cismaru full

7/21/2019 Cismaru Full

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ONLINE ISSN 2069-7430ISSN-L 1841-4737

PRO LIGNO Vol. 7 N 1 2011www.proligno.ro pp. 39-50

39

CALCULUL DE PROIECTARE PENTRUCERCURILE DE REZISTENALE

BUTOAIELOR DIN LEMN

DESIGN AND CALCULATION OF THERESISTANCE CIRCLES FOR WOODEN

BARRELS

Adriana FOTIN

ef lucr. dr. ing. TRANSILVANIA University in Braov Faculty of Wood EngineeringAdresa/Address: B-dul Eroilor nr. 29, 500036 Braov, RomniaE-mail: [email protected]

Ivan CISMARUProf.dr.ing. TRANSILVANIA University in Braov Faculty of Wood Engineering

Adresa/Address: B-dul Eroilor nr. 29, 500036 Braov, RomniaE-mail: [email protected]

Rezumat:Lucrarea i propune sprezinte o metodologie

de proiectare a cercurilor butoaielor, folosindcalculele de rezistenadecvate n care sse aibnvedere asigurarea etaneitii butoaielor simultan cupstrarea integritii materialului lemnos nglobat ndoagele din structura butoiului, att de la nivelulmantalei ct i al fundurilor.

Pe baza acestor calcule se pot definidimensiunile cercurilor (lungimea, limea igrosimea) n funcie de tipul butoiului (de transportsau de depozitare) i de poziia lor fade capetelebutoiului.

Definirea caracteristicilor dimensionale alecercurilor se impune n mod obligatoriu, cercurile fiindelemente de sigurann funcionarea butoaielor.

Cuvinte cheie: butoi din lemn, cercuri de rezisten,doage, manta.

INTRODUCERE- ELEMENTE GENERALEMeninerea formei i asigurarea etaneitii

butoaielor presupune existena unor elemente caresin n contact doagele din structura mantalei i afundurilor, care, sub influena presiunii hidrostaticecreat de lichidul depozitat, au tendina de a sendeprta, cauznd distrugerea structurii.

Elementele care in n contact doagele demanta i pe cele de fund sunt cercurile, de formaunor benzi din oel aezate pe circumferinaexterioara mantalei aa cum se vede n Fig. 1.

Cercurile trebuie s-i pstreze poziia de pemanta pe toatdurata utilizrii butoiului. Ele trebuie n

acelai timp sintroducfore exterioare care sinn contact doagele (pe canturi), realiznd la nivelulseparaiei dintre doage o presiune de etanare carenu trebuie s depeasc tensiunea de strivire amaterialului lemnos din aceastzon.

n plus, meninerea poziiei doagelor pe mantapresupune ca, ntre cercuri i manta, saparo forexterioar care s genereze frecarea care nu-ipermite cercului s alunece spre zone cu diametremai mici. Fora exterioar introdus prin batereacercurilor nu trebuie s realizeze ns o presiune la

Abstract:The aim of this paper is to present a design

methodology for the circles of wooden barrels, usingappropriate strength calculations, so as to providetightness while maintaining the integrity of thewooden material embedded in the barrel structure, inthe jacket and bottom staves, respectively.

Based on these calculations, the circledimensions (length, width and thickness) can bedefined, depending on the barrel type (for transportor storage) and their relation to the barrel bottoms.

Defining the dimensional characteristics of thecircles is mandatory, as these are safety elements inthe barrel operation.

Key words: wooden barrel, resistance circles,staves, jacket.

INTRODUCTION GENERAL ITEMSMaintaining and ensuring the barrel shape and

tightness implies the existence of elements to keepin contact the staves and bottoms of the shellstructure of a barrel, which under the influence of thehydrostatic pressure created by the stored liquid,tend to move, causing the destruction of thestructure.

Items to keep in contact the jacket staves andthe bottoms are circles, under shape of steel stripsplaced on the outer circumference of the shell asshown in Fig. 1.

Circles should retain the position on the jacket

for the complete duration of use of the barrel. At thesame time, they should introduce external forces tokeep in contact the staves (on the edges), providingat the separation level between the staves a sealingpressure, which should not exceed the crushingstrength of wood in this area.

Additionally, maintaining the position of thestaves on the jacket also implies the occurrence ofan external force which generates friction and doesnot allow the circle to slip into areas with smallerdiameters. However, this external force generated


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limita de separaie (cerc-manta) care sdepeasclimita de strivire a materialului lemnos.

when hitting the circles should not generate at thecircle-jacket separation limit a higher pressure thanthe crushing limit of the wooden material.

1

3

2

4

5

D

H

d

A

A

A A

Fig. 1.

Forma generali structura butoiului din lemn /The general shape and structure of a wooden barrel:1-doage de manta/ jacket staves; 2-doage de fund/ bottom staves; 3-cercuri de rezisten/ resistance

circles; 4-orificiu de umplere/ filling hole; 5-orificiu de golire/ drain hole.

Toate aceste condiii nu pot fi realizate dectprin efectuarea unor calcule n care sse incont deproprietile mecanice ale lemnului speciei din caresunt realizate doagele, de proprietile mecanice alematerialului metalic din care sunt confecionatecercurile, de modul de nndire a cercurilor i demrimea suprafeelor de contact dintre cercuri idoage.

Datorit formei paraboidale, cercurile aulungimi diferite, ele fiind amplasate pe zone cu

All these conditions can be achieved only bymaking calculations that take into account themechanical properties of the wood species thestaves are made of, the mechanical properties of themetallic material the circles are made of, the joiningmodality of the circles and the size of the contactsurfaces between the circles and the staves.

Due to their paraboidale shape, circles havedifferent sizes in length, which are located in areaswith different diameters and different specific


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diametre diferite i tensiuni specifice diferite(introduse de presiunea hidrostatic a lichidului dininterior) n funcie de tipul butoiului (de transport saude depozitare)(Fig. 2).

stresses (introduced by the hydrostatic pressure ofthe liquid) inside the barrel depending on its type (fortransport or storage)(Fig. 2).

a. b.Fig. 2.

Schema de aezare a butoaielor pentru definirea bazei de calcul a cercurilor, n funcie de tipulbutoiului / Layout for defining the calculation base for the circles, depending on the barrel type:

a - butoi de depozitare/storage barrel ; b- butoi de transport/transport barrel.

Calculul de dimensionare a cercurilor derezistentrebuie saibn vedere structura orientata lemnului din cadrul doagelor tiind c tensiunile destrivire sunt diferite la lemn dup direcie radial itangenial (Cismaru 2003). De aceea trebuie avut nvedere faptul cdoagele se debiteazradial, avnd nvedere c lemnul are rezistene la ncovoiere diferite

dupdirecie radiali tangenial(Fig.3).Toate aceste elemente trebuie avute n vederepentru corectitudinea calculelor care au efect attasupra siguranei n funcionare a butoiului ct ipentru stabilirea corecta adaosurilor de prelucrare iimplicit a consumului de lemn nglobat n doag,respectiv n butoi.

When dimensioning the resistance circles,one must have in view the structure of the woodstaves, knowing that the crushing strength of woodhas different values in radial and tangential direction(Cismaru 2003). Staves are cut radially, consideringthat the bending strength is also different in radialdirection compared to the tangential direction

(Fig.3).All these issues should be considered for theaccuracy of calculations that affect both theoperational safety of the barrel and the correctestablishing of processing oversizes that affect theconsumption of wood embedded in a stave and inthe whole barrel.

Lb

gb

bba.

A

A

A A

b.Fig. 3.

Orientarea structurii lemnului n volumul doagei / Structural orientation of wood in the volume of astave:

a - doaga brutdupdebitare / raw stave after cutting; b - doaga dupcurbare / stave after bending.


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DIMENSIONAREA CERCURILORPentru efectuarea calculului de dimensionare a

cercurilor se pornete de la dimensiunile elementelorgeometrice ale butoiului i de la forma stabilit carermne finaln execuie.

Avnd definite aceste elemente (Cismaru i

Fotin 2010) se trece la ntocmirea la scar a schieibutoiului pentru a se stabili poziia i numrulcercurilor n funcie de capetele acestuia aa cumrezultdin Fig.4.

DIMENSIONING THE CIRCLESFor the calculation of the dimensioning of the

circles is based upon the size and geometry of thebarrel to form the final set remains running.

Having defined these elements (Cismaru andFotin 2010) proceed to preparing the draft barrel

scale in order to determine the position and numberdepending on the ends of the circles as shown inFig.4.

D

H

r1=r=d/2r2

r3

R1

l1

l2

l3

R1

d

O O

Fig. 4.

Schia butoiului cu poziionarea cercurilor fade capete / Sketch of the barrel with the positioning ofthe circles relative to the barrel bottoms.

Prin efectuarea desenului la scar al butoiuluide transport i poziionarea cercurilor se definesc(prin msurare) urmtoarele elemente:

r1; r2; r3 razele interioare ale butoiului ndreptul centrului cercurilor (cazul folosirii acte trei cercuri la fiecare capt);

l1; l2; l3 distanele dintre centrele cercurilor.Pentru pornirea calculului se considerdesenul

din Fig.5., unde se ia ca baz o doag din mantapentru care se scriu relaiile de echilibru static.

Din analiza desenului din Fig.5. rezultc:doaga sub influena presiunii hidrostatice pix (ntr-oseciune x) i sub influena presiunilor de etanarepex(exercitate de doagele alturate) are tendina de afi scoas din manta, de ctre fora interioar Pix iforele de etanare Pex; meninerea doagei n manta i meninerea nacelai timp a etanrii se va putea face doar cu ofor exterioarPex care trebuie srespecte condiiaPexPix;fora exterioarPexva fi introdusde cercuri.

By making the barrel drawing circles transportand positioning are defined (by measurement) thefollowing elements:

r1; r2; r3 inner radius of the barrel in theright circle center (the use of three circles ateach end);

l1; l2; l3 distances between the centers ofcircles.

To start the calculation is considered drawingin Fig.5. which is taken as the basis for which a lagin the mantle of static equilibrium relations arewritten.

The analysis of drawing from Fig.5. shows that: the stave under the influence of hydrostaticpressure pix(in a section "x") and under the influenceof pressure of watertight pex (exercised adjacentstaves) tends to be removed from the mantle, by theinner force Pixand forces of watertight Pexmaintaining the mantle stave while maintaining thewatertight will be possible only with an external forcePexto the condition PexPix; the external force Pex will be introduced by thecircles.


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0Pex

rx

Pix

gm

Pex

Pex

pix

pex

pex

O

Fig. 5.

Solicitrile la care este supusdoaga de manta / Stresses to which the jacket stave is subjected.

Pentru a defini mrimea forelor exterioare Pex

din dreptul fiecrui cerc, trebuie definite valorileforelor care tind sdezmembreze mantaua.Pentru definirea acestor fore care trebuie

preluate de ctre fiecare cerc, se pornete de laipoteza c fiecare cerc va prelua fora creat decoloana de lichid pentru nlimea corespunztoaredintre cercuri i anume:

cercul 1 va prelua fora datde presiuneainterioarpentru nlimea coloanei de lichidegalcu l1;

cercul 2 va prelua fora specificnlimiicoloanei de lichid egalcu l2;

cercul 3 va prelua fora specificnlimiicoloanei de lichid egalcu l3;

Cercurile de la captul superior sunt simetricegale cu cele de la captul inferior (de calcul) avndn vedere c n transport sau depozitare, butoiul sepoate aeza pe oricare din capete.

n acest caz se poate scrie relaia de definire apresiunii hidrostatice interioare (Cismaru 2007)specificnlimii coloanei de lichid astfel:

xix Hp = [N/mm2] (1)

n care: este densitatea lichidului depozitat, N/mm3;Hx nlimea coloanei corespunztoare

fiecrui cerc; H1=H; H2=H l1; H3=H l1 l2, mm.Fora interioargeneratde presiunea

hidrostaticva fi:

xxixix lrpP = [N] (2)

n care: rx,este raza interioarmsuratpe desenuldin Fig.4. n dreptul fiecrui cerc (r1, r2, r3);, unghiul la centru al unei doage (=360/Z);Z, este numrul ntreg de doage din manta;lx, este nlimea coloanei de lichid preluatde

fiecare cerc (l1; l2;l3), mm.Pentru cele trei cercuri se pot scrie ecuaiile

pentru cele trei fore de interior astfel:

111111 lrHlrpP

ii == [N]

To define the dimension of external forces

Pex - the right of each circle, should be defined thevalues of forces that tend to "dismantle" the jacket.To define these forces what must be taken by

each circle, it begins with hypothesis that each circlewill take over the force created by the liquid columnfor the height corresponding between circles,namely:

the circle 1 will take over the force given ofinternal pressure for the height of liquidcolumn equal with l1;

the circle 2 will take over the specific forcefor the height of liquid column equal with l2;

the circle 3 will take over the specific force ofthe liquid column height equal with l3;

The circles at superior end are symmetricalequal with those at the lower end (of calculation)taking into account that at transport or storage, thebarrel may be placed on whatever end.

In this case we can write down therelationship what define of hydrostatic inner pressure(Cismaru 2007) specified the height of liquid columnthus:

xix Hp = [N/mm2] (1)

where: is the density of the liquid stored;Hx the column height corresponding each

circle; H1=H; H2=H l1; H3=H l1 l2,mm.The inner force generated by hydrostatic

pressure will be:

xxixix lrpP = [N] (2)

where: rx,is the inner radius measured on thedrawing of Fig.4. to each circle (r1, r2, r3);

, angle at the center of the one stave (=360/Zi);Z, is the integer number of staves in the jacket;lx, is the height of liquid column - taken over byeach circle (l1; l2;l3), mm.

For the three circles can write equations for thethree internal forces such:

111111 lrHlrpP

ii == [N]


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( )2212222

lrlHlrpP ii == [N] (3)

( )32213333

lrllHlrpPii == [N]

Presiunile laterale necesar a se realiza pentruasigurarea etanrii trebuie s aib n vederemeninerea integritii structurii lemnului, aa nct:

radsaexp [N/mm2] (4)

n care:rads

a este tensiunea limitadmisibil (Curtu

.a. 1981) la strivire dup direcie radial, n funciede specie.

n aceste condiii (la limit) se pot scrie relaiilede calcul pentru forele laterale:

mxaxalx glSPradsrads

== ' [N] (5)

n care: Sxeste suprafaa de contact dintre doage pecare trebuie so asigure fiecare cerc.

Se poate scrie:

mal glPrads

=11

[N]

mal glPrads

=22 [N] (6)

mal glPrads

=33

[N]

Suma tuturor forelor care tind sscoatdoagadin manta, care trebuie s fie preluate de foreleexterioare introduse de cercuri, se poate scrie lalimitpe baza relaiilor (2) i (4) astfel:

2sin2

+=

lxixex PPP [N] (7)

sau, innd cont de relaiile 3 i 5 se pot scrie foreleexterioare pentru fiecare cerc astfel:

2sin2 1111 += mae gllrHP

rads[N]

( )2

sin222212

+= mae gllrlHP

rads

[N] (8)

( )2

sin2 333213

+= mae gllrllHPrads

[N]

Ecuaiile (8) definesc astfel forele exterioare cetrebuie introduse de ctre fiecare cerc pentru a semenine structura butoiului simultan cu realizareaetaneitii.

n aceste condiii trebuie avut n vedere c lacontactul dintre cerc i suprafaa de lemn a mantaleinu trebuie sse genereze tensiuni de strivire care s

duc la distrugerea structurii anatomice a lemnului.Astfel, n aceste condiii trebuie s se respecte icondiia ca:

tgsaexp (Curtu i Ghelmeziu 1984) i

ca atare forele exterioare se pot defini cu relaia:

( ) cxmxaxaxexex bgrSSpP

tgstgs+==

"" [N]

(9)

n care:tgs

a , este tensiunea limitde strivire n plan

tangenial n funcie de specie, N/mm2;

( )2212222

lrlHlrpPii

== [N] (3)

( )32213333

lrllHlrpPii == [N]

The side pressures necessary achieve toensure the watertight must consider preserving theintegrity of the wood structure, such that:

radsaexp [N/mm2] (4)

where:rads

a is the admisible limit tension to the

crush (Curtu et.al. 1981) after the radial direction,depending on the species.

Under these conditions (the limit) can writerelations for calculating the side forces:

mxaxalx glSPradsrads

== ' [N] (5)

where: Sx is the area of contact between the stavesthat must an ensure each circle.

One can write:

mal glPrads

=11

[N]

mal glPrads

= 22 [N] (6)

mal glPrads

=33

[N]

The sum of all forces which tend to stave outthe jacket, which must be taken over by externalforces produced by the circles, can be written at limitthe relations (2) and (4) as:

2sin2

+=

lxixex PPP [N] (7)

or, taking into account the relations 3 and 5can be written the external forces for every circle,such:

2sin2 1111 += mae gllrHP

rads[N]

( )2

sin222212

+= mae gllrlHP

rads

[N] (8)

( )2

sin2 333213

+= mae gllrllHPrads

[N]

Equations (8) define the external forces to beintroduced by each circle for is maintained to thestructure barrel, simultaneous while achievingtightness.

Under these conditions must be consideredthat at the contact between the circle and woodsurface of jacket should not generate crushing

tensions that lead to the destruction the woodanatomy structure. Thus, in these conditions mustbe respected the condition that:

tgsaexp (Curtu

and Ghelmeziu 1984) and as such the externalforces can define by the relationship:

( ) cxmxaxaxexex bgrSSpP

tgstgs+==

"" [N]

(9)where:

tgsa , is the limit tension of crushing in the

tangential plan depending on the species, N/mm2;


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Sx, este suprafaa de contact dintre cerc imanta, mm2;

gm, este grosimea doagei de manta, mm;bcx, este limea cercului pentru care se face

calculul (b1, b2, b3), mm.n desenul din Fig.6. rezult c prin

introducerea unor fore de tragere n cerc Pcx, seintroduce fora exterioar Pex care trebuie realizatpentru asigurarea condiiilor de funcionare alebutoiului.

Pe baza desenului din Fig.6. se poate scriedependena dintre fora exterioarce trebuie realizati forele de tragere din cerc Pcx care trebuieintroduse:

2sin2

= cxex PP [N] (10)

Sx,is the area of contact between the circleand the jacket, mm2;

gm, is the thickness of stave jacket, mm;bcx, is the width of circle for which the

calculation is made (b1, b2, b3), mm.In the drawing in Fig.6. resulting that, through

introducing in the circle, the forces of "pulling" Pcx,is introduced the external force Pex, which be madeto ensure the operating conditions of the barrel.

Based on the drawing by Fig.6. we can writethe dependence between the external force thatmust be achieved and the forces of "pulling" PCXbythe circle that must be introduced:

2sin2

= cxex PP [N] (10)

0Pex

rx

gm

O

Pcx

Pcx

pex

Fig. 6.

Introducerea forei exterioare prin tragerea cercurilor / The introduction the external force by"hitting" the circles.

Dup o rearanjare a ecuaiei (10) se poatescrie:

2sin2 ex

cx

PP = [N] (10)

Avnd n vedere ecuaiile (8) se pot scrierelaiile de calcul ale forelor de tragere pentru fiecarecerc n parte:

2sin2

1

1

e

c

PP = [N]

2sin2

2

2 e

c

PP = [N] (11)

2sin2

3

3 e

c

PP = [N]

After a rearrangement of equation (10) can bewritten:

2sin2 ex

cx

PP = [N] (10)

Given equations (8) we can write the relationsfor calculation of pulling forces for each part circle:

2sin2

1

1

e

c

PP = [N]

2sin2

2

2 e

c

PP = [N] (11)

2sin2

3

3 e

c

PP = [N]


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Dacse nlocuiesc Pe1, Pe2iPe3cu relaiile (8)scrise se pot obine relaiile complete de calcul aleforelor de tragere din fiecare cerc.

Revenind la ecuaiile (9), acestea se potexplicita, rezultnd limile de contact ale cercurilorcu mantaua astfel:

( ) 111 cmae bgrP tgs + [N]

( )222 cmae bgrP

tgs+ [N] (12)

( )333 cmae bgrP

tgs+ [N]

care dupexplicitare devin:

( ) +

ma

ec

gr

Pb

tgs1

1

1[mm]

( ) +

ma

ec

gr

Pb

tgs2

2

2[mm] (13)

( ) + maecgr

Pb

tgs3

33 [mm]

Valorile limilor cercurilor care rezult dincalcul se rotunjesc la valorile imediat superioareprevzute n STAS 2684-87.

Relaiile (13) au valorile Pe1, Pe2iPe3rezultatepe baza calculului conform ecuaiilor (8).

Pentru calculul grosimii cercurilor se au nvedere ecuaiile (11) care definesc mrimile forelorde tragere din cercuri (Pc1, Pc2iPc3).

Dacse scrie relaia de solicitare la traciune acercurilor sub influena forelor de tragere:

cxcxacacx gbSPOLtOLt

= 2 [N] (14)

n care: bcx, este limea cercurilor calculat curelaiile (13) i alese din STAS 2684-87, pentru carese face calculul (b1, b2, b3).

OLta , reprezint tensiunea admisibil la

traciunea oelului pentru platband (STAS 2684-87),N/mm2;

gcx, este grosimea necesar a cercurilor, nmm i se expliciteazastfel nct rezult:

cxa

cxcx

b

Pg

OLt

2[mm] (15)

n aceast situaie pentru cele trei cercuri sepot scrie relaiile (Fotin 2009):

1

1

1

2

ca

cc

b

Pg

OLt

[mm]

2

22

2

ca

cc

b

Pg

OLt

[mm] (16)

3

3

3

2

ca

cc

b

Pg

OLt

[mm]

If replaced Pe1, Pe2 and Pe3 with relations (8)written, than can be obtained the complete relationsfor calculating the forces pulling from each circle.

Returning to equations (9), these can beexplained, resulting the widths of contact of thecircles with the jacket as:

( ) 111 cmae bgrP tgs + [N]

( )222 cmae bgrP

tgs+ [N] (12)

( )333 cmae bgrP

tgs+ [N]

that after the explanation becomes:

( ) +

ma

ec

gr

Pb

tgs1

1

1[mm]

( ) +

ma

ec

gr

Pb

tgs2

2

2[mm] (13)

( ) + maecgr

Pb

tgs3

33 [mm]

The values of the widths the circles resultingfrom the calculation are rounded up at the valuesprovided in STAS 2684-87.

Relationships (13) have values Pe1, Pe2 andPe3 resulted on the calculation based on theequations (8).

To calculate the thickness of the circles aretaken into consideration equations (11) which definethe sizes of forces of "pulling" of the circles (Pc1, Pc2iPc3).

If is written the relationship the tensileresistance of the circles under the influence theforces of pulling:

cxcxacacx gbSPOLtOLt

= 2 [N] (14)

where: bcx, is the width circles calculated withrelations (13) and chosen by the STAS 2684-87, forwhich is made the calculation (b1, b2, b3).

OLta , is the tensile tension permissible for

flat steel (STAS 2684-87), N/mm2;gcx, is the required thickness of the circles, in

mm and so, is given as follows results:

cxa

cxcx

b

Pg

OLt

2[mm] (15)

In this situation for the three circles we canwrite relations (Fotin 2009):

1

1

1

2

ca

cc

b

Pg

OLt

[mm]

2

22

2

ca

cc

b

Pg

OLt

[mm] (16)

3

3

3

2

ca

cc

b

Pg

OLt

[mm]


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Valorile rezultate din calcul conform relaiilor(16) se rotunjesc la valorile imediat superioare dinSTAS 2684-87.

Se practic trei variante de rezolvare adimensiunilor cercurilor din punct de vedere al limiii grosimii astfel:

Var.I.bc1STAS bc2STASbc3STAS igc1STAS gc2STASgc3STAS

Var.II.bcSTAS = max(bc1; bc2; bc3 rezultate din calcul)

igc1STAS gc2STASgc3STAS

Var.III.bc1STAS bc2STASbc3STAS igcSTAS = max(gc1; gc2; gc3 rezultate din calcul)

Pentru estetica butoiului varianta III este ceamai recomandat, limile fiind descresctoare de lacaptul butoiului spre centru, cercurile avnd aceeai

grosime.Pentru determinarea lungimii cercurilor se aren vedere desenul la scarefectuat ca n Fig.4.

Relaia general de calcul a lungimii cercuriloreste de forma (Cismaru I. 2007):

( ) xmxx

lgrL ++= 2 [mm] (17)

n care: Lx, este lungimea totala cercurilor, iarlx, lungimea de suprapunere a capetelor n

poriunea cu nituri.Determinarea lungimii lx se face ca pentru

calculul mbinrilor nituite (vezi Fig.7), astfel:

The values resulted of calculating accordingto relations (16) rounded-up to the next highervalues by STAS 2684-87.

Taking into account the width and thicknessthe circles there are three variants solutions to thecircles dimensions:

Var.I.bc1STASbc2STASbc3STAS andgc1STASgc2STASgc3STAS

Var.II.bcSTAS=max(bc1; bc2; bc3 results of calculation)

andgc1STASgc2STASgc3STAS

Var.III.bc1STASbc2STASbc3STAS andgcSTAS=max(gc1; gc2; gc3 results of calculation)

For barrel aesthetics, option III is the mostrecommended, the widths are decreasing at the endof the barrel to the center, circles having the same

thickness.To determine the circles length it is consideredthe drawing done at scale as in Fig.4.

The general relationship for calculating thelength circles is of the form (Cismaru I. 2007):

( ) xmxx

lgrL ++= 2 [mm] (17)

where: Lx, is the total length of the circles, andlx,the length of the overlap portion ends with

rivets.The calculation of the length lx it is made as

the calculation the riveted joints (see Figure 7) so:

x x

dN

Pcx Pcx

bcx

Pcx Pcx

gcx

lx

lx

Fig. 7.Schema de calcul a lungimii de suprapunere a cercurilor / The calculation scheme for the overlapping

length of of the circles.

a) din condiia de forfecare (Curtu i Ghelmeziu 1984)a niturilor rezult:

N

x

af

Nx

cx

f

cxf

dn

P

S

P

==

2

82[N/mm2] (18)

n care:dNx- reprezintdiametrul niturilor, mmnx- numrul niturilor

Naf - reprezint tensiunea admisibil la

forfecare a niturilor, N/mm2

a) from the condition of the rivets shear (Curtu andGhelmeziu 1984), results:

N

x

af

Nx

cx

f

cxf

dn

P

S

P

==

2

82[N/mm2] (18)

where:dNx- is the diameter rivets, mmnx- the number rivets

Naf - is the tension permissible at shear rivets,

N/mm2


10/12



48

Relaia (18) se poate explicita:atunci cnd se impune numrul de nituri i

rezultdiametrul niturilor:

Naf

cxNx

n

Pd

8[mm] (18)

atunci cnd se impune diametrul nitului irezultnumrul de nituri:

Nx afN

cx

xNd

Pn

2

8[buc] (18)

b) din condiia de strivire a niturilor (Curtu .a,1981),rezult:

s

x

a

cxN

cx

sx

cx

s

sgd

P

S

P

S

F

cismaru full

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