .s| t r r r rLrl l l l t t l r l t tgt t t l l r r r ' : i ' , f i i r r r l

I t t t ot t ' , r ' , i r t l . r , , r r r , , r

f t l tntrr l r r l , v , r l i

l r r volrrrr t r r l tL l r l ls ; r l r lc p is lor t i r t c i l inr lnr in l i rn l r r r lI t \ r ' ls l t f i l I i t t t t t t i t .

/ ; r l i r ' l r i r l r r l r r i i t t ( r . ; rv i r , i r r i r r t r r l i r r l l t , \1 ' ( i r t i r l i r t r ' . l

I l r lI l l l l , , ll { l In

1, , .1, 1, , , ,1 ' , , " , ,1 ' , ( , r1, '

, " , , , r , ,1,1, . r .

l r l l l , ' , I l i , , l , 1, , , , ' , , , , , ' r r ' ! l ' ' ! " ,1, , ! !

r" . , , " r i i .n| l . r I r r t | l r r ' , '

' , r r l ' / , " ' l l " l t r , l ' r l r l , . l l t i , ' ,11

{0

, l ' t , , \ , t ut n l , l , t t , t t t , , , , .nt

l t t r \ t ruu sr)r / /1r . . ( . ( ) l ls i ( l ( , t . .11.( , l t l ) t ( ,s i l l l l i l ( r . i l l t ( . r -l i r t r \ '1. r . r . l r . r , r r r l . r r . r , r , r r , r . , r . r r l r . r , l l i l (n. , r l l r . rn i l l i \ . i . lntr l r ru tub in <:arc5r ' l l l l i ' | !L t ' l r t l 'h l t | ] , I r , , . l t i , r / , r ' . r f i rL: o l i r r r r r i - r" s in i l i r r iL; 1.oul avci t

I' ll:,rt(Ltt I ,j,J) | i5,,,,

rtr t l I 'c l ' i in( l"" i,t.^ - - r:",1 d + (s I ct\V i,;t, : (o,,/") tl +( s I t"t\V ;"'l d 1' R :' brliso'

' l ' rcbuieobscrvLtc:- tvr tezct ' l ic l lc t - ' 'comparat ivmtirnar i 'pot f i

Inri| l{ iLlr: in tul)rrri rhr (halnctrc mai mari pcntru accc-a5i valoart-- i lui ft '' ' ' ' " ' ' i ' i " r , I " r ,

" dt pulcr l I I 'dt l lor i l : - r k ic l iuni i v l f i

lY (ri 7')t l lnr'Jo

( j )

tntrc-r r r r rL, / /_r . :1, . r r r . r r l r r r r r l I , r ( . . i t r i i i l l l r . r i i l i \ r . , i r lI r1.r f l 1, , l ) l l i l r t l " . r nr( . r l i ( i r l I l l ' .

Nl i l i r r t r r l :L l rsolrr t r l l r l r .s i r r r r i i i r r tu l r v lL I i

.lr^^ - , lr_ -. H,,. i rrt lxirrtrrl tk' lr icsiurrc absolutiL r, iL f i

?^", : t^ ,+H.l) l tcr'L y', cste prcsiunca intr_uu punct oa.ic<.art, al {cvii iar p" prcslunca

i t r l r ' - r rn al t punct, d i fcrcn!a

l t l , r - f t Hsin(a1 f r f ) (4)vrr [i.rlr:firritiL ca frcsiune sonontott,ict, i l.stat].ll irr( lntre cloul-t punctc iar fI este,r t t tp l i t r r t l inr . i r r . i .

l)rcsiunca sonomotricc cficacc r.a fi .-

,, HIV z.l lrigiutc. lntr-rrn curcnt altcrrrativ dc li<:hid intr_o tct\-ir., sc prod.uc

j:j,:,1':.,1,,.;:lll::ll.t,:,.':1.:'llil .1 t"'ii ;i in t:orpur ri.iii.r"riii "i,-r,,,;,; \.on, presu-

l::']::1..:.1: :ii::.1.:lr -dc presrurrc. sau. prcsiunea sonomotricc nccesari peitru a

l t l rx l t | l r , (urcnt l t t este propor l ioni l l i - r ( .u c l l rcntulr* ' .Itclulir lntre presiuneu sonomotricc ;; i cufentul sonic poatc .f i scrisi.

Sl crt 'L' i t s(' t i . iulslrl i lc putcrc intrc tlortr-r punctt" A sc giLsi grculit l i lc

r,,.ru','r'ir.',t, r''.'i^1, ''in'l tlansmisia'"t,IT-".1]].:'^]'l:*li^ii'ii'i;',','lltliil].I :rr ' t ' Di i l l uni l si lLl l , ' t{"ul ' ct l ( :( t)-,1, pr t ' ta l , c i l r ( l t lar lsrr lsra s- l l r . 1 ---^.- .^ , - i^r i -+r , .1 ' r r -

:ililX'',':l',,lii llt,i'll;,,l,l"li.li'..ti,,;::::i:1,:l:jln:l ,:lllill.:l;:il'1r' ,,.,i',.

illii iiii l::lll,lr;i1,,"'iii,r'1.i"',r,r"', :l *i,1,,;5ll lil,lllif,;,:,ll1ll',l,l, i;i';.lli;11fli,ll'.,l",rill\i.:ii,i.: i'"r,u'.r.[i"r rr. ,'ari pc'tr. ir 1,r'.,ritct t l l l l l t l l l l ' ' i l t ' i r ' l (x) / i :

r " r / ' / ' . ' : . , '2, . r . f ica.r ' ; i s t :ct in 'ca t t : r ' r t . t ' t ic t ' | i r r t i i or t'

1t1, , r r ; i ?u rcsl l t ( t i \ ' \ ' l l t ' :

r , r l , ' , , t i , , , , , i i t , - t1 i pt i t t t r r r r tu i t t l i l t t ' lc t t r {evt '

I t l l l l i l ( t ' r ' i I$l pu1('r( ' l l rulcazi ' t sir f i r l t lansnrisl"r ' trr l^ l lc sl t i l \1 ' lu

rrrt tr t t t ' t ' i .Lt ' r tr t

' i ' ' , ' t ' " ' " :1"i l ] " t ' " ' l ' t tclr tr i tr si ' t i tv(:rn ' l i / :

- l r t l t l t , i l t r r r r ( l { / / r / i / ( ' ' . . : , . . , , i . , . , , . . , , ,- - ' i ; , , i , i i r r t . , l , '1 i r r (?) ' r r r r r t l t t t tg i t r t t r t l i .cr ' r l t ' i {c l i t 's t ( r i r ( ( rc i r l r

,/ i , r i ' ' (/L'/ro,) (t 'y't),

/ i , r , , / /rr ' , '

t r .

kg,/c n! xl,

: r l r r t tc i

(3)

{., - unghiul dc

(.5)

ltllnhnl ft /ii, oblinc'm .lC

l l ' ( l /7 ) \ ^ ' , t { I l)

(AYi ' ) \ td1 - i t l 'z l2.J

(8)

(e)

r\r 'r.ttt pritr rrrtnlrc

l l '

l i . t tnf l t r

tiPi/ .-= IIIIL =' H.t' I.j.

h _ I t i ,rtttrk' / i r.stt ' cot'f icientul dc fricfirrne, in l ig .s/cm5.

/r r,,,,i,1:'liri ,llil",llll:,'olili"i"ffiri"nt"' tlispo.ibile in prczcnt' v;rloarca lui

Il e-i lr,.rl 2g<,tLI . (6)

ii" : |: ;;,;"J' *:llll:il::i,l*Illii;l,,li:'ill"llili,l:' ,,'"t:ll,i.l;,ill],ii':;lr ' . t ! , ?, , . r

' i1r 'zrL t . l i r . i * . r . , i r r r . r r t , /s, r1 c l i rLrrr , , t r - r i l i , , i . . i , , ,1 ' , , t tcvi i , i r . r cm,i , r t pr . r r I r ' t r l r p i t

c . 0,()2 f, t), I l i ,//rr,,r l *+*,.

, l i r .Pl l icrr( t ( \ i r ( . t ( . i ls l t l ) r i r : rct ,sLrr i sulr iccl l iPst ,sr , r rs l l r . l ( . r - r i t ( r . i ts t ilor r r r r l ; i t l l l r r r i r . { ( , r r5 i ( [ r . r . , r i . ' ! r l r r r r t r r i c ; r : r I roxirr t ; r t i r - i t .I ) i r r r . r ' r r r r { i r r (6) srr l rst i l r r i r r<l In. r , i l ! .cnr

A' ( . , . / i r r , , ) o,olr , j , t | ( t , t , t ) i t )V, , , ) i r t ) .

l r l

vlhzl^eficace--d-e 1oo .-U:

flnit de refaga!: o!:;If*, ",,,,t - D;pr"*';;,.i,ii T"lf ',i:l,u-. rcr),.czcntat prin 5 de.

Amflituilin ea deplasamer

",",ffi;#%:HiffiilftT'H.*if;"1'u,n u:o;#fienturui s&rt resate

il'Lff i"""'i:.?Jti"i'i;'::i;,"r,#lil,i:;,:l*,il:lH:-Tllllt,,lcitatea sonicir C.

*?::': Tt,j,-.^"il."i' :;i. il, ffi l'i'i"'::11, ..r,,;l ; il, l : :, f g, I :

CoeJicienl d.a capacitata sonicd. Coeficientul de capacitate sau mai simpluitattt, C, este definiti de rela{ia C :81k.

Cind un deplasament de lichid se produce cauzat de o schimbare deesiune ln lichid, de exemplu prin impingerea unui piston contra unui re-

, precunl sc aratl ln figura 6, in general cregterea deplasanrentului csterortionaliu cu crc;terea presiunii. Constantar de proportionalitate estc

ln cscmplul de mai sus, capacitatea C a unui condensator constind-un pi-s{611 dc secfiunc <o, asupra cirruia lucreazir presiunea lichidului

bcuatial - :<o./ : f , fu, (10)

I estc larialia dc volum a spaliului ocupat de lichid,7 ' vtrrialia lon-LaliL a pozi{iei pistonului, <o - scc{iunca pistonului, /r - r'aria{ia prt:-in lichid.

I Daci. pistonul este lin[t dc un rcsolt avem in fiecare momcnt / : ,-l /;,.1 cste o constantl. depinzir,d de rcsort 5i Ir o forlir lucrlnd asupra rt:-ui.Avem mai departe F : toft, in consccitL!:-L

J : A<,rh.

Din ccual i i lc ( to) ; i ( t l ) ob{ incrn C: lor l i

I ; :JlA:l<nzlc'

llpentro reso uri din sirmir. cu sccliune circulari rlsuciti in spiraltr

b ,.. (x;lozlFJ,

-B este volumul dc mctal al rcsortului, in cm8, o - cfortul admisibilin kg/cms, G - coeficicntul dc clasticitate transvcrsalit a metalului,

d.G oentrrr rcsorturi cilindrice.ilAccastu s() poato sr:ric rnti simplu

I) = nFl, ( t3)

diamctrulo corr$tuntf ctrc dopintlc numai tlc /i qi o. l)acf, d csttrrerortulul li J) rlilmclrrrl lncdiu al spiralci, irr cm, irvcm

l ' .o,a@tlrt lo,

,t *.vTfrifr;,

I:rui ui;l'-n'1,,1'#t?Jl"iil,1ii,l"lii"ll-.:"1 mai economicd.Incrt este mai cc.'oruic

" ,":1f";,,1".,'",,ll,lo ,"""r.Exenpl,u numeric

avind un

lr",;ff3:^,Y:,-]'l-: ":

ei R ' ("{i'ru)t'* (o,o;rl":.::F:_,*: .:1." ^h ':"[,,.';,i : ;,,; I i#,

rr,(ro a _ o,o I a,t d + 'care cstc linut intr,-o pozilie mijiocie cu ajutorul unor resorturi, este datir

An-g*t,, anterior, I:rdt, rezr:tti A:rO.

fi ir'fii,""i,ffi $#t.r.}i['T$T"j-um:l:m'**":r'#:it::g^d?fr?ifi#":Yii#g2i6^.if ";j:,"-:::'*.esteun.rezervordes-

( i l )

( t2)

.t.tl"i,;,ildffiTjf'ifth1l" j:i:.'^-.y:j.1.3;i;{.;i1;iir,r"a1"'"'1,'"Sii"r u rr rucnnd intr_un cilindru gi g.not a" ,il

Fig. 6. - Condensalorsoniccu lltstorl ta rcsortuai.

*t""ffi ::;1m.uprfirur"i:""iff Jffi1$??l'$Jri["TTlf;J,t'r,Pri;frt[?l"i]lJJi:_'^lrcarocir.curtruncurcnt

firfi,ffi "*t$f ,,j',tfi#tili,$"*ntf il]i{ri{irr,r;,nlff,ji":,T1',',",j"f;:l;.1'l'xi.ii!lli:fi1,1i... 'ulllli"':,.".111'ill$ *:HJ:f,|lf*i,:,l,,ilfi.T;1ii.tffi,#Ftx.Ti*XHli,,i,S,i,t*nl,iilfiitlcondonhr'r ,.n ;;Ati. 'iiffi; ,.t - nfflIt,

Valorilt: lrri r tl Dontru ro srnt datu rrc r*rrt,lrl .u o'n"ii,?ltutt

dc otcl pentru difcrite valori ale

tlB' :1,4 B

tt' == 0,88 d,

li,:i,-fl,,':1",*..1.:tl;,.{"ll.ruill fic c[ 1cso11rril.stnr tlc acr:r:u;rpisr.,ulul ii,,-.[",]*,i"",ri,1';,il-i,i;l'ii":' ili.ii;'Tiiii,ii'ii.,,li,,,l,l;Xt$,fiLl?,1u_pistourr lui; du nscnrr ' trr ,r ,_f iu , .n ro gnrcrf l , i i . i r l , t" ' j . ' , , ' i

1.{'riu, ,.u ;i;;d;r-;;;;;ii'ii;:itu'u n r,, corrrcr c, ,irrrrrrut hr ,rl''11,,'llli l ' l:|t..,,::..1i:ll i: '1.r.orrrlt1i,, rh, n ft rn "ii ir",i i:i i l i. i"",i 'r,i ', i, i ' l, i,

ln care c c dat in kg/cmr.,- Acestc ecuafii, agadar nc permit si. carcuri.m rcsorturilc necesare unuicondensator de o capaiitate anfmitl,-mcnit

" t".t. L-r* liort maxim dat.

. Pentru resortulrilc fi.cute din it.*l ." i".ii""i iltr"rr, daci luemrcoleagi valori pcntru C, D, I si G ii d;;t B;"J*;'".rirlr, resortului iard' latura pitratului sccgiunii,"avcm

: Aritclt: <ltl cotnprcsiuut: sttt tcn'siunc ln morncnttrl in cirro illtorvinc

iiri tk: Iottit; \'oln ilv('|it y irtul'tcr

t" - , . , r f : ! .

1. Dacir varicm forla

' AF - A:F' : tT >J- '"L"

J, Jr, .,., J, variazit' toate cu Al' astfcl cl

a> l ' :A/:+c"-cn

trP:<,r'?.AJX *:*nj

I : r,--1-'CCr

Astfel, dacl avem nu co-ndensator in c-are pistonul ;stc--ti11f dc doulL

,uri egale lucrind pe u*ot'", tJl"i'i"'t ql:":^"1tl"rr.t:tca unuia din re-

"li1l,'"'ili""iiLi."i"i"t'i' " ri d;ti de relalia

l lc : t lc- l | lc1 '

c : ctlz.

coloanel'or lichide din tuburi sau butelii. CaPacitatca C a

mai sus Prin relatia

c :81h,

lu i

ll gl d.Iiind volurnul slrmci resortului echivalent cu secfiune circulari... Slrma cu

-sccfiunc pi"tratir" va irnpun"-pri" ;;;;;; rcsort cu multtml geu; carc fiind complectrerortul flcut rli' strmf, fu" ."Jfiil1""f.".*#-fi

cu circa 25o/o mai lung decitr, Totusi, cfortut admisibil.

",_l^:lt._1_r^::".t*i d.e sec.fiune pi.trati, poatell luat corisiderabil mai mare decit pentru resorturi d.c secgrune rotund,i.,S cconornia de otel pentru resorturi iotunae nu

"ste ,1it

"Je rnarc cit pareh prlnra impresie, date dc formulele de mai ;..

-* -"" ''

. Cagul, mai multor rcsortwri lucfind, sitnuh,an, DacL mai multe resorturilucroaztr direct asupra pistonului ,;ri ;;;J;;;lil ,j3i.torir" "*",.itaforto date de

I:, : fotzlCr, Fr:JuzlCr,..., i,^,, = JazlC,.Fotla rezultanti

F:X4 :J"D ; : .

I)aclt inscnrnllm capacitatca rczultantit cu C, avcnrt lc . .= l lc t * t lc t * . . . + 11c,.

::f '1Hj'iSi,J;',is i:''"\ltil.1l"'*""",,xi1liif ".$:fi '*"' n'

h - E}lV,

' c. .=vl I t ,

0,0741 0,060

5 500

0,0.t0

o,071

0,027 | o,o2q I o,ot t )0,0821 0,0?e 0,07{ l 0,0731 0,07 o,o6e I 0,068 I 0,065

1'

lr

rlirr <l;rciL

( i r l l i r ' r t . r t ' . . r r . r l r , l r . r i

t ' l | ' z-r l ' l ' ' I nr ' . d l

-t l l t t lh ' "dk

, . . . . . , l r , , . i / i - , r .s lc lo, , I i r . r r . r r I r r I tLr , r l ; rs l i r . i l rL lo i r l metalu. lu i !

i;::'l';l"l;:,!l;;:llr"r''" 'r'i "''''ii"".. di' 1x'rr'!i, r(,sp".:tiv, t" ;"i:"'.'i."'ili",1';

Vour rkrliri cocficicntr.rl dc incr(ic I cantitatca

L : )l , <,t2 : P;gcr!,

in care P : .Llg, g {i ind acccltrralia gralitaliei.

Oblincm astfclh L(tLi i<U).

Ecuirtia rtccasta dit lelatia rl intre presiunca sonon.totrice cart' lrtt t".rz I

asupra unci nasc ;i curcntul i creat di rni;carc, masa {i ind prcslr1rrr.., l ' 'gat:i r i id dc un piston carc s( ni$ci'L intr-un cil indru cu sccliunct ( ') ( ) r ' r 1' I

de masi 1 i p istonul c i ' tor f i pr i | i t , ' , a o i ) rcr t i ( ' sonic i .

Considcralia convenlionalit a unui pistou atalat la o rlas.'! i tr( rrrrrrr.rr

scopul t lc a da un in(elcs poz.it iv cantit ir l i lol o 9i ?. asupra cit 'ot 'rt : ' 1rt ' 'supiunc ci-r lucrcazl Drc-siunca sonomotrice. Astfcl daci o forl i. lucrt ' irzi , l ir" I

irsupra unci mase, ircbuie sii presupunem ci. ca lucreazit prinlr 'rrrr 1ri ' l"rrde i l imensiuni alese arbitrar, cu scopul de a alri l lui un inlelcs ctttr ' tt l tt l ttt t

O coloanL dc l ichid cu hlngimca I va avc:r rtu coeficicrlt t lc itt l t t i ' '"rrr ' '

L - .iIlS^,

in care 1 tstc dcnsitatea lichidrrlui, in kgicm3, /-- lungiurea coloiLtr' i itt ' trr'gi <o secliunca interioari a levii, in cm2-

Pttditanld. Sub denumirta 'Je perditactlri tour lnlclcgc or-icr' .fi"rrl ' r' 'sau scurgere ile lichid prin mici dcsciidcri sau oricc altir pierdc'rc tl, , rtr' trldatoriti presiunii.

Curentul care se pierdc sub prcsiunc PIin mici deschidtli (st| f,rrrlx)rlional cu difcrcnla de presiunc.

Notind cu .S un cocficient pt' cart'-l vont numi cocficicutttl d' 1u r'lrtanfi, vom avea krgea gcncralir

i .- .5n .

Cu uniti-r{ik' alcsc, 'S la {i misurat iu crtrsikil s 5i sc poalt r' 'r|l rL I idimensiunilc sint inversul acelora alc fricliunii.

Fiind vorba de un tult lung alc cirui lt 'girtuli nu sint pcrlutr', r'orrroutea privi uitrdcrta totalii dc lit;hid prin scurgeli ca uuilornl (lislril)rril;i

i le-a hingrrl iubului: in acst caz coeficlentul de pcrditantir, clatorit sctrlgcrilor prin lnchcicturi poate fi clcfinit Pc unitate de lungime :t tttlrtrltri.

IiXI::lI PL(tL I

C,rbrci la l t t r , l t tor i l i nui i f l t i t i c i rctr l t t r . Si crnrsi t l t t i t r t t t t t crr tdt t rs i t lotfo lnr ; r l d i l t t r -o pl l tc.-L c i lcrr l r r t i t t ' lasl i l r - r I ixrr l i l r r r t t i t lg i t t i l , ( i ln ' ( r l l l r \ t " r r i r t ' i

in figura 7.( ) t l i [ r ' r 'crr{ i r l t ' ptcsi t t t t r ' / t / r , / t . ' r . t r , r t , .1r t t t t r | , , r r o r l r 'p l . r r . r r" l ' '

l ic l r i< l l l , t r '1t t |z | t t l r t l i t l t ' r 'o l t t t r t r t l r | | l , r ' . . r1 1 ' r i t r l r o l r l r r ' r ' l . r " l r r ' r i r r l i t r r l ' r r l

rh ' for t t t i r l ic i c i l r r 1x,z i { i i r i r r r l i r , t l r ptr t t l r l r i . r I r r l r r r l . r l , r

l i i r ' O "rr | r . r l , r ! . r 1r l i , r i , i . r r l . r I r l . l , r l r l r r , r i r r ' l , r ' r r1 ' r . r | l i ' r i I t l l r

l ) . r , , r / , l , r1 ' , r l , r 1 '1,r , r r I r r , r r l r r r , ' t t r

a : Etdrlr

t : Ei4t,ri cste groslnlca pcrctilor

oe:rdh- ' '^ 'rrsl fr: l ci-L

' d1' :cr fEr:r t rL l |EtL

lr

4 : t : iEt : r td.hl lErct i

c __ 2,5vlr2lE( : 1,Z5aDIlEre,rrnrk: l) cstc diametrul gi or secliunea tevii.

('apacitatea totaltr a tubr.rlui plin dc lichid, finlnd seama de compre-sibili la(r.it l ichidului ,i dc flasriciraiea metalului, ,; i l- "".

c : z", fla l+ 1g)lLL Lr \ r ' )J

I'cntru tuburile dc lier gi api Er : 100 E aproxirnativ, astfel cI

c:_!y(r + p ' l

^E \ 8oel(lum termenul D/gOe este ln pra^ctici. mic comparativ cu unitatea,t,ttl,'nr considera leava ia rigidiL, scriin'd C :1.7;;,t il#&;tru E, valoarea

l i ' " l ' D \='( ' -b; / 'Irrrl i t. l-urn s-t \.;r/_uf- capacitatca cstc o caractcristiclL carc <IcpinderI . c lasl ic i t l t r ' . Incrt ia cst t . r , propr ietrrr t . . , , . , . , t "p i i , , i . . ' , t , , i r i , , . , , , , , miyar" .stt (:(msid(:ri'rm un corp rt. ,n"ii ir liniit;ii,,,i;.:;;,'d,;'; 1ri,..,.r,,,, ."r" 1,,-

' , . ' , , ,1, : : : ,1,p; , : , . ' l ] ] , . i - l : t : f l ' t i t le c,cr i r r , r , , , r rn,r l , i 1u. , l i i . , . i i , ' r rn i ;c:-n. i i .r,:r( ir,, r ' \t( lrrcslunc:r \()noll1otrico l ir rur motnt.lt i . t l ir l , yt a rrt lczlr rn:rsr,i,4/, r 'oul rrvr.rr lc rrri { i;rf ini lcir ri i

It,.t i l t Llz' ldt ,r f i r r r l r r . , r l ' r r ; r t . r . r ' r , r . t t rcnlrr l r ' t tnr ,

, i l< l r

I l l l r , , (14)

ul l (hr ,4 cslr . . r ) r ' r , r l *n l l t depinzlnr l r rn l r r i r l , r l intcrrs iuni l t : q i natura pl iLci iiti rL' rtrxlul lrr lirrr. rrr oilto fi:xntlt la pr,rifcrir,. ltcntrtt volumui deplasat 'ar.cm

i iD . 2r\ - r , . r t l r

_ _\J l t (xr) .. ' Jo0

ctrc t este o constantf, depinzind dc modul de {i-xa19 al pllcii 9i dc. dis-

Abtc presiunii, E - coeficieintul de elasticitate "I

ptigii Si:q:9:ii"""pt^i"1i,iii"'o, i"pot"t^ pistonului ca:c. ar produce.acccagi deplasarc 8 ca 5icirculari pentru aceea$i curst /; Prm dellruIle avem

,l

f

8: O,f : o/\ o(:)d:,- -J0

Ia

ro:o, /o: l (o:)d:J

C : /Qf,II,

h cazul in care presiunilc sint aplicatc Pc plail Printr-ull piston dt' rr

lllrll <o in jurul centrului plircii, avem C = Aaz'I I I I I I IV

Fig. 7. - Condensator s()-nic cu memblantr clastict.

yig I : (xlr)z, atunci expresia se simplificl inl l

s : ,2.[rd" : o[ raz.di

_ Forma suprafefei deformate va fi ln general definitl de o relalie de(erma

v : lo(r),

.rtrrJr+ dr-u+|.--'---''1 F-;_--l

L.

fig, 8. - Vodurilc de solicitarc pi r6czarc a pltrcilor cldsticc.

tabloul urmltor valorile constantelor ?, gi co : Qu/O slnt (lat(: pcntrlt

Ftru cazuri ilustrate in figura 8.

O(r) fiind) o funcfie de :, astfel ci'

t :o7(o1,ya".J

.. Prin definilie C : Dii. Dac[ vom lnlocui I qi ] prinlrncr4 .

(15)

valorile ,Ior, ob-

( t6)

In - 0,017r ' :0,33h - 0,22

I I

0,070, {60,2E

Iu rv0,07 0, 170,25 0, {00,{3ls( ' t ) | - }d l i ' rI

(c :,4a,\ o(:)d:.

J 'batru cazuri sint:Placlt incastratlt rigi<l qi prcsirrnc uniform distribuitit,

Dacd. presiunea lucrcazl numai pc o porliunc a suprafetci plitcii, lingi{cntru, precum dc cxemplu in c:rzul cind prcsiunca cstc aplicatiL printr-unpiston dc o scctiune o, ccurLlia (14) devin6

J:AI;"Aak'iar variafia de volum d8 estc volumul dcscris de pistonul cu sccfiuuc nlioi <,r.

Accst volun cstc I :/@ qi obiincrn

C -- }lh , ' Aot'.

.Placl agczattt lilnr gi prcsiune uniform (listribuitit., Plucll incnstratll rigid gi prr:siuno conccntrrtlt la c(ntru asuprir

de rozlu a,I !lnc[ libor npzall qi prcsirtnr conc(.ntratit ltr centnl pc lln corc

mrrl rlc cfori ln nt,' lul iu cll ' putru crrzrtti irr fi

2r, \ ,;. t r , l -3 i '

In acr,st cuz, li;nrlsr, diafro$mt lucrcaz[ cr un l.csort I iar for.nrrrlr (16)po;r t ( ' { i comp nrt t r , cu ucccir g lb l t l l l )0 l l t f l l r : r rPrtc i lu l , ' ; r l luui I r ,Nort .

I ) r rp l t Inor ia t ' l t rs i i ( i l l l i i i p l l lc i I r I r . i I ( ' r r luro i r \1, | | t l Ar, t , t . l

t l t tL l l l ' . t t ,

' ;o,u! . , o1a.0,2r {- ,o, . . o, l l { j r r ( - ; i ) , " , ( 'I

f,tr crt lllnd prorlunm lol||llt rruprR pl[,|],nr , I lu t l t ( : ) r , r t r r rhr l l l pr l t t Inut ' l r r durt i r ' l l t l l l l r p l l t r ' l l , r r r ' l rnr luro; lr'fllo t |ltru errrul'l i

. .tt

, , , O1(r) - ( , ' l ) r , tDs(r) * 1 . . 1,1,1r.

tixtrMl't,(it. tt

I u.arliu *nt'i l'ldai t itaulurc. Iric dlll mirsr unui clcmcntdistantiu I rh: cuttl ru.

l:ortrL rlatoritl l incrfici accstei mase ar fitl.F : (d3yldtz)dM,

diLt.t vszt/2 P

dl l l : - r - t 2, t*6.r : - ] :L & =- d: ,

c A l>I To l ' t : l ' I v

lll'Il(ll'ltl,B cAPAfll'jtTlI, INHITII]|, l'ltl(illtjNll $l rrEnDrTANl'DlIN CURENTII SONITX

:'::tk:3{'":::Ki;i#r{,ii!I",,{,"p::;tr:K;{':#:::i:i:,.o'3'1.,':'"iiii;,'"".1"d" a" volum <latoritl curentului va Ii

al plircii la o

unde 7 este densitatea plicii, in kg/cms, g : acceleralia datoritir gravitatiei,li P : greutatea pldcli de raza r.

Am gnsit lnsl y :/<D(z), ast{el ci. z este independent dc timpd'] : o(") dr .Jt2 ' dtz

Ast{el obtinem

ap:3_. 9'{ o1"ya"g dtz

t l '

r :3.-44[oG\dz : .n P . 'd2Js , l , rJ ' s d/ !

Daci. insemnlm cu .Pr greutatea echivalenti. presupusir conccntrati lacontrul plicii, ;i care ar produce aceeagi forli de ircrlie F la cursa 1f, arnem

Pr:@. P.

comparind aceasta cu:t1ti,,FYrilfi: o, ei f,), avem

Ajungem, prin urmare, la concluzia ci. o placi ribratoare poate fi con-siderattr ca-un piston de aceeaEi grosime qi densitate ca ;i placa -de suprafa!f,O1, dati dc foimula O/O:torlpiston solicitat de un'dilpozitiv cu resonfictiv cu o capacitate C : lQq, sau C : .4o2, dupi. caz.-

l;-";oi -a"L

m"i *-t.i'p*iop*" cl 'placl

vibreazS. in direcga'normaltr suprafelei ei, punctele situite p-e cercuri-concentrice avlnd Ei$cilicgale; sc ruai presupune cI nu existi. vibratii ln directia radiall.

Pentru frecvcn{ele intrebuinlate obiEnuit, aceastl presupunere estelegitimI; dar pentru frecvenle foarte ridicate se petrec alte fenomene 9i altevi-bratii au lo6. Pentru scopuri practice, analiza -datit mai sus este suficientde riiuroasi; iar pentru ca-zul cbndcnsatorilor in care se intrebuinleazS. pl[cicirculirc in loc d6 rcsorturi, formulclc obtinutc slnt utile.

EXEIICIT'I I

1. A sc clsi capacitatcir <ltrtoritlt cxprttlsirtnii uttei sft:rc tlc tlitnltrtru dsi frosim(: r, iocfi.:idntul de olasti(:ilrttc il mctalrrlui din carr' crto flcutIitciit, ti ina liy Solulia: (

- *d,rlqliro.

2, A srr lrilsi oinrtcilntcu thtioritlt trxp.ttlrittlri i untti cilinrltu rk' lttnglmo Is i r l i r r t t t r , l tu l ,

" , r tu, i , t [ , ' f i l t t t l i rc l r l * , tL ' - t l r r t t l l r ' r r t i r ' f l r ' , ' .Srr / r / r i t I ( : - -

-{t,.,rlt(li lr ' lrir.)(l i 0,il1\,

Drc[ d :Isin(al f O), avem

h : - (Ilac\cos(a' + $ : (Ilaclsin(a/ l- o - r/?)'

irtfel *aximrrl valorii presiunii sonomotricc va fi

H : IlaC

moment vom avea

tu : H sin(at -f O - n/2) : Il sin(al 'f t!)'

:Q-*17.*,

-ptit''iitt"t", c[ prcsiunca sonor.n9jr.r,c, 1 ]:iif*^931t.'.: t:,[:

ff.';,fie rr*"I+ p*i"iai ca 9i curcntul din condcnsatot' <[ar ttn'ii'ri ,i'.itii.ii riic dccit aceia al curcntul"i t.1i1?.'I Li,"ii' figti" b, rur* on. vcctor oA - r l)cntru a rcPr(rzcrltit

bil;";jr sEnomotricc,'.1 t l;f:f:**: *i "l*3:"l,o,li,;,{{iil'iffitii "/r.'Lif .i"r '*to'i

iii invt'tesc ca $i cun ar fi lcg^fiiitii iri'i'ii"i";ililo ln po ox4 ox roprczintlt ln ficcnru morncnt vir-

J d ro$Poct lv ' l ' - .

r - . - - . r " i ,mrwrr i^ / r r \ .fi,.J"ili,li'Jti."'lt - I/aC, putom scrio hr mod simtrolic . (I/) ",': . 1iriiil,ii rirnboltcro lildlcl c[ vnctorul Il .stot:tt r/2 ln rtrmn

ilina amUto p[rtl A16 0curlldl rlml)ollco ctr JaC' ohtlnom I

'* FI - lrCll'l t t l r l l nt l t l I l r ' { - - l l l nr l r ( r r n/ l i r {v l r t t r l r r t l l r ! ! f r ' l l l l \ot lo l l l r ' '

'a : t;ai'

h : 81c,

r:- | l rar.

r5,rl;i,{,.ffil;i#i5,-{il y;i 4:r }"s:'t H#"'"Hir;Iiftcl. conbinal tl Jriclirutii, cu.lxrcitdlii, iu,rlir,i

trcld, I)at' l t irvom trgczirtq in scric r^ntr-o contlrrt. i iL:Si .ltuiiI,tttlti itr.lr-o

fr ic{ iunc, capaci t i r tc,1si l)cr(litantir, sct'icrrr :

l.iF, 9. - lteprezentarcn'rcctoriali. a presiunii so_

, nrcc ir a curentului sonic.

,ol nll$ottlf;."rluinJa ccuafia care leagr' curcntul cu prcsiunea sonomotrice

. Dtplasamentrl solrc cstc totrlearrn, in f.. j i ^- --^^:-.-fl avcm'8 : ct;r;:;fi' ;i'*:"l3nli,i"i cu prcsiunea sonoqotrics

. Rer,alia xnryc curenr, itttrt

(1) : jaA'

rlo inerfie; daci. curentul *r;to'uior!{rii{*ea sonomotrice' liie I coeficientul

i : Is in(ar*O),

h : Ld;ldt : Llaros(at * e),h:Llasn(ar lOtr ' l l ) .

Ilaci. puncm II : LJo, or-"

Hr: l l l , Hr- - j l laC, H".- jLaI , H.t . I lS.

I'rcsiune:t sonomotrice intre extremitl]ile tubului va fi

(H):HL+H'+H'+I{4:(R+1/s)I ! j (La- l lca) l . (5)

.r.iA. ro. - D,asrama zec- 2t1(1.-+)Itor ia ld a ul lu i c i rcui t

"on;" . -

_ l

(n* l*),va vedea cL vectorul Il este rezultant4 unui vector (R + l/S)/,

:L 11 !,i r unrri alt vector (La --1lC1)1,-in avans fati ai t cu' i1Z.Trasind diagrama de vectori, ie vede'ci l"lou."a nom"rlii a tui fiva ii

H:rv(FT1iryTT';=lefivectorul l[/ va {i ln avans fa}[ de vectorul.f cu unghiul r.! dat de ecua]ia

La _ tlCarsv:_n+Vs

Vedem ci { :o c lnd LCaz:t .Aceasti condilie corespunde cu o stare de rezonantl intre capaclrare

Lantitatea. La -.tl!a y9m numi-o reactanli; ea arc aceleagi dinrcn-ca $i coeficientul. de frictiune, dar diferi ile fricfiunc prin aceea cl

[unea sonomotrice, datoriti iezistenfei de frictiune, esie ln la'2,i. cu turalra,cttd presiunea. sonomotricc, datoriti. unei reactanlc, difcrl ln fazi'cu

(Il : jaCH.

(H) : jIzI,

(r),

o vcm

h:Hsin(at*O*r/Z).

--,-,_,9".r"d*, prin urmarc, ci- prcsiunca sonomotricc cste de {orml sinu_

Itfril t#ili112 ln avans fali cle curent; putem deci scnl lntreuuin,tr'nd

tatl -de

curent.. .Treb-uie notat c6. rcactanta poatc fi considcrati car s(, producc numai'lner.fie, punlnd Lt: llCq2 gi considerlnd capacitatca cri o incrfic nc-rd.,Ast{el reactanta totali ar fi mai simphi scristr consirlcrlnd, uumli

. lL - t4)a .O incrlie poate fi consideratil ca o capacitatc ncgrtivir <lirtiL dc

\2) Ct- l l I raz.

;l%.f'" tl$::,,:fr,t pif 'l:I,"i,*::To^lli?"^,".,s. l"n'"zentati. prin. proiecliape OX a vCctorului'I/ rnui

"u

-"-"'-"'!v L'Ls rcprL'zcltara p.nn- prolecpaqo \rctorul carc ronr^,i._rx -^.mcric

cu Lat Si in avans cu ""!t

ir.i lrTilrir ln acclaqi. rnrxl putcm privi cocficicntul dc fi.it:l iunc R crL o incr{it. sinr-;lj,

pul tll lnt" ca o.crpacit:rte sirn"bolictt; dc exemplu, rirloirrt,a incrlir:ido rec_torul cnr" t"pr"rinil nJ f.Pudita nld. Dlcil curcirirrlPudttanld.

:,11.,"111.1 c-stc dc_. forml sinusoirlali, deoarece avem(! puntru o rozistunfl R tr fi

i";,*;,,:ll,u:: :lTl:.J.:.:1,:i;i; ;r"i,iii,ii+il,"jl',ii"l.?J? ff?:""s r::if;ninusoidarf, ri rn f;rzr ;" il.,fi;"#;;:iTii il;i,'r:;"rf.,;.t, _,slt.

Frirliunt, l)t,fl l lu friclirrnc irvon, do ilsr,rncn(lit,

i l , . n| ,Itt fl zi1 r rr

(3)

l r . t ) . , _ j . ntn.

lJfcr'.tul.th, t punc hr,purnlcl rlzintcnfr,, incrlii, caprrcililli qi pcrtlittnlu.u lrll ' t lll lqo(l rut$lo{.,ln dccrl,criz,, rlg1.[. irsr,rlirittnr prin Il, ,5', /,, (.', rlif,rritclo 14lorl lo nron-I l ! pllfr l lol (l l f lr l l l TVom

r t t t r , t r l r r l ,(,r)

l l

rs{, ,- '(- .-lltl---.'5 I l/ /(

fi, -"rll::i'\"',i'illlil,'ll#*"t"

rczistcttlr', ircr'1ii, r:I1,ilt:ititli 5i percriia:rle

( l i ) : ( :R +: t is) I + 1[ , r>r . r : r7c) rgi condigia de rezonanlir va fi

\ 'r I

eZL:8t lc.

,4{ JPc-l;tu [lE;l';;'3'HHl";::lS + -J- )rt' Rt

,. ln acelagi mod pentru ciiferiJi curenli concentrali la un punct1:1r*1"*1"*. . . ,

f ffind suma geometricir a vectorilor rcprezentlnd Ir, \, I" etc.Analog oblinem formula lrntru 1(1) : (rs +:r/RX{ a j@zc _ (rla)ztlL)8.

Ji"tttriL;lyil[l:au nresiunea sonomotrice sint runctii generale, avem

r \ :Ri , h, :A4)\ idt , h:L.di ldt , h1 : ; ls ,

Itr presiunea sonomotrice int:atrtt i*'i[ * ;;iliil"ii'ii;*':Ti'ifl" tevii' care are rrictiune, capa-h: l r r+h+h"|- t to,

h : Ri + (t lc)\ id, + L. di ldt + i ls

!i _"Plg.S, curentul necesar intr-o te1vi, in care fricfiunc, cail pcrdiiinlr rtrtl"l.i"l".ii"r sau lntr_un punct comun, ".,o""l|tt;tn"ttt"

, : s/, + c. dhld', + (rttt\t* + ntn.

"n "ou.iif'lX"jiliil:r 11$11,,fi,.-r::'*''?:^;:$:i.I-'lrli.:gl,:" rungi poare.n.f""ri6, a,qi.fii',iiii i.tiili:iiilill"jlji:nff J.lrff,lflfiiii; rrrr;tirnir,coeii-

oh- t o i - 0 l . , , t )h

r l t " r l l ' r t r , * t '

, l r ,

fiind inerlia (serie) pentru unitatca dc lungime a liniei qi C capacitatearralel) pentru unitatea de lungime a liniei.

Acca.sta tlctcrminl ecuatia difcrcnfiali cu derivatc parliale

azk " azh*;

: r ' - r ; ; '

Solrrjia accstei ecuatii, binecunoscuti. in acusticl, este

h _ 9t@ _utl + ?z? +ot),care 9, ;i e, sint furrctii arbitrarc ;i

u : t 11[ Le

litcza sunetului in mediul conlinut dc linic.Corespuuzi.tor condiliilor la cirpctele liniei, apar o scrie dc r.rnde longi-rle, circ strirbat linia. qi se rc'ilectr-r intrc cipctc,la orice perturbaJit'Lsi intr-un punct oarccare al liniei. llai rnulte detalii pentru liniih:slnt datc in capitolul V.Ltttru nutqttic, Lucru mccanic efcctnat dc un curent sonic se rroatr'

prccum urmcaza:Fic dl miEcarca unci scc{iuni transversale de lichidl lntr-o conductlL

lir <o intr-un intcrval dc timp df. Lucrul efectuat prin deplasarcaintrc douir puncte sub o presirrnc sonomotrice /4, ar fi

dlt, : h,odx : h,o(d xld.t\cJl ,

deoarecc dl/dl rcprezintl vitcza instantancc in lcavi.(o' d'r/d/ - i '

fcl ciL avcrn:

dlr : Li( lr , rr ' : { l ial .*

DaciL /r' qi i sint funcfiuni sinusoidalc dc formi

. h .. Ilsin(nl -F tt), t == lsin(al 1. rf),

{ {1)sin(rrl 4 r}r)<U,

In connidr:rafic cl

rln(a/ {- tlil)rin(ar -F g!) .- (t/f)icor({r - {u) - r:os(2al * {r * {r)1,

fl f . , HI\ s in(rrr

'l

w * (Itllzlt(t /n)tor({1 -. {r)

- rln(lrl6 | tr

" (t/2d[iln(zd, "t {r .t- Qr) --1*r) l l ,

lllmt hrtto crln rl${lrut,

Vr.rk ' r r t r l i r r l t r . r , i rs l iLlx.r ' i ( , i t ( l r . ( 's t ( !

\ i rghiul;i / in iigrrra

I)co:rrccr:

putcnl sct' ic

Astfcl, nurnaiesto o component:'rnutnai rlc vcctori i

I I , , / ( ( ' r (4r I y) , , / ,o l r l i r r l l r r

tr rl2 =.. (H ly z) . (rlv tl _- H "r

. r,.t,

lI' -- H& - 1,.r . coso.

tV : (tlz)HI cos<u : (r/z;arr.(ornponenta H, producc lucr.u, cealaltii l r i l lUCfU. ln p,Cncrr l nrr tom cn, i , , , , ^ i Ifiirii

d rrr pr( ,uu(( . lucru, cealat t i l componcnt i . f f " ,ll.9i"j'ltl putcm spu.Dc cr-L lucrul cstc protlui..11 ;i /, carc siit parakili sau ii fazi.

'i, - *" (l)tz.

l()nlll l l r.;l lrrcrrtl mr.rliu pc sccunrlil ln tirlpul unei

ll ' (ll tlz)ros(,J1, {,).tsll urrglrirrl rlintrr, vcctorii rcprczcrrtincl pe .I/

rr i$. l l . ' l )ccalnjnl i , ,rre'rr.ctorrr pr.si r t tr i i sorr i i .c rt i

r " f (

11'r l soni(

A nu sc inmulti valorile simbolce ale lui I/ 9i 1 pentru a oblinelucrul

formir, simbolici din cauzi ci lucrul nu poatc fi exprimat -in

aceastZr {ormir'

crui *",ti" pc secundl sau puterea meianicir nu cste o funclie periodicir

lnrnultind accitstl cxpresic ct (llZ)HI, gisim {ormula datir mai sus

w : (t IL\HLI | + (t lz)Hzlz.

I i iA. t { . ( i | lcrhr l facto 'ru l r i , l ( 'p" l ( : r . .

'.",rr"rl;',t."|"'olll,"1l"]1.,#:;'ili,^":tc{reprcz'eDtat dc pro<Jusul

'ccto'ilor ca.c

##;;f ;":,:]y';;'l'i;;ilT:r',1' d:"':fi i.l. T:::i":.:".,:;r;#:' ll'l'"'fJ#(tI) "r?:t:r(tifi".' il.,i:l'ezcnt'.m

curentul cu 1' ;i prcsiunea sonomotricc cu

Astfcl, prcsiunilc carc t'ezultir intr-un curcnt cc striLbatc int:rtii sntt

ititi, nJ produc lucru sau,nu -c('r

nici-un lucru pcntru a intrclint' mi;-

d"orrr".J a."st., prcsiuni rlifcri in {:rzit cu 90" {a!iL de urrcnt'

l , ' ig . 13. - - l ) t ,surrrpn11.p, ;1,7pg1.r , ,1. ,1In,sr"r ' ( : so ' r i , : i / / i , r c. , rnDU (. , r r r -L r( l i " i

, r t s ' I cn(1, " ; r

/ t " .

l)aciL lvcm:

(il) _ r{t + jqz, (r) : rt + irl,,lucrul ar- fi. .sumr lucrului corcspunzf,tor cclor doul pcrcchi dc vt.r.lori g111."sint ptralcli inl r. r'i, luumc 11, ';;i .1, ;i 4 ;i t--

t^ " ""

tv ,. (t l2)IrJl + (t lzlnrIz.Acr:st rr.zultlt sc Doar(. ,:l]ti:1,.

i:tl" alr nrorl; obst,rvintl c?1, tlncll 7( f ig. l { ) cstc un unglr i ' l rb i t r l r $r i r l , r , rn:

I intrgiu 'fotttt. l i t l t i t tt 'nr' i tol>ucifuil i ' Lucntl inmagrzinat itr lr-o citP:tt it i ttr '

poatc fi calcLrliLt cu fclrnttt lt

r ' - [ r , ; .1,J

arn girsit (:i-r l(' lntia tlintttl curcnt ;i prcsiuncir sonomotricc csttr

l , , I I i.tr,tJ

i<ll ' Ctlh.

Subst i lu int l , ob( incntf

{ / ( ' \ hdh = ( :h\z t . A,J

lllnrl o constnntil tlt' Intcgrlrrct)lr,ll prcsuputt|tn cll lut:rul r!||[u zcto cin(l , 0, obfittttntpur 9i sitttpltr

lt _ chtll.

tlrr[ i rrrtl n hrntlir' In'rkxlk'tt, vllottrr'n lnltxlntl n lrtl {/ ve fi

u.- t ' l l t l l , .

H,

//rrin(tlt 1. t;, 1, / r'or7, /, /sirry,

ror, t l r ru i i r { r r ( r l r | , , ) | r l r r l r l r f (O 1

Entg|.rt tiut.ticd, u nnri iurrli i,Inlr-o i|lcrti(., prin fornrrrlrL

I)ar am girsit r:h

h : r- dild,t.Astftl ciL, printr-o metodi. similari.. cu aceea urmatl m"ai.sus, oblinern

;xrnlru maximul dc valoare a cncrgiei .ir"ti;"; i;;;;;;"io ,.,..-o ,rr.r1,.,u : LI2lz.

, ln c.elc c.(.. u rrneazi. dlrn exemple rle aplicare a teoriei launele cazuridc curcnti sonici in circuite, care conlin sepaiat ."p;taeltli i;"rt,ii. ------

Exemplul I

A sc gisi perioada dc rczonanjl a unci pllci circulare vibratoare.Coeficientul de inertie al oistonului .,,a fl I : pr/gffi, iar capacitateac:1f)() , .

i . Condilia de rezonanli pentru.o ast_fel de placi. i"stc LCa2 : l, o li in<ltgtl c'a 2m., undc rr cste rj," "iirul .,iur.fiiior p" 5"liiji. eiira .""-

l)ar

fl

undc 1 cstc gl.r.utatr'ir

| =- J,C6r - PtA!)f,Lfi. : !,49 o,.

l '1 - PQtlQ, .[Pa\lg : t,

a: VstT ,.= Op)VEsn-;,spccifici a pliicii

Iiternplul II

soi

. Sll prr.supuncn ci a\.(.r|n cond'cicrc r,; r"s;i" i,i;"';l,i.l"r!:lli,"l'i,ii,,lT:i','ji",Ji,':i#T,.H:rlcnsirtor r/ u cliruicirlracil:rti. t,ste (..

,. Sfi, prcru;runerrr. clt clrcuitut clto lnr.hir prlntr_un up1rlt cu^l

| ('nrxlivtl. /, ul cnnrr c't'frt'rrnt rrc r't,r1rr' drfhirr (u ,i r'iii. ,nr" 1..g[rl 'lltorllll r.rrrcnll pl prmirrnr,u rortorrrirl rkr,,

ln rtctllpl mod oblinem lucrul acumulat

\nw

Ir ig. 15, . Circuit 6onic.

l. ' ir ': ,l , ctrrcntul in , l, -- curcttlrtl In [/c, /r tttrt'ntrtl itt 0rr'

- nrcsiunca sonomotricc intrc I ii i c''AtLurci. cortsidcrind circuitclc D'l( li fi l.t. scPartt

\H\ "= iLaI " $ (

'\ " iCaH '

careI, -: - l.Carl2, da1 1 : It $ 12'

Prin unnarcI : Iz( l -LCaz\,

Iz: I l$ - I 'Ca2\, I r : - LCa2l( t - I 'C ar\

(H): j---! :^ I .

Se vede ci" In poate l i mat marc ca I ; i cr't H -;i.curtnti i

f1' /" dt'r ' irr

i daci condil i i de rezonantir I:Cat = l. estc lndeprnlta'

,..,,, i ..r.,.,,,ifi;il;li;H ;; ;il;ilt.1*"c R i' circuitu[ Dcc Atunci it'cnt

(I1) : (R t jl'a)I,, (1,) ': iCaH'

Astfel cl(IJ : (- I-Caz a iRCalIr, (1) : (l - I-Caz { iltcolt"'

Dac'a LCaz: t, condi{ia pcntru rezonanll, avcm

(t\ - iRCaI2,

\ I , l : - j l lRC,l"

(H) . . . l - i ( l { 'a) ) L lRr:) t '

Astfcl cir aritmctit:

rr -,1rr:Q\lfT(iiff.Cu ft suficicnt dc mic ai {rccvcnfa srrficicnt dt: lnaltll penirtt ir lntlcit

ta unitatca fafd de (Ia/R)r, oltlinem

H ' LI lC R I'tttl lR'

Ii xmt ftrul' I I I

undc

3Qr

mll(nrr.l 'u l r .n l

l r loc(f |8.16)un.8. |ncfotorproduc|ndculcnlsdnic intrrnt l t tc l t . l r 'gn|r 'dorI tuburl contlntnd c"ptcrtli]i incrlii 9i r'(''i'$tcnl(' (t"

ll:-JIL-il

[i""i'*l.lrluHf *lfif xl#l'"T fii'Jlll $::i:i il"fili,ffl":i:i rnbrr . ' , t l'I[TlpA crfl]ntll ,lr ;l 11'urrtrcum f! n1*lu,nor rctonotr{co }f'

,, Arnrlr,orrlllftt

irt) - l , t t", I l ' .r, ' l - 'r( 'rr

I l 'r ' ") '

( lar

astfcl incil

t . l# I" ' r 's-

(1): (1,)+(1,) ,

I r _R2+ idL"tz \ l jaL'-

. t r r r rL f i incir lz i t l l l i t t t t t l ' t ' t t t sonic, 1 i f i t ' ( ' , r r i t t loua l i lpr tc i t i r t r : foLtr t r t t i r

t-rt;;i ',i;,ii,:;i'tliit a" ti"t..SiL.pr.stt;'rr'''trr rit-cunoultcDr i'tl.|::11:1..,1,.11

t ', iu*fti"j"tl '"

,i t"utti*,1"i ,cliival,irt ' '. A st'13isi ltrcsiutrta,sottotrxrItitci;i i '; 'f;i;;i ,i" !",t.rtto,. si r's.tlrit ptntiu intil ' it"o rlislxrziti 'rrlrri

fricliunc.Avcm ccualiilc:

(1") -, iaCI!, (1,) : iaC,Hr' H - Ht : R11, (1) -= (1r) F (I'!)'

alC r '

, R" + iaL"\ r r l =t - '

RljaL'

Astfel glsim

61 :7 G''t iaL')(&+ iaL',)

fi pcntru a gisi varorile numt R I iaL

lrice alc vectorilor 1, gi .f, avem-FfTT;NT--Ftr+an-'

,:,|/ry+g#

-.__._s1.q.,",op, ̂" ,,

^"" ,:::::;:.r7, un senerator a, avind untTH "::'it*.ffi ,*r=r.ru,ill."."*;' ';ixl lrutrt T #

I'ig. 17. * Circuit sonic cu rezi3tonfl,

lproapc dc gcncrator. O *,r.,r*-::l-1"]tl!" ry"lg fi considcrattr cr un con_densetor ordinar, mentinut Io o._presiunc consiantl

"gail.i;lrr"sionon mc.li,.l"-i*t iil: irlilryi#.ti"ililgi,tistilt .tr,",,','F;lt* "l[]xT.';Jili;pnnclprll, dcssupro 9i dedesubtul

.prdrlunli rn*iffl'Ffd.iiin rllrporltiy rt.rncllunr llrxrrbin<l orrerglc, dc cxcrrrptu rrn tut.,--iln- iiiui,l,,i,.,r Ini(: rrLrnrnr

1rs: r tt!)ou .R! jaL -

unde R:n,-L R- r_r, I- - - r L"I

5

cl

rt t , lH

Rltt

pentru valoarea numerici. a lui jy', avem

Fig, 16. - Circuft sonic crr€Icmentc cofip{xrentc.

=c2

J,.R2

Aritmetic

' ln notalic sinrlrclicir, putcm scric

,r, .- ii(c + c') 19-9rl-tl - jac'nl "n

-: If o.,

, . lRaci * iG I c, ! rrc a2cifl.I f (rrCtR)2 -

Curcntul -1 arc o astfcl dc componcntr'r in fazi cu If tlatir tle

I . - H Ra2Ci

I + (dcrR)g

putcrcir ntccanicir absorbitit vtt fi

H I' l lzuzCillW:--'

z 2[ $ (aC,R)'z]

Slu inlocuind pc I/ prin valoarca sit at'itnrcticir iu funclic dc 'l

w... l ! ( : lR - ,_.

zl(C + C t)t | (d(.'(:r/t)ri

Valoart'ir fricfirrnii pcntru carc ptller('a mccanicl ]y' cstc tln Intximtttlt

acu'n tlittl l tlc(lll^l/t 0,

/r "(" t C,\ lu{t( ' t '

l)ncll /l nrc rtcctrtlt vnlonrc, obllncm

w - / t ! ; ' -- .

" !r" {ac(c I cr)

l l * - 'I

Ii tnrflrr nunlio

,_.. .- 51

"p r,.rr, 1>u u(.nl (:it i l lr.nl ltn gr,n(,ritlt)r r:onstlntl dintr-un piston osci-li l l{rr ir ch'lti cu'si'r cst(' rlc 6 ,.'r, s.i:{irrnr,tr pislonului dc i lm., iar numir.rul(l('rotirli i l)r' Ininul 9-55. Si Irrcsrrprtrrrur r.11, capacitatea C este o butelie deo1t: l . . tu rrr i volurn r lc 2oo0i . r r r : , , i i , . f , i , f i i f i " r i , . i ,o i"1" i i i i " j

"pa, avind un.rx,fitir.rrt <1. cl;rsticitatc dc 2o0()o k,{h,,ri; '; i.,glii i;; eieciut tichidului int 'ot t t l t t t l t . , ur ,cm'

, t -2ntr - t r# = t00 rad/s,

I - : raa:3 X l0O X - i : 1 500 cmc/s: 1,5. t0-3mr/s,

C == VIE : 5 00OlZ0 000 : 0,25 cm5/kg : $,Zj . l0-l mE/N,

Ct: Z 000lZO 000 :0,1.

llaximul puterii nrccanicc la generator va corespundc cu o rczistenri.

R=(+cl _ 0,2s +0,1aCC, t00 y 0,2-5 x o, t

: 0,14 kg s/cm5 : 1,37. 1010 Ns/mt

pulelca va fi

l l . -- I .500, X 0,1: 6 440 kg.cm : 0,85 CP :625,3 W

Coef ic ientul t l t ' f l ic{ iunc, d in crrpi to l r t l l l l , t t f i

, 1,ur e , r , , . Lsq , e _1[7.n. , r , r .n : -r0d7 * 1557 vwlLt roo-x-ti,o I ttio :< o;o I o,o

Astfel incit cocficicntr,rl dc fricfiuutr

R:ft I :

<o x l0o l0( 'x 0,282

cc nt' tli

I -

t7 ,91 :0,14kgs/cm5 : 1,3? ' l0ro Ns/m6,

0,14x108x0,282 : 2280 cm : 22,8 m.t7,9

i t :105, , -

Vedem c5. un astfi'l de tub este prea lung pentru a se lntrebuinta in

,cL. ast{cl cli va {i necesar de a lua un tub de drametru mal mlc'Dacit luirm un tub de diametru 0,32 cm, oblinem

Q : (144)' (0,32)' : 0,08 cm2.

Vi teza a:300/0,08:3 750 cm/s, 2", :2 650 cm/s,14x100x0,08 : 107 cm : 1,07 m.

'ert" llsrrotnt difcrcnta marc ln rezistenll produsir cle o miciL schim'ln dianrctrul lcvii cc formcazi aparatul dc fricfiune'

4x100x0,25(0,2s+0,1)

l'Lesiunca sonomotrice 11 va fi

l . ' ruu l l ,_ 9,1 , t / o. t rzto0(0e5 FoJ) f ' * or , - t (o25J:52ks/cm'z:5 ' t '106Pa.

. Iist.c intcresant de a nota ci produsul HIIZ:52 X I 500/2 : 39 000l:1.j.::/:_ilo " .putcrcr. apalclr_rn_ in cai'dc 5,r, astfJl .i i..t"*i-i'"- prt"r""i^gcfr( ' Ia lor va l r cos (J) -_ 0,85/5,1 - 0,167.

Vtloarca numericir a lui 1, gi 1, sc poate gi.si, de asemenea.i \ \ 'em:

Iz:aCH:100 x 0,25 x 52:1300cm3/s,

I t - d(:f l l { t+(ctc,R)i:100 x 0,1 x sz1fr l l roo x o,r-x o,rE.,:: 302 cm3/s.

,. Sl plt.supuncrn cir fric{iunca cstc rcpr.czcllttrtiL dc un tuL rlc 0,6 crn(lli l l l l{ ' tt tnt(.nol; s(,ctiun(.ir <o va fi

a - @14) x 0,6r ._ 0,282 cne,

lll u xirnul vitczci vir fi

u -. I l<,t , SttZlD,ZtZ .. | 07() crn/s - t0,? nvd

1i vitr,zl t,flr:acr v* fl

|/ur tol1ly I 7t0 cr||/n 7,.10 [r/r,

c A l , t 1.o i . t , t . \

l : l r l i l tN' f t IN c(rNl)1,( ' t ' l i t , t jNGI

l ) l r r r :cut l i ih ( t ) q i (2) obf inct t t pr in r l i lcr ln l lcrc:

d(I/)ll: '- .-. ja(/-) .(f . ' ! '.(.4 (,osll.v lJsinps),

d(I)/tlr - , ja(C) . (If ) : 4(,4, cos pr -- B, sin prr),

lnclt

I)nclIiind

pcntru r -0, -A: ja(L) . ( I lo ls, i i - l r =. ja(C) . ( I l )o lp.

(If) qi (/) sint valorilc lui (.1/) qi (.f) ia rcccptor, lungincrL corr-l , obf incm:

:i** :i'rl1ffi '{::3:i:,:,,,::: K,lf *1"k":g,."*i", fil;:"ffnff,n \;s{::iii!iiq''*.:,?rff l";i:Tii:.ffi",f,1"1,*.**.'*ilin_rn:lii,,T,1li,l'i,liljl csrc nccesar dc a line ,""."-i" "r".-ii'".,"pT;rdii li.i,,.{ii

ift'f l l i i"lilll".,.1t' llT"t'Artl. ", l""t conal it" r"'gi ;i ii' J"i'i;ft ';fi ialc prcsrunii sonornotricc ,,

'."(i];,Ttff"tt"' valorilc iimbolic" sau vcctorial'

i f,';f ":,1 t*#""T': "liiili'd,?:1"",t:'.,lii""ffi , nll*11':,.iliff ftTi'#;:l

(I/),.,= (.f/u) cos pl - illo'1 [ Q1Q sin iLt,

(I) == (1u) cospl - j(do) YaCE sin Fl,

schiurb[m {orma

(/I) .,- (11) cospr + j(4 f(Z)Tletsin F,,( Io) : (1) cos Fl { ;14 l/-1cyg-f in pl.

Accstc ccurlii sint gcncralc,;i dau solutia complctiL(I) qi (C) slnt sirnbolicc, astfcl c[ p : al/@=-' 1q

simbolicl.Dac[ ,lt pi S slnt foartc rnici, sau clnd a cste foarte,mare, valorilc lui

(3)

(4)

a problcmci. Can-va fi o crntitntc,

ilo uttdii.

lntruclt I{a sau 5'/a nr

d(I1) : (t).lid;"- { ja(r),Ldx,astfcl ci

d.(Il)ldx I Rg) : jar,(r),DacL considcri.ra

Q,) :L_jRla.

d(1) : (I1)sdr i ja(H)Cdx,

d(I) /dr:s(H) t 1aC(H).

(c) :c- j .s la.

(C) sint practic cgalc cu I, qi C, tcrmcnii complccqi j . Illa $ j .,Sl'rnd ncglijabili. Sub accstc conditii formulclc gcncralc (3) qi (4) dcvin:

(no) : (E) cospl { j(I) [tie shpl,

(1,) : (I) cos ptl g j(//) r(eiT sin pI.

ci miparca urmcaztr o lcgc sinusoidnll atlt faflr dc variabila J t:ltdc timp. Sc rr:dc, rkr tst'rncnba, clt pcntru v:rlori alc lui I datc de:

p"t ,2l.ll., (l/ ') : (I{), (10) . (/),

(I{,) 9i (/o) siut iunctii irrmonicc t1c l.

Lungimca I dltl tlc p]r - 2n cstc trtttgimoa

occstc ccualii dcvin:d(.Q/ds : jae) .e), <t(r)ldr: ja(c) .(H).

Difcrcnliind accstc ccualii, obfincnrd,( t l ) /drr - a"(C) . (Ll . (H), d,(r) ldr2 : &2(C) .(L) . ( r) .

I)irciL puncm acum p ._- ,I/E) .6, oblincmdr(I1)/dx! -f t "(H) _. o, dz(I)ldxz + p,(1) - . {).

Solulia gcncrtlt'L l accstor ccuafii ostc:(1/) . - l s iu p.r : - l - Bcospr; , ( t )(1) -= I r sirr pr {- R, cos 1l.r:. e,)

.,..,.. l9]rtr.t1 ir (l(tcnnirra. qqnstantelc,. sit consi<L,rilnr c pittrrl r.o rhrt.lciut

_l*.gcncra.tor' ';i fic (ff.) yi (/u), r.r,spcciiv, pr,,*l,rn,,,i *i,u,,,ii ir,1",, yf ,:i,ri:iii"iro nccttt cuplll.

Alrrrrr , i nvr.rn lx,nl t ' r l r , 0, D, ( ) , , , 1 i l t , ( / ) , , .

Accstc t:oncluzii, totugi, slnt oxactc numaiylllnbilc fnllt rle L 9i C.l'ormulrrlc gcncrnlc (.1) 5i ({) pot Ii scrise, dc rsomcnct,

UhtVOi " Urtv(!:i cos pt f j(r)[@sinl,(r,) yfli ,, (f /p.icospr .1. j(r) [jtJsin pl.

..1g)Ktri, d-(0f8, n-tr.llt$, do-(re)ffii g-c,, '1

.lto .* l uu r {- Jd rln r,Jo * j cor r .1", ll rln r,

(s)(6)

t4 V6 : iacn VfeT V6lG, @)V6 : lartl@11@ye_1.Daci notlm ,1':VOi6, ob]inein:

,ri : jach,h : jalrlti,

Sc vede ctr acestea sint idcnticc cuprin {rr $i ill prin /r.

^_.,,_ I_nt"rri pcntru a transforma Iormulelc exprimatc in i 9i I in formuleordrnarc, este suficient dc a lnlocui numai lr pr'in 0ff si- i nrin .f.Dac[ R 9t S stnt neglijabile sau dac[ f.;";";

",,l;i;;rtc inahtr, avem

Pentru unltrtcn rle lunglmo r cotrduct.,i. ntn

(e)(10)

formulelc ordinarc, f liind inlocuit

gitrtit /, * .,./xo qi (: .-

Pentru apll 0.-?to, pentru ulciul rnincrnl tf :9o Si 'l ^r (l/1)0)

Pcntru olel.'t Cttiw formule utilc. Daci R 9i S slnt ncglijabile, am g,ns!!;mi susFl -

- zrr,- a"i 'n - pl 9i p. : o\re, ' de asemenea, Vre --V\EE == constant'

Viteza de wtild a este egali cu lungimea de uq'll impirtitr'r prin pt:ri'

orda unei pulsafii, astfel lnclt:

t, :),1(zula) : alp, tt : \Yre -Vpi^r' p' : alv :?z/}.' : Ztctr'f u -' dlt'

'' Yiteza de undi variazi phi la un punct oarecar-e -cu

presiunca. ii lcm-prat"o;

""1"tbu arlttnd valorile.luiri ii_t q:,{T 91"j:::,Pt"tti:1t-ti :i,T;;rd a;t U sfirgitul cnrlii. Peritni -uleiul mineral, u este ctrct

000 cm/s.

Alticarca teoiei ptesiunibr 9i cwenlitor Proporlional'i

Eremph l

dc uscmcnca

lr ". Ao cor I -. Jio sin c,i , . r ;corc* j iednc.

(7)(8)

onal.

ei (1)

Vom numi cantitirlile h Si i fnsiuncL{'rrr rruru can r.rllt(' h $t | .bftsiurrc lrolo\iryaQ gi cuferrt poforli_rentru a schirnba formulclc ,,xprirnaic in ii li ,., fi i.11ii,r; ti (n)

Jt-ave:n d:dt si..inlocuim i prin (If)/@ gi r; prin (r)/je.Sc _vcde c[, neglijind pc R 9i S, O.t *;

'profor]ionali devine: H l/e- 9i curentul lrlporli onal i : t VL.

. -S3Jo-"1 valorii energiei .potenfiale pe unitatea de lungime a conducteicstc HzCl2 qi maximul va-lorii'ener$ei .fi"ti.;-;; iiii:

Vedem, prin urmare. ce in acest caz presiunea proporfionali este egali.cu_rEdlcina pltrati,a dublului energiei p66t;i;fr;,&:,J pe cm, pe ctndcurentur proporlional este egal cu redlcina pitrate a a"U,if"i *r,"r'jei cinettce uaxime pe cm.

Deoarece avem

,o : r"cos a * jla sin c,vedeq cl, ln cazul cird l 9i z; slnt ln fazI,

h3 +,po :' hz sosz * a ;zsing c f i2 cosz a I hz sinz q : fuz 4 1t.

,^ ,..-1"1{te-:e su'na energiilor- maxime cinetici. gi potenfiali pe unitatece runglme este constant5 de_a lungul conductei. ^

.. -Esje cornod a intrebuinfa aceste nofiuni de curent qi presrune propor_

fionali ln cazurile in .ut. ,pirute, p.".o* "ooa"n."1o".J'ril;;;ri, fiTi;_gate pe. cdnducte. Astfel, ecrialiile_ cire dau ,.Uli,

-in1r" *l"nt li presiuneasonomotrice, glsite in capitolui IV, anume:

(I) : jacV, (H) : jaLr, t,pot fi scrise

18. - Conduci[ lunglcondeng&toare soDrce

la cspct€.

.Fre Il : o( ca mal sus. Aven

11 : focos a f jti2 sin c,

do :ir ti ia:i, astfel lnclt:

,\ : hcos 0. * ji sin o,

{io - jaCr(ho - ht),

ho*h, -illlaCrlio,

q *veir..

, do -Jcotc + l(t - t(0/aCr)d) rlnc - i(coio $ (r|/cCr) sino) -p jAsinc'

:'l' I ur*'cl crpocltltlto condontdtootclor rl4t ohsi'cgsic, hctt C " C1 - C1d'ttrl nd dopsrtd

{/lc - (l - ccr)/dnr atl(r/l),

4 (r!/cC) rlnr) +id(l - r|fc{lCsieino - (1/C1 } t/C1) ({/o) cosol,

, r. Si. DresuDunem ci avem o conductl lungl (fig. 18) cu -un condensatot

ir ii"*t"'."pft. zu- frr, hz presiunile propor$6naie la capetele liniei 5i. f "

d1

urentii proiortionali la aciste puncte. Fie ho-', lh, cedetea prcsunrr pro-tii orooortionali la aceste puncte. Ire ko-': nt caoeinali: ii piimul condensatoi 9i hg - rr din al doilea.

r#l-atuncr :

ir : ir cos o f jft, sin ct,

ro: icosu{ j l4sincr.

Daci capacitlfilc condensatoarelor sint Cr ti Cr

'lo - lrcos c * Jd stn a - i($la0)i,

{ i : jaCr(hs-h),

h, -li - j(Slaceli

r vlE * ulli, trtfnl Inctr * * ol/iillf, /6 -

I 4. li rlttr

Corrdilirt Irtuhit d[ l

c . (rl/*) cts(c/2) . - ({la) ts(a _- u) lz. (r)Dacii r kn tlu (l) nvem condifia

+/( ,C . ' , (cos o - t ) /s ina- -ctg(ul1) _=ctgkr_ qlZ\,astfcl incit

c : (,!la)tg(E - alz), 6 : _ a.f jtsin a, hp:. _ h. (z)

,""d" ?;"i;'"$ltj" -(

I :'j:"lig"tl,niti, ycdem . cii ,'aroarea , .capacitr.fii c

infinit ;tnd ; ;";pil; t"JTt" ou c' pc cind in condifia ta,'ti.dilpi

.. - Trcbuie rcamintit

"[ *:tib",::n.cstc indcpliniti cind. l:1,12attrc rungrnea conducfei cstc-^o_ jumltate di, i;rgi;;;t; und.d. Rezulti,pnl urmare, ci., daci. c sc anropie dc rc, este a" a%.ii,-pi"tr* a putea in_trebunta condensatosre mici.-d6_a proie"t" condlir*ioli..i" urtf"t ., .irre rezonanti ln opozifie, adici astfci ca ho:_i1 ,j;: _,.

. Lapacitatca cea mai mici__necesarl iri practicii, cind .cxista rczdnanti{n.opozi}ic, va fi aceca corcsDunzStoare. ., ;-:3'C .ii l:,r". C _t!la., Aceasta cste, d.c ascmenca,, capacitatea minimi. neccsari. clncl existirczonanti dirccti. conform formulci'(l) cu e:"/t.-- ^" ^

Trebuie notat c[, cu citvolurnul resorturilor ra

'' .";il;:l'rXl:"

c rnai mici, cu atrt cste ruai rnare

nriq!'iL!9!*t:hLi;ix;xl;;,''fi,Ht1-fiI,#;Hi|1f iecarccapil,independcnt de valor'c i,*,il,r,i'i,-"ilii;ftiriii:Jf

-

ikff"',f,i ;.tC : (,lla)tg(el2), a <z;fz

: (r!la) tg (n - *lz), a > rf 2.ln formuhr gt'ncrall giLsittr rnai sus

io : i (cosr * ({/cCr) sinor) + j4(t -- r}farC,C.) sin* _(l/cr .+ tlc2l wla) cos dl.

I)aciL suprimirm conclcnsatorul C, ficlnd Ct: oo, avcmhn

- h (cosa | $laC.) sin c) f jl (sin c _ (r!/aCr) cos cr)gi punind +/aC, - tgp, obfinenr

lis cosp. : l sqs (q - p) -f j; si. (cr - p).Cu accastll conditic nu *,pg"t. ovc.r ,fts :,[, astfel cit nu c posibil dr:

l,i"i-,li",ft .u".tlluflt.cbmPle t r tir trc trui n llnil'un ;fifi; ;; nunai l r unulI)aclt ftccm c p, obfinctn ho *,.111"n* n.I'rcdrrnc* ln cnnlttrtl crr 4rncrrtot ul nr fl rrlr,r.rr Irni rnrr.r,r[.r.lt lrr r,,r,Jrlttut r:u r.nccpt'rrtl, illr to! iirrlopnn,t,,ui

'ii,,' ,.i,r,,,iti, i"il ' ",'

Si oresuDunem ca avcm o conducti lungi cu o iner-fie Ia un prtrt'-t

o"t".iti. "Si"il"*p*"t -"i

intii cir inerfia eite a;czatL lingiL cayitrrl ' l irrdrcapla, ca in figure 19.

Fis. 19. - conduclb lllnst h^ ;^ b X5|| n,, . , , . i , ,Ar! i . t f r , rn ln l " " -

lx l -I ' r ,pus 6" ' , " r r , , , ut , i ' . lZ:J

l ' ic ft. si L. r-espt:ctir', presiunca qi curcntul proporlionalc lrt tirpitlttlttine., i""i ft iii pt'esiunea ii curentul proporlionale la capniul.ditt-tltciLplrr '-fi?'1-

.o"ii.l"'ntul dc ihertic 5i 14 p-rcsiunea proporlionaltr ld st iltr1;r

E xcmpkttr II

hs*k: jrlaZl, astfel lncit:ho': h cos a | 1i ('lml f sin c),

io : icos cr * j(ft | j,!al:i) in e: i(cos a - ,|al sin r) -F jlt sina'

Dacl iner{ia se. afli la stlnga ca in figura 20,

Fic, 20. - Co'rducti t l rrnl l tcr o inerlie Z l;r coPltl trl

sprc gctlcrittoa.

1^ hr -- /r, coso .+ jisina, ro: f cosc* j/a sin a, 14-hr- 1'W I'lsi',

/ro : 7, ,tot,. -t- ji sinc * i{at (i cosa } jft sincr') ='=

: ,L(cos q - r!a/- sinc) f jr; (sincr { rfaL coscc)

punlnd 'lxr/, .= tg <D, oblincm

io cosrll : ,L cos (c -1- tl) { ji sin (c * tD).

f)irr iurirlogiir cu cxcmplul ppecctlcpt aiungcrn la cxcluzia cL o cortductlt{i bnltrrsuti'r nrin ineriil ln loc dc condcnsatoar."

S;c vc<ti' imcdiirt ctr o t:ondrictir. balansatir cstc o lungimc dc conductlt,continc astfcl tlt: incrtii si caDacit:lti lncit sit litr cchivalcnttr ln ccca ctt

;;';;,:;ffi;;;;";;;i;iJ; ii'."i"iii't <lc IiL t:apcrclc ci, cu o cirliductnim['dc lrrrrginrc t'gu,lit t:u ull m'ultiltu de lungimi dc -somiundh

ir curcn'oltu**tlu fin coiitluctl unilormlt' Lt pcriodiiitatca dat[.S-tr iiririaqlm or:ur! cctll ln iarc rlotil iticrfii slnt a$czatc h capctcle

fq In. fte, zl). ,,

lh,untlto u iltt,r

t l f, al, - (lorrln{l l l Irrrr{l l

brlan.rl l $r ltn'rl lr, lu

"' llFr'l

tr (ntr,ilgu(lrr..otl 0 t' l | r10 I t t !r '0It '

*ffi,,1i , il,t,,

f,rr lu ftx. d! | lCa; ohllrrenr rt unr:i tlirr ccuafia ge neralir,/ao

- 61st1sn "* r!a/.sinc) + jt(l _ {krt,,L1) slrra.l. (1, {_ tf arlcoscl,,o : r (cos o - rlatg sin c) * ji sin c.

Condifia dc balansare l3 fi Zr : L",. I. si

Aceasttr ccutf,ic cstL., dc asemenea, aplicabili la cazul arltat h figura 23,h carrl condensatorul C cste lnlocuit cu o butelie de capacitate C g ln caroconducta cste lnchisir dc un dop sau robinet la capitul opus teneratorului.

ln acest caz r:0 Si oblinem ho:hcosd,

fo : j6 (sina f (cCl{,,)cosc) : j}o (tgc + acl+),

cosc - {cZsinc: l ,

cosc-r !aZsinc:_1.

Izo : 77 s.t, * jd sinc,

i r : icosq f j l s inor,

ti2: iocho,

t'o : dr + ds : d cosc * j[ sinc + j(dclq)ho :: rtosc * ji sinc { j(aC ltlplh cosa _ (ccl{)d sinc _: d(cosc - (cclr|l) sinc) f ji(sinr * (aCi{) cosc).

Avem prin urmare

(10) : jt|llro (tgc + aCN) : jfio (rl tS.. * aC),

Ho:Iol@C*{tS") ,

IIo este, prin urmare, infinit dacl tgc : -aC/{gi este zero dacir o : rr/2.

Eremplul IV

( r )

(2)ln primul caz ho : 6 5i

'laL: (cosa - l)/sinc : - tg(all) :tglt _ ulz),pontru valori de (a- a.l}l <flZ or >lr $i < 3nl2.

ln aI doilea caz ho: - h qi QaLr: ctg (ulz), pentnr valorile crlrr.

Exemptrwl III

S{, presupunem ci avempc o pa'in rtrdrrii-i,-.i-riiril.:Tt""t*t" c ln paralel cu un generator ..4

h.lJ rig. 22. * Generator sonic

ce al.i mcnteaz! o liaie lunetinchise la caplt. '

upunem cL avem un generator ln -4, figura 2{, dtnd un cutctttgeneratorului gi f la un aparat receptor in B, valoarea presiuniila generator fiind IIo.

Averq:

astfel inclt :

,1t.24, - Linie lung5, intrcnocrotorul I Si consuma- AAt, torul 3.

Flof

- 500 cm3,

""' Dac[ If' este valoarea lui H la oprirea aparatului receptor, f -0,r rll/' sino, I/' - Io/qr sind.Este evident c[ H' este totdeauna mai mare declt ]I; dar dacl Io cstolcrabil mai mare declt l coso, presiunea sonomotrice va varia lbarto

Putem gisi valorile lui II for B 9i puterea disponibili.

Avem:/16 : /r cas6p a 1; .itrr, ro : i cosc * jl sinc.

ln cazul special tr _care aparatnl receptor din B nu are nici inertic niclitate, Il gi 1 vor fi totdeauna h fazl 9i obtinem aritmetic

fi : (f cosot)r -| rf, (Il sinc)2.

la generator clnd sc va opri aparatul receptor.

Eremllu lumetic

cosc - 0,44, sino - 0,9, o: 63"50',

'1, - 3J, tt -

I00 kg/cnl

Avorn atuncl

4 * fFni-t:ilnTr{|FrJ5ir - 3 rt? cm?r - r,157 . 16-1 6r/ri, | r lg- 21. MrntlJ rorrkrool l l v|! lnrt

I c r l , l r l l I l i fu.

i ( , l I r.. erll . 10. rr.

Prcsiuucn r{lurtqottlg| h goucrttor viL li

chld aiaratul rcr.r'irloL ur(c dcconeciat; gi

Ho =- [(tl c,rscr;, .1- [(7iin-ffi : 45,6 kd/cr1, 4,47 . t1o pa,ci.d aparatul rcccl.,t,r. v,r fi in functiunc. Trcbuir, .lrsr.rv*t ci. prcsiuncasonomotrrcc la rcccptor cstc mai mult dccit dnblul acclcia tlc la gcnerator.

Mclodd graJicd pentru, calculat utren!,ii in contluctc

,- \ Prin. irttrebuiirlarea .metod.ei g#ige -arltatc

mai jos; putcm a1ungeftrrtr calcule aritmetice la- valor e di{eritclor cantititi iarc trebuie deter-minatc,in problemele privitoarc-la curenfii fluizi in conductc: metoda totusieste apllcabili. numai daci frictiunea gi pcrditanla se pot neglija.

' t,Fie,/r'" si i^ presiunea si curcntul proporlrorrale la generator ;i h, i va_ll$";l:--,j': ci"iitali la r'cceptor. v;*i;; ;;;"1

-["i".,i i- care h qi i

slnt oelazatc.Putem scrie atunci

,&1.riind componerta rui (i), "#l;I*l?;, at i si, h,, componenta care

este ln cvadraturi. Ecualiiie generale care leagir acesie cantitlli sint:(h)": (h) cosc { ji sincr, ,(l); :;

"o." a j(ft) sinc,Substituind pentru (Z), oblinem:

. (k)o: nt cosc { j (i sinc { la, cosa) |. . (r). : i cosoc - h, si,'a 1 j i1 sinc j. (1)

, , i"."9.1t".ecuatii,a reprezinH cantitatea Ztrllt,I fiind lungimea con-ducter tl I lungimea de undi. Si punem:

Sit construiru acurrt tliograma tigurii 25 yrtt',ctrm urnrcazh'Sc tragc drcirptrt, 01 - ri flcind urt uuglti a cu orizontalir OX, l'r'

linir O1 se intcrccptcazh o porliune OHr: h. Se trage o dreapttr f/tll inperpendicular[ pc 01.

' Sc unegte 11 cu 1 qi pe dreapta lll ca diamctru se tragc un cerc; deoarcct

unghiul .F/ff.l, este drept, circumferinla va trece prin punctul I{,

Prin fl1 se trage orizontala F{f6 gi ordonata IIrHo tnind circumfcrbrlu,rcspectiv la punctcle 1o gi Ho.

Vom avea atunci vectorii (io) 9i (ft) dali de:

(io) : olo, (ko) : ofio.

Pentru a dor.cdi accasta si. considerim punctelc B, C la catc ortlo-'i{atcle prin "F/1 qi 1o taic linia OX gi fie *1 pu'nctul de intcrsec{ie al orclo.natci prin C cu circumft'rin{i.

Dreapta I/,,.ul !'stc paralclir cu OX, astfel cir figura lft. ollJo estc unifrcptun- tri. Analog, Iigura HJAH csle un dreptunghi.

{ Avem pLin urmaLc

t . AI : HHr: l1r .

, Pc dc .altit patte, avcm in mod sirnbolic:

(rroo) : oB -f jBHo,

..BHo - OI sina f 1't coscr -

I sina f /r2 coscr.

Substituirxl accstc r:alori, oblincm:

(OIII\ =' hacosoc $ i (i sinx { ft, cosct),

cc, prin 1:r'inta clin for:urulclc (t) stabilitc mai sus, dit

durl t l "

Ito : OHo.

ln ,ou,l ^,',nin5;

rrvcm (O1o) == OC + iCIo,

CIo. - BI\: OIIr sincr : lr sinc

0C' . - Ol'cosq. - 1.ll sinq. '= ri cosq, - h sinot,

hzl)'. : tgp : & (La - rlCa),

IrtA. 25. - l{ctoda grafic5,pculnr calcrr lu l cor( .n l i lorsonir : i in corrr l r rctc l r r r rg i .

._. _ l_,oi

/ . g i { ; f i inr l iu.r ' l i r r ; i c i rPir . i r r rrcrr . r r l r . Prrxlrrc r l i [ , . r ' r . r r{a rk. f 'zr i r i r ' r 'ccr) t ( , r . .Lonslnntt ,v cr l ( ' o ( n l i l . .1f , , r i r l lof i , ' . 'u l , vt lo i rr . r . i r . i l ) ( ,ut l r r i lp i l f i inr l i l r r l t tl l ) r { rx l t t ln l i \ ' ( lF ( l ] * 7. , t , r , r f i i r td nl ln l rc l l r | | r l i ( ' r r r l r r rJtei .

(2)

cl cl1 rvcnr. ()/n) ,.. y' coscr - /t, sin* I jll sina,

, io - ( ) l l0.

," ' Co |rnnr, 'p l tnr ' td ld O' l l / " '' l lnplr l r t l AOI , l l t r l , . lmporlnrr l l l , { l t ' t ,ut fcr nv( ' l l l

1l0l*Al lo l*hol i ,

: ls t l ( .1 c.r . -401 ( .s l , l | r rAIr iu l p. : r l {o]ruLr l t . i (2, ; . \ ' r . r lL.rrr , pr i I l r r rm:rrc, c i inoonslr'c1ra gr.lir:;-r rlir.t.r:{iir l i ' i i lor O.l, Ol li t)A .t,.1,i,i,1,, ,rumar clc con_sluntt,lc condrrctt,i ;i rr,:rr.t^nja reccpt.rului,' iu.. "i,i

l i i:;" de valorilc lui, r , ?, ,o s l ?o.

(lu ajutorul accstei diagrame, difcritelc problemc sc pot rczolr.a in_Ir-rrrr rrrod foartc simplu, unelc din elc vor fi tiatatc acu,r,.

Probletnq I

S:-L presuDunem ci ne cstc dat.curentul r la rcccptor si cir lucrul dcefrrt-rrat di comp-oncnta r a presrunrr sonomotricc carc cstc in fazh <:rr z,;i.r l)r(.supunem c:r cunoastem, de asemcnca, rt:actanta rcceptorului pi ulr-ghiul c. Avem dc.gisit p;esiunea sonomotricc la rcceptor, unghLul dc fazi1r: r' irlt lLccasta il face cu curcntul, precurn qi prcsinrrca'sonotnotrrce, (.rrr(,ntul;i rrnglriul de fazir la generator.

',,r, ,,t"l11lTr"tl'ii liniile ox' oz si ol-' dtoatccc r'rn6;hirrrile z si p

Apoi, pe bnia OZ (fig, 26) se iau scgmt,nrclc: OI -. i ;i OIIt .. hr.(lcntrul ccrcului diagrarnci sc va giisi pe pcrllcncliculrrii drrs:r pc 11rIlrr rnijlocul acestui scsm;nt.

..,Ccntrul va fi, se ascmcnea, rnijio-cul lui 1IrA, dar cunr ltu cunolstcmlxrzi l i : r punctului ,4 pc l in ia Ol , t rasi-rm locuI gcomctr ic rr l r r r i j tocului ' lu i.lI,l-pcntru di{erite pozili i a1c lui ,4. Bstc

"r.irt""ici'accrito. "rt" o tlr.captirparalcli'r cu oIl trcclnd prin mijlocul p"rp"",ri.ur"i"ia'u.,iiiii-ir, i,"'?iii

-., - -lnl"r.".t i" accstci l ini i cu pcrpcntliculara pc I{, / \.a (ia centrul .!

at ccrc utul .' I rasind ccrcnl r:u ccnlrul .t si razir .t1, punctclc I{rl l 1i Io sc girsesc

l-:lli:,t..ti .diagraura ostc.complcri. I'crrtr.u rl ,t, i;r;i;; l:^toi;t,. i',ri L.r0 lr /0 vir lr necL-siu. numai dc ir tna-rsurt sr:6rrrr:ntclc OII, OI{o Si OIo.

.t" ,,, ::Hl,i:l"f1o1 cstt: unghiul dc faziL la rr:ccptor iar trnghiul rloo1 accla

l>roblenru I I

Si! I)rcsrrpurniln r; ir nc-irrn dilt canlit i t l i lc i,r, IIr, d Si p.

.l)r.nlrrt a t:<lnstr.ni . r l iagra rn lr, cu rr:ulrrrl O si raz.ir (,1/,, sr: dcst:r. ic o cir._( t r tn l" f rn l ; r , sr . l r t rg I in i ih. O.Y, OZ, r) I ' r . rL r lu i ius-

,.-l 'r ' OZ .sc. intcr'<r.ptcnzir OIIt .., ,ht. I\. i1 /1, *r lr.agr: 6 l irrir. pur..1:1,1(:u (r , \ , t i r iu( l ( : i r ( . l l lnf( ' r in{ : r i r r prrr ic lu l / , , .

. l ' r i r r . / , , s l r l r t r r . , ' 11, . r ;u.rrr l i r . r r l : r r i i Pr. O.Y, ; r r r . : r ,s l l r r , ;L i r r I r . r : , r . r . | ; r I in i ; r ( , t l lI r l ) l I t { t l t t 4.

( , r ' t r t t l r : i r r l ; r l l r l r I i r171r.rrrr , i . , r , l t ; r . , r . . rz, i ; r l t r r r r . i 1 l r . / / , l l r l r r l i , r r r r r . l r r rI ' is l r ' , v i r l . r r l r . r r l r r r r . r r ' , i , . i r r , , r , r r . r . , , lu i | r ,10 lorr lc r . r . l . l . r l l r . 1, , r r r , 1, . . , , .

o l r l i r r i r r r l r l i , r t r r r r r i r r r i r r l . i

rt

( ot t t I r r r r i r r r | . r r r . , r ' ,1,r ( r r r r ' l i r l i r r (2) , ,1, ,1, , t l r r r r r ; r r . r , vr . r l r .nr r . i :

t i . . l ( ) l " :

,i \l , I l( n) tll l.t,

l ' . t t t t t ' l> l t t t t t r t t t t t t t

Sc ccrt ' i t s t ' l l r ' { iot t i r . ( ) I ronl l ) i i cate : r l 'so:r t l ' r ' Z '5( l I l ( ) (Xl kt t l l l / : ; '

l ) is t r r t t t :L t ransmisic i estc t lc 35nr i i I r (c\ t l ) ! i r tutct t tu l t t i srrnic <l t : ' l ( |o 1tr 'r r r i r r r r l , a<l ic i 6,7 pe sccundir , ast lL ' l c i t t :Zi ,<.6, ' l :42'

l)rcsiunca sonomotrice la pornpiL nu trcbuie sit iutrciro:L 50 kg/t;ttt"

Supra{ala secliunii conductei dc transmisie cstL' ' ') ' 2'85 ctttr ' irsl l ' l

c i { . 7 x2,8j .=20.

Lrrngimca dc undit va fi f : 1 130/6,7 ':2l '1 m 2l '100 cttt '

i)"nlt""" lungimea conductci I : 3 500 crn, avcrlr e Z;:lfL 3{ro

>: 3 5OOl2l 400 . s9".

I)rci [, cstc componcrlta Irri (/r ') in luzr-r cu curcnttt l Irr prlttp'"t (r"rt '

{ 'stf rcccptor;l) | i i estc curcntrrl proporiionni, ir|crn PcDtrtl l)utor' l rrrr '( 'rrrrr ' t

11' : HJ lZ = 19 000 kg crn/s ' ' 1 '86 l i\\"

Si-rprcslr l lutr t 'nrrrr l tnghi . t l t ' iazl-Ll lLfccePtof( I r ' . { . i . ' .1\r ' r . t t t l t l t t t t r r

I r : I I l f i ' - ' :o1 1lz ' - ts ks/ 'cm: :3"11 10r ' l 'a

<lin t:urt: ob!int'rrt

^r . 2 )< 19 000/.1-i .,, I 090 crr:lr: l ,0g ' l0 rrl lr ' /s'

I)coart'cc lormltlcle gt'ncrale pctltrtt / l i /to -t i

i , ' sitrt "mogt tt l ttt " ' ' t

<.c rrr i r , .s lc: tcrsr , . r , ; r r i i r l , iL, , pul l r r r in locrr i / i , / r l pcsr, ' I . l l ) r i l l \ . r l ( , r i l ' l " l

. , , r ' , "s l r t t t iz i l , , r rc 11 . . i / Io ; i i . iu pr in I l l , ; i Iu l t '

ln modr: I tccst l , p i r i r . 'm 1ua: i1 ' 35, t '= 50' I 1090/20 :) ' l '5 + '

Itcactan,ta itt motorul pomPti (stL' .Pr( v'-r/-uti ptintr-tttr rcs()tl :r ci lt l t l

cnpu, i late csl( / . Avcm alr lnci t$9 - , r / r 'v ' ( ' r '

I)coarcct: un6ihiul <lc faziL cste tlc'{5o, lvtur: \ lt)2 " - i l t l ' l tt l t ' '

i i .uul I , st , ncgat i \ ' , avcm tgJ; , 35/54,5 . 0,b{. ast f , l c i r P. -. 32".i6 .

(iapacitttc:L ncccsarit vir {i

1.: a tgpl,! , , 42 >'. 0,64120 -.. 1,35 crns/kg "1,37 ;< l0 r t nr i / ) i '

(irnstntitrtl diagrirma (f ig. 26) in modul

Ittrlicrrl irr prrrltlcntit I, gitsim: ho ='' OIIo : 33'

li i, () I \t . 65, cu r.tu uughi dc f:rz-ir

o I 29"30' .I ) i r r : rccirs l r r obl incrn:

I I " 3.3l ig/r ' t t t r '

l, ,l in 2o :" (r5 | 3(X) cntr/s.( , r r r r i j Ix r lc i r v l t t i t r ' l ( l ; l : i l i l ( l l l l ( ) : l l l ( l l )

r i l l r r rxf t l . t t l l l ' ( I I t ' I r l I | \ | t ' t l t r l i Pt t lcr | r tI t r r , r , r r i r i t . A ' , t l l l r r r , i l , rv l r r t l l ' ( l l ' '

l l l l l t / / ) r r r ' , , t ' l ' l t t ' l l t r r lx l

. j l l | ' .1 , l , , l , l ' , , , , r r , r t l l r l l l l l r.0r l l l ' | | '

z/A

/- ... ).",

Iot -

t0 20 JO 10 tO 60

' t t1 l . h, i , ho, to

I r | . 'a ( i '1, r r l r r l l l r ' r l r r r r l l t ,L ' r5rr l , , t l iW l l r , , . . , r -

, l | ! t , l ,1, 11 I r l ' r ! r l i r r r ! '

, t t , , h ' , t - t ) , l l I l l na' , | 1 '1,1

$,"/ , ' '

a

tt

l iroart,n r,rlo 19000 - 18600, 400, ndicll o croarc rclativi dc 400i/fq (XX) , . (lr{)21 sutr rircu Tln, cc(.ir c(. cstc rk.stul dc satisficirtor.. Sir. g.lsirrr tcum valofilc prcsiunii sonomotrice la gcnerator $i rcccptor

.si curcntul lrr reccptor cind pompa funcfioneazil {ilril a "produce

]ucru. G'enc_r-ltorul prodrre(. lcclaii curcnt 10. In cazul considerit i,:0, iar cerculdlagramci (fig. 2?) va trecc prin punctul O.

-De asemenea, punctele H1, B coincid

cu U.Rezulti c[ dac5. traslm o orizontali

prin O 9i pe aceasta luim O/o : do, obtincrnpunctul ,Io pc circum{erintir.

Atunci prin tlasarca ordonatei prin/o, care intilnegte OIl in ,4, obfinempunctul l.

Circumferinta se poate trage acumpc OA a diametru, astfel c5. puncteleI, Ho gi Il se pot oblinc imediat.

Gisim astfcl i : OI : 66,5, h" :=- oHo : 39, h:OH:36,s.

tJnghiul de fazL la rcccptor precumfi la gcncrator estc de 90'; avcm maidepartc ffo : 39 kg/cm', 11 : 36,5 kg/cmr,I : 66,5 x 20 : 1330 crns/s.

' Este de interes a dctcrmina limita uutcrii mecanice disponibile la re-acPtor. Trcbuic si gisim valoarea particulariL a lui ff1 la caic valoarea lui.{- lnceteazir dc a fi o cantitatc reilir. Uitindu-nc pe diagraurl, figura 2g.obscrvd.m c5. accasta corcspunde cazului cind punciele Ii, gi .I de" pe cir-cumferintl coiucid.

'l\ ' ltgind ortlonatir pl' in / Punctul (1(r inl(rrscclic nl ei ctr circumfctinllt

punctul J/.Accasta rczolvir cotrlplct problema 9i avcm:

h: i :oI :50, ho:oto:38' k:ol l :57's '

fir :50 kg/cms, lJo:33 1*7"*z' I{':57'5 kg/crn!'

1:50X20:1000cm3/s '

\raloarca limitl a lucrului este Prin urmare

'lV : HJlz: 50 x 1 000/2 :2s 000 kg cm/s : 3'3 HP'

Vcdem din {igurir ci }/o 9i -Io sint aproape in laziL' astlcl cf, costD - l'

Aceasta se colnlirme prin regula cunoscuti'

w : Hololz: 38 x I 3OOIZ :24 600 kg cm/s'

di{eri numai cu l,6oL de valoare gitsitir mai sus'

e."ti "-"-pi"

aratiicit de mult sc simplificir calculul prin irrtrclrttirt'

i""lta"i eiJi"". Dacir se cere a se construi curbelc caractcristic(! Pt)nlrllt:['fi:;'T ffi#iilA;;";;Pt"', mctoda. devine. aproape indiqrcnsrtbilll'

tlig, 27, - Clalculul gnfic al Drosiunilord curentilor sonici cirrd reccpiorrrl IuIc-,, lion('az.i tu gol.

,/ ln aceste condilii punctele ,{ gi IItrebuie sir coincidir, de asemenea. Cerculplin urmare va {i astfel ca l\nia OZ siaiic tangentl, de asemenea, gi orizontala

,! dusi prin punctul comun llr,l va trebuisir taie circum{erinta in punctul 1r, Con-structia pentru a gisi cercul este, prinurmare. urmi,toarea:

Cu centrul O Si taza OIL:io se

Conhurl, uniJorm -incdrcalc. .Ecuatiilc difcrenfiale Pcntru o conductlt

rri, tinind seama de lner]la $I ""piiit"tt" lichidului'-au fost gllsitc a ll:

d(E)i d* : ia(L) ' (I), d(f/dr : ia(c) ' (H)'

S5'consider5.macumoconducttravlndunnumS'rderamifica|iiuniftlrmioit. i"-" fo"Sof ui, ramificatii furnizind curcnli egali la un numllr dato'

de reccptoarel Variafia curentului I nu se datoregte numai comprcrl'

lii ii.rriitrti ci qi unui <Iebit distribuit Pe unitatca dc lungiuro' l''lo

debit 4.Avem atunci

d(r) : ialc) ' (H) dr { qdr'

d(I) /dr " la(c) ' (1/) { a '

pcn(l'rt prcsiunca sonolnotrlcc

t l ( I l ) /dr - l r r ( t ) ' ( l ) . (12)

l ) i fcrcnl i i r r r l (12) r ; i srrbst i t t r ind t l in ( l l ) , obl i t tcnt

r lu( / / ) / r l t r . ' i , r ( / . ) ' t l ( / ) / t l r ja( / ' ) ' [ ia(c) ' ( ID l . ' / l

\ - -*r(r) . 1q. ( f l ) * i tq( t . ) .

Nrgt iJtrrr l I t i t ' l i t t r t l r r ; i p i t ' rdcr i lcr 1i punl t t t l

' l , * twt '

' / l iBC

descrie arcul M.I1N; sc trag liniile OZ,OV, OX ca in cxemplcle precedente.

Apoi, din orice punct J de pe liniaOZ se trage JK perpendicular pc OZ,tirind OZ ln K, Prin K se tragc vcrticala

( i l )

( t3)

1'!: ,?f - Detcrrri_rlorea sralicd a putcrti KO' tlind orizontala prin J in 0'. Scmoximc cc poatc ri tranirniii'i"";iii".

"negtc Od, gi lie f,

Se trage 1r1 orizontal

uncAtc OO', qi fie ft puirctrrl undc accastirlinie taic arcul if.IrN.

so tflrgc ,frc v(trtical nrin I .r:ulc cu o/' i[ i;";i,, i ' ;; l i ." ' '"

. )e tragc ^,h.{ orizontal prin f,; apoi prrnctul de intersccti. al nccatsi

orizontale cv OZ dL punctull /. 1L. '

....,.. _:S:,|lj,gl, /lC vcriical prin /,; "punctul dc intcrscclic a1 ncortcl vortl-y , t1i l17, l r '1 ur( /r) ' l , rql . -ojltnrr Uttnrt,nlt,'r0u hrl (l ti' pl rrrbrtttirlrm d(fi)/rlv, dhr '(il) 'ilitln|nr

( t , t)

( ts)

tl

Sc trngc i l rcurnfcr lnIn pr ln prrnclr ,L, I / , t I . 1lr( / ) / r l r r I l t t ( l ) . ' i t ,

Din (11), punlnd(IIl - z -l_ la&lp, _ z I jaqLlaTl : z + j . clac,

dtZld*zlFzZ:0.Solufia accstei ecuatii este

. Z: I coqrr f Bsinpr.Astfel incit avem:

jaLI: f ip: BaIE,jaCH t q: Arrr : nra llT:C,

(r6)

(H):A coqr* { I sinp* +i. gloc, (fi,)( I ) : {coqr**Brsinp.t .

a u, rs3#1?-?l,fll"g*l^:,1*gltl1-gl .rgceptorut, "to""i p.""t*, j :]rrce gr curentul la acest caplt, astfel ciA-H-j .c lac, A, : r .

Diferenfiind (lz) 9i (r8) 9i considerind (rf qi (rz), obtinem:d(Eldx : iat@ :p (_ .,{ sinpr { B coqrd

d(I)ldt6 : joc (H) + e : p(_ Arsinp* 1 B, cospr),punlnd r:0, avem:

astlel c[

B:trVqe , B,: jE[et p ql$.**':T,::"'#:l ::tt3"li, j: tl, "::-'t,"fl *i ale tvl A, B, 11, 8.1, obfinemi*1e l'a"- r"..lt"i'"*""'"" 9r curent la capitul cu generalorul',' il-;;;

(I/o) - fi coqrl + jlt {Lle siapt a (qlac) (r _ costlJ)),(.Io) : .I coqrt f (s/s.) sind 4 j tfe 1L u coEJ.

DacI pl este loarte mic, put€m pune sinpl: g/ gi coql : I _ t.zplZ9i avem atunci:

(H;) : H + jLr [4C N * klac) (v"t l4]l(ro) : r I qt + jve tE Hsr I'sau

(Ho) : H * jalt (r + q . tlz) |( /o) - I+qt+jact t . I 'dirtribult cr fnptflt ln

Putem, prin urmarc, considern)uu cr tmptrrtlr tn doul otril

",1!1ft)],rt:31 gj-al.curontutul uniformqr.,,reufr cf rmprrgt tn doul r,_!rtl.eg e, qllT unriiir, t"miilfilii,*i..i",ii,:rltor tl ccrlrltl Jumltato rcurgtnou.ro tn rccontor. Ari.r.rn "^.,..rr .,rccoptor. AccnntI r i lu l ] t ' i ,J '1 i rrr .

(te)

(201

ugor minte. Atunci curentul din linic va Ii curcntul r.eccPtorulur-/ + q'J.'circ va da o Dresiunc sonomotrice in cuadratur[, egall cu aLl (I * qllzl'iar gcneratorul'va avea de furnizat un curent total egsl 9q I-t qllz.'l- qlpplus- curentul in cua&atur5. aClH datorit compresiunii lichidului' Atc:rstiliegull totugi este riguroasl numai dactr linia esie foarte scurt[ fa]ir rl'lrrrr-gimea de und6..

Transnrisia ile und,e tn leso/tt ri ,nctdlice. In discutia condcns:rtoa rllt tt'din capitolele Drecedente n-am considerat efectul inerliei resorturilor, ttr"cesare'pentru ; da elasticitatea necesatl. In cazurile in care frecvenla. r:slr'inaltl 3i in care elasticitatea este date de resorturi mctalicc, cstc cvitlt'ttlci asenienea inerlii vor avea un efect material

Putem considera un resort metalic ca o coloanl avind un colficirrtlde inerlie Z gi o capacitate C date pe unitate lungime.

ln coloanele lichide coeficientul .L are valoarea 1/gO Si C valoarca O//r',unde v este sreutatea specificl a lichidului si E coeficientul lui de clas(iciintr"Dacl'D esti diametrui spirelor resortului, a cf,rui Sreutate-.p(: ttnitatc lttlt'sime este t, Dutem consi-dera resortul ca un tub de acest diametru rrtnpltltiu o m.tetie bmogeni, avind un coeficient de elasticitate dat dc rc'lntia

E .J l t : H :FIA

ti o greutate specificl dati de

r :cp'unde F este forla totall aplicatl pe resort, f - compresiunea rc'soriultti ltrcentimetri. If -j presiunea -pe pistonul legat de resort $i Presupus a irvctto suprafati de. set$une O, ll:7.D214, seiliunea tubului fictiv ;i rJ - grcrt'tatea resortului pe unitate lungime.

Putem apliia atunci la un astfel de resort toate formulelc glsite prntrutransmisia soriic[ ln coloanele lichide din conducte.

Astfel, neglijind fricfiunea, o migcare alternativ6 aplicatl la un copltt

rl resortului ciriull ln unde avlnd o vitezl u : U VIT, dar cunoaqtcm cl

i l r -4.Rezultl ctr"

E:t lAn,lllnd lungimea resortului, astfcl cl

r .c - .J- .9 -94..gtl E 8tPcntru un rccort dc lccliunc circulorl aveln

A * E NDrld.G,

rc*. , t , r !u. - l - ,' tl f$ nDr

( l r r r Ar( \ r t { r le:r l t , ' r l ) , ( i l rNla\ , .y, , ,dln cirrc cstc fllcul. rcsortul, astf(,1 c,l

LC ._ 8nD? N2yn ,

gd2l:4).

lrnrld'to fitC dt rrsitrtca matcrialului

t t , , , 2D N lfn4i| " , i | "a i ; ' '

o: ui r f r .zDN | 2ao'

. lnlocrriutl t ' i prin valoarea 0,3g5E, unde E este cocficientul<:ltrtc lougiturlinalir l matcrialului rcsortului, oblinem

otr cstc dc circa .5 000 m/s.Astfcl, de cxemplu, pentru

N - 10, I == 50 cm, vitczi undei* 3 I m/s.

un resort in careva I i z :0,124 ( l

de elasti-

. : '

.pentru olel

d: lcm,D=l0cm,x so/l 000) .5 000 :

.\r'cm atunci

f ( Ig:.Al :e\rdr:h: :Lo,tJ z

o

1: i9.29. - pr6pxgalca undelor in resor-lur i mclal icc.

d fllnd rrclhr rlt'nIr l r I ' r r l l l l

a :0,t24 (atlDN) ViE1l,./Vold. Cantitatea /gEffi este viteza sunetului in matcrial:

Dac[ accst rcsort este supgs la o prcsiune periodicl dc 50 parioade pelccunrllt, lungimca dc undi. va fi I:31/50 * oi.Oj

-.

- -

Ca alt cxcmplu si. lub.m un resort avind D : 3 cm, Nll : Z qi d :0,4.Avcm

{ : o, l }4 (0,4132 .4 . s 000 : 3,78 m/s.

. S[ Prcspunem ci. acest resort cste supus unei prcsiuni altcrnative de1tt^e.,,I?Y !!-s,0 flioade pe secundi.. Lulgiirca de untl va fi i, : r 3,7Sls0:- u,z/J m, rar lunglmea de semiundi l,l2 :9,137 *.

-, ,,^ l]?9-I::9ltul are exact. aceastir. lungime, sau un multiplu al ei exact,:r vl ll.t{r rczonanlii ti se poate rupe sub prcsiunile inaltc care'se vor acumulaIn cl, cnlar dacir ar ti supus la o forlir altcrnativi micir.

,,-. 9 ! !:, it!,tto. condcnsa.toarelor, linind seantd tle incfiia t.csortt ni.ln p."c_$cl,.rcsortunlc intrcl)uintate la condcnsatoarc sint ;tit dc scurte fa_ti dclungtmea dc und"tr incit transmisia miqciLrii de_a Iungul lesorturilo. po.t" fiprivitlt ca instantancc.

sf, considcllnr cfcctul i'crfici datorit ni*sci r'ctalurui r.sorlurui irrsusi.sl'r p'cirInrr)crr cr rr'sortrrr (fig.'29) r.sr. ri*'ir in 7, ii* , i",iiir,:rl,""iil-'-( : r rro| l , t tnct racrunl (rr l l r ( r isranIa.r r l , . ;1. r)r , r rrnbclc pr l r l i i r lc st ' r ' l i r r r r | ' i r l ,v'onr avco o dlf*cnltt ,t r"-:il;; r,r;,,;',:ll .,,,

dL fiin<l cocficicntul tlc inertie al secfiunii dr 9i proporiional cu dr' I)rrr' /crtc plol.rot'{ional cu migcarca scctiunii d't ;i putcm punc

dH:h(xd:; l l )Lo,

& Iiind o constantl gi Io - coeficientul de inerlic a-l rcsortului, consitl't;rlctr un corp rigid qi complect liber.

Si iirscrinirir prinZ coeficientul de incrlie al unui rcsort clcfirtil prirrrclatia

H:aIL:hlL,

J fiind curcntul la distanla l, adicir la capftul libcr al rcsortrrlui, ;i l/ l)r(!-liunca sonomotrici (lati dc

In ==\dH.

ci, L : LolZ.

Rezultir cL cfcctul masei rcsortului cstc acclali ca clcctul a dollh cor-ficcare avind iumitatea masci concentral5. la ccle douir capctc. Accnsltr

ie aplicl la rcsorturile cilindricc.Pcntru rcsorturi conice, o analizit analogir. df, propor{iiltr tlc tttasll t'tl

tfebuie conccntfatc la capete pcntru a calculi coefiiicntul dc int'r'{ic. l)rriegulir, pcntru rcsorturilc dilindricc ortliuare, sc poatc spunc ciL incrlin llu'toiitf icsorturilor cstc cchivalcntir cu o datir ;i jumirtatc masa t'usot'tttlftl

ldtroilnd Ia captrtnl la carc cstc aplicatiL forla altcrnativir'Astfcl, pcntru ar calcula capacitirtc:r datoritit unur rcsurt l{r'('rr, i l l.,lrl l '

t lcular pcntrri frt'cvcnlc inaltt', ;itrtcnr proccda prccutn trrnrcirzit. I"ir'(" r';t-

Docitat(:r t'chivtlctrtit carc va da-act'crtli rt 'actarrfi ca rcsorttrl i i ', fr'r'\ 't 'rrl;r.hle {,' captcitut,' it rosorlului Prcslll)rrs rt fi fr'rrl grctltrtt(' l i fir ' 1. r'Irr'IicicttIItIdc int'rtitr

Lu - l lCu.. ' - l lC'a,

I lC' I l ( : ' . 1. i l ' ( t lCl \ t . t t l . { : ) .

l l c l l / l r . r r l r . volrrnt t t l 1 i y0 Ar( ' t l l i t tc i r spr,c i l ic i t ntc l i r l t tht i I |sot t t t l t t i ,

!vr ,n l

' 1. *- 1,,lll2jLlt,

I l r lor r l r t l lu cot l l I I t cu rrrot ' l l r l ,l l l l ' l r , r I r g l t r l l In r | l l tu l t t l l l l

t t . t ' ! t ,1 , t lU9'

AtunciC : zG(lQ)zloz B.

Avcm dupir accca a.rLC : (\olg .(Gloz) . (a112 .Dactr inlocuim aJ pin 2V, 7 {iind maximul vitezei oscilafiei. avem

azLC:4ftoGle"" lVr-

Rezultl ci

11

V:Vlt _ 4 .yyTlgozl.

Curenli sonici in cond,ucte ctt secliune neuniJormi. Ecualiile:

u? :: , t t lg, \zt)d-r

d!r) : io1c161. (zz)d;

,[rltc mai sus slnt general aplicabile.

. ,-. Daci-totu{ este o sectiune variabili. de-a lungul ei, cantitntile (I)fl (C) sint {unclii de secliunea conductei qi nu mai siit independente de'*,cpm er fi in cazul unei conducte cu secliunc unifor.mi.

.,. ^le g-..oldg-.ti cu secliune variabili., diferenliind accsrc ecualii;i con-

rldcrlnd (Z) 9i (C) ca varidbile, ob{inem prin urmare

t o'! ') + a,(c\(L\(H\- I .d(z) .d(1{) :o

d.xz , ', ', , (L) dr d.v

.' Pentru ^simplitate

si presupunem cE fric[iunea Ei perditanla sintllccare zero. ln acest caz produsul (C) .(t) estc independenf dc r;i punlnd4llCL : tt, ecua{ia devine

ff+nlor-+ +? Y:',

ln mod analog, reamintind c5. C este proporfional cu Q,

d8(1) I do dI' - i u.- t l | . - : u.

d,xz {2 dx d.x(24)

Rezolvarea acestor ecualii este posibili in diferite cazuri particulalcr'.

Exenplul I

Si presupunem,ci conducta este de o form5. conici.. Atunci

Q : Qoblxdz9i oblinem

1do2O d.r

astfel cl ecualiile (23) ;i (24) dcvin:'dzHzdH

-'" + - ' - - - - | p. ' r l :0,ax' t: ,:

dr/ 2 dIr __t&41 :V.

dre r dr

" Solulia generali. a acestor ccualii cstc

(H) : (r lx) (.4 coqr..r f B siqr*),

(Il : At (siqrr - prr cospr) { Bt ( coq.l.r { pr sinpr).

Erenpl*l II

Fie o conducti conici. ln lorml dc trombon (fig. 20) descrisit dc ccutlir?

- fo En'.

Ftg. 30. - Socliutto longituditrol[Intr-o conductl cu prolll cxpo-

nolrtlrl,

O r pr * 11713l'r

dar Z : 1/gQ

ti

crtfel cl

r .dog0z d.t 'dx

dLr ldodr L {l dr

rdn7i ' 'Tn- 'n '

ll obtlnom

$lt 1. *,17y +.1 , lln . !1{) - o,rlrP tl rl,l d,r

Avom

I lcual i ikr (23) 1i (21) r luvin:

d' l l . , . . . , tH, . . . t .L, t t - : . J rr r f / _ O,

ul- d.v

dll , ^ d,I_- f z ln _ r , , : r _n( lx ' dI

Solutia acestor ecuatii estc:

H - e-*' (A sinx|gtz - mz ! B cosx Ve - n\,

I : e" (Alsin rJlf - rn;t f B, cosxfyz *Tz'1.

CAI)I 'LOLUI, VI

(ufiDNTr SONICT IN CONDUCTE r,UNcr, l,'rNlNi) snAMADE FflCTIUNE

In ecualiile generale gd.site anterior, avem

(I1o) : Ilcoq.r.l .1- jlf(L)ftesinpj,

(e _ rcospl ! jHl[@) l(!)sinp.t,unde pt: a1[@1, qr1 : L * j(Rla), (c): c - j(s/d).

S5. presupunem cd, Rla nt este neglijabil qi si. punern lL: d -- jp,a.Vem atuncr

tLdIpa(C) e(C)JIW=6,eq:

vs:6:+::%:#,,.*,'DaciL neglijlm perditanJa, avem (C) :Cr, (L\: f - j(R/a) ;i

cospl : cos(c - jpy : cosal cosjBl g sinal sinjpl :: coscll coshgl { j sinal siDhpl,

sinpl : si1(61 - jp)l : sincrl cosjpl - cosal sinjpl :: sinal cosh pl - j cosc/ sinhBl,

Substituind ln ecualiilc (1) 9i (2), obfincm

"Uo - I/ (cosc/ coshpl f jtinal sinhpl) J.

I j(laC) (a - jp) (sinorl coshpl - jcosctl sinhpl).'Icrmcnul al doilea din dreapto ostc

)(IlaCl (ti sinul coshBl - j* cosal sinhpl - jl3 sinal coshpl -- l9 coral rlnhpl) *, 4 )(tlaC) l* sin*l coshpl - p cosel sinhp/ *

J(r oord rlnhpl "[- p rln*l corgpl).],

(llu) - /l udtrl crnhfl 4 (tlrc)'(r crrld rlnhpl .1. p rtrrat.rorhl,l) l.

( t )

(2)

t" tL(,/rc) (r tod tlolgl) l- fl rlud rlulr$/1,

. , ' r , r " , l l lx ' I t t / , , , i rvrr t r

(/u) / (cosal coshpl l_ j sincl sinhpl) g

i- itl lr( l@: I g') ("-1. jp) (sinc/ coshpt - j coseJ sinhpl),t l i r r c l l t .

(/u) 1 cosal coshpt -l- ]I [aC l(e2 ] pr)l (a cosol sinhpl f p sina/coshpl) ]-l jl-H laCf@z J- p!)l (or sincl coshgl * g coscd sinhpl) f f sinol sinhpl-r. (a)

,, r,,.,''tot",:t"ot":ffiil" slnt generale' Pentm a determina constantele z 5i p

i i i l r r r rr i r r r l o- . , , t l f Ct. , t t $ iz)VCL

(tlo\., II coshpl { tlft,lc sintqt it(hlz't\VI.l(.: sitl\$t.

(10) : 1 coshpl + HvclL sinhpl -l- i{(klz{lvclt' snntlt.

Putcrca mccanicl datiL la Sicncrator vat fi

II'0 - (1/2)j(I/ coshpl -y lllLlC sinhpl) (lcoshp/ | IIV(:It'siilt()tl

- ar ( J-).r"r',r:tl :. tr nlln t (coshlpl -l sinlrrp/) I

+ VWp + H"Vcli. sinrrp/ coshpl) rrr ( j' .r'r'Or)-].

l l t imul tcrmcn poatc f i negl i jat pcnlr t r f r r tvcnJt ' inal t ' ; i totrr l t t r l .dc diamctru marc, tvind in :rct'st c;rz

t l 'o:U12)[H1 coshzp/-1-\ t12)UlVI. l ( ' I r l !V( l t . s in l t2p/) ]

Yedcm cir putcrea la gcncrirtor cstc mai m:rrt' rk:cit putcrclt lrt r.r ';tl.tW =.. HIlz, Dif&cnlt fi intl cnergia picrdutiL sttb lbrmi-r tlc cltltlrttlr, itt r . 'ttdnctiL.

DaciL I cstt: suficicnt clc mic, prtttrm prrtrc cosh 2pl | ;i sirrlr 2fll l l l l ,in carc caz

r r , , - . r . l r l l J t t ( r , 1 u,) . l ." zL z \ I . )J

Putercn cerrtt lt p('ntru (:l gt:nt:r:rtorul sl"r [utrcliotrt:zc (l l l '( ' i l 'plrrt l l l

du:onectat sr: ob!itrt prrnind ,f 0 ;i lstft: l avctrl puicr(' l t l isiprrl ir pr' l t l l ir '

lf; (I/r/a) rf sinh zpl ('ll2) //; tshp/.

I)acir, p cslt nrnlt ' , ohscrvirnl cil pirt ' t l t 'rci l <lc pttlt 'rt cslc tottsicl ' ' t l t lr i l l l

; i estc pr in r t rnr i r rc tccomandabi l rkr a 's l rncnl i rx ' i rc p c i l r r l : r i nr i r ' l r r r i l t i l '

Am glsit t) $IZ)VCI., t lrrr /f :/, cslc cxPrt:sia invcrsir ;t ! i l |z, i stt

nclrr lu i in l ichid, asl f i ' l lncl t i tv lm: p hl?t t , p /V287 00O.

I tcntrrr cal< ' r tk 'L ' Df i tc l ic t 'Dtr lenr s i ' r in l rc l l t in l i - t t t r t t r tn i t IQi t rch' [o l t t t t t l r "

I r r r r :uaI i i l r (5) s i ( t r ) , ' t rcgl i j tnr l r r l l imi i l , ' r ' rncni corr l i l t in<l pr ' 1. r lcal l s i r r l

fo r t t . n i i r : i r in ih f r | r :vcn1ir r 's l r : i t t : t l t ; i , i lv( ' tn Prr l l l r t l ( . t t t t t I r t t I t ' I t ' i t l t . t l t t t t

hrngi tn l cslr . r t t t nt t t l t i l t l r t txncl r l l hrnf i int i i r l ' t tnt l i l :

Iln // r'oslr(l/ | / yr./( ' !ti 'rltp/, (7)

/n / corrhp/ | //[t ' l/. rinhfti. (rl)

No/r l , l4trrnl i i lc (Z) pl ( t t ) , In l tor l r t l lnr l n l t t r i r t l i l r ' l t lo lxrr l lonl lc I r1 i i ,pnl 1 l rct l r r ' :

hn /t rrt'rltfl/ | r ' ' irrlrfV'

. . . - t rnr l tp/ | I r l t thf t / ,

(1)

( ( r )

rr : a - jp : aye6 : aVe[E -TFi;;tl in carc

n" - 92 - j2rp : az67 - jaRC,

cgirlind componentele acestor vecrorr

n ' - 9": azCL, leg: aRC.

.\poi egalind modulclc cxprcsici pentru

q2 + p" : a,Cl[Lz -

t€@: aCWIjjE,rlin care obtinem:

.2 l Rz l aL), p: v utzl'ctvdoT-p_ -rr.

, ,Dac[ {recven}a este.in,lri,. termenul (R/aI), este mic fa}i de unitateiil putcm pune cu o suficienti rigoare pentni sc6puri praclice.

":alet, p: 1.nlz)tte lT1i

d.2 + p2 - e2CL.

Constanta a este valoarea lui_ F in presuplnerea ctr. conducta este lip_siti'r dc frictiunc. Accastir constanti'cste'atrin6i-ol;;";i";;;;i-; urii"i;rkr undi-r ti avcm d: Z?r/1.

.,..... 9.::,...onru ? ": fi^*4:::::!,ut dc amorti:ate,i cum am tulr- Ve lL : +,\ ' ( ,nr avca: a , . Zr l l t , g: (Rl?)r l .Accstc formulc simplc slnt suficicnt dc.riguroasc pentru calculele prac_licc l:r corr<lrrclr. lungi in'carc nu avcm pcrdrtantc..,\rn girsit, in capitolul III, ciu R .: Al-, asifel cir. avcm

I "= (hl4lrer:. I ):rr. i 'L contlucllr cstc rrrr urrrl l iPlu t,xar:t al luugimii t lc rrnrl ir, avcnr cosaJ_l , s i ra/ o, i l r . t i , r . r rr l , . l , . lsr . r i r . r . l l r . (3) 1i f . i j - , i , : " i , i , '

" '^"

(//,,) r.,rJt,fl I (//rrr.)ct silhpt j(tla{:)p snirrpt.,( /u) I r r t ,h l t t | \ l t r l t , , i t r tg l I i ( t l r t t . ) t t s i i l tpt

8f,

r r ! , , | , . i , | | | r . I I r , I | .

t i , ; , , , , l r . , r , r l l l t l j / ,

, , , , ' , t r , l i 1, , r l r l r l t / ,

r : | | ( , : , ( lxr l < l | r l r r r , . r i i r r ( r ) I ( t , t , l r r r r , l , r r r , l 1, , / r r r

, I \ , r r i r r r

_() , ( . l r r r ( l t l r l , r i r r l r r r r t , t , . l r r r r l r , r r r t r r / t 1, ,

r ' , ^o<,,

, , rs l rp, i . /s i r r l rp l I l r , l , r r r , . r , r , r r r / r( . i r . r r i t - { ) t (Jn( l t i ( . l i i r r l in i t rJ, . l r r r r , 1,1, , ,1, , , , , l ; ' , , , , ,1, ,I r r r i r . ' i , . . . ,1r , .

vi lczir r ' l ic i rc( , lx ' l r lnr : r r ) l ) l inc t ' f ic ictr l r r r r t r r r i t t t i I i l l ; tc t ' l ; t ; i l i l l l l ) l ) l l l t ' t l l t r l ( t l

l i r r r , r r r . fJ (r )ni l iu l l t ) r i t r spol i lc i t ( I i : I I I I i I I l I I t I i ( ( t l l ( l t lc t ( l i : rot l ( l l l ( l l t ' l l t l l i l l l

i , . r r , r i r r i l i r r t l ( :u l l i t . - r I i r ) l i r r i i l ( o l t ( ] lg i ( i vol r l r t tor t lPlrr i t t i \ ' ( ' [ ic i ( t l { ( ' t ] l i r i t i. l icrr l r ' .

I i rctt l l tr

A sc gl-Lsi cficienla maxinit a unei conductc dc I lor lttttgittt l l t rtr"

rri l irrrl 25 CP ]a un rcctptor, undc valoarca lui .I1 cstc dc 30 l<g/t:rtt!.

l l ' 2-i CI'> 25 ' 1 600 -= 190 000 kgcm ' ' l lJ 3lt2 \\:.

I ' t 'ntt tt l tp r-r

r . I IV( t , . 1<nl l ,

III Zll ' i<'t l l) 1t'r ' 30! ,... 2 ' !90 0{X) .1s0 0(X) l i i l ( rrl.

; \s th ' l int : i t cr 3f l0 000i I . 900 .60,- ictn: .

Asadar, (l ialuctrtl l ncc' 'sitr P(ntru con(lucti at l i 11 ' 8,7i lrrt 'I laxiurr t l t [ r ' i t tz i t l l t l t ' t ' r 'ptot- , spt t ' i t < l l r [ i t r t ' t l i t i t 'nta t t t l ts i t t t , l r , t l t

| ' / l l ?. l0 2t0 cur/s, i ; t r Yi t t 'zr t t f ic tct i ' , , z lo iv2 l ' l l ! i r r r r / '\ r i r loatcr t l t r i / , : r ' iL I i ( t :z i cLLpi to l t r l I l l )

r ++ i# l'Ii 0 2,2 it

i 0 lr r l ic iL, ( lcoiu-c(.c

tt,, t,l[Li, astt,tr l Jrr i r r I r . i r l iunc cst , ,

t;;l .,,1.l r r r r r r l I l r , r l i r l t r i r , i . r , r .c,ptur:

, r ,sr r j l ' ( i | : , : 1, . ) , , , i ,' \ ] t | ' r I t J "" '. - \cr ' i rs1a i5 i ;Lr . t , r , r lo i l r ( , i l t r r i r r i r r r i - r r . i r | ( l r r r r r r r i l r r r r r l ( , : ,1r , l l r ) tu in i l l t , cazlrrc nrfr loc cin(L (tli l)VLIO.. t.

. - . : . Ac( ' i ts t i ' i . tc lat i t . arat i c i t pcnt_nl ; r o l r t i t r t , r , l i r . i r . r r l l r r r r i r : i i r r r i i in t r i r ls- .nrrtcrea ('ncr.gi!.i, lr.cbuic si ,,r

l-T,-4-,:_ " i tt.lz, ,,r1i,,,i,",:,,i,rAi,r cinctic:L ;icnugilt Potcn{iali l i l r-cccptor trr.buic sii {ic cea1l. p,i,l i ,,,i,.rr,, cstc cazul..l* lrcc{rr(' p*.ct al liuici.ii 1r.;r'surisic (.on(liti.r i i.r,r;s;.lri,j ' i,r,r,,lrtinit:,.

,\sar lar.

r .o".- |

. , , - rprcosh2pl -f sinh26l

; i r1 arLr rrccast i r r ' ; r lo l r . t_, c inr l IVL: i lyC,; i arrm:11u .: Il(coshpl + sinhpl) =. 1lcBl,

,/,, . 1(coshpl _F sinhpl) _ IcBr,

29tr) ,21z.1000{)0

k 0,zt 2Zt, 2. 14.1 5{x)

0, I . ls ,

situ

rl in car-c oltt iuern

lo

l l IL. 1r r,1.r lc- . ,

T' H"- ] I' ' - . .1--o-Fr

14.1 i0{)

coslrO. l4 l l t , l ) l I , s in l r O, l ' l l i l , l50" l l6 l

. r ' l i , . l i r r r i i r , I l . l6 l { ) .s{ . .. \ ;ar [ ' r r ' , r ' l ic i r : t t { r r : t r f i ( l ( ] \ i l ) ' ' , , ) i l ) r r l ( r ' t r r r r ( ( t : : I r ; t I ' r s( t l t r i r t ( ) r v i r l l

25i{) ,S6 2()( l ' 21,336 1i \ \ ' . l t iL l rh tc.L;rr ' l r (ht i2t) 2. i t ( l l ' 2 ' ) ' l l \ \ 'I ' r r lcrcrr l is i l r i l i r l r t l in ic c i r r r l t t ' t r '1r Iot t t | ( :s l ( ' ( ) l t r i t i i t t gct t t t r t l r t t t t l t l l l t t

l i r r r l i r r l r r t t r l i r t r tc iLr I i

l l " ; ( l i { ) . lo: .7 /60. . i . . o, l . i0 l " l . l {X) l iKCnr '

\ ; l r l

l l ' , i 1,5 ( l l ' I l9rJ \ \ ' .

l i l t r l r t l t l t . in l t , i t t l r t l t t t , ' t t t l t i i t t t r t t t , l t t t l t / r r r r ,4t . l ) ; rc i - t l l t . i t r r l i r l r t r t tL l r '

gr . r r r . r l r l r , ( l ) r , i ( ' l ) g is i lc i r l l l r ' f i r )1 , r l \ ' r ' t l l :

( / / , , ) / / rosr/rosl ta/ ( l l ' t t ) \a coscr/ s i t t l rp/ l (1 s i t ta l r :osl tp l ) I

I i , , \ l l t t : l l r ' . ;111/ r or l r f t / [ t l rxr / s i r r l r f t / ) I . l / s iua/ s i r rhpl l ,

( / , , ) / r 'o:r l l / r or l r f l / | ( l l l r l l l t t r " , t l s i r r l rp/ I p rr i r ra/ r 'osl tp l ) |

I i l l t l , t , t t . ) ( r s i r r r i ror , l rp/ | p r o"r / " i r r l r [ t / ) 1 / I ' i r r r /s i r r l rp/ l

l { r , , r t t r t t l l t t t r i r r ! i ' | | r n ' I [ ' ' r r r ( I ] i a , r t t l t ' l t l t t , l l h l2r ,f l | | t l r ' r , r ' ! l r ' \ ' l l r ' / , t , t t l r ' l l t l t t l ( l l t , ' i t t t t t ' , ,1 l l , i l l l l l t , r i ' , t t ' r ] l l l r " r ' tv f l l t t r ' .1 l t t ' rr r , , r l r . l r r t t t t t t l r , l l l l l l l r l l r , r t l l l l , l l i ' , i ' r i . r i | ' r r l t t t t r l t r ' . r l r , , r | , t t { r ' t l l , ' r , l l t , ( l t 'o, l t | r r '

, t ! | t t , , r l , l l l , ( t l i | l ' r

( ;rrrli lrrlr:;r e I i - c-pr -1.r. .! !,qntu t'rccu uali a lrrrr,ri i i pcntr.rr.t:rfrtli nrici it lui pl r.rL cstc a1111-1i111i1i',.

" L N == hll\u."

. . , , . t . . , . , ,1. i ' Pt i r r . r r t r rurrr . , t

l ] j , l i l t l , ; r o l , l i r r l ' o. , . t ic icD1i i r . i t l icrr l . - r , . t t I r , l , r r i ,\ , r t . r . r ) r i . l ' ' l l r i t r l , . r r r i r . rxrs i l , i l i ; r r r . r , r . r . | r I , r - r r I t r , , l , r r i . i , ' i r r1,r t r r . l l , . l r . r i r r: r ( r . t Inrr ' l l r r .s i r r r r , . r . i i , . r r i , . r r l1 l l ) r ( , lx , r l i , ( , iur l , , ' i ; , i ; ; : ' , ; , , i ,

r \ { , ( . i ts l i i ( .o.( l 'z i r r r ,sto.rr t r , l i r i r l . ' t ( . i l [ i r t_Irr . r I r .1r i t t r l : r t . r . r r r . r r l r r l /l l : l i , i l l l r , l " l i l . f t .s l . . l r r r r r ! r ' r r , \ ' i r , ' / , , r i , , , , , , , ' , r ; i , , , i i , . , i i ' i " , , , , , , r , , , r , r , , . i , , r , , r , , r ,

, , , , , : l ' i " l i t i , ' l l l l , i I : ;1" i , ; ; , , ; l t l , i l l l t , , , i i , l , ; i l : , , , l l l ; , , : i l l ; l : l l , l l t , , l l

r0 I

, , , . . . a, . , t r , r , \ . r lur , r ! r r r l r r f t , r l r r l l r l rx l r rs.rsrrpr l r gt .ncratort t lur pr intr-o schim_

i l i i l ,r. '11,1'j, i '1" rlr ' l 'r 'r l 'r 'r iJrr; a'r t i i ' i ,t , i ' .., ir i i i . i. ' ' io".t" ,ni.i i l ,n-

. Sr-r r 'orrs i r l r . r . r r r r r r . r i i r r l i i t l rztr l . s i rnplu in r :arc nu cxist i . n ic i o migcarel i r ( r l ) i t tu l I i r r i r . i r r r r l r , ru, ;Lf l i rcccptorul ' . - - - - -^- " ' . . "

ln i r r . , ,s l , r rz / o s i i t \ rm pentru I1o, 1o:

(tlu) ., /1 (coscl coshpl i j sinal sinhBt),(Io)

-. (H lul)l-acosoJ sinhpl -i- p sina/ coshpl * j(c sin at coshgl _F

-i- Pcosal sinhpl)1.

Lucrul efcctuat de gcncrator ar fill' : (IIAIZaL)ie cosaa/ sinhBl coshpl f p coshrpl sinoJ cosa/ a

_f a sin"a/ sinhpl coshpl _l_ p sinrpl sinq/ cos*/l :: (H2lzaL) (c sinhp/ coshp/ * (pll) sinlat cosh2pl) :

: (ItrlaaL) (csintr2p/ * p cosh2p/ sin2rl).

.. --,.Sn pr".y?olem aclrm ci frcc'enta se schimbiL i.tr_.n astfel de mod,;i:

lll"il unghiularl a sir ctclinir a + ia. Spo.ui- io'.".p,#:,to, at lucrului

A\lt ._ (H!i4qll (sinh2pt -l_ 2/p cosh2pl cos2al).\a.I ) l r arcm c . , r1r , , ast fc l c i Ac: Aa/a gi in celc din urmiL

AIr, - (Hrl{aL) (sinh2pl $ Zgt cosh2pl cosZxt) \u 1a.I)acI linia cstc un multiplu de scmiundi, avem cosza/ _. |.('antitatea din DaranteT_i,! in cazul acesta estc prriiir,a ;r obscrviLrn

:,:l ,li:.::,ll,l.'.l"ta tincic si-t .,1"rd r,i.-ii,i ;;-.t,*fi; s:;:',:ii". crcetc, a'-ind:f. I,-r:rl],11

ci rna;inr rnorricc curc actionca-zi g"n i itonii (.slr. rnrirziari,r l r (onrt t l ta ca puterc.r accstuia s i nu r l . r . in i r cxccsiv, i .I)aciL frr:cvcnta sc nricsorcazii, Aa cstc negativ ; i AII cstt,, dc ascmenea,

:::.fl::liy !] ,lrrcrul .efcctuat _1L g",,"r,,tu. rlcscrestc rezultintl o accclerarr: rr.r:r frnr I lrotrcc pri'cipalt.. \ 'e dcrn a)r<lar .i .uu ,.".J.o"iiti i f,r".1ionoi",.*, r,.r.rl()rului ;i a linici rinde ta staiil itat". A.;;:i;.;;i,iti "r,stii

p",rtruIorrlr. r' irlorilc lui a t.art: satisfac conditia.

i t r lir'l-r

sinlr 2pl . | 2rl) cosh2lJt cos}et >- 0,l .\rlt 2ts1-

;i i cos211':' o'

. \ ' labi l i Ia l t , r lxrrr l r ' I i t t t iLsut i r t r"r pt i t t t r r lxrr ' lu l

a ' I I " 111- .-\,r 4a Y I- '-

I-imita dc stabilitate cste atinsi cind AI4lAa:0, adicr-r

cos2.s.l : - tanhpll?pl.

ln cazul. conductelor foartc lungi, accasta se rcduce la coi2a/ l),s.ru al : (Zm!l) . r la:ZrI l ) , , care di / : (Znr l l )1,18.

In acest caz echilibrul este indiferent. Cind cos2crl: _ l, olr{irrr.rrrcazul instabilit[!i i maxime ;i instabilitatea pcrsisti]" pentru toalc rrrl,rrl,Ircntru carc

. tanhzpl F coszc/. i o.29t

ln cazul unei cunducte Ioartc lungi, condilia maximului rL' irr"l.rl 'rl itate se reduce la

, 21n+l-L:-L-

Accasta aratir c[ nu este posibil do a menline {unc}ionarcrr rtt . lrr',vcntil care producc pe linic un numiLr impar dc sferturi de unrl:i.

Acestc considcralii au o murc importanll practic:r prin:rcccrr rii irrlr ,,conducti lungi conditii lc pentm maximul dc stabilitatc sint tolorlirli oplirrrll i pcntru transmisi:r cncrgici, constind anumc iu accca cil cch' rkrriL r,rlr'1,'ak'liniei sint puucte de varia{ie maximiL a prr:siunii.

I)acir liniir este scurt:r, pr.rtcru spun(!:

tanh29/ . _ ,z2t

1i , 'orrr l i ( i r r < l t ' s ta l r i l i latc sc r t ' r lutc l l r

I 1- cos2c.l > (1,

(( ' r ' i r ( ( (s ic r .s l rct lx .n l ru torr tc vukrr i l t r lu i a.l { , 'zul t i , pr- in urnirr( ' , c i l pcntru l in i i scurtc or ict ' f rccvt t t ! i r ls t , rot t t

p i r l i l r i l i r crr r . t l r i l i l r r r r l s l i r l r i l . ( i ' l t rn i l l tu i r . stabi l i t iLtr ' , 1<ttu; i , sc oIr{ i t t r ' . r I t t t t r tr itrrl l l lxrrtul l l l ' / .\rr cstr: rtrrtttcric rrn tt lrrirrlrttt l : l tcl icl"r cos2el L

l )at i r 'os2al - . . l , i rvcn AI l r /Arr , ( ) i r i o l lscrvr lnr c i t 1x: o l i r r i . r l , 'o l r r r rg i rnc tnrx l t ' r i r t i r , r : r :h i l i l r ru l cstc inr l i [cr t ' t t l atuuci c in<l l i r r i i r ,s l , i t r rprrr

l i t : ' r iu l r urr r r r r rn i r l i rupur r | , l rurgirni t l . s l i . r I r l r ' unt l i r .In rotx l r tz i r ' , r 's l r ' r ' r ' i r l t ' r r1 c i - r o l i t r ic (urc ( 's t { ' 1 l t 'o ict t ; t t i r Pl t t t t t t . r l i

r rPrrrr i t t l r l iv r r t r r l l iPl t t l r l l r r r rg i r r t i i r l 'sct t t i turr l i lx t r ln l f r { ' ( \ ' r ' t l t r t ror ts i r l , r t l . rl t r l r ' 1 i ccir l la i f i r l ' r l l i l l ) i l i i r r c lc i r r : r ' l t r ' i r r ' ; t l s ta l r i l i l i r tcr gct tcr i r lor t t l t t i r l , '

| l | | l r . t ' . .( ) , r t t , r l iz l , i t t t i l . r t . i lxr i r l r ' l i l . r r : r t i i t t i ;xr lczlr r i r l t r nt l r ' r ' l l l l r ' r l r l r l

l , r r , rp l l t r r l r l l l , r t l r r 'p lot , , l , r t , l r i t r r t l t l i r r I 'zvol l r t t I t l r , | i t t t t r i t t t t : t t r l , l r ; r t l r ' .( f i r r l r .x i r l i r t l r r r ' r r ' l r lor l r r t r r { tot t i t t r l l , r r rP. i l r r l

' ' \ t t ' r t l , r l l i t t t | . i , r r r t t t , r \ ' t ' i t

| r , l t r i r . r r r t . ' r , . l , r r t ,1, ' r r l rL r ; lL l l r r r r t r . : .u l , r . t l r t \ r ' I u rn \ r \ l r ' t l t r l ' t t t r l r ' , l ; t, ,1,111,qt1 ' 7 l t | | r r l r r r t t l , , gr t r , t r r l l , l t r r r . r ' , r r r , l ' r t r r ' r / l r , , . t r r | , t I t I r r I r ' , t l | | t r r ( t , r t t ; r t t t

1 l | | | , , r i l { r ' ,

Sr. pol l t . l r . i rg l o ronr. l r rz i r , i l t i ( , r r ,s iur t i r r l i t r accasl l " r r :o ld i { i r , ,. ,

Si l r r r .str l t r r r r r . ru r . i . r r .onrIrrcIr | , i r r r . l r r r rg i r t l r . r r l r rc;r .orrr l i l i i r< l . r , i r r r . r .os2qy'- .o ' r i r 'srrr l r i l i r ; r l . r r r rurr i r r r i .srr ' : r t i r rsr ' i r i r r r r , . , r iz" i , . . i . ' ' i , , , , l : r r i r r ; i r l i ( : ir r rs2a/ I , t l i r r r l . la l 2rrr : r r r r n/ r r rn, , , r l ,s t i i r i i r , , i a

" ' , r / , , zanf r l2r f , , r r l r l . i r r .str . l r r r r l i i r r r r . r r , , l , r r r r , l i , , , ; ; : ; ; , l " "" ; ; i i i j j "

l ) r ' , r i r r r r .err l t ; r r . i l r r . r r . r .111,1 l | l1, , , ; t . , r , lxr l r i \ , r . , |n. , i r r , , l | t ,1 r i r l r i . r . . . rI t r ' 111,t , ' , ' l r l i r r l r r r ru l l i r t i l i t r . , l ,1, . l r r r r l l r r r r i ,1, . , " : , , ; , ; ; , ; ; l , , ,

u3I

l r t i r l t r r r , I I r r r r I r ' I r . i I i tn:r l izc i sr . | |o,r l l , t t i l l l t lu (r . lcr i r l c i t or icc Sistemr: l r r r .sr . l l l i i r r r , l , r r r . r | l , t r .zr t t i l t r t i r ( .s l ( . r , , i l r , , l , r t r , r | . r , r ' l r i l i l r r t r dc putcrc. l )ac: tsc intcLcrrL. : rz,r r r ' / ,onir l r ) i r rc 1xr I i r r i r . , r , I i r I r r I t | , r I r . , r r . r r . i l1. . Acr i ; t i r estc, dt 'i lsc l l lc l lca, r ' zr t l r r r r l t tc l r ' lor ' l l t l ; r r rs i r l r . l r t t r r r r r t t r l t , : , i t lot . i l f ( : S;r l l inCTl i i SaUIl lo io i l ro s i l l ( ror t r . n l l t r i Iu l lc l ioni l l ( l l ) r : l intr .

I ' i r r t ' l t r i l t i t t l iu. i i lL: r rontut l . t ' . l , i r . r r l r , r r l r . r l r . t r r r l r . r r , iu l i r r i i l : sonicc auIost considcrt t r : in capi to lu l VI , l r i r l i r r rhr r , r . r . l l r i r . l , . l r i r ' l i r rn i i ; i a le pcrdi-tanlei, in gcnc,ral. Un caz parti(:uLrr irri lrr ' :,rrrrI sr. prrxlrrr;r: irtunci cind l inia,'stc .inchisiL la capirtul rcccptor, :rst[{,1 (.. i irr ;rr.r.st punct (: l lrcutul l cstet tu l , .Accasta sc producc cind rert l r lo l r r l

' : , t , . r ' I t i l , i r i t i r r r l , c , . gn crdiornlcont inrr i r s i funcl ionczc ( r r i r i -ccir j [ t r ' ( . \ ' ( .n( i .

P.cntnl a calfula. putcrca absor.lr it i r l i , l irr ir., irr tLsr.l 'r1r'nt:a conditi i , sclxrt uti l iza {orrnulele rl in capitolrrl \ ' I prrrrirrrl / 0. (]rlr:rrlt: lr: pot f i sinipli-l icatc obscrvind ci. raportui p/or cstc i ir nr(xl (, l, i tnlt i l rrrr nurnr' ir mic, astfcl{: ir sc poatc negli ja p'?faliL dc cre. Se ol,! irr rrstfr. l r.r. l:r{i i lr. sirnpli{icatc:

A0 : f1(cos) : I/(cos Coh I jsin Sih),

1n : jl/ '|(sin) : I/(],(cos Sih -l- jsin (irh),

nlir ' l 'o cll tLnitatc. Aceasta sc ptoclucc atunci cirt l prndusril cl it cxpdmit alrlol

i i r , , r . ' . t gf . . i . mic. .Din c, lc d, ntai : t t ' ' s t Lr i le cr i t icc s int 11 Prcz"nlr t " l ' r r r r

i i ;., sr"ri l ' .- i i"a putcrca absoLbitir ar putca atingc o asemcnc, rn:Lrimc irr ' i l

l . i ' ,"rr,tt i tr lplt i,, t i" i" i. Ac':tsta cstc- i lustratit r le umrirtortt i excmplrr:

L.rtntl ltt l 1

0l in icnror io{azat i rCSICal i l lental i t< l i rcctdcungcr l l . l . i t torcul l l l l ) I : , I llc t io lat c lc 6 marr iyel i r cu / : I c l l l tu t ) puls lLt ic , r : ' . l ;0t ld i iu l i , /sct l t r t ' l ', c Dtodur '" u l l dcl) l i l iJ lncnt cu.rnl l l i l t l tJ inc - \ 5"t t t ' ' l t Lu] ' l l l l l l / / \

" 5 iO.^; l - - ' f ] t i t - , , t " o t""1iuu" intcrni r l ' c ' l ,5eIn ' r '11 f" l ' i r l l l r

tudinca viicz-ci souice 1o/c'r : 500 cm/s'

I-ir.ria traDsmite putcrea sonici prin rpi, cu o ritczi a untlei t le I '5{)t) ttt ' '

tr i/sccundit 9i un factbr dc propor l ionrl i irLtL' g : 6'6 Lr. o ftt 'clcutit r l ' rr'-_' itz-

. . zi., l Hz, t1i1d r, ' lurigimc Llc rtudiL 7' -= tultr = 6'3 ' 10r cttt '

,f" t ".niirr

i,, -a"

,,.",t",,"o, ,! =. i; -= 15,2 ;i a -= Zt;l) ' ' 1 ' l0-3'

I)aci'1, sc i lr ' \, i tcZa cficacc dL' ' l5t) cl]r/S' sc ol,t ittc t l in Iolrnrrl ir (7) (. ' lr1'r

lo lu l I i l ) h - 5,26 ; i factolul . le mort izar" ! ' l t izu =' 1 '75' l { ) "1r t t t

ln rccstc contlit i i sc poatc calcula putclca absorbitiL i:r l iuitr t irt ' l r ' '

ceptorul cste oprit (cipirtul dc l inic inchis)'

I 'cnim o l inic irrf init lungiL se ol.rl iuc o piledclc finit iL (rczi (10))

, I t : I i lz+ :1,85' lOa l ;gf 'cn/s,

irtl icit l l.troapc 2,5C1). Pcntru aserncncir lirrii Tgh - Coigh - I 1i rrrl.rrl '

. t t i l r ' i tOi s i t t t r 'gal , ' asl fe l in( i t /0 ' +I10'" " n. , l , i . i ' , p, t ' t t , l i , ' ,

sr 'cst imit r t rnPl i tudin ' a pr 's i r r r r i i H' , i ' r ' : rPi l r r l 1 '

n( ' f l l f ot

II,t ' ' Iol'r/ - 7501t5,2: 49,3 kgf/cnrr'

ir carc ,,sin ', ,,cos" sint notatii pentru sinal 9i cosal, irrr. ,,Silr", ,,Coh,, sintnotatii p{'ntru sinhpl 5i coshp/, atlici. functiilc cirtulrrrr, ;i hipr.rlrolicc obi;rruir,..

Putcrea absorbitS" va fi obfinuti'L din componcntele- vqr:torialc dc maisus (vezi capitolul I\')

l[ : (,ffl,/2)sihcoh.

oblinlnd, clc ascmcnca, rclafiile scalare:

(e)

carc lungimca linici cstc rrnpar se ol)tinc

puterea absorl)it i t cstt

2+ YSih! + sir'

par (lc l/4, Pclltrtr ci!r(: cos:r I

lJ . ( iotgh.

.1 ( ot glr.

i rn l r ' r ' i ( ) r ' l r t (10) ; i l t r l t t l t t t r :

' '|//,j/r ,,ri tt tilz'\.

Sih. Cohft

l \ : tk ' : r l t iLprr l r , r l l ; r l rsot l r i l i i

l) irrl( ' , ( l irci! l ttttgiutcir I ir l i t ' i cstt: !tn nurll iu' ir plrl t l t: 7/4

vrt l i :

l l " . / | . ' l 'gh, I l ' . ,

/ r ' i r t t losl t l i r l r 'Vrr lo l i l r ' 1r , ' r r l r r t , l ; i

' , l

ilo : Ilfcos'z + SnF, 10 : 'l,Ijfsiil + Sih,.Iletonat$t crullcc. Considerind cazul in

intrcg dc s{crt de un<lir, l, : nt.. },14, pcntru ,r

(cosal)2: I qi (sinel),

clcoalc'ce a - 2rf), gi I =-. nt. ),14 iar aI : m rl}.Pcntru na impar, dc cxcmplu m' : Zk f i, sc objinc

at : (2h + 1) . i lz ,

ccca cc di. (cosctl)2:0 ;i (sinal)s: 1.Introducind accste relatii sc obline pcntru ?ta par:

Ho - HCoh, 10 : '{]Ilsih, r,r, : (rpAijlz)Tgh, It', - (1ilz{)Cotgt,.

l)cntrn ru impar, rclalii lc sint:

Ilir , . Ilsih, 1o ... QHCoh, 'rlt, - (I3lZ \Teh. IIru : (r!H1il2)Corgtr.

Estc intercsant dc notat ci'L pentru liniilc {oartc lungi putcrca alrsor-lril iL la rczonunlir nlr po:rtc dcpirli valorilc:

/ t :+11612 s. l t B:I i ; lal , ( i l ))r l i t t r ' ; r r tz i i l i r , i r r t r : r .st <: tz pl , , oo ; i

' lgh - . , ( i r tg l r . . I .

. ' l ' rnr t l i , i l t ( ' ; , ts i i r l ) l ( , | . l . l i r r t i l i r t r r t cslc c| i t t | l i t i l l l i l t r . l I t l r . f r . Ci r . l ,0 l | lcl i r r I r r ' , r ' I r i I I ' r r | r ' l i r r i r ' . sr ' . l r \ i ' rv i r 1 l r . l ) r r l r . r r . r r r l l r r t r r i r r r iU.r . lxr . r l r . f i

'1r1, . r, l r r l r i r r l i r r r r r , ' l r r l iv , r r t t l r '1 l r r l r r r , r t r , ( . l11lr , r t l t t l r ' , r ' , , r l i r ' r r I l r r l . l . r r r r r r r

o|l

Pr.ntrn l r t t t ( i t t t , i r [ in i t iL a l i r r i . i

I " j Si t r ' ( loh

Z,l y Cbhr- cosr

l ) : r , . i l t r t rFi t t t t . r l in i t i cstc t l l l l lu l l l i r

; i s i r r ! { ) , l ) l r l ( ' rcr iL l rsolbi t i cstc

ly, t . . j l . . l .gh, l l , ,

s. txrr t l . r ' " r l " t I ' r ; t l t t t l r i l i l t t t l ' r ' l t t tx l t t r ' r ' ( ) s l l l l r ' l l ( r l l l l l l l i t I r i z ' l l l l l l t i '

, , , , . , ' . r , , , l , i , l ' i " " t , t i ' i , , ' t t ' , . l I 'g l r ' ' ' i ' r l l ' ' , r

' l l '1 i l r " r" l h ' l r . ' r ru l r t . r l t t r ' '

, , 1, t , . r ,1, ' r1 ' t , t i , , r i r t l t t t i t l r i r t t I ' t r l t ' t r l r ' ' r l r r r r l l i / r r r ' ( lJ / ) l ' l ' r l r r r l l l '

f ' r , , r ' r t r r t t r , l , . r l t t r t r , ,1| r l r ' l t r t t t , r l r l | l t t t r l i t t t t '

' l ' t t t t ' l t I I i "

l , l r l i l l , r r t \ r ur t , l r t r l , t 11/ t , t l l ) ' , l ' [ l l {1,01'1, ( r r l6 l r ' l { t , ' l

+ "i,,'caLc r l i r pt ' t t t ru cosz : l , s in! 0 (r .orr ' . , l ) r r r rz.r lor / ) , /2)

( t t t t t i t r , r l r , . r l crr . r r tp l r r : / l | , , , l l r I ' t i r , | , t i . . r r l r . p l lc t1 cstc I4I" :1,02. l ( ) r r l igcrr t /s strr i ; r I r r ) \ r r r . r t r ' r r t t r r l ' , , , . , , , , , , . r t , . o v iL loare miciL.

l ' r ' ( l r . i r l t i p i r r t r ' , 1r ic l r I r . r r ' . r , r r t r , r

i l ' , 1 i ( ,otglr l , t i ) l t , I t | | r \ , I to ' l i1 i . , [ r /s,

rrr l ic i r r l r tosintat i r ' 40 ( l l ' , ( . r ' r ' r r ( i . , , ,1, , r r r , l , r . r r , r t r , 1r i , . r rL.rc rnarc in l in ie.St ' . l l l l l t l r ' tpuur: apr io l i i r : : -L sr . r , ' r I ' r , , ,1rr , , I , r , , , , , , , , , , . , , , , , , , t , . c i r r r . , {oarte pro-balr i l , - r 'o l l 'upc l in ia int int t . r l , . r r . , . . ,1, . , , r l , r , , 1,rr l r , r r , . r l i l ( l ( , n l i r re.

l 'ent t t t a calcula presirrrrr ' . r 1 ' r . r l r , r t , r / f , , , , , prrrr l l r r l i l iz l r n. la. l ia

S-:r | t r ' :u1t t ts. r ' r , t r ; r rL, i i ' , , l pr i : l r :Lrr i i ) i ] i . i . ( :ar re, , i ) l ranta ale lo, ' l iLt- iLit r i st inj( 'r l i t i"r rlc {iLpiul ci pompa crr tr ' ,. ' i ci l inrl i i iLrr.re.rzr-r. 5i rorlLcserLzii cu-rt ':rr.ul sonir: {undarlrc[tt1 dc 25 Hz.

Accasta e justif icat dooarccc iccilIt| l t ' r rLi u\:u'i alc |r ' iurti .uut\)rir ipr,), i lrc lase reflexii, intr-un cicht {rnt(l i i r lenL iLl, inttc lcccptoL i i gelrcr:rlor,astft. l ci. electul eslt cchivalcnt cu o l ini, rrl inuntuti i l .r rLn cipiLt cLl uo curoDlsoti ic cu frecvenliL rnli marc si crL ,.rl ' , ttul ccliLlrh inclri: l l ,, t. '""1r,,,r1 ,u'Pi.-rl oanc, distribuitoarc t 'tc., pitst cnlc nrr pot ulmiLri in nriscarea lol arnoni-r:r '1,-: clc inaltir f ie{r\rnti.

in anril iziL dc rttai sus s-ir r)rcsulrLls dc aserlencil cl-i lactorul dc nrnrntizall j l t.stc coustant (l( ulungnl l inrri. irr rciLlitatu cl \ ' .rri.rz:! cu vitezit cl ir 't i t ' iL iar erpr-csii lc l i ipr:r ' lrolicc cir siuh (91) ;i cosh (p1) sint, dc ascnrcnea, r 'rr.l irLlri ie, t lcpinzirrl dc curent, in f iccale sccjiunc a l inieri. In stir i le crit ice co-lr:pund crostcri i autorli l to it uurarnti lor si presiunilol factorul de amorli-zrrr cl 'c:tc cu rni.riLc:r valori i unghiului p/. .A,ceasta rccluce picrrleri le cri l ir ' , 'in atrunlitc se(:t iuni alc l inici si Ie creltc in ir ltc:le. Acesl lu.cru poatc Ii vlrif ir--at c:pcrirrtcntiLl miLsrrrlncl terrpr.r 'atura l inici in t l i lcritc loculi. l),r,.,l irt ia cupr-indc rnai ntultc lrrngirrri clc un(lir. se poate observa o difcren{i. irrrp(ntantir dc tcrnpcraturir :r. porliunilor la jurni.tatea distanlei dintrc rtruhrrr,rlr ptcsiuno ma\imir fI, carc rirmin reci, fafr-r, dc nrxlrui, undc culen{ul / , 'rla\iur li sc producL. incl'rlzire.

Clc;tolea prcsjunilor la sti. l i lc cri l icc de r'ozonantir dc ulai sus cslr:, '( onsccil lt i . a {rurctioniri i supapclor de suc{iur.re ce pclnit intrarca fhrithtlrt iin l inic in timpul cavitajiei irr cit lul r1e variatie a presiunii, pln5. itttt-rttt rrttrttui, rnontcnt cinrl cavitatia incetcazl'L iar presiunca. nlcdic reminc collsl iurl; i .

,\-olt i Llsttf i t le l i i . lr it l iunii

i t t i rn i i l iz iL ( ' iu( 's. i r lat t r ta i sus s-a l l r l rsupus ciL, coe[ ic jctr l t r ] rL I r i r { i r r t r , '/ l ; i L,x ' f ic i t 'ntrr l r [ t ' pulr l . i tanl iL . t s int constantc, iar l t 'g i lc t iur ' ! , : r ; i , i 1 ' t ,, i irrrr,, lr sotrlrrnotl it:t 1i crrr-crrtul :Lu fost atlntisc a Ii:

I lu: tcrgh = 7t0l ( r , .1 l i l l , l i l l / ( rnr .

I)u aici rczultiL neccsitatea de :r plasr )rr crrplilrrl g(.rtlrllor o capacitateirla cunl s( arati. in ligura 4 din capitolul U. ;\r.r.;rsl.r vir ln(.kni starea cri-ticiL de rez.onanliL in liniile avind lungimca rur nrrLlliplrr tk' jrrrnirtate iungime<lt: undi'1. l ' iri capacitatc, ascmenea linii rrr fi in coritli l i i l ririrl:rtc in fi6.ura 2<lin acclasi caoitol.

-_ Itxaminind pr.rterilc absorbite Ifr, IIl, Il '.,, l l l sr' olrs.rviL ci. tr,fi si

llt,, sint pieldcri normalc, adici pierdcri care se niic;r,.,,ari cu scurtareat linici,lcr.sl,-. pierd,.ri Ii ind propor{ionalc lu Tgh((r1;.

hr contrast cu accstea Il ', ;i l l ', sini pierdtri critic(' car(' cresc cu scur-larca.liniei proportional cu Cot6h (p1) factor carc cstc loartc nrar.e, tocnlaiirtuuci cinri produsul pl, cc exprimi amortizareir estc mic.

I)c lotat ci rczonanlclc dc rnai sus nu pot avea loc rlccit dacl linia(.stc un _multiplu dc jumititc clc lungirnc de ,rri,lir' .",, numiLr impar du sfer-turi dc lurrgime de und:'i. Astfcl, cea mai scurti linie pentru carelezonantelecriticc pot sr'r aparil este cea cu lungimca de un sferi <1t: Iungimc de undiL.

Pe ntru frecvenj-e de ordinul 2.5 Hz ;i o r.ite zir :r un<Iei in api de 15o0 m/s,ir(:orrst-a Lrscamnir o lungime ),/4 : l5 m, iar in ulei )./4 : | 2,-5 6.

- lotu,si dacir alirturi dc frecventa fundamentaliL iristir ;i armonici dc

ordin srrpcrior, linii rnult rniri scurtc pot producc rezonanle critice. Accstacstc r':rzul cu pornpele ;i motoarele ]ridrostatice hidraulice.

Sc r onsiclcrli r:;rzul unei pompe cu trei ciiindri producind curent con-tiuttu redrcs;rt, pentru carc prima arrnonici"r arc o liec\?nli n : l50H:z,<lr: (r oli lrt'cvcnia fundamcntal-L de 25Ht. Aceasta inseamnir o luneimc rk:l l r rdai i . . I 250/ l50 , ,= 8,35 m. O l in ic <le

^12.. .= 4,16 m, intre lompi; i "motor,

at'..putr'l_ inlr:r in rczonan{ir, gi :rccla;i lucru s-ar produce pentru toatc lungi-rr t i l t t tu l t in l r r < [ r , ) . /2.

- (i.rt tl iri marc pierderc datoratiL puterii criticc IVz, \lt2 . B(lotgh (pl)

i r r c;rrr . f | f ,7.5. f 0-6 ] i L =.^ lZ. :4 l6 im, c lct t : rnr in i r ( i ! . i , '15-416.tO-41,26. l l t x cu o anrpl i tudinc *r 0,0-54 /{ , ,40,Jcnr;}s ; i l } (4O,5)r / (2.

.15,2) 5.{ r :nrr . <Iarr lxrntnr pierr l tn. i r r . r i t i r ' iL

l l " , l t { ' r t rs\(gl l ^ l t lp l 5.4. l t ta l1,Zt t

; i i r r l i r r , r l l l ' , . 7, .15.11)rr ls11 r l l / , , . t t , r ) / ( ' l ' . o pir . l l r . r , . int lxrr l . r l l , r .

r ' \ . . \ . , t , . , ' , . t , . , r t r , , , . , , , , i r , , r l r t , , r I , , , t , , - , ,1r ! , . t , ,1, . , ( \ )

h - t i i , ( i l )

( t2)

Lir r ' ; r lcrrh i r r l ( :o l ls i (L( ' r - l i o vt lot t r ' r r tct l ic pcnt l t t l l ; i .S, pt t 'sr t l t t ts , 'r . r r r l r r t t lc in l i r r t l l r r l 1 l t io l t I r ' i t l l v i l l ; r l i r ' . \ 'or t l cxatr t i t t t act t t l l Pi t r i r l l t , r '

I ' r r r ( l i r ( r . i rs l i l i lxr l Iz i r lxrr l I l i j r rs l i [ i t : l l r i :

l ) ;u i i r ' tcr t t l t r ( l r r { 'n l i v i r l i i r t r l r ' , r o l t t t r r ' \ i t t t t r : l t t t r lot t i t r i t s i t t l l l l i r ,

/ / s l l ) r l l .

i , r | ' r i . r | | | r I r l r ' | | I r 'L r r r ' l i r i l r r l r t l ,1, l r i r ! i r r r r / i r " . l l r | l ' fot t t t : r

l i ' , ' , t ' .":t

, t l l r ' , ' , , t ) t l l r / l l r r ' ,

; / , r / t r r r I / r l l i

l i , l . r { r , r { l l ) , l , r

. r l l l r | | , r lI | \ )

Ambiguileton rutnnulut ,,:t" oste datoritl faptului cd. in serniperioadelesuccesive in cnrc curontul rm mnruri opuse, fricliinea este inversiti.; ad.iclcoeficientul dt: frr.crrro ltl rclrlntbl scm;lul, nu insi si mdrimea.

. Cind curentul i rc schlmhl din pozitiv ln negativ, ambii termeni ai ex-presiei pentru prr:sinnen sonomotrlcti l tgi schimll semnul cu toate c6 i2rlrdne tot pozitiv.

Vom considera scDorat tcrmcnul

*. 9zI2 sin2at : hz.S5, punem

hz : pzp!,

funclia y.fiint astfel incft pentru faze intre 0 gi zc sd. avem , : sinzr $ Irn-tru faz€ intre n qr Zzt, y: - sintr.Putem dezvolta atunci 1r y in serie Fourier, astfel

! : Ao t Arsinx { Drcosx } Arsinzx + B2coszx + ...Forna termenilor A^ li, B^ fiind dati de relaliile:

fA^: (Zl2r) \ ! sinmx d*,

I0

2/r

B* : (Zl?nll y cosmxdx.I

o

Trebuie sf, i.p{lr aceste integrale ln doul perioade: intre 0 9i r,t are va"loarea ,,*sin2t" gi lntre zr 1i Zt, y are raloaiea ,,-sin2;',.

Avem astfel:.tr 2r

l- : (lia) l[ sin 2x sinnx d.* - [sin2x sinzrr drl, I J J '

r- : 1r7"y [(sin ztc cosmx d.x-'(.inr., .o.r,, dr].TJJI

0

Flclnd integrlrile, oblinem

Ao : 0, B^ : 0, At : (8/3n)sin*,

An:-(8ln)(m-z)m(m{z\

9i ln finaly : (81") [s inr/3 - s in3.r / I .3.5 - s in5:{3.5,7 - s inT*/ .5.1.9. . . ! .

. Aceste scrii reprczintl curbq,: J, : sinlr (pentru valori de .t lnlre 0 gi n),9i -/ - - sinrr (pentru valorl do r lntre n gi Z?r),

...|ebq9 notat c[ prlnul tornon rl rerici estc cel nriri importlnt $i (lacllneglulm coilelfl tcrrnonl, putom rcrh eproximotiv

, _ (t/Jr) itnr,

. Valoarea cxtcll it prusiunii sonomotricr: cstc d,ate de {ormula (13) dcmat strs, care polrtc fi scrisir

l, : IlRo sinr {1p,.1(8/lr)(sinr/3 - sin3r/1 .3.s. . .)l

gi aproximativh - I(p, f 8prl/3n) sinr.

Fig. 11. - Reprezentarea graficea fuMtiei l , : - sine;r.

ln figura 31 slnt trasate curba exactl pentru y si curba aDroximativltinlnd seama numai de primul term,en aI serieii; la exlriinarea .oibelor aoarogYdgnt" cg pentru calculele din practicl putem, flrl mare eroare, nelfllototul afarl de primul termen al seriei, ca d priml aproximafie.

- _ Chiar ln cazul cel mai ri.u, clnd h :0, corespgnzlnd cu scurgerea tur-bulenti. prin orificii, eroarea nu este mare.

. Dlci se cer-e o rigoare mai mare, se poate lua ln considerafie gi armo.nlca a dorra $l obtlnem

1, : (8/3zr) sinr - (8/15n) sin3r :0,85 sin* - 0,i7sin3r.

Energia medie picrduti. prin frictiune este, lislnd la o parte termenulln p. sau -Ro,

2n 2^

w : (t lzdl hi.Jt : (4gzrzl 'z) [( t i l t '

a, - sin{sinl* ar.. .) .J J\3 3.5 I

Toate inteialele ,t't a" to.orlln 22l r\ sinr sinnrd.r - (l/2)\[cos(r, - l),r<1, - cos(nr + l)rdr]:dJ

,. Acclrltr rtl roduco simplu, finlnd rormB d do tormcpul tr t$ rru p1, h

tl, - fl(rril

' \s l f r , l i r r r . i l , r r , r r r

l l " ( / ' l i . ' ) ( l r , r ; j l ,11j3r:) .

l ( r 'zrr l l i , 1rr r r r r r r r , rL, . , r . r , l , r r ' : r I l i r r l luntai pt iuul lcrnten al ser ic i ; i. t rogl i j i .nt 1x: r ' r . i l , r l1r , r l i | , , , . l r , , r , , r r r . , i r , t roduce in I 'a ioarca obl inutb" peniruI t tc l t t l utet i i r r I r r :L, r r r r r l , r . l ' t . , i , : r r l l , r l ) , r r te, oste 1.rr ' , : i t posibi l ca in cazui i s j r f -r ' i ; rh: i t t u, ' t r t r , i I r | ) | , , r r i ( i I ( , r \ r : I , ( r ' r ( , . i i ! , l in sct i l lu i I s i prot iucir var iat i i in-l ) r ) r t r t l l l ( ] i l l natura r ' , 'zrr l l . r t t , lor ' .

In ploblenrcL irr r ' .r lc se rcr(, t l ir i nliuc pl 'ecizic, cousiclcrind fricl iun,'at.ir variind (lul)ar i( lr ir pitralului, i.\ ' ind i l) l 'cdere ci serii lc armonicelor lui/r.(nrverg lcpcdc, estc suficicnt a lua nurnai doi termeni, in nrodul acesta luind

- , \ ; ; r<l : r r( I ) , - I l l t l t r - l ' j (c, t - l /1. , r ) l '

Asl lc l o l r l i lcrr t :

H -- IRl]/| { )l!(Ca - | lLa)',

I,: I ltl La\17 +Fi@f, - ry,Y.G

/l, : 9a1:(0,1i5 si:rr - 0,17 sin3n),

l t - ,2:9212 (0,Si - ; 0,1?) =. | ,02 pI , ,

I iq. 32. - Cjrcuit so ic lDci ire rezrstenla Poatc genera

armonici importaute.D

l)cntru iU : ?i/2.A\€m

citto (l i feri. nunai cu 2oo diu 1'aloar-ca dalir dc h^," : prl2 s\n2x : 0"12.Analiza cazurilor in care u11 i{cncrirtor Dloducc curent absorbit (i,)

irrcrl i i , capaciti l i 5i f i icl iuni dc tipui lcgii piLtritului, sc poatc efectua prinItlctodil dati mai sus. Dac:i. sc cerc nLrnlai o prinri aproriir lalic, putem ad itcr:lt fr ictiunca urntcrz:r lcgca propon i0nalit ir j l i s:irnplc /,:1ii f i- luim p!'ntrul{ valoarea n :t-t.SSS"i.

])aci sc ccrc o piecizic ntai rnirrr ', l lrrtcrn introLhrc,.. o prcsiun, ., 'n,,-trtotticc suplimcntiLri l i l f.rpetclc organului dc fricJiule avind o flcc'. ' ,::rrLrlc trei ori mai marc ;i o amplitrrclinc cgaliL cu 0,17921..

Daci. cste ncloic a se ccrcctir o lcgc a fricl iunii diferi i ir, mctotia datir.lxrrrtc f i inci aplicatir. I 'entru aplicali i lc practicc totu;i, cste rnai simplniti suficicnt de rigulos dc a sc c rclatia clintlc prcsiunea sr,nornotricc ;i cr.ir, nt,stt lr fornta /a --, lt i ; i dc a lu;r pclitr-u ./ i o valoiuc nrcdic rlc-a lungul un,-iD(' l loitdc.'

ln geueral ,11 al i i clc torn.r', 7" . . r lr(i).

\ irm atlmitc pcntru Il o r. ir l<':Lrt ' uctl ic constiLntl-L pru'l ind pcntru , r)vil loilrc nedic, asticl ca vuloaica cfir ' irct: lr l tr i i l

i .- t,, . . rlvz,rl lrr l lccastir r:tcl ocl; 'L tr-rbuic l intitatir la cazuri itr (:arc nll Poiltc avcar l, ' : orczollrnJir t:u atnlorricclc srrpcrioarc rrlc lrrlsiunii ::ouonlolrit:c. I )tcir. ascnlcrt,-irc[ct:te <L: rr:zonnrt!ir sint posibilt, pr'olt( ' l t]a cstc difet-it iL ; i i l t luen]a a.rmo-ttict. lot rh: frccvuttir supctioari poatc [i corsidcralri l ir. Pcntru ir i lustra accasla,s:'! ( (nrsi([( 'r i[u urnlr-t loarr' lr nro]rletni.

ln f igulu 32 in G rLvcirr un g('n( r ' l t()r ' pr'<xltrcirrt l ru) r 'ur'( 'nt i -= lsin rrl.Itt / i r:slc lrn :rpitrat d,r Iric!irrnr: ulrrt inrl lcgt' ir yl-rl lululrri ; i arrrrmc o

cottr l r t r : t i r . , ru l i r rL ' t l i l r t r , . l ru tn i r : l l ( i r t lc l rccl : r l r l l i l i i lo l rL. : r l i r r tcntare l ,1f . l r r / ) y i , l i s in l , lorr i i r r r r r r i I ic i r { i i i r r l r r r ' : rL, l r .o l ( i r r i r r r l l r .s lxt l i l o inr . r t i t : Il i t t t i t I r ; t t i I r t I t : ( , ' ; 1t t ls i t t t t l r r sotrr t t ro l r icr . r 's i r , / r i l r t ( l r t ( ,nt i i i r r r ' , '1, ' l rc i r , r r r i r r r i

r \ r ' r ' t r r ( / ) ( / , ) I ( /u) I ( /1) , , , i , l , r r ; r r r r l r r r i l , r r r l r r , r r l r r r A' , r r , r l , , . r r r .l l l | i l l i . , , r | r , l t l

Accsrc lormule silt ob]inute in ipotezadin seria lui Fourier Dentru lr.

Daci linem seama de faptul ctr Z are o serie de armonici, estcca pentrul rinul din acettia, stzicem a\ ,ft-lea, si. avem C Lm2a2:

c[ pf,strinr numai utl t|tItt|rt

Po', i l , i ll .

Pentru aceasti frecvenli., inerlia Z;i capacitatea C sint in rez(trattlar

;i un curent tlc o frecvcnlir de zl bri mai mire se va scurge pin irr('rli(:

i i condensatori; acest curcnt, daci. nu e nici o pierdere dc energic in citctt i 'icle iner,tici $i condensatorului, poate deveni foirte marc. Astfel daci'L A'//.rrcstc o fracliuirc foarte mici, apr;ape intreg curentul f va trece prin {rir: l irrrrr '.rl l ; i un curcnt {iLri. lucnt, considerabil, de o frecvenll de rl l ori rt lar rrrlroca. cca iniJialir. sc va scurgc in rezonatorul format de inerJie ;i capircil r lr:,pcntru accasii arnonicir superioarit.

I ;orn ' t t l ' 1, ' r : is i t " mit i sus l )c l l t tu 1, q i 1" ar da in acc' t caz l t t r t t r i r i ' t trcntul. lrccvt:nlci. fLrn<larlcntlLlei ."." p-oii" i i negli jabil; curentrtl p( rrlrt lirrnlonictlc srrpcrioalc irr condcnsator ar f i considerabil mar mare'

I ) r rc i r t r r l r ts i r rvcnt / ,Crt ! - - l , cste intposibi l ca rezonanta cu , . r l l r l ' ,1r i r I l r '

srtpr:r ' i0rrr,: si ailr i loc.I 'rob!tnui.A src ghsi r:ocficicttIrrl rL' pcrdiirn{iL S printr-o dcschiclqe dc scclittrtt:a

r , r i r t i r ' - r r r t l ) r ' r ( ! lc i rs(z, i l t i t t dtutnul curcntului .

". l )rrl i-L Pl'sirrrrr ':r sonorrtolrirrr cstc /, l i curcntul cste i, l trt ' ttt prit l , l t '-

I l l l l I l r )

i 5r . I t4)

l r i . i r r i t , z i r l i , l r i r l r r l r i 1,r ' i r r o l i l i , i r r ; i / t r l i f t ' rcrr l : r tL: prcsi t r t re r l t ' r r t t r l ' l t 'p i r t r i r l , r ' r i f i , i r r l r r i : ; l i r r r r l i t r l r i r l t rx l i r r i t t t t i r : iL t i r

, pll zslnll,I t t r ' i t t r ' '1 r" '1r . ! f i t ' r ' r t l i r lcr spl l i l i l i l i r u i r l r r l r r i , I r , r r l t t lq l r l l r l i l , l ) i ' t l i r t l l l l l

or l l ic i r r i r r l r l l r lx . r . l r . srr l r { i tc r '11rr l i1 r ' t t l i t l r {1,(r l ,

At ' , , t r r , r ' .1 l r , l

{ t1}t l l t l i l t 1 l , t l f t l r , t1 l , i , . , i , 1, , , ' f . , , ,1r , , , | ' , , ' l t l f r1; l ,h ' ,h

9i deci

s.*rymnVedem ctr S nu estc r:orrrlnrrt Cl rtophrrle da i,Energia medie oierdutl po ro"urull irdf tJc||riuo, drcl admiteu pen_tru S o valoare meiiie, ar fi

w *.\ lr l t _ trt2;t,unde .If este auplitudinea lrri l.

Putem obline, de ascnrcncl, vulorrou lcottol energii din {ormula

w _(t t \ l ih i t .J

Dar am gisit

i:p,rVT&ii,dln care

h : Tizl?tL\nzg

il obfinem

ln modul acesta, oblrnem

W : (1l3l2ngi,2u') [sint*

dr.

dDar

q

I sincr a* : r/1,IJ

astfel lncit obtinemW :2tFl}rgvzuz.

Comoarlnd aceastd valoare a lui 17 or aceea obfinuti mai sus, anumoW : Izl?5, gisim S - }ng*ot?!\l, 9i punintl I - SH' oblinem S -: prl,lt tgla.tE.

Pentru api avem.S: 15{0por/ /F,

ln care & este coefici€ntul de contraclie, care variazS, <Ie la 0,5 la 1,1 duplforma aiutaiului orificiului prin care se Iace sorrgerea.

O vatdare medie pentnr aPd ar fi

S : 12oo rr,lllfl

ExemPLu, numuic

A se slsi Duterea pierdute intr-un robinet care nu inchidc per(cct,merimea ori-iiciuiui <,r llsit deschis, fiind o zecime de cmz, iar presiunolsonomotdce I1 : 100 kg/cm'.

Dnergia pierduti pe secundl ar fi

W : SHzlz, S:1200 - 0,1/y100:12cm5/kgs:t , , .1s-romfNs,

W :(rlzTspz.n\l F&.;

. Daci o' este funcfia arnonic5 simpli, d: lsinal, aver4T

W : (yls l|T&Lz.r\lsnsat dt.J

Substituind pe r ln locul lui at, ob{inem2E

W- (TIsl4ng,;''l'z) [ sins*dr.

;Dar

2n 2E? ? pn

\ sin8* dr : \ (cosrr - l)d(cosr) : lcosa*/3 - cosrl l' : o.t t lo

. .A-gS.t rezultat, lulnd integrala lntre 0 qi Zr, estc incxact deoarece1o^"!t funs totdeauna pozitiv, surna- Iucrului ln timpul unci pcrioado difcrlc0 zerc, Itroorea provine din faptul c[ la invqflsrco curenfului pr$lunooronomotncc e!te, de asemcnee, inversa.tl, utfol cL lnlognlu qrto do rcrangpur pontnr cclo doul somipcrioade. Prin urmlru crto hjcorrr r, cfd tui-riip jlmptl rrncl rcnript, ontlt. 7)2 ,;l l.l rlulrll rpr.r. I obllnn lucrril afr.ctunl

( l6)

( l ?)

astfel lncltW : lZ,100zlZ.:60 000 kg cm/s,

iar outerea Dierdutir, ln CP, este 7,9 CP.' Este evident, prin urmare, cl o deschidere de scurgere de o supn-

fa{tr comparativ miil provoac[ pierderi de putere considerabile. Curentulorin rleschidere cste dat de

W - HIIL, I ,-zWlH =- 2.60 000/100 : 1 200 cm8/s.

Amplitudinee vitczcl va Ii

V * Ilu - I 200/0,1 + 12 000 co/r,

Acclts crto o vltell lorrto olrc ll cfcctul rpcl ctrc sc mitcl lncontrct c{ motdut, lo lrrmon.t vlterl, lroduco roPldo rupr ncddr.e tlnodonr m.trluhl' Ertl olrr Dttn urrrrrc al ln rr m|r crlurl trohrlorwi lrl mrl Drr| |?Ur dl r lrcl Inchldrrllo Prrldct ltrnF D0ntm ! rvltlmrlolro no$luRturl,ln llurjrrl rrurl prr.loirrh, trtnploto,

i l

' , lnain_te de a proceda la discuiiu dlfcr.italcr tlprri do motoars rotative,lcflonate.de curenfi sonici, este bii. d Ji'.ii,irtiii.i n,,i"o'ia.1t pri;it;;;lr miqclrile oomunicate fluidelor ae miy.fiilc ,:.,1^ti"i,

-iintru pi'st"".r"- 9iclllndri.

Am definit prin termenul deflasamenl al uuui piston sau al unui curent,Olatitatea A:(;ar, in care I este cureDtul (frg. 33).J

I \ t ' t t | | l t '1, Vl , l , , ,

'rrr()t|IA l)Dt't,AiailttilTllu,l], il{ol.t)Alu.]llolht{txxr||ln

I

I

Fig. 33. - Piston autrenatdc un nrecanism bieli-

manivele.

(2) Deplasaurcntul rlatorit lotaliei rrrui cilindru in jurul unci tuirrri-velc sau unui cxcentric fix.

Rotafia unci manivele, legat' cu un pistorr printr-o biel?t lungtr, dl1 pirto-nului o miqcare alternaiivl sinusoidall iu directia axei lui.

Daci zo este amplitudinea manivelei gi a viteza unghiularli, ervt nrf : - ro co' A.l.

Cantitatea z s-ar numi maniael'a san excentricul deplasamcntrrlui. \'onravea de-a face mai tirziu cu manivele rotdtiae si maniaele dlkrnal.iac. ln rrr,xlulacesta defini{ia manivelei sau excentricului este extinsi gi include o nranivclllcare este variabill nu numai ca pozitie dar gi ca mi.rime.

Relalia intre deplasament gi manivell va fi insi totdeaunt 8, !.1r.Daci cilindrul se lnvirte5te ln locul manivelei, sensul rotatici fiinrl

acelagi,. curentul va avea aceeagi valoare dar va fi de sens opui. Pulcnrreprezenta un deplasament alternativ printr-un vector a cirui valoarc o.[trof,l, rotindu-se cu aceeagi vitezi unghiular6 ca gi manivela. Pulcm airrrrclintrebuinta notalia simbolicl.

Daci deplasamentul este reprezentat printr-o linie, deoarccc avr,ult : d8/dl gi varialia este sinusoidalL, curentul va Ii reprezentat printr.olinie perpeirdicular'f, pe prima. Figura 34 arati deplasarirentul datbrit ro.taliei unei manivele, actionind un piston intr-un cilindru fix. Curcntul ppodus va fi i : d}ldt.

Dacl cilindiul s-ar roti iar manivela ar fi {ixl, ajungem la condilileretati in fieura 35, avind i : - dE/&.

ln caruil general cind direcfia rieigcirii alternative a pistonului difcr!,de direcjia deplasamentului, precum se aratl in figura 36, avem pcuttucurent i : d(8 cos p)/dl.

dc osil

Reamintind cii : lQ : Adrldt ,

ln care u este viteza curentului in momentul , intr_un punct la o distanjiI de pozilia medie a pistonulur, avem

___ D::i

1 Tt..9 funcfie_ sinusoidalt gi dacl luim originco rimpului inmomcntut Ctnd plstonul este la punctul extrem, avem8 : Qzo cos cl .

Din definifia de mai sus obfinem

Fig,3{. - Deplasancntrr l I Fig,35. - DeplasomcDtul S Fig, 36, -- lntr(! dcphrn-chd ci l i rdrul oste f ix. ciDd ciuldrul cste lrobi l ment si dir(.cl io miscit l l l nl . '

jor Dl&nivala cste Iix5,. teuoiiv€ eriit!,url docllrJ.

' ln modul acesta, dactr se dl centrului O un deplasament 8, Ilclndsn unshi 0 cu axa pistonului, curcntul total ln cilindru, presupus ctr sc ro-tqteci o i,itozlt unghiularl uniforml 4 in direclia slgefi, va fi d(8cosp)/dr,

/lllr, .r7, - (Jlrrl ollindru. y'lui nrolr l l t l o ( loplrr& tm!nlulul o.| | trulul da rotr.

llo rl nn tvol.l,

a:toar:or*c. (u

\z)

i : d' ldt.ln opliceror teoriei lo motoaror vom oy!!' rlu conriderrt tloul. crrurl:

.,- _ {!)_ ?.".p,}."nonrul fntr.un cllindru flx. prin m[crror, pi*onrrlul logctOo o Inn lvr l i l r l | l l oxccntt . lc f l , lnt iv.

- -1T-- - '[, i- * i0pqrrr fldbrjuoco p * r,'t otrllnrm Drl d.poit6 prln

' \ ( ( , r \ l l . r r l l : r ' , i , ( : l l t l l l l l l r , l . r t r l , . l , r r r r r r r l . r ( . | ) r .s l l cchivalel) t cu doi

crr t , t r ! i r r rpt : r l l r ; i , l r l r r r l r r l i (1, . r r . r r \ , l , r , r t . r t r r , , l , . , ' l r r r16; int t ' l /2 invir t in-( lu s( : c l ! v i t r 'z t lc t t r tg l t i r r l l t , ' r , , , , r , r r | , r , r , . .pr . r ' t iv . ln modul acestar l r .PlrrsrLntr . r r l r r l l l lx la l t l i r :orrs i r l , r . r l r r r r . r ' l r i r ' ; r l r . r r l r : r r r lorr i r t leplasamentcrol in( l l l -s{ ' in r l i r r t t i i opl ls{ ( r r r rcr ' , . r r ' . i r i l lz i u lAlr i l l l r r r i r a.

_lr()t()AnD

CONSI DDR-1.1, 'TI GENDITAI-I]

ln capitolul II am arb.tat prin principii elementare ci, daci. sc comu-rrrr,t rrrei coloane lichide presiuni altcrnativc, trenul de rrnde produs, carcr'rtrrrli i dc-a lungul coloanei lichide, poate ceda intreaga lui cnergie unuipt,lorr situat in orice punct a,1 coloanei lichide, cu condilia ca pistonul sitnr. rriflr) clr aceea$i viteza gi in fazf cu stratul dc lichid ce sc afli in con-lqr'l irrrrrliat cu el. Aceaste conditie estc indeplinitir de un reccptor compusrlittlt rrr piston, o biein;i o manivcli, analoge cu pistonul, biela;i manivela11r'rrlrirlotrrlui, cu condilia ca manivelele gencratorului si rcceptorului s[ scIrrvlrlr';rsr',-r cu aceea;i vitezi unghiulariu ;i la o anumitir rclatie de fazi,rlrpirrzirrrl rlt ' relalia distan!ei dintre pistoanc cirtre lungimca dc undir, aIt, rrrrlrri rL.rrnde carc circuli. in coloana lichidir. l lstc clar, prin urntare, cirrrl rr1 { ltlor sau motor de acest tip poatc absorbi encrgie din ircnul dc undctttttttiri rlirr:ir funclioneazi. la aceeali vitczi. ca gcncratortr], lJn ascmencaIrrolor il v<lrn numi motor sincron,

lislr: t:vident ci un motor cu un singur piston, o biclii ;i o manivelii,lsllr' l crrrrr s-ir considerat mai sus, va cxercita un cuplu carc valiazi. in tinl-l )u l u l ( ' i r lvolut i i Ei daci sc ceLr o rotat ic cont i r i r r . i corr l ra rrnei sarcini ,c$((. n(:(:osrr a se intrebuinla un volant. In afarl dc cazul, totugi, cind unrrslf('l (l(: motor ar fi pornit si atins accca;i vitez:a ca generatorul, el nu vafi in sl;rrc sL invinge inertia volantului sau sir rlczvoltc un cuplu. De aceeacslc rrr:cfslr a da unui astfel de motor o vitczir unghuilarl foarte aproapctl rr,cr'.r ir gcneratorului 9i dc a-l prinde (agifa) la o {azii proprie pentru- a( l l .zvr l l l i l r )utcrc-

l):rt:i. intr-un rnotor sincron in loc de un singur piston intrebuint5.mItci pisloanc, solicitind acelagi arbore si mi;cindu-sc dc-a lungul unor axc

I r ig. 3 l i . - Motor s in( i r (mtr i f rz;r1.

tk: f l rz l r l r : l ; r l2O" sulr rLr : ! i r r r r r ' : r : r l lc i colorrrr l l ic l r i r l r . , i r t r . : r lc r . i r r r r l , i l l l r r r r r irL: r r r r r l . r l : f i rz;r t r : l :L l2O" i r r l t r . r . l r . , : ; r . v, ' r lc i r r r r . r l i : r l c i r l i r v i l lzrr r I r ' , , i r r r . rorr i I i r r rsr . v l r r l ,z-vol l i r un (ul l l r ur t i l r ) r nr , . r ' , l l r . l i r r r i l r r r r vol : r l l , , . r r r o.r l l . i i r r r . r l i r .nu : i i r l n i \ ' r ' r , i r t r ' ; , r r l r l r r l ,1, l l r r t r r i t r ' . lo l r r , , r i , v : r l i r r i r " , r i r r to lorrr l r ' . r l i i r r r : rl r r r l , i l r l , . r l , ( ' t t r i r r ' r r l r . r r r | | r ' r ' ] , r r i | l r r l r l r r l | l t r . r r r r , '1, ' r r r l , . r | | r ' . r l . r l r . r | | . lo, . lI t . r l r , l ' l r ' . . r l t , . r ' , l l r ' l r . r . r r r , I r ' r , r { t , r . , . r l t r . . r r l r r t l l r l . r l r , | | l l l , r I ' , I l l l , l |o

lotrr l r r i s i r i t l i t r l l : r v i l lz , r ' , t r r r ( ) t lat i r l l r o s i t t r i t t t i ro l i r { i r ' . l l r r t ts l l t ' l rL rrr , 'Iol i l v<rrrr luf rl i ur nolot sincrut lr i lc:ut.

Un cxcnrphr s inr l rhr r lc un i ls t lc l t lc l rot()r ( :s le i l l rstr i r I in I igrrr . r t ls .I-:r rrcesl motor rotorul consti dilttr-un disc inclinat, -4, I ixirl pr: t ltr:tr l 'ot, 'B care sc invirtc;te intr-uu lagil C- Statolul estc fonntt t l in lrci r i l irrrlrtt l ispuli uni{orm in jurul discului, ial trei trenuri rle undc, dif(rrirr(l i tr l .r/ icn l20', lucreazi. asupra pistoanclor D iu trei cil i l tdri, api'rsirrrlrt lr rutrlr.rrrnci plici inclinate. Este cvident ci. un asttcl t lc rnotot viL lttt:trt pt,.ttttts-ir dcsclis urai sus, adici va Iunctiona nurlai la o vitczil sircrorri r u lt( rllrtorul, sau altiel nu se va lnvirt i deloc; a;atlar, rt ici o virri:rt ic r|, r 'r lr r,rru va {i posibilir cu un astfel de motor.

Si p lcsupunem ircum ci in loc dc placa l , i r c i t ro i i r lc l in i t r ( ' pr ' . r t l . r , '|str: {ixir, lrvenr o pl;rc:r sau un scgrncnt 1', prrr:urn sc aratiL irt f igur:r :] '1. .,,r

I r i : . 19. - t r lor . r f i ls i rct i )n1r i l r rzr l .

/, ir l ir l)o uIr lagi-rr in hrrnrr"r rlc crtl l l"L sfcrici"t, f irati 'L pc lrrln)lcl( / i i tr rrrrul rt t r r : l r i t : , SiL l ) rcsul)ur l r r c i i . t t t t cx is i i r f r ic l iurr t ' t r ic i i t r ( rc pis l t t i t r rc l r ' / ) ' , r l , l . ' , . r7 , n ic i in l le pl : r ' i r 7 ' f i cupi ; f ic p istoi l r le lc act ionalc dc l r t i t r ' ( t t l t r i , l , r r t r , l , ,

l ) r ( ( 'um s- i t r lcscr is tn i r i sus i l l o i rzul nrr l lont l t t i s inr : toIr i l t ts t ra i i r t l r l l r r r . r l l tSc vt : t lc ' i r r r r r l i : r l c i r i r r rccst c i lz l l r \ ' : l r rvt i r ktc o rol l t ic iu l l tnr l , r \ r l t l

or izoulal , n ic i ; r scgrrronlulrr i l l , pc cart : i l vom t t t t tn i t ranst t t i l ; - r1()r , r r ( r . ltolotulrri 11. fol cc sc vrt itt l i trtpll cst(r cit I r i lr)slnil i !tortt l 7'vlt oscil i t i tt , rt lr.r,i rs l f r l t :a l in i l r rL ' , , i r nt ; r i t t tatr : i rx ' l in;r l i r : u f r ' { t ' i l r r i l } l i r t r ( 's i t l lcn( ' r ( z l r ! r r r r , r r ,i ; r t r r r : r 'asl i r l in ic sc v:r r t t i l r ' r r pt sr tpr l r fa l ; r cot t t t l t r i r :u v i l r :z i t s i t r t rot t i i .

I ) ru: i r cxis l i r I rcr ' ; r tc i t r l rc lnutsnt i l iLt ont l ? ' ; i ro lotrr l , l i , f i ' r l i : r l i r r r r ro rczis lcrr l i i l l r i r rv i r i i l r ' , i r l i l l t i rnsrt i t i r lo l l ! l ( i t f i ro iorul s{ ' vor i r rv i t l i l . rv i lcz l s inclrrr i i : r t r :oI t t I r i t r l t t i : t v l r f i r t l t iv i r l ln l l - t c l l n lo lor t t l s i t t t to l t i t t j i l . t l

I t r I igrrra . lS, t r . r r rsrr t i l i r lorrr l r t tcr t { i t t i r t r I o i t r r l in:r l i r ' ( :ot)s l i tn l i " r fa l i r r l r ' . r r r r l

0I iz()u I i l l . ll ) r r r i : r ' rntr l . r ro l : r l i r r t t ro lot t t l t t i s{ i ' l ) l r t l l r le is l l r r l i i , l ) l i t t n l ) l i t . r l r ' . r

r r r r r . i r r tc i t t i , r r l i l to lotr t l c i l :1 i I t i r t t : ; r r r i I i i I r r r t t I i l i vor i t t t l l i t t i t t tc t st t l i t t , t r l

r t ' , . i r r . r . , lu, i . l lo lor t t l l r , l t t r , . t v i r totr l i t r r r i r ; r r l lu rol l : t t l t l l l l l r l l l . Sr ' lxralc v l t l r . r

, l t t t i . t ' t r r , t l , r t ' t i l r f i t ; r I t . r I tLtrr i I i i Iotr t I r r i l . r { , r r l l r ( ,1(rr r ' r ' l r ' l } t i ) lx) l l lotr , r l . l

, r r r l r l r . r , ' r r l , r , l t r r l t l l t l l r . r r t t t I 1 | r t r t | . r r l t . r to lo l t t l t t t ' , ,1 v i l ' / i r " i t l l tot t , i .

i t r r . t t r '

t l r r rp , , r . ; , t , , r l r t r l r ' 1, t , t r l , t , r l r ' , r t t t11l l r l ; r lot t l . t l t t r { i r r r r i i , l , or ' r i l i r l i l r l i r r l r r '

I t , | | | , | | | | I i I I | , | ' , . t r , r l l t l l l l . r t r ' r l t t t I r Io,r I , | , r l t . r r , . r " l ' t I r l l l ' l l t ' . l t l l l l l I l l l ) l l l

,1, ; , r , r r r t t , , . r ' . t t r i r , r l ' , r l , t l r . r . l r / \ t ' l l ' r l , i l l , r r I r r , l l r t \ t l r r , r , l ' t t t . r l , r vt l , r , r

, i f r f f i l f r , l i f , r r , t t t r r r t t t r t utr l t t t t , I ' r t l t l t . t l t t t ' t t t . t t t t t .

,';rli \\L . , r l r ) /

\. D ,/

rnt

O;r l l . r l , , r r r r r r l r r r ro l l , r r r l r r r , l r r r . r , , , r ' ,1.r r . r t r lq l ) r i r . s | i t t ; l l i ! i11 f igur.a 40.Molot t t l t t rPt i t t r l t ' t t t t i r l l { l l ( l l , r t / / | . r ' l r l l r . , r r , t l l i l tsnt i l i -Lt()rul , iuportatdc pistoir ,n, : l r : ;1, 1 i , ( , ' urr i lorrrr { l r . l , r , t r j r r r r r l , r r , r r r r r I l r i r r I r . i l l i . t ln al doi lcincl , l j _est t : l l r ( , \ ' : rz,ut i r r i r r l , r r l ru l l r , . lu l l r / l r r r r r r LrAl" t r t r t L i ie cste dispuslntrc r : r ' l r ' < lorr iL i r r r . l t ' . l {o lorrr l r r r r r , t , r i l r r t t , t r i l i r r l r i p l .cvizut i cn pistoanc

^' ,

R' , C' , tp i is iur l i rsr tprr i r r r ' l r r l r r i / ' .

nr i r t l r l t 'u ; t t t t l r I r I r t r I i r r , t . r l r ' . i l t l t . \ ' ' t l ( ) r i s- l t l i t r \ i l l l l l t l l l (n l r l . i l l

\ r ' l ) \ ! l l l o| l l \ r ' '

ljl,l;l:lj;l:l t;lllrillil,i:,;.'l.t,i,itl,:l,iti:iJr,t;liiitl:ill,i]i]iiiillf";jli,t ic i cst( ' c t l a l i t t t t l t i t t t i t t ' , cu

i i t t , i t . , , i i " i '1" cr t r ' ' ' int t l i : r cslr ' l r l : rs i l l i ' I r i r " '

I r i l r ' r l l t r r i l f i r \ ' rn (rnrr i l r l

;;',,,;;r;:.;,,., ararriinrisrrr.{ll,li::-lllf ii.,\ll,;lllli.',lill,,,,lll:1,'dt'Jrlasamcntc rotirt lvc dai.orltr

l i js . 10. - ] Iotor nsincron tr i faot c.rCf," , , , . " l ic l r i ( l i , i r ( ) tor .

Cilinclrii rotorului sint in comunica{ic intrc ci prin mici orificii. I'is-toanele r1, B, C ale statorului lucreazi. in cilindli 1ic5i, in lcg;ituli cr,i trciconductc conlinind lichid, supus 1a presiuni sonicc tlcfazatc intre cle 1a 120',Aci:asta inscirmnir ci pulsatiile lichidului in celc trci corrriuctc de alirncntaresint proiluse de un gcnerator format din trei pistoanLr defuzate Ia [20. Aran-jarncntrrl conccntric ari.tat in figuri. este pur gi simplu diagramatic, iar inprirctic:r statorul ;i rotorul pot {i a;czatc rLlirturi unul tle iLltul. Inelelc 1)gi Ii sint soli<larc in cc.ca cc privcste miscalcl ccntlului lor comun O, da.r' scpot ir)virti indcpendcnt in jurul acelui centru, lunccu'ea fiind inlcsnitiprintr-un lagirr cu bile a;ez,at intrc elc sau oricc irll (lispozitiv contra fri.-citrii, binc lublifiat. Acest ntotor cstc pcrlcct arrirlog iu pr-inr:iiriu cu alltnrllttt iu figurt 39, rczistent:r dc fricfiunc dintre tlausrrri!i lor ;i rotor' [i inrlinkx:ui t i r pr in rczistcnJa Ia scurgcrr , a l ichir l r r l r r i r l i l t rc r l i f , . r ' i ! i i r i l iuLlr i r i ir ( ) lo l u l l l l .

LIn al l t ip ( l ( : motor cstc i lusl lat in l igrr t : r ' {1. l , rL rrr ' r 's l r r ( , lor r \ , (n lt lorr i r p isto;rnc ,4, l i , l l r rxhrcind o l l r r :s iunc rr l tc l r r i r l iv i - r , crr l , hr i r , . rzrL rrsrrpr;ri r r r : l r r lLr i / ) in r l i l rx:{ i t X,Y. l r r r : lu l , f ) r 's tc corrr : t r l r ic crr i r r r ' l r r l / i , r ' r r r r ' : rp i rs,ri ; i sc rr t i ; r ' i r t : r r p is lorrrr l / ' l l toIotr t I r t i . 0 i l i r r r l l i i , i r r c l r r , l r is lorrrrc l , / ' l r r r r r lz , r ,r r r r t r r ru ic i pt i r r r t ic i or i [ ic i i pt l l r t r r sr ' : t r : r l i i r r l i11rr t i ,

Aur v izr l r ; i r r t t t r r t t iv l l ' t , r l l , r r r r r l i r ' . i l t t l t in, l i r l r r , . r r r r r t r r t l , i r l i r , r l r , .c i r , , . . r , r , l r r r i . , ; r , l r r , r l r ' l r i r r l r r r r l l l ' | | r r r lotrrr r t r , r r r i t | l r , , | | I ' r | | , r I i \ , . r \ ' | | r ' l l i l

tnl

l i r : . { l i \1"1r ' f i t ' in ! " t r nr0rr"{rL7nr '

t i rca rotorul t r i v i l ,z , l , l l l lg l r i r r l lLt- t l t lc c" lor t lor t i t ic l ' lasl t l l t t :11( 11) l i l1 i \ r ' l r1 l

.ia?tr. ,,ri ', i ir,,rli ,,,,,,1 ,l,i ',,ltul, putcm prin invir.ti l.& r'otoluhri sir Ir.r' 'r.rtrr

o"oal* . r ,a, i , r* i r r r , l t r i , . i r r l , , r ' t , l . i r r lc1i6luc c l t t t act i . l tL l tz l . l ls t l l ) l : t p l ( r l r t l l ! l

; t ; i i l . . : i , - ; t . . . t i . t ' ; ' , , , i , ' , , , " r11' in ' r l ic i i ts t tpt . ct t t .n! i l . t s . r ' t ic i r l t . l rctr ' t t { : t

fc l^ t tv lnal l l l i l11 .

Nr 's i t t t t l l t l t l ) ( , i l t I l l l ) l ( ) ( l t l \ i r , ' l t ' ts t t r t t ' t tc l t ' | r i t l i t r t t l .a l l t lc t l r ' .1" 1 ' l t

t " r t " ' . ; i , " ; . , : ; i , , , . , i i , ] . i , r ' " r l , , i r , i i , , . , '1rr sc

' , r t crr .s i 'u i r t r ( ' lo iLr l ( i r r ( ' ( l : r r r r r r l

, ' , i ,p iu i^ '1, , , , t , v i icz ' . l r ' . ' \s t f ' l r l ' r t ro lor t rc l ( ' \ .ot l l n l r l l l i )n.L! ! )n) ' ' nst t t t t t ) t t '

, r t ( t t lo l t t , t l ' . l . l l l l l r ' l r ' l l \ l l ( l t . l ( \ ' : i l ( ) l n lo loarr ' r ' ' l r ' r ' i r r ' l ) r ' \ - ( ) i ( ( l ( r ) l l l l t - i l l r '

r t l : t t iv i i r r t l , l { t l ( ,1 ) l : l i t l r ) t . i r l : r iutr : t lc i r sr ' ptot l l t ' r ' r ' l l l ) l l l l '

' i

r i I r rp l r t l

nrr r ' : l , t t t t i lot t t t i r r t i r t r | r t l r lvrr l r r l i l i '

L l t : t t r ' t . l l tP r l ( l l r . l ( t l . ' l l . i t ' " "" "" t '

I l l r t r ' i r l r ' t t l r ' i t s l l r lot t t l 5 i lo lot t t l

l " , l f i , i i , , i^ , . ; , ,1. , ' t r r , ' , ' , ' , ' l ' l " r l t r r l i r r l * r l ' r l i \ i t r r ( l t i ( i r ' r ' / " t l r " l - ' t r r r ( ) l ( ) i r r . l r

rh ' l , t t t ' , r ' t t t . , t l l r ' I l l l ' l l r l l l r , r \ t t r l r " l ( 1r ' I r r '1. ' l t t r l t l l t l r t ' r ; r l r t r l r ' \ ' i l ( z l l s l l l ( l { } l l l '

i i r t ( r t t r t , , l , r r r t t l t r r ' l l l r r l l ' l ' 1 ' r ' r l r i l ' t " ' l '1 i r r" t r i ' t t1 '1 ' t t t l ' t i t l t l l l I l i l t ) t ' l l l l l i '

l r r t l r r r t . r r l l t l l | r ( r r ' ( l , r t r l r t ' l t r r l I I I I I I I I | | | t t ' r l l i l r l r r i l " r r l r ' t t to lo ' r l '

r l r , l r ' t i , r ' t l r l t . l l

i l l l l t \ t t i ' , t t t t , i r , / , l ' r l l . l r l ' r r l r l r | ' l ' r t t t r l l t ' r l t ' l l r r t t l

|o l i l l lz i l l ( ' r lof

t t t . r l r l t t r l t r t r l t l r r r r r . r r , l ' r r r" l ' r ' ' t ' l r l r l r l l l I ' I | | i ' | I I | | I i I I ' ' r l l t l r l r ' ' l l l l r r ' r ' l r i

l r t t . r , r ' r l " , r , l r , l r l ' r t l ' r r r r / l ' r r r r r r l ' l ' '

' l i r r l l r

' ; r ' r r t t l ' l r r l " ' l l ' l . :1! l . l

r l r , l r t r l , , r ' , i r r r i , , r r l r l ' | t ' ' , "1

r t t t t t t l r l r r l r ' r ' r l l t l ' l ( l ' " ' r r ' l l l l ' l ' l l t l { l r l t r " l l r r l r l r l

l l r

lt::i l?, r ltanivr.lir lrri yi o lrrr.l.i ttrrlJit. ArrrPrl Pistouului lucre;rzir o presiune

/r ,l/ sirr (,,/ ,1. O).Accasttr presiune protlucr. urr r.rrplrr inslunlirrrcrl rl,l ..= //re sin(a1, * g), ar Jiindvitcza unghiularl- a rrriurivt.l,.r; irl,{I v(, l ir\t.a

1;,,TTi,,1{,I"f,#(.,/'l q}), (ltr sinasinp : (r/z)l.cos(n- p) -M:(rHap) lcos (a, - a-1 -l_ ,1, _ q, _ cos@fr1 + p _F ql.

.,,,u,n t,t""'l.f""ot" pulseazi gi valoarea lui medie in timpul unei perioade

w.:1r1n1(a at,*

7'fiinrl durata unei perioade de pulsafie, astfel ci aven.rM.

- Q HAl27') [sin (a]---ar * { _ o)/(ar _a) _sin G,+ ot +{ rlt I o)l(a, { a)l[.

Vcdem ci daci. a, nu ".1lrlg1l:r.f: ar.est cuplu este zcro. penrru c.1{trrl,ii

.lcrmeni sint fun;tji penoqce o.e trmp.(ilnd lnsl at : a, avim 9i rf _- OM : (t HAp) [cos({ _ O) _ cos(2at T ,l + o)],

l\rlr.rrr :rrl Ir.l .irrr1rIrIicrr r I.c rrtonstrtr !ia pentru cazul curenfilor poiifazrrtil)r:rrtlrt rr g:'rsi r:rrplrrl plrxlus de un motor polifaza't avem nel'ole nulll irr

'rl: r, clk:rrlir lrrr:rrrl 1rr: sccundar pentru fiecare fazi, a lua suma 9i a o tlivirl,:prirt vitezt rotorrrlui.

Si. presupuncm apoi cd. avem un motor at m faze gi cl voim a calt:ttlrrcuplul constani corespunzltor vitezei sincrone. Fie f curentul @axinr tlirrtr-o fazi. ;i Il maximul presiunii sonomotrice. Avem pentru lucrul rnecrrtti,al un.:i fazc

Wr: ( t IZ)HI cosa,

O fiind defrzarea dintre curent gi presiunea sonomotrice. Cuplul motolrrlrrrva fi

XtI : (mlZa)EI cos <D ,

valoarea rnaximi" estc

M : (ntlza)Hl : mrQII lL - (nlz)JII ,

ln care r este lungimea manivelci, Q - sectiunea Jiecirruia din Pislorrttr',m - numi.rul de faz.e, A ,: z() - amplitudinca tleplas'rmetrtului itti t rttrcilindru.

Daci energia absorbiti de tnotor estc If iar' \ ' itcza Lrniil l iuliit,i ,t,avem, de asemenea, M : Wla.

Analog, <1aci considerirm ur1 Senclator avind rz {azc, cr.tplul r:rttr: ltr'buie aplicat rotorului pentru a producc m curenfi, defazali crr 2;/rtt, r',r ltM"- mWr1u, unrle IPi estc energia cheltuitd in fiecate' Iirz..i.

Dacir fazele produc lucru intr-un circuit avind o lrzist('nfit /1, o ittct

lie t gi o crpacititc C, energiir pierdutiL va fi Il" : (li})Rt!, irtr(h / ' .tr'curcntul unci faze.

Inerlia I ;i capacitatea C n-au nici un efect asuprt vrrlolii lrtplrtlrtllntrucit nu plovoaci. nici o pierdcre dc encrgie.

Exenlle

A sc girsi lrtngirtlca unci rnanivclc pentru un motor tlif:Lzl1 r'rt r i l irrrlt r<lc 2,5cm tlirrtttctt'tt, tlcstitutt a producc 20 cai putcrc la o vitczl"L rlt ' ('t)t)r,'volulii pr: ulinrtt, prcsiutrt:a sonomotrice ll fi ind dc 100 kg,/cntr.

(irplrrl rtr.t:r'sirt lx)lltrtl a olrlinr: 20CI) la fri 't:l 'eufa tlu ll) pc st't 'Lttrrlri,vir fi

I t 2{} ' ?6' l tx) /Zr ' l0 2 42(} kg crrr

r i i i rv ' r r l r 2 4Zl) (n l2 l t r l l ( .V2) ' l (n) A, r ts( f l l t : i r A l ( t , l r : t t t i r 1r ' t t l t r tf i r .crr l r . f i rz i l . l l i r r : i " r , lu i r r r r l t t t i r t r ' , l t t l t - r ' l r t t i t t { i r t t l Pis lor t . t t t : r l , r 2,5 t : l t r t l i l t t t t ' l t t t ,

Iurr l l i t ry ' r r t t l l l t ivchi r r ' , r f i r ' lJ /n 2,51 3,21i ( : t l l .

At t t v; l r , r r l r ' , " r | | I | | | | | i I t | ' I t ! t ' i l l t t r t t t r ' lxr l r l |zvr t l l l l t t t l r t t l r l t t t t r t l t t ; t i r l . r r i

v i l r , r , r t l , r t , , , r r ' . , 1 r r t t t , I r ' r ' \ , t ( | t l l \ ' l l l ' / . . r Si t l ( l t t l l i l .

l , r , r r l r r t v,rr i , r l r t l r . | | l ln |L r t t t t r i t rh. r ' t t |z , r , i , i | l r . , l t | | l { , l l r ; ( . r l , .zvol l ; r

r r r r l r1, l r r ' . r t I r | I t r t l t r | , r t lu,r i l t r " . , r r t r r ,6,r l i r ' ' r . r t , ' l i t t , l r ' , i rot l l l lzc r" t t i . r l i . r

v l l | , r , . i , ,1,r , J ! r l r ' / , r I t r " , , t r ' , , t r r" ' l r t t r l t t l t t l r l r " , i r l | r l l t ( ; r \ ' l t |1,1 , . l l l ' l l | | l i r t , ( . r

t l ( , t r , , t ! l l r ' / i r t t r l t ,u l r t , r l l l l l l l l ' l l l r . r t r ' l t t t r l r ' , r , r r r r ' l t . t r ' , ' r ' t l t t ' l r r t t t l

I r i t i . 4,1. . l r is i , ,n n rni-/ . l t ' s i l , i , , l .1 tu rrr fL.

:IH"''&i"':':"Ii3ii: medie uu este zero' ci este

*,g_??iif,tr:e,li,ru'"f i,?iil:'."u#r.':'lr:."'.tnum5.r. .I\[ai mult, -daci cilirunshi uri J;pt' *; -!-"i,

-il'',":}'" J,',' .lnfuT'1l T

constant, cici suma ! cos (Zat | 9 q O) tlevine

il!1'',-"li1J?# :li ix,ln'l/"ff"i:$ T,ffi*i;cu o prcsiune defazati, fafi de aceea a ciiindnluirrrmetor, cu unghiul d.intre ixele citinaritor. *-"*'-."

lrrplasamcntul I cste in [i,,cirrc momentD == rO cos(rz,l 1 r)).

( rrrr.ntrrl stutic va fit =_ (l8/d, , , _ rr,r() sip(a,t _f ,f).

Lrr<.rrrl r:f.ctrrrrt in fi{\::rr(. l.(,urcnt . hiit; ,si .(:r.5lir t..l 't ir. \.r tir:r '11,r f r r r l r r l r r r l n.z is lcnt , . . - l l t , l l : r rst fc l r : i r , , r , . ; ; , " ' " '

t ' , t , rh0sirr( , t l l , l l .Ar.r.crrli lorlrrrllt a foll 11,tlit;i rrrrr,i r,rr:;,

u0 {ll

,,,,u lli';.;;li;i,illl'l;;: ll:,,;;;i :,),,J,,,;',1.,1;,,;,1,,i1u,,,';L::\l::T iiJ,,ii.:,:,i;;t t r : ; l r ' .1xslr . o , r r r . r r r r r r l . r l r r r r r l , r .

,", ,',llil;:;il,l"":l'; ; llll ,J ; :;iiil:': i lll'llll l;'l'rJ'il:i""'JL'.';u, deoarecc cupr,,r

r,i'.r',",,,.",it"'iiil,'l,,,li'ii,, ,,,i,,,;]li:l;ill l..ji"lll;,,":11,,T:jil:1 ffili:Atlr , ldt = . l t r l IQ sin(a, t J {) s in( . , t l - ( ) ) :

irstfrl incit pctrtru lxrrnirc /

I)aciL ./ cste momentulsliu, in jut ttl axci, exPrimat

., {iind ;.{rcutatca spc'ci{ici a ntctalului din cale c comptls roi('nrl i. rl

ittr, . ti l i".t ci t rotorul nu ta Pomi dacir o arc o valoarc crltrsirlL lrLl'i l

E xuttflrt

Si luf,m un motor dc 20 CP al ciLrlti rotol cirtiroltc 2() li! { ' r' ' l

f i l i rz,a t lc q i rat ic:r rotolulr t i pcnt l t l cr motol ' t l l s iL poa( i t pot t t t t t t t r t t ' !

<le lotatic l1 : n1, r ' i teza clc sitrclottisut f i i l ' l 'r -- 100'

t ' i . . r "maxi Inul r rz, . i r le gira1ic. - \ tunci

A:20) i2 l98l -Z ' 20 ' i600 ' l : , ' ' { ' l (X) ' i ,

d in calc r : 3,4 cm. Daci . a ar f i 50 in loc dc 100 l tm olr l i t r t i t ' r r t r

\ icdcnt, Drin utmare, cit motoarclc sincronc sint gl 'cu (l1 l)()rr)rl (r 'rrlr ' l

inert ic i s i ar ' f i imposibi l de a porrr i uu ast fc l r lc l r t , l , , r . ( utr1r.r l r r . r '1r . , , , r r

volant chiar de dic i d imcnsirrni . \umai la h" \ i r ) lc forr l t " i " ' ' ' ' ' l " ' I

bil dc a porni {ir ir dispozitive spcciale. La astlcl clc nloloarc ('s1( rr( r)Lrr'rt l

dabi l de-a intrcbuinla volante loartc r . lsoar( ' , c i r l 'c 1 l :c l )urc, 1t . l ) r . l ' r : rL l rsl fic de diametru mic.

i lotoale boLil&:dte ttsittcrott,:. Cu tnotoirrcle Poli{l lzi lt(: irsi lrr r(!rr" "1"posibil a oblinc uir cuplu de poluirc' : i l)r c:rrl i t lrrL trr t 'L in lt. l t ' ' 1 lt ' 'un culcnt sonic unci matr ivcl t ' s i tu l l l lu i r ' \Lcl l1 l r ( i r r t l l l l ' l r , (o l l : l l r l r l r r ! r r l

motor ca cel i lustrat in {igrua '19, clL'strris tnlt i srts'Curen{ i i carc c i t 'L:ul i r iu { iccl t r t mr, t r tcnt in cci t le i c i l i r l rL i - l l l t t '

i , -. l sin cl, ir : l sin (al -; 2;;3), rr : , l sin (a/ - J; \;

cornuoncntcle unui dt:plasltncnt o-.' Lir acegti c,rreufi . 'u. cotl 'spurdc dcl asanicniclc tlt lr: t l 'r:

- a. . .d-r : \ t rd/ - . ( / / , r ) cos ( ]1,

8. : - ({a) cos(nt )- 2nl3l, l ' , - ( l/tr) cos(a/ - 2tl3)

! 'edctr atnl tc i c iL , ) t rs ic ul l tct : t t t t , t l t r r r t t tp l i l r t t l i t t r r A f ' r , i l r l i r t i r r

du-sc cr t o v i t ( z, i - t cor ls l iLt) l i t i r t j r r l r r l r t t t r t i I ' r t t r r I l ix .

I I i i ;c l t rcrL l t r t t tct t t l r t i O, | t . i i r r t l r r t : r r ' ' , ' " 1:r" ' l r r f

i i ' r ' i r r ' r r l r l l r t i t t { i I r t . ,

v i tczir t tngl t i r r la l i r t : t t t tst : t t t l i t , r 'ot lspt t t tz i t t r l v i l ( ' / r ' l r ' l l l r ' l r r l l r "

l l i i t :u, t - r : l t r :n l r r r lu i i r r r . l r r l r r i , / r \ " r l ) r1r( l l r r , i r r , i l i r r r l r i i t , r l r ' t t t l t t t , t r t l . t t l t

. i r , . i r , : j ' , , t lc t : i r t 'ot vr t lot ' i l t : t t r t t l , I , I l t t t r t t t I r .

l i i ( ' r r r v i l ( r i t t t t t ; J I t i t t I I t , I . r t . l l r t t l l t t \ r l r ' / ' r l ' l ' r l l l i r r l t r r l t ' r | . 1 ' l l r r

l t , ' t r l r r l . \ : , r ; r i r ' lo;r t t l l , to lot t t l r t t l , r l t , t , r r

l . r t , t t t t t l , , r ' \ ' " r l r ' l l ' , r ' r " r r t r r I r r r l r r r r r l l r l r " l l l ' l l t r r l ' l " l r r l l l

'1, l , , l r l , r ' . , r r r t , t t l r r l , \ l r t r l t l t t t r l t t

' . t r r !11, , / , r , l , , ,

; : ; ; ; r ; l , i=f , . . . ,

t rCl , r r i I s, -L l l , l l l . r l l t l i { s i l l l ! 'g i l l I r l

A, Zl l t r ' l , lnt \ .

de i l tcr l ic volr tnt t t t ic a l ro lor l r i l r i t l r \ " r

ln ccntintctri, \ 'ol l l i !\ 'crr

A : (-;! _!,\ j : ztrl qa3 ,

-,- (r fl!!iz) lcos0,r -;iIislc tlificil a ir r t cg.r-11

1xr:rlc girsi pcntru ntotoa-rclc

+ + _ (i,) _ cos(7 n--lr + + + ql.acoJs; i rcur,{ . , ( , d l r u st lu! :c ;Lproxima t i t . , , rlo lL laz] tc. [ 'c l i t ]1. i r .1 lc l de rr , , , t tare

) I - ( tu l te l2) , .os(,1 _ - , r r r {_O) _ AJ.t tdt .

In ntontcntul l :0 arr : rI r r t ( r l atulc i punc fcnlrrr , , "L 1 ' , , . -0

Drr1r i i t ' r r ' l 'u l 0 \ 'o l l l ?\ '€2 4r :4 jiiiiii,

"j" i.".i""'i:"iil:",)l f,'i|:;"u (L( p{'r'ro' tiacit' ;rccastit perioadi <ie

( , r , - a) t : u( t l t t _ j ) i .

, . Motorul va poi.rri d.rci 0 cslc <lcstul rlc rnrc, ri irr lrcbrrie si. f ierl lci l pr,rioada dc- timp 7'.Sir presuprutcrrl iondil ia inclcplinit i. Aii-r;cr rrr.cm

d.ottt lt , . (mrH!tl2A) (t., -( .u i tn l l tatea

cos.. : g6s(1t-:7 + + - d))iuc o vuloarc cuprinsii intrc zcro ;i un;tatc. Dacir motorul ia prca putin tintplr.ntnl a porni, astfcl iucit in accst tlnl) s:r putcm considera aceastir caD_t l l ; l lc ( :a constant:r , punind.

h . coslq ---ot -l- + l- ,t,).olrfirrcnr simplu q : hiutrlIctf2A, sau clacr,r ar : d si I _ 0

a: h\mrI.IelZA.Constantei ft i se poatc <l..,, ,'*,i--{"io."#iu' ;,i;ii'p:l"ill'","*ii";:'l:"

zcro ei unitatc. conditia

,,,, ,,, il,lll" . i,,oni* '{,'il,,",1;,_:l,rf ;,1;,,?i::,'illlllu.l,l Tf; l,li,.i"?/tll l { ' I l t i l l I l l t ( : i i t t r , !a l ct t

. l . , i lv ! , ) . t , . , , t2.( r r r . i l r r r f i nt l r i nt iu. t . r . ; r l r l t lc i r l t r i 17, r . t r i r l i l_r . l r I i r r t l r i r r I r r .c lc t r lxu.rr it l . l ( ' ' r l , l /? t1, l ) l ( ,z. l r t i ' ( l { r . i r r , { iu ' r , r r rLr ' | t , r i . i r rL i , i , , , , , i i , . , , r , , t , ,1 i i , i , , , . . , , , ,tur) l ( ) l l l i t l i l tK{, r ' i l r ,z;L r i r . s i r r ( . t -orrrsr l .

_ \ i . r t . r r t . l l l i r r r t l .nt : r r i . , r ; - , rsi i t r r : n l r r i nr jc rh. i t , , , , , , , , , , , i , ; ' i l l l l : l l ' . t t l

r l . i t r . r l ic i t l r i i t { iLr l t r t , l ' iL ' l r , l r r i , '

l , i r : l / 11q111.1q,11 ul(r . . r t t ( . . r i t | | I | | | r ) | . | | | | | i . A\1. l l l

mar nltc

I

:tII

i

n2

l l ' ( t '1\ t , t l l ! . t ,

\ l i f r ' r t1. i r s.rr n l , r r i \1 1.r r , . r l , r , r I ,ur , . l r ln i { ) r ,s l t : . \ / ! } , ! ) f i ind sccl iutearrr t r_ l , ls l ( ) r r r l s l r r (otrr l r i . l io l . r r r l , I r r r r l rntrr( , , r .st( , sub i rct iunea unei nta_rr i ' r , ' . r [ r : l r r r r l ; i r r1r :

/ a/ ! r t ld!) , ,

ttr lrttr lrr-sc crr vitczir unghiu)rrrr"L rr , lr. Sub aceste condil i i curentul in fie-crrlr. r ' i l iutl lrr rLl rotor.ului viL fi t lc forrna:

j, . J sinl.(a - ar)tl, 1r: - J sini_(a - nr)t !Zrl3),

73 : - / sinf(a - ar)t - hl3],

Itt crLr: f - (IQr/C)) (I - arlt), Q, fiind supra.faja secliunii unui piston a1I t lo l ( ) f lut-

Iric M cuplul rezistent si 11, presiunea sonomotrice in rotor. Ilotorullr lc rLt:f iouat-de o rnaniveli t ictivl r:.\/O gi r '1 punem consiJcra ca un ge-ttr:r ' .r lor irvind o maniveli / care se inr.irte;te cu o vitczi. a - a, ; i dezvol-l l ttrI trr cuplu M lntre manivcli.; i rezistcnia antagonisti. Spre a

-giisi cuplul

tt lr ls,rr pcntlu a lnvirt i gcneratorul, este su{icient a cunoalte lucrul efecfuatr r '

' l l l ' . l l t l l l ) rodusI.l i ir.5 t:ocficientul de pcrditantiL a1 curentului dinlr-o faziL a rotorului.l,rrcnrl ntcdiu e{cctuai itcr secincliL in rotor va {i dat de

ll '1 ' 35'H'lz *) '

.,r ;" ,,1, :rlt.L p.rrtc, cuplul M inmultit cu vitcza unghiulari a - e4 dd W, :

/U(. f , f t ) . : i [ puncm ,r - . r l : c [ . a l l l r ]c l

ItI - 3slIilz(rt - t.tr') : 3SHil2r. .

-l).rcr"r./ cstc curentul in lotor;i ,!, C perditanta si crLpat:itatcir irr i ie

r;rtr. l irzir, avcm in notatie simbolicii:

(-/) : ls I JCa-, rr,, Hi =_ J,16l, _= c",") .I 'rcsiunc:r rezultanti asupra tratrsmititorului, prirnit l din partca pis-

loirrrrlor statorului la un rronenl t lai, cstc o for{i i constanti. ci nirr. i inc.Arr ' : rst . - r lor i i , .s lc propor l io l r r l . r r r r r rurr t inr l p is lo:rncl , l , l i r r st : r ror ' : i , .u.url ' l i l_u([inc r prc.siunii strnomotricc 11 si sccliunea Q a pistoanelor- statorului.

l)ur:ir considerirut rotoru] ct iLviird at:eler;i numirr dc pisroauc ca 5r sra-l.lttlt., I tNrclitr,rtc(L pistoanelor rotomlui asupra transmititbrulrri di o a1tir.lor'(:"1 rczultantir, propoltionaliL cu nurnirrul pistorLnclor t i in rotor., presiuncnr,ottotuolrico fl, t l in rotor ; i scctirrrrtr;1 Q, a pistoanclor rotorului.

I1'rrtr-l l ir sc nlcntinc trlLu srni i i 'Lt orul ht, plttt irt, cck douiL {or{c lczul-lrrtt lc, t l:rtori io :Lc!iruri i pistoanclol stirtorulrri ; i rcacliuuii pistoanclor roto-rrrlrri, lrt: lruic sr-r f ie cgali, irfrrri-r tL. r 'tzrrl r: lnd tiansrnil irto.,, l ,r.t,, ro"rte gr"l ' t 'i i i lrcrrvcufrr hrrrlt ir. l \Ltorrr sr:ric <lcr.i FlO . l/rQ,, incit f l ! -./J/(.!, i ,C!a) =

, (/fr)/{),)r ; i ,1./ (3lzl ..rJilz(.\2 | C2rd2)a.I l ' i tsr ' t t l r t l ( : i r , : rvom

./ , . r lA, / r l / ,

A, l i i t t r I r l rPlrrsrLrru:nlrr l r l i r r o f : rz: ' r r r r r lo lont l r r i . I ) r r r l r r ' : , i r . o I r r r r r ' ! i r . l l r . r io-r [ i l i i r [ 'o l l t lsrL{ i l o r , r t r ; ; r l i r ( l i r r ; rvr . t t t i r r r r r r l r r l i , . : r i r r t lxr l i r ' ; i ( / , ) /a: \1,i : r r ' l r l r r l t r r r I r I I I ) I i I r | ( I i | | r . / l .a, \ , .

' r | , r . r r i r . r t , . , . , r r , l r r ! " , , ' , r r" , , , r . , , , " '1, , , , ,1o, r , l ,

l?. ' , l l l ' , 11. , . I l i l , . , , ) \ l '

l lxplrsirr lrri ,1f irr [ i rruncr

It : (3lz) . SaAj/(Sc + Czo2).

Valoarea maximl a lui .&1 pentru o pulsaije a este dati, de re.latja \== Cor, prin urmare

M^,, =- (314) . Ailc : (3lz)cui: Qiz)c@alal),.Cuplui de pomire cste l4o : QIZ) . S ila , maxirqul fiind

ru,,". : (3/2) . SHila. ,lncit

XI, IM^" ' : 314 : | - ar la : s,

s {rind, alu,necatea motorului.Energia comunicatir. rnotor ului l'rind, Ma si energia consur'r)ai: ,il/,/r,

cficienta rr este dati. deq - t r tar lk lo: 1 - (o - d l ) ia : I - s.

Astfel peutru a oblinc eficienlc inalte, alunecarea s trebuic IIr, ||(I||||| |cit mai mic6. posibil. De exemplu, dac5. un motor este destinat rr ,l, z r', ,ll rcupiul slu maxim cu o alunccare de 5o/o, eficienfa urasirnir. posilrili , t, ,t,95 o/o. Cuplul de pornire ar fi de 5 o//o din cuplul maxim; dacit s. ( r'r, r .r'obline cuplul maxim la pomire, S trebuie sporit intr-un motl orrt, r'.rt, lrvaloarea S: dC ti imediat ce motorul a cipitat yitezi, perclitarr!:r \ trr'buic redusi la valoarea S:(n- at)C - ' :seC, in scop c1c a ol) l i r r , t r r l ) l r r ltnaxim in vecin!.tatea vitezei srncrone.

llotoare monoJa:ate asincl'o 'e. La motorul ilustrat iu ligtrrrll I . lrr'ar viteza de rotalie a rotorului ;i 1curcntuL maxim din stalor.

Dcplasanentul ) r 'a f i o ' : - ( I la) cosrr l : - - . \cosc/ , r t r t r r r l r r l i t rstator fiind i: I sinal.

l)ar dcplasarnentul allcrnati l poatc {i cor:sideratt:a rczultanta a doui. deplasaurente tlc jurlirtatea am-plitudinei, lnvirtirrrhr-sc in st:nsuri opuso cu o r.itczirunghirdari-r a.

Vtloirrca fict:ir.rci conlpone ntc va fi (I l2,a) cos at,; rc , i r t t l : r r r rp l r l r r r l inr ' : r r l , 1r l : r s;rmr.r t { ' lor re lat i lo \ - i r f il lZ,r . . i v ;1 r 'or , 'spunrh. i r n l iur i \ i . lc f i , t ivo t le o I t rn-girrrr ' {2a(l r.

( , t t r r :n l r r l / l l l rx[rrs i r r ro lor , vt f i i r t r ruci suma atloi r:ttn:n{i rLriot'rr{i rtt i l t: i t l i i lolonrlrri in rlport t:u celerkrrr i th:J l l ts iur t r .n l ( ' r ' ( ) l i r l ivr) r :ousir lcr ' ; t tc.

Vi l t :zch: r r lotrr l r t i l r l r r Ior ' l r : t r r r lust rLrrr i r r lcpla-r i i rn l ( : r r l ( : , v( , r ' l t : c( t t t t t t , q, \ t r - l ( t .1. t . . i t i . 4: t . t ) ( . r . ( , , r , t {

Al I l Kl" ls i t t t t i t i sr t : r r 'ar r ' r tPlrr l t t t l r l i r r ( l i r l ( r ' i l 1 l ( : - ncrcir r rn.r r r ' ; rhr i r r l

; r | ; r r i r r t r 1 r . r r I r r I r r i lo l l r l iv crr v i l r .zrr r r r111Ir i r rLrr ' . r o l : r r ru l ( : ' t r i i iv ' in t t r r t (ht | ( r ' -

t r lo l0t l tsrrrr ' r0rr r . r t l r r ' i 1, i : l lo. t t r , . r ' : .1| r :urrrrr r r r ' ! t r rctr I i ' l ) r r r i '

r l / ( r / . , ) . r . ,a, \ i / ( \ r I { xrx)

l l l r l l r r r r r l , t r ' . t r ! ' r . r l , r l r t r t l r ' , r l , l r l r , r l , r l , . r r r ' ; t r l l , r r r t , r , r r I r r r l l r r roto.r t ' r .r | ' r | | | r | | , | | | r , r l r r r l . rv i l r l r r , r l l r r l . r r r r r . l . r l r r ' , i i r , r r . r r r r r r r r r r . r r l / , ' , , r r r , l . il , r l l , , , r l r t t r | r , r r r r , l , r l r r , r , r I , r r r l | r r i t r , | | l / . , , r r r r lx l , . | | t | | l r r , r r r | | t r ' , r l r r, l r t ' , t r r ' , , l . r r r ' r l ' l , l

( r r l r l r r l r , , , r r l t , r r r l , r r l r . r l r r r r l i r l i l r . r ' r . r r { l r

, l / , \ , \ "1o, / ( , \ " r l lcr i ) e2l( .sr - l Csel) . .

I r r r r r ' , r rst , r l , r r r lu l i r r rn l i ru lu l i i t crr factorul 2 in loc d.e 3, dcozrrccet t to lot-rr l l r r t rstr l r , r , r l , r r r . r I r r r i | i .1oir l t : in loc t lc 3.

l ,r t lxrt-t t i l l t t a . r , si i ! \ 'el l l -)1u .= j . 11"ru1, ' , cir !- lotol 'ul nu

l)(n' t l t sl l lgtLt (-t \ ,r ((.r(. 1tr inrpl ls pontlq i t st l l rrpt i l tnirsclLr..Sr 'L l r t t t tcrrr 1. t ,4 - t t t .=s(r , i tnnci a, i t l l - s) +.1 - 2r l l i

s ( \ { t . t ) r i ( - , i r . \ ' ( r l

POare

( lac a

I- t , . ( r rJr / .S) rs/( l f (Casi5)r) - - z l ( t 1- (2Crr lS)r)r .

( tt| lul cstc l)ractic rna\irn cind ,9: Cd.s si \c(l,,nr (ai ix'ntnt a( cirsti-!vrr l l r t i . l r , rntertul i r l doi lea din Parantczi-r r lcv inc

zi( t - i 4 ls!) - s2lz ,( :ecir ( - ( .cste negl i ja l r i l .

( r rp l r r l nraxim cstc, a;adar, i r l ) roxirnul i \ '

,1I,,,,..= rrs.\r/2.9 : \!12.C ,

(o('.r c(' fste analog cu r-aloarea giLsitr-L pcntnl motorrrclc in tlci fazc, a.\. inril irclorul 2 in loc dc 3 ca multiplit ator al cuplului J1, : J't4/-, rlttorit ir uncisil i l lu c [azc din rotor,

Xlo[ourc crt, colcclor, Motoarek' dcscrisc l]rai sus dczvoitar ur cuplu (lepornirr: comparrrtiv mic, car,: po:rtc f i sporit nunrai prin dispozitive carcirtrPlicir o picrclcrc tlc cncrgie. Ascmen(.a motoarc nu sii)t al)tc [),ntru clr '- lr iin catc sc cerc o vitczir variabil i! f iLriL picrdcrt ric putcrt '. Iu scolul, a5arl:rr,t lc a obtinc cupluri (lc potnilt ' rnrrri estc ncccsar a irrtr(,1)uirta o coltstnlctiL-difclit iL.

' l 'r 'LsiLtura caractcristic:r r:rccstui t ip du motol rst( c.i (urcnti i produii(lo pistoanele rotorului slnt colcctafi t i distribuil i in mod potrivit dc ciLtrelln organ {ix pc calr-l vom nunri (olcctor sau distribuitor. Acestui t ip dcntotor i i vom clir t lcnumirea gurericir dc ttrolo,vt cu colaclor, Ro',orul cste{ornrrt rl intr-un nurrl i lr dc cil indri rrniform spa(ia!i purtind pistoanc i i ca-pabil i dc a sc in\-irt i in juml colcctorului {ix sau distribuitorulrri. L,nolgan, pc c:lrc l-am numit mai sris lransmili,tor, estc intcrpus intrc pistoa-ncl. stirtorului ; i rotor ca ;i in variatclc tipuri dc motoare asincrorle dc-scnsc lual sus.

O formiL t| ' rnolor-cu colcctor cstc ari ltatr 'L in figura 44.It irt i lc lst 'n(ialc sint err:rtatc in l inii plinc. l lotorul R cstc Iormat din-

lr-un rrrnrirL dt: ci l indri ptrrt in<l pistolLnc 1) dispusc unifornt in jrrrul unuiccr': l ')t i ci l indti i conruuical cu un spatiu cil indric impirrl i t plin o dia.lragrtrit 7 in <lou r-L pi-Lr!i cgalc (I, r. l) i:rgr;rnra 7 t 'stc concentlir: iL cu rotoruli i i lx'urtito atcstui;r si-r. sc invit lclsci"r. l ibcr astfel clL t: i l inrlri i rotourlui siL fitI, l l i i s (:ccsiv irt cotttuniclIf ic crt tk\rir c<lm1lltr ' t irnL'n ic rr, l. (]r ' l t rL-\riu <:om-l)l l l l ir l( 'rtc (I, 1,. slnt Ir 'r 'hrl lgilc irr u[:rl ir r lc rot()r ' PIin tlorriL tt 'vi r lt ' iL'; ircl i r r . I r . r ' r r tc l , . r 'onr t l , . : r , ' r r t l iL, ( l t : i lsctu{nt i r , l ) r in l i1(r( l ( . r l , l r .

St . r lo lu l crrpt i l< lc t lo i c i l i r r t l r i l r r ' : rxa XX, : r l i r r r l i r ' ; i r i l r ' . l y i / i . l lj t t t t t l to lot t t l t t i s t ' r isr ' ; lc r r r t i r rc l , / i i r ! ( ( ) r l i r ( l r r r I r is torrrr l l r , / ' . r l , r , r lorrr l r r il ) t in l r l l r i lut i i rhrrr t ' r ' i lo i r t r ' lxr t r iv i l r ' , ( l r r r r i r r lorrr l i r r , l r r l r r i / r qrrr l r . r r i r r r | r r i r r r : rI t t l r t tot l r is lo l r r r r , lot to lotr t l r r i ur r r l l ! r i i r I r ' I r I r l r r r r I r r . r r I | t i r l r r r r r . r l rLr i l r . r ri rc l / ) , r r l iot t i r l t l r ' | i r l r r r r r t l l , s l . r l , ' t r r l r r i , , i , r , t rorr i r l l i r r r . l r r l / ' l r r r r t r r r r r Lr / ' , i rr r r l , i l , . , r r t ot i , , r r , r r l l r l i , .1r 'zr l i r In l r r \ t l t l r r , t t r , r l t , r , l l

l)acir o mi;catc altcrnati\ ' :t cste comunicatir dc statot- irr ' lrt l ' t t /r ' '

ccasl : ' t mi ;caI t va a\ ' ( ' l c i l col IS( c int i prr-rducl ia unot.-cur(rr l i i r r r i l t t r ' l r r r t "

t ( ' l r r lu i i i acc; l i cur( ' l ) l i l )ot I i col(ctal i^ la ic l i i i le a; i b ' l lc tot . ' t t r l r r r '

lnainte i lc a l rccc I t strr t l iu l i .orct ic x l acestui t ip ( l ' l r rot()r ' \ ' . r r r ' r r ' r l l

.r i .otoi i i fu un nrrmirr (lc pistoanf, ca in figuri ' estc eclri\ al( 'nl t rr rrrr rt ' l , l

. , , anui 1, i r i r"n" , lc o.r ,nrnni t i s( 'ct iun( ' O aic c iror.axc ' . ' r f l i ' t

lJ ; i ' " l l ] ; l , , l l , l l '".lri,:r,ii,1.ii-ii

l,c lirir zZ ,lirr l anul diagrrgmci 7', rrsl

i i -*"r "

' t i ' ,^ i i , ' ' r , l t l i t t i 'ut . t , 'pt^ i i ' i i i r r r lu lui ' /9; ' in ac. , la; i t i t r tP t0t ' r r rr l l " "

i r rv i l i r ' ; l t r i t t j r t t t t l c t ' t t t t t t lu i t l iaf tagnrci

x

l r - . l l .

Yty

\ fo l or sonic cu colectrn

i i ; , : i ' , , ; ; ; ; . ' i i i , i , l , , , , c. t t l - r t t l " - t t r t - Y

It ,

or.-\.,

-)$g'."''na/ }_\_ /z-.--/r- - ; r

v 1w

, , , , ' r r , ' l , , , , I ' r l , , / ' ,1

r '1 '

i iur t lu i , lu, t , , , t rk: i t r tctsrr l i . a l l i r r i i lor. \ l ; i ) ' l ' ,

Si 3rtr ' : ,1r t t t I , t t t r . i t t t t r l ' 'p l l ts l l t t t r l t l

( ) i r t ( ' ( ! r f ( l r r i t r r t t ,x i t l l t r r r l t tcr '1trr

rrr t t t t t r i l , r l r r i t t i r r r ' l r r l , / i , \ ' t ' : i l t l t l ' l i rs i r -t t l r ' t t l v t t l i l r ' l l l l l i l l l l l l l l l l l l l l l l l l l l ; r l { l r '

r l . l l , r : , , r t t r l t r l r ' , L t t t l t I I I t I r ' i t l r l i l ' ' ( 1 i ' l, l i i r i l , l , , r l , t l r , r t tc rr l , l r ' l r ' l r l l r r r ' 5r ' l

1,r , . . r rpt t t t , t t i , . , i t r , ' l r r l / ' , l . tgt t t , r 4 i t . r ' r '

i , , r ,u i ' 1u , , i l r " l , r r r l '

I r r r ' l r r " t r ' r l l ' l l '

' . r i r , i t r r r , l i l ' r r r l t l l l r l l r " l \ . r t t t r r r t ' l t t r

l r t r l r , , r t r l r , . t z ' l .

{ r ' r r t I r | | t t | t t t , r l l l l , , r l t l l l r l ' l ' , l r l l l l l lr r ' l r ' r , l , l , r i l l r t l l r , ' ( r , r l l \ , ' l l |

" l l r l ll ' r , , , , , \ l l r l r , I | l l " l l l i l r r lt

l ) r .Pl i rs:rrrr r . r r i r r l l i r l r i r l r r l r t r l r r i r r i r r r .s l t ) is ton va f i

I)r , ' l : rsurrrr.rr lut , , , , , ,r . ,r r i ]r , i ,r , ,r1, i ' rrp*"r, , a'a f i pr irr .rmare

..\ t)r .- f , orsinp.

,,,,,,,,J:''illl',.;''ll,'li:1,,i',"i1 ,li HJ:i,x"irii:,n;?::ffi.i'.""i#i#::"1,:ll.;.il i rh i r l r r l r r i , t rebuie sr-r i r \ tmO :

i osin p, sau A : I .zsinp.

,,, n.,,,tliij i f*f,',Ii, ?"1#t,,lijit,lt 3;:ru"1ngl,, .o0,o,, oo,n avea Dentru

9, = z,cl.f , pr: z.zrl.p $i e : o,'--f,' sin (hhlp;.l.uirrd suma. .oblincm O : <o ctg (rf)

iii:l"H:l,l/,t"::':i1"3:.T.T*,:::ilTti"t;1"illi,*i"X":Jf;f ;;i,;li[fi-{"Til\;"1,.?:,t'ff;"1"'rii'""'.t"ir':* d";;"t';;ru pe iinia ,'tv,,,'1,,i,::,':":ffiyu:;l*n:,"'4la ci pentru o rotatie instantanee a roto-rrrr.rrrur richidurui cst-e rncr;*r:S:f:ii#?J,',1i3,i;.*

directia ZZ, iJeptasa-

Motor cu colector auind. cone:ciu.ni in faralel. Un motor cu colector rL'tipul arltat ln figura 44 poate fi legat cu un generator precum se aritliin figura 4?. Pentru simplitate rotorul este reprezentat de pistonul siu cr:hivilent i a, b sint ie;irile fixe din colector, care comunici. cu rotorul 9i l/tconexiunile statorului. Cele doul tevi, care duc de la stator 9i colector irr.4 ;i b, sint in cornunicalie printr-o teava comuna cu unul din polii trrrrrigenerator bilazic G, pe cind ce'lelalte ie;iri B 9i a sint legate cu cc'lilall p,,lal generatorului. Generatorul poate consta dintr-un singur piston cu <hrlrlrrefec"t, o fa{ir a ciruia este in'comunica{ie cu,4 9i b, pe cind cealaltir frr{;reste in comunicatie cu B 5i a.

Sl presupunem ci inelclc transmilitorului sint limitatc in miparc 1,rirrghiduri paralel-e G, cum se aratir in figura 44 in linii Punctate, astfcl c;r rrir iun dcplasament sir nu poatir :rvea loc in direcJia ab sats ba.

Si prcsupunem cii aria de sccliunc a pistonului statorului ('slc ((irli icu aria dle sectiune 1) t pistonului echivalent al rotorului. Dacir cut't 'ttlrrlprodus dc g('nerator cst,' i, ur:esta sc va imperli in doi curenli ti,, ir, ttttttlicurgindu-se instator ii celilalt in rotor,;i lom ar"ea in fiecarc morrtt'ttl t

Singulul deplasamc'nt care polte fi cornunicat -transmi{itorrrlrti cr'l l

deplasamintul in direclia lD. Fie'accst deplasament -8' Fie a ;i a' vilczr'1,'

unghiularc lle generrtolulrti ;i rotorului respectiv. Din cauza rota!ici, 'r 'va produc. in iotor t t t t r 'urr ' r ) l d i r tatnic t . . t ,8.

^ I)aci neglijirrn picrdclile prin perditanfi ;i frecare, turentttl i vrr ltln cuadrartulir

-cri presirruea sortomotrice I1; ;i dcoarecc curcntttl i ' I 'slr', rl '

asemenea, in cladiaturiL cu deplasamcntul D, urmeaziL cn 8 ;i 11 sittl irr [;rzi.Deoarcce 3 cstt' o furrclic pt'rioclicl'L tle a ;icunoJt lem r i i | ' ddl , l /1 Pulr : rn sct i t i t lnotalie simlnlicr-r (f1) =

- ja.\ , in care A este

ampl i t udinca t leplasarn, t t tu l r r i d.'

. \vcm ;r l r rn,- i i t I t ) , ' lat i ( ' s i ln l 'o l i ' i

, rs l f r . l r i : t l r , c ! orr , : ' i l l t , i t . t0

ii3-E

f, or sin p, ircr:t'a;i r.l ir l ir, olrlinul ir mti

Ile{crindu-ne la figura 46lx,||lrlr plstonul ir c;irui axi esteI tu l i r r i r t iL cu un unghi 3 iatr i dctxt ZZ, vatiltitt dcplasa mcni uluirlrrloril rot:rliei rotorului va fi8, cor, 'cos p - cos (p 1. :1y =

: e(o/l sin I ,r fi ind rrnghiul inst:rntaueu de zrol i r { i t ' .

Vcdcrn atrrnci ci deplasa_rr(.nlul total al lichidului in-acest, ; rz va f i

1,. u I0

(o/r Slll I .

I)acir l t istonrr l cchivaft l t t :rr . I ' iA. {6. - t)ePlls,a.nrentul pistonului sirD^t lart :r t ic <10 scr:{ irrnc (}, A, . c(Ir, ,

unRnr l i l i l f r t lc.rLx zz.

(4 == (1,) I ("r,) , (1) ' j , rA - i - , r rJ

si pentru aruplitudineir ,I a r 'ttrcltttt lui lag"icr"tur lr_--A'(rt i + a!) . astiel in< it A

-: I lV &1 -W. I-ucrul cfectuat dc lotor cstcM4t - h i2 rr ,D[ . Cuplul inst i tntancu, pr inrrlttt irrr ', cstL' LI . 3h.

Anl gi 'rsit rrt ir i srts l ir d;i I sittt irt fazi.:rstfcl r:r-r rl ircir ittst 'tturirttt prin A 5i 1I a.rrr-pl i l r r r l in iL. lc i 's lor ( l ( )u i r crr t t t i t i r l i , pulr 'nt

| )urr( 'l f i t : l - Scl tcrn:r c, l t i r : t l r t t t , r ; r t t

l ru r ' l r ) l rnul \ , ,u ic ( :u ( : rn. , 1, , r .h l l . l t t l ,

l l v( , l l l i l \ l , l

I .\ sirr rrl

l l l /I,\ r. irr rrt l .

( r rp l r t l , l r r i r r t t t t t t . r t , , pt t l " . rz.r ' , . i r ' . t lo; t t , ' , t l r r l l r r , ' , l i , v ' r l i r1/ I I ) '1t

l , i r , / r , r l r . r i l . r l r . , r , l r r r I i r r r r r l i r r r , t t r . 'n. , . r r r r1 i , . , r r r , t r l r t l t 1 , r l | . t t t ; r t t lf l r l . l l f I l , l l l , r , \ . , r ' .1 l , l , . i , \ t l l ! t l l , \ r / , ' l

' ' r t | , ' I t I t t t t t r I l t t t , \ l , t l , t , t t , , r l i ' t , t l , r l l l , i l r l1, , ' l , l t t r r t t r

l ' t t l t ' t t t i r r - r r r l s l r r r l i r r r r r r r , l r . . r . i rzrrr . i r l r . t lo l ly ;111., . , , r .o l . r . lor . , r t l i l i r i r r l r r*l : , . t j :11.. .:1,,]; l ] t l : . irr sr,urt rtr..,r .. in,lt i t i t . ,r ., ir,r i , . , lui i , ' i , , i , , , , i l ' , . , , ,,,,,,,

",",.,,,r r . t r . ( . r r . r t r ' l , t r l r '1 i , , I r l r r . , , l r , . r r . l . r r l r r , , l t , r l i r r i r11rrr , r .14. l r r i r r l r r r r r , . i r r l i r r rpt , , l or r l r l r r r . r l r . r r l

W

I'/

4

'Km\

\

\ ,,inn I )

t'-t/

r

Y - Jlt(rr I rl)U ,

l ' i r ' . \ , , , r l r ' ; '1,1 , , r r r l r t l l ] i l r ' t , r l | t l l l I i ; i r \ r I l i l t i l t c l ic 1iu, i t . l / l ; /2( l l | ( , r , , r l

aJ,, , r r ' ' f l

_ Vt ' r lcrr ( . l 'L t : r rPIrr l (s l r . 1 l l l l t i tx i l t l r r r I i t r t l r r1 . , zcr.o, e i t l ic i r la pornir , : .l ) ; r r r i l rL 'Acrrr pt .n1r ' i r r , i l lz : r l { r r r i l i i r l r , 2rr , lLcl ic i r -otolul l r rncf ion-eaziL cuo t i tczi r l r r l r l i r i rccL: i s i l r . rorrr ' , , r rp l r r l r l l l ) r ) rn i rc va 1i c lc c inr : i or i mai:1. , t , :t r r r : r r l l lu l nol l r l l .

. Vi:rlcnr, ayatlar, ciL ac('st t i l) ( lc ltolor estc potrivit penlru scopuri dclrirctiuuc;i caz,rrri in carc sc cerc o autoreglar.c a puterii.

I)utcm cisi presiunca sonontotricc prccurn urmcazir

a, : I2l@2 i lli) .

l)corrrecc J=,=aAo, rvcn L - Sol{l + (,tllrrY ;i rnai rli:paric .l,I ==

^lc =-- \olclll + @lldq.

. Vcdem zrtunci cir ,FI cslc, dt. lrscntcltca, ma\imum la pornire si (lescrc:ter ' l t t r l v i tczl t rcste. l ' tcr( . t lnociul ic i "L \a i i

W -. Xt[c\ : . tAi i2ct l * ( t r la)" ] ,r: ltto irrc un maximum pentru \aloxr( ;r lui ir- Ia care etipresia lf a1{ arl,t,rrlo n nlinimum. Accaster sc intimpl.i cind ar : n ;dic:r la viteza

- cle

I{||r ' t '{)nlsm.l);Lci. cosO reprezintl factorul de putere, a\iel]r

(HIIZ) cos <D : lV

f icos tD : ,ttlV trla!.

\ ' : r lourol a(Fsl i ie\Drrs i i r . i tc z,r , , la 1 'ornirc, i t indc -orc

uni late r ind,rr t i r r l , i la inf in i r . A;adr i r , ,51( ' i ] r tn la jo i de o fac, . - i f r rn i t ioncze motorull , r r r , r \ inrurn de r- i tc: i r posi l , i l

l ; r v i teza dc s incronism cos, l r : l , l rZ-:0,71, ta o v i tcziL c le doui or ir r r i r i rnare cos q) :2/ / t : o, l ig.

ln studiul de mai sus am lLcglijat per-ditantcle, cle care insl nu e deloc11ri 'rr, intr-o ar.raliziL mai conplcti, dc a tine -.carna; este su{icicnt de a urmarrtr lrroccdcu anirlog cu accta dat tnai sus pcntru cazul motoarelor asincronelirir colcctoarc.

IltJresarrc. curentiloy sonici polifuzali

l)r:utru_t t-rlrt inc curcnt r:onti:tuu dc l l un gcnoratot: sonic cu P faze,sr. rrrorrlr:rrzir la f iccarc faziL o snpapii clc rrdmisie ;i una <lc refularc iar in acestl i . l , l i r o \ : i r r i i r l ic s i r rusoidal i "L i r r l in i : r souic i i , o artunt i l i r ; ; rut i iutc t lc l ichic lvrr f i r lt.scitrc:r l. ir plin supirpir rlc lr ' [ulrrr ',: ttunr:i ciurl f lrrir lul arc prcsirrneIt l r l r ' , r r l t l r r l i i r l t ' o i t rc i i l r ' ;uc t : r r f lu i r l lL l i l i r . i i r r iu lcn, l r lu l dc srr<. ! i t rn i , .

l ) ; r r ' i r l r r r l r . r r t l r r r is i iL. ; i lc l r rJ i l i lc s i r r l lcgir lc l i r u l r <. i r r r r r i l urr i r . r r r l r r l -r r r is i , l i r r : l r r r ' , lL l r r r r r : i sr : s l r r l r i lc i ; l r : u l r l l l r i l r r r r ic l i r . r .c{ iouirJ r i r . I l r r j r l . Ar.csl i rr . r i l r ' l r r i r r l igr i r r l r r t r . i |o l r1x. I r i r I r i r r I I ic l o| , i tJrrrr i I r . . ( ' r r rAr:rr . l lu r .s l ( . r . ( ) t r l i t ru i ir ' i r r r t r . I r r r i I r . r r I t l , 1r | r r l r r r I i | I I r t r . r r r I I r t i r . i r r . l | r . r r 1t i r . r r l r r i lx r r ) t lx , l ln. t l | | tz( . i lz . ir t t r i t r t l , r r l , , r l r '1r t r , i r r r r , . , , . i r r r r r r l r l , , . r r r ( r r r r r , i r r , i r , r r i l r r l r r r r i , l i r r . r { iorrrr l r l r . r r r r , . r r l

( ) ; rsr ' t t t r ' r t , r r ; r , t t t l r l r l to iL l t l i r l , t t t i r l , l i r l , r r i l t l t l l i l l l ( ' l i l l ( ) l s() l l t ( l l l ( ) l l ( )

i ,zrr l 1r t r r r I t t t i t t r I t r i r cr i t l t r i sotr ic t . { 's i r r , r / l ' r r r r r / '1, 1- f i inr l i r r t r 1 I I i I t t r I i r r ' ' r ', , , i l , r , , t t rg l t iLt lat i r c lc rotat ic i l c \ ( (n l l i ( t t t t t i s l t t t l l t t ls i t { i i r , i r t t r r r I i I r r r i / '; i j t imPLrl , i [ sccundc.

l )acir . accst gencrator estc pol i fazat ; i i i r ' ' ; r re l i rz ' - r arc sr tp i tpc r l r ' ; r r l

niisie si re{ularc c;ncctatc la un i i |crrit dc turcnt collt iuurr, rt i i t (: l l l l l s ir (lr '

s . r is1;ai sr ls, l r l lmlml imprr lsudlor ' , Pcntru f iccate r-ota1i( ' : t ( ' \ccrr l r i l r r l r r r

r r ; . i ,n i r t ' lc i t . \a f i ? ' (nulni ' ru l d, {azr '1.i r r nr l . , . l o l , i ;nrr i t f ,z ' lc s i t t t coal r l i . t r i l r r r i t ' in j l f r r l ' r 'n l l r r l r r i ' l ' r ' " t r l t '

a1 r \centr i (uhi i ls t l t l c iL ccl t ' 1) impulsur i rozul tatc s int , t lc ast l t t t t t l r r ' t t t t t

form distr i l ru i tc in t inp.

Consiclcrincl ca variirbil ir -1: ' rrl, sttt l l i ! curcnti lor ctlnulir! i irr i.r i r lt

ci in l iccare faziL in circuitul dc curcnt contiDur.l poattr f i calc:tt latir rrsl l ' l

Presurrunind ciL debiiul unci fazc urn:trc;te <lcplasalca pisiotrtrlrtt

c etteratorul'ui, atunci o iumitatc clin p.rioarla dc rc'olulie a cxc.nlti.tt l ttt

iunaoa d" rcfularc cstc tltschisiL, iar i ir cclalalt l-L scrniPerioad:r cstc it lr l t i 'rCrir.cirtrrl in t impul unci rota,ti i complt:tc poatc fi cxprimirt pri ' t ' . r 'rtt l ,,r

Foulir:r discontinui.a-IJ$),

in carc

i ( . ' ) : i ' '^ l '_f , r f , l i ' : r : . l ,2

- L ' i ' (2rr) '?- lJ

,r ti ind numerelc intrcgi de la 1 la inlinit.I)aciL se atlaugir j '- 1 curl ' ,, cit cca rePlclcllt l tt iL t lc' rc' la{i lL t lrr rrt 'rt

su-(, ; i se ia f =. 1, curentul rczultat tot;Ll pompat in cilctritul cxl( 'r ior \"1

li ,:xprimat de

Y- S /{ . r ' . - / rs) ,f.to

in a:arq

t -Zr l I '

e-s i , r u l lg l r iu l i t l t rc <louir Iazc col tst ' r :ut i r t .Tl i i /4\ \ , .^ l ' r inn

( l )

. ] .

( { , )

)o

(1)

I l - r ' - r I f , i ' - rcr)s2, / ( . \ F, /de)I' ' -

; A s i l l ( t f - / r : ; , _ Lr '

2I - (z/ ; ;_t l '

Sc st ic ci 'L

' i ' . i r { '

r l , ) ' i r r ( / 'c i 2t - i ' , [ ,

En sin(c/21 L

\ r r lo i t lcr t

( l r l r ' r i ! s i r r ( r / , rasi t t ( / 'c /2) ' i t t l

. ) t , r ) l , l l l l |

r ' l l, l

r1

. , \ : ' \ : ' " ' / / r ( \ | / " )

,?, , -" t : t t l ) |(1, ' )

ul

I)entru ficcare armonica! rlo orrllnul l sc noatc scrie

'f,'"n.;2r,1,.r- Ae)r : +## .*"1r,(.+4#")]. (7).. Acea-stil expresie este cgali. cu zero pntru toate valorile lui z cu ex-

coPlra acelora pentru care nE: Mn, M intreg.Aceasta determini conditia

t : PMlz. (S)Cind aceastii conditie este indeplinitl, relalia (?) deviue

\ coslZn(x + Ee)l : P cos[Znr + (P - 1)Md: p cos pMx ,t:o

dcoarece conform condiliei (8), existe

sin (Pel?) .2n sin MPzt 0 _sin(elZ) -2n sin MP

Arnpliturlincn tccstei armonici va fi

At- t : I . ( t l t t ) , (z l ts\ : o, t l I ,

adici mai mult decit de 3 ori valoarea de Ia maSina trifazatir.Multiplul de frecvenli a primei armonici a unei magini cu 4 ftz.c r':l fiP). : 4 x 1 : 4 ori fundamentala.

Numlrul de rang ra al armonicilor, care apare in relatiile (6) 9i (7), ttttsemnifici cl existl oarmonice in acel Ioc. Singurele locuri in scria rh'numere lntregi n : 1,2,3, unde asemenea armonici existi, slnt detelmirurttrnumai de relatia (8)

n:N:PMIZ: intreg.

Astfel pentru o ma$ini bifazati., nu existi armonici cu exccpfil rnn'gurilor 3, 6, 9 etc., iar lrntru o maginl at 4 faze, numai pentrtt tt l,4,6 etc.

Pentru 5 faze, rangurile armonicilor date de condifia (8) siltt tt '* 5,10, 15 etc.

Formula (10) de posibilitatea de a calcula efectele combinate alt' frc-venlelor fundamentale gi armonicele datorate redresirii.. .Valoarea negativi (- P) corespunde unui num!.r par, iar raloarea

Porlttve I corespunde unui numlr imDar de faze.Corrdi{ia (8) aratn cL n liind intreg, dac6 p este un numir par, M ar

pltol, .1"ftS orice numir M -

t, Z, 3, -.

._._.Totuqi, daci. p este 'impar, MlrcDule sa lre un numer par, de exemplu M' :2, 4, 6, . . .etc.

- .. Aceasti reguli este echivalentl cu a spune cL produsul pM trebuie![ tic un lntreg, aga cum s-a ari.tat in refatia (8).

. Cu substitufra de -";

sus, curentul total iniectat in circuitul de uti_Iizare (c.c.) in timpul unei rotafii a arborelui generaior poate fi exprimati prin

(e)

( 10)

' ( t t )

yr. . r :PJfr+t totPtr* . | ,rc | - (PMY_tJ

f fiind_amplitudinea curentului in una din faze. Factorii M : t, Z, 3, ...dacl . P este par t i M:2,4,6, . . .daci P este impar.

Fo.t--rr]1 (10)_gat6.ce acest-curent total contine ioun plrfi, una fiindconstanti Yt: PIlr iar cealaltl, o serie de aimonici al6 crirentului cuamplitudini din ce in ce mai mici cu cit ordinul de multiplicare al frecventeicstc mai mare.

. D".qi a este pylsalia fundamcntali a unei faze, pulsaliile armonicilorslnt multlDlu de ,l-_ll4-

Ampiitu<Iinile 11 ale acestor armonici se obtin multiplicintl curentulcontinuu constant I'1 cu factorul zILPM)z - 1l

At. : Yt 'z l l (PM)'z - 1l .l)c excmplu, armonica cea mai micl pentru o instalatic trifazati p :3

c.orcspundc _numi.1ul-u-i - M j 1, din cauzl cd. P : 3 cste impar. lfultiplul

dc fr(.cvcnli'r va fi 3M:6 ori fundamentala gi amplitudinc.aAt-z:Yt ' (2/3.1) : 0,065 f.

. ,

. , l'cntru o instalatic cu ,{ fazc lt -

1t ccu mEi lrrrlc[ urmolicll corcspun{cll i/ - l, dcorrrdcr /, -,l erlrr un n0ltlAr Dar.

llt

I) irci it\ 'ctrl o grcutatc tinuiir iutre donir rcsotiuri sub iDfluentr. ull,: ilor 1r ' tu,1, , , , t , " ,1, ' l l r r r :qul axci rcs( 'n l l r i lor , { r , .u1. i l i , j r v;r incupn sa orr i l , .z , ,, lrrf i o .rnurnitir leg,:. Dacit, a;iLdar, dinrensiuuile relati lc ale icsortur-i lor si11r.r 'rrlr ' i{ i i sirrt astfcl alcsc, incit lcriouda nnturqli deti ltyeie a gr.cutir{i i ( l isatiLl i lu l i .u.osci le dup. i cc {orf i pc:- icdic i a incetat r ic a lu i ra) , ,u i r r . i , l " .u|r ' r i r ' i r r l . r Ior i r ' i impr i rnulr ' , s istr 'mr i l iorrnat c i I gr |utat I s i rcsortur j sc numrste|r t t :o| |d lo/-

' l 'colctic, un astfel dc rezonlrlor cstc caplrLil ( l(,:r 1n:rri aurplitudinear r,r ' i )rr. l i i lor' lrri .pinl la inlinit, t l i ici nu r,-sti {r.r,r 'r irc. l)aci cxisii frccare,lolrr; i, accasta l irnjtt:azi-r amplitudinca Ia o iLrruntit;-r r.aloarc. Sii presupuncm,rlrrrrr cii in loc de a consrlmir cncrgiri i ! l t.r,carr,, c.lr. estc risipit. l intr_unllrri"r-^ (l(: lovituri, l trr:curn sL. inti]Tr|)rr, . lr c-rcrn;i lu, dlc.i grerrtatctr cstr:, ,pr i l r i iu cursa ci r l r c: l t r -c un,,1 'st . rcol l r r l iecare lor i tur iL, asi{el c i r lLmpl i -trrrl i lea rnisciLri i sir f ic l iniiratir. in acest caz o desci-rrclrc rle cnerg.i,; 'r,a,rvr ' ; r lu l . ,nr : r ' l . r [ r , tur , percu,. i r rn, . . Sc r . r .d, , i rnct l iat . i c ]1, , ! ! i iL l r r . r r Lr : i , t r r i i, l , 1,rrrr l t ' ' [ . r i tezu grcut i ( i i in nomentul lor . i tur i i ; i cstc pr;poi t ional i cunrrrsrr ; i piitratul act'stei l i tczc. Estc elident mai d(,partc r. i c,,n niai put"r_,irr ' i lo' i iurl

'a f i obtin.tiL at'nci cind lczonat.iul esic astfel con^:tr rl ir

ittr i l r ' i icza izbiri i sr-L fic maxinrir.St: Poirtc arr"rtir l-ratcrratic cir, <lacir for{a pcriodicr-L carc Il lctcazi

i . r l ) r . f l rcut i r t i i c .s ic c lator i t i r inci scr i i de unde- longi t r r t i i r r i r lc , c i r r . l iur li r r I r - ( )_conductar,) i lucr ind asupr- . r unrr i p is i , ,n l r ,gr t dc 6 gr- , ,u i i r tc, condi t i rL,rrr( ( l i t l r1: lxunut fcrc l lSl lu l r l v i l l l r . i i r r l r t : r1, . : r S:r j ie j l t cL. l r i l i l r ru i11 col l t i rc lr r r , ,1 's lucohr l r lc iz l , i1, snl , pt . .s in. i , : r c\orci tat i t dc r-esor i r i r i s i Prcsiu: t , . : rr r r , \ l r r . dt l l conduct i -

O rrlt ir conditia rrcc('sirriL |(, l l i l . . 'r:Lxinrul

<le ltert..:, ir ' tc .sta it.(.(.:r (: lt , : r . , t lut i lc s i r l ie ast fc l proiccl t r i t : , ca s istcmul s i r - I ic r r r r r ( ,2(r l i l ior lJ( . t - l1rLllx t i , . r r l ic i l i r tca pi r t ic t r lar i r a l in ic i . I ) in i r (cstc ( louir conr i i l i i sc porr lc 11;r) , uLLtt t t l r l i ; r l t t t i t i t t ' r ' t r l r l t r l i r l ' r i r r lsol i r r l i l l t r , , / , )n:r1"nt lu i . l ) l r , i i r r loc <k, ; r r . r r l iz : rt r 'zot l r lotrr l l r r . r r lnr l r lx i rurr l rL l r l r r . r rs i r rnr ' , nr i t . j l t I r r r I I r I i t r r r I i I I r r r r l r i : r . i r . i jt , zor: t lo l r r l r r i i r r i r r i r r t l t ' l r i t l t i l r ' : r o l rs l l r to l r r l r r i , r , r r , . r . t i : r lor i l t l . i i r l r , : r r , _t , ,| . r l t t I t t t r | i r r i r l is lurrr ' r 'orrr l r l t l , r r l r r r | i , inr l srr r r t i r rs r r r r r I r I i I r r , I i r r , . r , l : r , . r r , .( , r t ( ( , n l i I t ( . r rLr i r l r .Pl t r lL, r 's l ( ' i r r rPir , r l i r r r t i r l l ' l r . r r . t r r | l r i r r I r r | . i l , : r r . r . r I . i . r ( , r r . r l r ) -t r t f r r i . \ 'orrr L l r '1 i r r i I r r r r ; r I i t r r r I i I I i ' i I l t l i t \ i | l r i t r 1r | r r ! s i r r r r i i tu t r t t t l t l i /n l i t t t o l , ! int i .l ) r r r i | . t r r l i ( r ( ) r ' i r r r r l l ) l ihr( l i t r r ' ; r str l r r l r lorrr . r i r r ' r , : rsrrr , , t l , tgr : r 1, , ; ,n.1111,11'n ' \ ' i r r r i (so' i r r l i r r r r , r r l r i r r i r ' i r r r l

' r r r l is | , i r r , ; r , r ' r i r l r , r r r i r r r r r . r r r i , r r t r r I , i r r r l

, I r r r I r I r I I I { I I r I r ' i | \ ' , r ( l r . \ ( l r i zr , ro, r ' r r r ' i l l t r . l l l r l | i r t ; r l i , r l r r r r r i i r r , , .1, ,n l 'I r r , r1 ' l i , . r { i i l l i r r r I r r . , I r i . r I r ' , r1, . r lzor.r to,rrr . lor , r i r r , l . , . ( , , r , . , . r ( , r r , , r t r l

' , r r l r ' . r t t t . r t i t r r r r l ,1, , 1, , r , r r . i , , .q11 r l , 1,r1lr r , 1r r , r r l . r t r l , r r r r r r r r r r r r r r r r r r ,1, r , rl . r l , , r , l l r l r ( t . r , l , | | r . r r r r . r . r | | l , l r t r , l r r r , ' l , l r r r r , r r r r l r l r l r r r , , t r , r i , , r l r , , L, t ,

l ' ) r i : l i t r , l r r ' ; i i r r p l r r r i i r ' i t iLu-r t t - i , c i t t t l sr ' rcrc s: ! sc construia:r i (

( \ r 'n l r ) l r t . r t t t t io, , t t t r t r ( l l IL( ' r , ( t l l 's i i :a l l l ln l | l i l tLt l intr fo i i r tc Inaf( l ' ( lar ( ] ( 's1irr i

. , ,1. , ' 1, , ' , r t r , r , , , ' , . , i , . in r i (st ( l rz rczt i l t l lu l ( lor i t sc poatc ob{ i t t t 1 '

,,prl ir" 'r nr,,...,1 rczonirtcLuhLi 11r;ri aproirl)c t lc atnpli iudinca rl l ir\ i l l l iL i l l l ' l lr i I

lrnplitudinca opl irniL.-frr 'biric ()1)scrvat cir (l irci rrr:/,( )nli 1 ( )rt l l lL' 'cart: ir cncril ia sil priD lrrl i

suarfsi\ 'o, l)rectl lr s-a tlt:scris rt l l t i sl ls, cll l ' i)1'[ r( ' l)rczf1)ti l1d vitcz:L siin t t i l ' :L

l . r r i " .u i r i f r l lzotr . , torului , nrr cste () c l r r l ) ' r c( t l t i r lu:r ( i fs1{ t l i :cr)rr l r

, i " , , , i t " , , in mot lcutul lor i r i i l i t t rza i rccc l r rusc c i t ' la t l l rL loatc l t t r r"

zcr,r. r\ccaslir. ( i i scolrtinuit a tc iL cufontr.l lui sU poatI tLrnutui t l t. l ttr n',r! i ,t ,

tulir i Iurniz-at rczor:rtoru]tl i .

5r Doatc vcdu& t : t def . r rurat i t cstc l l la i prol i i intat iL i ) { n111! (() l l I r l '

; rml l l i t r r ' l i r l i i ont i lnc ; i c l is l ' r t rc c ind se at i l lgtr amPl i tudinLla r l la\r i r r rL l r l

ir it i ' i-t i . '"r, ctr 'rba vit irzei curcntrrlui fstf o crit l) i"r arnoll icit lcrfocti l r ' I

i" i, i i ,r i,, i--a.lo""rdJi .. i ft l icir abatcr-r'., i ' Iormr-1, ir curbci ctrrt:rrltt l tt i , i , i

curl)a arrnoil ici-r perfecti-r. \ 'edcm ciL P(rntru it olrl iDc o tlcloli i-t l t! i t ' I l .r lt l

i , i1,i o curentului t 're6uie adoptat:r i, r, i zo':rtor o am'litucli ' tr 'r 'ci ' ir

t l , .Lr,r ' l

tudinea maximi.

E{ectul formt:i ncarmonice a curdrtului, datit dc utr ciocatt ' r ' t" l ' 'introduce armonice superioare in conducta dc transrnisic' Itt trtz'tt l ttt ' rt '

" """ i i i i f "J" l r ic i undl te acl ion.r tc pr intr-o ) in ie dt ' t ranstrr is i t pr i r r ' r1" l

..a.1" a"tot-,t1ii nu caurcazl dil iculi i ! i , der in clzul Itzotrrt lorrtt lot 11r' i '

ir.".t- aitaatt, j" rlc {oric, defornra{iit ' curentuhli poattr plrrv.r rr lrtt l rtr r

i r r 1unt t ionarea al ior unel te, xcl ioDatc s imultan l ) r in ac( ia i i l i r r i r ' t l ' l t . ' '

* i t i " . l i . t gcner: : r l uncl tc le mici c i r ( .1r ' lc ter for t r l iv l )ot I i , i l t r I i tc I I r t r ' 1"rr t t ' r

" ' r i r- i i"; ' i i i ,t, hrcnt ctt t*inimrl 4t qrtt it le, 1:c.i.ci astl, l trr r r t r t 1 r I i t r r , I r ' '

,

ontimir. Ciocancle clc {ori ir sau instmrlrcnl(le .1rtlt ' sittr i lrr lt lx)1 lt l 'r"r" | |

r 'cnlni rr da o I{t)/ollnotic ttt icd a ctttntului Calculcl; prit itoru(' lrr rl ' ' rr ' ' '( 'ncrci f i i l . l lotr t r i r . c l t r Dclcusiul l i s int apl icnbi l r , c i r ' lLsi t t r i r t ' I l r ' I i r l

in cr i i , , "n"rgia

se, l t ,scl t r i iL in or icc al t n lod u( s i l l l ( ' t r ic , 1 l ( t \ ' t r r r l r l r r r r r ' I L I

i , i r , l i i t , tnt t t " ' , i " : tp i . i : s i t lp lu cf tct . in ascnl f r l ( ' l ( : rzr i r i 5( " r ' l t ' ' t r

c lec i t r rmpl i tut i in( i r o l ) t inr : ! .

Vott t s l r t r i i r r lnai in l i i c i lzul i l r cale c l lergia sc t IstrLr ' I r r r l r r \ '

. i r un c i rz l i l : i l i . ( .c l t ' l i r l l t : t lz- l l l i s int intc lmccl iat t : i t r t rL l r r ' l r ' l r ; tL I

r l , r ih 'n c i rz l i l r r i l i i r l ( i l r t ! f l l { t -g i lL ( : i tc furnizat i t uni{olm ( i r i t t l l r t t r " r r 'f r i r l iunc r t l r l i t t r r t .

\ ' , , t t t r ' , , r1, ' l t t r i , t l r i t r l i l r r l rzr t l l in l j i i l t l t l t l t t i c i rx 'atr t i t l r : t l i 1" t ' Lr ' t ' t

r ) l r . | r i r r . , I ) l r t t . l l t \ i t I ) l i l i ( ; t r .0rrs i r l r : r ' l l r i l ( l l lcul l l l ( ' l ) ( r l i i i ( i f t t t l t izrr l , i L , . r r l

I , , , r I , i i r , , ' t t ' ' i i , ,1, l i r r r" 1; i r r i l , " t ( r i r ( i t l t t t s t r i t r l i t t r l r l i Di t i o r l ' i ( l r I I r ; r I t ' | '

, r r r , r t l r t l , : ,1, i r , l l , r I l t t t t t l r t r i l r r i t t ' l I r |s i r r t r ' r - t I I I | ) | I I i I I I I t ( : l l l l l r ' l l r l l l ' 1

i t r l r tz,r . i t r ( t r l l l l r i ( ) r , r l t l lot r l r . r l ' l " r l ' : r l i l r ' r r l i ' l r r r l l l l ( i { | I I I ( ) I I | | I I I ' I

I r r | ( | r I l r | | r i l r r r l , r l r ' r1, l i r : l i l l l i r l i r r l i r l r lxr l i ' i ; i r ' ; rzt t l I ( ) t ( s l ) r l l l r l l l r r r"r ' i

r r , , l ; r i r l 1,r , ' , i r r r r i i ,ot t i I r r r r ' I r i r , i l l l l rz l r r ' t t r ' t t r l t r l r l l '

At t t r , ; iz t t l , r t , l . t , t t t t t , r , r1 ' , , r l , r r r r i r r r ' l i r i ' r r1 ' l ' i r r ' r l l l i : l r ' / | '

I

r i l i r l l r a , r 's l r ' ; r l , r ' , r l i r r l r , , i , ' l , , . r r r . r l i ' l r i ' l i , " t ' 1 ' t t l ' " r 'zr ' t t l ' r ' I ' t ' I : '

' , r r l t r r l t l r ) l l i , r ' / t , . r l r . t r t

( \ t ' t I " l | |

' t ' t t0 lA I t 0(: ; t \ t i t , ( f l t l xt , t \ t | l t t

t t | , l r r l l 1 l r ' \

r t l r L l t ' l t r r ) | |,1

rr , ' r r ' ( , I l r r ' r l r r r r r r"r l ' r l r ' r r r l l r r r r ' ' " r r r l " r l l r r r r I r l r l ' r r r { r l r r r ' r r t

l , t l , r l l

. ,S. t . Prrr t r . t r r , r / r , ; r l r r r r r . r . r t . r . t l r In. t t t t . l l t ) l ) r ( ,s i t t l t ( ,sol tomotr icc armonici_r/ t l l s i r r ( \ .1. ( l ) ) .I ) i f r ' r ' r 'n{ i i r r r l r t l l ( i : r ( l ) i r r r r rpor. l r . r r . r , o l r { incm

i l- LCt!(<lt i lr l 12) ,r(.<lhldt _ aCll cos (.v { <D)

li rh.oirr, 'rr, /- 1i C sint in tozolrallt i i

LCt2 : I, i + (d?r:id.r!) : aCH cos (_v * O). e)l ) : r ' r - r I r rcsul tunem ro:0, c ind l :0, solul ia ecuat ie i estc

i ..,, A sin _r f B.v siu (.r. * ,l).

. , [ - r r i r r r l c lL or ig ine a t imptr lu i ntolnr.nt l l l in carc r _ 0r( . r t l I r , ( I ) (L i

ho : L(di ldt)o : L,t(di I dx) o.relalia (3) gi substituincl, obtir.rcm

A : (Hlz)Crt sin <t), B : HCdlZ,

I t t t l r . r ' r . r r r r r r . r ' r r r r ic i i in t t r t t r . r r t tot t tcr l r " , l , r l l t l i rL '

dL' l t l t - I I4 l4t . (n)

I )acir mont ntul consi t lcrat cst t ' l l r t t t i r t t t ' rval dcstul t l t ' lung <l , l i r r r l 'de la inccprirea oscilatii lor rczonatorului, lolntultlc (n) 5i (S) pot fi rirrrlrltficatc prin neglijarea primilor tcrurcni din parantt'zi, fi avcnl :rl)roxitrrirlr\

i : (r lz) aCHx sin (r r q)) ,

iar cnergia inmagazinatii cstc tlati. dc

L' : (CEl8)x! . (")

Daci scriem expresia lui r in lorma

r. :1sin(r+( l ) ,

in carc l cstc amplitudinea lui i la un moment rl;rt, avclrt

I : (aCHlz) ' . t

gi substituind in exprcsia lui L', ob{ineur L -- l'iZo2C.Reamintind ce LC a.2 : l, oblinem

L: : Llzlz I ltl )

Accasti formuli arati. ci cncrgia inrnagazinatl intr-utt rrzott.rlol , 1.t'galir cu maximul energiei cineticc :r mase'i care lormcaziL rtzott:tl,rtttl. lrranaliz.a de mai sus am neglijat {ricfiunea in circuit. Dacit lt 'zonrtt,,tttl r".lr'intr-clruinlat in lcg5.tur5" cu o afini, cate clcctucazit luctrt rtr,,.rrr,, .rrdat r-r cxistir Iric[iunc in circuit, condilii lc difcriL pulin.

I)a<:r-r, cocficicntnl de fricliunc este Il, prt'siunca sonorrrollit, , t, ,l.rl 'rt lc cr r ra l i : r

r t , - Ri I r ,d i ldt + ( l /c) i rd/ .

( l t )

I ) r rc i r / t cslc o f r tnc( ic i r rntonic i r dc lornra h: H sr l1t l , r ' ( u i r l r . r ( l , r I ' r t t lr l i [ r ' r ' r ,n! i r . r r .

L<l2i l t l t2 \ l ld i ln l I i lC -- Ha cos , t1 .

I ' r r r r i r r r l t ' r i ; i r r l r l l i l r l ic i r r r l tu C, o1r{ i t t r r r r

/.{ ,r1 (rl! i /r l.r ' !) I / i( i,r((l i i (1.1) l. i , CIla cos.r'

l ) l r l ' i i rv l t r r ,our l i ( i l r r l , ' t ' r 'zot l t t t l l - r / . ( r t? l , ( \ ' t l i t l ia ( l ( ' \ i l r ,

r l ! i / r l r ! | A ' ( , r r r l i / r l r ' I i ( / / r r tos.r .

Sol t t ( i l r r r , 's l l i cct l r l i i ls l r '

r ,1, . i r , ros(r | , | ) | ( / / / i l ) s i r r r

r r r l r r r r . l rorrr l t { rct r . r f l l i ( , t l l l l l l i l , " '1 l t r ' l r ' , r t l . . r t t i , i l r r l i r l , . r t r t t . r t , ,ptr . r r l f r l i ' l t t ; i , t r , t ; r l r . r / . l t l l i r | | | t t | ' | ' | | | | | r ' | t i | | l l ( , .

t ) t t t i lu l i i l iht t t , Sir I r t r ' , , t t I r t t t t r ' | | t I i r I r | | ' ' ' i | | | | | ' i | ,ot t t r t t t r r l t i l l r ' "1, ' zr ' r r )

1 l r i r vrr l t t t r , r t r ' r r r t t , r l r l t t t l , i i r r r t r / r ' r / t [ , t ; , t l t t t t r i , r l . r r i / r " . l r ' . t t t t I ' I t I t t r I i t t | I rr r r t r , r r l r r l r t i l r r t t tot t t i ' t r I t t | / ' i t / , , i | | | | | t I i | | | t | | t t , ' r t , t t t , t t l t t l t t t , l t r r l / r l , . r \ ' r ' l t l

(3)

y! :0,

I )ir.-.r-cntiind

Ir [ i r r r li : (tlZ\dCH l_sin;r sin @ f

^, sin (f, + O)1, (4)

rrrr ' t i i r r r l , . r ( ! . \ . ' : f t /a) [ i (1.r , obtrnemJ

J' : (CH|IA) fsin rcos O - .r'cos (.r + O)1. (5)l:rr,.r'giir inma"azinatir in orice momcnt \.a Ii

t - - . \n i at - L i l tz + (Q,c) !

r , i dr ,r l i t t r l loirrt 'ce

olr l i r rcur

l i I i i r r r l o constant i .Sri prcsupunem cl-t

srr l rs l i l r r inr l pc i ; i r , , obl incnt(i , (t/8)CHsirr +_ sin

:t t r ' tt l ' i t ' ir lolrrt. r.sl1 indt pt,n<lln t:-rI l t . r r r l t . ' r ( ; r ( .u, . rAi . r i l l , : ( , r l ) i l i ' r

p i i l r , r l r r l t i r r rprr l r r i .I ' i r tcr '6 i l t r r r t , r l i r . l i l u l t ) l ( ) l tc l t ( t i t l

I ' ( t l$ l ( ' , t ru! t

. \ ,1| , .1t . l r r i r r r r r r r r . r r , . , r . i r r r r r lzorr . t lorr l r ,

' , , l r ' t " | l l . r l . t , . r l t , . t t , l

taa

)r dr - : { ) . r .

Lt :L i2lz +Q_1'/2C + I i ,

L: este zcro cind i :0 ;i -r. _-- 0, atunciU . = (tlzl (Li, | (QzlC).v2\,

x - 2.r sin .r cos (r: -l- 2rD)l (6)rL. tlr irr or.ir.c rrr<lrrtcnl tlul rft. .r , kzr.th. r rn rczonlr lor . r .s l r . prr lxrr l ion;r l i r r :u

vir l l

l l2t ' j lu l . . (7)

r . \ l r . { . r r t t [ t t t l . t l r , r rL. r , r t , . r ] i r r . ( | ] )

trt

/1 / , , r r ; r l l ; t l l t t

. . . . t . , . ,1, ." ' r ' i : r r r r 1 r I i t r r r I i r r r , , r . r lc , , r r r . l tc ( r r .pt i r t ( .u t iurpul , g i for .mula mai

; l l ; ,1 l . l , l ,sr ' - \u l t l r .ut t t i rPirr t i r r i rhr l r r t r . r l l , .ast .opr i6sci laf i i lc ,adic i r ina_l l l l , ( i l / r

- (1, I l l pr l ( . t i r . i ' l ln rr . loni l lor .Drrs ln osci iaf ic sc oprcste duuir un. l I r l ) l ' ) l t , ( t i r lor i r i r fa l ) t l r l ' i . i r . L,gr.rr ' . r r l i r

a t r . ic f iuni i ' d i fer i i pul in de'acec^pr,'rupnsir in analiza iltti," rrl,r srrs.

Ar..fl:rr::i:;t,d:^a'aria!iuuca A,f a lrnPlutidinei 1 intr-o perioadi dc timp

rI : - (RlzL)Io exp(-(R/zz)r) Jt: _ (RTlzL)r .

. Iicamintirn cl, l {iind nurni-rrul perioadelor pc secund5, avcm lZ.: l,obtiue rn l/. ,f -- - Rl2t I. .--\ccasti'! cantitatc vom denumi-o tl ecr eme nt uI r ezon al oruhti.El sc r':r insemna cu r, astfel incit avem

u : RlZnL ..Lgadar, daci, misuri.rn timpul prin numirrul pcrioadelor, punind , :

i !,:T : rr/,r, _putem gi-tsi muniirul ^pcrioadelor

m'la ciri o implitudinedati'L este atinsiL.

Daci considerim ci amplitudinea este negliiabili cind 1 scadc lao srrta parte a valorii sale initiale, relafia

Ecuaf ia (13) t l t :v i r rc at uuci

/1 : (R+R') I : I r I+zwl l9i obfinenr

din careIlI2 - HI * Zltl :0,

I : (H |VFF - sff i l lzR. (r . t )De aici rczultir in mod evident cS. r,aloarea lirniti ce se ooatc' olrtirrc

Dcntltr lucml cfectuat estc W : H2l8R." ln formula pentru .I, din semneie pozitiv gi negativ trebuie siL lrrhnrnumai pozitirul, tieoarece pentru lll :0 irebuie ie aiem // : R/, prrx rrrnse arati pril relafia (14), astfel lnclt ob{inem definitiv

dl

gi avem ,, : .{,6/8.

. De exernplu, daci'r un rezonator are un d.ecrcment 8:0,1, numtr:rulpcrroaoeror rnalntc de stin^g-crea oscilatiei ar Ii,m:4,610,1 :46 gi dacllre''\ '( 'ula cstc dc exemplu 23 pc secrrndiL, timpul scurs ar fi

t : 111111 :46123 :Zs. .

. C,t:trl osc-ilaliilor cotttirtui tIt. ant.fl,iludine ma.nirlrd, Stud.iul matematical. t,:zonatoarclor., linind seama

-dc fricfiuue sau perditanti., se poatc sim_

plrllea prin intrcbuintarca notaliei simbolice. -

Ionna sirnbolici. a ecnafiei generale (ll) este

H : RI I j(La - tlca)I .

f)acil, agadar, La - llCa: 0, avem simplu

\iedern ci pentru valoarea limit[ a lucrului efectuat, amplitudinea cstrredusi la jumirtatea. amplitudinei oblinute atunci cind nu sc cfr:ctrrc,rzlnlcl un lucfu.

Iu cirzul in carc R este neglijabil, avem din (14)

I - zWlH.Am gitsit cir cnergia, lnmagazinati lntr-un rezonator la un tnolnent

dat. este exorimati orin relatia U : LI2|Z.Si preiuounem 'cl lucrul' efcctuat ia'forma :ur.ei bercusiunrj la fitrolo

cursei rezonatoiului. Este clar ci in moncntul Dercusiunii se Detrecc o schlm-bare brusci. in cnergia inmagazinati, iar micaorarea energiei cincticc tr llaProximati\'

LU : LrM, (16)

sirnbolul J inscntnind aici variatia lui U Si f.Itlesupunind cir aceasth. vnrialie a energiei estc micll in cornprtrrtlln

cu tr, 'rucrsia nrmanicir de furnizat iezonatoruliui ln timpul unei pelidado TInaintra pi.r'cusiunii urrnirtoarc, trcbuie ̂ s5. fie AU : l ' lz7'- llr/rl qi prtnurmrtc rlirr ( 16), obfincm \I : W lLltt. Implrtind prin .I, avcm

\ : LII I : WlnI-12 : WlznU : nWlaU-

Cantitatea ,.r vom d('numi-o daJormalia curentului produsir de rczonl-tor, atunci clnd trl este lcgat dc o unealt?t pcrcutantl

Estc util dc a rcamiuti c!\ doJotm4ia 9i decrementul slnt cantitlfi sirni'Lrc gi deforrnalin eslc idcntici cu dccremcntul rezonatorului, dacl se atlmiloc[ fr:ictiunca I{, ctrc intcrvinu ln cxprcsia pcntru dccrcment, cste datorititlucrulul mllloctu nfoctuqt do rczonntoi, hr ifoteza cf, nu sc furnizeaztr lucrutlronatorulrtl pcntru u lnlrcui picrdcrco dc cnotgic.

Arn \'ltrut cit (lcc;oncntul orc vllorroe tL - ItlZnL,

Drctt htloculm po Ji prln ftlclluncr oclivulontl R', dntorittt lucruluiiftcturt do rcronstoi, R' ; zl[llrobtlnrm J r

r : HlzR +v@lzR)' - zwlR. ( t1)

\ - VllnU'' ( t?)

olro €tla Ilcntlcl cu ut.rflt [llrlll nlrl rln, Vlrln hnlntl tuvlntul dr,'rr-

tog(Itlld : - 6lzL)t,

4,6 - (RlzL\t : Rn421L : um

u - nf

. lincrgia furnizatS, rezonatorul,,j cstc intrebuinJatir mai intii la pornirea;i uccclt.rarca. tlcptati-r a nrigclrii piniL cind amplitudinca curcntulu'i atingi:virl{r.u'(' ir nh\ir)i 'r

"rlatiL dc ecuafia (131. Itrcsiunea sonomotricc /f gi curcrrt"ul

I srnr atullcr ln lirzir ii ytutcrea mecanicir furnizati estc

tv - HIlz -- RI2l2.

I)ac;'r r|zorratorul r.stc lt.g:tt <lc o ttrrcal t cattt cfcctutrazitoiurvrl(' \ '; l l(,irrc rncrlit ', prrtt,m nd[rrgt frictiunii Il o frictluncr t r . r ' t l r r t i : r

It ' ." ztrlP.

(13)

Ittcrrr dc t,fictl,vd dnt it

,$r, , po|ltru r dcrer nr ullird |. dalu|lt

i i i ( rv l f r l r l l t lornul i t ;x,rr l r r r r r r l r , , , . r r r r r . r l r l r r \ in l l ?/r ( l : l io l i t lucrului r ' fectrratr lc l .zotut lor- .

l ) r ' [ r rnt l r t i t r r , inr l ic i r sr ' l r i r r r l ' i r r i l r . prrx l r rsr . in curent pr in unel ie pcrcn-i rut lc srrrr r r r r r . l l t ' r 'arc l r r t l . : rz i yrr i l i r r r l ru lstrr i la f iccarc pcr ioadi , pecumsit t i c i rx l r r rcL. <l t fo l j l - r s l r r l rorrr l r r . i r ' .

All i tdrtta teoriei

Sir prt:sLrpuncrl ci ave l l lr ciocan constlnd dintr-un corp €Teu, legirtrL'un piston (lrc cste mcnlinut lntr-o pozi{ic medic prin resorturi gi supus,Pe o frrf i 'r, rctiunii unui curcnt sonic, a cirui perioadi de pulsalie este egalicrr pt'r ioarln naturali de vibratie a ciocanului, adicrt LCa2: L

Rcsorturilc condensatorului trebuie s[ {ie astfcl ca presiunea medierlin coloana lichidiL sir f ic balansatir. Fie -Flo prcsiunea rnadjr.; r lc.?.sta \.alroducc o deplasarc, l,o, a l) istonului si ccualia nliscirri i ra fi

Ho +_ t, : Lcti.lclt ! (A/C) (,i, t_ r..),I fiinrl prt'siuuclr sonomotrice gi ri curcntul sonic; (lar rlrciL prcsir:nea ritcdict:stc lralansalir stlrt ic 11. -AfolC, astfel lncit obtinLrm

h : L<lilrlt -f @lc)t,ceca cc cstc irlcntic cu ccualia considcrat:r mai sus ;i cstc aplicr.i.:il cr.zrrlirit:onsidcrat acun, cu conditia dc a lua, ca originc a ltr i . ir poziti., ; r..r ' ,yristonul ciocanului o ocupi sulr ac{iunca presiruri i mcdii.

Pcntrn a <'tl.'t\ine maximu.I d. cJt:ct prir:, lolirea ciocanului, e.i.r trr.ccsarcir, lu rrromcntul

'clnd ciocanul poit

"lf" ln sus din pozifi:L i ir i, i ,,:cpr,t is,

prcsiulr: lt sonolnot!-ice I sii l ic ncgativir, pentm cir ciocan'rl ..- roit iL f ir ir l icat plirr sc:it lcrea prcsiunii srrb vakrarea ntedie.

-. Accs1.a. cste t:az,ul niculiouat rwLi sus, al unui cirx:an luciind cir arl it l i-

t uclinca optinti '1.In gent'ral ccuatii lc g:rsitc lnai sns dan (l) : - --. Oi,t inrnt atunci

i -- (l lzlHCut sin -r., r ' == -l- (nclIt l) (- sin r -j- .! .cos .r.), ft : - i l sin .r '.

Valor i lc l r r i r ' ; i i s int r i r l ) ( ' r ' l r t i . ln,urL, i , i igrrr . r - l \ . I r i t r accstc cui l r r :tt:zultir cit J' csle un rrtaxintunt cind .r ' == r ! i r l i . |,r lr. clrrpir un tirtp, rl iLtr l r ' 19 l t , i r r l icrr . r =_ ̂ - * 77'25' - 1.49.

Valoarc;r lui i ln accst rnolncnl, citre cstc monlcrrlul iz,l ir i i , a:,Lc 2,2IICI..Valoarca nraxitriL a lui l va Ii ./ , ICIZQ.l i ru:rgi i r c iocanului in momcntul izbir i i sc olr ! i lc prrrr inr l r ' . . ; -1-

- l - 1 '7"25' f i q) . , - n ln exprcsia l t r i L i , t i obl incrrr ' l i ' 2,4C112.

l )ut : i r t r :kr tkruiL resol tur i a lc rez,ontr to lu lu i : r r r , : rp.rc i t , i1 i t , , ( i . ; i s iptr l is l r r rsr . , r r i r f iguru 49, rrvcrn l lC, l . l lCr l l ( ' . -

l ) r ' r lc u l l i r^ptrr tc rcsot l r r l C' , t r r ' l r r r ic r .or I r1r l i I r1Ir I pr . o , l i , . l r r r r ( . i / srr l>,r- ptcsi t t t t r ' 11, , . l r t pr ; r , l ic i r / / , , r .s l r . [ r ' , r r t r ' . rpr , r . ryu. ,1, . / / , r ] , , . r , . r r r , , r icIIrI /f)|Ct, din t:;rrr: l/(. '1 lt l . l l l .

l ) r l l i r r f . i i rs i l t t t i r i srrs l l / $ lZ\ l l t , i rs l f r , l r , r r r l r l i r r l r r r l7( , r . , ' ; r ) (1,{ )f ) i r r i r r r r r . r r r r r r r s i l r1. ; r r r t r . r , r l , l / , ,1.1 l l l l t , r | t r l \ t l l , , r 1, . , t1 l l r

q, i ; r r i r r r r t r r i r r r ' / / , , ( t l ) . l l l , , l l . i l l . 1,1 I I l .

{i. - l )i,r-,l,,nrc',*.jl i] i i i;,""I,j i.,i" t, curcriturui so'ric rn rrr | 'r

/ i ,, / i , s rt vollttnllt ' r lctir lului lcsorturi lor.6r (" /t,f( "r

l l(

: tst [ t ' l r ' . - t l - l t

/ i . . \ i r l t \ ' ( ) l t l l l l , l r ! l lcr i l l t l l t l l Ic :

1i1"1 ts r) , r r ] l i , f i , 1 i , leoattce B1 * 6r / i o l r { t t tct t t

l i " ( t - 2 l r )B ' 0,3628'

l ) i i r l , ' r r t t t t l ; t (13), o l r { i r r r r l i i | l crrPi l t t l t t l l l l petr t r r r rcsott t t t i ' l tvc l t r ln: t t l t r tolr ' l

l ' ru l l l , ] ( / l r rr r1, l i , . r l i r l , l ' r ' r , l i r ' r '

/ | , r ( l / t ) ( / r ! ) ! t ( r \14) l l2C'

l (n l ( l ( ' 1,4 ( ' ,1/r , { ,1)( i l rcnl cr t rL 'st t t l i t ( 'x l lc t i t i l t t r l ) r ' l l l l t l

l l , r l '

. r r r l t r , r l , t l . ,1, , r ' ' t t | r ' t t | I t , l | r ' l l l l l l l l l l l r "nr l l '

' t , , I r . r l ' l l , r r , r r ' , , l l t t t t r t l r r t ' l r t l r r t r l l t t l r " r ' t l l l l l r " ' l r ' . 1 ' r" ; tot { iot l r t l t t t t t t . t l t i

r t t t ' r r , l / i l . r l l l l l l l / . l l . l l r l l l ' r

l " \ l l l l l " l , t r . r t r ' lot l r l l r ' l r l l t t l ' t l t r r t r ' l r r t t l t t t i ' r l l t t

, , , r , t1,1, ' i ' t ' , ,1, '1r ' t t r | r ' t r l r | r ' ' r l l " r ' r t t r t l ' lL"

\ ' . r1, , ' ' , r l t t t t " , l r ' i l r l r I r t " r | l l r ' l r l l

l l l l ' r ' r r l r t t r l l l ' t r l l . r ' lot l t t t t ' t r l t t t t

, r l r t l , i t r l , , ' t ! r l l l

dl

I ' r ' , , ( i i . . . r , . , , . , . iat ' ; '

l , ,Lr , i fc \ , ) f tur i .

, ' l , , r l . r r r r ' r r ' , . r l r | ( . r l r l l i r nr i : ( i t l ) is l ( )u l l l u l l l iI i , r i ' r , | | . , r t r , t I r . ( ) ( l l ls i / , rs l t . . l i l l i i ( le

t l ! . ) : t ( . ( . ; : jZ) l t ! ) t ,5.UI!) .

l),,, ir(\ '(, irvctu clr.rLriu rcsorturi in rezonator;i Lrrrsirl, r, irr t iL f iecare din

"te suc.".i, s"

-cies_

trrr l . r ' r r , r l , l , r , . lu.o cursi cgale cu f , r laci inscm_n.rrr t . . ( u / t , , , f . : lOrtCle nCCnsafe I ) t 'n l I l t a compri-rla ecalc dtn aceste resorturi cu cantitatei f,rclalia de mai sus aratb. ci FC : Frar_ irt;s,au,ir, B ,,1-. tl Bt : Fr7B" ;i deoarecd b= fi+- i- 6r, l uzult i l :

F .: F, 1, Fz , Ft :0,638F : I1e,1;, : 0,362F : 0,5?HQ .

. , Pcrr t r u ,calcrr lu l . pract i , a l r r r r r r i c i . , . r - r , . lu-

Cl l r ld. ln. .c0ndl l rL lC dtsculdt( . rn l i Srrq, . ,drL- la

lTplr ludlunr oPi rmi, , . - r , . i r r , . , , r r , . i i , l r . , . .ur Idn_OilDl t Oe a nru{! .da l ) r ' (Cl ln) I t ! , .JZi .

, Avcm.datc canlit i l i lc: [/ cncrgia ]a l iccar-elo\ i tura. in kg cm; H. | rc. iurrra . , ,nomorr i . . , l i r rlurr : r dn t ransnl is ic, in J ig/cm2; , r -_ Dl l :a, i - t rL_rcntului, iu ladiani pc sicundi; P I rrrlu;rtcaciocanulni, in kilogr:rrne; D1, I)" - cl it imtlrl leresonuulol. '

Dirr 'relatia U - Z,lCH2, cirlculi inr rr,. iraci-

l )utcr l r r : r l r ,ot l , i l i i r accsl (az \ : r la / / , / / / : , . i l r t ( r r l l t ' l t t l t t ; r l i t r l i t r t l ' t1 l 11111 1siugrrrc osr: i l r r l i i v iL l i

U : Hllztt ; l l I l t fIIr{, .

I)ar am gisil mai sus

U :2,4CH2 : ( ,81r)HJO ,astlel ci. avem

r - (,8lrcz)J ,sau aproximativ

/ * Jlz.Putem prin unnare trage urmitoarea concluzic:. cJeclul ourtiu nlrl

al unui ciocari, avind o cursl dati, poate fi calcr.rlat simplu prin l. 'rrrrrrl,t

W - HIIZ, I l si 1 fi ind maximul presiunii sonomotricc fi maxinrrtl r ttr ltt

tului date de ecualia f : reA,ca qi cum curentul ar f i dc o {ormiL sirttr: "i ' l ir l f lsimpl[ si in Iazi crr 11. Acest e{eci maxim cstc ol.rJimrt numai dacii cirrrrrttt l

esti construii astfel, ca impreuni cu condcllsatotrtl siLu, si f ie in tczott;ttt l i l

cu Dresiunea sonomotr ice ihpr imal i , 1 i : i l ie in cchi l ibru, la pl t t t ' r t t l ' r t t ' l

undi se produce ciocnirea, iub acf iunca resor lur ior condcn<ri" l l l l r r r ' r r l

presiunii hedii a tiniei, presupusi. ca lucrind static'^ Pe de al t l parte, dceste 'condi l i i a le t tnui c iocan, lucr ind ct t i r t t r l ' l t l t rd inea otr t imi . , pr ; ( iu. in acelasi t imp ccrt mai mare dc{ormaf ic i r ' ' r r r ' t t l

si asemcnea cioiane trcbr.ri,: si ' f ie dci dinensiuni relativ mici, lsl lr ' l ' .r rt l

absoarbiL un curcnt relaiiv nic dir.r l inia de transrnisie princilxl ir.lu cazur i lc in carc se ccle o d( ' formal ie micl , se pot aPl icrr l . r t t ' r t l r ' l r '

( latc pcntru caz,rrl irnrplitudinji maximc. I)c cxemplu,- pentru a r rrl ' rt l .r tt l tr : iocar i c lc for j i '1, cruc i l gcncr i r l ccr t ] o r id icarc destul de sus l t r r l l ( i 1rrrr l i i l l

; i o r l ru l i la i i r ( l i r t iv nr i ( i 'L t le rr tcrgic pc secundi , proccdirnr l ) r r ( r r r t r r r r

t i t t l rz i r : p ln l t r r t o l r t int 'o <t t ls i r { t tat t l n l l t rc tstc reconandalr i l : t i t t l t r l t t t t r l r tr r t t Lczorr i l lor , <or:s l incl t l i r t t - , , nr l r ' iL t l , c iocau de o intr ' { ic totrr i r l , t , r l ' t l i l ,

l )u l l i r l i r ( l ( ' t lot l - t t ,sot t t t t i s i r l l , , rn i r r i l iLt i . Jrr l r . rc , le a incerta l r o l ' l t t r r ' I t t t tiovi t t r l i l , ' i l r l r r l r t t , t r i t t t , i t r l l ' r t t t ,n l rondi ! ia ca dcformat ia c l l l ( ' t r l l t l l r r t ' r l r '

r r l i ru ln l r ' lz i r i rxrrrrrr l : i l i l , i i o rrr t r tnt i l i t ia l t tarc mici . Sir Pt tst t l ' t t t r , t r t r i tr I r ' IoInru{ i r r r r , f i l r r r l r ' r r r l r rccir I l i ( i \ } f r l , a l r :or I , i t s int da1c, ; i t iL 1 ' t ' ' r i r t t t | i tsorronrol i i r ' , / / , I r : r ' , r ' r ' r r { i r t r s i t t t ts l t . / s int cr t r toscrt tc; putcnr r I l i l t t I I i t I I r r l i -

r r r , rs iurr i l , ' r ' i . r iut t t l t t i .Avlt t t l . t t l t t t l r l r ' :

I t . l l ' l l l , r r , lVf uLIr .

\ , r l l r ' l r r l r { i r rcrrr I . I I " f l t r t r t l l .l ) , r r / . I ' l i i " " ' ' , . r

I l , r ' , i ) . tLt t lo, / ' l (x | . l l ' l . l l t t t t t r , , <t Zl 'Vlr l l t l

I r r t t t ,u l r r l i r ( r ' r , l ; r l l r r ' t t l r r l l i r r i rx rr t t t t l r t i 1 i r r ' , { i r r t r l l r f i ' , Iot t t r I r I i ' i r t t ' l t 'l r t t t t i r r i r l r ' .

c L , z.4l-l!,\ |oi din conditia tlc rezonanlr-r ZC ai - 1 , e51i1.1"1r,

Q -= (a/3 t ,3) l /Pt l(irLrsa se obline atrrrrr;i tl in rclatia J : ftHC)i2O.lrorla maximir" asupra r-esortur.ilor r-ar fi

Fr : HA'

;ii volun.rcle rcsottndlor \'or fi

dt: i tyFJ)t ,

?i, .- 0,-i7llQ

8' ,r l;., II), , rr F, J,

. Dirurct.elc si..rsi cclof cloui. rcsor.t.r. i s. cirlcul.azir rrs'r |r. i ' fornt.lelec;rpi lo l r r l r r i I I I

, { : : ; tV t " t , . , .

Asl f t l to iL l c c icnrcrr lc, lc c ior :ar l r lu i s in l th, I r . r r r r i r r r r I r , .

Nr, , l r i . SiL corrs i<lcr . i r , r r . l i r i rx i r t lu l ( .s l ( . u l t t ( . ( ( .1) l i , l i t l ( , t t l t i l . r r tor r l r ,

l : : : ' : . : : . i . l l , . r r r r i l r r t , . ; r ( ; r r l i r i r l r i r r , l pLr.s i r r r r . r r : ,o l i r , r sr ' , r r r l l t r r l i r r t , , r . ,1 . , i , i

' f f f r ' t r f l t f l l i t l r . , l r . r l r ' o lor t t t , i : , i t r r t , .o i r l t r l i , i l \ . i l , l , , t . r r l , , t l , , r r r ; t . , i r t r , , I t , t l ) .

t Jl!t l l I

I \ t , t l , , t I L t \

(:lr ttYll Dr,l lN,l lJ.,l tlt t(:vDN'l'a

,",.,#;i11:.:# ,!:':ilit'n,!:J/;%,:;ii:f fi,"::J:i:i:,:":;!,1:.,e cu secrrunead(f f ) /dr : ja( t ) . (1)

|d(1)/dr : i , , tc l .@l, l '

l , r ,n l r r r r I r I r ' r i I rk. I r : ordirr l r r r ' r r i r i r r r r l r , l i t t r 'o l ts lat t l | l r ' / . , ( ] , /1, I r r r r ' l t

, , ' t , t , i i i i tut , " i l , t t i , ' tot" dc propr i r '1 i r { i - r r t ' r l i f . t i lc lor .nrrr l r r i r r l . ts l ' r l ' l " r t i i r

, l i f | r i tc l<- ' r t l r t r i i l l t ' aceslor can1l1. t !1. l t r r r r ( l ( n l i l lcr la lc '

Trcbuie obscrvat ci, constanttlc tru siut absolut ind( Pelr(l( tr1( i i ' \ ' ' '1"

r i lc lu i I l i i 1. De exemplu ln cazul ut tu i gaz, ca-paci tatea C desct ' ;1" " 1 ' t ' '

s iunca, pe clnd coef ic ientul de iner l ie cret te ' La I l rh l ( l t ' ( l r ' ; r ! r ' r r r ( r r ( ' r ' ( '

i" i i .t i f i ' i"t ir1ii; viscozitatea varia/l cu tempcratura i i cu. (ur'(t)lrrl l ' l ' l t

citatc; sau hisierezisul varjaz5, de asemenea, cll acestc l l l i i lr l '

O oroorietate de mare importante, totusi, cstt. cit irc(stc Yirlr" I i ' l l l

, ,rnsiderite'ca functi i ale valori lor medii a luiH ;i l seu a tcmP.rirlrrrr"r ' i

i . ;, i i ;; ptit i i" io"ttunte in tot ciclul miqclri i vibratoare' cu c't)rlr\r 'r ' l

;;":;;;i; !i ri" *ii.i""i de inalti 9i amplitudiner rrrialrilol lrri ' l l r / t 'tompcrilurii mici, in raport cu valorile lor absolulc'

Putem prin urmare include solidelc printre di{eritclr'-lcluri tl ' rr'rl.rli

n, ."i"-i"' .,iJl"-, -aplici",lu-te

acelea;i ccual,ii ' in rnorlul rc.sl r r' lr 'tti l

in" ,J icf , i " t o s i rnr i t iub tensiune maie 5i suPl: i l :L-v i l ' raf i i l . t t f i l r r ' l t t t ' r lo

"o^G-li .ot"pntoti cu o coloanl lichidi in ribralie longitutlinal:'r ' rr"l. 'r1i

i . . "^ i i i - t i i .J ' r r i i . iu i i " t , t ambclL cazlrr i ' \ 'om a!ca t t1[ ' ] ' l t ' c( ' r l . i t l ' r ' r r l r l

i lar i ' "at ia l ia l insiuni i sau comptts iuni i pc uni tate dc srrprr fa(r-r ' l ' r ' r r lnr ' ' ; l

tt;i i;t; ;; intinderea sectiunii transveisale; ea corcspu.dc ctt // 'r " lt '

mesunte -in kg/cm'.

vom avca dcci de consideral arruthrl in barir, adici- vil('Zi| l '| |t;|||.|

particulc, inmulliti cu aria secliunii transversale'

Din cxDfr ient i cunodi tem ci n ic i un mctal nu este pcr{r ' r ' l r l r r l r r ' 1 l4". : , , "pur, . , i " o l ,ar i r dt .mrtal 1a tcnsiunc, , ; i apoi r id ic i rm lcnsi ' l , . , r . l , , r r r l

ir"-i" irtinnt.., cract Ia acciali lnngimc ca inainte' Aceasti-ptopticlrrl" r'tr "

i;n:t, .,.r l,lnurl', t '.,1 ltrdilutlti, t 'Ttsficitdlii -s.r histerezis ti.;i.1ri' r. ' l ' r"r th'

iui,ot ,tnttlriiL ,i cst.' r"pr, zirrtit:r prin SIl ctr intr-o coloani liclri ' l ' '

Vom r l i r , pr i l n lmltrr ' , t l t t :et ts ntai gcne r .a l dcl in i ! i i lot : f t i t { i r r r r ' I r "r r r r :zcrr t l t iL de , i r t r . tanl lL , /?, va ct tpt in, lc <- ' i ice Ior l i r int i rz ictrratr" i l r ! ' r l i r l l

i r r r . ,ntul , drr tor i i i t l l i ; r ' r : r i i cot l ' t r l t r i , s i 1 ' r r l i tanta, reprezlnt l l : i l ) t i l r I r ' l r " l r l r l l l

.s , va inclLr, l " loai i t 1, i , r t lcrc l t i l , 'mi ; , :at : . ' in fazi crr presiulrca ; i t l : t l " r t r " t r " t

1, . i1.( inztr l gt ' t r , ta l l l 1t ; r t rsnt is i t i pr : tL1ir , dc ' 1r ' r 'g ic pr in rr t t r l t r lotr i l i t r r ' l t r t ' r lo

vrr f i at : r l i t i t r , : t t , ' , r t , t i l i i t vrr nvcrt i l , l r iL l ( t l lsrr coio"t t , " , dc s": l i t t t t . r ' r t t l r l ' t l11'

Sl ' r s l r r r l icrrr i r r : l i i r i l , l t i t i r l ' r r l , to i rPr ' .

r \ ru r i rs i l t t r t i s t ts

( r )ln ca:e

ti(L)

(c)A:lt gisit pentr-u R, cind I :

:L_jRla

: C - 15 la.lcm

R: h.ilg^.Avern de asenenea L:.1lgco, ast fc l inci t daci l :

(L) =." el_la)ir _ jhld).Attalog putem scric .! = l.rf, 6u

C : atlE ;i (C) : (orE)it _ jh,la),i 5i -ii

sint constante ale cir.oroe h6ttte:isur-s,au plasticitatef"l?i,1flt0.1,:u'

p'imul clc tisco:itutcr;i ultimulru tem dctrnr ...rrsco:r1ir1crr, unei {orme particularc oarccare a materiei

l#':,:1.;llif,rtrt R sau A, astfet ca cnergia pierd.itil.in ?,1"r" interne si

llt : Rl,iz : hLl2iz,tnltci a fierdere tle enugit cirtctit:ti.

,il" ,i:'l,Lil'ilJ'.31":!:l1;t't1:l'"",prin coericientul s sau ,t,. astrer ca picr.dc-

H'r ': SH]z : lt.r CHJt2,iul;reit o .itiq:ylay2 aJc au.crgie t'.tettliald.'frclluic notat cir l, si /,;, sint sirnpli, coeficien !i nurner.it.r, rqpr(,zultindPtrlrrrli i rb rncrait: cinc(icir iau poteniiali, ,,,,i

-r,: i,lu.ti.l, 'rrriL i,. r:itrrrrrrir.s i t r t - ' , . r l r i [ ' r rn;-r dc cucrgic, r l ispiLr i l r t

^ . j i i . f , f1, , ' , r , , : , ] , , r , , i , i , ' r ] r , , r , . , , , r . l i t , . ,1, , r< ' r r r . - r , , ,11sr;11;r1, c ' r .c imlr 'eu.r- i c l l lnasiL . i , , , , . , , , , r i , . i , . , , i , , i t t , . , . r r rsr i r . i r ; r r , , ,( t , t tu, . . ( ot i { , . fc l ( l l u l i t tL:r i ( . .

o' ,.,, 1i,: l i ,1l l l l ; , i i l ' l i l , l l ' i i l : , i l , i l i i ' l ;" i ' r 'r"."r ' i ,rrr \ " ' i

r ' , :, i ,,, z.r '

rN{

U.l ( , ' , ' i l , ' , ) ( l i l td) , ( ( )

r l i r r , r r , o l r t i r t , t t t

( ( ) ( / . ) ( , i : t t ) \ t 1/7,r)( l 11, , / ' r ) \ '1 lv l i ) ( t . l . ] ' , l ' l . : - i ( / i I / ' ) / r ' ) '

Vlt l , r r t r t l t l t t r i , , r l ' r ' , , l t r " r r l ( ( ) ( / . ) t \ l l i r r t I r '1r l r t r l t r I t ; ' ' ;11i '1 " ' ' ! r r r r r i il i r r i , , i r l l i t ; r l ' , t r | | r , t r ' .

At t t 1 i . r ' . t l . t r t i t l t , r l : r t t ' t . r l .1

l, avcm

r tu( t / ) / r t r r 1, , , ( ( ) . ( r . ) , ( r / )

, t " r ' r , , ( r ' . r r r . r l , ,1 i , r lxrr l r r r ( / ;

, l '1r1i ,1, ' | , ru(( ) ( / , ) ( / )

(iolti)(t * jtt ' lt),

( l ( / ) ) ( ,1( / ) i , l r ) ( ,1( / / ) / r l t ) r )

( l { } ( ,1(( ) i ' l ' / ( ' l l / l i ' l

\ ) r l

|iulnd seanrtr dc valor.ilc lui (L) ql (C), obfincm:di!!!t,1rl { a,(c\(L)(I).f (r/q,) ; luola*y . (d(.r{/d.r) : o,d\(I)ldx2 { a'(c)(L\(l . (t/.). (d,7irr1. liliyia : o.

Aceste ecuatii sint eener;Ll_e;i slrrt itlentice cu ecuafiile (ZS) Si (Zl)tolul V), cu difcienta nimai t::t valoarca

Funcfiile Cor c qito&rele :

Sir a au proprictltl lntcretrnte, unclc fllnd

Sir2a{Cor2cr:1*0r2,

sin or Cora - cos c Sirc : c,

cos a Corc f sin cr Sira : l,

urrn 11.

(p,):al/@:@este simbolici. gi egali cu

deoarece p:at{Cf, avem atunci

t . .Pentru .frecuenfe tnalte termenul hhrfa2 devine foarte mic gi putem luatimDlu

vr - *V[-yn af f i ..,..o_, Expt'esia se mai poate sirnplifica lnci. ln ipoteza cd. fi.ecventa este inalte,lulnd

pr -p( l _ j (hth,) lza).Si considerim acum o conducti de formi- conicL; in acest caz secfiuneao poate fi exprimatb. Drin relatia ?: qr",.""a" ,

".i"-&.t""!a secliunii dele vlrful conului, q fiind o constanri. nurirericd. Relafia di

---'

(r|a). (doldx) :2lrecuatiile generale deYin:

d2(H)l ile + r,i(r4 + el x) . (d(H)l d,x) : o,dz(I)ldx2 + r.,i(4 - elx) .(d(I)ld,r) : o.

(capi-

De asemenea,lntre doul variabi]e a gi B, avem :

sin c Cor P * cos c Sir p : sin (cr* p) - p cos(c{ p),

cos €rCot B - sin c Sir p : Cos (c + 9) * psin (af p),

CoraCor p - Sir ct Sir p : 5s1 (n* 9) - ot p cos (c f p).

SirocCor p * CorcSir p - Sh (a * 9)-aPsin (a* P).

O alti serie de propriet{i a acestor functii :'

Sir ( -oc): - Sir a, Cor(-a)-{Cora,

(d/dct) (Sir d) : cr sin c, (d/dcr) (Cora) : a se. t,

(dzlda2) (Sir cr) : Sir a f 2cr cos c, (dldct'z) (Cor a) : Cor e - 2asin c,

!

ti(t)

. . Tr-ebuie notat ce in aceste ecualii constanta q nu apare. Rczulti derici cl, daci un numar de conduite .ooi"" .ini Ji-"tit"t" J5i" aceiasi sursil$:.s-e_Pol.l"T!"pune iar perctii lor se pot-suprima. Rezultatele vor fi iceleagi.r^utel, consrdera apoi un minuncli. elementar sau o ,,razi,, vibratoar,e,Igrmata oe once conducti conicl fictivl, avlud unghiul de con clt voim deItlc, rar peutru a studia fenomenele din orice conducil conici., nu avem decit!!,.adunem rezultatele oblinute din consideraiei t"t*", ,"rif.,

"".".orriii-tuie conul.S[ considerim atunci, ce se lntimplf, lntr-o astfel de raz6 gi si. punem'Substituind

in ecualiile (t), oblinem :d2(H)ldx2 + (2/d).(d(r l ) /da) { ( r l ) : o ld1(r) lde2-(z,1z1.1ag1a4a(4:0 l '

Q)

Solulia generalt a acestei ecua{ii este(H):(tla) (.t{ cos c f B sin c)(/) - lrCor a f 81 Sir cr

Corc-colc*csinc,Sltc -s in i -dr 'osd,

l

Cantitifile tr $i p pot {i valori numerice reale sau cantitlti comphraSubstitriind a : prr in ecuafiile (l), oblinen:

d(rl)/da: i(4 y(zto l.

d(.r)/dcr: i@v644 |Avem astfcl de considcrat cantitatea complexi '(@11t'1 pc clt. o vo*t I

lnsernna cu (r!); vom avea apoi, inlocuind (C) 9i (f) Prin valorllc Io ddllr,mar sus,

('ti) : oYtE:' 1/[=frl aji6=ini$,

dar am glsit mai sus c6, { : alt{ilE, astfel ci

(,1)-t'Y[=lM)nt]F).' Dezvoltlnd radicalul ln puteri ale lul [r/c ai {a,.ob}inem In caml lrcr'

vpfelor lnaltg, ln carc acesti functii slnt foarte mici,

(0)-Stt - l (h ' -h\ lzt l ,Valoucr l(,1)- y[ti@], vr'tt drill dG

t / (0) * t ( t + l ( f r - h) lzal .

Dllrrntltnd ocurllllo (t), gttrlm :

d(H)/ttr r - (t/d) (l Ccr * t ilt) ,

r l ( /) /r lr - r( l1eon 1 11 r lar),

ln care(3)

{ i r r r r i rL ' t iut l r r r ' , ' r l . r ' r ' r r : r ( i r r r l r r , l r , r , r t , ' r ' r r t { i i lc (4) , ; rvent

( l ,a:) ( .4 t i r r r , r . I / i ' , ' / ) j ( / ) / ( l ]J) I (5)

a(, .1, , os z i /1, \ r r 7) i (Qt (1f) |

Si-r reprczcntirrn prin p virl()irr( i! lruli l l iului c in punctul unde este alezatltr:r:ptorul, sursa saLr generatorul f i ind Ia rrn punct definit de cantitatea a;vorn avcil pentru punctul p

si i r r ' | , r .zr-rr l . r r r r Pr i r r c,- ' i p [ i ' i pala ' tc.z iL valor i le numerice ale acestor rrrr r

:lll.:!',1]'I"l:l':.,,; lrrr rr|glijirr,l pirrarul camitetii(k I kr)l.za.Iatd. de rrnirar,;.t , (ntnl i l s [n l ) t r t t ' . r ( lernonstrat ia s i studiem cazul part icular ln care r( . ( . r . rFlorxl si gcncrato.'l si't la o distanti. considerabili 'de virful conului,.rst/,.1incit si. putt'm reline numai lermenii continind pe a gi g multiplicind iurrr !ii.Formulele (10) se simplificl 5i devin:

H" (9t ') l lHd cos(,.) - (p)+ j((rp)/(. lp)r. i"G)- (p)l( l l )

ACorp I B Sirp : - jP'(/) /( , | ,p) I

lcosg+Bsinp:p(IJ) |Prima din aceste doui ecuatii este dedusi din ecualiile (5) ;i a doua din

ecuatiile (3).Din ecualiile (6) oblinem direct:

a: -l(H\ sirp { jp((r)i({e)) sinpl },B ' (H) cor p + jp ((1)/('lo)) cos p I

({s) reprezentind va.loarea lui (Q) la punctul p, ({) fiind o cantitate varia-bill cu r gi, de asemenea, variabilS. cu p.

Pentru punctul p putem scrie de asemenea ecuafiile:

,,t, cos ct f I, sin p : j(+o) (H)/pl.AlCorI + B, SirP : (1) |

Din acestc ecualii, obfinem:

a,: ( ( I ) | i l s inp - j ( ( , |p) ( I / ) /p 'z) Sirp I .B' : - (\I)/il cos P + i(({lg) @\lP'z) cor P I

Substituind in ecuafia (3) valorile lwi A, B,.r{,, B, date dc(7) 9i (e), avem

I": ("/il 1(1u) cos 1") 1e; -! j (He) . (+t sin (*J-)l-(6)

(7)

(8,

,._ I)ar c.unoa;tem cri t laci avem unghiul complex (a): ar * jtr.zulti i rclati i le:

sin (a) : sin c(r cosho.. - j cos cc, sinh ar,cos (() : cos a, cosh cq f j sin a, sinh c, ,

sinh Si.cosh fiind functii hiper.bolicc. Daci. punctele a qi p sint astfcl r..r ,h,,tanla dlnlrc elc si lle un numi.r intr(.s de lungimi de undi ;i dacir l,rrrrr.rrr(") - (9) : ("-9)( l - j (A+ h,) l la) . - ,s i dac: i mai a\ .em a_,1 )ntu,oDtlncm:

sin(c) - (p) : - j s inh(c. - i l . (k + ht) lza,

(e)

ccuafiilt

cos(a) - (9) : cosh(" - i l .&+hr) l la.Servindu-ne dc accstc relatii, formulele (ll) devin:

(H,l (lla\ [(]1e) cosh(e - p) (A + ht)lza +l+ (( Is) /(*s)) s inh(a - p)(k 4 h,) lza) t .

(t) :- @/il [(1e) cosh(c - p) (t + h,)lza l[-F (I1p) ({e) sinh(a - p) (h i h,)lzal )

. - l 'rchuic Dolat cii putcm inlocui.(t lrp) prin r. i., tclrnenul conlirrirrrl 1r, 1

itr crplr.si:r plnllrr (r!e) l i iutl rrr.gli jabil.

. l lepl'z-cnlinrl rurrnirml dc lungini de undi. dintre receplor.; i l :, rr,r.rt i, llxirr rz ; i frcclt 'n{l prin rr, avtnr in caz,rrl in care A0 si 1g siDt ir i l irzi.

l l " . ( t la\ [ , f lp coslr l - t . ( /e/{e) s inh.y] LI " (dllt) | /1, cosh - -t . {e //p sin 1 I J

( l . r )

| , ' . l r , . . l t , . ( l i / ) r ' ,

l l . (11/ , ' . ) , ' l l l t I I r l ,ht , 1. , \ , . i ) l t l r ' l / . | , fp/ /p l ,

i rr r ;rrc .,, u(li I ltr)lht .Olrsr . r t ' inr l c i m' t " l , < l is lan(:r t l intr t rcccptor 5i gt ,ncr.alor. q i , r r r , r i

rfr,lrar'fr', r' ir, r). . zr vilcz,a srurclulrri, avlm 7 = -\1t1,) \k + kt) .

. ( i rnrqrar i r r r l . lor r r r r r l ,k. (13) rrr f t r r r r r rL l r ' (?) , ( l i ) capi to l ; l Vl pr . r r t r r r

ror t r l r r r '1r , lc c i l i r r r l r i r r . , v l rk:rn rh r . l r . t l i f t . r i r uumai pr i i r f r r rc lor i i p/a; i 'c /p.

.. ()ottlurlt lr o lrll i itttt iu.ltuili, ltari in formtrk.lr. Irn,r:crlcntc Irrrrrr,rl

l l t t t<t ' ; i I txr , r ' r r r i r l i i l l t [ 'v t t t 1r , r l t ' l r . r t t t i r ta lc. Vonr 1-al lu i l i . r 's l r . i lzI r r l t r l r r r rx l r l i l l r i l

s i r 1r t r ' . . r r1,rrrr | t r r t ; r r l r , , l . | | ' l , r / r l t r r l r r . 1rr | l r r r lor . i I r . r r . l , lot ( .s1, : t l i l ( l r .t t t , r t r ' l t r r l l . . j r I ' r r l , . t t r I ' r r r r ,

( t r )

(&")-((Hey(4)) isin(0r1191(9;cos1"11p;1;11p)/(6()).((Ip)i(+p))sin(-+-(p)l '

(IJ =((ro)/(p))L4cos1[--1p1-sin1"t -tpll+itt+ottHa)/((p,))lsir(d,) lor I

+ (') (P) sin(ccJ=lP)fl( l0)

Indicii a qi p aplicali la valori diferite ale lui (1), (fl) 9i (,|l) indicn va-lorilc acestor cantitirji la punctele definite de unghiurile a gi p, rcspectiv.l'ormulele (10) sau solufia problemei.

Dacir luim fricfiunea gi lristerezisul egal zero, putem inlocui (11), (1)9i (Q) in ircsstc formulc pin H,I gi r|l, respectiv. Daci. aceasta nu e cazul,toltc cautithlilc ct, p gi ,! sint complcxc;i este nccesar a scpara tcrmcnii con-tinlnrl pc j sprc a ajunge la formule cxplicitc.

Arn {:hsit mai sus cf, c estc dc forma

(a) . - y. , ;u - l r r ( l - i@ | l t , ) lzul .

. t t* , , ,* ,1, , , , , r 'u1,

t . . , , , r , ! , , , L 1 "r , l r i . t ' ' t . r , r , . , , . . , i . ,

nr, : ( l , I r " l I r ' r ( l r r l . " I r ' I I ' ' | ' r I | ' | , | | | ' , | , i I t , l ' r r ' r l r ) l l t )( l l )

' r , ' r , ' , ' , , , | , ' , ' , , ' l , l , r , I r , ' r 1, , , I

Itc ,

. ,ttFttrllll[tI r , . r , , i r I t ,nr ! ,n I I

, " '1/ , ) {0)1. ' r i r , l . ld l . / '

l ) i r r r r r cslr tkrr t . i t r r r ; r l t t o l r l r r r , . r r r

, u, / iJ \*" , , (

" / '

:4,6CP. Acest rezul tat este indcpcndent dc f revccn[ i daci aceast i r Is l r :

srr l ic innr d ' inxl t i r 1 i e ' tc I i rn i tat (1. ' cavi taI ia 3Pcl '

Sir t t:pt czcrrl r-rtn plin lr ' , :rrtt1rIiIrrri irIcrr vitczci la punctui a ;i prin <o,gi <,.rp ali ikr t lc sccfiune il couthrr:1t' i l l l tcr.lca;i doui punctc.

Vont avea: +s: o4/g|E .,; i I": l / "<,t,.

Substituind (14) oblinem

#:; eftl+Dar, pe de alti. parte, avem

(o, _ c2.

(,)g 9'

Oblinem atunci relatia importanti.

v": H"VlEls. (r5)Aceasti relatie arati. ci amplitudinea vitezei este pur ;i simplu pro-

porlionali cu presiunea sonomotrice, atunci cind curentul sonic circuli laInfinit firi piedici sau reflexie spre sursi. Aceastl ecuatie, de asemenea,nc permite s5. calculim energia maximi" carc poate sii fie admisi de o supra-fof[ vibratoare. Lisind de o parte indicii q. lie H, I presiunea sonomotriceti curentul intr-un punct din calea unei raze vibratoare conice. Fie <o ariasuprafetei vibratoare presupusl agezati. la o distanfi. considerabili de virfulconului si de-a curmezisul axei razei.

Energia pe secundi, emisi de aceasti suprafafi spre infinit, va fi

W:HI lz:a.HV|ZDar am glsit ce

v-g yE

IOblinem prin urmare

w:(alz\ H"WE7ctrc cstc o cantitate finittr.

' Exemplul I

Se ccre a se glsi maximul cncrgir:i vibratoare carc sc poatc cmitedc o suprafatl vibrrtoart: tlt-' un ccntimctru piltrat aric in api1, prcsiunclmcdic a apr:i fi irxl dc I kiloglrrrn/crn'?.

Avcnr pr:nl lu apl t

Vlnn ",t .(hrr I r ts i r r r rc i r i r r i r1r ,"r r r r r l r r . l r r r i r . r i l t rL.v i r r )1 rrc l lu l iv l : rvr t t t Pr l l t r t vrr

loulca rrr i rx i r r r i l l l r r i , l / t k ;1/r ' r r r nr l f r . l l l l l , 1,1 k11 r ' rn/ : r ,I { r .ar t l l f r r '11 o.urPrrr f . r { i v t l ' t , r l , r . r t , r l r , r r t t r r r r ' l t r r I ' l l r , r l l r Inr , r l r ' l t . r l ' ,

nr i l r i r , r l , ; r r r rat r r r r r l lh l r r r t l i t r . r l , r i l , r r , , , r r l l l ;1 , l , l l r 1.1 l l ) ' hg r r r r / ' ,

in crcmplul prccc<lent se cercatului supr;rfctei vibratoarc, atuncicncrgic vibratoare, frccven!a {iind il

Avem tr/ - rLt : Zftr . Dar V

E,rent.flul I I

(I l) ( l/a) (.4 cos ct

(1) . ' t ' ( ,ora i R'

a sc gi : i anrpl i t t rd inca / a dcl l i r : . r r r r ' t r

c ind " t ransmitctn

maximul t ' * i l ' r l ' i ': 100 pe sccundir.

: HVIEIC, astfcl cd

r : (Hlznt) 'WEIS:112r x r00:0,011 cm'

Cu o i r (cvcnt i dc 1000 pe s, . 'cundi i rmpl i tudinta . r 'a. i i r1 ' r ' " ' r1" ' l ' 'o sutime de rnilimctru. \'cdc[r, prin rllmar', l ir tstc lnutll dc a Prlxrrri ' ' trr

irf.t.*""t" mari dc suprafclc i-ibratoar-c sub api' sprc :r ,ob{in. rrllt rltt

int tcmi,^, , ( l r . ( .ncrgic. Pent^r a pror l 'cr "ub

api und( '5ono!.( t l , ln:r l ' r ' l l r r l r r '

l i ; ; ; : ; ^ i i i

t , ' " i i i t i i i i , i l i , , , i ta, iu, ", ' o n'u" anft i t trr l . i t t i ' i t t a' t l ' t r"rr '

"" i - " i t " analog, 'cv 'c i i f , rcnla c i ' , ampl i tudinea admisibi l i p ' t r l t r t ' t r ' l ' l r r r t '

inu* i .u n, , n.r I i , ' i ra. l iat , ' r l , l i r o i r tpr l fa l i t l ibratoar" . rL l t i r i r r ' r r t " l ' ' t t

inut i - " i

rDar, i d, . , . i t in ap, i . I , , .nr Iu i r ' .1:- t . i rat iunI o : i r | t r i l ro: t t , r l , t t t , " t

un sunet loart( Pt l tcrnic, dar prcamic in api t ; i Nic( i ) ( /s. t ' ( ) sul) l r l ' r1 r . r r l r l '

ta l ' Dcntnl a . , , , l i i r , ,n sulr( ' t putcrnic in api t Poatc t l ; t u l l s t l t l t t . l r t l ' l t t t ' t ''Daci t oon. idcr l - tm nl i ;c i r rc:r in imtdi i r ta apropl t i ( ' i l s l l l -s(L l l l r i ' l r ' r / r '

couicc, r,t ' t lcur din formult- ' lr: stall i l i tc mai sus cir apai. oil l-( ' ' ir"t1' lr ' l l l l( rrl ' l

i : i i l i i i . ' , f * d iscrr tat nai sr ts cazul conductclor in{ i r r i lc , i : r t i t tc p tLr t t r ' t t r

i i , i i i ' Ai t . t t l i . , r t r t t t | I t i t a | t t r ' r l i ' i (10) iLr r t ; r ta t t st int i r r r l ' l i t l ' t r ' t l ) r r r r t l r r l ; i

"a i" f "" t f " , ,1ta, , rp i 'd" . r t r i r , r lu: : i rc la ' t r" t d is 'u( ic l l r or 'u l ) : l I ) l i i t l l l r r l l I r t r r r

s i i lsc r l l t t r : r t l ru l pr ' z ' ntr i Jt tct i - t r i '' Con, lu, l t cot t i r lc t lc Lungimc i t tJ i t t i f i c t t gt t t r t t t lotuL i t t ' t l ' t 'o l ' t i t '

i ' r t t l

l l lvcnint l l t r r ' t t r t t i r t (3) , avt 'm:

I l ( ' )

ln c l tzt t l t t t t l i cont l t l< l t : r l ' l r r r rg imc i l l I i l l i t r ' t , Pt l t ' 11] ( | ! I I I t I I I I I ' | { ( ' r r ' ' l i l l l

t , .1, . , ' i , ' i l ; ' ; t ,

.1, \ corts i<k'r int l t :L t l r r t I t a: co, r r r rnr ( / I ) o ' ; i \ r l ( 'z ' l

l ' I lo o, ( i r r t ' ( 's l ( ' ,chivalcnt cr t rc la l ia

11d.2 , . . 0. ( l / )

Si t t lc t t t i t t r l t "p l i r f l ( r ' t I ) | ' t I I I t | I t I t i r ( ( 's t ( ' r ' t rnr l i l i i r l t ' r r ; r r" " l r l " r i t '

r l i , ru r" i , i , r r , ' r ' l : i , i r f , ' r l t l t t ; l t l l I ' ' t I ' I r tct ' ' i t t r t r ' : t l i t l i ( l ( ) \ i l r l i l l l r ' : t I ' t ' l l l t l l l

1, i r , , ' , , l r r ) { ' i t i . r l i r l l r , l r r l t r t l . t pt t l t r l t t l cr co'' Srr l , r ' l i l ' r r i r r , l i t t | i r t . t t r l l .zrr ( l ) v ' r l t } r i l ' ' r 'x lxnl l . l l l i i r l t ' P( ' r l t r l r ( t ) r i r ' ; l

' , l t t a, , l r l i r I

r r r , , r ( ' r ' I , ' r ) / / , , iu r

r , r u,r l t tL r l " \ ' l l l

( , . , ' , " l l l i t { , i , , l ' ) . i 2,

'i:.o "" 4I .

5lr c. l

( ,1) . ( l / . , ) ( , , ' r r I r ' ' r ' ) ,

t . - ( l , l ) l l , , r ' I , ' r ' t , , ( ' r ' , . l ' ) l I t t l l t ) l , r l , ) ' | ' r ' ) I i ( ' r '

I, u ' ) t l

( l r ( )

I I r l t r ' / t l l , t r l l l l r l l t l , l l l l r i t l l l t l l l { l ' ,

, . l r r ct : r r i r l i iL. ( l l t ) prrrr i r r , l , r cx.r 1 i l r . r r r r r int in<l re la l ia (1?;, ob! incnrI) - l l .

I !xprcsi i r l r r i (1) , c inr l a r .s l r . iuf i r i l , rk:v i t rc

( r )"__, ( t /z)cF[A,( t - su) _&("+ j ) ] .Itntru ca condilia (17) sir fie satisficuti. cind .{ : oo, trebuie)si aveur

L\l",h-*: (et"lzd) lA1(t l,t - j) - B,(r + j/,)l :0

srrr <lcoarccc cic/e devine infinit cind cr cste oo, trebuie si ar-em - jA,-

infinite, expresiile pentru

(H)"

Br : 0, sau At : jBr.Vr.rlcm apoi ci, in cazul unei conductc conicc

(I/) ;i (,I), devin:

(H) - (tld.)E e-," : l la)E (c.os e - j sin e) |( I l :Br(Sira{ jCorcr) i '

. Constantele D, B_r,y,or li determilate rlc r rlorile (I1) !i (I) <ie lalgenc-rirlor; insemnind .e (Ao).: (/.

")t ee, valorilc corcsprrnzirioare de r gcneraror,

ir\'r 'm 1)entru un punct definit de cantitalclt a -

\,',l, trr prirr rrlrrriLLe cir o r-clatic foarte simpld. lcagi pc f 9i I/..\, 'r:;rsti l ltrr{ir'ostr importanti Si ne permite a calcula tnaxirnnl ctt, t

,qici, r.rli: porrtc li radiati tl i la o sursii intr-o conducti. conicir'Iirhtia diuirc vectolii (H) ;i (1), galsiti la (21), se poatc scric

I,Il = Ql") 11 (Sir a -l- j Cor a) (cos a I- j sin ct) ": (rf/a) '1{S,r a cos z

Cor *s in c i . j (Cor ccos.r + Sir asin ct)1 : Ql") 'H( l - " ) .I)aciL Q estc unglliul dc faziL dintre .Io ;i llo, \-cden c.i

tg q) f jz. cos <D : t lll t 1 *1--:-=:.

Putcrca mecanici-r, dczvoltati. la sursi, r 'a f i attlnci

w : (HIlz) cos a : (+12\Hz.

Tablorrl urmirtor aratl factotii de putere pentru

0, ()3

( l e)

(20)

(1. r)

diferitcle valrt i rt l, '

E:

p-

(H")",cose- js inc cos ao - js in ao

(10)(r)

lu i a.

I "t' 5nl4

0,9i

\ -et lsm ciL accsl f i rctor est t foartc apl() lPe ( lc l i rn i t i , chi l r r l ) ' l r l r r ls , .= 3n14, : r r iLt int l c iL, in cct . r , . ' pr i \ .c; te formtt lc le t l -c. intrc l r t t inIr l ' r t t t

gt:tt".^iot ay'zat l ir o l l istrlt l t ir r lc scrniuntl ir de l irful conrtltt i ' poale ft ' . l t t

i ir:rat ca un gcnr' l i ttor', a.,sczrtt h o <listan!iL considcrabil ir ( l( ' \ ' irf '

I lela!ia (22)

I '- t?tt| l lA + t)

r rat i r c i , r ' ) t i rn l rnt t ' t t valorrr t ' t lu i ao ' : t t , .vonl .avci l 1. I , l )5r l ' ' / / , r ' r r r

"dift:r i ' t nuuui ,,tt .s'1/u ,l, l valortre:r f ' ' r l,11 gnsitl pri lr corrsi(l l ir lr"r l l i trr 'r 'rlorulrri, sitttat l l o lorrrtc n:rrc (l istanll dc virf.

Itczull iL ciL tl)roxitl l ir l i i t t l l tt ir tnai sus va fi aplicLth IiLri i ( 'roitr '( ' irplr '-

r i r r l r i lh, r laci i g, , t t t ' i r r t , r t t t l i l t t rcccl l torul ostc s i tuat l : r o t l is t r r t r l i t r l t : r ' i l l '

' r l , ' nrr ttr:ri prtl irr rft: o Itrtrgitnt: rk: st- 'mitlnd[.

I ) : rc i r r l is t r r r r l :L ( ' r i l ( f l l l i l i l l l i ( l i t c i r acoast l l , putcnr fact ' t tz ' r | l : r 'ot ' r ' r '1 i r"

r , r r ' (s lc rc l r r t iv : ' i tn l r l r ' r .

I t t r t t t i t l iz , t I r r ' t t l t i l t l t t i r ; t t r ; s l t i r l t l : t l r [ r 'sPrt ' tot t I I t t t I I 'L ' t lot t i t r " r l t ' t t l t r t rc

.rrr ' . .1r ' ; r : l l l ( " . r l t l . r t t t t : r t , i t t t I rDr t : r t t t . i ; l t l t t t i r ' i Arr ; r l izr , l r ' l r r l i . lx ] ; l i t l l

, r r l . rp l i r l i r l . r t , ' l r r l l l i l " . r ( . r l ' , t n ' r l l l l t lc v.r l l . r / i i 'hrpl ' t r r l '11 . ' l i l ' r l l : i

l l l I " r tl r . i ' , . . ,1, . r l i f i r . i l r t , . 11 ' l r l r r r r .

, r vrrr i . r { i , . r , . r r l i r r r t i r ; r r , r ' r ' t i t t t t i i . , r l : t . t .zt t l l i t l l l r '

r , l , l i r r r r l , : . i r r t 1, t . r , l t , r r t l r ' . t , . t I ' t r ot t r l t t r l r ' l l r r r r rs l i lu i l r ' r l l l r l ) r ) t l l r l r r r r r r t r

l , r t i t t r ' , ; r l , r i t r r i r l t i r t t r , l t , , t , " . i ' , t t t 1h"n t ' ' i l r l " l l r r ' \ iv i r r . l t ' 'p l r" I r l . r

( | t r t l t l l l

, , r l r r r r l ' t t t r , ' , r l , r ' l l l l t l l l lot ' ,1 l l l ' l l l t i , r l t t t r I t t t | ' i r t i r t t t I l l l l l l l , l l l l l r " l ( l | l l l l ( l l l

| . r ' , t t t t1, l . r l l r " l r " l r ' ' t l , , r t t t r t l ' t ( l l ) , r " ' lc i | | I l . t I nt I | | . ' l r ' ' r I ' l r ' r ' t \ ' ' r r ' l

, . r t , . r . r ,n, t |or ; r . r . r r r ' r ' I , , , t l | . r . r r l t , r ,h ' l , r ' r

. , l l l " ' i , r " ' l l . l l r r r i l r l " r " l l l r I

( l r '

,n1i , r l , t1 ' t Jr t ' ta l t r , \ ' , r ' f , , r , ,1, , r t l t t r r , . r r r r t l . r i t t t r ' r t l r ' r l r l r l ' r { r ' l l

r ' r r l t

1,rr : ; , , ,1 l r r"r , r ' r r i r . r l ' i t r l t u I ' t t ' r l r r " \ ' r ' i ' l f 'ut t ' l r ' r lJ I r r l l ' r ' r l ' r ' \ l l ' l

t r r r r r r l r r t , l

.a '

Siraf jCora Sir aof j 'Cor cro

. O relalie interesanti se poatc obfine prin cliferenlicrea ccuafiilor (19)ll irnumc 4

tl(H)/dcr: - (El"\ (Cor cr - j Sir c) : j(l;/a,) (Sir a f jCor a) :

: j(81",). (I) lB,\.I)ar am g[sit mai sus formula

d(r/)/d(: lQ)va;t@,rrstfrl c[ ob]inem

ElL: ezY6^q,irrr it tl irr ccuatiile (20) rezultit

( t t ) lg) - "14r,) l (q.(cos

a - . j s in cr) / (Sir r I j Cor a).l '{.trtnr fI.r.\ 'r 'nt(: inalte prrtcm inlocui (/_) ;i (C) prin /- 5i

r . ln

( l t ) i [ ) " ( - t ,1C.1c<'s

r js in z) / (Sir . r I iCor a),

r , r l )or tn l r i r lo l iL : r l i t r r ret ict :

Ir /iJSiL "1tl-6ii"y,) r"V'ila trVl t-Ai.

, f r t l r r r i r ' . r ro l i r t . , , i Prrrrhrsrr l t ' tv L l ( ; * l r i r r rL.1Ir . r r r ! , r r t r l r . Prrz i ( i . r ; r r r r r l r r l r r r

' r i . r l r | | t l : | | l I t | ' l , t i l t . l . . , , t l ' l | . t | t , r r r r . . r l r r | l r i

r . l ,uVl t | , , \ t , , '

C ;i obii-

(21 )

( \ l l l r r l t \

r.rNI fNt:, [r l t :Ai l lo pcrdi tanl i 51 i l ser ic, scr ' r r lcrea prt .s i r r l i r ' , ( ) lot lo l r i ( t . dalor i t i r r l isconl i r r r r rtirlii (vezi capitolul IV) cste

(E) : (R, $ l . rS,)1 . i j ( / , , r t ,Cf l l l ,punind

(Lt) : Lt - 1lCta2 - i(i?t/,r -l- l/Sta)

oblinem, simplu

(H): j (L,)aI . ( r )

in acela;i mod, dacir la discontinuitate aven o cilpacitatc, ,r irr, r(i,.,o frictiune ii o perditan,t:l in .t'aralel, sciderea cr.rrentului

-va Ii

{I) : j (C,l ta,

I I , -TII,,, -

SciLzind, alem

II , , , - t * 211,, -1. H,,+t : jLu[ , , , . . I^ . , ,1.

Dar avem, de ascntcnca,

I ,, - I o, r, : 1Cr 11,,,.

(4) , o l r t incnr

II,)-t - 2H^ i H^+t --= - LC'r.:ll.

uV Ta- .2 s iu (o/2),

II. , - 2ll ,,, ttt: ( l

Ho h Ht 12

l t r , , ,

illliil'. ili,i+i+i*1.+1r,,,,ffi f .r*:ffi ;+".,;n:i iiill . u",li,, rill : #ir;i;n rr ;l*if EH r?:##l;lr. il i * fi l.: ffi *:iir:xtir,i riri*iri \*i l';'ffilll'l.ii:,"r,*!;:1, l.l.lxl.li,"illjii'lJ"lH?:i r T:l:"1,;ii*-iii*ii::n ll *rl"i *n,l"l.il,.T,:,1,;.1t,*$i

-;i *ir

i*ii'ryiHJ"''''"..t*l'i**l{U*i-i:t:"','#i$,,,,,,,,,fli:1:'A01.1,"":'.#lii:i:."#l?,j1.:li-ril.;,rH:{#ffi",#:,i

fl.;';ffi HfiffitTgibibffi {ii:r"..#;;:rii*ir"*#.ii $fr l,,l-l.'il,;;di,{#I-tfr}*ls":il#r,,;,r ; ;,ir;iii,l)':f ii * t ;,Il:'l ,.,l.l* ; *ni# til;, f , :;; ;;ri' r ii iiiii, : *tlililt #*:i*,*ii,,i rnl,, ri";rili,l ::i; 1;.r qllg: ii :*"li;U:g[i::irp;;n](ii,:]rlir i; i, iri,iirr:;r ::,lr"iii rrlir;iI;jir;iririifl*ti,iii,:,r;,i:1,j,,jrjl;:,r,r;r,,lliri:|,t,l

( . ' )

inseurnind prin (CJ o cnpar:ittrtc simbolici, care irrcorporeazi-r toatr' rli.r orrtrnuitil i le in paralel, e\istentc la punctul considcrai. lixprrnt'r, rr firrrt.r l.rcapitolul IVrelativla interl)retarea forrnclor simbolicc ale incltir.i. ,.!t,. .rr.rlogi cu cea de mai sus.-

Dac[ adopt i rm conlen{ ia, c i l i terele H, L, I , C r l in iorrrrrr l , . l , ( t1 . , r(2) reprezint iL toate ta lor i s imbol ice, reamint indu-nt c( ! ( , i r ( ( . : - i r \ t )u. , r r lsus, ne putem clispensa dc paral'rtczi. si scric simplu

LI ..= jLaI, I : jCaH,

ajut.tgind ast{el la conclrrzil ci-r, daci dentonstri-inr plopozil i:r r(,.r\t r., r, lexact i pentru iner l i i le ordinalc in ser ie, sau cal l rc i t i t i le i r r l t r r r - ; r l , . l , , ' I ' r r l i . r r radmitc-ca exact i l i pL' l l t tu o r l t i forrrr i dc, l i ' , . , , r r r i r r r r i j i t tc . '

S[ presupunem ci i ; rvcrn o l in ie a]c l ' r tu i t i - r ast lc l l t r t ' r ' r r r r t - ( , r r , r l . r l lf igura 50, avind iner l i i Z in scr ie ; i cap;rc i t iLt i f i r r t , r r r ' . ' lc l .

Putem scr ie urmir toa|c lc ccuat i i , c . i - . lc i l : : . i l r r ' i , l . r r r , .Dt, (o| l f rdt l r I r ,

- H-: jLr t , , , I .

I I^ , r : j l r t I , , , , r l( l )

{.r)

Substituintl irr

I'rrni nd

oblincrrr simplu

(.1)

lNcullh tt) ttlrr rnllrflll.rrtll rlnr,tt lrrrrr,rn11,, , .1, , , , ( / , r r r ) l ) | / i r . i l (1,- t t r ) t t ,

I 1 i / l f i i r r t l r l r r r ; ' t r r r r r ' ,1,r r r l l i r r l r i l r r r l r . , r ' i r l . lxr | [ i t l r : tcrrninlLlc

I)aci yrunttrrr l i o f i 17p -- p, succesiv, in ccuafia

Ho:Acos!0 { B s in 101Ho-A. I

Pe de alti parte, putem scrie -uccesiv

H^-' :..4 cos (? - tr + l)0 + B sin (l - nL +H*: A cos( l - tn)O + Bsin(! t -m)0.

Din care obtinem

(rt

l )r t jcunl unur' i rzi i :

(6), obl incr l

l7)

1) 01I '

H*-a - H:,: Alcos (N - m + 1)b - cos (1 - m) Sl +

{ Bfsin(1 -m+ t) 0 - s in(1 - rn) g) .

ln]aceste ecu a{ii,ldaciipun em 7n :1, oblinem

IIe-r- HF:.4 (cos 0 - l ) f Bsin 0. (8)

Dar din ecualia (3), punind rz,-=y', oblinem

Ho-r-Ho: jLoI ,

Substituind in (8), oblinem

,4 (cos 0 - 1) * Bsin 0: jLalo,.din care

B : jle' La /sin 0 $ Ho tg (0/2).

Introducind aceste valori ale lui I ;i B in ecualiie (7), obtinem

Ho - Hn(cosp0-|- s i r ry 'O,s*)+ j I , - !Ls 'nfs." " \ - Z ) -s in0

Iteamintim ci.

2 sin (0/2) : nVII,ccualia devinc

1l-rHo: H,cos(1 - t lz) l lcos (0121 +i I , | / :s in10/cos(0/z) .

(9)

Aceastl ecualie leag5. pe Ho, He, Io: adici presiunea sonomotrice delir capetele liniei gi curentul de la unul din capete, anumc acela cu rcccpto-nr l .

O ccuatic similari poate fi obtinuti cu pritire la legitura ,Jintre Io,l, .,si I!o, printr-o ana1iz5. similarir, porninrl de ia ecualiic ,ichivalente:

1, , - , - I^ : jCaH^-1, 1, , - I^*r : jCaH,, ,

din care oblincm

I^-t - ZI , " - l - ,1, r r - j { )a( l l^- , - H*1,

146

.ltrrI l^-r . l l^ . - i l t | , , ,

' t l l , l r r r r . r r t

I ^-t - 21,,, cos 0 .1 /,,, , , o,

r , r r l ls l r : ; rnalogiL ru ecuaJia ( .5) , s ingunr r l i f t , r t r r l i r l i i l r l c i i , / a i l l r r r r i l1r, //, l lslfcl incit oblinem

r _ r cos(/ r I /Z)0 , . r r r l f - l - ts i t r l0

'o - '" - t

1q21 'r t" e Y z t* 1074

S[ presup'unem acum ci considerlm o linie fictivl, l)c (];rrr, (, \,r,rrrrLrmi linia uniformi. echivaLenli, avind o lungime l gi iner{ia /.' tr.rrlrrrrrnitatca de lungime, uniform

-distribuitit ;i, de asemenca, r.iqrlr,' i lrrlc,r,irictiunea gi p_erditanla C', R' ;i S' respectiv pe unitatea de lungirne, rtrrifolrritlistribuite. Dacl presupunem ci. aceast5. linie arc accer;i hngirrr,. ,.rr rll inia discontinuS. considerattr mai sus, gi dacl presupunem ctr disr.oiitirtrrl ltl lr,dc pe linia discontinuS. sint uniforrn distribuite, linia echivak,rr t nr. li,r.tca inerfie si capacitate, {rictiune ;i peditanli pe unitatca dc hrrrli irrrr.

L' :i.LJ:; :'.,: f :!.'1. (rrDc' : pclt, s' :.rsl I

Dar am gisit (vezi capitolul V) c[ pe o ]init, unifor:rrli rrlr,rrr

Ho: HecosN+ iI , l t ' f te' sinpgi p : ! l l | r : ' .

Substituind valorile lui Z';i C' din (10), obliu,'rrr

Ho : Ho cos p.t. j jI oJlLlC sin pl ( i l )

;1v: @ilt)VTe : z(Ilt) sin (t)/2).

. Pentru ca ecua{ i i le ( l ) , ( tO) ; i (11) s[ poal i ' r , 'x l ) r intr j r r r , l , . , r1t l , l r l l l ,trebuie s[ avem:

cos pl : cos (y' - 1 lz) 0 | cos (0lz) : cos (2y' sirr 1 {)/i)),sin ul : sin 10/cos (0/z) : sin (21 sin (0/2)),

care pot fi scrise:

cos (1 - Il2\01cos(B1z): cos (2y' sin (0i2))ls in pO/cos (0/2) : s in (zp sin (0/2)) I '

0- fiind-un unghi mai rtic ca,2r, relalia (12) nu poatc fi satisfllcrrtd rl;rrrrrr,decit daci 0 :0.

Dar trebuie notat ci daci 0 -este

atit de mic, incit slt prrlr,rrr pr1tr,sin (0/2) : 0/2 'l.i 6ot (gl?) :1, condiliie (12) se rc<luc lt

cos(? - 1 l?)0: cosl0, s in10.. , . s iny '6.

A doua din aceste condilii este o identilatc; prinra sc rr.rlrrl.c lu

cosy'0 cos (0/2) } sin p0 sin (0/2) . cosy'0

t l / )

ut

crtF, dtc l C r l i r un rrrrphl foar ln mlr , r r r , . ,1rr , , . l . r

l , , t | t / ' l , {1. ( l r )sarr sr t r tp l r r l l r

s i r r / 0 () .

I)acir fricfiunca yi perditan{a din tlisconlinuitirli sint ncglijabilc, accirstirsc rcdtrcc la 0 - a hfl.|. Am gi.sit rnai sus

p.t : zf stn (0lZ\.

Dacir 0 estc un unghi foarte mic, accasta se reclucc Ia

*t : !0. (14)

La capitolul V am glsit * :2r.11l ), fiind lungimcrL de und;. a linieiuniforme echivalente; substituind in (13) obtincm zdl), : lb -= + litr, sau2U1l : t k qi 0lz : ill!), si t : hxlz.

Rezultl prin urmare ci, conditia necesari! pcntru ca o linie discon-tinui, in care Iricl iunea ;i perditanla sir.rt ncgli jabilc, si-r po&ti-I f i cchiva-lent5. cu o l inic uniforrrir., in care inertia si. capacitatca sint rl i tr ibuite uni-form cstc, ca unghiul 0/2 sr'L fie atit dt'mic, iut:it si i putcnr lua simrsulcgal cu rrnghiul insu;i, ; i ca hrngimea conductci sr-L l ic Lrn nlrlt iplrr cxact<lc lungime dr: scmiundiL a l inici uniformr: echivalcntfL.

DaciL s cstt. r lum5.rul discontinuitirt ikrr dc pe o lungimc cic untl ir, l i lcm:

hs:z! , i : ( r ' /s) i , 0 .= ( l /2) . (2;1s).

Conditi i le pcntru cchivalcn!l-1, a;adrr, sc rcduc la urmi-rtoirr( 'a t ci{rrl irpracticl: daci'L imaginirru un ccrc impirrl i t intr-rrn numr'u- dc pirf t i ( 'Sirl cunumeml discontinu it i. j i lor clintr-o lungime clc rrnrl iL ir l inici cchilalcntcobfinute, atunci, pentru echivalcnti, trebuit. ca rapt-r|tul arculni c;-rtrc'coarda unci strbdiviziuli sia fic at'roritttuliz egal cu unitatea, ial lungimcaliniei trebuie si f ic un numirr c\act <lc scmiunclc a l inici rrniforme cchi-valentc.

Ca cxemplu, si pt'csupuncm ci! i lvcm de calculat o l inic inciLrcati.,ln care inerti i le in paralcl. ; i condcnsatoarele in serie sint introthrse ca dis-continuitl.t i intr-un mod, astfel, ca pc l inia incircatiL sir f ic C : {) ; i r- : Q.

Referindu-nc la formulelc (3), (a) capitolul V, obtincm.

Ho: H cosvl 1 j I lR/s s lnpl l

/o = / cosp/ r iH l/s/R sinsl I

i i avem pcntru accst caz

P:a- j9 '" :o '9: fRs:Astfcl obtinem:cos u.l : cos (- jp) : cosh p, sin pr.l : sin (- jg) - - j sinh p

t iHo == iI cosh p/ f i |/?r.S sinh pl

1.1o =. l cosh pl p rI /s/n sinh gl I

( t5)

148

( r6)-

- . n -?3r

Prr lnrnl mrernlnt l l r r r l r r r l l l q ' .nr . t r lorrr l r l r r l l

l l " , l l r t , t l ) \ t l . ' l l l l t r r r r l r 2[1] / | ( / /1s l tat i ) l2v n. \ . . . r r rh /p/ l

1, , I ic icn{a t t r rur , r r r is ic i l r l l i

1 t t t l t t , / , , = I / fcoshz' t t+( t12\Wlr)V. i l t i I UI I I ) l /Rl( l s i r r l ,2f ] /1. (17)

l l irxirnul de eficienli se obtine atunci cintl

t1!s l2 : I lRlz, ( t8)

.rrlit:ir ^picrderilc

de putcrc siut egal impirlite intrc fricliunc 1i 1r:rrli lrrrrll l,ln acest caz rnaximul dc clicicn{i at fi '4 .: c-20r, valoart:l lui p li irrrl

,1.r l ' r cr t p: /nSVcdcrn dc aici ci, <laciL putcm rncrrline pclclitan!a ;i fl ic{irrncir rrrit ' i,

cfir:icn!a poatr: fi mentinrrtiL ciL voirn dc ridicatir.Pcntru a calcula o linie incri'Lcati, constituiti rliutr-o linic rrrriforrnll

<rbignuitiL, in calc s-au int(.rcalat discontinui ti.ti potrivite, {ic:. L, C, /i 1i .f,r:lracteristicile rezultantc rrnifor-rne alc linici incircrte; 2,, C,, R, qi ,t,(liscontinuitl]i le in sazie conccntlatc pc linie; 1.,, C", Il" ;i S, tliscorrlirrrrll it l i le'in faralel, concentrate pe linic ;i L', R', C' fi .t ' carilr' l r.r' i$t icilrtrrniformc ale liniei continui initialc, neincircatc cu discontinuil lt t i ; rrlr.lrrrlin ccle <le mai sus rrrmirtoarclc rclatii:

L: L '1-( f l t ) (Lt- r lcp!) , R: n '+ (y ' f t ) ( / r , l l / , \ , ) ,c : c' :,- @lr) (c" - 11r,,a21 , s : s, +- (11) (.s:, I t//r.) .

Putem calcula linia inciircati exact ca si cum ar [i o sirnpl.r lirrrr, rrrrlforml, al'lnd caracteristicile L, R, C, .S, cu conditia dc ;r rrnnu h.gr,,r rlr,distribufie dati. mai sus.

Rezulti cir, daci sc cere a se obtine o linic incftr:alh, lr lrr,, \tlr,rrlde undl si fie infi-nitn, trebuie si avem fit' Z fie C cgal z(.rr). ln r,rr.llpllldat mai sus, ao luat un caz in care Z :0 li C :0; accrrsta s-lr olrlln', rl r,lL' :(PlD $lCra2 - Lr) ii C' : (pll.) (rlLra2 - C"l, a(licl'r tlr,lrrrtl rlintroducem ca discontinuitS.ti condensatori in serie, avind r'rr1rrrliIn|,, | ,qi inerlie Zr gi inerfii in paralel avind inerfie 12 gi capacitntc ()r.

Aceste ecualii determini. val.oarea capacit:.{ii;i inc(iilor c(,f lt. lx, trtldiscontinuitl!i.

Exemple

Prcblema 1. Se propune a se tra"nsmite 2 000 CP prin o liuir, lrilrrr.utllde transmisie de unde prin api, la o distanti de l0 km, cu o cficitrrln rh'90o/0. A se gisi presiunea sonomotrice de intrebuiniat gi sccliunea conrhrr lr,lolnecesitate in cazul liniilor neincf,rcate obignuite.

Linia este constituitl din douil. conducte paralele, trrnsnrilirrrl l irr',rrr,clrte 1 000 CP.

La capitolul VIam glsit ci maximul de eficicnfiL la o linicrk:transrrrr..ir,<:ste dati. de relafia

( te)

l,le

. r r e.ru gr, | t . tuFt l t , F lU'Oq $ l l e0.U,

. l th l lnrnl

' l l ( l ' , ) . '11/ h i l . l l t i . l0 i . Arr t i ; r , . r t lx .ntrrr . ,1, , , l ,t ; l )Ul |Xl l l , , r , , t l r , l r . r , r r r . r r r / , t ) , { ) l .1.

, l : i ' . i . i nr l l l l i , r r r r r , r . r . r l r l l r I r r<|rrr . I r . | r . r : r . l r l r r rsrrr i l ( : i l ( : IO(X)( ,1, : l l ll , r ' i r , l i r r i r l , l t l ' l 1,r ' r r r . r . r I ' r r r I r r i l r r I i l l t , / , { .1/Z t i ( lcorr(xxr p.nlr . r r ' r : r r i r i r r r l

r lc clir: ir:uliL avr:rrr / l l lCll. t!,11, oblinem

rr' - HIlz : QH,lz :3,5 aH2 .l)aci d cstc diarnetrul interior al conductei, avem rnai depart,.

A rrr pl l l r r r l lnat

r , r t lv r l , zrL cf i r ; i tcrr

vll'rrrnl lr fl

t ' I l<, t I , ( , r ur /x,

rlt : t,s (rclt) (Hd.), .

Fie z, viteza efectir,i. din conducti. qi Z arnplitudinca vitezei,

I : aV : l2H :7ofidin care

v :7 H , a":v lyt : 4,9sH .Substituir.rd in ecuatia (20), oblinem

I,y:1000 x 76 x 100 :O,rz( I )d)e

(20)

avem

?.d:825O.

_ Ap glsit anterior. Io0 k: (a"ld) (t + 9l\i4, dind lui h g zt"d -:ato-rilc gi.site mai sus, obfinem

a. ld:1,36. Q2\

__ Din_(21) qi (22) oblincm z,: 105,5 cmf s, d:78 cm, pi mai departe

v 1, . V-z. 150 cm/s. H : Vl1 . - 21,5 kg/cm,.v edem, pnn u rmare, cir. penuu a transmite 2 000 Cp la o disranti

rlc l0km cu o pierdere de l0o/o, cele doue conducte trebuie si {ie de ?gcindiametru, qi trebuie intrebuinlatri o presiune sonomotrice ioasd., de numai21,5 kglcmz. O asemenea linie ar fi ancombrant5 gi costisitoare.

. - Problema -I1. Aceea;i putere urmeazi. a se trarsmite la aceear.i dis-

tarrti ca in problema I gi cu aceea;i eficien{i, dar in loc de o lini6 obis-rruiti, urmeazi a se intrebuinla o linie inclicatf,, avind inerlii in paraiei,distribuite la intervale eealc.

Aceasti. problemd. poate fi rezolvate prin incerci.ri succesive, precumulmeazi..

Avem pentru puterea intr-una din conducte

l,f : HIlz : qH,p: I 000 x ?6 x 100 kg . cm/s.

Luind o valoare arbitrarl pentru 11, de exemplu lj:500 kg/cmz,obtinem 4, : 61.

Apoi avem

I : ,1/H :61 x 500 : 3 050 cm3/s.

Si presupunem cl alegem o conductS. cu un diametru interior d - 10 cm,r l r.lllcl

a, : 3s01[I :216 cntf s.

t or:ficientul de {rictiune R ar fi

R : (v/g,) 'Lo,ot a"ld + (0,osld)lt;ldJ

z0l : Rl,! :0,2s6 .

Eficienta in acest caz ar fi z1 : e-0'256 0,775.Vcdem'ci. e{icien(a este prea sc[zutl; trebuie prin urmare sl lntrt:luitt'

{iLrn un calibru mai mare de conductl sau si a-legem o presiune sonomolrit'r'rrrai ridicati..

Si oresupunem c[ lulm o conductl de diametru interior do 12 cttl,()btinem -

a : (n l4)122: 113 cmz , V: I la:270cmls,

t , :210 t [2 : r9L cmls , z\ l : Rl{ l :0,104,

iar e{icienta ar fi

r : e-q,lor :0,g.

Vedem, prin urmare, c5. diametrul de 12 cm este bun. Cunoscittrl rllu .metrul conductei qi valoarea lui {, putem calcula capacitatca rt('r!'riitl[ ltlconductf, pentru a obline eficienta ceruti.

Am gls i t , l :VCIL :61- Aceasta d5. C :6tzJ. 372tr . , . l r tL:y lg( ' :0,00t/981 x 113 : 1/1,1 x 10E, ast fe l cd C 3, ' l l l l t t { l -x 113 : l /3 x lot .

Capaiitatea uniforml pe unitatca de lungime a linici r:ste

C' : a lE : 113/20 000 : 11t71 ,

E fiind coeficientul de eiasticitate aI apei.Inerfii ie Ir, cerutc a fi intercalate paralel ar fi date tL: rr.lir{iir

C:C'-pl lL2a2. (r . t )

Pentru a determina pe p trebuie se gisim lungimca du rrndll a llrrlr' lincircate.

Viteza undelor ar fi

t : \ , ( rC : I 820 000 cm/s.

S5. presupunem cL alegem o frecvenll de z : l0 cicluri pr. rrr,r rrrr,lirlrrngimea de undi. ar fi ). : t 8ZO OOO/10 : 182 000 cm 5i nuuriL|rrl rL, lrrrrgimi de undL din lungimea totali a liniei incr5.catc ar fi

q : 1 000 000i 182 000 .: -5.5Curentul ce stribate inertia ar fi

( / 1)

t l150

a - (nl4)rlz : 78,5 cm, . (12\ : - jH lLsat

l l , r f r , l r t r r Inr l la (v;r l f r r rr t r rr l i r (?1))

t r l l l ( ' t ) t l l , .

. . , .Sr l . l ' r , . - . l l , l l ' l r r , r , t l l r l l , i l l . i i l lurrgirrr , . r l , . l t ) l i l r r r r l i r r i r . i , lxnr, l l l0{}i r r , r f i i , l is t r i l , r i l r ' l , r i r r t r . r r , r l<. ( l r ' ) ( ) lu, ; rvr , l r i r l r t r r r ' i I l , )n: ; i l , r r r , , , , . l r r , -lot i l l rnrr t to icr . i r r Iornrrr l l r (24), o l r { int ' rn

I" 5no ( l l l71 l /30 000) l } t t l l } t l . . 14 000 ( : rnrys.

- Pt ntru rt gtisi grcutalca si dcplasluncntrrl A, al incrl it. i , avcrn /^ rr\2,

l l f ( r t l - ( ' r f : Lnl l : OZ. l i ..{stiel ob}inem Az : 14 000162,8 :223 cr-nx .Si-L lrlc'supuncm cii alegem, pentru cursa 2/ a pistonului dc iner-tie 2r:

, l0 (:rn, ob(inem pentru sectiunea acestui pistbn ll: Lrlr: {i,6 cm2.ljn piston dc 7,5 cm diametru ar fi aproxlmativ potrivit.

.. {iLcutalr.ir / ' a incr{ici ar fi dati. de rclalia cr.rnoscutiL Ie: Ir,S{lr ii,l irr lormula (2,1) cunoa;tem ci Lr: Hiazlz , 5OO 162,8, X t4 ir00 :l ' loS1 a 44,6r ast f t . l c i P . l i , - kg.

Curn ar.enr doui linii, diferind in {azi cu 180", iar incrtia se aJl!. inrer-calatiL in celc douiL linii, greutatea pistonului neccsar pentru a inciirca am-I 'c1, . I i r r i i r l f i 2 x 17,7 --35,4 kg. -

In modul accsta am determinat toate elcrncntelc r.reccsare pentru con-structia unci linii incirrcate. Calculul de mai sus cste un caz simplu dat :rirmricrL cxemplu al mctodei generale pentru determinarea liniilor lungi de ilaltiIrrcsiulc. Pcntru cazuri practice, analiza tlebuie sit fie mai completi, rinin-clu-se scarna dc pierderile p n ine4ii. Acestea pot fi determinate, daci con-sitleriun sarcina incrtiei intercalati pe cele doui linii in serie cu o frictiune,incluzind in accastiL lricliune pierderile datorite frecS"rii pistonului gi sci<1ereacncrgici cinctice datoriti, schimbirii bru;te a sectiunii ramificatiilor, la le-gr-Ltura lor cu conductele principale, carc ar ii obligatoriu in unghi drept.l)icrrlt:rca <latoriti 'r perditan!ei prin pistoane trebuie, de asemenea, luatiiin considcratic. Analiza completi este pu{in mai lungi. dar nu prezinta 1're-orlificultate spcciall.

Ilezultir din exemplele date mai sus, cir la liniile lungi trebuie si inlre-lruintim presiuni sonomotrice inalte, cu scopul de a putea intrebuinla nririmi<L: corrducte rationale. Pe de a1t[ pafte este dificil a se intrebuinJa directirscrncnca plesirini sonomotrice inalie la distribuirea energiei pentru scopuriplacticc si sintcrn prin urmare silili de a intrebuinta aparate speciale, des-linato a reducc presiunea sonomotrice la valori practice, spre a evitapresiunicxccsive in clistribuirea puterii la punctele de utilizarc. Asemenea instru-nrorlte so n:lrncsc tr artsJortnatori; ele constau in general din pistoane diieren-(ialc; Iinia dc transmitere principalir de presiune inalti este legati. cu ur.rcilintlr-u, in carc lichidul lucreazi asupra unui mic piston, ce la rindul luiirr:tione:rzir. un piston mai mare, care lucreazi. intr-un cilindru de presiunejousir. Cu.accst dispozitiv oblinem simultan o transformare a presiunii ;il curcntl l l t l l .

ln capitolul urmitor se discutir tcoria acestor instrumente.

r5t

I IJ l t - I l2! ! " . . j ( / l / . i { ( ) , ! ) j - l7rr ,1!)1!)") !J" /1

UUI

( 'Al ' lTal l , r ' t . \ l

' t ' A\St( t l t , t ' l '0 l t l

l : r crrpi lo l , lL, 1rr-cccclcnte am stu( l i i r t cotrr l r .nsir lo l i i 1 i i t r , r t i i l r ' . r rprr , , ., r , l r r r t i i unci acclca; i prcsiuni solornotr icc i ) ( ' i rnt l ) ( l r ' l i , l , . \ 'orrr l r , t t i r l r . l l l' r l . r t r t , r .put i r tc dcst inate dc a t ransforma dir-cct ln; 'Lr i l ) r ' i r l ) l t . : , iu l i i : , r ,uorr ,l r i f r : . , \5frrr( l lc i t aPatatC lc tou mrmi iD cgn, i i l l i r t i ts f r t rat l \Ltr , . ( r ' . r t t r , r ls inpl i . ior-mir dt t rausformator con:t l -L <l intr u l p i ,< lorr r l i [ r lcnl i r r l i r l ) r t r r I1r , en. i i lc lu i i i ' tc crr l ichidul t l in l in ia c lc u. : rnsnr is ic; i ) i l , r ' r i r orni l ; r ,1, . , ,p i r t l l i i ( le al ta a pozi{ ic i lu i mi j loci i . Pistrrnrr l io l rLyi lxrrrr l l i r ,o l i r i r . r r r l ,r ( \ r r r t i i i i f rccuur csto i lust lat in l igura --1.

[ ,a acost t ip dc l tansforrrrator ' , l ichidul c l in l i r r i r ,1, r r , r r r . r r r r r , / l l r r. rc i rz i , pc un piston d, .sccl iunc (J, , l tgat r ig ic l crr r r r r 1rr torr r l , . r r ! t r r , r r U,cat, ' i . . r r : rcazl : rsrrpla J i r : l t idulrr i d iu condncta D. ( ior 'pr l l r i , , t , r r r l r r r , . t r t , r ,St lPi is a avca o grcLl t i t to - l 's i , p lecum se atat : i in l1grrrr i , , . ,1, . r rprrr l r l ,1, r , r r<l ispczi t i r -crr lesor- l i r r i sarr un condcnsator, at . ind () c i l l i l ( 1( r i { r , , r \ r , , r l , l l l

L)aciL lu6.m un i l ts tn lmcnt exact s imi la l cr i cr . l r r l i i l r r l , , l | \ ' , l , l r i r i , ldiameirele cil indrilor R ;i 1) siL fie cgale, putlnr sr:rir.

I I , - H:r :1(Lra l1Crt t ) l , , ( t t

in caic 1-, :1 ' tgQl, Ct -= AOi s i I1.1 cstr : o plesiLrrrr s( ) r ) , ) | | r ( | I I | { r ' , r l r l r , rlent i , a ieasl ast fe l ca in f i t 'ce rrorrel t : i ar ,cm 1/ i ! ) , / / . ! ) , . ( r r . r l l , r r rv inte. io4a exerci tat : r dc l ichid in c i l inclrul /J asupr:r p istorrrr l r r / ' , , . t , . ,1. , r1rla a.r.Lele instrumcntc.

in ascnenea condi t i i ur iscirr i le pi-stoanr- 'Jor ' l r r i rnr l r r . l l i r rstrLl l , r r t , t r lident i , :e; i rezul t i c i , daciL subst i t r r im pc r?i in ccuiLl ia ( l ) , o l r { i r r r . r r r r , , r r , r l t , rmisciLl i i transformatorului i iustlat.

i l \-em prin urnare

Ht -- IIz ' (r)r/Or) : j(P'tlglti - | ltr;l lti) t,.

.l-ct'asta se poatc scrie

i is 5 l . - ' l rarsf . , .m:! t . , r s. ' r i ,

VL,h: PlgaLe.: L,iar mai departe

ct : Ao?, c": Aaz, Ven:,40ro,1:lc.Curenlii 1r, 1, sint totdeaunain aceeagi Iazi, c6,ci pistonul trans{orma-

lorului se miqci in bloc dintr-o parte in alta astfel cl vitezele trebuie sL fieegale la ambele capete,

Ecua{ia (2) poate Ii scrisi

(8,)1, : HrIr l j (La- l lCa) ' I r I ,

ll numerrc- '^ ' - f2nl1: t2 l t t i+ \La- t lLE) ' t i .

Exemple

Probl,ema /. Un transformator cu un piston de gieutatea P ;i cu sec-liuni O, gi f,l2 este plasat pe o ramificalie a unei linii de transmisie primari,in cate iresi-unea ionomotrice este flr. Nici un resort nu este intrabuintaiin transformator. Linia secundarl este legati. cu o linie de transmisie inde-{initi, de seciiunea or. A,se gili curenfii primar gi secundar 1r, .12, ,si pre-siunea sonom6trice secundari I/r.

La o conductl de o lungrme indefiniti, avem (cap. Vl) Iz : qHz.Din ecualia (3)

gi mai departe avem(Hr)Ir : H"I , t jLaI, I ,

I l l I2:A1lQ2:tn '

2r fiind raportul de translormare gi Z : P/gOpr, din (4) obfinem numeric

H | : (I,l I \)V7.r""4{TEny,din care obtincm

l6{

ft|nt -' rr,q,nJVtl, ,{f,Itt , td,l - I,ln*:nH,1ll l*11$fuif '

I);tr:i, I cstc foartc mic, precum cstc cazul cind sc luttcbuinlctall unlriston loaltc utor sau daci seifiunilc Q, ;i Q1 sint mari, accstc foimrrlc rcl l ' ( l l t ( ; l i r

[t - nfQHrLl - (tlz)(!maL)'1, H" - 6pt11 - (tlz) ({nal.lt)

qi cu o primi. aproximafie

It - mzQHy H2, - mHr

Problema I-L Transformatorul din exemplul precedent est6 logat curn rczonator care nu absoarbe lucru, sau cu o capacitate inlinitl. A cc 6tdcurentul primar.

ln icest caz avem Hs :0 iar ecuafia (4) din exemplul prcccdont rll

sl avem numenc(Hr) : jLaI,: jLaI,lnt

It : mHtlLa.

| ' l l l

' l l l

tlr

( I ' ( , l r r . r f t l t p l {11 r l r r t l r r r r lxrr t I l r l l ( 'cu ,11, /g r l i r t ct ' i r lo i c i l inrhi , f l g i / ) , i rvcnr

HJ | - I tJz,- i lLo - t lCal. I l1. Q',Aceastd. ccuntlc cstr, grrreralir dacl sc ncglijcaz[ frictiuncl gi pcr<litantr

din tlansformator. I qi {,' sir)t respectiv coeJicientul' de incrlie muhal Si ca-bacitat ca transformatorului.- Trebuie notat cl, daci Lr, C,;i L2, Cz reprezinttr inerfia pistonului9i capacitatea resorturilor in relatie cu cilindri respectivi B gi D, avem pen-tru coeficientul mutual de inertie gi capacitatea mutuall a transformatoruluiL :fL;L;, c :Ve-,c,.

Accasta se poate verifica utor, deoarece prin definilie

Lt: Plsa|, L,: Plg0lSi obtinem

(3)

Se fede imediat de aici, ci dacl pistonul trans{ormatorului erto forrtrugor sau l' foarte mic, curentul 1, absorbit poate deveni foarte mrrr. Dfaici rezulti ce este recoman&bil a prevedea o inertie suficient[ ln tranliflrmator, pentru a menline curentul absorbit la o valoare redus6, atuncl d0dide exemplu, sarcina se suprimi. brusc din Iinia secundart, presupu{ lqrtlcu un circuit fi.ri. reactante sau frictiune.

Poriectind aparatul cu o inerjie sufieicnti Z, putem tltrrlrrhlfl ransformatoare la instalalii de distribufie de iortl, cu scopul dt f lld||curentul furnizat unei magini date la orice valoare voitl. ,,, ri,f

.\old. Un transformator cu raportul Qr/Q, : t sc reducc tr o Inr{hsau capacitate obignxiti, dupi cum inertia sau elasticitetd prdonlil hvaloarca reactanlel totale.

({)

Ir:rtf,l'H1l[t a$m@,

At' l,r:t ' l i l t , I s0|\ l(t ' t ' I l ' t l

\ I I . 1. \ I0'r 'OAITE Sr GIi\ t i l t - \ ] 0?l| | I i SON|Ctr St]\( : t tONl.:

Gt'ncratorul si receptorul sint de construclii sirnilare, iar functionareacstt ' rcvcls ib i l i .

ln figura -52 esle prezentatl o ma;in:i sonici sinclolir. dcscrisi in dou5,scc!iuDi. Penlru le.\' i le cle legiiturii intre gencrator si rt'ceptor sint prcvirzuterrlil icii lc rr, l,r, c. Aceste orificii comunici cu camertlc ul,ltt, cr, liccare iiindin conrunicalic cu trei pistoane trt, lt", t '" aranjatc radiirl.

Pistoanclc s int in conthct cu uu r .xcentr jc, / pr in i t r termccl iu l unuirulmcnt raCial. Excentricrrl cste montat pe axul l.

Spa{iilc cc comunici cu orificiile a, D, o sint r.rmplutc cu lichid, iarpistoanelc stau pe ercentric irlpinse de rcsort. Un fluid convenabil pcntrusistcmni de transmisir dcscris ar {i ulriul mineral, de;i in princini,.r oriceliclricl sau gaz ar putca {i rrtil izat.

Se observiL ci-! aranjxncntul din figura 52 asigurir un dr:pleL:amentriat tl: trci pistoane pentru o singuri fazi.. Acest lucru asigrrriL o col.lstructient:ri compacliL, presiuni mai mici la suprafala dc contact inlrc rulmentulcrcentricului fi pistoanc, dcplasament mai n:are pentru o fazi faJi de situa-l i . r in carc s-ar t i f t - r losi l ' rn - inSrrr f is lon pe faz5.

Sistcmul plezinli. analogic cu sistemul clcctric trifazat. f.n in:r.ortantrL!autaj fali de transmisiile;lectrice cste acela ci poate [i rrtil izat, , 'ono-Drir', pcntru viteze de rotalie {oartc scirzute.

Pentru malina din schita prczcDtatil se constati cL llL o^rotati, ' ir axu-lLri se producc citc un impuls dc 1-.resiunc in fiecare {aziL. Intre fr.:c'-'entarnilci.rii l ichiclului I ;i vitcza de rotalic a axului r (rot/min) existir relalia/ ' n130.

I)aciL motorul ',si gcr.rcr-atorul au construclii identicc, r'itczclc 1oi torl l ( g i l l { , ' .

l)rLci-i l i tr.za clc rotatic eslc micl '1, sau distanla intrc 51r:ncralor ; i i l :otor, sr(' r l ici Ia(i clc lungimca de un(l:! ) ' , ), - 6ll (r; { i inrl viteza :r:: ier-uluii r r l iu id, m/s), atunci fcnomenul dc propagale u undclor de prts iu:re de la{cncrator l;r lccepLor poate Ii asinri lat cu o rni;care ,, in bloc" a intr-guluil lrrir l, iar conceptul ric incompresibil i tatc a l ichidclor este poiri l ir pentrurl lsclicle:r fcnourcrlrlui.

J)aciL distanla intrc gencriitot- ; i receptor sc mirc;tc, in lung'.: l l iniei

sr. girslsc, Ia rrn moment da[, zor-tt cu pre siune mare ;i zone cu depresiune,

r'r 'r ' ir ct ' arati. ci. sc producc o propagare de unde in medirr elastic. F'.:nctio-

ruirrr. ir 1r'ansmisici r.ru estc posibil i dccit in anumite condil i i , descrise analit ic

i r r l i ip i tohr l pr iv ind stal i l i latc:L l in i i )or lungi .

156

A-A

Fig - i2. - - \ I i is i r r i sonic i srncrona

Se pune problema dL'a construiun sistcm de transmisic s( ' r r r r i I l ' r r l ' l l lcu rnasin ' i s inc ' rone avincl \ ; tczc dc |ot : r ! ie di fcr i rc. De cxt t t t . l ' l r t , / ' , r r ' r , t l r r l r i lj ; " ; i ; ; ; i "J l ;

" i i " ra tnr t . sc dorc;r ' " c;r molorul s i r ib i o. \ ' i l ( / i i l ' I " r ' r l l '

;" i f i ;;. A.;"tt. ar putea {aloriza pornirea motolului ' t l irr ' iL itr. ' t l t 'r 'rrtt l tt lnu estc prea mare.

Un'asemenea motor cupr inde tr t i grupe-dc pis loarte i t r < i l i t l r l t t l l l r r t tB

(-p [ i i ; ; - . ; ; . i " i p. l " a i rurni tc legi tu i i la i r ' i coloatr" l ' l i ' l r r r l " r r . .

?r"i."rit '"r.tf"iiiiJa"i"-J" g"""rniorui trifazat. l{o1.rttl csit' rrrtxl, l.rt ,r'rl6l

i*if frirto"""f6 in contaci cu cl d.scr.irr . milcir'c sirur:rrirl,rli 'r r.'r'lr'll

I t t

t t ' r l " r r l r l , nr t f i l i ,n ' - i r , l r . . t l l , . r , l " | . r i t r . \ t \ l r . r r r r rpr , r l r r lh , : r r l , i r , l t l , | r r r r ru, | r | , r I

, | | t . l | l | | l l , l r , r r r , r , l ' , , , r r r1,1, 1, . l | | l , t , , l r ' l | l , t l I l r r , r l l . r r r r r r j r r r . , l r . . i t l , t , t l , r l . lr , '1, ' r Ul | | t \ . r r r , r | | t t r r r r l ' r r l r r r r , . r l , , l . r i . r l t l ' . , t o. , r r l , r { t r r l l I l r \ ' . t | | l I | | .1

l , r , , l r l r t l r , , r , , t r r l r 1, , , , r , , . , , r r i , l ' . r l / ; r ( , r ,1 l l r r , l , i . r r l r r r r , r , t r ' . r l l r r l r rr . r l . , r l , l r r u l i I l r , r i r l ( ) t l r i l : tz : r l r l J t , ( \ ' ( , r1. t A' , r , i l , z t r r r ro lonr l l r r , r l i\ , r l / I i ; r l r r r r l r r l , l ( r ' ( ( l1r( r ' r1 l l l r r l i r l i ; r l i l / , ' l / .

l r t l t t t tsal l , .1, , ia l ) l l l l r ' l ' s t r l l . i ro l t , i r ' i r , l l l l t t l r l t \ r 'n l r ' l ( l l r { r l { ' r, i , r , . , o l r l i r t r i r l r i l l l ) i : ( i t l ( ,1 ; ' r l , r , t r i r r l r l r .1r ( r r r r t r r ro l r i r r t l s l r l r ' i . r l ) .

I r r l lscncl t i l l i - i t r l r l i ( s i i r t l r rc,rr . i r i r r l : I igrr l l t 5. i . / cr l ( o sc{.{ i l rn( . l r r r r ,r , r r l l r l l r i l l inrotorsin(r 'o l f i r l l l t i r : i . l loscr! iurrc1x'axi lA A ( l i l i l i l iurr J l , r ;I t , , r r r : r : r .1 i l r i !1 i s( l r ( 'ma si : r r ( ' I t i lht i r l t ' t t - l rnsnr is ic - !c l ( ' l i l t ( ) t l r i f r rz l r l r r ro l r , rr" , r . i l , i l ( t \ r : / . . " l r : ' . I r .

I lotorul cuIr i r rc le c in( i d is( l l t i asclDiL Dl ' t i o i r rc ( / , tnont i r l r . 1rr , r r r r r l / r ,l i r r r . t r l iu a(, : i ( , ( l iscrui f i ind plol i l l i t iLSa cul l l sc j l ra l i - r i l l i l l r r r r r ' r l / , ,,1. l , ' l r rL i ) r ' i r r - ! - l o r-r ' r 'o l r rL ic. a roi() iu l11; l )unctul d( ' cotr tacl i r l , l i r , r , r r l r r r , r rr r rL. i r l i r t l r i l t 'L: , i l in c i l indi i i r l osci l l lz i i td ia l ( lo c inci o l i . I ) isr r r l i r r r . t , r l r .( l t lcr '1ni1l ir deplasarca bi lelor c inir ' ,o tr l iscarc tur- i to1-i i{ t : ! crr {r ' rr :rr,rr l i r r l r . r trr , r()r i 1lrai mar(] clccit vi tcza de rotai ic ir a\rLhl i , .

I l i le lc c in accast i l r ra l in:r a, r i , ' r l rz i c i1 l is toanc i i r . in l l ) ( ' r l (1 Lr ' ; , . / , r t ' .in i : i rpt ' lc alunecirtoare in ci l i r .rdri i 1. , \rcrrr i lc sint l) t cvi"r/ ,rr l r) I)r .r tr t tor l

lJLl lsal 'ca lnert ici pistoanelor.l r ) aceast i i construct ie bi la sc poate rot i , i ls t le l c i r i l t rc l r i l r r r . r , , i r l r , , , r r l , r

' \ i . . t r r (o l l r . r , ' ' l ( ro:r , ,gol i r " .

l ' i r rdcr i lL: carc sc ] ) roduc pc l ingl b i lc s in i ( ( ) l r lx . r i , i r t , r r l r t r r , ' r l ,i I i r : : r l l l lSlC.

, t ic i r r l p ict t lut_dt: 1a pistoarrc sc adunir in nn; i r r ; i r l , r r r r r l , 1, , , , r t , l r( l r , i i r i l ) Dl f o col i ( l rLcta! / .I - ; r inctoml t ) r 'czcnt:r t , c i l indr i i notat i 7 (c inci c i l i r r , l r i . r i r r r r r . r Lr . , , ) r , , r r r r r

r r i r i . : 1 ln canl l colcctoL 1, c i l in i l l i i notal i 2 i i l ( ,s l ) ( ( l i \ . i 11;11111111,.1 , ., :L,r .1, ' lc i l s i I l l . . \ccstc 1r 'c i canalc comnl ic i r cu l r r , i i , , r t ' . , r , r , l , r , r r r I. : . , i i . , , . . | . . r . . I . : , r . , raru: .

i i t l igurr . i . . int r r r i i tate sr ' l rc: : tat ic concr iut l i l ( . l r r r , , , r t , ,1, , r r , ,\ '11 : , 's l , '1 l1r ' , . i r t i l t ! tobj t t r t r le i i t t ,cLsaLc a scnsului ( I ( I | ) l I I I i . . r r r r" t ' , r r r l r r rschi in i , in( l ( { )nr . : i i l r l i lc a ( lo11ir fazr ' .

-1I

T

r_)

-T ' 1i i r ] . 51. l i , l r | | r ,I ' rn iur (1. l r , r r ' r r ' r , r t , r ,) r r1r)r ' l r i f :Lr , r l r r , l r , , r ' , . , ,srr , ; l r r v j l , / . , r ,LL, i l / |

Trci condensatoare s int col tcctato la l i l i t in I t : r r scopul r l l i r l r r , l r r , rlocurile dc presiuDc care s-ar producc la inYctsarca s,'nsrrlui strrr t it ol|||r,r lmotoruLli prin inchiderca l inici cu robinctul / i. CcL trci fazc l lr. l i l i , ,r ,1,transmisicr pot l i conectatc t 'n punctul I prin tr-ci coll( i l l(. lc crr scr.{irrrrr '.r rlrtrecere {oarte mici 'r intr-un prrnct comuD lp.

ln pur lctul . / / l 1tu cxist i -L var iat i i dc plcsirui( . ( l ) rL lc l l r l r r l r r l r r r r r l : , i , ,1r .urului l r i lazat) s i pe aic i s( , i loat( l ) . ) t r t l ) t uL. i ) rL pr ls i r r r r r ' : r nr l r l i l r lc l r r , r r

| 5!)r58

A--lli

l r i . . : i . . - l l , rof sor ic cu c i t in

c)

a _ sec1iu,,c ,, ,.:i",i.:';'i'i:,:i),11,:,,':,ilfl:liilioarc. rororu,ui:( ' , n ' . ratorul es te,rcprczel l tat concct iL. t l i r l iu i , . in prrnctrr l n. La o rolat ie.r l i , 'ncr l lorului o, axul rnolorului a, i l t nr i tc,rr f s i l tc , .o i , i < l"scr i , j 1,5 d; ; ; t i ; .In,figuli le

.5?,.:16 i i 57 se prezlntar o lom.ra-r coustructiviL de motor crrrir ln,rr,\.(c cL'rnultrpllca-r(' l /6 cu a;iczarc axialir a cil indrilor Statorici.rltscllt d este mod,jlat dc _pilrt i lc latcralc alc cir.cumfcrinlci aga cun selrtrzintiL in dctaliul c. c irxh'ii /, z,',; r" .oii"ct"ari'i"" i.r,r..r"r" I, II, IIIi r r r , , l i r ; i . ruot l cr lu cct lx l l : r val . lant i i consl fuct iv i - t .

,l ' l lgura 56 s, prczi'ti 'r o formi. co'strrr<:tivir crr ciri 'trri srirtorici axiali: rs(zalr r )unl i l l p. o t ) l t r tc l r Lotorului . .Efor. l r r l ntccl i r r r l t . i r r r l l ing|rr : l l r tcral iLi r r r ro loruhr i cste pr. t : luat t lc ru lmcrr tu l "* i , , i

, . - - - ' - - ' " " '

Siut posibih:-nrul te v l r r iantc conslruct i \ r , i i r r . l rcrr tnr : r r r r r r ru l r . l rp l ic l r l i isc stlgcrcazi chiar o coll,strucl,ic -cLr

rnlti nrrrlt,, r<.rtoll j ur,,ll irlc 1rr. rrr.,,l i; i :rx,l lccar( ' . rotor avirr t l o t l , ' rnrr l t ip l icarc <i i r i ' r i r i r dr : iL r :crorrrr l t r i . l l r ( { } r r . ( r i l lcarol(xrr( ' l ( ' r ' l r r l i . i r r r lc i r ' , r r rsur is i r s i r srr f i r . i r rs l f r . r . r r r r r r

' . i , ' i i i i 1, , , , r i r r r r . r r r , rs l I i . l r . l i ' l ; r r r ' i r ' .nr i r . rorr( . r , s ' ' lx) t or) l i r ( . , , i i , , r , ,1 t r ' , : , r r r l : r r r r r . r , r ,c i l r . r ' i r I i l r .zr . s incrrr l r . ,

. . t | , r | | I I I i I I I . I r s( ' lnr i t l r . r . r ' . r l iz l r r r r ro l r i r r , . t r . r | , | | , . t r i l r , , ,1r , r i . r l . r . . l l r . l r . r l l

t r ' . t l i r r .zr . r 'otrr . r i r r l r i l l r l r r l i t l

I0t l

Crrr-ul i i , l , i r ,cvenl i ma: i oL, l i r ru l i ast f , l pt- t t l i r r t i l izat i Pet l l r r r . ' | r l t r t r . r r t r

rnotoarc siuri l ir l t cu alt raport clc reducctc a tura!ici, ircir combinittrl trr"l" r t 'ca c:1. clescrisc sc poati obtine orice raport

.dc rt 'ducere sarr t lc t i ' l t ' 'rr '

a turaJir' i . I)c cxcn.rplu, daci" gcnelatoml ardun rotor Prcvizut cu tlttttrt trt l l tt

Iali i pt pcrifcl ic caie i l iL deci"douii oscilali i pe rotali;, iaL curcnli i tr i[ lzr{r '

odlinuli 'comandi'L rtt iscarca unci maqini cu rc.ttorul aviu,1 trei ondula!i i :r lrrrl r

riruortul transnisici ia f i 3/2, iar : irotorul sc va roti de 1,5 oli rttai r ' '1r"1' '

dt'cit eeneratonll.. iplicatia irrportantir posibilf, a motoarelor dcscrise este i lct- 't rL t ttr ltr

cer-i i tuialici turbini ' lor siur motoarclor cu cxplozic pelltru i lntrcrl itr(rt l.rrl i

. r \ I l t I l i l t s , i l t ! . r r I I l ) r . . . . t t , . I , | , , | . r | , . | | | ( , r l i r r i r rs l . t l i r l i r , . I j r r r r r i rnornetru in

l , l , , r ' ru l . r l r r . i r r r l i r r r l ) r r ' \ i . r i , r r r , , l r , r r . r , . r l r rc l r . . ( ]orx luctc lc I r r tbuic i il i r . srr . l i r . i r . r r l th, l r r r rg i : i r . r r , l r , r r r , . t r r r , ' , l ) ( .nt l1r "- , ' , i

, ,1-p, .oau"" pi . . a"r ' iI t t . r t i in , l , ( r t .z, istcrr l ; r s, , r r i . r ' . . r l t , . r1.rr , . ) j , r i1 i1ci lz i r , . .

I l t l to i t t l l , r l , , r i l r r t , r i s t ts lxr l l i r t l i l iz : r t , , , r l l ( l l l l r t lo i l r ( ' . l ) t t i l r l r r t t t l

cste i !utrcui t t r l r r t r r r r r t lot Pt i t t r r t t , t r t tcntr t l sr t t l i t : t l t r . ' l t l t l i r ' . Pt l r t l t ts i t l l i t t i '

dc tr i lqsmisi( ' \ ' t i rv| i l o l f({ \ ' t 'nta' t rnt i mare, raPorlul dintr( ' l t t 'cr ' ' : l t ( l t t t t t ' t t

t r r lu i ; i Yi teza totot t t lu i f i i t r t l < lctcr ln inat dt : numirr t t l ondulal i i loI t l t P| t r r l0t

l : i , .1. i r ; . l lot . , r sr)r i r cu( i l i l , l f i sr l r r ) r ' i . i a\ i r ! l i pc

r) l ) iLr l t a rolorDlnr.

a t' l icelor rlc vapor,lt irtru acfion:-Lri lc ca.rc au inctti i trrnri, pomirca se recorniru(L-! rr

fact plin intlrnic(l iul trnrri r:L:mt:nt cu'alurt,:clrr-c intrc rotor ; i lrborclr '

ic;ir,,, t, s| ir locltoazir cluPii lxrrnirc.

, t , .

\ tLl . ( ; l i \ l i l t . \ ' l ott Dri i \ \ l , l . i l f l t lx:\ ' l t r ' ! ' l

( lcnr ' l : t lot t t lsonicrc l l r t lzetrr i t idcpistotrulat t t r tn;r tduul l . r - tccl l l I lc iLr( .1r( \ ' -

v. . r r t i : , r t t t i r t i r t i , l , ' r ' i tL 'z.r ' . t r r t l t t i 9 i d, tc i f t ' cvcnl t l ( l )u s i l l l l ) t \ " t l l l : r l r I r r r

s i r r r ' , l i r i , rL l t i l i ,1, t , ,1 i , ,1- , , t ' l isPozi t i tuhr i ,d: l l l i t l i ' i l r r l I Iccven! l ' t | r ' r r ' l r l l ( r r li i i i ,l in ,,o,,rt rrcccsitiL!ii tlc i:Poli viteza arl'orelui motorului dc anLr(]trrrr' ' '

R",Llizar,,,t unui rbtor ctt p,:r' imctrul Inotlulat cu mai lnultc situtsrrirl ' '

t:a[c si lri {iotrczt: :rsupra ultrti r,rirll irr dc pistoenr-.r'rtl iale sau, axialc -- rrslltl

i,,, i.r' ,, i ' i,,1i,' ti,r:rui pist'rr s.-r t:xccute miti rntrltc cicluri dc rni,sca't: rrll ' r'-

i i"tirl.i,,,, ',.i lr,ti, ,, solil i,t rlt gtrn.rittc a frecvcn(clor relativ ridicat("SL rlr 'sr:ri l tttr gt'trt:r ltot sit i i rorr rlt: inall i-t f lccvcn(iL antrcllat de tttt ttttt iot '

p l inr r t l r r o v i lcz,r ' r i i t ' .1 5(Xl r ( ,1/ l l l i l l l to lorrr l prof i lat , ( l in, . ( ) tc l l r l l t l l l ) l l i { i

l l l l t l l l ! l l r l t l l l l t t ' ( l t l ) ls l { ' l l : l )1 ' l l j ( t i l l ( t ' r t " " ' t

ax" l lc t '1x:nr lk; t t la t ' : -L l l t ' I t r r I i l l r l

ur , . l t ' r , r l t r r I ot t t I r t i .' ' i 11, , ' t , '1, r l i s l , ! i i i t r , r l , l r i I ' r r r I r i i '1r t 1r , ' r t t , r l r f i r l i r t ' r l ' r t l l t t i s i . l

' r r r l i l . l r '; r . r l t , . l , . . i , i i r . r i . r l r l r r r r , , , r r l , r , I r : r r i . s l t lx ' r ' ' i i i i i l t i t r tst . i l . t . r t t t t i ; r ' i t t i i , i r r t '

j , r , , r , r r r i l , l rxrr l , ' : l f i t t t t , l i t t t i t t , l , " l i l r r l r r t l ' ' t t l t ' i , t t t t : ( ' r r r t t i t t t tA ' t i i l ) lc l - "s1,"

1, . , | | i , r , r l ' r r t . ' t r , r l l r l i , r r , r i r t l l i ' , r r l ' p1r ' l r i t t t t l r r l . ' { i t r t t l r ' r r t r ln ' r r t l ) - t r l r '

i i1, , 1t ," , , " , , , , , , , , t ,

, 1u, i r r t r l t r . r r , t t l . r r :1. i r t t r r ' r l ' t t r l ' lu ' r i ' r l r '

l l , r r . i , ' , , l ,u l t t l , ' . , ' , " , l r r t l l r r r l l l r l to l t t t t t l t l i ' r l

" l l t l t ' t t t t t ' ' I t r | ' t I ' i r r i t t ' l

, r r ) l ' . r r , , r l l r , r t r r | l1, 1, ' . . r l r r r r , t l , r ' '

I I ' l ' l l r '

l l " ' 1r ' l r l l r ' r r i r ' 1r ' I t l l l l l r ' r | | r '

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I ) lc i i r r j r r l r l . r l r ' . , t r r i rotot s l r l isPurr l r r l r r l ; l r i r r t i lgrr | 20 r l r ' Pis lo:rrr ,dc constmcl i r ' : ,1rrr i r r I r pctr t r t t t I i c i t sc lx) i r t ( ( l ( r rsoirr( , i r l l l t ) ( i l ; r l i , , r t t , 'Tot t t ic f i ( 'crr( ' r l i t t r ' r '1t 20 dc pistoant: \ '1 l ) [o( lu.( 2t) r [ ' i tnPrr lsrr t i ( r rur \ , rde doui ori mil i nlur(. ca anplitudinea sinusoitlci rrrodulatt. lr rot()r '.

Prc.supu nind o cu rs i r dc l mnr s i o scct iune ( lc0, . icmr, acl iunc:r l l l l l r r r l l l ) i \toanelor va dctcrmina intr-o corrcxiunc comrrni un dcplasamcut <k l crrr ',carc dcii este mic, rlut(r 'rninli un cnrcnt sonic mafc (latorit:r frc(]\ '( 'Dt(,i tr)ir|.

lr if igura:l ,r, , sr' Plrz-int:r un aselncr)cil gL.Dcrator, antrt 'ntt l ir | )01)rot/ lnin.

.\r 'borclc csto solidar cu blocul . a!in(l ci l indrii d si r ' alcza(i r,rrl i .r lin carc se rnigcii pistoanclc 1, g. I)oui scttrri de l6 pistoane ii ci l ini lr i \ inleBal distribui.t i Pc pcliferie. Capctcle pistoanelor- sint adaptatc si"L l lr ' ,:r( /r 'p(, supriifata onrlulati /r, i f ixati 'r dc corpul nra;inii. l)rofi lrrl pc|nrit( l) i\t(,r,1;t ' lor o cursi 'L t lr ' 0 25 mm.

-\xelt ' pistoanclol nu sint c\act pcrprn(liculalt pc suprtfatir orrrlrrl.rtrci ulol inclinatc astfcl cl-L punctul dc- cont:rct intrc supralattr to{i i orrlrrl,rt,

ir i piston nrr catlc pc a\a pistonului. In timpul lucrului, sc pr()(hl(( {) r, lr, 'url i lorrni. a pistoirncl()r in jurul axei plopli i. Accasta asigura! slrl)f ir l, t, , l ,Irrcru

^r-odatt, i irr uzurir trstc uni{ormi..In dcscnul ali-rtulirt accst ({cct cstc olrt intLt prin curbar(iL ri(),r,r .r

plofi lului cu ciLtnc faliL tlc plamrl cc trcce prin axul arborclui rot()r '. 5ul)r, llafa t-amei r)n cstc palalcli cu axul rnn;iuii.

Iu spntiul /r circuli-L ulei carc r:rceitc i i uugc supralctclc tk' r 'orrl,rr Iintlc piston ;i pr-ofi l.

Spaliul / cornunicir cu pistoanclc /, r ' ; i t lansmitc curcntrrl sorri, irrl inia r1r t lansmisir. carc sc Sa'rsclte sub o pLt'siuno medit ' <L al)ro\inlrtr\250 atnosle rc.

I losa rD cst I proi( 'c tat5. cu scopul dc t l iur inu:r volumul, rcsl) , r l i \ . i . ,1, ,1cil ir lr,.a iustalatici. l , iuia clc trirnsrnisic st' po:rtt- t:ont:cta Ia fi l ttrrl rr.

I '-olmtlc conslr'ucti le pot {i {o:rrtc virr-i irtr. ' , lr irz,:rtc pc plirrr: ipirlr ' ,. irrrorlclrrl p: ez,crttnt.

1)r ' r 'cnt : r r ( :ar t c. t so pot olr t inc r l t . l i r un gtuclntor curcn! i sorr i r i , r rtrrri nrrrltc lrt 'cvcutc, plofi l inrl suprafc!t: lc /t si r crr o cu.rbir ol)l inuli I l l i lsrrl)rrl)r1r'rcr'(. i l rr <louir silrrsoi<k'. I 'rofi lul rcz,rrlt irnt rL'slirsur:rt vrr l i o r rrl ' , io l r { i r r r r t .L r i in srrPlaPrrrrcr , r r n cLrrr iL s inrrsoi t l t cu l r ruPl i tudiui crr t : r r '1r ' r i r l r , , .l ' r ' , , r \ . .nt( 'Lr .o l r { i r rutr ' i r r r lost t l t ordinul 2o . 30 l i l l / , .

( icr tct : t lo i r t t ' l t ' sotr icr ' t lc in i r l t l - r f rcr ' r ' r ' t r { ; -L;ur lx t t t r is rc i r l iz , i r r - r ' r r l l t t ( ) t sr ' l l ,r l ) , \ i l l ( ' l )cnl l l l ptc l r r r l r l s l ic l i , r ' i l t r r t - r ' i r nrc l r r l r r l r r i toIr i I , r rpI ic i t { i i r r r t r I i r : r r1, , t , .

\ 1 l | | t r ( ) \ lU: s{) \ l { : l : \s l \ ( ] l l l l \ t . :\ lototrrr l r .s,rrr i r ' , l rs i r tcr- , r r r , ln,1 i r \ ' { i l rorrs l t r r r ' l i i ( l i f ( r i1{ i r r r i r lx ' r I l r l

l l t l , t , ' r ) i r lcs l i l r r l i i r .\ to lotrr l r r l rs l i r r l i r r l t r r r r s l r r lot , l r l ( l l l l ( r l r l r ' l r r rst t r i l r , t l i r prr l , ' r i i

t . ' r l l i r . t r ) r 1 i t r r lotrr l l , t { r l ) r i l / , i r ' l r tcvizrr l l r t ut i ikr i tcr ' 1;r t , s i 1r ' t t r r i l , r r rl l r r r r , , r , r l r ' l r r l . r , l , i t r r I l r | , , r r l i I r , r l r . r ' r r l r r l i l r r l l s l r r lotr t l r t i .

l ' , r lor t t r , r r r \ , . r r 1 r I i t r t , ; r I r ' t t rotrr t r t l r r i ,1 ,111rrot t , r 'o l r { i1t l r l t t t t t ic i t r r I r r I r t t t l r ; r t r ' , t

to l . r t t l r i , r r . r ,1rr ' r ' l iv v i l |z i r r I r ' r ' r , | . r I r r ' ; i r r r ; r l r t l l r r t I isr l r i t t r l r i t l r ' r l t tPi r I r r i r l ( ; i .Jrr l , r r r r r , r rorr ' , l r r r r l r r . r , r , r l , r l ; r r r l i l l r t r : r 1 l i . . .1:r lotrr l crrPt i r r r l , . l t , i

( t l r | l lu , r , / , , , . ,orr , rLr{r Lr " l r r r , l | | l , r / . , r l , r I t , r r r ' . t r r i 1 , , | , ' r r r I r 's l r ' l l | r r r r , r l

r l l r t t r r nr l r r ' . l l r r t l , r l , , r l , . r t r r t l r r ' l l r t l t tot r / r " ' l r ' . r l t r ' r , r l , l r ' I t t , |o.r t t , I r 'r l , r l r r ru l | | r | | r | | r l r U| | , , l r r l . r ' I ' | | r r ' | | | r ' | r , l r ' . l | r , r / , ( ' r ' r r ' r | | r l , r | r r r r | r , r t r ' , rl r l , r , lor) l l r ' l r r l t r r l , r r ' , r , l r . r r , r r t l " l ' ' l l l l l ' t , l r ' , r r i l ' ,1 rolr t t r r ' | t l r ' l 't t t l r r l r l , r l r ' , l r r . r , /

T Ti-!

l l !

. I io lot l l l r r r rpnl( l ( . t t , r , r l l r r l l l , 1, , h, in ( . i l l t , l ) t r t ( , i1r( j le l t , t t . h ls l l l l r .st ts( , tDl t l t ' ( l r . r r ' : , r , t t r r . S| ' , r l r r r l . i r t | ' l r r , , 11, . Pis lo;rrrr , l I rotof ic( . cst( l urnpl l l tcu l r ( l r r ( l s iu l l l r . r l , . t i . r l r i : , , t ) r , . l i r . r r r t i r r r ( i r rotor. t rht i este dcterminal i - ; ( lct (s(nl ' r i l ( ' t r r r ' : r r t , l t rcr . r . : rz i r ) is l ( , r . l r , l ( . . t : i l indr. i i / , g, / , s int conectat i pr i r ior i f ic i i lc i r rgrrste l , n, n ct { . i luror;r i ) .. I) i( ir ci l i .dri i r,r, l , r: sirrt co'cr:t ir l i Ia o l inic trifazati. de curen{r so'ici

I t i I , t t r r r t i r i . ' (n l1r l in( l ( lor {1 : . i_{ .s( . \ ' i r c leplasa, c lcplasam"r i l l i i inJ; . ; ; ; i

, , r : r r r r l ' l i r r r , l i r rc s i rot inr l r r -sc Ia l i d l cer i t ru l staiorului .(l i l intlr i i rotorului au tendin!a dc rotafie fa{i. de ccntr.ul (cil indrii

,f- g,. i) r'utorrrlui i? liTp. cc pisroa,riclc./r, gt, ,i urmlr"sc ;it;;;;"'i;;j;;r ' i l t transnltt irtorulul. i\ l igcarea reltt ivi. a pistoanelor fr, gr, lr, in cil indriif, g, h vor pompa lichidri l din cil indri prin orif ici i le ir irr ' t,

-, o.

I , ig. j t l t (nt , r so i ( ls i l ( . ro| .

S-a at i tat nratcnat ic c i r .czistcnla r lc f r ic{ iur t r . I r r crrrglrr , : r l ic l r i r l r rhr ipr i r r or i f ic i i lc l ' . r r . a. prcsiunca rcsortrrr i ior s i 1-- r ' r 's i r r ' , , r r r i r . r r i<rrrrrr i i r r c i r i r t i r . i iroro!ltIur \ i)r (t3 tl Cuphl Constant Ca ml-rrinrt, ;r i r l ir.rr.{ir.. ( ir | l l .ul: lr(, rot()_nrI,\ 'a pon il \( ' \ 'a rott cu o vitezi-L unghiulari l miri rrrir. i i r lcr.i l ! i t,,za urrghirrl r r r i i i r ( l ( .p la-s i r tn( 'n tn l r r i rot i lor a l t r .ansrni{ iLtor.rr i r r i . l lotorrr l . l i r I . i r ) l lu l ( i r t \ . ; rln l l ( 'a cxcrci ta rrn crr l l lu asrr l t r .a s l r r .c in i i l i r : r r l r , , r , . ., - I lotorrr l sc nr i l , : i r l r ' , . i i1 ; r r . r . r , l ry i r l i r . r . r1 i , . r r1I | . | |L| . . , I r r r | . I r I r r I r r , t r t i ) t . .l ( r r l ( ) r l t l : t t r . lo lu i i o i r I r r r r , , : r l r . r r . l t r l iv i f : r { , i r l r . rh,Dl : r , . r r r i r r l r r l rotr t , , r r l ; r l r rt t l . - r r ' l lc l r r l r r i r l . I 'orr11' ; r r , . : r Pir lorrrrr .Lr l r . i r Iu l r r I r r r ' I , r

i r r , , r r l r , l , l , . l . , , t . t t t r rr ; f nr . r ' r , . f t . r l r r I i r r , l sr . r , l i r r r r i l r . r , r i f i r i i l , r rh. l r . r . r . , . r . r . / , t t t , t t . ,111111,. , r r , . r 1, , , . r t , .I t r ' r l t t ' , : ' i . " i l i l , l , r r r r r l l , t ' i r r . r , r r , , l r i l , ,z . r ro l , , l r l l t . , . . r l , r , , l , r , l , , , r t , , , , r l t .1, ,

t0 l

vi l r .z;r s i r r r lorrr : r c i r r tPrr l t r i ro l i tor . l t r [ t t t r t ( iot t l t t l r :s l r ' l t t r ' l ' r ' r ' r t l t , 'g i t t t r r l ,1, 'f r rnc! iot t i r tc r r r r r l r t t r l iLr i rn ic i . I ' t t lc a l t r ' t prr l l r ' , r laci st 'c t i r t t r i l t t l t ' t t l t . t r / ,nL, sinl foirllc Ittici, cuplul de pomire al molorului va fi tttic si pcttltrt :rob{inc un cuplrr dc pornire important, trccerile l, zt, rr ttclrrril sr"t [i, , rrs(r:tlunc mal marc.' Accst reglaj al secliunilor de trecerq se poate realiziL clirt ( \it 'rir,r (tlrrn disoozitiv de obturare. In o anumitl formi. constructivit d( la (r(i 1r'icilindri ai rotorului pot fi colectate iegirile printr-un colector in itfrtlrt ttr,,l,,rulrri unde un ventil convenabil construit inchide, dupi dorinlir, ,r,rrrrrrrrca{ia intre faze gi punctul comun. Aceastl constrxclie prezintd- ar.rrrl.,;rlci putcrea disipati la pornire in lrunctul de strangxlalie este transnri'lr rrr,rlusor mediului exterior.' Construclia motorului asincton cu colector permite realizaltit rrrrt,tmontaie mai complexe. Astfel, ieSirile rotorului pot fi concctate la cilirrrlrristatorici ai unui motor similar, rotorii celor douit magini fiind cuplali rtlt.rnic. Un asemenea aranjament a doul matini, pcnnite obtinerca 11pq1i rttplrrdrrblu iar viteza de rotalie iumitate fali. de pcrformanlcle laomalini srrrr;,l i

ln figura 59, stat'onil maginii ire cite trei pistoane pcnltrr lir ',.rr.fazl. Aceste pistoanc produc un cimp rotitor de mi;ciri care ;1r'{i.rr,,rr'rasupra transmitetomlui.- Fazele liniei de transmisie sint legate la racordurilc 3,4,5, r',. 'r,comunicind cu trei pistoane statorice pdn canalele 6,7, I (Iig. 5t)).

Transmilltorul consti dintr-un rulmcnt g atezat pe suprafetcl(' :l ' tt( '10 qi 77 a,\e statorului ii rotorului. Rotonrl 72 este previzut cu nou:r pisl,,.trr'aranjatc in trei grupuri si sustinut longitudinal de rulmentul 73 r'rtttltrtpicsei 74 a statorului. Ilotorul /2 este blocat pe axul /5 iar cilinrlli i r'.ri/6 comunici cu o gauri in ax prin orificiile 77. Un ventil gu nc /.\ r:tr'corstnrit astfel incit poate fi aclionat din cxterior pentru a obtura tnli rtullsau nrai pulin comunicalia intrc cilindrii rotorului.

l ' istoanelr: rolorului sint apilsate Pc transmiti,tor dr: rcsorltrli l, /r,/.Vrrrtilul cu ac sc rn:ule vrcilzir tl in cxtcrioml motorului prin toata tlc l)tirt), \ 't;l2(/. \ ' irful are o irscrncnca formi'r incit modificiu deschiderilt ' intrc cilitr,lri '; ipurr t : tn l . r 'omun, r-{ spcci iv f r ic ! i rut i lc sol t i tc catc se opun nt i ;cr ' t t i i l i l r , r , i rl) lsl oilDcl()r.

O r :oncr i r rut r ' : , t t pt t ' r ' i rzut i r . 1a capir tu l cxl( ' r ior a l t i jc i / l 1x 'nt l r r . r t icrrpl i r t i - <:rr o sursir ( l { ) l r lcs iunt: consttnl iL. Accirst i r l lompcazi t l i t :h i r l i r r t i l i r r r l r i ixrlorrrlrri l ir o prtsiurr c(DStirnlit, irst{f l ca presiunca ntt 't l ic sit lsiggttt, rrr r r r rpL r t ut t r t t : r r rct t t i " r : r c i i int l r i lor .

- l . ic l i i r lu l n(((s i r r lxntru ucest scop poate f i luat d in l in i i r s l i r lorul l l i

pl irrl l o lr ' :rvir lrrrgi crr t l iarnctrrrl <lt ' trccr:re mic (rezisten{a sotticr-t trt:tr, ),l ) ( 'n l lu t nr sr ' Ptor l r t<:c pi t ' r lcr i t r tat i <|r cncrgie.

l)r 'nllrr ur;r.,sirri ttr itr i cstt ' t:otlt t l ta.bil r Prcvedca o lxttrtPit lx' l t lol(tr,11 . , , , rprr l rL ' l r t tcr t l i r r , o Ptcsiut t t ' cotrs l l t t r t i t t lc u lc i in to iot , ( ( ' r t iL ( t i r l '. r r , . r r ' [ , r l r . [ . , r , , r : r l ' r l , . r r tPtrr r t lg, t i i .

l 'orrr i r r r l , l , l r r r r r r t t tu lot r l l r r r r 's l 1 iP, lnt l l r t l l r o l r l i t rc t t t t cr t l t l t t , l r :

1 lorrr i r l t r l r , . , r r t t rur i t , l i r ?/) s l r I 'sr l r i r l o l i f ic i i l , ' /7 Pir t i r l i t o i t t t t t l t t t l l t, I i t r r l r r : , i r r r rc r orrv l r r l r I r i l i l y i r ' r ' r r tPl l r rzr ' r : l . t lor t t l l r r t l ' l t i t r r l l l r i f i tz i r l i s() t t l ( : - r .

( i r r r l r r ro lorr l i r i r j r t r l , l i r r r v i l lz . i r tot t r i r l r i r , r ' i r r r ' l r i r l l ) i l t t i i t l t r r ' r ' l i r l i i i, ' r r l i r i r , r r r I I r r r . t , r i r r r I r r r . r r r ivr ' l , r , f t t r r r ' . r o l r r r l , l r . . r r r . l r r r , , . r l r11t , r ' i rL, . l r l r r r r r i r r i t t t

1ro. , t l , r l .l ) r ' r , r r r , r t r i r l , , r r r t I t r r l r r I i t , r r I ' r l , , l r ' . ' r r : r lx ' l l t t r r l ,u r t t l t r t t , t l l , t l l ' t i l

l r l r r r r I r ' r , r I r ' | | r I | . I t . l pr t r l t r r ' r ' t t l r l t ' r t , r l " , l l l r r l r l r , / . ' l , r l l , , l l 1r ' r r l rvt .

( l14 I ) t ' I r lc lcr : r I . r l , r ' l ) r r 'v(( lca o l r r r r r : i ' , r ' r r t r I r r ( i r ' I ) ( r t l l i r r l is i l r r r l r r l t l l t : rp ic l lut iL i r r r r lo l r r l r r ru: i < int l accst i r l r r r : r l r rz i r l r r l rh lnccir i I l r i r r i . I l { iu l ( l ' '

i r r rgcl t ' po:r l t ' l i cvcntrr iL l c i rculat cu o IX)nr l ) i pr intr ' -un l i l ( l i i r lor , ( \ ' i r ( r i t lrlrr-sc rstfcl cirl( lrrra rotorului in exterior.

I-a motoarc mari, circuitul rotorului poate {i cuplai ir ,\ l ir i i ,r l ,rIr '-rrn arbore geurit; i cu colector special construit pentru a l i corrcr l,r l ,ttcacta-nte exterioare (condensatoare sonice sau inerlii sonicc).

ln figura 60 sc prezintl o 1orm5. constrxctivi i simpli in c:Ltl L,lr,rrrlnrr urai are pistoane gi cil indd. Cele trei {aze ale l iniei de presiuni sirl ( ul, l.r lr 'cr statorul 22 care prin trei pistoane determinir o miscare oscilanli r' 1,r, ,r23 care are un contact sferic cu frecare cu rotorsl 24.

Resortul 25 litde si. menlini piesa mobili pe care se spri jiniL irr 1r,r r I r.rrnrmalir fati de axa molorului,

I ll r

Rotorul este cuplat mecanic (cu pann) pe axul 26.In acest model constructiv, reactanla este furxizati de r(s()rlr l . ' .1

acest caz un rulment 27 are rolul de a Jinc pe acelali ax lrir rr '1, ' l2E.

Vedere d in B

Funclionalca motorului este urmetoarea: cimpuluulsatiile curentului alter-nativ trilazat in slalorrl 22jiaruiui frontal a piesei 28 care se incliniL fa![ de axutrnaximi. inclinare a acestui rlan rotindu-se uniform inirrclinare se face impotriva- tcndin{ei arc;.;J:r 25.

23

rot i tor pr <, , l r r ' ,1, 'detcrnr i r r i i r l r ' l l , , l r , rmotonr l r r i , l r r r r . , ,1, 'jurul a-rc i . A, , . ' t . ,

21,

A-A

28

l r r l . 0{) . - r \ lo l l ) r s i , i ) i r lrs i [ , r ( , r t : - ! f i r i i i r ( l f r f { ,1( , / t

v

l ' r i , f i r r r r r ' , r i r r l r , p i , : , , 1, .11 : , , r . l l r t r r r r , l r r i i t r r l c i r l t ic{ i r r r r , ; r l r r l r r , l r r l r r i, l r r r r r rx l , . l r r l rorr , l r r r r l iv r l , , r , r r l , , r r r l r , r ror , t lzrr l l r r l r r l f i i r r , l r r r r , r r l r l r , r r ( r .t r r r , l . r ' . r r l ' t , r p icr , r ' i .1, / . , , i r , r l r l r ' l . r r t i t r . r r ( '1r( i r t : t r r t l t t i i f r ' r . l i t i r ( i r r r r r ' ; r i r r l t r 'I r r ' , r ' l r ' ' .1 , , r -1. / l r l l , r r r r , . . r l r , , r r l t , r , r r l r l , r r l r t l l r r lnt . r l , r , r ' ' r r i . r l r r r r r , l i r rl l | . r l l | | r ' r l r

' r r l r ' .

I t r l r o lot t r r , r i r ' l , l t l r l r \ . r r r r r" l r l r ' . r l . r , . r r . r i . r l . r r r r l rJ ' r r t , r l '1, r r r lor r r lt r - ' r , r l r t l r r r r , r t r ' l i t t r t l , . r r . r t r r , l t r r , r r r ' , r l r r , ! ' I o,( t l , r r r l , . , r r l t l t , , r ' . r r . r l t t , l i r r r r r ' ; r{ r l l l , l l , f f r ' ,nr( : r l r r r l , l l , r r , ,1, ' r r r l . i ' l r r r r l , r l , . r I r | | ' | | I | t ! i i r . r r r , |o|Lr lorrr I,1. i , l , r , r l r ' , ,1 r ,1, l l , r r r . r . l / , r r , , I ' r r l r r r , , I ' , r , '1, , r i r l r r r r r 1 ' r r r r , I l ' r , , . r

| 0rial i

l i , l l l r ' ( ( \ . l t , l l r ' l l t l l I r l l t l

r l ) l l r l t t l t | i . l - ] - I l r r r r r l r t r , r r l

; t l l ; r r ryrr , i , / .( ,orr lor r r r l , or i l i , l i r

s( l ) r (x lu.( . l t r t r l r t l | r t i i tc lLt I l . t i n l l r t l . . I ) r ' :15( ' | l t ( .nca,s in c t r )n i t .

33

al l , r l . r l i \ r ' r l r . r l , ' l , i t ; i 1r l r ' , , i r r r r , , l lotol l l l r ' r l r i l l r r l r r , , r r l l r r r l r , r t l ) r :o,rr , . r , .( . \ ( , r t t l t l r ' t l , r l l . i r ; i , l , l , i t r r l l ) l i | | t { ) i { , r l l l l r r , l r , , r r r l i r i , r . , , . l r r l | r l r . r r , , . r r , r r l l , r l r | r i r r Il ) r ' l l r t . l , l , r . t | | t l l , r r r r l | lorrr l . , r ' \ . r

. . i I | | r , l , . t , r , i t , r , t r l | | r . r { r r r , \ . , . | | | | . t ) r , , r

t0h

l l l ( ) l ( ) i r r ( ' l l l l , r r | l r r t i t t t r t r i t r lc l : t pol t r i l t s i : l t l ( i l l i l ( l l t is l i r i l t r t t t t t t t l t l r i ) i t 1r ' r r

I t r r l tact i r r r r r ' . l r r l i t r r ta t r2 se prczint iL l l l l l lo( l ( l col ls l r l l ( l1 iv,

Al imt'nl.Lrca rr i i ' torului sc face priu ori f ici i lc 7, 2 ial mit iurca cxccrl lr i -

cului cste stabilitir hidraulic Prin actiunca pistonului P cu cremalicrir. Aclio-

narea pistonului P estc dctcrminat6" dc diferen!a prcsir'rnilol la oriliciilr 'p. Pistoanele rotorului cornutrici cu o ficiul 7 sau 2 in timpul rota{ici.

ln regim dc molor, constlxclia functioueazi atit cr'l flux continurr (il

si cu curenti dc {lrrid alternativi.Teoria stabilitir pelltnl modelul constructi!' crt pistoanc ratlialr' r:t '

r.alabili ,ci in accst caz.

\ I I.-5. POrll ' It SO\ICE

\tI.5.t. l ,ollPi CI' IIEIIBRA\.\

Aceast i . ponrpir a fosi t lcsct is i in 1913 int l -o cercrc de brt :vt :1. At t lorrr l

o clcscria ca o pompiL tlcstinatiL pompirri i sau comprimirri i oriclnti f lrrir l ' ,rrr

l ichid elastic ca dc excrnpltt benzina, benzol, api etc. Autorul consirlr.r

accastir pompl clcoscbit dc uti l i . pentru benzini, deoarecc nu se nai pttxlrr,

pierd.eri le de fluid in cxtcrior, a;a cum sc ir.rt impli la porrpele cu pi:lt 'rr

obilnuite foartc mult uti l izatc la data invcntiei.

Invenlia const:r in uti l izalca unei Pompe cu diafragml avind o tL;' l .r

sarc l imitati ast{eL ca elortuli lc in metalul discuhri membranl sit nrr (lcl ' ; l

lcascir in nici un punct l imita dc elasticitate oricarc ar f i prcsinuca apli, ir l r

dc la cilindrul nolorului.Pompa estc compusir din diafragna nt'talicit clasiicr"r c, l ixatiL la 1,, r i

f r r - ic intrc douiL pl iLci t le rr tctnl scobi tc spre disctr l c last ic c; i d. l t r ,atr

latca fornrati i <le o 1-.artc a tl iscului elastic cri i-sl ir o lcgirlu:i i crt un cil i l

t lru al motorirfrri cu ctunlruslic intunit in t iup ce cavitatc[! curl.rl l .t

r.sic itr comunicrL!ic cu t:onducta dc alimentare a ;i de rcfi l larc I l"ttt

supapclc lcspccti\ ' f s t i / (f ig. 63).

StrL aclir inoa prcsitrnii r l in cil indru st' ploducc o tlt ' lomlal: a tl iafl ir l l

nrci, r 'r ' tcrtintltt-sl conlirttr lrrl tk f luit l din corlcavitnl( ' prin supapir rlt ' cvit

curr( . . [ . ] r l isplr l i { i r t pr-csiLrni i , sr tb act iunt 'a c lasl ic i t iL l i i , mcnr l r rat t l r r , r ' i t t , '

i r r 1x 'z i t i l in i l ia l i r . ; r l rsot l r i t t t l I lu i t l pr in sr tpapa t le at l rn is ic.

A( ( : rs i i ' \ IX)r i l l ) i l fosl fo losi l i r t lc l l t t lo l . : t I ) ( )n l l ) i t t lc l rcr tz i t t l " t i t r in l i t ' -

t r ro l r i l , l , . 1rr . r ' l t t , l , ' : t lx r l t . ' 1 i ( ) r r i r tl 'orrrp, l l r I l r t rz i t t i i l r r I r t t I I , t t to| , i I I ; r t t i t r l r r lz l t t l Io rot ts l t t tc l i t lo i l r l r '

i t , , r , r1 i r r r i r l6trrr . r l I i . i t i l l l l l l . r l . r i r r l r )1.1. l \ l r . r r r l ' r ; r r r i r l l ls lc l t r l iorrr l ) i t l ' l t tcstrr

rr , , , r r l iu, i l i r r , l l r l r t ro l r r r , i , l l r r 1 , i r 1 ; l r r r ' , t t t l t r t t r t l l r r l l o ' l t r t l l i l ) t l r \ l l l t t l ( ) l ( '

r r r l r r r . l ) r . , I , , ( , | | I i , I I | . , | , { ' , r . , l l , . l r l r r orr , , l r r r r l i r . ,1, . l r r r t r r l r i r t I r | | | | I r t . | | | I r | . r , l (

| | l t l t / . i l ; r r , r l r ' ) t r r | . r ,1, r l t t r r , t r l , r l r I r l r 0trr I , I r | ' i I Lr t I r r ' I r ' r t r ' I r ' l ) i r " ; r ' l r l |

l r l r . | | r . r t r r r t r t l l r ' , , l , r r , l l r r i r r r l ' l l l r ' r ' r , r , l l l " { l r , l r r ' . r / . r ' l l r r r ' l l l r l l l r l r ' l l " l i t l l

l , r q,r , ' , l r r ' l ' , I r , ' l r , | '

. r l ) r . , . | | , . r l r , t , , . | | r , . ] ( ' r t t . t \ | l l ls i l ) r in l ) i ( . \ i r os<: i l r r r r t . ii r \ r , r l Ix ' , r l , l i r , r ' r , l l r r , r l r rurrr l l r l intr . i ' Pistolrncl t , 3J

trro| ' . r r r . I r ' r1, , , r r r : r r , r r r r r i srrs t : r r l t lu l tnaxinr posi l t i lzr , to, i r r r l r r l ro l r r i t ' r . r l r r l lo l r l r , [ i obt intr t un'cuplu

t l l l ) ( ) i l l ( l i o l r l inrr l l r o l i l t 'z i - t nai rnare t lcc i t v i tcza

3t, .t2

Firr . r , l . \ 'arr iLrr i i c( ,n-strucl i / : ! a rDolo.uiui sorr icrLsirr . r ( , I f ; ra c i l i f t l r i ror o

22 3l

. Se sulr l in i r rz;-r c j crrplul mar. i rn la pont i rca rnot\rJt , lor u: i r lcronc cst t .(1,' lr.r 'rnlnat dL. r,.zistenta si capacitatea sonici a r-otor.nhri. Daci. rtzistenta('sl( ' lnlcgorat:r srrlr 6 2numi1:t l irnit iL, crrplrr ' l dc ltornirc se mic;or-eazi. inlo( .-\i crcasci-r.

.. Constlucli ik: t lc motoar.c rnouofazalc, rnai sinlplc, au dczavantajulc.'L nn cuplrrl dc lrornirc nul.

sILl. rI{)fo.\nE (:( ' (;{)t,t. l(:r.olt

Accslc tipuri dc rnotoarc sint din ptnct dc vcclcle constructiv foartc

1.-.. "].'l,]ilo1', " cu p,nnpL.le de debit continuu si cursiL variabilii. Aceste pompc

pot. l r . totost t r 'g l ca motoare hidr.aul ice, iar s istemc cL: accst gcn sint ' foar icut l l rzatc.

\outatca arlusiL de sonicita.!c l ir aceslc sistcmc dc lctionate cst(j ur-ma_toi.(, ir: s-.. i . l .crrit pourpa cle dcbit co't i.uu c. rr ' g,. 'c'rator t lc impulsur.i

I

x 1. . r l r )v l , I \1() l , l r i \ l t . l ' r l ( \ { r r l ( l l ( )Nr\ l r1: s()Nl( l

ln pompa ilustratii in {igura 64, apa este adruisir. pr-in supapa inleriorrtii,/10 in camera pompei gi este trccutl priu supapa dc cvacuarc 'l'12 ittlt trrrvas cu pernl de iet 743, de ur<le este cvacuati. prin contlucla rlt rrli l izlfe t 44.

l ig. t , l l l ' r r r l , ; r , r ' l r r r rx l r r 'n ' , ' , r I ' i ' r r r ' r , r , ' | r ( l i .

( ) r l t t t l t t t l ; r t ' r ' l ) , r t . r l i r / , / ' r t t | | t t t l t t I r ' . t r , t r l i ' , |ozi l ivrr l r r t t t t r r l t r l t ' l l t t 's i t tnr ', r l l ' .nr i r l ivn Arr ' , r l ' . i r | , I r ' r t r r i t t i l r I r ' | , I r t ' r i t t r , r , r l l r t t t , t l t r " r , r I r i I . Iotr t t I r r i / 'y '7,

! f f ! t f f f l r f r [ ' ! " . r r r l t r t t l , l l \ ' , ,1 l ] t ) / \ r , , r ' ,1,r l r l l , r l ' r l r l t l r l r l l l . r " r

l t i l t t l , , t r t 'a

vrr l r r r r r r r l r r i l r r ' , l r , r l t r r l r l l t t l t , ] ' t t l ' r t | l l

- H- ,-A-_ _

---l----=U - =

l ! " l t r l ' h ' r r r ' r l ' rnrx l

I ' - l l r t r r l r l r ' l )1)rr l ) i r r ( 1slr . r r . r \ r r . r l r r r r r r r i r r r l t l l rs l ic i t lLtcrL rcsortur i lorj l r r i r : . i r l ) i : l ( )nnlr i , l ) l l ls n l . r5.r , r1, , r ( , , r { r r r t , r i r r sqrrr i i r r l dc lLrc lu i i i jutnir-l t t l r ' r l i r r r t t t rst t I r ' : . ( ) I I I I I i I ( ) I ( ( ) l t ,1 l lu l , . r r r r , , : , , i l ; r lor n lccal t ic in r 'czonant i r Cl lf t { \ 'v( l l { i t inrprr lsrr l i lo l sonicr ' l r r i r r r i t , l r r i r r l i r r i i r / . ' /5.

Ar ls l nrorLl r l r : |onrtrr sorr i r i l r lost l r tvct i r t in anul 1917. In acclasilrr-r 'vct r.r ' :r r icscris si ciocairul soni< c:itrc cstc un dispoziti\r mccduic compusrlinlr-o nlrsi si rr.sorturi clastice carc oscileazi la rezonauti sub actirrnearrnol os<:il l t i i sinusoidale transrnise de la distan!i. printr-o conducti! culiclrid sub presiunc.

I)upiL c:um a indicat autorul inventii lor, ca rezultat ai multor cxpcrien!c,rcsortu lc nctalicc obosesc gi se rup destul dc rcpcdc la frecveDtelc relatir 'r idicatc alc dispozitivelor sopicc. Inlocuirea rcsorturi lor rnctalict: crr rt.sor'-ltrri hidraulicc (capacitate sonicir echivalcntiL) a condus la rcalizarca unorpompe li ciocane foarte robuste.

rIL.5.3. POMP-4. IrAR tr SUr',\r ' l l

Modelul descris intr-un brcvet din l9t8 sc re{crl la o polnl):r cu pistonr::rpabilir sir lucreze la vitcze foarte rnari. Pompa constit dintr-un pistonr:lrc lucreazir intr-un cil indru, pentru o anunit:r porliune l cursei, cursarrrrnpletir arc loc ;i intr-o portiune in afara cil in<lrulrri. Cind pistonul estcirr irfara cil indrului se facc admisia fluidului iar cinrl pistonul sc miidr inirrtr:riorul cil indruh.ri impinge fluidul in conducta conectati cu cil indlul.

Couducta lcgati la cilindru are o lungimc alcasir astfcl ca ine4ia lichi-<lului impins din cilindru si produci o deprcsiune in pornpir, atunci cindI)istonul s-a rctras in afara cilindrului, accasti-r dcpresiunc producind admi-siu l ichidului in cil indru in fala pistonului.

Conducta pompei poate alimenta un rczcrvor cu perni de aer saurlt t ip de rczervor.

ln figura 65 se observi pistonul 1, carc cstc ghidat in spaJiul z undese gilseito lichidul ce trebuie pompat. Lichidul de pompat este adus prinorificiul o la presiunea atmos{erici. sau la altir. presiune. Corpul cilirr.druluis-r notat cu c. Conexiunea d asigtrS. legarea cilindrului cu o conducttr lungi.;i ligidiL. Cu f s-au notat nervudle de ghidaj ale pistonului.

Dactr linia lupgl este rcalizati. cu o conduct!. cu diametrul interior1,27 r'nr ; i lungime 6 m, iar cursa pistonului estc dc 2,5 cm, diamclrul pisto-nulrri f i intl dc 2 cm, qi aclionarea sc facc cu 1 500 cursc/minut, atunci seoblirl ' rrn t ' fcct de pompare a fluidului intr-un vas cu perni dc acr montatla tirpi"tul {cvii opus pompei (dactr inif ial conducta cstc plirrir. cu l ichid).

I-it lvansarca pistonului in cilindru, lichidul din {r:lrvir. r:str: ar:cclcrllslttr: vasul rcceptor cu pcrnl"r, de acr (dcci sub prcsiunc). I.:r curs:r rlr. i l loirr-ct'r ' t: i t pistourrlrri, l ichidul nu va urrniir i pistonrrl ci va <:onlirruir" sri sr. nri;1r.i t r l r intr : pror lut : inr l vacuur l in c i l inr l ru pini t in r t romr:ntrr l t : i r r r l p is lonrr l prrrrcI t t t :ot t t t r l ic i r rc c i l i rx lnr l cu ( : iun(.r i r , r . ?n l r t : r :s l r r rorucrr l l i , ' l r i , l i r l r l i r r r v:r I ir t l rsor l r i l in f r r f i t p istorrrr l r r i 1 i v l r r rn l>lc spl l i r r l l i r r r r : rs r l r rp i i r r r1r , . r , . , r ro lo;rrrc i rL: l ic l r i r l rL Ptsl t t r r . l ) i r r r r r ' r 's l n lor l ( . r1, p inr-r t i r r r l Pr:r l r r r r r r l r ' , r r r r r l r r r l r .c i l i t t t l r r r l l rL tutrs i r i r r r i t r l r . , l i r l r i r l r r l corr l i r r r r r i s I ( r r ' , : i i i r r r r r r r l r . , rn l r , . r r i r r r lt t t r r l l t i r r l r I i r r : ; 1 r I r I i I r I r . | ) r rp, i r r ' l r r r , lorrul i r r r ' l r i r | r . r l i r r r rorr r i l r r r , l r r r l Lt r l r r l r r ' , r .<; t t l i : t i t t . r t r r l r ' , l i r l r i , l r r l r l r r r r o lo.rrr , i r ' ,1r . : r l r , . l l t , r l , . r , r , l r r l , ,

' r 1, , t . r l ' t r ' . it i r r r l . r ' , r l r t r r l ' r ' l , r , , . r t r r t t t t t l , r I ' t , ' . l rn, . r r r r ' . r ' , r r l , r r lu rrr , r , l r . , r , . r r . r r ' rorr l r ' r

lill;li::'llil,,;;ill,l;'1,;']i.iit;'f,l'.,,i1,;:,1;:1,'.i,lli;,1',,11i,1,,,,i]il:*:ilil:;l:.1".:*i,:i,; ;llJil:';i:.,,iii':l;l,l';,,lli';';],'Jii. 'r,, ',,',,i ,i,,'rl;l';';i,:':;.. o*ip'*i"""^,,", . lli,l;',1 'lil,':,1 ili'l'j'';',;lli,l;lJ ,i;il,;:: llli i:li;;:i, ,',,11,;",.,.['"$'ili#J

ilJ,l:: :: :il':;:*i'*1'1. *ir ril,*# ttt",u:r j; txff.:* ;:;ll.tl;,t[[ti;:ii:#i:rx":::1n"?l,o:":i'i1i'",'i'i*i.,.0"n1'#,,T'l,i

i:i"'1""""'.'.?;]11'.i,t'r,1',T,P'-"'' ll.'i.,1.: '-':l"ti.principiu.."nru -ui J "f Lo i ;; ;;, ;;;';j di .",": :'; i" i"jlf,: " l""lh,l I "lil #,ffi "*:.1nlarl .

xIL5.4. pol1t,r\ r .ot_LlrETHtcA cl, I)rBIT \_AIIIAIIIL

:;::.,.g:i,::tt:1.:"1!r:,::3:"':i.;i:l ,x""*",,# #'ii}j",,.,,luj,1,",:1."::"1:Hi[i;i:"ffij:q,fi #i{';#{';;ffi:rrffiIIn figura 66 se prezinti

illl,l;1 iiilj"'":;,*qi",;[,"', ,#:i]I "' :_i:frii !y X;:' *"" c u r,ebi,,,,<,nt at'e'in ..p"t J" .",rui*ii t'il;i,lr *?,* t*Lrt",#rml

r r l lc r l r . l i r : l t i r l l r i t r i l , i r t r l ' , l t , l r t , l r t l vr t l i r l r ' l r r I l crr o l r i rg l r i l I lcr i l r i l i i r r l r r '

u is lotr t r ' .' l )aciL l l ( \ 'v( l11,r t r t t , , r r i i , r , l t r ' , i r tcr{ i i r t t t l rs, i t l sc v l r o l t t t t tc nt i ; t i t i i

r i i r r c i l indl i i 1xrt t r1,r ' i . r1, . r r l ' r , \ l l l l l i i l t t lx)r t i rn|r ' . Atuuci t i l t t l l lotnl l i t t t t t r lc l ' i

l , .az-.-r , I ' r .s iur i . . , r ' . r r l rptrr , l , , l , r ' i tcza pistoi t t rc lor r ; i I ia l punt ' tu l I r ' ' r

avc:r aceeali cursir crt; i pistorLrlrrlL , ; i ./. l)acit ponplr rltrbiteaz,iL.l i t i ir l , pr' '

s iunea scacic iar dcl t l i rs l i t rL yrrrnctr t lu i t l ispozi t iv t t lu i incr! iaI va [ i r r t r r i t t t i ' , r

dcci t cursa pistoanclor r ' l i / .La fiecare cursir clt: a<lmisic l l pistonrtlui l lolt lpci, tt scit lcrtl a pttsiltrrtt

se va produce in c i l inr l r r r l r t 'sP,1 l i \ ' . Uisp, lz i t i r ' ' r l " r i r r ' r l i ' t r r r \ i i I ' r r r ' l

urmir i imcdiat coloana dc I ichid; i se va d, 'sclr idc supapir de acl t t t is i " r r ' '

va pcrmitc iutrarca unci .rtrtttnitc cantit i-rt i t lc l ichit l in ciLindri.^ I -a cursa invcrsi , pr ts iunea gtncrat : ! r r l l va Putca clel l l i rsa t t t r" l r ' r t

d isooz- i t ivul cu incrt i t f i o lar tc r l in l ichic l ra l i c l iminat pr in st tp;r1 ' , r ' l 'au"at,"r. ' , t lac.-L contia prcsiu tri a nu cstt ' tnai ntaLc dccit prt 'sirrt lcl t l i t l ' r l lr

drul pompei.Daci contraprcsiunt:a ; r t ingc o : rnurni t l - r l imi t i r , supapa t l r ' ' r ' r ' r r ' r r '

nu se dcschide ia i d ispozi t ivul incrt t . t l v : r osci l ; t tu ampl i tudi t rLrr r r r ' r r t r r r r

Migcarca sc prot luc, f i i : - r a l 'sorbt ic dr 'Pr l . r i ' r l " la molorul Pr i r r r : ' r ' \ "1 '

t ind putcrr- i ncccsar i PCntr t r invingL'r ' . r l r " - : i r i lor .Presiunea maimi obt inut i l la supapa dc t 'vacuaLt ' PL'ntnr rrr r r l ' l ' r l

constant estc lunclic dc frccvcn!a pompci, deci accelerind motottt l 1't trrr ' l

sc poatc obtinc o crcltere a presiunii pcntru arccla;i clebit.

Fig, 66. - t)onrpc volu_rr)ctrrcc cu d( l) i t variabi l

cu masit osci lar) l i .

l ' , ,nr t ' , i / { '1, , , r ,

1 ' , ( r , , , rI ' , l t r ' l , , , t , ' l

, l , l r l / rUrr l , r l , , , , ' , , , ' l , r { l , r ,1,

P;t t i tL l i t l t 1 i l r , c i i r - r : arr uol l , r l r . srrp.rp. ; . t l . r ,vrrr . r r r r . o l i / , , I , i .( ) lnrs( .? l i / ( - ( 's( .u isosc i ' ; t r . , .st i r i l i r i r l r ' i s i r r r , , , , , , , ' i . , r , ] r , , ' i , , f , i , . f , , f , .o Pirglr ic ?/ ( r , i l r - ( . nr i rstr r , 1, , l l t ! { . i l l ) : r l y i i r r t icrr l i r l ; i i , , i ' , ' , , , , 1, , , r , , tl { r 'sot l r r r i l l l ' , s in l l ) r . t \ , ; izu t rr r r , , r l i r . l ) r ' l l l t l t i l t t tc l l l i l l ( l t l i l . ' i l ( ) : ' ( l l ' r l l l l i l l

. Alrr l , i r i r r , l 1 , i

, , I r r ; r r I r . | , . t , , . t / t t , , r i l r . , rz,r . r . r r i r r t r r l ; : , i , . t . r r r r r l , ., r r l r rh i , l , r r . , , l . r i . , r , , , . \ , . r l r , r r ,nr l , . l , r r r r l l r r r , l 1 , , , 1 i 1 , , , , , r , , , , , , . , . . , . , , ,

t ta

' l ( ) i l t l t k 'j , , ( t |

lx , / | l t ( .

l r l r l r l

r i r r r l r r r t r

| | | | r r ' r r " r , lr \ l l , r

r ' , , , r l , r r r l , r .

, ,1.1 I t r r l r , i ; r r r r , l r l , , 1, t , ' , i t t r r , t t t . t r t t t t t i t t t t t t , t i r r t r t l I i l i t t r l t i l r l t r r l t t t r . r

' r i . l , i , l , l , r t , t . r t , r r ' . r ' , l i ; , r , , r t t t t , l r t , r r i l r t r , i , ; r r r ,1I I I r t i { ) r r I r | . ' ' r r

\ ' , | l r , r r l . r | | | r ' . l r l | , l rv,r , t , I t , / r ' r r i , r l r r r r l t1;r t t . r l r l , r r ' l l r l l l l . r l , l l t r . l . t

t , r r r r r , r l r , r r r , , , r t r ' , r ' , '1,{rr r , l , ' l , , , l r " l " " ' r r ' l r r ' l r r r t l r ' l r l r l r l r '

, t r l r r . r l , t l , r l r , r , r

l 'o

1'z--\ i)/ t , ^ -

\ \ D

t t l

1*i*i+:+-4i i' ir rl ll i l )l ;i ;ii;,irli:*{ir *ir,lxilX''i!,:,i:":,".:.1ii;.'i:l'!),,,1;il;,1;t:::'i:l,nllii:il,:,i:,ii- racordut 24i[, ;t1 t1t**n'i*l1;lll*'*'".:1'i::J:1".1'.";:':'""*' *:*lt

t , i rc i sc renunt. i Ia supapele. .dc rcfulare,--montajrr l poatc f i ut i l izatliii:lilf; ,i::i:?J,'.."]:i*'['J.i[:: #iji*;""i,.j'"-,1"mi1r"r,,.,*xrr.6. GEt;EllA,r.on soNlc p[NTnu stsTE]lr DL rltr\(:TtuNIl

,,,,,",-'lr'i.ttili; ii";i t::'ilt ta-supapele de.cvacuare, pistoanele r, L sint

r''i,1i"..t"'".ig","i. .r.."iir,i.i"l.lT;,i):ii','::,,i l*,:,':llrlrX!?..1i*ii,':.#* "1:fi il:"1i,*','i,T;. .ii l: i': l"i;i; i;;i J;,;.1 ;ifi "i;ii ;' ;;;;

,-$-rliri,:,,Wiiit'ii$ri:x":t**iiTi:*ji*:,ifi""r,l:?: :lll'.",:H't J"::t i*ij"iilld:T n"T,*"'t'#:.1,:;n,i":liru;,xrijl

( r r nxrtor r l , , t r r l r , , r r . r r r r r ro l ikrr nrolorrrr ' yx l r l r ' 1 i r r l i l izr t l tut t t l r lot l r t r l t . r r r l r ,o l r isrrui l , i t rs i r . i t r i rcr 's l ( i rz lx) tnpir t ' l t avcrr tkr t t i t supl t l tc t lc ( v i r r ' l r i r t ( , . r . lc t ln l s-a t l t 'scr is antet i . t , asigur inr l t r -sc utr dtrbi t col t t int t t t ( l ( [ l l l i ( l l ) r l rruotorul h idraul ic f lu idul va f i recirculat pt in strpapl l t ' dc adnt is i t r r l t ' 1, t r r 1 ' , r

\f i .:. ,\P-{n,\tE trlLIz-t ' l}: l \ I \s'r ' .\ l-,, l ' l l l l . t l s{)\I(:}:

Instala!i i le sonice, pentru buna func!ionart', trebuic si"r crtlrrirLri rl,.rrate de misuri, dispozitive dc compcnsar-c a picrdcrilor, dispozitir, , l , ,, ,,rant5. care si. izolezc porliunea de circuit dcfecti, pcrmiJind frtttr 1tr,r '. 'r, ,altor aparate din instalalie fir i" pcrturbati i. In cazul circuit(lor rrrlr. ' ,r lcu motoare rer,ersibi lc s int nccesarc robinctc carc s i pcrmit i 'L l ! r t tL i r l . , r , . la doui. fazc. Dac;'r intr-o instalalic soniciL sc rrt i l izeazir mni ttttt l l , l lrrr, l,t lc exemplu ulei mincral in malinilc sonicc yi apiL in l inii lc (l, rr. 'r l ,,r r,cste necesari, o scparalie a fluidelor si rl ispozitivc de conpt'tt:rLt, ,, 1r, r, l,r i lor dc l ichid pentrrr ambcle fluidt'.

ln { i6ura al i l turat iL 69 se prczint i - t r rn condensator pt i t t , . r r , , t , I ' r t r r leste suprimat prin dcplasarea pistonului din pozitia mt'<lic. I ' i : t, 'rrrl ,r , l ,.f inut in cil indrul , intr-o pozil ie nrcdic dc lcsorturi lt c.

lntre piston gi t i ja f ix i d cxist iL o dcschiderc. Cortc luci t l t ( l ( i r .ur ' r r r ' t ,a puter i i s int conectate in e; i .1. In mod obignui t d ispozi t i lu l p, t r t r i t , l r 'cerea curentului sor.ric. Daci insi. intr-o parte prcsirrnca nt't l ir ' .,.,,1 1,,r1rrr.ea se poate restabil i in t impul oscilalici pistonulrri r i. I) ircir ittsrr .r ; 'rr,, lrrr,o spargere a conductei intr-o parte, pistoDrrl ,t sc cleplascazii sl)r, u,l] l i lr lcapetcle t i je i d obtur ind complet comunicl t ! iar intr t ' cc lc t lourr , , , r r , l r r , l , '

Dispozi t ivul t ip condensator sau i r tct l ic prczir t t i r pat t icrr l i r r l . r l , , r , .1di lercnta dc prcsiunc al tcrnat i r , i apl icat i - r t :c lor c loul-L strprrr f t l t r r l r \ ! . r l ,p istonului cstc maxini l ; r capctclc t le cuts i r in t iurp cc pcntr t t 1xrzi1t , r r r r , , l t ,d i ferenla de prcsiunc cste n, . r l i , astL ' l c i r dcl) i tu l in act 'ast i lxrz i t i r ,1, 1,rrr , l ,numai de prcsirur i l t ' r r rcdi i . l leci pr i 's i r rn i lc ncdi i sc pot t 'gal t i t t l t r ' , ,1, ,1, , r r ' rconductc atunci cind pistonul a trcct'plin pozil ia mrrl ic.

O funr: t ionarc asenr i rn iLtoarc alc 5i un dispozi t iv crr i r , r { i , .

in f igura ?0 estc prczcntal un c l ispozi t iv cr . r o construcl i , i rs(rr . , r . , t , ' , , r ,cclei prccedt 'ntc cu urmir toarelc rnodiJ ic i r r i : p istonul a arr par l l i r ( , r l r i r l . lde o {orrnir s1r ' r i l l i ; i sc spr i j in i pc suprafc{c lc g, / ra l t ' t i . j t i t l l t r i r l r , / , . r r ,arc; i e l o formi-r m(,( l i f icr t l . In accst caz pistonul condcusator ulrr i r , ' lu,rr l ,dcplasa o anumitir (l istanti. fa,ti de pozil ia mcdit 'f i ir i a punc in ( ( ) | r r r I r r r ( . I I r ,celc doui-L ctruclur:tc. I)acl sc produc scirp:-Lri in una din piLr!i, ptlsirut, ,r rrrr. l i lin act ' r rs l i r partc scark ' ; i p isrorrrr l is i t l t 'p last azi ' r " pozi l ia nr i j lor i , s; ' r , ; ' . '11, . ,ctr prcsirrrrcr t nr t ' t l ic r l ic I r r i r1 iL. L ic l r i t l r r l \ , : r c l r rg( yrr i r Pis lorr l l r r . r1,r ' l r '1,crrrsci , p in i r c inr l p l r .s i r r r r i l , ur l r l i i sr lc l r i l i l r r l r rz i .

l ) is lxrz i l ivrr l Ixxr l r . l i , r , r r ' , l t r r i l r r . , t l , , l i r rc i l s i i . r ' r r rorr l lz l r r , . , r r . r l 1" 'ar : r lcv ikr t rk l t rursrr i , i , . ln l i1;rrr , r i ' l . r ' pr lz i r r l , r ( ) r , i r r rn l i r rotr : . l r r r r ! t r ' .

S( | l l l 'z i l l l i in l iT i r t t , r / . ' r r r r t r r I r r l . r i ,u i r r , , t l i , , . r t ' ' l | fuDitr ' ( l l t , ' r ' .1l i r l r i r l r r l r r i r l i r r l r , , ; ' . r r l , r r r , ' l t , r l , r r . r1, , r l r r l r r r r . r . i

I t t l t1| t t , r l t " i l r l r , ' l r ' l . r r l | I r , | | | . | | | | | | | . I I i

' r , . r l r ! r , lqr ' | | . r " r / . r | ' I r ' ' . | l l r | ' i t

r r r r r l t r ' l , r r , r ; , . r l r r l ,1, ! l r | | l ' r l l r r l l r r t r l r l ' r , r r l t . r l

l ' r ' t r l r r r r ; , r l r t ' I r r t r , l lx . r l l r t r t '1. l r t | r , , , r l r ' l t ln ' / t t t \ , l i l . r l t r ' r t r r l '1t . .

t l l5 19 10 31 32

r , ! . 0 i . . ( ; r .n. , i r , I s() l i ( : l )c l l1ru s jst( I r r l , . r r : r ( i i , , , l

S<: l r i rn l rarc l l i lczci in l rc ar;cslc l imi tc lxc( l l lc( , \ , i r f i i t l l t lu i r r ! i , . l , r lstu.rrc l1 pr ln11'11 rL ' l ichid sarr r i r ( r - r r r . r : r ronr l , . i , i ,1. i i , , , , i , , i , , i ' ,1r i , ,

r , , , , , t , . , , , , , , , .nr t l r i l 1n1111111 rr l . t i r r . ( , i ! vr , l r i r r r l , . l . r ; ,1, ;* , . ; r r l r i , , ; ; ; , ' ' ; ; , , ; i ; ; , , , , , , r r r t , j . r r ,r r l , ur : i l ) ( ,1t , . l i r r l i l iz l r l In.ntrr iut l t r . .n iu. , . , , 1, i , , , ,1u. i : 1, . , , r : i , , . , , , , , . 1, , . , , , , , , , , .01, r ' r ' l " ' t i r t r r . l t l t l ) r t rnolrrr L,r , l i , l r , ( i r , ,1 i l , . r r r , , t l , , r , . r t r r i . l r r , r r l r r l r r r

a16

ia i l\ - - , /

b,/

l ' i8 . ( ' r r . - - 1) ispozi t iT ( lc s iSuranld 1ip con-dens:itor.

Dispozi t iT t ip condcrrsatof cu

Fig. 72. - Var iar ] la l co strucl i . / r " r . lc montaj cu inert ie.

Fiq. I i . - ' l fa ls lorur l iof .

I i t . l . I ) is tDzi t i / l i l ) o{)udfns;r1oI crr j l f f l i f t )cnirr l I r ( ,nrr ! r . r r ! r ; !1. ' r

I r r l igrrrL 74 l in i i r pr int : ipal i r r . r r p lcsirrnc s()ni( i i ( .s l r . r . ( ) r ( r . l , r l i l r l i r -r -or l l l l l . f s i I i r r i : r ctr l i : r l i rncnlr ' i rz i ut) l ( \ ' { ' l ) lor srLrr o rr . { r . l r srr r r r r r l t r r j , i i r r l .( i t tgt t . t r l l r r i r l r r l r r i ts l . c, l l ' .1;r l i r l r ' l t is l r l r r l ( ,s( . i l i . l l ( . srrs l i r r r r l r l . r r . r , ' r l r r lr t l y i r l r tc t r tc o r lcsclr i r l l l r ' ( ( ' l l r i r l i { i l t ( i r r l l t l lc t r i r r l r . r iotrr l i l l i j , i i r I i ( . i I I ( . I r i ( I r .crrrrr l r l r . l ( jocrr l r l i r r l r r . l r is l r rn : , i t tnt ; t f l l i i r i i I ) r . ln i l r . l r , , r , , r , , , r l r , l r r , l l l r r r ) .

l ) . r r ,q 1111 i r r r r , r r r r r , , j i , . i r r ' l , r i r ' , r { i , , r r r , l r . , l r r r . lorrrr l r \ . r i r , r r l , r r r , r r i ,' ,or l r r l r / , . t r , r t r r , l r r , l , . l r r r t , r , r l r r r r , I i l l , l l , t . l , , r r r r l r . r . r l r r r r , . , . r 1, , t , . 1, , , r l r l r , . , r

1?ll

I r t , ' l 1 , ' , , ,

' , , r ' r , " " , r " ' r ' , '

,1, ' l r , , t

, i ' l l ' l " " l r I r , r , l r , l , ' , l

I ' r t i , , ,1, , , l r r r { r r ' ,

i i r l i l , r l ( (u l t i l l ( . l ) r ' r ' i , s I i r t l lc lcrr t r r t t r l r t r l l i r lc r l l r i r r { i r ' s inr ( l f l l 'c t iucir col lsunl i r -lor-rr l r r i vot ( lc i ( rn l i l i l i r rc l r i r l , r ' , r r l in i , i ,1, , ; r l i t r r l r t l l r r t : l iLt i -L l lcr t r r tbar:ca l in ic ipr int : ipal .

ln rrlt ir [orruiL coustructivi-!, [ igrrla 75, l inir principaliL estc concctat:-rlrr rr irLl t lcrivali iL in l, pistonul (iste inlocuit prin diafragma g cc arc o des-rfrir lcr-c ccrrtralh (:c sc inchide cv ti ja h in por!iunca cu tl iametru maxim.

$i lrccst dispozitiv ca si precedentul permit lucrul cu scult r:c atlurit micipi r . r ' r l , r i dc f lu id in t impul Iucrului .

In figura 76 sc prczintl un transforruator carc pcnnite picrdcri delichid atunci cind linia estcin {unctiunc si in acelagi timp estc un dispozitivrlc siguranli..

'I 'ransformatorul se compunc dintr-un piston dilerenlial /t, l cale alu-rrtrl crr joc pe o tiji cenhalS" m,. Conducta principaliL, spre sursa dc puterc,cstc conectati. in punctul n iar linia dc derivatie in L. Spaliul dintre piston:;i ti ja centrali. este menlinut curat prin faptul ci pistonul oscileazi. Inirccst caz consumatorul poate avcir" mici pierderi iar cind acestea dcvin rnarisau sint uule, undelc sonice sint intrerupte datoriti faptului ci prcsiunearncdic va cre$te pe partea cu pierderi sau pe partca opusir pierdcrilor', de-plasind pistonul la unul din capetc oprind astfcl oscilafiile. Se recomandit:ir l:r acest transformator raoortul. de trans{ormare si {ie mai mare ca 2: Ilxrntlu ca presiunea maximb. in linia principali si nu contrabalanseze lorfa1>istonului pe partea de joasd. presiunc, ceea ce ar producc anumite lovituri{tit dc ctocan.

tn alt l 1orm5. constructivi., { igura ?7, este uti l iz&t tot un translormatortu pistun difcrcnlial .o, p, cu o dcschidere centrali prirr c,rr" trcc, o ti j : ictr di:rrnetrc difcritc. ln iona contlali intro piston gi ri j i r.;t,. un j,rc impor-ttut. Sprc capetelc cursei pistonului jocul foartc uric asigurir olrturarea gf,uri iccntnllc a Distonului.

Linia 'principalh

e conectati in a iar dcriv:rl i ir in l..Accst t l ispozitivt:slr: r:onvcnabil pentru scule carl: au pier(lori irnl)orlxntr', cir rl l cxcrrtplut:iocnnc dc glurit roci pentru carc apa cstc rrt i l izrtiL i| l i l p('rtru rrt ltnrDirrlrrscult ' i t: i t $i pentru sphlarca giruri i proclusc gi ov:L(:ui!n ir rlr ' ;r 'ul ikrr. I ' icrrlr 'r ' i I , 'rkr l ic l r i r l t rcc pr in gaura ccntral i r i r p istonuhl i c inr l r r r ls l l sr ' 11irrr l lc i r 1ro-zi l i i r r : r ' r r t la l i r .

Slr l r { i r r l r l i r r l rc l ) is to iur 'cort t l t r i ( r i r r r t l r l r r ros[r ' r r r I ) r 'u1rrr i r . r ' i l r r . r r r r r r r r rl i r r - i r l r ' l i l l r i r l c iu( i r r l ) lor ' i r r l i . , r rozi l ivrr l .

In l i l l r t r ; t 7 l l , r r r ' prczi l i . i o r , { , , r 'orr i , . i I ' t , \ ' . i / l l , i r r r , l i ,1,r , r r l r r , l , ,1,: , r ' t l , i . l t | l r ' t loI

o

Fig. 76. - DisPozi t i / t iPtraIrs lormator.

Ir ig. 77. - DisPozit iv . . t i t 't ransformiLtor Pentru lncr(rcrr

r)ilri dc lichi(i.

41'9

_s,_q'

l l

I ) ispozi l i /

( , r ' r r r . r I r Ionr| / : r l i r r r l r r l r , , rz i o l r r r t l I r r r r r rPrr l i J . ( ' i rPaci l l l tea , j l r . f , i l l irh l i r r i r r Pr i r rc iPrr | - r r rs igrrr i I r r r r r 1 i , , r r , r r , . , , , , r , . , i i : r i rstafat ie i r .h i . r a l i rnr ic i t t r l corrsrr t t t i r to l i i nrr s i r r l r r rp l r r { i_

i r r t r r l i r r ia Prrrr , . i | . r l l i 1r corrsrrrrr ; r toru) 7 der i r l r t c l in accirst iL hni( , r .s letr l r ' t t . t l . r l r r r r , l is l , , rz i i iv , l , s i t { l r arr( i -L c1 piston c1 inchi t lerc 6. Rolr i r rcrult :onst t t t tatotulrr i ,stc urr robinct t l t gol i r t ,9.

(lcl iLlalt consrrrnator .9 cste dt_' t ipul cu pierdcri mari de l ichid ;i esie, u l ) l : r l . . (u l in i ; r p l in,- ipal i r .pr i r r t r -un r i ispozi t iv /0 t ip t rans[ormator. Cinr l\ ' . nrr t r ld( . roDln(. t l t l l t r ( l t ' r ( lur l 7/ t l ( ( .s lu iJ, d ispozi t ivul t ip l rJnsfornl ; r lorrrsiguriL prcsiunea ntedie in conducta dc dcriYatie7 dar nu pcrmite trcc,.rcarrrr<klor dc presiunc.

\tI.tt. ( i lOcrt\ s0\l(;

Aqa cum estc descr.is in teoria sonicit l l i i , un ciocan sonic consti din-lr.() masir sustinutir dc nigtc resorturi capabile, si. oscilcze la rezonantir cul t i ( \

' nta ului gcn, ' rator So1ic.In^figura 79 su plr.zinlit un ciocan dc nituit. l istc compus dintr_o car_

r.r \ . r / lU. carc arc un minlr / l / in r .arr .se af l i o pirghir d i act ionare /22,, ir lc l)rin intermediul unui ac /Jj , lus, lr ide r.cnti lul i/, admiti;d l ichidui,l, Lr l inia de transmisic la scull '1.

I-ichidul suf,,^presiunc, ircliolca/,i-r asupra pistollulu t I25 care poa ',tl l r 's i r ( l | rovlr l ' lJ0. yr?sr r l l ' lovrr , . (s l i .pr_e\.r ' r rut i cu f lan;a /?7 pr in int t . r_rrr . r l i r r l c i rc ia estc t intr t iL inrr . -o pozigi , ,m,.di . ,dc c l r rc resonur i lc i2t ; , t t : l t .l ' r rs i r 126 transmitc lovi tura pr in pi t .sa intermediar i /J0. ln acest ( iocirn1i irr toate sculele unde rmplitudinci cstc rclativ micr'r ; i unde curentul tolal, \tt nlrc ul raport cu curLntul total al l inici, pentru a ob{inc cel mai }run

I . ix . r t ) . ( i , { l r sor ic.

r ' l .c t t r r : l r r r ic ca k lv i t t t r . s i - r s( ' pr(x l l l ( . i i ' yrrrnr. l r r l l i r <.ar.r , l r is l . r r r r l i r r 1 i i r rer ' l r i l ib l r r sulr rc{ i11v1111 us{ ' r l . r ' i ior ' ; i Presiuni i r r rcr l i i i r r l i r r i ' : r r l r . l r r r r r , r r r is i r , -Iu . r ( ( . . rstar J)" . / ,11r, . \ r . , ,1 ' { i r r ' , [ r , r l t r l r r l rx inr : r l lovi l r r r i i , r l : r r . 1x.r l , . ; r l t . r P;rr t r .sr . Prrx l r r r - t , ; i r l l lornr:r{ i i r r r r r r r r r r r . ' r : r r r I l t , r r t r r I r r i sor i , . i r r l i r r i r r r l r . l r , u r , , r i r l . r r . ., \ r l r ts l i r | r ' Iot t t t , r t r ' ; l l )1 l r ' , r , . r ptoloir( r . 1 r r . r t r r r l r : r { i i l l r . r l l i 1r , r r , , r r r r r I r t , , r r r . r r r .' . r ' . r l r r r r , r r l , , ' , , , , l r r r , r , , r ' . r ' , . r l r t r r r , r , r r r r , r

\ l t , ) sts l l : l l so\ | | l r l t l l r l l | , l l l l i

( ) lx)nl l ) i sorr i r , r | ' t lvr , I r r I r"L in Atnt ' -

t ica in l94l i i r r r ' o (()rs l r r ( l ic or i f l inalar

1i estc c lcst inrLl iL lxrrrr l r r i r i i lxr t lo l r t lu i ,f igura 80.

f,n gencrator (l( ur(lc fste plasat lacapitul de la suprafa{iL :r conductci dc

ln ' t ro l pe un supor l ( ' lasl i ( . I 'ndclc sc pro-

i ragi p i in tub iar in ' iecrLr ' , punct a[ 1u-bului sc produce o nli lcirrr ' oscilatoric.Petrascu sint plasat( mai tnultc muft. cusupape carc pcrmit tr((crca l ichidului

in sus.Oscilati i le P('rmarlcrltc Senerat(' d('

la suprafali detcrminal astfcl pomParca

lichith.rlui prin trcccri succcsi\ '( ' Prin su-

pape eialonate in lungul conductci. Lrn-

dele sr: propagi prin ofcl - matL'rialul

Genaralor \onrr

fubing

{elc cu bt ldlsupopal

Coloand

tubului i irr- studiul rcgimului (lc Pro- tris. to. - sistcnr soni, ,t ' tn,i ' ,t, ' , .pagare trebuic s:r t ini scama dc aParit iaundelor statiorlare gi dc sarcina dc pomparc carc cstc distribuit:r itt lrttr l l tt l

conductci.

\I l .10. (lol{.1\l).1 SIIP.IPELOn Dt: ,\D}IISIF: l i t EVr\(:(lrUtl l

tr .1 r\,Id:I ' lnl Dr: (:olrltusTlnll LA uoTO^nItLH (:U Anl)unl: I lt ' l l l l l ' l

I) in aria lar6i; i diverstr dc iurbunlit it l ir i ir le ntotoarclor 'tt ' tt ' l ' t ' rtt

terni pc car., (icorac (,ottstantincscu lc-n brevctat in primclt ' r lott i i r l |r |tttt

alc acrstui sccol, in-r'cn!irt rcferitoarc la aclionnrca supapclor 5i rr rrrl"lr ' t

de combLrstibil aplicabiir-L indeoscbi la motoarclc dicscl polici l inrlrirc r" l. tr '

prezentlrttt ' ir-.At:castir invcttl ie cstc inregistrati in :rnul 1918 ;i constituil o rrpltt r lt ' '

dircctir rr sonicit i 'L1ii.l ) r rPiL crrur : r t i r t i r ;ut torul , invctr ! ia const iL in l t : l tonart 'a sul) i l ln lo l ' , r / r ' . r l l

r r i r r i r r . l i i , i t lc r .orrrbust i l r i I l i r mototrrc lc c l r . ar( lcr( ! i r r tcrr t i l r t i r r i t t I r ' t t r t l . r I t t t I

i r ' t , r i ls , i r i l , , r r . r r ' l ) r ( ) r l t t v; r . i l l i i dt

' r t 's iune 1i v ' l r tm i t t l r - . r ' r t t t l i l r t i r ' ' l '

l ic i r i , l , , r r is l , r r r rz i t i ' r ' , l i i t r i l r r r i t ; r i t t rut t r l t t r te 1i r : rp.r ' i t i ( i '

l t t 1 l I i r tc i1 l r t | , t t t i iLr i r t : t :k: lxnlr t l l l t : ! iot t i l r t ' t s t tP Pci t l ' ' ; r r l t l t is ic r i l l t t r l ' '

( .v i r ( l r :ur ' , , 1111l l l c i l i l tc l l t t c t t l r r i t r , l t t t t Rr ' l l ( ' t i l lor tk: i t l r l l t t ls t t t i ' t t r t p is lotr r l .

: r ( l r ( ) r r : r r r ' r l r t i r t r ' s t t l ) i l t , l t r 's tc t l r 'sr l r i : , i r l i t t t t l t l l l r is lo l t r l t t - l r ' t I I I t t t t t i t I t t ' I I ' t t t r

I r o rrrrr r l r t r l . i l t t o cr t1r ' rc i I r t I r ' , l i r r r l r ' i { i r r i s t tp l tpr t i t t r l t is i '

l \ , l i j l0rr , , , l r . 1r | r r l r r r t , . ; r l izrrr | r r i r r i , . r . l i r , i r l , . rorrr | , r r , , I i | , i I . r r r r r r ; l : t t t r l i t t l t t t t t

1 i , r r , r . , t , , r , l , , ' , , , l , , r r l t , l r i , l . ' r r ' I r t l l r l l l t r ; r ; ' r i r r t r r l ' t l r r " l t r r l r r r r ' i . r ' t t ' l r t ' i '

r ' r r o r , r l r r l r , r ,1, r r r j , ,1r , ( r r r l r r lorrr l ) ' ' ' ' t r t | ' t I I t I ' t I r r I l l r r r ' l ' r l l l r r ' r r l ' t l i t r i t r l r '11

.r . i . | | r r l , l r i r l r r r r r r r ' l , 1\or, , , 1, , , ' , , ' , , ' r r I t t Lr t r I r ' r ' ' | ' ' ' r r r | ' r r ' I t | ' t I | t r t t r r l

r , r t r t , , l t r r l r , l r t , l ; , t r r r r , r r , l r r l " l0rr l l r " l r ' ' r ' l l ' r r r ' r l

( ,1) l i l i r l ( , ,1 r l t . rorrr l , r rs l i l , , l i r r j r r l r r l ls l r : v i r r i i t l i r pr in val i r ' t ( . i r pr , . i l t , r i lr r r l r l i i r l i r r s is lcrrr .

.\srul:rr, yrcntru (:()nlir l( l i l sulxrpclor de tl istribu!ic i i e{cctuara-a jn-

1,r{ i l i r l t . rorulr t rst ib i l s int r r l t ts i r r i t rc i generator i de impulsur i , unul adap-l:rl si lt:t iorrr.zc sqpapele de atlnrisie, altul adaptat si actionezc supap,rlr, delvir( uilr.(i i ; i rrl irci lea adaptat sl. cfectueze injec{ia de combustibil.

l i irtur: gcncrator are una sau mai multe came care se rotesc aclio-rrirrl rru rurnriLr.de pistoane conectate prin coloane de l ichid cu supaptlc de,rrlrrrisi,, t lc c\racuarc fi respcctiv cu injectoarele; pistoanele unui generalorrrr (iorri l t l sul);rpcle dc admisic la toti ci l indrii urotorului, cele ale generatorului'.,, rrrrt l supapclc de evacuare ;i cele ale celui de-a-I treilca generator injrc-trr.rrclr '. ( l: lc trci generatoare pot f i convenabil montate pe un ax contrrrltrr jrrlr l cr'rnri ir sint dispuse rl iferitc pistoanc in faze corcspunzartoare prulru.r lr rrr ' l ionirtc de camele rotative la pcrioada necesare.

Nlt canisrnul pentru actionarea supapei de admisie gi a celei dc el'a.ltare, . l, sirnilar;i cuprinde un piston actionat printr-un impuls care se propirgi, lc rr lrnrgul coloanei dc l ichid;i aclioneazi in directia ridicErii supapti t leItr ' ' ,rrrrrr. Supapa este presatr-L spre inchis pe scaun de un aJ doilea pisioD,r t ir,r ir l l)r intr-o coloani de l ichid carc comunici cu o capacitate constl 'nd,lrrrlr rrrr rtr: ipicnt plin cu l ichicl (tot acrul f i ind eliminat). Aceastl. capacitatc, ,1. r orrrrnir. pentru sistemelc srlpapelor de admisie gi evacuarc. Ftnctia.r,r. 'r lr. i capaciti. l i estc si. acumnleze lichid suplimentar in stare s[ previnirrrrltr rrrr ':r r.xr:t.siv5. a presiunii in coloancle de l ichid conectate cu ea- ln timpul,rr '., lor t l l lctragere alc diferitelor plonjoare in elcmentele dc actionare,rlr ' ,r1;v;q1r,,1,,t, l ichidul din capacitate este comprimat. Revenirea plonjonrlui, , l l r ' l lr lrrrrl i 'L prin expansiunea acestui l ichid inapoi la volumul s5.u init i i -() lx,nrpir este previzuti. pentru a suplimenta l ichidul carc se pierde,.r ,.rr, r ' ,rrnrricind cu aceastS. capacitate, menlinc o prcsiune medic constaniiLrtrlrr ' .r lr i (rlc excmplu autor-ul preciza valoalea dc 70 daN/cm'). Capacitatta, , lr ' . r l,, :rscrnenca, in comunicalic crr conducta care pleaci de la gencratc-,rprrrrir rr r:orrrlut:t ir cu orif iciul interior mic (dc pildi, arati. autorul ci o con-,lrrt l ir rrvintl canalizalia interioariL de ordinul a doi mil imctri si lungimea de,rptrrxirrrt iv t loi metri poatc fi corespunzi.toarc). Daci in gcnerator eslclrttvizrrlr-r o singure caml, accasta vir I i rotit i 'r crL jumi"tatea vitezei arb()-rr ' lrr i co1il. I) irci sc dore;te o l iteze dc rotalie mai redust, pot f i prelirznle,lrrrrir t:rrrnc pc accla;i ax. Pistonul care l ine supapa pe scaunul siu este cevarrt:ri rn:u.c in diametru decit pistonul de aclionare la dr:schidere, astfel cir' 'rrprp;r cstc l inuti. sigur pe scaun sub forta crcrcitati. de presiune pe dife-tlrrtrr <lt: :rrir:, cu cxccp{ia nromcntului in care impulsul care se propagir d€r-alrrrrtrlrrl colourlri dc l ichid de la genelalor aclioncaze pistonul de comandi.

(lorrrlrrt:trr carc conduce dc la gcncrator la pistonul dc dcschidere trc-l,rri l si i uilr ir l ln orif iciu astfcl incit viteza instantanec ir ir lpulsului siL Iic, orlrir lcl irbil:"r, sir so cvitc capacitater i l condu<:ti l i si! sc asigurc irproal'ro i r r r l t l rcndcn{ iL int lc cursa pis ionului s i v i tcza t l r : ro i ; r ! iL ' : r gt r rct i r toruhr i .l ) r ' i rscutcnr:a, r :onductclc car( ' l ) lcaciL dc la gct tct l t tor l l t r l i f t l i lc s l l l )ap( s:rl r , r l t l r r r rg i r r i s(nsibi l ( ' i j iJc c i r s i 'L s( ' in l : r turc ( l i t icrr l tar l i l ( ( iu( iu i r l ) i r r ( ' ( l i ! ( . ir r t vrrr i rL i inr I r r l r )c( :osir l d( i l )11)| i rBirrc l r i r rpulsrr l r t i r l t : l ; t 11r ' t t t ' t r r Iot l r st t l t i t l t i .

; \ r r lotr t l r r t i r i i r c i o vrr l t r r t t lx) l r iv i l : r i t l ) r ' ( s i l l r r i i t r t t l s l t t tctr l i t t l i t t, . r l ' i r ( i l i r l r ' I r i r r i r r I l r r r r , . I i r I I yrorrrPl i , s l l r l t To t l r rN/r ' r r r1r , , l r r t : , i t t l I ' r ' r r t t i : r 'l ) t , ' , i l | l r i | | I I I I I I r r I r i r r r I r r i r I I r , . r | ( } r r r l r r r l , l r , r l , l t : r r r . i t t t is i r ' r , i r r l r l r . r I i : r t t I r , I t r , t t t I r t t t t i t t .

l ) i i1 '1rr Lr t r i r ' , l t t l r t i r r r t r r l t t i I r , l l l , t t r r ) I ( ) . I t r ' I r ' r r r l t .ur l ) r . i r r r r ; ' i r l r ' . Arrt , ' r | r l . r t . r l . r , . r r r r r , r ' .1 l , l r l , t r r , , . r t t t r r r r l r ' , r r 1r , ' r r , r r , , l . r r l ' , t l , r lor r" .1, rotrrr ' t l

r l , . l t . t t , l l l , r \ t1, , , , l ' , r r , , . , r ' . r l , , t t l , ' , r , l r r t , , , l i l ( l r ' . r l ) r r r \ l r r r , r l l \ l r { ) ( l r r , l / r r l f il ) . r t l , : r1r t , . r r r , l i r , r r , i I r | | | , r r r r ' I r ( I ( , ( , l t r l l ( r rz,r r o l t t t i i ) . i l ) ( r r l r r r r r to{o. r , l ,r l . r r r ,1r i , l r ' . r r r , . r r { rorrrrr , I , . , l r r r to l r , . r t r ' l r ' r ; r | i r l r ' , io l r r1 i , ( ,1, r ) i1 r ' r ' i r l i r ' ,

i r t i . ' , r i r r t ,z, r l r 1rr , , r l r r , . r r r r i l i , ' t t r l , ; r t rot l iz ; r r , i t t r ' t r r r l t t r l , l , r ' r t r , , , , r , lLL,r l l i . r : , r t t r r l . r l , r I , r , . I , , . r r r , | , r l r r l lsc l t idct t r r st tp;rpl l r t ( r i . r \ ( r ' \ r l , , i r l l

crr l t r l i l , ; rprrr i l i , i r l l r r r r r l r r i : ,1)r( i l ( 'uor i l t r ) r ' r l i r r c lur : r - r r I r l ) r 's ic i i t t t 1 r r r I r r r r r | , 'l ) r .ntrrL i r t l r , r l r r : r i r r j , r ' l i r r t l i conr l r r tst i l r i l i r t t i l i r th i i r r r (

' I ( ) I I r I r 1 i , l r , r . r r ,

c i i i l i l ; ,1 , 's tc l ) r l r i -1, / .u l crr . r ' . r t t tc l i - r . dc i r j , r ' t i l c i l i r r r l l icr-r i r t ru, r ' - r l ' . , l i .L , 'r : t , : : r : 5aia! pc st ; r r r r r r r l sr iLL ct t a jutot-ul l l ] l l l i i r r ( :1 i rar I i r I r I r i , I , | , r r rLr , r r 'cotr . i r :1] sprc ol i i ic i i l ' t l t Puivcr izaLe. - \ r ' r ' r rst i c i r t r t l r - r csic i t t r l i t l r Lr r , , r 'r l i !af i , r cu o colx luct i " r carc plcaci iL, . : l i r gt ' r t t r ; r {ot . l iunt l r t l r t t ls l , r r . , r r r , r ,

c i l in4r i , L estc i r )chis r lc l i r fu l acuhi i s i ( i r l ) i - r iu l o l )Lrs c lc r lcrL:rr1,r . r , . ' r , , , ,

e 'str i lc i r is c lc un pistorr sol idar crr arcul . . \ r , :Lr l lxralc [ i tcgl ; r i ; r l , r , l r r

c( lasi : i . canrcr i r s i i r r : rn j ; r t s i l pr-esczc i IL jos l ) , ' p istor tu o lor t i (onr ' r , I r l , r lS-:r p i . , :at o micl 'L capaci tate i l r conlul l ic i r l i ( 'cu {r)n( l l tc ta in i r t tu IL rr , 1 . ,1,r , 'p i r - i , i , qenerator ' , pcntrn a asisur ' : r ur t r ' , , l t t i t t l t l i t ior t : r l c lc l i r l r i , l , . , , l ,n lcoi l l - ; ) i i l1r1!rea sn i I dcpla.nrea gcnc'r ' : r torrr l i r i ; i I | r lucct-cn c()r)s( ( \ ' t r l . r ,L | , l r l

rn ' rhr i va : rcumuLa su{ ic icni i r cncrgic fcnlrr r Pror l r rcc o rnr( l i ( i r r ( l i r l , , l , ' r

c5l . - - r f , .cLis, asigur ind ast fc l cal l t i tat( 'a n((r '5 i r r i - r i i ( combust i l ) i l l r t i r r r r r l , ' t , ' ,t onrbust ib i lu l cstc [Lrrnizat dc o pr,nrpr-r dc cor lbust i i r i l r r r r , i , r l t , , . r1, ,

c i t i i i ionst ind dintr-uu t i 'c ip icnt ! inu1 lo l t lcauua compl( t | l i t r , r r , , , r r r l , ,

t ib i l ; i comunicinr l cu o conchrcl i . crrr-c 1i l ' ; rc i ( lc la gc[craior l , r i r l r , ' , . , r1

l izat i , mici r , de pi lc l iL curr prccizr i rL l tonl l , dc c lo i n i i l imetr i ( l iaur( l r Lr r r l , , , , ' ,s i {1{ i i nr t t r i lungirnc. In i rccst c;rz gr:uclrr to lu l (ste previzul ( l ( ' r . r r . , ,

ac! ion:rrc spccia. l i ' r , rapi( l : r , ast f ( l c i - ! poatL' 1 i ptor iLrs iL in con( l l lc l , ( ) r , l r , lfoar i r laPidl a l ) rcsiuni i . I ) resiuuca r lc iut l t idcl l t lator i t i r 1r ' r ts i r r r r i i . r r , r l l r1,a i ; . lnar marc ( leci t i ) lc .s iuDcu rrr td ic c l iD l in i i r ( ic t lansr| is ic r i r r r l ' r r l

' r l , r 's i : . ' ra ledea ca!, ( iu o ascrrcncir aLlal l jar . , u l ) iml) l l ls c l r ( 's( l ) l r ) l ) . r i , l , l ,

gerrrr : r tor de-a luugLr l conclur: t , - : i r lc conLl l rst ib i l i r crr t rc la r l t i r r j l r Lr , r r ,1,

plas,- ' l ) is tonul in sns; i r ' : r rk 'sclr i t l r supi l t ) i r ac, lnLrnai ( la{r i i r t l r r r l r l r . , , ' , ,

an1, ' i t r rc l inc suf ic icnt i "L p( ' r r t ru a r lcpirs i cont | l r i r I r 's iurcu i i rcrr l r r i -

- \u lorul iu l r t l " r car l - (duccreiL i ) rcsi lur i i (sL( t r ( ptal i r s i po:r l , I ' r , , , l r , ,ledr l r , rca cu of ic( cor: l i f i ( ! i t r lor i t l t r iu r i isPunclr , , r r :orcsprruzr-r lo;r t , . r , . r r r r , rdr- ' n, : t rorurt-r ' in l i rnp cc i r r jcc{ ia i 'a i r \ -ca l (x r t i t l t i r rqr c i t | tcsi r rn,"r ( l r i , , r r r , r .Lt lc in i 'Lr i l cs l i tn:r i ln i l r ( ' dcci t l ) r ( , i i lur l i r r l rLtor i l i i r r r - r :u lu i , rLrrr : r l r r r r rq,r{r , rsau r , . r ' ior ic la <: i i i rcul i t t jcr : tot-uht i cstc ! i r tu l 11, ' :< l r is t lc i t t tpt t ls l r t ,1, l , r r r , l ,r l r : i ,a lo l r r r : t r ln 'csi lur i i r r ru l i i . Alar l l r t , ( r i I I I I i I ; r i ( . i L r l , , r :out l r r rs l i l r i l i r r j l r t , r l ,1 ' , ' . r i ,l i t tsot lcgl : r l r " r l l r in rcgl ; r rc i r PlLsirrrr i i i r <: i r l l rc i l r r i r ' , in ( l l ( ( ( ) t l l , r l l l , r l r l( : t , j l i r r r r ' t l t : t I Pr iD PornP;-r .

I t t r 'otr l i t t t t i r t r ' , s( \ ' i r ( x l ) l r r r ( o t r ' ; r l izrr t ' r ' l r l r r l i r ' ; r : r r r r l l l r r i ! ( r r r r r ( , r . rIc l t i r l , . rorr l r r r r l i .

i r r s is i l r r r r r l I r ( z( l l i r l sr ' l r l t t l r l ic i r r l igrr . r l r l 1r '1111q1 :r( l ror : r r ' . r ' r l , , lp, l , , r . i i r r i l r t i r . i r l l l r r r r r l r r rs l i l r i l r r r rnrr i t r to lot r l i r , . , , l r r r ; : rs, r i l i r r , l l i , r i r r l 1 ' r ,r ' . iz i r t t l t l i l i r , r tctrr lot i ,1, , i t r t 1 '

r r I , r r r t i . r r , / r , r ' , r ' ; r t l r r r ' { iot t l rz;r r ' r l ) . r l ) { l l r l ,t \ . f f l r r , , / . r , r r | ) , r l ) , l , r l , r r , l r r r i r i , , , t t t r i r r lo, t r r l , / . l , \ l ) t \ l i \ i , r t l I t r to lot t t l t t t

, r , l , r r r r . l . r l r ' I r r r r r , r r r r , . r r ' . r l , . r r1r . r1 ' , I r ' r r l , : r , l r r t i . i , : , . t , r ' , r , r r : r t r ' : i r r t , r l tr l ' r i . , l r . r 'u l i r l r i r l r l , l ,q , r 1rr t r r1, , r r r l ) t , r r r i , r , r r , l . r t r l . r , . r r , lx , t r t l r , ; rz,r l t , l r t , li r l r ' , ' . r l , , r r r t . r l I r ' r l , l , r r , f l , 1, | | r r rotrr l r t , l , l , / r , I r ' . l , r l ' r r r l t t l , r 1 i | t r , r , rl l r r r , l , , r r l t r r t , r r . , . r r ' \ ' . r1 rrr , l ' r t r r l r , , . r1| .s1' . r ,1, ,1, , , . , r , , r r , / . l r r l r r r l r r l 1" ' . r1,I t r , t r r r r r r l 1,r , | , r r r1r1 | r ' r t r l , r r t t l , t l r r l I t ' j r r r r r l . r l r r r r , t , r l ' . r r t l

'11 / r / ,1,

l . ' , , l , , , r r l , r , l , 1,r , r r r r r , , , ' r l . . r r l . , , l , l , , . r ' , , , , l . r l r , , , l , r r , , , r , l r l r r r l . r r rl r i r ' r r l " r r r l , l , r r r l , ,1r ' . r , , , r r r l ' rL l r l ' r l r r l r r r r r l , l r r r r l l r r r t r r r , l r r , , l r r r r l r l r

trl

l ) l ln \ l r l ) i r l ) . r r1, ,1, . , . r r , , r ( r , . ( l lL l i ls(

r l ' l , r l i l l r r t , l ' r . l r . t . r lot l . r ; r r ' \ ior l r l . i r

; r rs, L i l i r r r l l i s i r l r oI l ra Lr l t . i | | r l ) r ( ut ]arrr ' t ! . , i , l , l .

. ' i , / i r ' r r t - r ' r 'orr , l r r ri t t jc t lo l r l r ' pr ' , , rr I i i r t t t t I t r r I i r r l , , t i , , r

( 'onr l r r r '1t l l r r r t r ' p l l r r r i r lc l t gcncratol i i r r , , , . ( l ig. l i2) s in l p l r . r ; izrr t ,ct l scr l )c l ) t j l t I l ( / ' , r rs l l , ' l r r r . Iurrgimi lc condlrct( ' lor i l t t tc g|nt 'L lL1<rt ; i r l i l , r r l , l ,sri l)a.Pc (lc adlnisic si l ic rLr t. lca;i pentru coi ias(' ci l i tr(lr i.

Sint prcvlztr tc scr l ) r 'nt inc egal izatoarc s int i l i r ro Pcntm r-orrr l r r r l , l ,supaPtlor dc cvacuarc fi capacitdli s in conductclc car(l conduc lrL inj,,, l , ' . ,r,

Genctator i i r t , D de comandir a i supapelor ( f ig. 83) cupr inr l l i , . , . r r ,sase canc dc aclionarc 77 care actioneaziL tache{ii l2 ; i prin bila /..r ' tr,rrr rrrrni;carea la plonjoarclc. / /, care lucrcazir in buc;clc cil indricc /: i, crrr, !,r 1'.rrtca supcrioarll comunicl-L cu mai multc supapc.

Pcr ioar la; i g ladul dc dcschidere a1 supapclor dcpindc dc l i r r . r r r . r r r r r , l , rdr prcsiurc calc sc plopagir de-a lungul coloanci dc l ichid, cind ac(.irst:r.rlrrt,,supapa. In ntorncntul accla, l ichidul l i iud corrplimat, forma irccsl,.r rrrr, l,nu coit 'spuudc cu {orma camci gi perioada dr' <lcschidcre a su|JI),i r lr " 'rrcicie ctL pcrioacla lcal:-r in t impul ciireia pistona;ul gcneratorului ( sl(, ir ,,,r1tact cLr profi ltr l camci. I)rin urmare, csto neccsar: ca la proicctallrr r !rrr, | , rse aib:r in vedt'rc vitczn dc rotatie a arborclui cu came, astfcl crr r | , , I ' I r r ' . r r

, , r ,datolit i undei clc prcsiuuc la capitul conductei clc transmisi, l,, r l 'r . l

l ionarca supapci sii dc;r clcsclfdcrca dorit iL a supapci.Gcncratorul in jcctotului ( { ig.8a gi 85) cstc construi t s imi l : i r i r ) l ) r r \ r r l . l

dispoziti lclor dc irc!ion;rrc cu pistonas sau plolt jor, dar pcntru .r \ ' .rri,r rr"mentul injcctici, axrl l ?/ ir l tachc!i lor 22 cstt ajustalri l in loca;urilt i ,t. \,, . l: rx ?/ estc antrcnir t pr in l r r -a i t ' lc- 2/ ?/ s i r ; i schirrr l . 'c pozi t ia in l rxrr . , , r r r r l ,2i, ie axnl 2(/ prin mtcanismt.lc 25, 26, 27, 2,\.

I ) ispozi t i lu l ( l ( 'act io l larc a supapci c l r ' : r r l r r r is ic cstc I ) r ( r ( r r t . r t r r lI igura- 86.

Coada supapci . i / cstc concctat i r cu c i l iurh ' t r l , j2 act ionat prrrr r l , ' r r , rp ionjoar-c opusc:,?. i , , i i . t r lonjorul . i ,1, c iut in<l s i l t i l l , ' r supapa p, r . r , r r r r r r r lsiu, r ',{tc aclionat (lc Prlsiunca rncdic din sistcrrtul dc 1l:rnsmisic rr rrrr, l,r,lptoxi;ratir- 70 tlaN/curr, prin conductir . i5 ial plonjotul , i.r ' atl:r lr ir i srr rl,chidir supapiL t 'stc i(:t ionat pcriodic printr-o unll ir lrrnsmis:r <l ' l ir i l , rr, r.rto lu l I i r l in conr lut : ta , ) ( . r . Supapa cstc amort izai i - r la c:apir tu l tkqr l i rs i r i i : ,pr , 'i l sus tl i l iclrit lul rrIat rlcasupr-ir pistonulrri , i i .

ln j r t to l t t l dc t :onr l r r rst ib i l . / ( f ig. 87) cstc pr ' l ' \ ' i rzut cu o supalrrr r r r / /( : r t r r l puir ' : r r iz l r lo lu lu i ) ( inut iL l ) rcsir t l )c scaunul sr ' r u pl i r t t t - -uu i r r . l t f i i r ( l r lz i r t r l t t r t l t t ' l r c i r tc couthrct 'c i l r - r 'or- i f ic iu l t l iuzci y l r r l lcr- iz, : t lot u lu i /2. ( : r t r , t , r; / / i r t c l tc l r r l r r ' ; rz i i rurr l Prr lvt l izaI otrr lu i cstc l (Brr t i r t l i t r t l cr t r : r ' t t l t r r I r r t r r Ipt i t t i r r l t : r t r ' : r / ,5. Acrr l l l r r lvc l iz : r l r t t r r l r r i : r t l l l r r ' : r l l iL l r t l sr-ru sr t lx ' t ' iot r t r p l , , t r1, t t, / / , l ! r r ( i fu i l ) i l l l ( ' i l l [ ( ' r i ( ) i r r i r r r ' { iont : rz i l ) r (s i r r t ( i r f l r i t l r r l r r i . I ' tcs i r t t , r r , r , tr i l r r l , , r l , iu( lx) i l l ( l i r orrs i rL. l r l r i l t t r r i t t r r tc r l c i l Pt ts i t t t tcr t t t t l t l ic i t t l i r t t , rr l r ' I r , r r l r r r r is i r ' , r rs i l r ' l l i l r i r r i c i r r r l r r r i r r rprr ls ls l r ' 1r ' i r r is r l l l l r r r tgrr l l i r r i l i r l ,l r r i I , I r i l , r I ( ) | , : rcrr l l r r r lv l t iz : r lorrr l r r i ls l r ' { i r r r r l i r r t l r is | l r ' s t r r rurrr l s i r r r l r ' ( ) l ) r ( ': r t r r r r , , rPt i r i ; r l r r l ; r .

I t t r l i : r l i r r t t r r r l i t r l t l i r t r r r l i / , r ' . r t ; r l r r l r t t t r l iot t r r t l r t r l i lpozi l ivr t l r t i r l l i r r

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{ . r | | | . | , | | . | | | | , l r . I r l , I t r , l , t ! , I r | |1, ,1, , , l , | | r , l l | , , ] , ,1, , t , r_, , r . r1,r , , , r1, , ,

r r r , , r , I r r ' | \ | | , r | , l r ! { i , , r t ,1, . ,1r , . . , 1 ,1, , I t , r , t , l r l , r l , , r ; r r r , r l r t , , l l l l r r l , l t ( r t l

: , l t r r ( l t \ \ i r l r . l l r t r { iorr , r r , r '11 rr ' l r r r r . r l i t r r . r l r l r ' ( , r ' r , r1gr.()orrs l iur l inescui l l l )atc i l iu lI r l r ' / . , r l i r l . l ' ls l I l r i [ t . (u|oseuI l r rPlrr l r , r r , l , r l , . r l i t r I ) : l tcnt au {ost apl icatcr lc l i r r r r r r r l rn)r l l :L I ' iosr ' l r , l r rcrrr . .u l , l r l , r l r , . r i r r t : l r , l r r r l cc ln i dc-al 16- lcrr( . r , t r lqr1 5l l11qlrr , ,1 iorrrr l c l t : ls i r r r i , r ) . l i i r r { r ' i , l i r r r r t l rL I iucure; t i iu \ ' . r t . t arru-lur l ' ) l i l .

I ) (s i l ju l un s istc ln ( le i r r jcc! i , .c lasic ( s l r ' ( :onrpus ( l in l rur : r toarclc Lle-nr( l l l ( . : Ix)r pa de in jccl ic, supapa de reful iu( r [ sau f i r r i i s [papa ( le an]or ' -l iz.Ltr', corrrlucla dc inaltir presiune gi injcr:lol inchis, Nu vom tl iscuta cccirr c rl i l t 'r 'r 'nl irLziL l)ompelc sau sistemcle de injccfic (cu pornlre irr l inic cu pislorr,lt)tnli\ ' t. cu rl istribuitor, crr acr.lmularc) cale sil l t cLlrroscute, 5i niei J:cnrinJrc.r.io l re c lcrnentclc construct ive, inr lcr- ,scbi a un, i pompe t lc in jecl ic i r r l in i rl i t(ncratorul dc impLrlsuri (clrn;'L dc injcr!io, lrclrct, rol.-r, pistor, sLLlrrrp.rr l r ' tc lu larr : , supapi dc amort iz. ! r r i ) c i r re s int evidcrr te t l in r lc,c l i t tc . t 1 ' tuz, r rlrrlr-r. Vorn aminti ci din punct dc r,otlere {cnoncnologic sistcrrrrl dc injcc{ir 'lx)rtc f i tratat ca rrn cil 'cuit sonic. Porlpl rle irrjectic este un (:az tipic (l(

11r'rrcnLtoL sonic tle impulsuri dc crrrcnt (dcbit) slrrr tcnsirrue (pr..sirrnt ) a citror'.rrrrpliturl inc l i duratir sint dcpt'ndente rlc rclirrrul dc funcfiorrarc aI ruotorrr-lrri (turalic-salcini) . Suyrapa dc rcfulrrri, carc sc l it l ici. <irxl irnpulsr.rl dc plcsirrrrr actioneazii asupla sa, colxhlcta cle inalti i prcsiuuc l)riu cale i l)rplrlsulrir ' l l lopagil ci lt l 'c injcclor | i injccioltrl carc lcprczintiL silrcina uti l ir a. circ].l i-lrt lrri sonic, collstituio elemenlc alc rrnci retclc sonicc ('chivalerl lc circjlt , ' . r r u l t icat impulsrrr i lc pro( lu\e dt genr ' r i t tor 'u l sonie ( lx ' rnpir) .

l)csigur ptezella lLccstor elcilente yi indcoscbi a conduclci irr rt lcarr:r:.,,rricir t sistemului cle injcclie sc ni;rnifcstir printr-o intirzicre a inrpulsuluir.rr, rrjurrgc la injector si prin nrodii icar(.a {ornrci accstui inpuls {a!i de cclrl.r l r lt: pompir. datoril. 'r neadaptirl i i care ( \ isla'! i trtre conduct:! ; i injcctor'.Arlr, l luctrt previzut tcoretic d,r (i. (,trr r st lrtrt inescu, ast:rzi rsL(. \ ' t l i f icitt

Pr i r r rL lcrnt in i r i curetr t r ' (osci logl i r tue) in t :ar l t r r l cerc( 1i- r r i lor e\ l ) r ' r in l ( ) l ta lu(l, l)r '{xrcs ale echil>anrcntclor dc irr. i(,cl i(..

Sistcurul pcntlu corrandu srrpapel()r lr lopus rl, ' ( i. Corrstarrti lcscrrrru s-a impus, motoarclc cu ar'(i(.re irrterrri. crr <listri l iLrl ie f ixi, sint l)r 'cl irz,ut('(: lr iLcliorlare nti:canici a supapclor d(' achnisic lsi evacuare, sistcmril l i inritrt ir i sintpln, sigur;i lobnst. l otugi, sisteruul sonic pc l ing[ avantajcle aruil-t ite ar tccltrcc nivelul dc zgomot, ir l spccjiLl la rrrotr..ralel: rapid,r.

xt I. l l . l n,tNslul t r,]trA t-l l lur,sLltl l(rtt l lL l lonli i I ' l t tr Lt(:t Utl

Sprc drrrscbire dc ttansmitcrca puterii prin l iclride, descrisiL in paragrirfclc precr<lt- 'ntc, in care mitcarea oscilatorie arntonicir a l ichithrlrri er':Lcirrirctcrisl i( ir, transrrtisia forfclor cu durat:! scLrrti. qi forntiL tlcturnirI lr l.-rplin l iclrir le cstc rczolvuliL in rnotl spccial.

Urr t lc lc tnnsnr isr i pot i lvca ol ice Io ln l i r l r l r :s l r r l r i l i l i "L l i l t ( . l , l i ( : Lcrrotatr 'la rrrt capiLt al colounei l ichidc de rrn generalor'proit 'ctrrt irr irr:t 'sl strrlt, rrvirrrlin vcdclc;i rcccptolul undei, plasirt la cclir. lt l t (;al):rt :r l (r ' lo.ull i .

Apl icat i i lc r le rLcr:st l ip s int int( rcsanto alrrnr: i r : i r r r l cs l ( n( ( r l i iu i r l rnrr \r r i t r : [ r l r ' lc t r r l rL l iv r r tn l i , rLr drrrat iL scl l r l i t , ( : i t ro ur l recol) l ( ) r 's i l r r : r l l r r r I i : r l i r r r { r if i r l i r r l r ' lqcrrcr i r lor . ' l ' t i r rs l l i lcr( i r r l l ( : i l r : i ls l : r r l i r r l 'o r i r l l 'P i r r r l , r l r ' \ ' i l ( r . r, l , l r t , r I r i r I I r t t t r r sr t t l l t t l t t i i r r l i< I r i , l r r l r r | | | ' i i r I i ' I i r I .

I r r , l i ' lurz i t i r ' , l , r l r . . r , , r , l l , l , . r i , l i , ' , r , r r r l r r , | , r | r 1, ; i l r r r . i t r r l r , 1, 'r | t , r l . ' t ! t t r ' ( r ' l r t0t t , r t l r . r1, t r ' ; ' t , r r ' . r I { | | r ' t , | | r

' | | | | r r | , r ' r t t1 'L. tu i r l . t r ( ' r r , l t t , l . l

, r , ; rPer i l . r l r ' . l r r l r , , ; , , , r . r l , ' r , r l , t , l r lor ' , r l r ' Pr ' , f | r i r r { i i r r . i I I ) t I ' I ' i t I I i I l " ' l '1"

t , r l , r i , s . , , r ( )Dl( , , r / . .1 rrrr , l r .1r , r . r t rv l , , . I l l . r I , r I l I : | r ' , I r r t r , l , l , ' r ' r ' , f l r . , Lr l , . , . f l ,

' r t : r r | r t r i tc t t l ' t l i ' ' ' l ' l ' r " ' l r l ' r t l ' r Hr rrut r l . r ' l r r l i | : ' r " : ' l r r i r l i : ;1" ' r i t i r

r r r r r l t ' l r : utLr l i ip l r r r r ' l l l r l . r l l , , r l ( i l l c i r ( lu la i t t l t l tc i lptot l l 8t l1( l , r l { ' l . t t

i r r tct fct :L cu i :out l r rz i l , l l r ' r r . l i r l t ) l r t l l t i f i ar i l \1 la ut t t r f t 'c l t t r '1 ' l i r t : t t t r : ' r l l ) r ' r r .

t r 'p lo l r r lu i .

, \ t :est t l isp,rz i l iv r r r l ) t r t ( ' i ! f i o supapi i cart ' s . ' . dL' . ' r l r i ' l ' s l ) r i r . r ' l ' l " rc l i r t iLviud o tn i t r 'L rLr: t l r i r lcro l ) l ' in co] 'p[ l c i . ] lkc lu l 151i ;1r ' r ' l ' r r I r r r r ' l r ' l rt ( 'c t i . t rccc l ibcr pt ' i t r supal) i r ln t imp-cc ut l t la tc[ l | r ' i ; r i ; -L is l ( ' i r l ( t r r r ' r l i ' l r r rr . r rzu t rcccr i i cLr i r .ecar.c

-n] i r r .c pr i l l t lcschic lcrc l l dc:r , r6Jirnrc rrr i r i i r l i r r , , , r1,rr l

sr t l )apci .

- \ct iur tca ac( 'stui d ispozi t iv cstc dcosel ' i t ( l ( i I r I In ' I I I l I IL i r t i ' l i r r r '

r lcr .c c l - i ptact ic cste iml)osibi la Proiccta ul l r ( c. l )1() l c i r t I r ' , i rL i r : : r ' r t r l ' r r r r l r | l ' r( [(]rgic ir undci dirccte.

I )acr-L sL: t totcazi t ( l l l , v i tczir s l lat tL lu i r lc l i t l r i r l 11i11 r ' r t t r l t t r I r r l r1r"

l , i r ' rc l Sel lcralont l r t i , l l l tcs iLt t rca la r tn Inolnt t t t ( l l r l , i l I l i i i / ' ( l ) r r , l j i r i ' I r '

i r r l i , r i r i t rc acestc calr t i t i t l i cste i r f r 'oxirnrt t iv l ' r t /7 plrr l l r r r r l ' ; i , r i t t "

p( . r r t f1 l lc i ; i l r lodu5n pcl fo l i^rc.

I )c mriat c i r prcsi [ r rca c lepin, l , , r r r r r r r . r i L le r i i ,z ,a rr . ( ] , r t l r . r '0r l r l r r r r r , r , I

5; i . prcsupuncm ci t sc ccrc la rcccpl , ' r t r l lLcsi t t t lc qL l l ) t t l iq/rrr rx (rr l r ' t ' r l

t i , , r i , 'zc ic urt p is lo l l t l r ' I ut t t t r , cu u (rr ls i d, . lc l t t , l i r r r l ' ' l ' l / l l ) { l { r " ' r r ' l '

S. i 1 ' rcsuptrntrn c: t sc Io l ( 'ses(c ulc i i I r l in ia t lc t r l t rstrr is iL i i r lc t i v i l ' z '

l r ' l r r

, lrrlui la genclator: trcbLric siL fic

t . th =9 x 100 . :90()cnr/s.

I lcplasatt tctr tu l , lc l i , . l r iJ la l t l 'cptot la f i lc t r tx i r t l i r r r l ) ' l ' l / loorr ' '( autr tatel rnc( l ic , lc l i r l r i , l In ul t t l i r la lcccptor va f i l0t t t t ct t r : r , " , i ' l r ' , r 1 ' r 'r i l lDl l l lc ln c i t t t t I r is t i 'p i t ' )1 lcr i do crrcrgic iu l i t t ic , s | t ' { i t t t t ( ' r t rorr ' l r l . i ' r l r ' l ' r r t '

s I f ic 1000/9011 .- 1,1 c in:1i l , r 'cs i r t r r , . r lagr:nct i r totSi l : r r l r r '1r l . r ' l ' l r r { r I " ' r r '' I i t t i t r , l sc; i r t ra rJr : l t ic td l r i l , r dalol . i l ; -L v i tczci l t l r r r i i r l i t l r i ' l r r l r r i 1 ' r r r ' r1"1"

r l0 l tnort izarc, r ' l r l i l t t l t< l i . ' ( i r la ia l l ( r&tor sa!s(r t i t ( ) l ) l ( : l l l lLr ' r t \ ' l r l r ' l l l r r r r r

l ' ) r r t : r61i ; r . p icr t l t t t iL sc t r i l r ls lo l l I l :L i r t c i r ldur i r . t [c-a l r tngtr l l i r r i ' i r l ' l r ' r r r r r r r . ' r '- l 'c t i t r r r

lL oL{ in() l i r f icncrator, s i" l spl l r te l r r , o l ) f ( i i i r r r r l r l r ' l l t l f r i / ' t t r '

sr : pt tatc fo l r r r i o carrr iL l , { ionind p,r l t t t p istot t ; i . t l '1r l , r i r r ' l . r ' r r r l r l r l ' r l '

l ic l i i ( l intr-o c i r l )aci ta l r ' . l ) r : cxr: t r tp l t t , sc pol l tc I r r l r r : ; i r r r r l r i r ' l l t r r l ' ' ' " r r r

r l i ; r t r t , t r r t , act ionlLt <L t t r ' : t t l t ; i c t l o c l t rs i" ! ( l ( 0,( i c l t l , Ptor" ' i ' r ' l : t l l ' | " ' l '

p l i rs i r t ' r ' t l , : r tPt<lx i t t t l l iv .1 r ' t t r : l ; i o c;r [ ) i lc i txt( : rL: 3 lJo r r r r r r , l r r l r i r l r r l r r l r l r ' ' ll i i r r r l r r lc iu l .

Oott tpt i t r t r t r r ' ; t l i , l r i , l r r l r r i i t r l . r lxr t l t t l 3/ .1S0 \ ' i l r l . r r ' 1 ' r ' i r r r" ' l ' r1 ' r"

r | | r i r l iv ( l i ' l l0 kg/cr t r : : i r r l r , ] r i , l , , , ,nsi t l , r i t t r l r I r | I i | i I r t I r r I r l . ' r ' l r ' l r ' r l r i r l

r r l . i r r l r r i , l r ' I l000 | i117'r t r r r '

$rx r t l r l r 'Prcsir t t r" i t t r ' r1r : t r t l ' r l t l : t l tcrctr" t I i t t r r l i l r ' l ' f i " l " r r r r l 11' r r ' '

r , r l r r r r r i ' i r , : r

' r i ,vo, , r

o rrrrr l i i r r l i r r i ; r r l , . I r r r r r i I r I i | , i r ' ( , r r , i r r , r ' r r r I i I i i | , r I , , , r r ' , , '

v . t l r , r t t : , lx) I l . l r , r t t l i l . t l t . r r l , ' r ' r r r ' r1 i i r ' l l i ( - "1 i . l t l t ( ' { r l r l l r t t t l r t t . ( r l r r r ' l ; r l r t r

I , r r r r , . r r t l i r i , r , l r ' l t . r t t t t t i i r '1 ' , ' . r l , l i i r t r I r i ' , ' i : , r r t r l r " r , l r i h r l r r l r i rLrr i r r { . r t r r

i t t t t , i l t t l t l t t to l r i r t r ' l r l , l r r r i r '

| | r ' . r r i ' ' t r ' , r r l r ' l t l , r l ' , l l r ' l r r l t t ! r " , ' l ' | ' t r l l r l r r r l l t l r l r " l l r l r r l l l r ' r r ' l ' l r ' l

"u, , r . t | , r l - r t t t t l ' t t l , t t t t . , r r r l r ' l r i t t l l t r ' , r l r ' ' l , r l , ' l l , r t i l r l l r r r l l r l l l l r l l l ' t r ' l . r lot

r{ l t t l t i l to l t l r , , f l " r | to l r ' . , r1| r r r r , l l ' , | l r , r t l i r ' f ' . l t r r ' r l , ' l ,1, ' l t r r t r r , r r r t r r r ' , ,1

l , rvr . , r r . r , r 1,r ' l , , t r r t l l r t r t , ' , ' i r ln ' r t l ' l ! , r l l t l r r l l , r r r r l r r l : r l l l l l l l ' r l l r .

l r r l i lqrr l t l \ iS l r . l r ' t lptr ' .u,r ' r r l , r t l r r lc l ( t i l { t , l , lc i r r rprr lsnl i r : l r r r . pto<l lL cur)( l ( , I ) r i r r i r l ) is i r rcr l r r r r , r i r , r , r r l , l r 1r i l , , r r r r l r r i / ( t lL cxcLnplu la t rccctc l r r rnLiI t cr t ) .

I ) is lorrrr) / lLrcrc i rz, i i i rL r ,p,r l i r r l / i . l ' r i s i rLucir i r r carucru / r , carc apirrc:r l rntc i c incl | is lornr l / r 's tc lc l iorr iL l r lusc urr o {ol t i ' r nrrue, act ioncaz:r asuprasll l) i lpci conicc /,: alirrcl la ctlr"rlalt capiit l l l t piston I lucrincl ir.r c:rntera l l l cull ( l i irmctru considcrirbil rn:ri rrralc dcr:i l o|if iciul /r sl l] ci lr lcra itt t i :r 'mccliarir o.

hnotm

Fig. E8, - Generator de impulsuri ( le fort i .

Catucta rr. cste couectatir. la l i l ia de transmisie y' prin dispozitivul de ate-rtuarc a undelor g caLe cstc destinat a absorbi undclc rcflcctatc, iar l ichiclulcstc translnis l inici 1a o presiunc nrodic rclativ scirzuti-1.

LIu orift iu r trecL- prin pistonul l i sripapa /r, I ; i in cirmcla i so rror-lcrziL o supapiL cu biii ii lcsort 1.

Apirsind nsrrpr-a pisionului f, prcsiLrrrca crciic i lr caurcrir /, l ir valorilolttc Inari t i accasti ]rr(,siune lctioli l ld asLrpra Lrilei 1, dry-r;, 1te plcsirrnL'irl irt ici astlcl cir intlcgLrl pisLou-sup:rpiL, ft, l , si: uri;ciL inaintr:; i :rtc<liat t:csttPalln cotric ir sc dcschiclc l)rr 'f i iru[ it dil l cainrcra /r Poaic acliorrl l)u o sllplir.-laJiL nnrlt r lr i l l tLc a pislourlrri (rl irrnrctrul caruclci rl).

l ! fcctrr l csle c i i sc ] l -o(1[cc o r ] r i l rar ' { r b lusr ' t r r r l ) is l ( ) r r r lu i r I i I r : tctr( i r r Iast [ ( r l c i r o ur)( l i r dc inrpuls {oal lc puiolni( : r"r csic t l i ] r is : i in I r r r rgrr l l in ic i y ' ,iu | l ( ) r l izo| lL l ( ( l ( u l ) ( lc : j ( : dcsdr i (Lc Pcfnr i l i r r ( l l rcr ' r ' rc;r r r r I f i | | r ( l ( ' (11' l | l i r r ( ]i t r l | t rs i t : r l , i r t l i r r i ; r ' ] , t r ' , r r r \ r I | r " .

( i t t r l r t cslc l t i r rstr t i : i pr i r r l i r r i l l r r < l ispoz, i l iv , , < lc r rcr r r { i , , ( . r t l i l l ( 1,( ' l t i l: i i r t l l r is l r r ; t r t l sr t r l i r r r r lc r l , r r ' :urr l r r r i . Srr l ' i r r rprr lsrr l r r r rc i pt , : i r t t r i l , t t t \ ' l , i ll i r r r r ' , 1, i : r lorrrr l l l tor l r r r , r r l rn i i r r r , r r r rpr i r r r ( ( r l r i , ,nr l r l l l i , l r ' , i , r r r l i , . l r r , l . rr l l l , r l . r l , i i i r r l r l ) i r ( l , r r . r r '1r l , r ' . , l r r ) l ) r i . r l r r r ' , r r , t , r l , r t t t t r r l , i r t r l t "1 ' r , , ' tI tvr t l 7 ' , ,1tr t i , t l t l . , i r , ' ,1

i ) rs lxrz i t i r r r l ,1, ' . r r r l r r l rz,rr l i t l l ( l ( lo l t t l l l r l l l r ' po;r l l l i r r rorr l t r l , r l . rt1 ' ( ( l ) lor- s i r { r Ix) . r l ( l r I ' r ( . \ , r / , l l l i r r r ' i rcrr i l i t t t tn i t t t t t l l r ' l r turr :1. .

I )acir / r r 's l r . prr , i r r , orrrurr icr t f ic crr t - t :z,r : rvt lnt I crr t r ' : rstgrrr ' i r I ) | r ' . , r | | r | | . Ilnct l ic in s ist t ' r t t , 1rrr , : i r r r r l r r s( ( l ( .s( : i r rc:L in accst Lr :zcrvor 1i nrr lyr l t i i r r l r r r r , rdr: transrnisir: nici o rrrrrl l i l trrnr:i cind sc apasir pc./.

Fig. 89. - Schema de pr in-cipiu a. instalaliei de sincro-nrzare a. tfagcrii cu nritra-liera printre pa.lcle elicci.

Mecanismul de sincronizare a tragcrii cu mitralic,r.r l)r.il ir,. l).r1, t, Lclicei. in migcare, la avioanele utilizate i"n pdmul r:rzl)oi mor)(lirl. roir,trtrrr,o aplicalie a transmiterii impulsurilor de foiti ric la o canir soli(lirr.r r u .rrult:l icei la tri.gaciul armci.

ln {igura 89 se reprezinti. schematic instalalia. (.lrr A s;r r(,lrt 1,.r1ratorul de impulsur i _montat pe axul e l icei , cu i d ispozi t ivrr l ( l ( . r ' \ r . r r l r , ,eirre este constrturt dintr-uD piston sustinut de un rcsol-l. []islxrzitrvrrl ,1,cxCCUllC cste dCSCnS.a un miC ciocal l Sonic.

. . C" 4 s-a notat d ispozi t ivui de comandf, a t ragcr i i , r l is lxrz i t ivrr l r , , r r ' , t , rdintr-un piston l inut de un resort. Pistonul putea {i ac{ion:ri ( u rrir.r.

- Pistonul generatorului acliona l ichidul dintr-ul cil irrrlrrr ,1,. I.r ,.rr,

Plcaci o tca\'al dc cupru cu pefrol, 1a mitralicri., un(lc s(, l l l ir r irx.,rrrrrl r,rr,.lovea trS.gaciul mitra-lierci. -

- Rot ind cama generatorului repede, se produc impl lsrrr i i , r r , . , ' l r ,ur , ,

In i t pr in coloana l ichidl la t r [gaci . De rcmarcat c i i r i : r ls i , . rorr , l r l l r r r r , l . rnu aclioneazi- pistonul B deoarece devialia din l inia lr l irrr iprrlr i :rprr, / l r".trar;rnjarti. si ir itrt 'L o incr!ic mare, si la- frecven!c ridicatc t:rrrr.rlrrl rrl,r,orl,t l ,nclnscmnat.

Apr"Lsind pistonul B, accsta ridici. presiunea mslic iu irrslrrlrr{ir. r,r plrttt i l tr ciocanrrlrri sonic clc la triLgaci si. atingi trirgaciul. ' [ 'r iLgirrl

lr i:r lorrrrl / i ,

l)rr 'siuucir mc<lit: sc miclorcazi. gi chiar daci ciociLut:hrl osr:i l t. lzi i, r ' l rrrr lr,rralirrgc triLgtt: iul lxrzit i:r sa mcdic fi ind deplasatiL.

. f r r l r r i t t r l insl : t l i r { i iL <l in l r r r r rct r l r : vt :<lcrc hi t l roslrr l i r , I ) I ( . : i i r I r | , . i I r l , . l , l

l i r ' r rct : r iot i r t i r r ' l iorrr l l p l i r r r r r l r i r r<l p is lor l r l lxrrnpr. i /3, i : r r c ior ' : r r r r r l r r r i l r , rl icrc i r r r r s rr t t t i ; r ' r r . Ar ' , 's{ l r rc l r t : r r . i r r l i r r rPl i "L : r i r rn<: i c i r r<l ! i ( .n( . r i r l ( ) ru l r ' , ,1 ito l i l [o;r t t r . l r . r r l , r ' r r r r r i r r : r .

l , r r ro l . r { i r r t r r l r i , l , r . r l i , r r , , r . r l r r r r r l r r i , i r r r { i r r r i r r ' r r i l r r l r r i l rorrrpr. i / l , r ,1,t t t , t t r ' ' , r i l r i r , lor t r t l / l t r r t lu ' . r l , n l t l t : r t t l t l r vr 'n{r t i t t t I r r t I r ; r r t i Iot , i r r : ; r l r i t r r l r. r r r , , l r ' , r . r r { tor , . . r / . . r r r , r r , r r r r l I r , r1, , r Iotr t I r t r ,

l r r ' , l , r l , r { t , r , r lo, l r l , ' r r , r l t t r t l t t r l I t t o l r t , . , r r l r ' r l t , r l t r . r l r . ' t , r 1 t t t , , . , 1 , . t , . ,I r t1r l l l , r t t t r l r 1r t , ' r r t r l r l , 1 l l r l { l l l , r l t r t , r , , l , r , , r r , l r r r r l , r , l , . r l ' r , r r i r r r . r l i l o

I l l l r , ' l , r l r ,1, t t t t t r r t ' ,1, , ' l l r r , l , l

xl t I . r . ( . | |1\ t t : tu t ) INtL

\ I I , I ] I , I ' I ( I .ZI .N IAI( I ' ( ;ENI iRALA

Mccanismul dc transmitcre a putcrii Constantinescu, pe care aulorull-a numit sugcstiv ,,convertor", a stirnit un considerabil inlcres in lumeaspcciali;tilor in domeniu gi indeosebi a automobiliqtilor, spre sfir;itul anu-lui 1923. Existi. convertor mecanic si convertor hidraulic.

Varianta. hidraulici a convertorului este o aplicatie dirccti a soni-cilr-rli i. ln parte, accasta a fost descrisi anterior.

-

Mult discutatul convertor de cuplu este cel mecanic care in cele ceurmcazir va Ji numit simplu ,,convertor" ata cum a ficut-o autorul.

Dqi convertorul mccanic nu constituie o aplicalic directi. a sonicitir-tii, se cuvine si. fie prezentat aici, deoarecc reprezinti. o rcalizare notabilla marelui inventator, actuall ;i astizi ca ;i teoria sonicitirlii ;i rezoh'irproblcma utilizlnd proprictllile corpurilor care oscileazir.

Aceasti invenJie care funcfioneazi pe principii noi diferi faji de toateaparatele anterior cunoscute ;i formeazf, sigur o clas6 dc mecanisme, cupirformanqe superioare, care aga cum a demonstrat matematic autorul,iru pot fi itinse'de niciun alt mecanism, fie el mecanic, hidraulic sau elcc-trici ,,My convertor is in a class by itself, thc results v'hich can be obtaincdwith it are not obtainable or even approached by any other mecbanism,whether mechanical, hidraulic, or even electrica-1".

La invitalia editorului, G. Constantinescu a expus in coloanele revis-tei ,,TIIE AUTOMOBILE ENCINEER", un material privind mcca-nismelc de transmisie variabili pentru automobile, articol care a provocato ampli 5i viguroasi disputi, publicatl in paginile acelea;i rcviste din noiem-bric 1923 oinl in iulie 1924.

Autorul a precizat de la inceput ci, convertorul nu este o imbuniti-tire a cunoscutului mecanism schimbf,tor de vitezi., ci, este rezultatul apli-ci-rrii principiilor matematicii la solutionarea unor probleme practice, folo-sind integral metoda cercctirii teoretice cS.reia i-a acordat o mare atentiernai mulli ani.

Convertorul, prezentat intr-o diversitate de variante constructive,r.slc un mccanism care are mai mult decit un grad de libertate. In staretlc rcpaus sistemul poatc fi deformat intr-un numlr infinit de moduri,:rstfcl incit configuralia sa iniliali si poatl avea orice formi. Nici un ele-rncnt nu arc o pozitic nrcdie fixiL in raport cu altul. Eslc foartc dificil s1sr. prlvatlir. pozi{ii lc difr:ritclor elcmcntc cintl accstca sc mi;cl-r. f)e aceca,rrrr s-;t rrrr;it siL sc cxplict: irrtr'-o manierl populariL funclionarca convertonr-lrri. lrrr, r'< rrlt rr clc ;r cxplica comportarca a., slui;r prin simplificiri in schemelt:rlr' 1rlirrci1lirr, sau prin corlrpirarea sl cu tttecanisnrc prcslrpls(: cchivaltntt:(r'rrrc rru lxrt [i cclrivalcntc), llu s-a putut rcnliza fi.rir a crca conlrtzii slnr crori-

Argunrentintl nccesitutca <1e a cxplir:lr rnatt:m:rtic pritttiJriik lrr, catcst' lrazcazir. convcrtonrl, G. Constantiucscu rrlrli"r t:ir, <lificultirlr':r girsili i rrttcir .xpl icaf i i popularc a cont lxrr l : " r r i i convcr lor t t l t r i cs l r : r ' t t t r t I r : r t l r I r i I i r r r r s l t i r -tLrrr i i r rL: i r cxpl ica, tcor ia r ' , lut iv i ( i l f i i , f i r r i r r r jutorrr l In i r lc t ! r ; | | r ( r r . , l l r r 'r l i l l r r : r r l ly of f inding a lxtprt l i r t lxplrut ; t l i t t r oI l l r lx ' l t ; rv iot t r ( , f l l r t , ] r \ r ' t l , ti ' . 1r : r t ; r l [ 'Lr l l ty t l t r r l t r rL i r r ' , r t t t t r r cxpl ; r in, t l i l l rorr l l l r , ; t i r l . l r r r . r l l r r r r . r t t , ,l l r r ' l l r .oty oI rc l ; r l iv i l1,"

I llll

( . r l l l r l rur \ . r / .11. , . t l r r l . r ' ,orr t r r | , r { i i ( :ur . \ r . (x l l l r . r r l r . I t . rust t r r l , r r ' i r r . t r r r i , , rPt i r r i t t tPrt lsrr t i i r r r l r l r r r . l . r , , l r r r . , l r ,krsr . l t l r r r r r logi l r cu rrr ; tu i l r .st i r r i l l r . r r r r . r r I r r I r r ri t l lcrr t l r l iv i t r r r r r r r r t l r ' l r . r l r i r r .

I is lc i r r l r . r l r , ; r t r l r l r . r , l r , , r . rv i r l ( i , i l r l l i t t i r r (a teolc l i r . i -L rr r .o l rv l r lorrr l . , r: r t t tont l apt l t .azi l l r : r r r . l r , i l , , i r . l t r r t l r r te, analogia dintrr . fcnonrt . lc l r , r r r . r , r , r , , .1 i cclc c lct : t r ic t : s i r r l i l izr . i rz i r ; rcr la; i instrumcnt ntatcmat ic i t r t r ' ln i l i r r , . | r . r t r , ,tehnic i . . lJxpl i t : : r { i ; r l lc l r r r i r . c iutal iL in idcnt i tatca pr.oblcmcr r . r rnvr.r lorrr l r r rt l aceea a compor ' l i r l i i c i rcui tc lo l t ' lcctr icc atrrnci c i t rd sc rr t r l i r . i r r , r , t , , rcircuitc, curcnti elcr:trici pcriodici. I) in tratart 'a pt: r:arr-. G. (l<irrslirrrlrrrr..r rro face pentru a glsi lormulelc fundamcnlalLr ulc convr.rt or.rr lu i r,r. trr.rt,observa u;or de citre un electrician c[ ploblcm;r convertontlrri s,. , , , , , . , , , , , . , , , . ,cu cea a te lefoniei Idr i { i l aproap,. p in; i i r r ccl , . r rn i mir ' i i r rn i r rur t , . . ,Arryshrewd mathematician rvho happens to bc also an clcctrici lrrr rvil l rrrrt l,r.long in pcrcciving that thc problcms of thc convcrtor irnd of wir.lr,:,. t, l ,phony^ arc the same almosr in etcry (l,.t ir i l".

Inainte de a prezenta firnclionarea convcrlorului, uncle rt:fr:rir. i lrr r orr, lrrzii le analizei crit ice pe care G. Constantincscu u intreprinsFo ir:\ul)r.r rr,.r.rrlmelor elab_orate pentru a rezolva problema transmisiei Iariabil. si ,.rp,rr rr.rt,.racestora de a sat isface transmisia aulomata-! r 'ar iabi l i , s t : inrptrrr . Arr . r , t . , .pentru a evidenl ia comparat iv posibi l i t i { i l t convcrtonrhr i ( | r . . r r , . , , , t r ,1t ransmisia automatf, si variabili.

Problcma transmisiei dcfinit i!, in scns larg, cstc ca dc l ir rrrr .rx prrrn,,rcare se rote;tc continuu aclionat dc nn motor primar, si st lr:rrrsrrri l . ' i lrr lrgia gnui alt ax nunit seclndar, in aga lel incii indifercnt dc f I r r r r I r r r r I i i I r , r lr.cuplu ,gi turalie a1e axului sccundar, motorul primar si-r <h zr.oll l irr rrrorlnatural puterca cu

-eficienli 'r maximi-I. Dc obicCi t leosebinr rkrrri-r 11rrr1x, rL,

motoare primare univcrsal rrtilizate:

- motoare pr imar-e cu cuplu constaut 5i t r r raf i ' . r ; r r i r r l ' i l i . l r r , . | ' ,categorie intri aproape toate feluri lr- ([. ntotoar'. crr yrislorr, ]t i | | | |r,. lspccial cele cu alderc internl, folosite in gcncral pcntnr':rrrlorrrri l ,r lr.

- motoarc primarc crr turalie constantiL 1i crrplrr valirrlr i l , , l ,r,. jr lrrc; l r , s int cupr insc ntasini l l ro lat i rn cum ar [ r t r r l l , . t l r l ' i1, . . .1 t l t ' l r , . r rt ' lcctr lcc.

- . In gcneral , toatc fonnclc de transmisi i urr :carr icr . , pr i r [ t , , , ; r r , . i r l r r r l r . r r r

l icc, cunoscute pini la apar i l ia convcrtorului Constani inr .sr . r r lxr l l t r r r l r r r r . r ,in urmirtoarele clasc:

I . Rapoar '1r : l ixe di ' t ransnis i r ] caro pot i i mot l i f icalr . i r r r r r rx l rorr l r r r r r r r.slrtr rl iscrntinrttr rlrrl l i cum (lorcttc opcratorul. l l lr cxcml)lu r(,1)r'z(,lt i tnr' ,.1foar l r : r : { ic i r : r r l a l i l ru lu i d isconl inurr is t t : cul i : r tk v i tcze -ol , isrrr i i l i i

1 i rorrr l , in;r,f i;r. t:rr arrtlrrciaj, Itompelc 5i moloarelc hidrarrl ir:c (: l l ( lnsir viuiir lr i l i i , lr iur,.nrisii l : pliu frrr ';rrc, rcprczinti t ipuri r:onlirrrrr..

l l . Mctrr l isrrr , l r , r l i r r r l l rs i r anlcr io l r l i r l i r t .arc luxrr l r r l r | , . I r ; 1 1 1 . , 1 , , , . , , ..s l l o f rnrr ' l i t ' r lc crrPlrr l r l r . l t , i rxul sr t rnrr l ; r r . I i r r , xr i r r l , l r r ror l r l r r r r r r i r l ' rr .str . l i l r r r l t l r . r r r lc i r r r isrrr crr r ' l i r l r r ' l ; r ' l io l l l rL. l : r l l tn i r r - l ; r l r r l ,orr . l r r i I ' r r t r r . lpt i t t l t r t t r l r tp l : r j r ' l r rs l i , ( r l r .o l r icr . i pr i l r r lcul i ) .

l l l . l \ l r . r ' i r r r isrrrrr l i r r r i r r , ' , r r ; , l r r l r , r ' r r r r r r l r r r r ' : ,1r . I ' r , ' r l r r , r r r r r rotrr . r r r r l . r tr | r . lor l r . l r , r l r r l r i l r r11, . r l r r l r r . r l r . l r r r . r l i r . i 1 ' r i r r r . r r r r I r r i . ( r , l r r r i r i r , i r r rp l r r t ip i llot t r r r ' , rz l o to;r l , r r ' . r t t . r l , t l , r r , r r l t , r l r r l r r r ' , r r r r r r , l I r l , r l l t r l r r I I i [ r r1 i I r | .

lV l l , r . r r r r , r r r , l , l , r r , l r ' l l ' l l l

r . . , l r . l r . r r . r r , . l r r r l ; ' r , r r | r . r , , rL. r r r r . r1,rr .I r I t r r . r t , t r r r l r l r r , . r ' t r r l , l r l r l r . r r t r r l ' l r . r1 l l , r l r r r r , , i l r r r rL l rgrrr l o l r t r r r r r r l l rI t t , l t r t t r , , , r r t ,1, t r1, l r r , l r . r r r l t , r , r t , r r l t l t r r , r , ' . r l r l r r , r t r , r r r r r r r r l t , l r t r l l , r . l l l r

; I l ) i r ' ! ' ( l ( r 'nt rg i ( . l ' ,x is l r - r l t t r r t torrs, i r rvcrt t i i t l i t t r r t r rst i - r c lasir , at t t t l r i i lo lr r r ' I i i r r r l con;t i t 'n! i r l l [aptul c i ls l lc l t lc t ransrnis i i nu vor putcir t ransmitccrt l , l r r , l r r tot i t : r 1,r i zcrr l , i f r t r j r i i .

Sc pot facr: conbinati i din aci:sle patru clasc intr-un numir inlinitr L. lclrr l i , 1o:rtc pu tind {i inr-cstigate prin metodi denumite de G. Constantinescu,,rrntl izl tr idimcnsiolali", care ia in consideratio pe l ingi ecualia vitezei

,or lo: I { ( r l r , ) , (1)

(rrntlc co, t i7, r, 17 sint vitezele unghiulare gi rcspcctiv razelc nauivelelor:rrlxrrclui primar gi cclui secundar; I( - constantS" carc depinde dc mccanism,() .. 1{ < 1) 9i ecualia energier

l rc s:r i r l l l r ; r l l l r , r , . r . , , r r t l r . r t t l r r , ,o r . r l l r . r l l r r r r l l r l 1 i , . r r l , , r l r . r . , r ro l 1, , , r rr l is l l l l r r , r l l t ( ) l r t l , . l r r r lx ' , t l lorr ( ,n ( \ ' r ' t \ l l r i l l i l l t r , r l r t r t r i r : r l r r l r l r r . , l r r r r r l t , .o l syx cr l : r r r r l l , ' r , l r r r ' . r r l r l r l r r i t l t l , is r l r r r '1o I I r t r I i | | i t r r I I l o| l i r r r l r r l l . rs i t l is l i rc iofv srr l r : , l i l r r l r , " .

Sl t i r o l rs l r t . r r . i r . : r1, . i r r r l rosi l r i l s i r s l r ' t , l r r rx l r r t i r s l r r s l -L s( i lu l i l , r .nrl )or tarc i r (J l ) isnrr i l ( , i r r r l i i r l r . v i lcz- iL s i i r r r ru a nisnr t r l r r i t r r arrr l r r , i r r l ,1 1, ,int tomobi le cu mi j lo;rr r ' l r ' ( .n l lmcratc.

( i . Constant incscu aral i c i r , prol cm:L nr l s( l ) lu l t intr t ' tu l i r r < l , r r r , , ' ,numit i r nedrept , ,brut . r l i ' ; i unele imbuniLt i . t i r i la nccauismul cu rrrr r r r r r , . , rinfinit de viteze, ci intrc un mecanism loa.ric cficirrrt cunr ar f i olri rrrrrr.rcutie cu 4 viteze comandatl de eforlul mcrrtal lLl unui gofu irrt,, lrr,,

' , i r

rrn mecanism automat de transmitcrc a puterii catc va face col l)rr1il ,,,.1ce poaic face un;ofer inteligent cu o cutic dt' r ' i tczc obi;nuit:-i r lr irrr ,,., , 'rpedormante mai mari : , ,The inssurc at stake is not bctween thr. r r r r j r r l11,called - brutal - gear box and somc improvtd mcchanism rvii lr rrrr rr lrnite number of speeds, but beetwen a vcry cfficcnt mechanism likr. rr rrr,,, l ,

' 'rfour - speed gear box controlled bv thc mcntal cffort of i in ir l, l lr l ., r ' ldriver, and iln automatic mechanisnr lor transmiting porvcl wlrrr lr ,,

' l ldo at least what an intc l l igent dr ivcr can cio rv i th the ortho( lo\ r , , r r . , ' ,1posibly give an cvcn better performanct.".

in sf i rg i t noua clas:r dc mecanisnrt- , convcrtolul Constaulrr ' , , . , , , . , , ,cstc un aparat pentru transmiterca putcri i automat de la urr rroti" ,r larderc interni sau al t motor pr i rnat ' carc dezvol t i un momcnt ( l t 1r , r , r , r ' , 'l imi tat la un ax sccundar; momcntul dc tors iunc ; i iural ia a\ului : , r ! r , , , , l . r rf i ind variabile intrt ' l imitc foarlc largi.

Convcrtorul actioncazi'r secllndarul printr-o scric dc impulsrrri ir rr., , i ,, 'rapidc care intotdcauna au o f recvcnt i r dubln fatn de cea a motonr l r i l rn. , r .ampl i tudinea impulsur i lor f i ind cortrolal iL autonat dc incrt i . r r r r r , r r , , ,carc cste l ibcri sir ost:i l t 'z,c t lt ' o part( ' f i dt' alta a rrnci poz,it i i nr, rl i i lr ' ,, , rro mifcalc atmonicir -sintpliL de acfraii frecvent:L ca cea a pri l lr iuulrr

Asl f t l , sc poatr ' o l r t inc un cul)hr rr : i r i t la un ar l )orc sf(ur( l i r ( , , i , l , r 'dc la rrn motoi pr in] i r r cu c l rp lu l inr i tat carc ar( o mal l i \ ( ' i i ( | l lL rr ,(onstrr l r la ' r . ] lccanisnl l r l carc a-( igura i r ( ( 'asta consl i r c l i r t r -o cornl , i r , r l r , .1,lc\ . ier( ' l i i i jc t lc iL gr ' r i r r r : -L osci lar l , { r lar carc nu sn r .ot t .sc). - \ ( , .1, i r r lls t fe l contr : la1c inci i s i r pr imcascir ior l l lcgir i ivc s i p<lz i t iv l dat()r i lar r ' r iL, lunor mirs( ' l ' - t l t r valr ' r ' i r r t pr 'ndul t 'azi i l jurul nuor pozi{ i i f ixr ' . l . r r i , r , l , . rl i jc l r t lc l t 'g iL lur iL s in l , r lc astmenla, ( oncclatc in mot l adccvat l l t lorr i r r r , , . rn istnt ' os<i l r r tot i i t l r ' : r r l ior l rLc rrni t l i l l r ' l ional l -1, carc t ra lsforrni r ( ( ,s l r l i r l .i t t i l t tpr t lsrr t i ro l r r l i lc intr-o dir t t l ic in : rsa f t l inci l f r r 'c l r , r l r r 1 i j , l . r r l ,( ( )n( 'x i r l r ( , lcv ic l r t r r 1 i nt i rsci s i i f i t , in lo l t l t ,auna (gal :L cu numiir l r l r l r . r r , l , r t r rr r r t t t l rk: l t : r l , nrarr i r , ' l , i t r ro iotrr I r r i I r inrrrr ' . Ampl i lut l inca osci la l i I i l t t i r . ( | i . l 'vrr t i r r l r i l i r 5 i c l r r r r '1 lc rrr l : r l i t :u ( r - r 's lcr f i r r i l l )or t l l l l l i ( l in l r { ' t l l t i r l i i l ( , l rot( , r ll r r i pt i t t t : r t ; i r r lc r r t Ixr t , I r r i sr ' ( nn( l : r t lorrr l rs s i r l lsr rcslc rx l : r l i crr <l lscrr" . l , r , . r; r r ' r 's l t t i r r l ror L

O i l r rs l r : r r l s i r r r l , l r r , r ; ' r r r r , i | r r l r r r , r , r r r ' , r Iorrr I r r i ( l iyq. t )0rr , ) , s l r , r l t r l . r r l , r r r rl , \ t r ' t | | |

' I r I r I I , ( : I t i r I t r r r | | r i r l i . r l I t r l r r t r . r l r ] r ' r r r r ( \ r l . l | l l t r t r | l r t t l i t l | r l t | l r r \ ( ( r , l

r l r r r . r lot ru rrr : . ( i t r , r l r r r , l , t1r , r , r r l . r r , rgr , r l r r l o;rrr , . r r , . l r r rc o rr l l . t r . I r r I ' r r r r r It r r I r ' t t t t l r I t r r t , r l l , r ' t , t t r l r r t r " l ' l r r r r ' , l r r lorr , r l , , r r r ,1, , , , r r , r t r r r r , , ( , r r r ' . r r l r i

r r ' i r / . r r r r . r t l rot l ror , l r r . ; ' r t r r r I r r r . r r l t lu,zr l t r , r l , . r r l t l r r . r t , r r r r r r l r t l r { torr . r l r ' .I t r t r r . r t r l r r l , , r , r t r ' , r r r . ' r l , r lot t , , r l . \ t r r | | l l | t l l r r l . r r r l r ' .1, | , , \ r t l t l . r r t | l r o rrr l , r , t r l, l , r r l . r l r , , r r l r " , l r , ' l r ,

, l r . l , r ' , , r l r \ , l , r r r r r , l r r , , { r , , r r . r l , , ' ; , , r r r r , l 1, , l r ' . , r r , l ' r r r . lI r l , '1, r , , l r { r , r . r t l ' , r , l r r r , , , r r , l r r ,

' r , , . I l r r | , t l , ,1

(.2J

(irr carc M si M, reprezinti" cuplul la primar ;i rcspectiv la secundar) ;i olcliL[ic intre cuplul sccundarului ;i alti variabilii independentir a sistemu-lui. Astfcl in clasa II, de exemplu, cuplul secuudarului estc o funclic de cuplull)r'irnarului gi existil o invariantir. dc forma

(3)

(4)

LI r,o, -- lef 6

. l (M,Mt) =o,

irrr in clasa III invarianta este de forna

,f (<o!, M,) : 0.

0 transmisie din clasa IV poatc fi cu greu numitl transmisic variabill,{h!oirr(:cc transmisia este in sine un absortrant dc Dutere si nu numai unnriiloc de transmitcro a putcrii.

Il imin, deci, clascle II gi III ;i combina{iile lor posibile. Aceasta reprc-zinlh tot ce se poate face cu mijloaccle consideratc pini aici ca fiind capabile<Lr a obline transmisic vadabi15. automati. (avlnd la bazii arcuri sau refiula-Iorrrt: aplicate la mecanismele din clasa I).

Pc bzza acestei analize, G. Constantinescu & demonstrat ci diferite<lispozitivc, care au fost discutatc, nu pot rezolva problema transmisieivrrriabilc.

Rezult:r din acostc consideralii ci nu este corcct si" se afirme, dc exem-plrr, cir orice transmisic variabili cu un num5.r infinit de rapoarte de trans-rrrisic posibilc, cu toate c:r sint sigur comandatc, poate fi fi.cutir automatiInin nrontarea rrnor.sisteme dc a.rcrrri, regulirtoarc siru servomotoare pentru1l ( onlrola transmrsla.

lntcligen!a umani'L nu poatc fi r.rsor inlocuitir. prin miiloace ap de simPletli r:virlr ntc. Nrr este u;or de 6;itsit o solutie la accasti problcrniL. Nu estctlr! ( unr sintcm inclinali si crcdem, cir numai datoritl" l ipstri rk: intcres aingirrr:r' i lor sau invcntatorilor sc mcllinc inci cutia tlc vitczc la automobiL'ii i l:r rnrrltc altc nriLyiui indrrstlialc. Se poatc spun(i cir nrotivul l)c)llrtl caroalir ulrruitr cutic d(: viteze ,,bruti ir" nu a tost inlot:ui1r-L dc lrc lxrzilia safr:rttiL 1x: carr'o (xllpil pcstc tot in rnt:canici urt(lc cstc tlcv()i(: i j i l sr' l lrodificcvi tcz, : r ; i crrplrr l , sc datorcazir d i f icul t i l i i dc a girs i un in l (x:ui lot srr l is l r ' r t i tor; r r l i l r rn(nl ; r i tutorul : , , I Iu lnan int t l l igcnctr cannol l r ( . r ' ls i l l r ' r '1r l ; r r r r l 1,1 ' sr lc l rsirnl l l r : r r r r ( )bviol ls t r ( ' lLns.

l l is orr ly sr l ) r ' t l i r i r r l ly l l r ; r l l l t r ' l r to l r lcrr r l ) l r i r ls l l iy { ) l

is r ro l , r l l . i ( , r l l . i r l r l ) i i r t lo l l r i r r f ; , , l t t , :u, lc l \ ' 1r , l l r r ' : rprr l l r l r , l

i r r r ' , n l , , r l l r . r l l l r , . r l . , l . r j r ' . r t l " , r ' , l i l l l r , , l , l i l , , r t r r r

. r r r , l r r r r t , l , r r t , r l l t r r r r r . r r l " l l r , r r r r ' l r r . l r r . , l r r r . r , l r r t r , , . r ' r r , l l l l

(lr o lstli.t rL' rlislrrurr.r'r. st. !ir \ '( '(lriL r:i (|rcil rczistcnta la rotafic alxttlrri urnrhrs cslc ntit:ir., nlirsir tl(' l)c l(:vi(:t nu se va dcptrrta prca mult inlalx)rl cu lrozifi:r nrrrlir: a fit:ciLrci oscila(ii, iar valoarea deplaslrii dispoziti-vr'lol rr nidiltr:tionitlc va fi rnrrrirnir cincl lczistcnta la rotatie a arborcluicorrtltts cstc nitli-r..

[\: miLsur-ii cc rczistcnta la rotatie a axului condus cre;te, deplasarcarrr.rs,:i r:rcftc, ilr timp ce dcplasarea unidircctionalelor descregte. In conse-t'irrli., lrL {imrrc rota}ie a arborelui conductor, datoriti deplasf,rii unghiularetttli trrit;i a rrnidireclionalclor, atunci cind lezistenta este rnare, cuplul cerutrl, lu rnotorul primar nu va cre;tc prea mult, a;a cum se r.a ar5.ta mailirzirr. Cu un astfcl de aranjament, se poate deduce ci dac5. de exemplurrrol,.rlrrl pLimar cstc un motor cu ardele itrtem5., se poate mcnline o turalier'orr'i(u.ntiL sau rni.riti a uotorului, desi cuplul de la axul condus a crescutrtnsirl,labil. Desigur slnt posibile multe modificeri ale aranjamentului. Dar,l)('u[rlr a rcaliza scopul invenliei arbolcle conducS.tor si concxiunea de aclio-nrrr'.' unidirectionaid., trebuie si {ie prinse in doui" puncte diferite, de uncL'rrtcnt oscilaut sau care penduleazi., cr-rn ar {i uu ler.icr flotant, levicrulprrrlinrl sau fiind conectat la o mas!. capabilS, sir, oscileze sau si cfectuczeo rrr i i r .uc al tcrnat iv: l in jurul unei pozi ! i i rnedi i .

xII. 12.2. CO-\STRUCTIE ;I TTUNCTTONATUI

ln figura 90 sint prezentate sub forrni. schernatici" citeva din aranja-rrt.rtlclr: posibile pcntru realizarea accstei invenlii, cu apiicatie 1a locomotive;i :rll,. itutovchiculc echipate cu motoare cu ardere interni.. Forlele carel(:1r,)nca/-i. iutr-o form5. a acestui mecanism sint arS"tate in figura 901.

[,'igura 91 eslc o diagramS. carc prezinti- valorile relative ale turatieirurololului primar:, cup1u1 ;i turalia axului secundar condus, atunci cindrnorn(,trtul dc torsiune a1 rnotorului primal este menlinut constaD.t. In figura92 siut ari.tate valorile acclorali luncfii, atunci cind turalia notorului pri-tn3: , s l , m,.nt inut i constarr t i .

ln figura 90 a, nanivela 2 a arborelui conducitor / este direct conec-tll.i lrr uu lcvicr flotant 77 care poarti o masi. l/2. Un punct intermediarirl :r,;, 'slrri lcvicr este conectat prin 6ar..-1.- de lcgituliL 6, 9-ta douiL elementetl'..rrl.ionarc unidireclionale car-e aclioueazi rotor[l axului secundar 70.

Str va observa cA in acest caz va cxista o mi;carc de oscilatie pevt:r'tic.LliL a nasei cit ;i una pc olizontaliL, dar accasta cstc neinsemnate<l.Lui truplitu.dinea oscilaliei masei /2 csre considerabilir in raport cu Iungimearnrnivclei 2. l)aci. sc cere sir se cchilibrczc forfele de incrtic, doui sau maitnultc sistcrnc pot fi montatc pL' arborii con(luctor- si cel condus, unghiuriledr: [az,i intrr: rnanivcle fiind adecvat alese.

l;ormn tli.t;rtir. irr ficrlra 90 D estc sirnilatii <lat in rtccst crrz, tnanivclat :or t , l r tc i r lo lur ' 2 cstc r :oncctat i i la rLtr puuct i t r tct t t t r r l i l r t iar ' l r i tLcl t : t lc t : t l t t t : -x i rur , . ,1, Lt l r crqr iLtrr l srrpcl io l i r l lcv icur l r r i Ikr l r r r r l / / .

I r r s, , l r , , r r l < l i r r l igtr l r t { )0 r : , r r t l ror t :Lr r :or t r l t t t : i - r t ot / r 's l r ' r 'ot t r t l : t l l l t i t t l t -orn.rrr i r ' , l i i . - l s i o l r r t ; 'L rk: r 'orrcxir t t tc i l r r t , ' r t l t t t l l r : r ' ic t t t l t t i f lo l r t t t l . ' / t l t tc

su.r l in( . r , r r r ; r , ; ; - r 0 ' f i cs lc : , r rsp, ' r r r l : r l i ; i l r ivol t ' r rz i i r r l r r t t t , l r t l l i r 7. ( lc l i l l r r l t

r ' , r1r . r l , r l l , , r ' i l r r r l r r i l lo l r r r r l , / , , 1 ( ' , ( , t t r ' ( l i r l l r t i t r l t , r l r ' l l r l r ' l r l l , r l r t r ;1 , f , l , l l r rr l r r r . r r l i , I rozrI ivr . r I r , r r r l i r l r , r t l r t r t i , l i r , , l t , r r r , r l , . . cur 'o l , r ' t r ' . r / , r r l l l t t t , t l iv ; r t t l t r '

r r r r r I r , ,1, ' r , r l / ( ) r r l r ' | , r t r i l r t r . r r l t t , ,1t ,

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. . . . . i t r l , , r r r r . r | ' | | / , | | I . I I . I i l I ' l i r t l , t r )0, / , r r r , r r r t r . r , l l r r .ot t r l t tc i r lo l t r . r . I r ,s l t , cotr | r .

l l l . i l . r r r r r r l tp i l . Lr r r r r r r i l ' r ' r , , r l l , r l , r r r l / . i r l r r , , l i r rg l - r ( . ( .nt t . l t ( ,str ( - ( )11,( . l i t ll . r . i | . t r r , r t I | \ ( l :L / . , I 1r , 1111 rol , r r r l r r . l r t l . r r r l /5 r . i r r . r . 1r<:{ iotrcazir ca () n l i ts i ,. r ' l i r l : r l l r r rPiLl i r l l . r ' i . r r r l . i rL ' r . r r r r r r r r r r r , , , r r , , t i r t 1,r- i ' ' i r i ie rrnt ' r r i r r l bar, , l , , rr l r ' l r 'g i t r r r r ' r , \ ' , ! , / l r r rkrur- t r l is lxrz i l r r , . r l , . r r l i r ,n,rr . t . u niOi," i [ ior . , " t " carc act iot t r ' . r2. ' r l rst r t , r t i ' l ( , t l l l r i

. l , r . t igrrr , , 9{) r : , arborek, r :ondrrr . i i lor . / {acc- un unghi drept cu axulrorrrlrrs /1j, rnauir.cla 2 fiind concctatiL prin tarele J la in capiit al lcvi,.fl,l i i l !l: ',, ' l, l

/j,,carr sprl centru este cone,ctat la o manivele Z; f',,, ,,i ""f,r,t,.1 ,jj,l i] ':, 1t: l;ifi l.rl.l. cap+t al .levierului flotant fiind concctai prin bar(.t(,. r . / r . r r r ( ,U.r ( t tspozl l tvn de act tonare unidircc! ionele.

ln ccle cc urmeazl sc prezinti. citeva din cele mai simple realizi.ri corrslnlctivc ale convertorului, brcvetatc de George Constantincscu in anul l()22.Ar:este schite reprezintiL solutiile unora din schemele cinenatice cxpus. irrfir:rrra 90.

0,! o3 os 0.7

1(),0

q906a60.1,0.2

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Fi8. 91. Caracrrr isr ic. I cor:zcrtorrr lu i . i r r ( l l r r r r t i i i ! t r r {nr ' r r r l r ' lp imar este constant i : Talorr I t ' l iL l r /c: ' l . I r _ .u l , i r r l l1 artr l st r t t t rdar; M - cuplul la ar l rorc lc ' pI i r r t r r r ; d1 - lufut i l l I i r r ! ) . r ,1 s, ( r r ' r ( l i r l

in construc{ ia din { igura 93, ntotorul pr i tna. t i tc t iot : r ' r tz i " t r r r r r l , r , . r t 'poart i volantul b s i estc concctat pr in l rarde r ' l r t cct t t t t t l lcv i rTt t l r r i l lo l . r r r l , /i lapi tu l super ior a l accstui lcv icf cst , ar l ic t t l i t l in , l r t t t t t l , r i , t . r r l . r r r l /cr t rc pivoteazir in r ; i sus( inc la capi t r r l i t t f t l iot o I t t r rs i ;1. ( ; rpr l r r l r r r l . t l ' tr r l lcv icrului { lotant estc concctat p l in c lorr iL l r t l l r l r i r l l l r r r r ' / r ' I1. , ' l " r r , 'l r r i r te duble L, tn cata osci lcaziL in jut t r l i rxci t r r lot t r l t t i , , r r r r l r t r ' l ' , I ' r ' r { ' l '

o i< ' i lantc in 1, ; i respect iv in r ] t . 's i l l1 r t t ' t i r t t l r r l " ' r t l r . l " i r ' r r l r r ' ' i ' r l ' l ' ' ; / 'r ' i r r \ ' po: I r t i - r ar t iculat i sabol i i dc f r ic l i r rn, r ' , s ( l ig () t / r ) . r r r t r" ' l ' r tprr ' r I ' rt l ' l { , r . ( :u partca c i rcunrfcr in lc i oPusi t l ) i \ 'o1i l t } r r l i t r , ' r , l r , 5,r l r , f r r ' l r r l. r r l r r l r t : r ! i ' i i r l )csc pc c i rcumfcr in{a I r t t -o lot t t l r t i ; i . . r I '1, , , l r , z ' r " l " r r r l l rr , ,1 i r , ' i l l ;a {c l inci t s i r - l act ionczc IoIr I r r t t t t , r i r r , l i r , , ( r , , i r r , r ' r l " ' l r rl i r r t l s i r s l i rpr-opi t 'dc rotor dalor i l r 'L fuplr t l t r i r i l r i r r t l r r l l i , , , r r r t . r l t r r l r r r ' r ' l t t t lr " r r t ; i 1 l i 'o i r t l f i lc i -Lrui cadru in l r l l r t r r l r l r ' r r l i . t r ' r r ' r l r l r l l r l r 1" " I r r t t 'i , r r , l r l l l i ! ' ( ! 1t : in cctr t tu l l ( ) to lu lu i . \ l r r i r l r r r l t , r t r l ; i l r t r r l , l r r r l l , r l t r t t r ' t t ' l r

l " r l r r r ' l rccf t i l ) i \ ' { l t i . sc s i t l lcaz: ! ( 's t i l r l i i i t ) l i ( , l , , i l r t r r l i l , r t t l r | I t r t t I t t t t I ' r otr ' '

l , l l l l / . i1()r cocf ic i | t t tu lu i c l t ' f r r 'c i r tc (r l ) t i l l l l l l ) ( l l l l r l r r ' t l i l l ' r l r ' l r l r l l , ' . r l I l . r I o l li r . ( 1 i i ) l t iu( i r . r i l t l t fet t ' lo l dt corr tact i r l ( , : t i lxr l r r l r r i : r to lo l r l l l t . l l . r r . r , l r ' , r ,u, \ r r r r r/ i cs l l sr tPt ts l - t l : r int i t tdt ' rc s i l rarrL / t la, t t t t tPtr 's i t t t t , Sr l ,o( i i " r r r t ' l '

l r r r r l ' t t t r 'r t t l rstr t t t t i l t l iL (x l r l ) i l t ( l a l ) rorrP( ' l ln sf( ' r l ( l i l l r ' i r l t t t t t l , r r t r l : t to lorr t l r t t \ t l t t l r rr r , r ' \ ' , - .1( ru l l1:r i s i r tncrt t in i i salxr t i i , l , l t ic t i t tnc i l l ( ( , l r l . r { l r r : ( ,1 \Lr r r ' l r r t r r ll r r , r r t , . l r i r r gol .

( r r . rP; tnt t t l i l t ) l ( ' t i ( ) r ( l ( ,scl i \ , to l l r { i : t l t l lx t t , l t t i ( ( ) t | ( | I I ( I i t ' ) I I ' lo\ I ' , r r ' r

, r ' , , r l r r l i . r l , i i l r r r l r t i f lo latr l r / ; i ; r t , ' ; ts l iL osci l r { i t s , poir l t i r r rpr t l t i r r r lor t . r( r ) r l lx) l , r l ( r ' r ' sr ' l r r t tstni l , i i ( r l i ls( i ( l ) r i r l l ( \ i i t l l l / , ! i , 1,rr l r l ' . r r , l ', l r ' , r , t tcxi r t t r , / t , / i , , l is lxrz i l i r , lot r t t t i r l i t r t t iot t r t l l r l r ' p, to lot . : \s l l , l l r t r , r { i . r. t r l l r r , l t t i cot t r l t t r i lot r ' t r " , ' l r ' , l l ' t l r i t t r i t r r r t r ' t t t : r l r ' l ) , r r \ t l l lot l r l t ts , , r t t r | l i l r t , l t l r , , rr r r ' r i l r r l i l i t t t : ts l i r ; r l tsr l r ' : r l r ' , i I t t r r" t . l r t t t . t t l r ' lot l r r { i . t l : t l r r l ' l ' r r ' l ' / r

" r / '

r r r" ;1, , , rst fc l , rc,r i t t r l l r t r r r { i . r to|ot t t I t t t ,ot t r I t t , i t r l . r lxr t I t r l l r l l r l l l i r l r ro l r } t l l l l l l

l r t i r ; r t . l ) l l ( r - r ; r | r r r r l t r l , l r ' l rDtr t i l r r t 1111 r 11|r l r t ! ' ' l l . l I l l l ! l l l l r ' ( i l l i l r 1 l ( t l l r ' ' l / l

l r ' . rxul r ( ) t t r l l t , , t t t , r " . r o r l l . r I l , r l r , r ' | r , t t t t , r l t . r l , r ' , , r l l , , / r . I r , r t t t ; , | r I r t ' I t t r ' , ri , , , t r r , r r i t t t , r [ t r , , l r t r r t r r l l t t , . r | | , t t r . r I t r r r t r l t r , r l , t t r l ' , r r , l , ,1, r , , t t , r t r l r r , / t , I ,

l l r l r l r l t t r r r l 1rr , ,1r l r l ro l . r l , , r r 1 ' , r t r . r t r r l l r r r . r { r . I r r r ' ,1, ' r r r l r r r I ' r r r r r . r r ' r ' l l ' | ' r

r l , r , . r l r r r , r l r . r l r , , i , , t t r l r r r l , r r r . l , . t , r r l t , r , r r l , l ' r t r l t , , r l , r , r r1 ' l r r l , l ' 1, ' , , . r r l

I r t i . ' r l . ( i | l , r ' t r ' r r . t r ( I r , , r r r r , r I r i I I r l L, ,t , l , r1, | , r r r . ' , , ' r r t i r r 7,r l r , r r l . t , , r r r ! .

, ' t r ' | r1 ' , ' , , ,1 ' , r ' .1[ t l , |nr , r , .

( i | ,1 r i , , i r , . I l r l r r , , l , , r , r l r j rl . ' , , \ i , l r , , , , , , ,1. , | , . , 1, , t , , .

ol

. l r r [ i11rrr ; r t ) ( ] , r r l r r r ivr . l r r .? r . r , l l r .orrrr l ; r l , i I r i r r l r r r r r r . f l , r. r l l lvrr . r r r l r r i l I r l : r r r t / .1 , . r r r , l , r r . r | . - r l r r l . , r r ; r , , r i i , r , . . .1, , ro l r , ,r r ' l . i , / , / r . r r r . . , r ' r r r i . , r , r i r r r l , t , . l l r . i , i t r r l lo i . r l l o. , r r l , r r r l / j . It r t t t t t Lt l . . . | r t I l l t l r l . , ,1 l t

l ! | l r 1, , r r , .1, . , t , r , , l . r r l r , l r r r l ,l r r r l r l l r | r l t r t | , t1, , r . r t r . , t l t i | | i . r , , , r r r r l , r r r r l / ( ]

l r r l , , , r t , . , l r , r t | , l , , I ' t \ r ' l | | l ! , , r l r r i r r r , l r , , l r , l l , r ,

r , r1r , r IuI t r r l l r i r r rl . r l Lr , ' r r r . r t r t. r t | t r r l / ,J r , , l rl r , r l r . r , l rorr . r t r

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(on' lus csl( : l rv ins , l , tur t l rn isruul r r r r i r l i r , r l r r r r r l 1 i l r r l l corrr l r rs i r r r ' , 1u , . ,s,l roteasci. Pini 't cir lotitr ' ir si-r itrcctl):r l lu s it r '()t)surll i t l crrt tgir ' r rr r 'xr', l)!t.rcaltt it i t i i absorbitr 'r lr in frccil ' i intclnc;i pcr)l lu r(trc( r.( ir rrrasci irr lt ' i t irrr ,1,

'osciialic. Axul condus se rotcitc atunci cu dirniuuari:a (:orospullziLto:|t-(. r (1.plas.:tri i lcvir:rului oscilant, cuplul invingc rczistcn!a [a irxul t:onrlrr ,, l i irr, ldi:ect prorlusi. de fortelc carc actioneazi prin balcle dc corrr:xirrur' /r, / ; i lr irr, lprorJortiona-le cu pi.tratul vitezei arborelui prinar'. \,-alori lc re1a1ir.r ' rrlr ' lrrr.r! ir l,:,r; i cuplului produse do rnecanisrn sint ar:ltatc in {igura 91.

l lulte alte folme alc inven{iei, altelc (lccit cele (loscrisc ail i , sirrt 1,, ' rb i l r . 'c i rnul tc al te forme de mccanismr: pot I i adoptatc iu locul nr , , r r r r i , , r r l r I ' r ,de actionare unidirectional i lustrat; i lc cxernplu, t lei mccanisml r.r . l , lrscris, diferind pdn {azcunul de altul crr 120 glaclc poate {i previ' izri l :.r r, 1r,,nezc pe acclasi ax s i in acest caz aproapc ci rotal ia cont inniL i r r l , , , r r r , , l ,rotatia discontinuir care s-al f i ob!inut. l lec;utismul unidirr.r '! ior r;r I ,1, .r,l ionare folosit poatc fi de oricare tip aclecvat. De asemcnea, irr l,r, rrl rrrrrrrlevie_r osci lant poalc f i intrcbuintat un volant osci lant s i lu o rrnsrr r1, . , , r r , ,IOt ina.

La rtu astfcl dc necanism, dcplirsaLca pc vcnicali. a oriciir-L i;r rl irr , r rrtr, .cum ar f i cel a l axei rotorului , a1-axei rnasei , s i l r l a l axei ar-bolr . l r r i 1,rrrr , r rva producc un {oartc unic cfect asupra mi;ciri i , \[ai lrrrlt, dcPlasrrr,rr rrrr,.,Pe orizontali a accstor ccnire este, clc asemenca, pernisi-r. Deplirsirr|rr rrlt ' rnatif i a ccntrului rotorului in directic orizontaliL va scrvi numai Irr r:rr ',,,|, r,..rnr:insemnati a turatiei rotorului. Este posibil dcci, ca uD astlel (l(. Dl(\.:rrrr 'rrls:r pernit5. nici variali i ale distantei intre oricale douiL din c{rnil i(.:,r l 'rrl i lol arborilor conduditori, masei si axului condus. Accastir csl(. ( \ l lr.rr (1,convenabil la autovr:hiculc. I ' ] irt i ale aparatului pot f i monttLtl ' I),,u, rlti alte pit'li direct pe rotilc motoarc daci. sr: dorc;te.

ln fot'ma de dispoziti.v unidireclional dc acfionar-t ' i tr:rt ir l i l t l i l irrrrr 'r l,l .r:rreir de conexiunc de la notorul prin)ar sint concctatlr lrL b<-rl l;uli l ,, .f/, ."carc s int purtate dc c lementclc maniol l 2 i ,2/ , capabi lc s l osci l r :z, , i r r ; r l r r l:Lt: riui ?J pc lagirclc cu rulmcnti 27. Sabo{ii r lt: fr icfiunc 2E, Jll, r, irrt .rrlrcuia!.i prin bolluri lc ,10, 31 , in r- ' lemcutclc cLr tit i i alo cadrului l) l ir( i i . i ' , . i l .carc ,sint clc insilc articulatc irr clcmentcle rotolrrlui . i ' l , . i5 Drin.id 1i, iz', rrr,. t,r . lenr- : r r . . , lc lo lor f i ind f i r . r t , . l r in p:rnir r l , ;1xr1l r ' , , r , ' r 15.

in accst {e l c lc act ionart : unidirccf ionrLl iL s iLbotLr l r lc f l ic l i r r r r , r ,1, ,1, . , rsrrl)[a, pivotat pe rotor csto l:r locat | i lrotionirl. (] ind clcrn(lntul rrsr:i[.Lnt .]., ,,nri id. in dircc!ia sr"rgr:! i i , sabotul dc jos pc ci ' ir lalt i l) irrtc a r'olorulri l i ir, lb locat i i invir t i l in : rccc:15i <l i rcct ic in t i rnprr l osci la l i t , i r lc inrr ; .o i , r i . prrrrclctncnlrrl t l : oscila.fit: 2' ' l .

ln [our l l u)nstru( i l iv i r i r i r - tvurt t ic i , l r l t :zr :n i l t r ' r i r r l igul iL () . j , l ) ( , l i ) r r ll ) r in l . , i ( rs lc ( :on(xr l : r l Pr i ! l l ) iLr- i l ( l ( r 'or)( ' r iunr: ( l r i r : l iL) . / / l ;L rrn r : ; rPi l : r l l l r r ,l r r l r r i l i r rLrrrr l /?, r : t lc lxr l l l r r i rs i ln l l ) l i r r ( 1 lorr l r . l i f r i r r r l r l i r r < lorr i - r l ) r i t1 i , r r t rr : r t l ; r l i r t / , j rh ' vol i r t t l r t l os<: i l iLrr l / j0 r ' r r t r . osci lcrrzr i . i r r j r r r r r l : rxr . i . /0. l - r .vr , r r r lr ' ,1, . r r r r rcr : l r r l l i r r : , ' l i l l r l l c i r l ) ; i l i r l s i iu / / r ' r r r lorrr l r , r r , . r l r . r orr , .s i r r r t t . .1. t , l t t( . r t , i ,n i l r . lzar t lspcr l i r ' { l { )u. ' r . l ' . l r l r l , , i l i r r r l r i r r ' ( l , r r r r l r r r r i ) / ) ' , . / ,V, l , , l r . r r r , . r r1,1, , i l i r r r l l i , r , : , i t t l r , i .Plrr ' , , i i , , r r r . , r r1, t . r l r { r . l r . r l r ' l r i r ( r r r r r . / r , / , l i l r , r r r . l : r l r l r r r r, rn l r ( r t ( ; rzr i ( r r r ! i r r r t l t rz,r) r t r r , r , l t r r , , .1, r I r r r . r I 'or{ l l l ! / , . , ' ,2 . r l r . ro l r r l r l r r r. . r l l , r l , ln ln l r ' t io l t l : , . r t t , , t l i l r , l , r , , l r t t l r ' , l l . r o 1,r , r l r l r , l r ' , . r l r l ' { r r l r . l r r rt l r r r t , ' r l ) , ' r l . l t r r r l , r l I Lr , , r1r ,1, .1, l r ; , lor , r1 , , r l r r 1 | , i , r , , 1, l r l r . l t r r r r lf r t r , { r l r l , I ' i ro l , , r | l r t l 1\ 1 l r , ' | r ' l l ' | | l | t r r r l ' | l r , r , , r ' l r r l . ' , l , , r . r i , l r r r

t.:i

I

-l

!* ) r ) r , : , :1 ' r

I r r r r r ' r ' l rs l i ' r lourr i r 'ors l r r r r l i r ' . r , r l i r l t : f i l r tL ' rn i5carr . in carc c lemcniulosr i lrrrrl /7 lr lot:hctrz,iL rolonrl csl, irri lat:r lnin sirgcatl in prima pozitie dinll|] lrra ():1.

Vtriarrta hidrau.liciL l convertorului a lost prezentati. dispersat inr';rt lrrrl paragrafelor: pompc volumice cu debit variabil gi generator sonicpcntltr sistcm de tracfiune. De aceea aici vor f i descrise numai citeva €le-ntlnlt. noi.

Accsta este aLcd.tuit din montajul {ormat dintr-o pompl volumice ci1, L l,it variabil firi. supape de refulare ;i un generator sonic aga cum 9a de-.r r is in figura 68, ;i un motor rotatiy aclionat prin presiunea alternativa deliclrirl produsil- de acest montaj, figura 96. Axul pompei este antrenat derrotorul primar, iar motorul unidirectional antreneazi, axul secundar intr-cri r rgrrr i r d i recf ie.

Inertia este asigurati de o conducti. cu lichid 2/, de lungime cores-lrrr rrzir.toare, care inlocuie;te masa oscilantit.

Cclhlal t capi"r l a l p is lorrrr lu i - / r 's t r ' lq l r i r l r r l i r r l r r r r r r i l inr l r r r / r , iar r r r rarc .s aclioncazh :tsuprl pirrl iLrr clr rnifciu.o l irrirrr. i ;t l lcrn:rtivlt.

' lcnsirrnca arcului s trL'buic r-r. {ie aslfcl crr in pozitia i lustratl pislorrrrlsi f ie in cchil ibm sub actiunca arculrri 5i a prcsiunii medii din l inia dc 1rrru,.misie a unclci. DacI masa ptrrl i lor oscilantc cste considerabil l, sau frccr,.rr{,r

Fig. 96. - Convertor -varianta hidlaulic;.

. Sc vor- prezenta citeva din aceste motoare rotative unidireclionalerrt:fionlte prin curenti alternativi dc lichid, brevetate de G. Constantinescuirr ani i 1916- 1917.

Ccl mai simplu motor rotativ fi.ri. supapc conlinind un piston aclionattkr iurpulsrrri altcrnativc periodicc intr.o coloand. de lichid gi producind ro-tafia rrnui rotor prin[r-ulr <lispozitiv unidircctional cu clichct cstc aritat in[ igr nrr t)7-

Axrr l r t r : : r t l ls lc t : r rPl lL i l r r ro l t l crr r : l i r : l rct l t :s tc Prrs in luf i r t r rc pr inl l i r l r r ' l i i I i r l l r r I i 1r , . t r r t I r I r r r l r r I r ' :1 i yrr t .srr{ ip l i r r r r l t : r r r i ; r rkrcvrr l r . ( r r r r s i r r t r r l r ' r t : r l t , )1r ' to.r l i r r l i r r l r r l i . Ar r .s l l ; r r r r l r r r l r .1 i l ( . r , r l ) ls r r r r r . i r r r i i r ' i r l i osci l ; r lor i i , l r r i r r l r ' : r -( r r l r r r rp l , r t r r r ; r i , l , r r r r l / . r r r r r , l r r r r r { iorrr . r rz, ' r i r r l r r r r r r i l i r r r l r r r r , , ,orrcr ' l : r ll . r o l t l t , r l r - l r , r r r ' . r r r r ' . r r . . r r r r r , ! , r , l ' . l r , l r r , l

t t t l

Fig. ' ) r . Forn):r s implJ dc rnoror rotar iz.

curentului altcmativ tle l ichid este ridicati, este necesar un al rloilcir rr.:,or Icarc si aclioncz-e in- dircctic opusi. Dimensiunile accstor arcuri dq,in(l (l ' .cursa pistonului.,/, frecvcnta, incrl ia maselor cu milcare l iniar.iL altr.rnulivr'rsi Dutcrca motorului.' -

l , 'unr:t ionarca ircfstui rnolor cstc cvidcnti i, pistonul / sub imprrlr,rrl( ;urcntului a l l r . r 'nat iv r le l ic l r i< l r l r . l l rmin.-L osci la l i i tambumlui r : i r r j r r r r r lccnlrrr l r r i s i r r r . l )cnlnr o i r rnt i r l i r l r . t l : lx . r ioadi <lc rotaf ic in r l i r tc{ i . r s.rg, . l r r ,I r rnr l r I i t t t tc r I i r : I r r ' I i i r l nrKr,r( ' : rz: i r r r r r l in l r . a l ro{ i i ro lorrr lu i l . l r r I i i i r l , r r Il t rut i l ( ) i ln. i j r r r l i t l i r f i r l r ' p l r io i r r l i l : r t r r l r r r r r r l sr : r l r ' l r l i rsurzi-r in r l i t r r ' { i i r r rpr l r f r ,i i r l r ' l i r l r r ' { i i / l r l r r r r r t i i p l ro lor , i l r r r r r r r i i to l r r I r l i r l r , l crrr l l i r r sprr lcL' r r r r r i ilorrr l r r i r l in l r . i r l ro l i i / r . I I r r r r . r I . r r r , . r r , r r l , i r i r r r i r r i r ' . r 1r i I ; Iorrrr I r r i rh lcrrrr i r r i rro l ; r l i : r t t toIotrr I r r i 1r , . r r r r rorr r r r r l i l r r , ; r . r ' , , r r r r r r r i r l r '1r . r r1, . l ) . r r i i l . r . f ixr . ; rz i i r r r rvol : r r r l | l r ' : r r r r l , t , i r r r 1 r r r | ' , r r r i I r ' r r , , , , . .n l r l . r l , r r , l r i

'1"r l r , . ( l i r l r r , l i r r r . r r l i r rr { r l t t r ' . t ! r | | , | | | | | I | | | | | | r r l t t r ' r l t . r . . r l , r l | | . , l , r , , r r | r r 1, , , r l , t | | r ; 'u l ' . r r r r l r . l r r . r t , i . r . r ir r r r | r I r r '

I ) i r r ' ; - r nrrrnirrr r l r I i r r I ikr l r l .p l ro l l r r lotoluhl i cstc, f f . ru, undc K gi zr ,sint numcr(' inlrcgi, urrrrirrul clr. r' l ir ' lrtl i cgal distribui!i pc circumferinliLtt'r:buic sir iic /i(rr. l), iar cu rlu ilscrrlcnea aranjament, vor exista lntot-rluirurra K dinli angrcnrLli in actla.,si tirnp.

In cxemplul ilustrat K: l, iar z:6, unghiul rniniin al oscilalieilr\rosarc pcntru trcccrca de la un dinte la urmitorul este:

Zr lK'n(m, 1) :h16.5. :1115.Se observi. ci daci roata rotorului are 11 dinli cu l0 clicheti, unghiu I

vl fi numai r/55 gi se vede ci un clichet obignuit ar necesita I l0 dinli pentrurr obfine acela;i rezultat.

In forma invenliei aretati in figura 98 s-au utilizat doi tamburi c qirfrxrl biele l, m, o bield" gi un tambur aclionind axul a prin clichefii d qi roataI in cursa inainte a pistonului l, ln timp ce cealalti bieli m printr-un al doileafirrrrbur ;i clicheli acfioneaz| axul a in aceeagi direclie in cursa lnapoi a pis-lonului f.

I r i8. 95. - i lo ior rotr t i / cr ? i teza ur-, jh iutLra mrr( . r rotorulur utrLzind douar i is tcrn, , lc

' hchc!r J, . r : t ioorre in( t i recf i i oIus(! .

A,I t

;:'lffill lltl

l r r l , , rur . r i l r r . l l r , r | rczr.rr l , r l , r i r r l r ;1rrr . r ( ) ( l , . rxrr l rotrr l t ts n a5lc tnol l ; l li l l r r r , l l ( i ts i / . T. i l ) r I I lo l l j r l , I ) r , r r i r r l r I ru i i l l t t r r<,ntc di : ar { ionarc ct l t, t i r r r l r i i r r l rLrr :1t1, J, ,1,rrr r l i r r l r r l , , r l i , l rct 1r l f r , i r lc c.r l ) r , tc lor loL ; r r laptatc s i, f r l r , ] | (zL,crr

-c l in i . i i c l i r l r r ' l r r l r r i r lc Pc l ; r rc;c lc. i , , / , car, : ] s i r r i I t . t , :atc i t i i l ) tc

ri,r t lc rrrcuril-e .5. []rrc;elc i, I sint capirlr i lc si-L ahnecc rlc-a lrrngrrl axulrrir l l l tc l i r t r , , I j lenrctr1r ' lc dc cuplaro 2,8 s int acl ionaic pr. in Li t {c le d, 6;,., 7, r 'r,s1rt '<:l ir ' , accslc biclc f i ind inrbirralc (ru doui glisicir ' ..1, /0, car.e sil j1 ' r , 's : r lc . i r in lcr ior pr in iurur i lc l / / , 72. ( i l is icr .c le g, lO, s i r r i . at( ionalc pr. i r r, l"uir l) ist(ranc. fsalc l. i , I '1, carc trcc pr-i l i l lezajul bucstlor. /.5, /d. Pcntiu arrrrl, icclica r:otir:clr itccstor glisicrc s-au prL.\:!zut canalc ,si Jrcrtr: :rt lcclate, in, l i r l r ' f ic longi tudiul l i '1 . Arcu: j le 1/ , 11, au tcnsiunca ncct lsai . i l . r t . l r r r r a fuLra, . , l r i l i l l iL presiuut,a urcLl ic c l in l in i ; r tLr t r i i r rsnr i -s i r : l r r rnr lc i , po car.c f r r t rc l io-r , ,1, / i l r ro lo lu l .

L i t r ia r le t ransut is ic : r rLndei sc af l i ' r in { jo l l r r l l l i ( rat ic cu i l lcr . ior t r l c i l i r r -, l r r r lu i crrpl i r rs intrc gl is ic lc lc 9, /0 s i galni i rLr i l t 17, 1. \ . Pis iorLlc le se af l r i .i r r , r ' l r i l i [ . , ru sub a. t iutrca c()ntr . r i a P.csiutr i i tncdi i d i . l i l i r . ; i a tctr . r i t r r r i i. i c l t r lor l / , 72,

( r r l r .ntul a l r , : , rn i r l iv dc i ic l r id din I in ia unLlc i dc, tcrnr iu iL I is toartr . lci r r r l r rLrrrr iL. cr l_ gl is icrc lc lor- 0,70 sir o:c i l t ,z t . l l i ;carea pis io i ruclor

' p l in l i ic-

lclc / i,/ i ,; i 7,7 {acc sit oscilcze picsele crr cliclrc,, 2, 8, iai- fcfclc accsior picsc' r r . , l ic l r ,1. xngrencrr : r .cu diul i i de c l ichct dc pc c imi; i ic a, 4, ( l i r l t i i i inrd. ' t f ' l i r r r ' l i r rat i i lc i t t t r i ;carcainsplc in icr io luDisioal , . lu l i i I ) r , , \ , , . r ' , .oscrrr, l r< i l t r { ic r axului pr intr-o pcreclr , : dc t . lcr t rcrr le cu c l ic l rcL, i i r t iurp cc diut i i, , ' lor l i r l i t 'pcrcchi c lc c lcmcnte cu c l ichct s i r a lL luece unul l rL,stc

-ccl i la l t . ln

trrrrlrrrl pclioadei misclLri i insprc. extcrior a pistoanelor., pcritru nrmitoarcascrrr iosr i laf ic a axrr lu i , ccalal taL pcrcchr ' de r . lcurentt cLr t l i t l ic t cfcctucazr- i; r r { rorr , r r r .a in acelal i scns, ust fc l rar i rx l l l urc o l l i lcare ul i t l i rcct io l r l i r , apt .oalx,I I l l l l , ' l

l l I . r .

l r r forr ta i r rvcrr{ i r i ar i i i i r t i i r r f igrna 100, c l ichetLr l r r rc l r r i r : este in l r -r r r i l l r r i r r i r ' -un lnr l r rc i : r i c l t : f r ic f i rur t : acf ionir t r lc l in ia c lc t ransrrr is ic a rrnd,, i .Arrr l lo lorrr l r r i 2/ srrsf inc uu clentsnt f i ) l l i ( t ( lu l lh l ?2 : r r lapir i s iL poat;-L [ ir 'rrlr lrrl r;rr f iccare clirr clenl('ntelc dc arrrl l ,: iaj 2,1,2.1. El',tn,,ntajt; 2J, ?1sirr l osci laLc in plauur i lc lor , pr in bic lc le 2j , 36, I tgate dc pis lonrLl 27, car. t ,lslc rr: l ionlt plitr lt lcsiune;r clin [ini.r , lc transmisic a untlei. I ' istonul 27 estc{ i r r r f i r r . cchi l ibrrL intr-o pozi f ic mfdi( i , sul) i rct iunea arcur i lor 28, 2g, r<i nl , rcsirrr r i i r r ter l i i d i r r l in i t .

. Axrr l 2/ . .poatc alul lcf , r pe o distan{. i sclr r t i i in dir , : r : f i r : longi tudinal i ,rrri;r:arcl .sa fi irrd controlair"r priutr-url pistou cu drrbli ac{i irnarc j i, cap.ltulinfr 'r ' ior al accstri ia f i ir ld dirctt concctit Ia Iinir dc transmisic a unclei 'ori lcorr<lrr : la_,J?, in t imp cc fafa s;r supcl io:rr ' ; -L cslc srr lxrs i pr .csiurr i i c ; , r . r , e i is l i ,i r capar i tatc l r , .

I - ic l r i t l r r l t lor ' , : i r r ar 'cast , i capaci tatc pr i r r interr l " , l i r r l . r : , i1r , i r i lor pr-I ingir i r is tonul , - i l , . .p l t -s i r r r rca. d i r r capaci tat . f i i r r , l pr- . rct ic , , , r r , i ; r r r i : i i i cgi l ir r1 1 '1r ' .1r1111 .1 l t r t , l in dirr l in i . { d( j l lansul i . i , . r r r r . , l , i .

St o l rst lv i i c i i in t inrp cc fa l i r inf t_-r io l r r i r a pistor l i l r r i r ,s l t , \u l ) r r r , , \ ' , r r i . r( i r lot lo l r r )c <lc pl ts i r rnr : c l i t r l in i i r r lc l r ' :ursrr r is i r : , sc in lpr . iu) : t ( ) r r r i ( l r . ( : oscrl r r lot i r , r rxrr lu i 2/ . As{f t ' I , c i r r r l in l in i iL <l t ' l rarrsrrr is ic crc l l ( . l ) r ls i l l r l i r , ; txulcr lc i t t r l r i r r : ; i r r srrs, i r r r I ) i ( 's i r col) i ( i r < l l l l l i - 22 sc va cupla r : r r l I , . i r r l r r I r r I j , j , , ; r rcr . l r ' . r , 1t , r r r , r l , l , Pi : i lonrr l .17 qi r ' . r l r r r r r r . i t r l r r { i r r r r r . lxrr l . ( i r r , l I r r , . : , i r r r r , , r , l i r rl i t r t , r , l t r . ' r r , r r r i : r i l r ' . ,1r ' . , r r l r r ' , r l , , , r r , . l r r r , . r l i , . , I r r ' , . : ; i r r r r , : r ,1, . ,1, , i r r1,r , r 1,r . t , ,t r r r l r r r i / l t r r r , l r r r , r i r r r . r r , , , r r ' , 1 , l r r r l r r r i , . , r ' , r . r , l r , r r . r , r \u l .?/ i r r y, , , , ,1, . , r i l , l i r r , l

. t t t

coCD

T

I

( l { r r , , l l lu l ?? ( l ( ' ( , I ( r r r t ' I I I1I I : l j . i ,1, I , r r l l i r r i r r ( I I I - I l ) r ' acest i r s iL sc t Lr l t lezc t r rr , I , t t t , t t t r r I ?/ . ln t i r r r l l r r l l r :estc i j r r r r r"r l i 'L{ i dc pcl ioat l i r , p lcsirrnca scadc ; il r is l r r r r r r l pr i r rc i l r r r l s l r l r 'p i r r ' l tazi-r r l r ' axtr l 2/ .

Sr: o l tsLt l iL, ls l f ( ,1 r : ! rxrLl .J/ r 's1r ' lc , t i { )n i i i i t } t r o s ingl l t i ( l i l l r t i i . , .u.

l ) l iuf t s1 1r ' rx l r rct r rs{ l r l i r rc i i in t in i l rLr l nr isciLr i i p istotrrr lu i ?/ : r [ ) re ax, i r ( ] .! ional l r sc rL ' l l iz t r rz i . p l in elcnrr l tu l 2, i , in t imp cc utunci c ind pistonul srrrLPhl lL:rzL rLc ax, ar : t ionlLcl cstc cfccturr , t iL de r : lementrr l 2/ .

Sint posi l r i ) , lurrr ' r 'o i lsr) \ ' l l i i ln l ( ' (onstruct ivc a accstr i sohl l i i , I ) ,1r ' \c lu l l l l r , caplr i ta lur , i . i ar I \ l te i r [ i inhrL:rr i t l ' r pr intr-ur] rc-sol t , t lar crr d i l i -{ l r i ta l f i r ( l ( r t r ncnt in, 'Plr ,s i r r l , . lL nr( ' ( l i ( i l l l in i r : r ' iqrrros c( 'nstant i s i r -cglarcalr)r( spl lnzi l t ( )arc l t r t r rLLrr i .

ln Lr i :uL cr tprrc i t :L l i i , p i r iornl , r t r . t l r '1r1.rsclzr-r axrr l I rugi l r r r l inal poatr ,l i l l r rs r 'n cornrrrr ic i r f ic crL o l in ic t lc t l r r rsnr is i r : t r r r r t l l i cart : i l i f t ' r ' I t in fazir crrl l i0 ' t f i r d() ccir car() acl ioLrcirz i r p istorrrr l p l i l lc ip l l s i iD rr t : r 's i c i lz r ) lotor l l l r i !I r rnct iora in rnor l s inr i l r i t crr ccl r l rscr is : r l i srr-s,

I ) lcr i sr : loktst 's t : r l , ru i r l i r i i , Pis lorrrr l pt iur iP;r l r r ( .1)Lr i ( r l i rcut , i l ( r ascurr-n(, i t , cu act io l larc r l r r l r ] iL, r r l ) i r { l i i r r ( l ( ( ) r I { ( I I i r I l -L cu l i , r< i I r , fazi t a l iDi t i ,1, .I r t rsnr is ic. I js ic r l , ' rLr l i t f i - ! i l r r ! . ( : t l i l ) ( l ( 'nrot{)r 'p i - i r l iL,ost i l i rnt i - . s i a i l r rt t t r rs i t ct l r rsr-r . s l lL s:r l ic celr i l i l r t lL l r : r l , rL l l -L l r t l r r t i c l r t , : uct i r r t r , : i rz i r . iu <l i rcct i ioPrtsr ' ( i :a l t tLt latr ' ( i ! s :L font l r 'z , r r r r , , ' r r , l ' r r . . r t ' , r ' ) .L. l . r1, t . r i , s iL r ' r t r t t racerei lr '1, ' r ' l r lc int : r f ie i .

I r r uvrtorrr l l r l r 'z l l la l i r f igLrrrL l l )1, r rsul currrhrs, / / sui l i r ) ( ) u l r l ) l )c - / - ,1i t t crrr t : lucrcazir r lorr i r sctrr l i r l r 'Pistolnr: J, i . ,s i J, l , - r \cestr t p istorr , r tc l r rcr i 'nz- iLi r r r ' i l inr l r i nni fotnt t l is l r i l r r r i i i i l j r r t rL l rxr ' lo l l r l lx , ' lu i ; i c t l t : dr i r r iL sctrr t ' ir l , r ' i l i r t r l l i cotrurnicr-L in l tc c l r ' pr i l { l , sc l i i ( l ( ' r i l ( ) . / . ' i , rc i i r t ,ct iv /d. Un piston./u, <lrrc sr 'poir ic Dr i )c l in r l i tcct i , r x\ i i lL-r , ,st( : Prt : r ' r ' rzu1 cl l Di l t ( i canalc J, ll ) t i l l ( i r r r ) l ic l r i t l rL l Pottc t f r t , sPrL- rr t r l r , ' l t 's t ' i r r t i rLr r ' i l i r r<l r i < l i r r Iotot . [ ) is t<.-rnt t lls l r g i r r r r i l ; i cstc al inrr ,ntrLl r 'LL l i r :h i r l I ) r ' in or i f i l i r l l t l , 'aclr t r is i , ' / ( t . Ol i f ic iu lr lc i r l l r r r - /9 t :s i r : conrt t ' tu i r - l r r o c lp l r , i la{r ' , sal l ( l l o f r rz i r i r l l r lo i l in i i l r i fazt t r ' ,i t t { i t t t l r cc ccir la l l i r lazir a l i r ic i r l , '1r ' r tnsnt is ie ( 's tc (oncct l ! t i r . l rL t r i f i r ' i r t l r l ,i t t l ratc i0, ast l ( ' l ( r - l pr ,Jsir ln l l a l letrr l t i r i r i rct i ( ) lcazi lLsrrPt l t l l tp l l r r i cr tet i r r rr r l l r is tor l r l r r i / i .

St : o l ,scrvi i c i i in rrcr . r rst i ror is l t r r t l i r : a l l , ' r ' t r rn! , le r l i r r l in i r r dc r t r r , i , 'l l r ( ) \ 'o i rc iL rr is( i r raa al t r l l l ) i r t i \ :L rr p is lonrr l r r i . /7, ast f t l c : r I ) ( ' I ) i r fc l t rs l l l ur ] ( ) lj rLmi ' r l ; - r I i < lc pcr- ioarL: su((- fs i \ ' ( ' j i iccar, st t r l r 'p istoaur: ( l i r ro ior cste pus i r )lot t t r r r r i r : i r t ic , in l i r lp cc ccl i r l l lL scl i l r ( ' l ) is t ( ) iu l ( ' l r izol i t tc r l t ' r ' iLt tc pis lorrr l. /2. l )c jLr l imprcjrrrrr l p is io i ln( lo l r 'o ioni lL l i s i l t t lour"r . l laur l l je prof i latc cx-r 'orr t I icr . . t / s i , t2, cor l r :ctato cLr c l ( - 'ur()Dl( .1( ' ( :u mi ical .c al tct 'nat iv i r 5,7, 5/ ,r r r ' r 's lc t ' l r 'nrcntc l i i r r r l r rn i rcr i r lc i l i : pr , r ' r : r : l r i lc t l r 'p is lo i lnt :55, ,51i { iurr tc intr-ogroz, i t i r : nrccl ie c l l a jn lorul t tnor rr 'sortur i I i sLr lnrs( i l r r :c lc doui i crPcte la pt I\ iu l i i r l icn) l t i \ ' ( dc l i r ' l r i r l r l , r l t r l , r r r iL l i r r i i r l , t r ru isut is i , ' , o l i r ic f i inr l conr:r"l . r l r - t l ; r or i l ic i i l , r lc r t r l r r t is i l JT, - f , l i r r l i r r rp l l cr ' ; r l r t l t iL t 's t , ' l lg:r l r - t l rL intr i r r i l ,i i r ) , ( i0, r t lL ' tkrrr iL l i t r i i r l r . r r r r r l , : r l i l i ' r ' i r r l i r r I r rz l r urr : r f r r t i r r l , r r l l i r ru 1110".

I is lc lx is i l r i l r rL i r r r r l tc lot tnr : rL ' r ' i l l r ' : r i l r rs l r r l i , l , ( l l l r t ( , to i r r ( i t ' r t t r r l lt t t l r r i s i r sr : r l l i r r | r ' r r i srrrr r r r r i t t t r r l l t i r rPrr lsrrr i l ) is l ( ) iu l ( ' l ( , r to lotr t l t t i .

l i r r t t r l iotrrr t , ; r i r ( r 's l r i n lo i r ) r ls l r ' : r i t t t i l l r t i l r r , r ' lc r l r ' : ' , t i " l r : r i I r ' . ,r ' t t | l r t t , r r r ' I r . t t t l t t I r t I r r i o, i , i l r r l , r t l r r to lor I i i t t r l r ' l l r l t t : r l r i , l , l r t l r , i t t t t , ' : r l l r r i r l r r l r r rr r"r tPtrr f i , I r ' r r r r , I , ' r l , l r ) r r lur l , r 1r , r i , r r r ,1, , r ) t r ' ( l r ' l r r ' r l r l , r 1rro, l r t , r ' ru\ i t l i r , , t, , r | | l r r t l l , r t t t l t r ] , l | | ] i | l t , r , l t t , , 1r '

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. l ) t 's igrrr ' l r ' r ' r ' t l . l r ' ( i ' - ( i l . c i r .b iect c ' ' r 'cr1.rul s i ' t uunrt ' roasr ' , s.r , -r i l icrr( i i l . r rc.sr . r iL sur ' int l srrr . t lc .pagir i , . ra jor i tatca r i in,1 inrcgiJrat , : ' , i , . :( . i . ( l . r rstrrrr l i ' tsrLi i r r t rc ani i r92t t i rdz6. Acestea sint in i i r . i te sub dir crserlr.nurniri cl: ,,l letodii ;i mijloace pcntru transmisia puterii de la lroloalr:l)urlarc crinl ar fr motoarcle cu ardrrc interni. la axe condusc, in particular|eutrr I<x orrotivc sa* altc vehicule actionate^de motoalc cu ardcre'intcrrii.i l,,,Imbu niLtirtiri in transmisia dc puteie',,. ,,lmbunnti!iri nf" ai.poritlr.Joirrridir, ctionalc de ac(ionar e''..,, lmiunitifiri. ale mecanismului pcitru 1 rarrs-Irsra putrr-lr pcntru a fi util izat cu motoare cu arder-e intcrnf,, elc. I)ar1x-ntru scopul si intinderea accstei lucriri nc mirginim la matcrialul tle-scnpttv arailat, sperind ca el si 1ic si edificator. -

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N c vom limita la o ne todi simplif icatri . lr tratarle ir pr olj lrmci pentru a (arsiccuatii lc fundamentalc alc corwcrtorului ; i curc siL'pcrmitiL cit itolrl,; i sirrrnalroasc:i in l inii mari comportar(,a accstuia in difcritc imprcjur.i i i .

l lclati i lc cc vor fi datc aici sint de formtr cea mai cL,ncntarii.S(. va pleca dr la faptul ci, convcrtorul cste ul ntccanisrn asli,r l .on_

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lnrl, \.rrTlurint,r o distanti parcursil, o viteziL, sarr o lor.t ir, r lup;-r cilt:, ,.,stl, : l , r , , l , , . ] - .amplr tudrnca unei asemcnea r .ar iabi lc; o _ r ' i i r .z, i r uugL: , i l : r ; -L a.rr r l , t r t | prrmar : 7 - r rn rrrrumi l unghi J, . fuzi .

. l 'r ' in dcfinif ic ; i constru_c!it ' cont.ertorul rste ul) al)arat ca1.. jr:t j :rr.t i .t l r l ) ( l l r ( .1 arntOtt ic i obl i r rut i r t l " la un ar l rorn l r r int , r r ( ' r r r t r i . , . . r r .^ ,1, . r . , r , t i ,( ( ) l l l l l lur ln douJ compon, 'ntr ' . ( ) Cotnp(, l l i n l i , , : - t , . , r | l i r , r r i r r r r , , i , . ,_. . , i r rl l l l lJ) .cr 'a l t . r cstc aplr( at i unut pcrechi dt 'mecar l r isnrr .c l t , : rct i0 l l rc rrni t l i r Ic-l l,] ' . ,.,]1

.1", r 'onvcrtesr' mi5carca armoDic:-r ; i for.tclc unn,,nic,, in iDr1,|lsrrr. ir0 l : l t r \ ' ' . l l r ' r rn l t , r l l I i l l l r , r r l i let t ic .

. r ' , 1 rn:r i^ . inrPlrr r : r , r . : r r r isnr pr i r r car ' , . r r r i . , : rn, : r r , , l i r t i \ . r ( . ,ust .ur l i , . . r , .

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l I r

SiL prcsupuncnt c i l l \ ' ( I t l ( l r ' ; t l i l ( r ' ( t t l l t l ( r ) l l \ ' ( l lor t r l r r r r r"str P'r ' i l r i lun rcgim. pcnlanent. Ac( 'asl : t corrr l i ( i t ls lc i t r r I rot | : r r r I I r : ; i r l r r r r l r ' : r s, i r rs is l i ia$rpra cr,

L in t - r - -Sirn permancl) t , sau condi l i i t r lc s l l l r i l i { lL l t : < l i r t r tnr ic i , i t l r | l i r ' i ica reactiunile intirrrc alc diferitelor Pitrt i l l inirtt(riorul c()I1\'( rtorullr i si irrl) iin or icc momcnt o ascncnea mir imc; i d i rccl ic, inci t d i rccl ia; i r tnrpl i t r t 'dinea lor medie s.1 formeze lizuri de echil ibru stabil cind sint in rni:,r:rlr ' .Se poate ca echil ibruI sn fie d-e tip indirect, in carc o {orl ir cxtcrioali r rttttar f i gravitatia, un arc, sau alt mij loc, sL aduci intrcg sistemul irr l irrrl,rrlmi;cirii la o anumiti. pozilie medie.

In figura 90, condil ia de stabil itate a con\-ertori lor prezentrr(i 'r l 'indeplinit i.

Se va observa ci in toate araniamentele schematizate dcscrisc rrtt l 'r ior, negli j ind inerfia masei oscilante, mi;carea pirl i lor dc actioDirrt tstcncdcterr i r inat i , De aceea, este necesar se consider;m'stabi l i ra lea : is l , t t r r r l t t tcind acesta este in mi$care, deoarece in cazul pozil i i lor incorectc alr: itr, lotfixe gi alc pivotilor mobili, amplitudinea oscilatiilor volantului sllr trrirr,r'lpivotante poate tindc si. creasil indefinit. intri:gul sistem, va dcvcrri r l 'r i .i .nstabil, iar aceasta va avea drept rezultat blocarca ;i ruperea sisttlrrrrlrrlde lesituri.

. ) I 'onrnr r l t lnt , l i r ic . ' r l i i ( . r i te l ( : i i ,nrr , , tcrr t i l iz , r l r r r r l , , r r r I l is | | | r tnt . ' r r r t i ( : ( i r r . . I 'crnr i lcr r l i ( i i l ' , ' ,1, . ( : rk" l

i12)

( l in rcci lst i t fat . r f i . , ( ; . ( ( ' [ \ l j r I l . i , : \ (u . r. (nr t , . | l i r l : i i r su} i r \ t i \ i r r l

. j \ l l , i r 'orrdif ic i.r 'actie.L l,r 'ntru clio(le este ca convcrsia {or.tt lor armouicc

;t. :r uri leurilor intr '-rrn-cuplu unidirectional si i l tr-o r.itezi-L unghiularl uni-rl i t lr f ionalir si. sc. produci. f idl ?r introducc rlcfonrati i apreciabile ale mis-r:ir i lol armonice simplc necesare siL mcntini stabil itatca in sistcrn. I)c ase-tlr 'r l i t, o astfel de couvcrsie trcbuic sl 'L f ie in asa i l araniati ca un echil i lrmrlirrirrrric rrl sisi:cmului sir f ic p,rsibil : i si nu colducir l i blocare clinamicir.

l rr l irnbajul matctnatic convertor-ul este in csctlt i un sistem cu clr,,-:,-rpllrrL' rle Iibr-rtatc considerat t l in punct de r.cdcr.c static. Cu irlte culi l:t, r r r . r l i i l , rnccarr i t i i .s t r r t ic , ' ] lu l rot l i apl icalc dir .cct , a;a cun) se iut iurPL cutt | : r l ( ) r ' l t i l t ( 3 ntCr-aDisr ' ) ' ) r lor r r r i l izur, in lc lu: ic.r muloarc]Or. .

l, ir convcrtor-, avcrn de-a fat:t: cu diferite picse a cirtor. lx)zit i i , in i;f-cil( ' nrolncnt, trelruic consideratc frrnclie de timp ;i de r.clatla gcometricr"rrl irrlr 'c t l irnensiunilc ; i poziti i lc cclorlalte piesc iri sistcm.

.. I)r 'oicctarca nrasinii ttebuic l i"LcutiL in asa ft: l iucit miscurclt obtin,_r.-isi f i ' t lc t i lul in i i ir(, t l lpa ur.r anunrit numirr cL' nti;cr-rri ir i t irnpul a c,..e(( . . lx f i r t r . f i Durni t , . r ' rg i t tar iabi l " , r 's tc at insiL o star-c dc r tg int , l tcnnrui : ; . ! ,irrrl ik'r-r,nt care au fost conditi i lc ini; ial.,, I)e as(' incn(,a, aceasti i starc trtbuicsr' i sc ntcntiniL iutlc{init, indifir lcnt <:c schimbiLri sr' l .rot pr.oclucc in prir. it,ta,rr l , l r r r i l , ' r ; i turat i i lor ' pr inutului s iur secunt larrr l t i , l r i p l r rs, , ,ut , l i t i ,n , : , ,r i.Airrr. Pclnraucnt nrr t lcl,uic n.rotl if icatr'L dt: unelc r,;tr iati i iapitlc posibilr alcvrrloli lor trrrati i lol si crrplrrri lor- prinranrhii ; i sccundarului.

0cl mai simplrr caz clt. r.r 'ginr p('nl.ulclrt t 'stt ' lrt ins alu lci cind dif,:-r i l ( lc l ) : t f t i tnr i r t ins to l r tc o nl iscar- t ar-r t ronir : i r , i l r r - r rccl t 'c lctncnlo caLt, : r rrkrrr i r g l i r l t . r l t : l i lx . r l r r tc rk ' -_ut i ;calc au l r r : r t urrurrr i t t ' lxrz i i i i r t r r r l i i , c iut , l l ( ) tl i r r r r t r r i lc tx)7, i t i i { l ( , ,s labi l i ta(c c l i raur ic i r" .

Pentru a i lustra aceasta, forlele care actionead in diferitele piLr'{i .r l laparatului lntr-un exemplu al invenfiei, sint prezentate ln schema din figrr tir,90 /. Considerind echil iErul volantului oscilant /5, se poate. ari.ta tit t,ztt l 'tanta mcdie a forlelor de compresie care sint transmise prin biela A rrr l iintotdeauna lntre i inii le punctite indicate de sigeli le ar ; i a1, in l irrrlr ,r '

rezultanta medie a {ortclor de intindere carc sint transmise prin biclrr 1/ r.r

f i intre l inii lc punctate indicate cu slgeli le ds;i ar. -frebuie si pt,rizrrtrr I refortuli lc inveise din biclelt ' 8, 9 se datoresc inerfiei piuli lor ctL rtri5,.rr.alternativir. i l iu dispozitivrrl de aclionarc unidireclional ; i sr^ut [ortt lr ' ttttr ' iin compat-rLlic cu forlcle dc aclionarc la care ne-im refcrit. in colrstritt(. ' t.in dispuncr-ca prezentati in aceasti {iguri, for}cle rezultantc carc at {iott ' .rzirasupra lolantului oscilant 75 r'or f i indrcptate alternatir- sprc rlt i l tpl r 1tspre stinga, f i ind in acelali t imp in direc{ie contrari axei in jurul cr-ttt irt rr: ' ileazi volantrrl, astfel incit stabil itatca sistcmului in miicarc cstc I)rI II{IIIIII.I

Si t considcl"rnr, d i r cxemplu, col l \ t l to lu l pr ' ,2-cnt t r t in { ignrr()0 r" I i t

/ forla axialiL din birlt priniaiului. I 'r i l lni j lo&I lcvicrului f lo1irn1, rLttrr. l l tiorl ir.cstt: inpir{it i i iu rlouit compont'nic ;i aplicatir./s' ' rurLsci ; i./, r l ir lxrzit ivclot rr nirl ir cc!ionalt '.

I ) t 'n l r t t r r s i r t t t l l i [ ic l r cr t lcrr lc lc, st ' t :onsi<lcr i r c[ l l r i lsa lcvielr l l r r i l lot l r r l leste f i r i r r tc l l t l r rs i , : rs l fc l i r rc i t for lc l r ' l , . l r lz , ? 'Pl icatc aclst t l i r t r 'or l i t t t . r t iin cotnpir ta( i t : r : r r fot l l lc t lc acct lcrr t ! i i , lator i t i migcir i i s l t lc osr: i la l r r l i i l r rr ( : ( 's i crz, r l i r r ,orrr l i ( i i l l t lc ccl t i l i l r t t t i r t t t t : Ior tc lc l rp l ic l r t ( r r tcost t t i i l , t lz t t l t iLrorrr l i { i i l l ch / , ; i / " s i r r t p lopot( iotrr l l r ' r t / .

| ) ( r ' i : , i l ) ( , r l ( s( t i r ' l

| '1. l ' ' ( | l )

l r ta l l i r r r , r ' l r I t t t r i l i lo;r l l r , l r ' l r l i lor{r ' " i t t l i t l l r rz.r ' \ , l i r ; i r l ; r r . r : r r l i l rpr i '

r r t r r t l l r l r l i , r l i t r l rurr ' ( i r r l r ' l i r r rp

I l w," l . l , l , r t t , " l l , / , t t r i " /

I ' r r , , ' , , , ' . , , r r l , '2, 1, ' pt t t r r l , l , , t r r" , l " i l r \ r t l ' , r1 ' l t r , r ( r ' r l l r { ' l " r /

/ , , /u l , r l r r r , r r r l l l r r l , r r r t l , , r l , l , , t r r l r ; r l r r r t t t t r l r r , r l ' i l t t r1t t r r l | ' t t l ! l

j \ l . l (n l r ! , t r rs l r i r t r . { r ' ' . : r l " r ' r i r i v ; ' r j l , i l . l ( , r ' r t in l , r r r r r r l , , . r , , i r t , . , ( , | | \ t . , l ' t .1, . r , , , , ( l, r i r ! , r . r1. , , i I l " r . r . ! ' lo n.r ' r l ( , ' . ' I ' ! l r " r ln

' l r ' ; ( f l l | : i s i ru l ! ' l Si l l r l r rhr t t , , t r f , r t r r t i l ' arn, t , l , l

l ' l f r I . r ' r , / r l l " r ' r i ' l . r \ l r r r l , i l . . i l ) , , \ , ! r t , l | i ' r l , r \ : i \ , , : , ! r , , tL \ , I I , 0.. r . r , t | . t ( ,

r l , l , ' ,1 ' r / , r , " \ , r " l , r i

l In . , [ '1, ' r / , r , IUl t , , r1, , r1, . ] . . , , r r , r , , tLr , , , / , r , , , ,1' r r , r , l ! r I l l " l r ' l r , \ , , ' r , '1, l , , l , ' r ' l | l l , r , t ' , , t r , 1, , , r , . r , l , Lr l , r t i , r l t r r , .nt , ,

r , ' t , .1, .

l , ' r r ' , . . i1n.( l i . r ' , l ) , . r ln r , l t ( .1, ' r ( . lx . r l i r . ( r : t i r r ln)z i t ic i nodi i u lcyier-rr l r r iIk , t . l l . (

' r r r . , . r t r r r r r l r .s l r ' . t r t l I l { { ) t | { : ( ,1) t r l inci t , in gcneral , ( :omponcntclel) iu. ; r l ( ,1r . cr l r l i lc t : ( i iL pozi f ic i r r rcr l i i l r lL:v i t ' ru lu i { lotant s int mici . - Dcsigur,a<:tstr. lr lrt: lrrLir. lrurtt: irr t:onsick.r' ir { ic l ir o irnalizir completi.. ' I 'otugi ncgli j ircai| l | i t()l k)rf(: tI l l va (l(.rratura leztrlt i l tclc obtinute. !-ortele sccundare, dcpindirr plirx:ipti, rI stalri l i tutca sistcmului si dc introduicrea arrnonicilor

'mai

I l l i t i I ( r .

irr anirl izir clcmctltar:r carc nrrneaz:! nu s-au luat in consideratie arrno-rri l ik: rnrri inaltc din sistern. I ir-ident, formulele oblinutc sint aplicabile numailr 1rloicr;It:Itr convertori lor in care efcctelc secundarc sint mii i.

' l irtrr; i, iu practicit, almonicilc secundare trebnie consirlcrate Dcntrur'. i r:onrlit i i le dt stabil itatc sint dcpcndentc de act:stc;r.

irr notali i lc adoptatc. I itcr-clc f lr i indice, ca /, v, a, lI ctc. sc referiI r r I r | , . r t r r r r r r I.t primar, l i tcrcle cu incliccle unu, cum- ar f i Jt, 7:t, ,o1, M, elc.,sc lr, l i .r ' i 'r l ir sccundar, i irr l i terelc cu indicc doi, cum at {if2, a2, a", Li" e|c.sc h.1r.r ' iL la inerfic'.

. l)cscourpuncrca r.itezei primnrului ir, aplicatiL levierului f lotant, inrLrrr.i r 'orr.rponente, z.',, transmisit mccanismeloi unidircc!ionale alc secunda-trrlrri ; i r '", t lansmisir incrfiei sistcrnului, poate fi cxprimat:r t lc ecualia

' i : .r,1 + .r?. (14)

. ,Accirstiu ccua,tie trcbuie tratatir cu atcntie, dcoarcce, daciL sc rc1>rczintiLvrrlrri lr. r ' , rrr, zr, functic de tirnp, trcbuic avut in vedcrc cir aceste trei \-i-l rzr . r r r r s int in faziL,

, \ , r ' . rs l l inseamu.-r c i S- \ t scr ic:

r t , /s in(<ol* { ) , ur : I / , s in col , zr , == I , ' ,s in(ot + p) , (15)

.f.,:; i p f i irrd tlour'L unghiuri carc trcLuie detclminatc, iar I,-, I 'r, I/e sint am-plitrrrl inile rcspcctivc alc acestor t lci vitcze.

Yitcza I-, este transmis:r. unei inerti i in acclir; i t imp in carc forta l,cstt irplicatiL accstei inerti i . Sc ;t ic cir

, di , ,

dt

lrtttucit constanta dc pr opolfionalitatc dcpind<' clc accclcratia gravi-talit i ; i r lc incrfia sistcrnului carrt. oscilt azir sub atctirrnca forlci 1", iar aCestcasint nrl in(loul-r constirntc, sc poat(' st: l ir: ccca cc dcja s-:r gitsit (13)

1' ' - ' .1". ( t7)l ' r i r r rL ' f i r r i I i r . r rn i r l i l r . r ' f iorr i r lc lc s in l ln r t l r l i ' l int : i t for ' { rL / , s i v i lczt i , ,

s i r t l i t t l . rz i , i ; r r ' l r , ' l , ; rz:r r ' , . l r r ( i iLrr ' ( t ) , (0) r , .zrr l ta

i , , I , s i r r r , r / , . / , / i , s i r r or l ,

; i , orr ' i r I r ' r ' i r r r I r r . l . r l i iL. ( l r r ) | i ( l7) , sr . o l r1 i r r , .

t l t " l r l l . / ; , s i r r r , r / ,

(16)

r l t r r , . r r r .

, . . / , I , r r r , , , r , t r l , t ' t i tnt l I , | - , .a| ( t \ ll ' r l , ' l l , ' , , ,

Nu |x is l i t r i r io r orr . . l . r r r t . r r l ' . t l , l t , r l r . ,1,o.r t , , , . \ ' ; r l r ) . r r , , r l t1, ,1 ' , . . rlu i r r , cslc z l to i r r l t u l r i tn\ ' , t l r ' t t l r ' . f r r r l ! , l l i t l r . r l .

I i<:rrrr ! i ; r ( l . l ) r l r . r ' i r r , . i r r l i r l r r t r , r r r r , l . r ( r r lor (15) ; i ( l t t )

Is i r r (or l | , | ) ,11sirrr , , / ( . / , , /or) coso/. | , ) )

7 { i ind ampl i tut l i r r r ' : r l i l r .zci aLrnorr icr . o l r { i r r r r l i ' t r l in l r ie la I ) r i | ) r ; r r r r I r r I t i .proportionali cu vitcza unghiularir to qi lrza rrnrrivclt i / a prir))iurtl lr ir.r lmanivela este invariabilir astfcl ca! sc l)oalr' scric

I)e asemenea s-a gesit din relali i le (lt) pi (tZ)

Vt - 't'tr

Fr :'l l lt '

Daci. inlocuim aceste valori in (19), se oblinc

6r sin (tol * {) - .o, sin to1 - (.-11,/o) cos <o1.

Sc observi. cir ecualia conline cinci vaiabile t, 6, ot, ,V,, i. l ' , ntr rr ., .,reducc numi.rul de variabile se va folosi conditia de stal)i l i tal(.

Conver lorul t rcbuie s i lucreze gi s i ' ment in! . o miscarr ' : r l r r ror l i r . , . . , , . ,cum este exprimati. de ecuatia (20), indiferent ce valori sr) .rl( 'g I)i r l lr r lr lr.r itele variabile, l, co, <or, ,01r, rf, compatibilc cu gradeL'rlc l i l ,r 'r lrrt, .r l lsistemului. Singura rclalie carc eistf, intre unele din actstc lrrrirrlr i l . r".tr.principiui conservirri i energiei, care sc poate scrie dac5. noli lr r 'rr , l / , rrl, lrrlmotorului primar gi se considcri. pentru simpli{icarc, cir. r. irnrlrrrrrr.rtrrl rrr,,,rnlsmulul cstc unLl

E l lc" . - l / , , " , ,

in car-c.D cstc cnergi i r c;rrs t rcbrr ic t ransmisi s istcmului r l l r r rot . r r r l l , r r r r r . r r .ln v i r tutea {aptului c i cor lv( ' r torul arc un nurni l r srr l i r r , r r l ,1, l r , r , l r '

de l ibcrtatc, {omulrr (20) t rcbui t ' sat isf i rcut l r lc or icc sr , l r l , r . r l . r r , r r l r l r . r ralesc pcrltru a tJrL tinrpul varial; i l ,

I)acir sc rlcz-t oll ir rt ' lal ia (20), sc obtinc

(co cos L,l .ar,) sin o1 -l- (ro sin ,, l,, -1 (..r1-11t0/co,)) r 'r 's a,/ t l .

l ) r rxrrcr l acr ' ; rs l i lcrrr l ic t rc l l r ic sr- t l i t sat isf i 'Lcrr t iL I r r l r r r , r r ' \ . r lot: r lc l r r i / , t rc l r r r i l s ; 'L i rv l r r r i r r r I r ' I rcnrL' l I :

r , , r os, f ! ( , ) r 0, r , r s in , | - l - ( . ,41, /o) { ) .

l ) i r r : r r ls l r ' : r r l r r r r l l , r lzrr l t i i r r r r r l i ; r l :

( , ' | l )

t t t )

( ) t l

. , | | r , l

' ; i , i r r l i r r i r l

( , .1/ , / ( , ) r r ) . , , rs ' i . ( r , r , / r , r )

r r , ' l . l l , f r tu, .

. l , l l t l , | . t l ) | . ( r , r , / r , r ) ' I

l , r , r , , , ,1, 'kr t , r i ' l , r l l l r , . l r r r r , , r , , , l l , l t , . , r ' i t , r l t . r , l ' t l . t , l

l ' . t r r r ! i r r (2-)) l r r r r r l r ' ! i s l l is ; - r ru i r i s i rncl l ic ast{c l

. .1/ i l . . ( toorr) '?. : t ra,

dc ascmcnIa, cu. r r r r i l ; r1r , ( l t ' l l l is l t r i i , l r r r l r ! i : r | . r r l i r r r l , r t , r . r ' , r ' r r I r r r I I r I t t I t t i , i r , , l

Dr imarul t r i :cr : nr in lctst r r r i l l i l l l l i s{ l t , I t ( . / . i | | l i I ' t t t l r t ' , r i r l r - I I I I I I I I

l ( | I

iare mlsoar: , <o f i 'or , in ast l t l t lc l rn i t r ' t1 i , l i ) r r r r r r l ' l r ' (Z l ) ' r i (25) \ ' ( ) r lLrrr l ( t r r r ' r

nutncricil sirnPli,:

I , tL: M,Ur + t l ' , t i , eU/,- ' l , r \ 1 r1,r i - ( i r )

' frebuic sir sc aibi 't in vcdert- faptul ci it l 'r((stt ult im relali i r ltr (xisl r

constante nedcterminate. Formuleli (2?) ;i diagtrrrnr din l iguta 9l' r ' ;rtI

o f-oJ i l."l i in concorclanli cu act-ste rclati i. pr:r 'r itc s:L se tragit cortclttzir

interesante, in spccial in l igituri cu ap1icar,l l co'r ',.r iorului itr stt.r ' tr ' i r l,

tracllune.ln continuare nc lorn re{eri Pe scurt Ia fu-nc-tionarca convet't orl l l l l i tr l

cazul unui motor Prirnar dil grupa a doua, deci cu turalic constar)l: 'r i t

cuplu variabil.

ln acest caz, considerind turalia motorului primal collstant'r, rtrrir lr ' l

cnergici devine1]: . i1 : - l l1.or,

iar ecualia fundamentali (23) ia forma

Mi+.(oi :1.I) in accstea sc obliue

,11r : .1/1 - .. i -t/ : .tur / l ., 'Ji (2s. r 'r1

Acestcrelar j i ia lat ic.rat i tmomerrtuldt . tor .s iuncde]aar lnrr . ' l t ' l l t . i t r r . r lcit ; i cel de la arborelc secundar dispar cind co1 atinge o \ ' 'r loarc rlr it\rrrr ' l

exprimatit Prin .<,l i : l .

Sc obsc ,ir,, dc asemcuca, ci cuphrl sc'cu:rclarului-art t 'aloaLell ttraxittr,r

1a start, aaLici, 'cind cl1 :0. Daci cxprim'-tm ctrplul . la start prirr -11'' I

Iuirm ca unitatc cie misuiiL pcntru turutic turalia a: borelui seculldar', i I( r ' :rst; l

turalie maximS" carc corespunde unor condltl l ( lt sit lclniL 7'cfo, t l r( ' l) l( ' / ' t- l l

i :r '- 'p.i" ar numitrul carc- nra-tsoar:t c)r cu o astlcl dc unitatc, fornlrrl:r (21{)

ia urmitoareir formir

jur : i l f . l / l - ,4, . ( io)

l 'onnula (29) arat i t c i cuplul r t tot ' r ru lu i l l intat J ' [ cst t ' t t t t l la s i ' r t l

$ i cre$t i r c in( l tur l l t ia sccunr l l ru lu i ct t . l tc prnir l . r r , \ ' i r l , ' i I11' IUaxl l l la ( i l l l '

estc aiir.rsiL cintl , xPresia

1' = rr i ( t , t i )

t lcrr ' pr in l t t t t t t t l ; t r i l t t . Atc l tstr str int inr l l l l -L c int l :

,r'; , | (',, ,,, lf [12 - o,'tt'

l ) r rpr i r , r ' r , l r ' l r l i l t : ; i l ( ( : i l l )1 l l l ( l , l r tot l t r t t i t t l t l ' l< ' ls i t t t t ' l r l I t toIr I t I r I r t i

1,r ' i r r l r r ' , i , ' , , r , l , t l i r r r rot t r , i r ' l l t t l t l l i tz i l rct t l l t t r l ' l '

l l r r lxrr l r r l ,1, , I r I r r rLrrr iL i r . i r r l r , l r r r , r { i i r . , , , r r r r , l i r t r r l r r i r , , t | r ' t r . r . I

r t i t t I i r t t t I r r r

, r ' l , t t l r r i t , t i t r , t r r ' : ' l l r t t t l r l l ) l r r" ' i r ' r ' t to l r"rz ' r ' r l r " l l r r l r i ) l I i l . I t : r r r : t t r i r i ' t r t rs i t t r

r ' l r / , , r , r ' l ) " l l r ' I t l r '

/ r . l , r r l , r ) l ' l t / l / , ) . , , '

( l l )

I ' r , l / , , I r l , , , r r ' ' r t r r ' r \ l l t l r ' r ' r r l ' l " l ' t t I r l l l r ' r r ' r l r r l r r I I I l l ' r l l ' r ( ' l r ' ) r l r ' \ ' l l l r '

l l ' l / , , , , , Y | , , ; { l / l

(zr)(ir lt t I I I I ) t - ( r I I r l i-t crr ctuirf i ir cncr-eici reprezinti ccUali i le fundamc.utalC lrlc( l ( ) r l \ ( ' l l ( ) r l l l l l i .

Si' olrscrr': 'r., cir cxistir. nurnai douii constaute iu ecualia (23). Accstc.rlxrl l i rrsri l olri irrulc iu or-icc convcrtor prin identif icare. Ele'dcpinti dc sisteIrtrrl r lt ' incr!ic si t lc sistr:mul de ti je dc legi.turiL. ' fotu;i pcntru a discuta( orrl\)r 't i l l . i ! rrtnvcrtonLltri nu cste nevoie siL sc clctclminc constantclc.

I 'c birza truati i lor lunclirmcntale deduse aici, sc va ariita s[cclnt com-Ir,r '1iLr.i i convcl-trxului in di{critc conditi i .

Sc va arri iza rnai inti i cazul in carc'cuplul motorulni p:imar cstc nr:n-l i I | l l I - (

oDSlar) t ,lrr at:cst caz, ccuatia cncrgici ia forma

E:.<,r : . r l l ._1ror.

lrrturi lucind accnstir laloalc in ecualia luldancntalir (2.i1, sc ol{ine :

^1/, :.1/l + (.1/,\"),

[ : .c,t :.1/;a+ F,/,it. (25)Accstc rclati i arat:L cunr laliaziL cuplul sccundarului si luratia rnoto-

rrrlrri plimar cintl variazi turatia secundarului -{ceasti-L lelalic este prezcn-l.rl,r srrlr formi'r graficir- in f igur;r 91. Se obscn'ir cir cuplul secundanrlui

' ,1, lr)lrtc mare pcntru lalor-i mici ale tura{ici se.cundarului, i i , dc irscmouca,lrrr,r! i;r ; i cncrgia rnotorului primar sint mali. Pcntru r-aloli foirrtc mali.rl, lrrrrrl i t. i secund:rrului, cuplul secundarului cstc practic constant ; i t indr,I*rlrr .)r = co, cr-ltrc o l irniriL, numiti cuplul noln-ral ir l sccLrnclaruhri 1it r , ' t . r l , i r ' r r i {o.

l 'r 'rrttrr valori mari alc co,, tulir l ia pr-imarului; i cnelgia crt 'sc continuust irr ltrcrnenca ctzuri sc poate scric {oarte apro\i lrrativ

- l1r : ,11, , , t : . ( r - .o1.

,\r 'r 'arla irtscatnuir ci-r, pcntlu. ttLrati i ale sccunclarrrrlui pcstc' o anrrnii ilrr l, ' ;rrr ', r:rrPlirl sccrrnclLrrrLri l-rminri constant cintl cuplul plir lalului csttcon!lrr1l. I)cnttn ascrncnca colrdit i i , (:on\.crtorul estc plnr:t it cclrivirlt 'nt r:rro lrrrrsttt isic l igidiL obiyr.ruit iL, c:rrr: transntitc cuphrl primarului, inir-uu raportl ix l i l t - r 's t ' r :urrr lar , ( l r r a l tc ouvir tc, pcniru valor i r ic l icatc a ' lc l t r t - r r ! ic i sccrtr t -<lrr t r r l r r i , sc olr t ine ccclr . cc auionr l ; l nrrr l i t -o con<l i t ic t lc v i tcziu srrpcr ioul ii r l , ' r r l i l iL r : i r c lcr : tc cu 1r ' : rc l . iurrcu ia tu l r r l ic inal t i i i r urrui r r r r1orrroIr i I t '<:hi1. l l r lcrr r u l ic t l l v iLt 'zu olr i luui t i i .

I l r r lxr l t r r l r l i ' t t l rnsrr- t is ic olr t intr l in NS( 'nr( 'n( 'u t :on<l i l i i cs lc ct ' l tnrr it l l , r l , l " ' r l , r l , . i . , \ ' , r Dr) l i r r ; r

,v i t , t [ , , . (2{, )

r \ r , . ,1 r . r l i ( ) l l \ r . ln) i r l r ' , r r l , r l r r r tsor r l i r r c l l t r t r ' r r I l I r ' r ( )n\ ' ( r l { ) i r t l r r i . l ' . : i l r ' srr l ic i , u l r , r r , , r ' r r r l r ( i r r i s l ; r ( i , r r r r r r s is lct t t r t l i r r l r rz i ( i r r r r r l r l i , ; i ' , i ' , r ' lurr ! { ! ( 'r t r r r r . r t r r l , l , r r r l r r { i i : r l r , r , , r r r r r , i r r t r r l r t i . i pt i tn:r t t l r t i i r t ; r r l r ' : ry i p, r iorrr l , r r l l t i r r rp.l i , r1r ' r r r r l , r ( ( , l r r rurr , r , i , l i l ) l r r ' l i r , i l r r l , t t r ,

( r r r l ' l , , l t r r l t1 ' r r r , r r ) l . r r . r t . r , . r l r r r . r l i . r | ' t t t t t , t t t t I t t t l t r ' r , l '1 r r r l r r r r r t r r l t r l t r r ,

l r r l | | r ' , r r r r | | r r l .L \ , r l r , r r , r l r r r . r l t , i , , r r r r , l . r r r r l r t r l ) . ' , . r I t . r r . r r r r r t l , r l | r l ,t r r | 1rr ,1 I ' , r l l l l l l | r , r l r . r I | | I | | | , | | | | I r | | , r r , , r . l , r \ , r l r r , l l , | , r l l r r r r l , r r r t r t t r r t l t t , t , . t ,

rll

t i { i r r i | | , l , , , . l | r , , (1, . i ] t ) : , i ( . t2) . , l i r r ( . ] l ) s, . ot , { r r r , .

.v , , . ( t lz) i t tr , . ( . i t )Ae.rrs l ; 'L rr ' l * r i . l r r i rL i r" l .gr i t r r r r t t l intrc morncatul crc torsrrrn. r : r sr . r r .r ' rprr ' l r r l rk ' l ' i . rsr . is ic rrr i l r i . r s i cuplul .maxirn ae ra-moto.Lt 1, , : i , . , , , , , : , , i , , , , , ,r i r r r l l r r r ; r t r : r r r r r r t r r r r r l r r i I r r . i rn;rr s, . rn|nl ine ( .onStant i .

iiil$,ii:il',:ffi ,:iti;,t*.,m:{.#'**:&":::lr j:#Lii t t ) r r l0 l l ts i s inrul tan,

,.,,,',,,,iii,iii.':1j'i ':r:JP::l;:i',:.:, form'i graficiL rcrafiilc- (30). |i -(32) . Pe 't

r r

't rr'rrrr <rc ,r".ir .u"-,"p."iifi Jiiiif: #'l',t':J ixii*.f'.',101f,.1".t"'J.,ljli,ii1i ll, r'r' 'r 'r 'zint.i unitaica ocntru

-misurirea momcntului dc torsiunc pri'rirr.l;::f

.:i. jl.*th: dcci, cuplul ".ro."r"i.".o"a".',ii;';;i." oncc var.:rr,.r l l l l . t I r l r : t l l ( .1 sr ' ( 'undarUI l r ] , prczcnlat : i in abSciSi , num,irc lc

f .:ll : l,llii:l . ; :;!1, gr' se' ior multiptic-a cu va.loarca .,or,ri,1'llolli#iil,.

;jnlll;ii;iif ';i5*i*rt111*.f;J'ir'if i:xln'ffi i":','1r",3ili:lI,,,,,",,,1,1',1:,,i 'li:.I"',";'"Ifit r"';.,Ltrt"'i.ti::,i,':.":::,,I:i.r ;',:,,ff"|i,,;"li;,,i,.irnt' ( l; l t lrt i v;triazii f ie prin nfro rrrr.rrlirirrrr r,,.n1i. .,ioto.,iti?!tl""J:il;tJ,']tutt

motorului Primar constarl.

I r r p l i rnrr l caz putcrea cstc c( ,a mai marc pcntru turaf i i rcdusl s i , r l r .l r rntr .nr . . r , Jrcnlrrr l r r rat i i mar i a l , , secundaru[ui ; in t imp ciIntt'r r.('(li'r;!, 1,,,t"r,,u ".i" -rii-n. a.tt"t de condiJii ,tr, '*.ti,I#llt #,l.llliclrrrl *r. ra.irr. r.onsidera(ic problema motoarclor p;;t;-;;i;;ehicole.

,t... i il. ii, lilllil,' T": 3ll""li xtif,: :itTlf ii Tf,i frlrliild;':1 j*Tfl :clnrl rnol.iLrc rlc crrrent elcctric altcrnati" a'" tlp'.i.i i.* sau cu rotor. irl*:rrrt.iR:rit aclioncrLzi. un utilaj printr_111 .";;";i;.. ^i; ';;

avca in 'ctlt,r.r,,:|.i]':i,i;1,:''1i,,,:i,in:T'i'Jj'J ':":,',";:r":ni:,.;j'n'i;;; .;'i;; potrivit p,'riri'

.u.,,.,,i,]::lf::i'.1;"1,]:;Hf ,*1:.:l,,,nii 1".3;:l::,,T:.: ::li":.?:[1',:il,iiliI t tc i t . r r rsunrul t le r .oml,rrsr i l r i l ; i , , r , , r f r - , , i " r i r i " i ' r i " j i " ' , , r ,n i , r r" .lrr orit t. irnpn.jur.ir i, I)cntru _o -

fu n<:l iorrarc cconomic:,l, cintl cstc folosil

l.ll,;ll'1;l:;:ll .,l',1"1,,:'lli:':iollr liXiill',,:::li;;il;l.llli;i.itlT;i,1,;;,l,,illti:,rt l l lr.zIrrI irrrl l rr rlr l i lr str:rrrrrl irr.rprrrrabir i v i r .z. i*r t , r l i r . , , , , , , , ,1 ' r l l ] i , , , i i l , , l i l t t r : t

( ) l ' s l l t : ' r .srrut t r l l l r : i r t : r ' r r r rr ' , r

x I t . t , ;zt , t . t i l t , t i At . t , t Al , t , ( : I Iut s(rN(: tTA, l . l tt., l / l l | | i | |uA (;(r xl,r t, l , lr,0tt

,"i,,,,1.11;,i,till';,,rii;l;';i'jl',,:,,':l';i;iil!lli'::,11,,:il-i,li:1,:li,rll,;l',,,1',,ili,,l,i;i;;lii,',( l . r : , l t r . l r l r ' I r , r i , t .u, . , r ' t , , , . t , l , , rvr l l l r r t , i . , i f i , t , , , ,1 ' , , , , . , , i ,a"" '

S iut lo l r" t t t t r r l r , r l r r r t r t r i In l r l l r l r l r l ' t t l l t " r t " t r l ( l { r r l I t I I I | | } I t I ' I i I ) i I I I I I I t '

( r ' r | r ' l I t r ' i t | t l0r r"rr l r r r ,1, , r r ' l r r ' " r r ' ' r ' l ' r r " l l ' r t ' l ' i t l r t l r l | t i l r r t t ( i ' r r

i . ' i ; ; i ; , , , i ' , , ' r . , , i . , r ' r t ' l ' " ' r r r l ' t t " l t l ' r l r '1" ' r t t l ' r t . i t t l . r i ' r r t i ; i tL : r r i r l " '

i i f " ' , i t i " r r t , l , t , r ' r t ' l r r r r r r" t I ' r r l r r ' | ' ' | i I | ' ' I I | | ' i | t '- l - ra l r t t r ' i r l l l l l ( l ' l r ' r l r l l l l r l " l r ' l ' ,1 t otr I | ' r r ' I t | ' t I Pt t lv l t iz ' l t t ' l l

t t t t l -Nl l st ' l l t r I

".''''i{'Jj'.ll',ii,',i11;;1;;;;-:, lii','l'ili"',,'ll;'i";l;l:,I'il::lil-J';ii'ljl',illll,,;iiili'::'l;i r r , ' i r r l ru l I r 1 I I i , : r i i i | , , r '1r ' r t ' r l ' 1 ' r ' r " izrr l ' i t t l r t ' r ' - r t t l " 5 l l i a l l t i r l r ' ; l l ' '

S-au prot lc l : t l . i l ( l ) t l l - i tLoi l t ( sot t i r ' ' r l ' i l l i l l l i "L f r fcvt 'n l i r ' l0 Ll lz ' ' r r '

s i r t r i rnsmit i scn) l l i l lc l )ut( ' l - t l i ( r ' i t t i r t r r ts l r t l t l t l t ' act l i conr l r r ls l i l r i l l i ' l ' r ' l

mrlvcrizat.t " ' . ' ' c" . . i " . r tor l . l l sonir : cste alc:r tu i t ( l in c lemcntt ' t ' t r i t i r loerr ' [o l r r r i r l r ' , l r r r

,.fr".ia"'t"r..l in1i itttttis" la un capiLt' rnontat(' p(' url col{\' lot ;rlttrr.rrl 'rl

i i ' 'n , t

f " Prts iun'a dc 3 r l : r \ /cm'?'

l . ig. l0: . - ( ;cncr l l r ( r r sG

nic: . i - colcctor drt t rF

l , r r r lor ( lc acr; I - . r . j t r ta j ;

. i - - ca)ncr i l i le rcTolratr t ' ;{ - corP cl( lDcnt: i i i i i

l . l | p istol ; 6 - rct l ( d" ;Z-$tst i l i ' ! ; S-Pirr l t t l

' l ( . r 'cglaj ; d . ' cr lmcrrrc

rrnrponer l t . / ( { lc fe;r ,nr{r l iu ' r { pr i t r . t

r r r i la l ' ) ru1\ , t r i ( : : . - /c( tcr ' { aarzal , ) f r lu i cchiPtt t ( r ' I qe'r . f r l

l , , rn l sorr i ,

ttt

""."..oJ.:,T?:)l,,,iTil.l?,,, n:lllllr. rr srn jrrr . rrecvcnf ci, resfr gL-:iin.qd#s',1ffi #-:l$,*ffi ,}f H-.:,j

t**pA*:tri:.i{'t*Trpft i:*'ru*::*t,:y*':.:l""riiffi##*ff**;+sfrq*,r*,rrffi*rt"n"i*i**l ;i:rtt,, -cere normar

"uti^, i"'., accraei a rzd. tor;Tr {: 1:{:t s;idr*rT},ih'T fi ff Tr? :,r,/fi :T,';l.;ff:

t6./.

o)

1

2

0

Fia. l0J. - Cimpuri lc chi-m/ce

- rr| flactrrtr: CO. _qroxro de carbon; Cd_

monoxid de carbon; O" _oxrgea; -.- rariatio ;._

triiffifdHf .,:.r,ii:n4Fa concentratiei ln Drrn-cte dtarnetral oDuse .i._.pArtate Ja 2'J0 mri, pe a.xarongrhdrnattr a flicerii:_r_._fl4cari obiSlnitl:-x-xJacdr{, vibtattr._ 18'-aflz; -a-a- flacdr{ vi_Dratd- l0 tHz. a_concen_rraF4 prodGclor de ardcreln tlacira obisnuitl /devi_Dret!); 6 - conccnirat iaproclusclor dc or( lere lnracara tratslil c$ (|lcrRic

sonrctr (vi l ,mltt) , -a)

c 02'02'co,f/.

. t1

t2

to

06

) -^J'Y- .4-- . . -1

::----':':---t'-

- - -t . - . t r .w t i - i f f i f ; t rNr '"qrth, ,,r,, ,,,,,, ,,. ,,ri'iorii"o'io, ir,,

2

ov vt vtr iiFfiN. sacl iuhi i normol. p, oro t*g. o f td. l larn

- Fltrcirilc produse in cinrp sonic sprc r|r,osrrlrirr, rlc celclallc sint scurtegi compactc. prczenlintl <lianietrc tlc 3+.1,5 ot.i rnai rcrlusc ai lrrngiuri crr6irca 35 o/o rnai scultc.

Intensificarea procesclor tlc ardcr.c ;ivolum mic in apropierr' dc gura arzirlor.uluivlbrate.

Analizind comparativ compozitia pr('dutilor dc arderc pc Iungirn,;aflnclritor, se constati ci in prezcnla cimp,ilui soiric gr-rsim compo;ilii s"irsil)ilegale ln aceeagi secliune a-fl6.c5.rii, ceei ce denoii buna omogcnizarr. yioxigenare a fllcirii.

Valorile care c racterizeazi cimoul tcrmic indicir faptul cir llrrcirrirobignuitn estelungi gi prezinti parliculc'solidc ca ulmare a calburlirii lr,rLrtiridicate ale facto"rilor 'energetiii de cmisie' pc inrreaga sa lungimc).

Arderea a fost apreciabil imbunirtiLJiti in cimp sonic, astftl: r,alot iltrtemPeraturilor reale indcosebi la inccputul fliLcf,rii inregistrcazir t't'r'Jlt.tl

Nt sccl tun" normdte pe oro loag o t locar,

o-.-?--..-------f

ryi,I

I Il III lv v vt v vltr lx x

I t t l l t tV V yl Vt t v t ta ,Nt Vtt 'u"" ,r t . . \et aa r.a ta.a a t 'atal

(x)l lcolltt irrca Il l ,crlri i int r '-rr lrcstc caracteristictr f l irt: irt i lot '

l ' ig . l0-{ . - ( iur l 'ur ih t r r ,Dic{ : ck f l {c i f i i r a i l . t ltor d. omisir ! f l | l r tat f ro.mal i { : ( ro) f i ) i . - f ro l , r fdc en) i i ic t ,n l t / r l r . | | l 'pcr . r tur i t r lc lu ' l i r l l . i Itc t l lporatr t i r R!ul [ ; , . . - .f l , rcar l ( , | ) is | |n i l l l j , - r - r -{ lacdrA vibrut l , - . . . l8 k l l r ;- -A- f l : rc i1r i , v i l ' r^ l lJ0 kFlz. , . r . vor i r f i [ f r ( . t rFr i lor dr : c l r is ic in l r r r rgul l lA.c i r i l , ) r ;6 - , /or i01i l r l t 'nr .Peratur i i l r hrngt | l l l l tccr i

lor .

o)

0,9

0,8

0,6a o.j,4

" ,

.0,3

o, l

0

t1@

tw,motno

D) 8' ,! eoo

100

500

1n

sensibilc, trrrrpcraturilc dc ratlilrlrr.sr. rrrlrrc, cocficit n{ii t.nt,rgt,tici <lc cmisir:l)rczinth vakn-i coboritt, pc lti irl ir lrrrrginx:a sa cu inaxirnc'spre intcputuli t ( cstcia-

,. M,odificind frccvcn{a cncrgiei sonicc, s_a obtinut o nrai buni inlensi_t lcar( ' la l rccv(nt( . mai inal tc.

,l n trnsi ficarr:a proceselor de arderc se datoreazit in prrncrpal cleclelor

gaz.odrnamlcc provocatc de _propagarea energiei sonice in amcstci, cu impli_citll l :rsupra schlmbulut turbulcnt de masi.gi _ cilduri, car,, facilitcazi procc_slkr dc Iormare a amcstecului combustibil. Omogenizarca amestec;lui siorigcnarea miezului flicirii acti\.eazi. arderea in t.ji .of,,-"i

"."-.G.--- '-

, ., S" plT ci turbulcnfa produsi. de cimpul sonic gi cea crcatiL de mijloacc

Ir i rsr(( j oDltnul tc se dt lcrcn( laze mai ales pr in scard.

_,,.._._l: ":,:lqti, tim-p .:c P91le realiza.qi o imb-unirtSlire a calit[]ii putverizirii(urtonla dezlntcgririi piciturilor de lichid, alit ca rrrnrare a implificirii

",yli!]rl"l proprii. iniliale, sub influenla.cimpului dc oscilatii sonici, cir .-i(ritronta! regtmutur neSlal.ronar al migcir.ii relati\c picirIut.i_Saz.

.. l-itla probabil 5i alte cfecte ale energiei sonicc, carc conduc la crestc-

rcir vrtczel dc ardcre, ca cele asu pra . structurii clrimici, a particulelor'dcconrbustibil gi a produgilor intermediari in di{elite fazc alc irderii.

Mctodelc sonice de intensificare a procesclor de arde.c a combustib ors iur dovcdit mai cficacc decit metodelc actuale. obiqnuitt. Accstea se pre-l.irzh ;rlit pcntru arderea combustrbili lor convenlionaii, cit ;i pcntr. ard'erczrrr.zirlrrrilor sau a combustibili lor de calitate inferioari.

. Mr.todelc sonice asiguri o ardere de calitate superioari. rndiferent dc.s;ur ll ir rnstalatlcr de ardere, in vreme ce dispozititele obignuite utilizatelt l)rr.zr.nt. produc numar o macro turbulenld, carc s(, dinrinrrt.azir scnsibil lasrrltirri rcdrrsc cind vitczcle aerului scad.

,,, _., -,lt,l!1,.r-l :i, p:itrt diferite valori ale frccventci sonice s-au obtinut|lir.c,rn cu caractenstlcl dtterttc, pcnnitc conc]uzia ciL sc pot obline flicirilrr proprietir{i prcstabilitc.

ln aplicaJii uncle metodclc 5i mijloacclL. obilnrrirt. tle rntlnsitii.rre al'r(x('s(Ior dc ardcre nu sint su{icicnlc, cind sc cerc ca" ar.derea s:, s(. d-s{;_yrirrc in camcrc de arderc mici, iar {li.cirrile si. aibi. incircirri tcrmice Joartcrriu.l, sc rccomandi. folosirea metoclclor sonice.

.. ..lntrcaga ccrcctarc estc in concordanl5 cu a{irmatia ficutil de(; . ( 'onstanl incscu in lucr i r r i l r : sal t ,_

y1t Dt,tst, tr t ' ot'r\Gi\t ' i ,\ (:( t i t,:\ l ,()i l s'\t(:t I, ' r, l \ r.t\( ir ttt _\ttr:_,ttL.:ln, sr [ ] ! .1 ' t . r ( . t l t r l L; \ r . t \ t , t t t , t . t . t ( r r ( t , j . l \ .1t .0( i r , t ( : t ,Lol t sorr | r . lil.:.

( ; ( ) i l l r ( o l r l r r r r l int ,st : r r i r r r r l l i r r r r r l c ; r l ) i t ( ) l a l t r : r l i t lu l l l i sr . r r r sr . , , , t r r r i r, l , prr ' l , l , r r r r r i t , z , i r l r . ,p l r '1 ' . r ; . r r i . r r , r r r ' , . r r l i l i , r sr , ;1 i1 i ,1, , ; , ;q j1s*,r1 i i , , i i i , , , . , , , ' , i i , .l | | l r l ' r : . t l | l ( . r t , . r t t ' U l lornl t ' r r s l r l ( i r r i r l isr l i . t r . r { 'nt i | l i r r r l , , r l i r r ( | l l t i r r r r i t i l i , , .

l , i l s l ; r l r i l r ,y l r . i rst lc l r . iL rrr . r . i rs l i r , , , i l .z i r . r l r , 1rr . rDr1gr11r. 1 l , , r rsr . r r r . r r , , , r l r r r i i

l , ' , , r1, l l s l ' r , r i t i s ; r r r l r . r l r rs i ' r Lr1, , , l , . r i t , ,z . r , l , . 1, i , ,1,"g. , r , , 1r , , I i r r i , r r r r r r t , , r r r r . i .l l l l . r l lx l l l . i l ' r l t \ l i r t | l i r . l i l t r r t r r . i r r r l , . . r r r i t r i | l | | I r I i . r . I I | | | s i r l , . r r . r t r r r . r l r r r . I ' r , l r r i r ! i| | | | | | | | r . | : r , I r t r . r ' i t t ( l l t r l r ,ZVr ' l l . t l . r t t t l r r . r .Sl r . i r l ) i lo l . , . i l t - l r sPtr | l i t r , l r , t , l . r | | l , , , t t l, l , t r r r , l '1, ' . , r r r l ,1, , r . .1.r ' l , r l . r r l r { r l r r . r r r r l . . , , , i i , , , t , . , , i , , i , , , , , r , l , l , , r r r ,

Irl

souic carr : i - l Plrrrr is l r r i ( i r r r lgr ' ( i t r rs l t r r t l i r t l r , r r r ' " r l r . l r l t t l r r i t r l i t r r l r l i sorr t ,

toate rezul tatJ le olr{ in. . tc tk: ' t . l t t . t | ic i . 'u i i r r l , l r r r r , , r ( t ' ' ' . ' l i l I ) t r t l lc t t t r t l ' ' i ,

vom obl inc.c.1. .1 i t i 'z t t l latc i t r I I < I I l l , t I i t I I . l . r ' l r i r r , r "1" ' l r \ i r t r r l r ' t l t :

( i t ' . t 1 i r 'Constant inqsct t i t t r lotnt t t i t t l sot t i r '

. in part icular, vom putca ( l ( l lcr t l l inr t l t ; l l r t t r t s l t t t i t t i lot <l isctr ' l t r ' r t ' '

introduse pc o l inie electricir uniformir lrrDgri, srr i sPrltcrrsciL :r(( 's1r' l1r vllr ' /..1

d" ptop"gi ." a curenl i lor ; i tensiuni lor c lcpi ; i t r t l .1r ' i l t l ( ( r rst iL l i l ( 'z i t ( l ( l r r"Das;re tluminii $i anumc -j00 000 lcnl's, t l irt [ i ind ci vitf/ 'rt r lr ' plt lt ' t1i ' tt '

i iurent i lor pc o asemen( ' i l l in i , ' s , ' : rpropi ' dt accasl - t ' . r - r t l " r t '

Si ' t raduccm acum f i ] l imbai i lectr ie mcto( l ' t { "1 ' )s i l :L t l ' ( ' r ' ' r t1; ' '

constantincscu pcntru calculul r ' i iezei dc propaglrc 1r' ' l irr i i irtr ' ; i lr"rl,.

metodi exprimatir in limbaj sontc.

Astfc i f ic L, C, R, 5- p.Lranr. t r i i l in ic i uni{ ' I r t r ' r ' I r i I I r I ' I I I I ' l i t t t i t

incircate; 11, Cr, R\, '9r par- imctr i i sarcini lor ( :o l l ( ier) l r ' t l t i r r t ' ' ' r I r I ' l r t

ser ie de-alungul l in ie i ; l r , Cr, nr ' f , parametr i i srrrr ' i t r i l ' ' r t . ( ) | ) I i I I | | | | | l r l

der iva{ ic pe " l in ie ; i L ' , -C' , -R' , .S' paiamctr i i l in ig i 11 11 i f t ' r ' r r r r ' t I r ' I t t r ' ' r t r ' r I r ' '

George Constantinescu denonstreazi cd intre accftr l);rr'rrtrr' lrlurmi.toarclc re'lalii :

L : ' L ' - (Pl t ) ( t lc 'az - I ' , \ ,

R : n'+ (1l) (Rr 1- l /sl) 'C : C' (:PlI) (I ll'2a'z - C,),s' : s' + (!lt\ (s, -t 1lR2)'

i fi ind numirul total al sarcinilor concentrate' 1 - lunginrcr lirri ' ' i ;tpulsaiia'r' ibraliei transmisi..

Si presupunem acum, sPre exemplu, c|r am xles pr'(, :r"tfl l

L' - (!lt) '11 lC'a') : 0,

iar pe l, astfel lncit

C'-( l l t l ' ( t lL"a ' l :0

Atunci relalii le (t) 9i (r) se reduc la:

L : (.plt\Ll. (n)

c : (!lqc,' f,,)iar v i tezele de propagare a undci pg l in ia-neinclLrcat l ; i .Pr. l i r r i r r u i f ( t ln lc l

eihivalenti l iniii l ircfircatir, ncglij i;(l picrtlerile datorittc lrti It ;i 9, vot fi

datc de

{r l( / )( r )(4)

I r ( | |

(0)

| / )

i l

rcspcr: l iv , i ts l f r ' l

l , , l l r r r i r r l ru I

( l (D

( )

( | , r )

( t t )

II

a' , I lvi:c'

( t ' l t ) .gv t . t t4]) ,r) tll/ r.(:l r rc l t

r t l l 11 I ' t 't t t l f ' 1. , ( ) r '

pr, .y ' / / l r r l r l r r ' l l l i i l r ' ( f i ) , ( ' / ) r r l ( l , l ) , r ' l , l l t r ' ' t r l

t ' l t " I lV I l " t l l t t '

. l )ar , l - r ( rax - et cst l r l lx , r t l l ( l i r r t t ( ,s( r ( ' t i r r / . r ( .2d! cr r i rpoi l r r l < l r1 l r , .dcnvat l ( . .

l r rkrcuind in rc la{ ia ( t3) , ( ) l , l incrn

. Dacrl vrc.r deci ca r/2,,

ala' : I lv 'r%' (11)

::nitJ;,tt,",.1$:i:ii*"\:*#:'Jh:,+"i?",i,,:.#'"i::,trT*::l*l.si.i i'ii'itr,';;ir;'iJ'::,:"" a liniei ncincircat", r,n li

o;"1,'?;i:."*:

llti:l ;fl , :'&i:,'l' b'i I ill3, ::.x;l,ti:i*$"1#,"i',L:li; b,,' z, i"t i,r".

rr. irclrrnt. ' lc dc masi f i elastice,rclctanl(' le elasticit gi de masa,

Fig. l0-5. - I-inic et{:crriciechi /a lcnla I i , r ie i i i rctrrcate.

Ac Dl l \ l l \ l { ( ) l \1. \ N.\

l icdinlr d in l { t , , t i . t r r l ' t , ' l ' ,1 ' )

corI t:tu\'l'A

I | tut tnglnrr (;oGU (:a)\S t, lYt l i \ l ls(:U

,, . ) l l .v i ' * ,1, . , r ( r . r . . r c l r , , ; , , t , r , I | , . r I / , , . I i | | i , | , | , r I | | i l l , , \ r r r , . t r ! t r , . . , rL, ,L , r , r , , , I t . ,1,r , !r r t ! , ' | ' tx . , . r f ' , s t i j l f , ,

' , rL1 , l . . , , , , i , , r . r ,n r , . r , l , r I t | , , r r , , , .n, , , , , . , . i , , , , , " . , , , , , , , , , . , , . , , , , , , , , , ,1, , r , , r , . , , 11. . t r r , , ( : , r , , ( , . ( i , , , . , r , , r , r , , , , , , , , r . , r . , ! , , , , r , , , ; , , , , , r ; . r , , ; , i ; . ; , , . ' ; r ; , , ; i , ; ; , , , r , . , . r ,n, , . , ,1, , , . .1r ' , , i ' ' l t ' l r , , r . l , r r t r r t r t r r r t r , . , n,r , , , , , , t , , . r r , . r r , , , , , , , . , r . , . , , , , , , , . .1, , , t i ; ; i ; ' : , . , , , , , , , , , , , , , r , , , , , ,r . ' r , , r ' f l , .1 ' r t l , l ' , . l r rxt . , r t , , . t , , . , r l { ,1, , , , . . , , 1, , . , . , ; r , , , , . . , , , , , , ; ' ; ; : l ' ;

.r , r ' r , r r ' , ' l r " ( t ' r " t . 1t . , r , , \ t , , r r r r , . ,h,

I)oannior 9i Dotnnilot,

\-oi inccpt' conlcrinta 6u 6319 voi alca onoarea a t ' i i t l trcl inc l ' lrr ' rrrt l

uruliumiri le meie domnilor mcmbri ai Academiei Romlne, caf(: rni irrr l ir( rrl

d.oJebit^ onoare de a mir inrita si expun, ir.r fala unui aurlitotitt t l i tItrr: '

unrczumaltal lucr i r i lorr . t - rc lcasupraapl icaf i i lorv ibra{ i i lor in, t ra l lsr t | l l . |1. |cDergici mecanice. Aceastir sali este ull sanctuar al ltuntcl roll l i t l l t - l l ( rr rrl l

;;; i i-;"i dc vencralie gi cu oarecarc teami ci nu I oi {i la inr-rl{ inr.rr ' '1teotiri lor dr'., r 'oi ir itra in subiectul ce-mi propun rr dezlolta itr lr-o 'rt ir 'i l . i^ltf"l. r ' i oromit ce aceasta

'a fi maxim.l de tirnp, in car" r '. i alrttzrr rlr '

pacrenla o1'.

ln aceastir conferinlir voi trata despre o it i intri noui l i autrm( : itrrrrl 'rcare sc ocupi ctt transmitcrea enerBler lnecanrc( Prrl l \IbrJ{l l '

Cuvintul sonic are oarecare analogie crt -sunctrtl l)clrattct' qtl l tr '1rl l

sint rezultatul vibra{ii lor, denumirea dc sortic sc Potrrvcltr ' '

Aceast i t st i int i r este foartc t in l r i ; i pot z icc c i r cstr ' o l i ic i : r r t t r r r r r r r r r ' l

ntuzicale. inrudir . 'a estc cam ncastePtxt ' t t leoaLtt t ' l l r I ) ; r l " t r : i t t l l tz l t ' r t r r t

arc ce c i ruta ln chest iuni t lc : r t i t l in i , io.otnt ' t i r ' , . r ru l I r r r )u l r i l r '1 i i r l l . r r1 ' l t " ' l t t

a lc st i intei sonice. Sin1, d,al t t t l , ur tL l l t carL ol ' i l t t r t i 'sc:r sr 'P ' t r ' r ' r t l ' r t l ' l l

int i 's i i int q i ml i mul! i act i cnt t ' prct inr l c i -1, s i - r l i i orrr ( l ( l l i i r r l i t r '

Ui i ie l "" f r : r ru i s i stai in iSis i ' t r - r r . Iu l r . rator cu st ic l s i t r r r r r i r i i r r i , i , r t ( l . , i . r

vrui sir ;Ludie/,i o rrroblcm.i dc fiziciL-matcmatici-t, ntt c ir l)5(thrl lr{(r" 'rr "l

tc ocupi clc Haydn, l lccthovcu silu -\Iotzart.l )eoarccc estc obicciul de a su {ucc c i tc urr is t r l r i t i l l { ) r r ( ( r ( ) t I | I MI| , | .

i l voi facc 5i eu; t lar ar :cast i inten{ ic i r nrc i l = i ' r Du- r ' .1 i r t ; r i j t ' t tzr ' l r r | i t r r r l r l l ,

dcoarccc, f i ind i ,orba r1c o; t i in! i r 'no. : ! , . r r ro i tnct lu. is i ' t ic t t l r t t t t t ,1 1; t

Greci sau dc la l{orraui cli ntinrai de-aLia rcunt 20 rlt ' irni ' <ll citt<l ' ttrtinccDul : . : t I I r i t ocul) r r t stut l iu l l i l ' ra l i i lor . Ci t s i l is i1":" <l t i t l t l : r t i i ' i t t : ' " r ' r ' t t r r '

umb' l ' i - , r l , 'b i . r r t r ia l i , l in p: t t t , i t r lv .c i t i rcL's( str l ( l i l r l - i t ; l i i t r r r 'pr t l l ) r ' : r t ' l t t r r li l i i i i " tnn."k dc ztn"u sau ur.r . ip l t , lc dc la I lo l i , l in s i l r - t in[otr t tcr i11 .1, , l r r ' , t

t i i t i i . i r r . , atun<: i . r 'earr t l7 nlr i inr ; t l i ' i l i ; i i t r ' ' r t t t t ' t t r t r : r t { i i t

'1 i t t . t r r l r t t t t t '

la pian. ' I ,c acci l v lc l l l ( : ro i l r l ] r s i r i r r \ ' i " r { l r . ( ) l i i t l t r l t l<, t l i , i t l l t tz i . i t l r ' , , l l r t , r t t t t r

t t t t ar l t pr ict 'pt t l t t t l r r t ' l r t t : t t t t l i l l c i r r { i l I rL: l t t l t t0t t i t ( ( ' l l l i ( i rzt l r . t t i r i t t t r t i t t i '

an in l l i ' l l l i ls a f l t t : t ' s i t4. l t t t l r l ror i r ' : t ; tcotr l t t t i l t ' t ' t t l t tz i r i t lc l ) t l ] i lzr ' l l r ' r l '

r r r r l i r ' , . ( l r t t t t l t l i i r t t i t l t t l i r i l ( t ' i l r ' l , r . r t t l l ' t t : , i l s i r lcsct t t t i t t t t tot l t t t t I | | t t t t t i I t ' t

Plrr l r t t r t t i r r ' l , or i r r l t lot i l t t l iL, t i t t t t tot t t l t 1rr ' l " rz ' ' ; l i i r r l i l i r r " . Arr" l l r t i t t t : r r""

t t r - r t i t r , r t t , r i ' r l i . t r l t t r (ot l l i t r l l , r l ' ' r " l r r ' l i ' a rr l ' r ' r l i i l ' ' r i { i r ; r r l i r r l t r ' pt i r ' l l t t i t

r r t , ' i l l t , r t l l t t l l t l r l l l l t t i l ' r t t t

I r t l , r , " ' l r l r t t t t l ' r l ' r r t t r t r r ' t t | ' | | | ' l ' l l l r l r ' l r l ' l l l l

' . t t l r l | r l . , t r t l l t t \ l r t ' l "

. l l l l

,,,,,,ll'ii,igi,f "lilili'l':';'\,;::1t":1,,0;:1"'1" pierrrerilor nu schimbi esen

,,i"' "ll:;,x:l,ii1^:Tl'.T.tr';,1"""'"'ui

rezultat parad"xal: actuala teorie, una-

ilry,?l,,-..3.lli.'Trsl fi ff i:'ifu,:l ffiiTj,:iIi.",l",krJ'li:,,e#ii.,*: .f.*;T:mil;lJ,:':'*i: :i:::,U:milititrj1",1..,,';::ryr"fl I'Jr:l"ltrX.H:tli:li'uii":llT"'T a-,i'i"'i"'r'onau'to'iio.

".",,.i;"ili:1'::*:'::f.ttTT"lt--11-:1':"T "jo"' nu.race decit si'r conrirmen,,,. int"i". i'"#.l"ii'],'J,i ii.." il[i,1ti"J"Tj#tl J,,.?:lt"u de ccr mai,rlilllii'i:"',?T"ffj;:ii'.ili""'""'ii'i;;"-;;;,;i-;i;o:-u:':it;l;::.ll-lil, :| 1'.,,1,.,g:,'pii,i,,r".i'.i',1.;'::,1':i,l:li'i,li:l!i ,l]T.i,ii',i,,*,:llili ' l i,;]'],l,"llli;li ': ' l i ,l,i;Jllu,,,l ':ll: ' l".lll lli ' i;i, 1'';","i11',.;,,i ', ',,'ri-orrrirrultilir,,,rirr,.,rr ,, ,r,il,,,,,"iint-'i, ,i;1,:i,,;:l,l"lli;,li,,il:;il:li'';tll,,;,;l,.;,iii,:1,fl l:;l-l i l ," ' ,1,i,) l l : i l :" ' ;] i l i i l l , : l l '" l l l l i , l l ' tazrrL,.r.rir i, ' , , ' ' , :,,,", i ' , , ' i , ' , ,r.,,r:, 1,,or,i,.,,,{ i, :rr.rrrir'.r,r illirrl'ill;l:j',.;i'ilil'll"ll..ii' liil,t:ll:"1;i,,1;11'

[l

Strr l i r r l I ; t r r I t :ot t l i r r t t ; r l ( lu l r , r i r i r , r ' r l ; r r l i l l l i l r : i r rs l l rLrncntc rrrr tz ic;r l t , :arn s l r r r l i l r t t ronr lx: lc l r . , tu l r r r t ' i l r . r r , r r . , l i , , , r l i lc l i t r , [cmlrnctrc ar:r ts l icc y i incetrrLcrr i r tcclrr l r t t - i r tn f : rut i l iar iz l ! t ( r l , r l r i : r v i l ' r ' r t i i lor .

ln rc i r l i latc, sunctclc nlr s i r r l , l r ' , i l r r l i r lnr ; - r dc cncrgic 5i t lansmitcrc i lsrrrrr ' { r r l r r i cst( ' ru l caz part icular rr l 1r :ursur is ic i dc ener3ic. Accast i t ransmisicsl f:tcc prin undc sonorc ;i atunci mi-atn pus problcma: oarc, dacii energiiir (:iuiit:rli foarte mici cum c de exemplu energia unei trompetc, se potIlrrrrsrnitc Ia distan!5, prin vibralii, nu cumva s-ar putea transforna acestevilltfi i in energie mecanici ?

tintlcle sint de doud. feluri: sau le transmitem in aer, sau le transmitemirr lrrlruri. Primele sint undc sfericc, care se pierd sau se distribuie imprejurulrrosllu fi.ri. sL le putem concentra; pe cind cele din catcgoria a doua sintrrrrL: concentrate in tuburi, pe care le putem conducc Ia distantir. Exemplulccl nrai simplu de unde conduse la distan!f, este transmisiunca vorbei printr-untub: tlacir vorbim la un capf,t al tubuLui, vocea se transmitc' pini la capi.tulr:cliirhlt gi toti ;tim c5. foarte pulin din voce se pierdc. Sc poate lntimplac;r vorlrcle si- nu se inleleagi totdeauna bine, dar cnergia se transmite cufoallr. putinc pierderi, asa incit un tub acustic reprczinti" o linic prin careprrlr:rn transrnitc cnergie, fi.re car aerul sl circule dc lir un capirt la altul,

Vilrratii le sonorc, pc calc le transmitern printr-un tub, au o {recven!5.rL.slrrl rlc inalt:-L ;i de aceca se aud. Am putea conccpc foartc bine ins.'r si vi-lrrr{ii crrtt'nu sc aud. Dupir. curn in luminiL sint razc carc n1l sc vircl, tot astfellx,l l i slrn( l(' care nu se aud. Sub o anumiti l init:r, 32 r'i lrralii pc sccund:-r,rrrrrr.lrrl nrr sc mai aude; iar pcste o anumitar limiti, pest(' 20 000 \'ibrafii1tr.srtrrrxll, iarirgi nu sc mai audc. Aga incit, ceea cc se nume;te, in vorbirecuri.ntir, suuct, este gama de transmisiuni vibratoare, care sint pcrccputc desirr(uril ' nolstre. Astfel fi ind, intensitatea unui sunet nu cste in gent'ral orrllsur'li a cantithlii de energie care se transmitc prin tub.

Problcma dc a dirija undelc prin tuburi nu prezinti. nici o di{icultatt';singura dificultatc este dc a concentrir. o cantitatc importanti de encrgic.

Ilroblema transmisici cnergici prin vibratii rni-am pus-o in modul urlrfi-tor: la capf,tul unei conducte sir produccm vilrratii, rcprezcntind o energit:considcrabilli - conducta ne scrveftc de mcdiu dc transmisiune - iar lat:aplLtul cellllalt si transformim vibratia iari;i in energie mccanicS,.

Problcma este destul de grca din mai multc puncte de vederc; undel'<:irrr: sc transmit prin aer sillt necesarmcntc loartc slabe din cauza marii elasti-citl.ti a aerului. De aceea am invcstigat;i posibilitatca transmisiei prin altemedii;i anr studiat in special transmisia prin tuburi pline crr ap.L. Am con-statat, ln mod tcorctic, cir s-ar put('a transmitc cantitil i considerabilc dccncrgic vibratoare prin lichide. Intrr:lrrrinlintl o frccvcntir ricstul dc joastr c:rsL nu sc au(lh acost('un(lc, nc girsim in prczcn!:r rrnui fcl tk: curr.nt, pc cirrt:-lputcm tmnsrnitc plin tul) li r:atc rrc foirrlr: m:rrt: analogit.<'u crrrcntrrl ck'clrir',duplt cum vc{i vcdca rniri tk:1xrrtt.

Nu v<l i int lL in <Lrt i t l i i l l tc i r : rnr i r . t t r rn l i tc tsrrpr i r l t 'or ic i r r r r r l l l<1, iusir l r 't r r l ru i s i t v i t r larr c i tcvir r .x | l ica{ i i : rsul t r r r ' lcrrrcrr lc lor crrrr ' lar : c i t o t r rnsrrr is i r ,l r r i t r l r r rk.s l" t f i r . posi l l i l f r . Accsl t ' r , l r . t t tct t i t s int :

"hsl ic i l l l t . i t , r l i rs l t , f r lc iur . r r

; i 1r ic l t I r ' r ' i I r ' .I r r r ' r .p l r r r l l r r r i i rxr t l l t t r t l t i rust t t is i r r r r r r l r f t r t pr i r r i rp i ' r , pr i r r r r r l l r t l r r r

( i r r r . r r i . , l iut ; r r rs i r lo: l t t r . t r . r i l i r l l r r r I i r i r r I t t t i I r . r 'ot t r1r tcr , i I r i I i I I r t , I r i r ; rc i , ( ) r l i r l , i

l r ' r - r l r . l . t r t r ' t t l , r t l t t t l r , r , r ' l t r t l r ' ( l r . t t rotr \ l l . r r , r : , r ' lxr l l t ; r t r r r r r i l r . 1111r l r ' I t t r i r1r , r

1t , r r r , . , l r . r r r r r l r . , , r ' | r r l r . r I t t l , r , t t l , , t t r r t l , r r r , t l l t t t . r l i r r ' , i r l r r r r , r r I l t r , r . r , l , r l r l

r r . lz i i i r r l rcrrs i ic i "L tcor ia l i l r r t l i i lor :Ltr i l t t , . I ' l t t r t t t t t t r t t r ' , r l i t t l ) r l r l ( I ( | r \ ' r r l ( l t

t t ,o l l l i r ' , r ,s lc posibi l dc a l ransmi l t ct tct l l i t r l , t t t t r t t r t l l r l i r i jatc i r t t r r t t t l r t l '

pl in crL apl.Elcmentul care a fost foartc mult (rollt( slrrl i tt pt ttcl ici-1, a lost cottrltr. t

bil i tatca apci. Existenla undelor in apir cst('t;r irrsirl i rI probiL cir af,l ( 'slI t|)t||presibil i .

-Dealtfel, s-au ficut expcrientc foirl l( ' r ifNrroasc, carc tlt 'ntott"lt rrr

comprcsibil i tatea apci; cu toate accstea, prinlr-o tra<li l ie lumca I losl .r{lrrr"lsi. cieadi. ci apa este inconpresibil i . Ccl mult st: admitea c[ apa, (l l( i i lr '

comprcsibil i , eite cornpresibil i . intr-un grad aia de mic, incit si porrti l i rr '1ilr

iat. -Totuli aceastai compresibiiitate a apei nu este neglijabilit.

Sir vi. dau un exemplu: si luem o conducta de 10 km htttgitrr ' ,t , 'presupunem ci la cape.tul acestei conducte ptnem un piston pc citt , l t t r t ,,, r t tr

alteruativ cu o manivele, conducta fi ind p1in5- cu apl, iar 111;111i11111 rl. rr

lungimc, sprc exemplu, de numai 3 cm, invirt indu-se dc 1 00o r'r i lr ' rrrrtrtr IPrin invirt irea manivelei se produc pulsali i in aceasti. conduct.-L tl, 'r l ' .r | , lcapiiul conductei punem un rezcrvor, care s[ menlini condrtt lrt l) lr lr 'r I rr ,r lr 'rDici am calcula ic trebuic s5- sc intimple in conducti in t inrlrrt l .rr lr.rr,rlr lpistonului, negli j ind comprcsibil i tatea apei, calculul nc-at rltrc, lrr tttr t ' ;rt l

tat absurd, anume c5. presiunea trebuie s l at ingi 30000 rr l r r r r rs l r r r ' \ " ' r ' t reste o absurditatc pentru cit, daci facem experienll l, Pllcti( rr tr"l.r trttrtt,tt40 atmosferc. Iat i r pr in urmare cl nu putem s. l l lcs l i i : tnr cot t t1r t , . t | ' t I t | ' r I r , r

aPer.ln fond, ce se produce in aceast i conduct i i ? [ ' is lot t t t l t t t t , t t t t ' l t t r ,

Droducc o serie de unde: aceste unde circuli. in conthtt:t;"r ( rr vi l{ /.r 'rttt, ' lrt l tttinergia pistonutui se t ransformS. in encrgie v i l r ratoalc, ( i r l i l t t i r l : , , r1 \ l l r , t , lsunetului in api (cam 1,-5 km pe secundi) i i s( ' t r lnslr i l ( r ' i r l r I r , r l , i l r r l r r ' l i llaLt al conductei.

ln hidraul ic i t , mai toate t ratatc ' le incclr t 'xpt t t t , ' t , r r str t , l i t t l t t t . r l t t t t t i t t r lc i apa este incomprcsibi l i r sau ala dc pul in cor lpr ls i l ' i l ; ' r , , . r prr l , t r r r t r '1 ' l t1rrcomprcsibi l i tatea ei . Unn din apl ical i i l t r h ic l r i r t r l ic t , r ' i t r l s r r i I t I t , | , t t t t t | , t | ' l 'aproape o sut i r dc ; rn i , a lost Pomparea i rpei i r l r r r i r r r ' . I ' t i r r r . r i r l r ' , , ' r l , , t \ r ' r r l lin mintca l lnor oatrcni , care nu St iau (arr tc ml l l l i ! , : t lo: ,1 ' . r t t t l r , l ' t t t t t l r / t r rpomDi in l r rndl l rn inci , i rct ionat i t dc c loui t" colol t t rc l ic l t i r l , , r r r t r ' r ' , r l l , r r r l ' , , r , r l ; liLtt:mativ priu doul tuburi. Plccind de la ipotcz,rr, ( ir ir l) r , ,1, t t t r , , t t t | ' t r

' , t | , t | ; iq i t in ind scanra in c; t lcul nrrrnai <lc iuer! i lL lpci , s- i r r r ; t t t t ' , l r ( r , r t r , l r r r i { l , r r r l r r r lmai iDi ( lc lornparc in c i r t - r ' , in t lot l r l r tut i t l , t rur t r i l t t t l r l r ' l ) l l l " i l l l t l r r ' l t l l l r l l lestc ( ,x l rcr l t lc t , ' t l r rs, lO+20. Accsie l ) t i r i i t l i c \ is t i t 1 i i t t z t t t i t r l r ' , t ' . l , rzt . r r tmrtx i t r ru l r rut t t i r ru l r t i t lLr I t ' r 'o lLr{ i i , (ar( 's- i t l ) t l t l l t o l )1! l t r ' ( l l i r r , l l , l r l | ' t r r . r ' ; t t r t ,r :stc r lc 30 l )cr l r in l t l , Or, r ' r t r tut lu l i ts iL J lc l l l i r i i t r i c i t t , : i r i ptor l t t r , t l . r r . t l r , r l t t lunt . i conrhrclr ' fo l r l l l l t t l l l i l ) (s l ( ' . ] (X)0 l tu ls i r f i i 1x ' t r t i t t t t l , t t t t t t t , r i l { l r l l l l ' ; ln- i r r r r r rcgl i j l l c t t tn l t tcsi l r i l i l r t l , ' r t r tp, ' i i r t i t I r ' t t | , ' I t ' t t t , I , : i i r t t t t pot r t i l ; rs l l , l , l ll r r ; - r t cr t is l t t l r i u{ iot t r t I r ' .

t ) r rc i r ' r r l r :u l i r t r l i l l r i r l l l , , l r r ' l r r r i r ' , i r , l t t t i l l t t t c i i , l , 1ror,rr l r r r t r l i 'y ir ' I l r r r I i l i I r r I r ' : r ' l i l i i i r i l r t l l r t r , i i t l t i r ; i r ' , i t t l r I r r t ; r I t r r l r r i l t l i l i i r l r ' l t l . r l r ' l i i i , I i l l is i r r l r r | , ' r ' I r r I r ' ' r i nu i r ' lx) i r r , l i l i i ; r r r i , i i r r , r r l , r t l r r i r i i r r ; ' r r r , l i r ; i . \ lo l l i t r lot t r ll r r r r l i { i , r r t r r l i , ror i i t r I r i , I r , r I t I i , , | , . i r r , . r i r r r ; r t . r I I r ; r t 11.r ' , i r r ' , r ' l l i i r l l , r : , r r t t i r l t t t i t ir l lvr , r r r , Nrt t t t i l ; r l r l r r t r r I I | , r I r ' t t t l t t I r l r ' , r l t . r t f r l , r l l r l t t l t l l l l t l t l l . r ( ' i r l i r I ir . l r , r l t r , r r r r ' r , r r t r j l , r ' l ! r ' , r l r ' l t . t t t t t t i l , 1, t t r r t t t t , l , ' r ' t l r t t l r r ' r t , ' l t r ' . r l l l r '1, r" . l r ' ' ; ir r r ' l r , , l r , , r l r ; r , i l r r ' l r41lr . l r I ' r r lx ' l r r r r ' , r r r l r l I r ' l r r l l , r l r r r r l r l r " , l r r l

" i ' . r ' , r l l l l l t r ', l r l , r , , r l l r l r , t , ; t l l , l r r , l , l , l r l t ' t t l rn rrrrr l , t . t l , t l r , i , r l r r , r l , r l t t r t t , ' r ' ; r l t r ' ,1, 'l l r l t r l r i r l r l t r r ' l ' l i i t " l r ' l l l l r t t l l l r r r , r t r | r t t l ' t l r I t t l r ' , r l r ' r , i ' l r ' r / \ l l r ' r l i r l l

. r l i r r l r t r ' \ l ) t r i ( , r )1r , r i l l rorr . r ' , r . r i l , r l r { ) r . I i ( i ( . I )1 i r ' - \ i rc l i i rsul) ta coml) lesar l ) il r l i i ( i i ; r1r l i , r rL i r r l r r i , pr , t ro lu l r r i , , i r r l lor r r l l t ( . l ic l r idc, l )ar cc c cul ios cstc c i lt ) i t t t ( ' l i l t - i t r l i t t i r t lxr t t i r t t { : r I r . r r L i r r r r r rvcrr i l . i l r r 'qstol ' oxpcr ic l r te, g i lumen i rlx ' rs is l l t i l i r i l r lc i r r a corrs i tLt r i r l i , l r i r l , lc l i r in conr pt 'cs ibi lc din punct dc vcdcrePtiLt:l ir ' .

' lolLtiL luttreu cstc rlt rLtorrl t: iL otrlul cste clastic; or, a admite ci-Lolchtl cstc cl;rstir ' , r:sie ir :Idlrit( r ' iL csr, r ' critaptcsibil; toli ingincrii admit elas-licit lrtct ofelrrlui l i construircir. r( 'sorturi lor cslc bazirl l tocmai pc comprcsibi-l i tatca;i cltstici-. irtea lrri. Totugi foartc mull i ingincri considcri apa ca incom-ptcsibil iL; l ir construirca pompelor hidraulicc, foarte des sc l ine seama dc

'' l irsticitatca otelului dar se ncgli jeazi c.lasticitatca apei. Or, proportia intr! ':r 'r 'stc douir clasticit i ' l l i cste urmetoareir: olclul alc un coeficient dc clasticitatcrk: 2 rnil ioanc kg pe cm? pe cind apa numai de 20 000, a;a incit apa este dc100 ori mai compresibilir decit ofelul. I)acir am lua un tub dc un mctru lungimc,l-irrn uurple cu api gi am suplurc apa la o prcsiunc de I 000 kg pc cme, amvdloa cir aceastl coloani dc api. s-ar scurla dc 100 ori mzri mult decit o tijdrk: f icr la aceca;i lungime ;i care ar f i comprinralir tot cu 1 000 kg pe cmz.

0 alti. cauzi Dcntru carc cred cir nu s-a irirrns rnai clevLcme la transmisia(.t)r,ri i ioi prin vibraii i , estc rrn fci t lc conveDti,: irr lumea ;ti infif icn, prin caresl rrl i tmiL cir cncrgia dcgcncr:cazi-L cincl sc triur:; brrriL in l ibra{i i. Este ugorrr lt;rnsllrrlna combrrstibilul in ciLldur':-r, dt' t.xcnrpl'.1, drLl cste Ioartc greu s6.olrl i i r l in cirldur ir" comirusr.ibil. Tot astlel s-ir putut clccle eir, d:rciL cnergia seItir l:r[otntir rr:1c-,r ir.r t ibrati i, r 'cciproc:r n-ar i i posil) i l :1. \u (s',t totu$i nici optolrir sl i irrf if icir a accstci piLrcli, ir.r catr, t lcirltfcl, f lr n-arn crcztl l, 5i atuncittt i rrl I,rrs prol-rlema inlcrsl-r: sri transforur l i lrrali i lc in cuutgi..

Sirrt rnulte fcluri dc e erqii carc s(' tr irns{ormar (l intr-una intr-alta:rnrrl l sirrt lt 'r 'r:rsibile i;rr altclc i ievtrsil ' i t .. \u tla aia dr: u;or a prcsupunelir vi lrrrr\ i i lc ar i i o formir dc .rr. 'rgic revc.rsibil ir i l i cncrgic mccanicir cu cfi-cilrrtr 'r irrl l t i . I)caltfcl, nu sc cunoaitc <lccit urr silrsur e\cmplu dq ,- ne rgie'vilrrirtoirrl rcvtrsibil iL in cncrgic mcc:ruici., ) i accasta lstr L'ncrti ia curcntu-lrr i r lcctl ic altcrnattir ' .

l 'r, cinrl l iLccam tco:-ia vibrati i lor-, am girsiL in {orrnulclc rclative la cu-lr.rr(i i sorrit: i citeva rclati i carr: scmirnau {oart(- mult cu cclc cunoscute inclrr ' lr ici latc. in loc dc a face tcoria vibra{ii lrr pe bazelc urmatc, dc pildlir lr, l .rrgliLngc:,; i Iord l lal ' leigh, am luat-o pco calc rnai practictr gi, in loc drir plct:a tlr: la ccuali i le gcnerale sprc rr rLjungc la particular, am plccat de la

lrirrl icrrl irr spre a ajungc Ia gcneral. lu cle<rtricit irte sc incepc prin a se da( itcv (lcfinit i i foalte sintplc, pe urmi sc cxplicir citeva e-xperientc gi se tra-rhrcr: r ' i 'zrrltatul acestor cxpcricnlc in [ormult ' l ]r irtetnaticc. Astfel sc obtinco lt i in{iL cirre sc Poato rt ' t i f ica prin rtoi cxPt't icn{c, duph cum;i bazelc pcr:irtc s-rr iutctnciat ;t i iu!a arr fost vcliI icittc l)rin cxpcri(frIt i"r. ()r, cxpcricn-

$clt. rrsrrpriL (lastici i ir l i i sirrl loartt: sinrplr ': t xl lL'ricufelc usrrprr ntasci sinti l lr i l i sinrplr '. Astfcl lr:gilc, cirrL: lcirgi 'r inttc elc qtrr4rl ict:1li lc cl:rsticc:,; i t le grctt-t r r t t : a lc t t rat t , r - ic i , s int Lgi fo i r r tc s i rn l r l r '1 i st ' r r l t ropic rnul t t lc lcgi l , ' < l in c lct -t l i ( i l i r t ( : , <: i rn: st ' t t [ r 'Lr ' r . l l r c l rPaci t i r t l i r c l lc t r ic l 'L 1i l : r i t t r I r r t l ; r t r t ; r r ' l r t t l i t r - r .l ) i t r i rcc;rst i -L s i r r r l l l i arr i rkrgi , i rn l ( iLul i r t s i i l r i lg avirul . r j ( ' y i ; r l r rnci , iu lort lc i r l lo l r i r l r , l i r lcor i i 6, ' r1r ' r i r l r ' , l r t r t rL l i r r i l r l r1rrrr i I r r I l r r sort ic i r , i r rct l ia sot t ich,f t ' i r : I i r r r rc i r r , i 1r i l l r I r ' t i I t , r l r rp i r crr t t t s, l r rc l r i i i t t r l l l l t i r i l r r l r ' . ( u r t t l r ' lc p i tt r r r r l r ' [ i r r i { i i r r t r r r l r r , , i l s , - r l l r l lot i ; r v i I r r , r ( i r r t r i IoI , r r r t l t r r t r l i l l t , i i r t [ r , l r l ,L 'I r .ot i r r r , l r . r l t i r i l i l i i r l , , r i l pr i r r l r t r r r l , l , l , l | , | | | | | | l i I t l r l , ' r ' t tv i t t l r ' .

r \ lo, , l o i r r t i t r r I r I i r t , , , r l , '1 i , i r , l , l r i r l r r r r r r ' , r r r r i r , i r , r r ; 'o l t i l i l r r t l r '11r ' , rr r .z i . , l ' ' r r ( , r t r r r , l , r l r r r r l , r l r ' . | ' r ' r r r r r r I r ' | , , l , r r r , r r r . r r , l r t r r r l , r ' , l l , l r , l r ' r l r i l . i | l, t t r r l r r ' l r ' , l t t t r l r ' , 1111 ,1 l r ' r l l . , r t l1 ' 11'r , ' , , , ' r r , l t t r ' / , l r t r , ' l r r l t t , t i , r l ' t , r r l t t t l t r t t l

r l ic f ionar; at t t l r r : r l o 1rtrr I r t i r . I ; r Ic c l l r l r i r ' . r , ; i r r r l r , r r l r r : , o i r r r rorr i r ; { t i r r { , r .Ata aln f i -Lcut t : i t ruotout-r 'L, r ' r r r lzorr ; r to l t r ' l r . i i ( r I ' r . r l r . 1r t 'o;r t i t . I : ' r I i I r ' r lcrrrolstratc in c lct : t I ic i tat t ' , pc c i l i ' i r t t I Prr l r r l s ; i l l l l r , l r r r ' i r r r ' lcrrrcrr tc sor i t r , ' . r \ t t treu;it si. traduc ;rst{cl toatc lrrotoarclc t I , . r ' I r ' i r ' r . i r r rrrololrrc sortit:c'. I lnrri r ' ,-zonator elcctr ic care dcscatcir sci l tc i , i i cot tstr t r r r t lc i r r sonic i t iL i t ' rur c i , , , ; r r rsoitic care dcscarci, lovituri asupra nicovtlci.

Analogi i ic s int a;a de nrar i , d in punct r l t : vc( lcr( ' tcoret i ( , i r rc i l r r r r r r ringiner, care ar cit i o cartc dc sonicitate, i s-ar pitrca ci-t citt ' ;tc o crrl, , l ,electricitatc.

-\I i glsearn prin urrnirri ' in posesia unei forrnulc dc tradrrc!ir ' ; i rrrr rrlr imiirea <lccit si r ' .-L11 car,- ' i int (l i feritele aplicati i practicc alr. rroii ., lrrr{,.

in pr i rnrLl r in. i , apl ica( i i lc comprcsibi l i t i . ! i i l ichidclor s i r r t r l , , t r r l r l ,importai l l ( i r t . ' lc insi is i : t luprL crr t r r , i r r c lcci l ic i tatc, pot inci i rcu ul t colr( l r ' t lsato[ f i - l pot r l t 'sc i l rca la rc lo ic, rot ast fc l puicur inci . rca o bulr . l ic r l l o{r ' lin carc rr ' . . r r r rD I ichid, cor i r r r I iDr iDr l l ichidul la o presirrnc foar lc nLrrr ' . l ) , r r ; rse cornpr imiL rr l r i , t le crcmplu, intr-o butt ' l ic la 2.500 atmos{crr , , r , . r l r r r r , r r , , rvr-rlumului o aproapc dr l0'1", atl icr-L din t0 l itr i faccn 9 l itr i. Or', ;r( r,.r ' ,t lrerluccrc dc volum cstc consi, lclal ri l iL. Cind l l-rsiLm lichidul siL rr.r ' iui Lr r,r,Irrmrrl primitir ' , cncrgia cstc lcrlatl pc de-a intrcgul.

S-zrr putca z icc: b iuc, c lar ; i cu aerul sc poate lacc aceast i " t cxpr.r i r . r r t , i ,dacii conprimiLm acr intr-o bulclic, inmagazinirnt cnergic mecanicii qi rl irr ifacem crpansiunca aerului cigtigi 'Lm cnergia inapoi. Nu cstc toculiri lr l lr ir.,, i ,pcntru cir actri l dat--ir-l cornprimi.m cu prcsiune marcscli inci-Llzr.; lr., rr1;r irrr l lencrgia depusri in comprimurc s,r transform:r in cncr.gie lx)teutiali (1" ( ' lr lpresiune, dar ;i in cncreie calolicir care se risipe;te; nu sc l)oatc tl.r i rr,, rr;,, r.1toatit cneigia ce arn chcltuit in comprimarc. I)aci comprirnirrn (l ir r orlt iun l ichid, rit l icalea tcmpcrirtuli i cstc foarte nrici-r - <lactr o fi o f r . r r I i r r r r r . r I r .grad ccntrigratl pcntru I 000 atmosfere - a;a incit mari toal.i ( |r l l l ,r \r.translormir in cnergic potcnliali, l)e care o putern conserv:r ; i uti l izir , irrl I r,,rrr.

Ca si . i lustrcz avantajc l t ' cc l t : l . rutcm tragc t l in cornprr .s i l r i l i l r r t r , , r l rchidelor, i rm luat r rn obuz, t lc tun in carc aln l tus ulc i , f i indcir r r l r . i r r l r r r r11,rrai binc. ln obuz cra un cil inrlru 5i un piston i it contract crr l ir lr ir lrrl, ,rri ir ijat astfcl ca sit nu Iie nici o scr'rparc dCliclrid. lmpingind 1>istorrrrl pirir l,rfuntl ; i puninrl o grcr.rtatc asuyrrl lui, drrpi-L ce am lcS;at pistonrrl r:rr o rirrrri 'r,am comprirnirl l ichit lul din olruz l l | 000 dc atmosfcrc. Lir accirslh l)rr.\ i lnr.,sirma cato reIinr: pistonrrl sc nr1>t: ; i t 'ncrgi:r ltotcn{ialiL rl irr olruz, irrrrrir l lrrzinutiL strlr lonuir t lc cncrgit ' clasticfL, arLrnclL pistonul aflrn"r irrrprcrrrrlt crr gr',.rrtatcrr . Asl fc l , c l r un obl lz rrr ic, carc c<lrr f inca <l iunu"r tatc l i t l r r r lc r tk. i , i r ru rr . r tl i t sr ' r i r r rnrc o gr ' , ' r r r r r l l - r l i r 150 nlc l l i . l , ) t r , ' r -g i l i Prrs iL in rrr ' r .st o l r r rz l r rovr. l l l lnum;r i r l i r r v l r ' ( , . j nt i ic i r t i rk ' lxrrrrpiL, t l : r l r . tk: r rn bir icf t l . l )acir l r r : r . l l r i r i r ' { r ' l r r rf i voi t s i r t turrr ' r . gtr ' r r r r l i r cu l t in l l , l - l r r f i l ) l t tut nt i r rgt : < 'onccut l l r t r . i r r l r .r .n, . tAi , . ( , i l ) , - r t , r t . ' r i r r f , . l r r l rL.sr ' t is .

Sr. r , r ' r l , , r ' l r r r ( l i r . \ l ) i r r rs i l , i l i t t r l r . ; r l i r ' l r i r l r . l r r r .stc l tn f : rc l ( ) r i rn lxrr t r r r r t ,r l i t t l r r t r ' Pt t lc t t t l t ' i t1Jl fo lor tsr ' I t i r r l i r ' , . . At t t r r r l rs t l l r i r l r .P: t r t r ' , q i i t r lor : r ; r s lt t t i r l i t r t i l r .z i r i r ruul l o l l t l r r r r r l , ' r , i r t r t l r l r l rnt l r r l r r l r .o(r .1, i t t < l r l r . l r r r r i l l l rx l r rsl r r . i l i l r i r l r . r r l r . i ; r 'orrr1 ' r i r r r I I I r I u l l i r r l l r r ,L{) l ) ( l i r I r r ro l I r . r ' r . , l r r r t r r . r r ; i l r i l i r l l r .l l l o l ' lz r l r , l t l<1i l r t 1 l ) t ) r r r ' l r r , r r . r , t l r r r l l r r r l l r rPropi i r r r r r l r . r . [ r . r ' l r . l r ; r l is l i r . r . i l rl lur l l l l r ' . | | t r . ' , t r t t r r ' . I ( l r , I i l l l l l I | I | | | | | , | | t ' I I . r . ' r l r , r l l r r r r ' l . t1 i o l l i l r r r r | r r r ' , , i r r r tc l rl r r t r . ' r . l r t l , l r r r r , l r r l r r l r r t i l r , o l r l l r r r r l l r , , l r r i r r r . lp[rr l l r . . l r r ln r l r . r i r ,1 l i r l r i r l r '1r . ,| |

' | | | | r | | | | | i I I . I r | | | l |ht | | | l r r r t I l t ' | | t r l , n l | | l [ t | r , r l l , t l l r r r l r l l t l r . r , r , , i l | | ror l r r r , l r , r r | r

l , l ' l I I | | | | | i I l I r | | | , i r l r l r l l r , ! r l r l r | | r | t r l r l | tn l r l l |

I ' r ' r ' I | r ' ( i { | I r i I r r I i t ( r 's l l l l ) i r r , r | , , t r r { .u l i t s i - r f i lc un tuntrr c i r r r . i rut ar l t r ) ( . i t lo lxrrtt lr:-L rlt. I{)l l I, ig l i t I i(,0 rlr.tr i t i"rrir for: i; i f iLri zgomot.

\ - iun ( l i t1 i rcr 's l r . ( , \ ( 'nr l ) lc l ) r . r r t lu i r i l r rstra c i t mai binc faptul c i com-plcsibi l i t l r l r . l r lpt ' i t 's t t ' l rn fact( , r ' ( iu ' ( ! nu sc poatc negl i ja. Negl i jarca inlr(\ 'ut a courplcsilr i l i t ir l i i l ichi<tokrr l f ircut ca rnultc aplicali i practicc, careirslirzi sinl c(nsa(:rat(' ci l atarc, si nu sc poat5. descoperi mai inainte.

l.)stc un pclicol ft i inla fi-rrr-r cxperiente: autorit itea Stiintif icS. rcu;e5teli lrrxlatiL a impunc idci eronatc in mintea studentilor;i gcnerali i lor urmir-toirr(., in a;a-fcl ci-L nimcni nu se gindcite mai t irziu s[ vtrif ice lucruri, c:rrel)riu o consimlirc gurt'rali au {ost trecutc in rindul cunoitintclor pozil ive.l)r';rltfel,- tipmul rlu c dcparte cind o formuli. gresitl a lui -\ervton, ile pildirr impiedictrt invcntarca acroplanelor pc cale teoreticiL. Linii au ajuns 1,rinrrllcmtrticir, cr.r ;rjutorul acelci formulc, siL rlemonstreze cir pi.siLrile nu potsr"L zboarc; s-ir {iLcut totrgi expericnla ;i s-a dovedit c;r... pisiri le poi si-Lzlxrrrc. I)caltfcl, Irrcruri le s-au aranjat prin schimbareir formulci ; i s-iu i:r-\ '( 'Dl ut dc atunci :reroplancle.

Y am dat citeva cxemplc dc aplicarc a comprcsibil i t l l i i l ichidtlc,r;rlol|sc sr-r ! i-L dau citeva exemple si asupra aplicirri i transmisiei cncrgici delrr rrrr qrunct la altul pri l l unde sau, cunr zicem acurn, prin transmisie sonicilL.l)r 'oirrer:c sonicitatca - ca sl-i diLm o rlcnumire analogi cu electricitatea -r.slr. o lt i inl ir aga cle apr-opiatir du clectricitatc in Iormulc, rLr trebui sii re-zrrlt l r: iL ; i in aplicati i lc ci practicc siL mcargiL paralel. $i intr-adevi.r, putemlrrlr. irr souicitatc mai toate aplicati i le carc' au fost f i.cutc dc electricicni.

(l lrL tl in aplicati i lc ce'lc mai curioasc cstc transmisia c durii la disrar{ir.t , r l I \ . l l ) r i l l l l .

(, lr sir produc ci"rlduri prin vibrati i arn luat un gencrirtor sonic, carerorrsli-r rl intr-o pompi.; un simplu piston care se miscl alternativ intr-unril inthrr. l) in cil indru plcaci conducta, carc cste in cumunica{ie cu o butclit 'r l t 'o{t.I plitr iL cu irpit. Accast:L butelic corespunde crr ceca cc in elL-ctricitatcnllnlinr ul) t 'on<lcnsator electrir ' . \[ai t lcparti, continuiim tonducta pe o lur-girrrr. oarcr:ure 5i o tcrnini.m printr-uu tub cu dianctru loartc mic, spr-ecxt'ruplu rrrr tulr t lc rrtr urctru lunginc, invirt it in spiraliu ;i aviud diamttrulitr t t 'r ' ior dc 2 mut. [.a capiLtul ac:t stui tub puncm inci. o butclic p1in5. cu apiL.Ir:r 'st ar:rnjantcnt, din punct dc vcclcrc hidraulic, estc o alrsurditatc; vorbi'sc,lr ' lr ir lrarrl ica cute ncgli jeazi" comprcsi I r i l i t iLt ca apci. I)acir {inem scama insirrlc rrct'st factor, lucniri lc stau altft l ; inctpind se mifcim pistonul altenrari\ 'lrr irrlr o bicli si o rnanivcl. 'r., sc produc prrlsali i in butclia de la inceput^uliolrlrrctci. AccastiL butclic deviuei nn fc1'clc gener:rtor dc undc sonici '. inIrrlrrrl nostrtr circulir atunci undc, erL, sint foitatc sl tr-r.ar r-r prin rubrrl rclsrrlrt i lc ; i t l in lrrl lr l srrlrt irc siL trcaci-L inaintc in butcli lr r l i : l lr capittul tron-rlrrr:tci. Mift: irrcir r:slc posibil iL rLiu t:urrzir. corrrpresibil i i iL!i i I ic:lr irLulrri si t l irr,rrrrzlL posibil i t ir"f i i tr-ansmisici cncrgici prin rrnde. l.)nt-.rgilr onrhrlutorie insi 'r.l rcr ' i l r l pr- i r t l r r l l r l sulr t i rc, prot l r rcc c iL l thrr iL intocurai cu 1i in t ' l t .c t r ic i t l r l r ' .

Cu aplntul pc c l r r r : l -aru f icul am tkr l t incl i t o l (n l l ) ( t i t tur i t ( lc n l i r it l l l l l l i l . r lO0 gr;r t l t ' . l 'u l ,u l f i inr l i r rv i r t i t in spir-al i '1, iu l l in l r r ) (hrs i r ( : ( 'usl i ' r sr ' l; r rnt i r r iL intr-un pir l r :u ' r r r apir

' , r r r ' , i r r , : t lz inrhr s, t luP.r 2.- .1 rrr i r l r r l r . : , l r i r r

l r '1 l t t l s i r f i i t r l r i r . ( lor l l t tc l lL, i r rs i , r ' i r tc cour l t rc, . tnr . r 'g ia sorr i l r ' r l r r i rc ls l l r r l r .l i r t t i r r l t i t : r ' l i , r r r r r t i r r I r r ' I r r r i r r 1 r r r r r l rPl t iL rrrr . r l i r r t l l r i r r rsrr is iu I r r . , : rnr \ l ( , \ ' r , ( l r Icr i r ' ; rosi l r i l s ; i l l r r r : , r r r i l , r r l r l l i r . r : i rLr l ic i Pr i r r l r ' -uu lu l r crr l tPi i . r ' r ' r r , .

l ' , r | l i r r r { i r r lo l r t l i , lorrr l r . r l r l r r l r l i , l i i r r I i r I r ' r r , i I I r I r . ; I r ' r r t l r r I r r | r r i' " r t t i , i t r l t r l , r r l r , l t r r i r r ' . ,1r ' l , ! ,u l , r r ;1, , 1 i . , r ' Prrx l r r r , , , , | l i , r r l l r , l , r r l r , r . r r ,' r , l l t r , r . l r l , , ( r r r l , l l r , I ro, l r r r , . I ' r r r r r , zr ' , l , , r r t . r r , l r r r r r r , r r r r r . l r . r l r t r r l . r l r

I t t l t ( r l t t r l ( r6( t t t : r i r IP;r t l r . c l t { ' \ l , r ' r r r , r l . r . r r r lor ' r ' i r s i 'L l ; isr ' t t r r l r r l , r r lcql tu ic s iL i t tc i lzcrrsc.r i r l ) i r l i r lOo Alr [ . , Prr l r . r r r , r r r I r , . I r r r r r r t i r r r I l rn ( : r l { ) r i r r r .t ru, s iL lacct t r ca c l letgi i r s i l n l l nr i r i Poir t i - r l i r r l i . r r l , . l . r l r r l r ( i s i t s( ' i t t l ln l r l ( , / , (Ast [ t :1 l i ind, in mod tcoret ic, l ) r r tcnr l i ! ( i { r ' r r ; rcr ,s l l r r l r s iL sc poir l i . i r r r r r lzrpinir la or icc tcmperatul-aL. Li rni t l la carc Icnr l ) i . r i r l l l l r r l i r r i rcest rur) \ ' i r r lur l : i .depinclc dc punctul dc i icrbcle al l ichidulrr i r l i r r i r r t r . r ' ior ' , f i indcrr i rp,r , l r r rtubul spiral ia dcsigur acccai i tcmporatur i r ca l i tubul . Eu iun,rr . r r l . r r .in cxpcrictt(it ce am ficrrt, ca prcsiunea rncdit sir f ic aproapc 100 alrrrrr, lorLa accast i - i l ) l 'cs iunc apa nu { icrbc nic i la300 gradc, a;a inci t punirrr l t r r l , r r lin Virti, r ' irta s-tr carbonizat. \-am mers mai departc ca sit- ari it r ' .r .r,...1tub s-ar prt tca lacc rosu, l i i l t lc . i .udur i lc tubrr lu i s-au topi t , ic ; i r r r l r l i r r t r r l 'aburi srt praiuciLlzi t i , ct 't 'a c. cla (lc aticptat. A;adar, din acecaii ,r ' tr(lr ' t lputctl luu iLI)i! r 'cc(, apiL cakliL ori aburi suprainciitzi{i.

I 'ransttt isiunsa ci 'r lt iuri i prin unde sonicc poatc siL ail l-r yi ,r1,lrr .r lrrpracticc, iDsiL cxPc|ie'nta tle Driri sus aln ficut-o nai rnult t l in Prrrr, trrl , l Ivedcrt : a l iutct 'csuhr i i t i i r l t i f ic , ca s i . arai t c l i fcrenta qnorml i l l r , . '1, . , t '1,sonicc i i efcL:tele hit lraulice. I)aciL am fi plecat de la ipotcza int:orrr;rrr '..r l,r lrt i ! i i I ichidt:lor, expcrien{a cr' \ '-arn dcscris, cvideut, n-ar I i fost 1xr'.r l,r l,r

Cind arn ccrut brcvctul acumulirri i cncrii ici, bazati. pc corrlrurr.rt,, ll ichidtlor, cl mi-a lost rcfuzat in Statslc Unitc, pc motivul ci m;rpirri l ,. rrr, l,.nu pot fuDcliona; or, ac(ste malini funclionau, erau ir.r f i inj iL l ir l .r,rr, lr,rgi a trcbuit ndrturia sub juri lrnint a unui mcmbru dc la ,,I{oyrrl Srx ir.tr,din I-ondra, ca s:r se convingi ,,Patent Office" din \\rashingtou ci. ;r(r ' ir ' ,t, linventie nu estc o imposil)i l i tatc. Nu spun ci. lumea nu lt ia ci lrrlrrrLlls int comprcsibi lc, dar nu o; t ia dcstul de binc; i a t rcbui t i l l i i t | r . r r rorr ' , | r r r |prin expcricntc, nu numai cf, sint compresibils, dar ci. clasticitatr..r lor , .t lun factor important in industri:r mccanic:L.

In loc de a intrcbuinfa acumul:rtoare hidraulicc, carc siul ( ( | | | , . | | | | | | | | ,din o greutatc enormi. api"sind pe rnpiston, putcm intrcbuin{a cit, r ' .r I 'rrtr ' lrr,obuze vechi, astupate biuc, in carc comprimi.m lichidul la o yrrr,sirrrrr. lo,rrtr,marc. Ac(stc aparate pot sh cost(: dc zccc ori mai pu{in r';r ul i | ( , I I r | | I | | | | | r I thidraulic.

O al t l apl ical ie s-ar putca face la rcsortur i : un obuz, i r r t ; r r r . ; r r r r r l t r r rduce un piston qi carc c plin t:rr un l ichid, poatc servi drt 'pt lcsor'|. r.rrr.si rczistc la prcsiuni enormc. Pistonul intrind in l ichid i l (orrl)ri lr ir, r.rlcind inci.rcitura cc apasi pc piston dcscrcitc, clasticitatea l iclrir lulrrr irrrprrrtr;r.pistonul inapoi in pozil ia inif ialir.

O rLplicatie a transmisiunii prin vibrati i, carc nu ('st(. in forrtl rhrit , 'consccinfir a aplicirri i clasticit itt i i l ichidclor l)e o scirri rI:r i irrl irrsi, r.r,tr.distribulia rh' pulerc ftr {l lrr ici, lntot:mui cull oa so [ur:t: irstiLzi (]u rrol()rt lc lectr icc. lu l lc probk.r l r . in<lrrstr iaL. l l - lu fosl rczolv;r l r : pt . t r r : l i r r l r . r . l r . l r rc i t l l ( . . l is l ( . l t i { ) r ' i r l r i tnsr l i lc cnctgi( ' r ' lcc l l ic i i l i r r l is t lLn{r . ru i r r i , r r r o r ' l rc icrr{ iL r l 's t t r l r l r ' l l r r r i r , r ' i r r r I r .s l l vor l ' ; r , t r r : , i r , r l , . r l is t l i l r r r l i : r ptopl i r r z is; ' r i r r , r r l rg i r . i iu nrrx l r . l , r ' l r i r ' , r . f ic ic l l i r ( . i ( .st , ' : r l r r r l , . r r r i r ' i r , l r r r ' i t , r l i r r prrrrr l rL.v, , l , r ,col t ( . t ( i : r l , lu l - r .n l ( ' i rz i " r . l ) r ' : r r , , . , r r t i r i to i l l r . h l r r ic i l ' . , r ' l r i : r r ' -5 i <.r ' | r . r r ror I , . r r r r . .c i r t r l i r rs l t r l r . r rz i r r t t : r l i r r i i r r l t r r r r r r l r . l icr ' , prr . f r . t i r t l r . r r r r r l l r . or i s i i r r l r r ' l r r r i r r l , ' r , r .s is lct t t r t l r ' r r I t l r r r . , t t t i r r i r r r r i rL. r r t t r . l , . , . r ts l r . t t t vr . r ' l r i rL. r ' i11.1, , , st r l , . r l r . r r r r i , r , r r , .r .s l r . i t t . ; , ' r r r . | | r . ro| | r , tut i r l i t r Prrrrr t r | | . r ' r . r l r . t r . r ' r , t t | r . t ( i i t l , l t i t t | : . t r t is t . t r . r r , lr ( . r ( , lv , t , t r ' r . , t , r l r i | , |o| |L. | | | ,1, i r r r r . r l , r t l r , i r , { . lx , i l l r , r r r l iorrrr l i r . r ; r r r . l t l l i l ; t , l i r ' ' , l t r .. , lu r l l r , l r , , i l | r t |o l t | t . i | | i r I t I t | | . I r i , | | | | r , | | | . | | | ' ' | | | | | | |

. | | . l r r r r r l l r . l l t l r . r r r i r | i l ; rl . r l t , ' '

r ' l l r , t l . l . | | | | r I r ' r ' | | r . r , : t r r r .Ptrr l r l r , i r l l l r r r ' t1trr i1 , r r , r l , r r r | , , r r r r l r . l r r r r ro l l r, l , r ; , l r , r t , , , r r t r t t r r . l , l r l , 1 ' l l l r , l t r ( , l l r i t l r r l ' r r r t l r , r l r , l t i l t \ l l , . l r .o l t r r .

si l l ru l t l l rntr i ln l l in ln. ! icul( , l t \ r . ( | r . r . i t r ' r , rx l l t ( .1( l { . r . l r r . l r i r : r , , i l l )o i i l l )ar3l( l lr lc lontrol, r '<llr int'tclc <L' porrrir.r. s.rrt r[. oltrirt. lr lc motoarcloi s,,nicr,, sintrl l l l t lr)ai it ' l t inc. I\ ' lotoart,l(. (.()sli i irpr()irJX' pc .i l lmirtatc sau o trcime dinrrrstul nrolo:rrt: lor clcctricc tlt: acr.ca;i putcra. (;rcutatca motoarclor (, camitr ircu.a;i ploporlic. Aga incit, r,rt lcfi, in ceea cc pri\:cite distritrujia cncrgici,soDicil irtea poate concura cu succcs electricitaaca.

In ccca cc privcftc transportarea t,uergici la distanlc {oartc marr, eslcllolr;rbil ca rlcctricitatea si. aibi monopolul, f i indci inl 'rrri le sonicc s'r, 'irr gr.ntral mai scurnpc dccit conductelc elcctricc'aeriene. .{.stfcl f i ind, intrcvidPrrsilr i l i tatea unei conlucrirri armonioasc intre electricitato si sonicitale.Sprl. r.xcnrplu, pe tercnurile noastre pelrolifcr(' s-a gisit ci c mai corrr.cnali l,r sr. lrtnsmite cnergia electricir de la distanfi,si_a sr". ataca difcritt le aparattprirr rnotourc elcctricc. Riscurile dc incendiu si delicate{ea motorului electric,Irrsi, sc opun la ace'asti. aplicalie, 9i de accea transmisia sonici va inten.rnir:ir o lcglturir intre sondi. si curcntul elcctric. S-ar putea aduce cnergia elcc-Il i .r-r l ir o stafie centrali l , ̂ transforma in t.nergie sonici qi transporta apoila sontlt 'prin luburi de [ier. In acestr. luburi ar putca s:i circule chiar plcurar' l rrrcrl itr, sau petrol or:rpi, iar sondele ar f i ac{ionatc dc motoarc sonici,,citrr.nu prezint;. nici un pericol, sint e-rtlc'm dc simplr., pot lucra fir i l aten-{ir. slrccialir chiar srrb api, in noroi, in oricc condil l i ci i de grele.

InIrrlxtin{area motoarelor sonicc in fabricile modernc ar elimina toareIrrrrrsrrrisi i lr. prin cu_rele. _Chiar ; i costul va fi mai ieftin cu timpul, c; 'rcir ' lr i ;r l t l lci"r lransmisia prin curclc cste mai ieftini. decit cea sonici, toturio r.r 'orIr)rl l i( ' s-ar realiza la constructia atelicnrlui, care n-ar mai trebui si,I ir,rL.o z.ir l iLric atlt de solidiL, nemaifi intl nevoic sii sustinir toate roti le sif ir.r ' ir l i ir cr.;L Sr('a necesarir. in transmisia cu curele.

l-ir rnololrele sonicc nu intrir dccit ionti. i i ote]; Ia motoarele elcctricr,irrl l l i ofcluli <lcstul dc scumpc, intri cupru, mica ;i fcl dc fel dc produstcrrrriucrrtr. ; i de iLceca, f i ini lciL un motbr sonic e'foarte robust, i l poat,.sir rlrrrczt' infinit, pc cit ir vrcrle motorul clcctric arc nenrrmirratc picsr-, car,., rr l irtPul :.t ' r h'tcrir rrt 'azi .

I n ult tcrcn dc aplicart ' al transmisici sonicc, este in rczolvarca unr,rprrrlr lcur', in.--carc transmisiiL clcctrici-r" nu se poatc aplica deloc, dc pildiil ir :rr.roplanc. ' l 'endinta astizi la acroplanc cstc dc a ajungl la o puterc mr-ci.-rrir 'r 'r r l in cc in cc mai marc. Astfcl s-au ficut acroplanc' dt: I 0OO li Z 000r';ri prrtt.r ' t ' , i i tr acum, ir.r t impul din urmi, sc studiazii un acroplan de 5 000liri ptrtt,rt ' . Or, ca si sc ob{iniL aceastir. puterc enormi, estc nevoic dc nrairrrullt: nrotolrrt ' . Am studiat acum un tcroplan in carc 8 r'notoare vor fiinslir l:rtt: in naccla ac|oplanului, atacinrl opt gencratoarc sonicr., iar |atnrr,l icr., prrsc l iL aripile iLcroplanului, vor f i aclionate do patnl motoarc sonic,.Itts(ulir l i ir.cor_cspunde. intocrnai fchtlui cum sc prot:trk'uzir inlr-o instala!itr cr l r ' : r l i r rL. r l is l r i l ru l i t r : lcctr ic i r .

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c i , rcatr t lc r r t r c;r l put t ' rc cu c i l r { ' s( ' l i r i l r ' { r ' l r r l . , r ( : r t - t ' s l t \ ' ($ l t ' 5 i l ; r r r i l r r r l

ar ' , 's t c iocan fr ' rcct acelal i lut : ru ca t t t t c i r rc l tn I r t t r t t t t t r t1 i r ' , i t t I t l l r t t i t t t i t t r | . r ' t

t : r t rnpr imat, r lc l l cai putcrc. l )Lnl t [ t l , r 's t , ( u l tosr t t l t l - t i t r r l l ts l t i r t : l ( l l l l l l l r r r r

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ct : totul st t l . , apl- t , inclusiv motolul , ccta c( nt l sc lx) i l t ( l i rc, t ts, , t ( r r r l r r l r r i r l ' r t

t l l ]c t I lc .

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, \mbit ia tcorct ic ianului cste totdcaun;r n i t rc; f iccnrt vr t ; r \ i I . r r ' r i ' r ' r r lnoi , insiL teor i i le carc sc {ac in c lcct l ic i tate pot f i tot at i t ( l ( l ) r r ( i r r l r r l t l r , . r l ,ca 1l tcorii le carc s-ar putca facc in sonicitatc. O idtrt ' gctrt rit l iL ( 5lr ' (.r l lr ' r l: l lnu i)oate s5- mearl; iL miri rerpedc dccit sunetul in nlc<litt l irt t.rttc o lrrrrr ', lrr l lr rrlOr, - im cis i t c i sc poatc foartc binc cu encrgi : t s l i r l ( ' i t rg i r t t r : r i r , l * r l t r l " t lsu11, ' iu l . Am calcul ; r t conducte sonicc pr in carc al l l l ) t l l ( ' l l l t i t l l l l , r l r r i l , , , r l '

sar incargar, spre cxct lp lu, cu o v i tczir . dc 10 000 Int ' t r i 1x : r r r r t t r l . r ' r r r , l r l r r

l0t) l )00 netr i pc sccundir . Or, da.c l - r ar-eur 1:nsi l r i l i l at i i t s i l ; r , , t r t . r \ ' r r r r , lv i t r :za. uudclor r lunir vointa noastr i r iu mc<l i i l t r r t l r lcr i r r l , ' r r r r \ , r ,1 rr l r l lra l i r t i rc t lc cc nu amfacc o tcor ie nouir <l i fcr i te lo l r r i ; t i - t t i I i l r r ; r l , ' r r , t r r r r r r ' l l r r lma-t , ' r ia l ; i pc urmi- t s-o i rp l ic i rn la c lcctr ic i tatc, cr-Lkl t r t i , : r , r r i , i t r t ' , r ' r l t ' l ' l r r r ror L-: i r Ig l l .

L-ua din urr tscciu{ele teor ie i t ransrnis ic i sot t i lc r ' .1, , r , ' l . r ' . r ' r r ' t l t o

con, luct iL fo:rr t t ' lungi , nu putctn invir t i gcl tcrrr l r r t r t l r l , r i t ' r l

. , r l r r r l l r l l r

sel , r r : t ic t lc { r t :cvctr fc cal t d i {cr iL uuclc dc i t l l t l t pt i t r i r t l , t r ' . r l r ' r r r rp l r ' , \ r r" '

t r : i r r i iut f rccycnlc l t cart : iutpart lungimct t r t l r t t l t t i i t t l t l l l l l l l l l l l . r l t r r l r ' 11 ' l 'lungimi t lc scmiun<|. ' , a;a inci t tur-a{ i : r posi l r i l i i t ;1 r ' t t . t ; r | . t t t I t t t t r r r Inr . r l i l l

ret)r , zfr l l : t t i ( lco f t t t rc{ i t 'cont inui t . Aceastat lstco i t t r l i r : r { icr . r t l t l l t l ' t ( ' l r ' l t l l l l . l : l

ar i in,rr , in ucn{ i - r asupra f rccr-cnf t ' lor posi l r i l t i r t l r r r t t ' t t t i . i ; r ' , r r t r i r r i . l ) r ' i r l l l ' 1,

i r t r r rntoni t : t t t t t t t t ' t l lc intrcgis i l t t l l lzc lc i t rnrotr i t i . ( ) tot t r l t t r l ; i \ r , t l l ( . r \ t i t t l l ' . r l l l

lo i . r ; l t in t rutnt ' l r i t t l r t :g i rk ' l r r r tg imi t l t r unt l i t . l ) t t t i pt t t l l t t t t t t : r i t l l t t l l ' 11r ' t t r 'l i r l r l i r t r ' , P( ' r tct ' r ' i t ; i t r r t t< l t t t ' t i r , l t l f i [oal tc lxrs i l r i l s i - r in l i t l i r r r l r , r r r r r r l l r r | { l t l t l

lvolrr l i r rn i , l l lu l l i r 2(X)0, i r l tu l la 3()(X), sPrt ' r 'x t t t tPl t t , i t r \ar I r r l l ; r l l l l " r

d, 1r i l , i l - r . I ) r i t t t t r r t t i r t r ' , c t rPl i t r t l t gr t r rnto: t tc lot sot t i t , pc r ' . l i r r i , r 's l r ' l r1 l r l . r

r l , i , , , r i : r ; rcol t l t t t i l r r t t r t tz. ic; t l r ' ; r ' l l sr ' pol i t r l i r l i t t t l t t t : t i l r r l t r r v. t t l ' r . r t '

s l : r l r i l l l l . r ' l r : i r t l t ' t t t t r i t lxrr l <| ' t t t t t t r . t . i t t l t lg i ' o l ' Pi t t . r i - r l t l l i . l r l r ' l ' ' r t l ' '

g , r r , r , r l r i i r r l i l lur i i , ( i l l t tcr t t t i l ' s i r sr ' 1x ' l tc l t t i t t t t t l t i t i r l t tp i i h l i i l r ' : r r t r lot l i l i '

nrrrr , r l l l i r r l t r l l i : r t lJ l r i r l r r r l t t t t l i t l is t r i l r r r { i r r v i I I l I r t i i lor r l l r r r i l l t t ; t l t t t . r .

Ar rrrr r r ; t , , r r ' . ,1c i r r rgrr ' ' i l r i l r l , , t l t r t t t . t t t i lc l t t l t l i i ; t Pt i t t l t t ' ' , i " l r ' l t l r lcrr t t ,r . r , r l l . . r ' . r t t i t t l t , r ' l | ' i t t t . r l r l l t l t t t i r l r ' t t t t t r t r ' t t t t t l t rJ l t .

l ) . r , , r r r , l i i t t , l t t t t Lr l . r r t t . r ' r i r ' r r r t r ' , t t t , l r t t t t l , . l , , l , t t t , t 1, 1; t . t t t , t l r1"r t ' r / r r l , t . t , r r r , l r ' \ r l l t r , l r l r t r r l r r l ' t l t t , l t t l l t t , ' r t t l t , t t l r ' ' l r r r . r l : l l l r ' / l

lcorirt rtlontikrr. Aur prrtca loir11,, 1,in,., insir, sir imnginim o tcoria a vibra-lll lor (.1('rtrentclor ca lrazl'r a clrirrrir,i ;i ;rtunci act,stc numere intregi in chimien-.r fi (l('(it c\prirna'eu faprrlui .ir 'c.r'binaJiire'

chimice nu sint decit acor-(lurl :rrr)tonicc ale unor r.ibra(ii tlt. rnatt.riei.J)rintrc acordurile muzicalt: avem acorduri consonante gi acorduri dis_

Ionantc; foartc prolrabil ci gi in naturi {cnomenelc sc impari in doui clasr:l('r)onlcnc consonante gi fcnomcne distonante. Cele dislonant(, nu sint dc sinr.stitf,toare, ̂ tind citre forme mai simple care sint Iormele consonante sauarmonicc. ln chimic acelaqi lucru: c6mbinaliile se .ra.rle.r:r si fie in ra-l)orturr intregi cit se poate mai simple. Cu cit combina.tiile sint mai com-Illlcatc, cu atit sint mai nestabile. Aga incit, incet incet, cred ci <Iaciag continua conferinta, ne-am intoarce indirlt la muzici.. l)csigur pacien{a d-voastri. a intrccut timita adrnisibili. \'oi termina

dccl aceasti cuvintare cu congtiinla implcatiL cd. mi_am ficut cjatoria de avir lace o comunlcarc ce, in orice caz, a fost ascultat:r cu bunirvoirrfiL. Mlrtu_riscsc ciL nu-mi fac iluzia a fi fost prea clar in e*puneiea mca, in oricecaz m[ consolez ci ar fi Iost foarte greu si'r se poati face mai bine cu unsubiect atit de tehnic, 9i special, intr-o ixpunere caic sir fie pe inlelesul tuiuror-

,. Vtr multumesc dar, doamnelor gi domnilor, pcntru amabilitatea de all vcnrt la accastl conferinti qi spcr c[ nu v-a obosit prca mult cuvintarea mea.

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I Tr l roduct ionlLElementary principlcs of physicsITI Sonic cDrrents in short pipes. Definitions1\' Elfects o{ capacity, inertia, Jriction and perditance on sorric cnrr.rris\ ' ( urre is in I , . A l in.s\.T Sonic currents in long lines taking accourt oI Jriction\'IT ]'heory of displacencnts. lfotors\ ' I11 Th€ory o{ nrechanical hammersI\ High ircqucncy cur.r.ents. Variable cross scction lil('s\ I : ! lud br c,\ I L. ' , , . f , f rn(r :\ . .1 . ' t , , l i .1rr ' , r o l . .orr ' rhcor l '

\ l l . I Srnchronous sonic motors arrd gercralors\ l i . I l r i f l r I r 'qu. , , r f , ' rer l i I\ i l 1 \ " ) . ,hru ' t r so| ic\ I ' . r a-ol l r , or - , r" i Ino r-s\ I l . . i : ' I t r rnts

\11.5. I l lcrnbranc sonic puntp\ 11 .5.2 \ 'o lunl ic sonic p}r lp\11.5. i \ '1 l "c l .sc -^: ! " /puml\ l I : . . \ . r r i L l , . t l . l \ volun . tnn I

6 Sonic gcnerator for t ract ion systcnrs7 LrIr : i t , r I r , r r r . f^r s^ r , increl l r , ,urS S , , , , { I r r t r ru,r f .. ) S"r i , t r Dl , i !

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\ l l . l . ' . I r , ' r l r , r l r r rs\ l l l . ' , , ' l i r r r l r r l r , | l r r , l r , lx . r l r i i ( , r l\ l l l . ' | 1\ | I I I | | r , | | I t I | | i | | I n l lh l r r l l l r , , ! ' | / . , r l , . l

l l ( , r t r r l r ru l l l r | r ' I ' r r t l ru l r t r r r r l r l l l I l rl , l Alrrrr t r ' , r r l ' , f i r I r r l ! l , r ' , l t l l l ' , r t r r r r I r r rg l l r r |crUl ' l lhr . i r i . l f t l l | , , ,1

Lq url l lhr , , l l ' ' , , r r4 l r l ! r { , | t l ' ,1 l ( ' l ' , r ' , l l | t . l i r r r . r l , r r { , I r l , r rv rr l r , l ' ,