p644l (2)
TRANSCRIPT
-
7/26/2019 P644L (2)
1/62
74
VI. VERIFICAREA LA REZISTENTA A ARBORELUI COTIT
Motorul de referinare urmtoarele caracteristici: D=103 mm, S=127 mm, n=2400 rpm, t=4 timpi, i=4 cilindrii in L,P==64 kW.
Verificarea presiunii specifice maxime si medii
Pe baza calculelor anterioare au fost stabilite valorile maxim i medie ale forei care acioneaznlagrul maneton. Priurmare, presiunea specifica maximpe fusul maneton este:
pMmax
RMmax
10dM 100 lM 100
:= pMmax 193.353= daN
cm2
La rndul ei, presiunea specificmedie are valoarea:
pMmed
RMmed
10
dM 100 lM 100:= pMmed 80.564=
daN
cm2
Ambele valori nu depesc limitele admisibile indicate:
pMmax 100...300:=daN
cm2
pMmed 30...100:=daN
cm2
Rp.max Rp.max 0
Rp.max max R pmaxj 1+Rpmaxj
, Rp.max max R pmaxj 1+Rpmaxj
,
-
7/26/2019 P644L (2)
2/62
75
Rp.med Rp.med 0
Rp.med max R pmedj 1+Rpmedj
, Rp.med max R pmedj 1+Rpmedj
,
-
7/26/2019 P644L (2)
3/62
76
Verificarea la oboseala pentru fusul palier maxim solicitat
Valorile momentelor de rsucire care solicitfusurile palier
Mr.II Mr.IIj
R Ti1j
j 0 72..for
Mr.II
:= Mr.III Mr.IIIj
Mr.IIjR Ti2j
+
j 0 72..for
Mr.III
:=
Mr.IVMr.IVj
Mr.IIIjR Ti3j
+
j 0 72..for
Mr.IV
:= Mr.VMr.Vj
Mr.IVjR Ti4j
+
j 0 72..for
Mr.V
:=
0
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
0
10
20
30
40
50
60
70
80
90
100
110
120
130
140
150
160
170
180
190
200
210
220
230
240
250
260
270
280
290
300
310
320
330
340
350
360
370
380
= Mr.II
0
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
0
3-2.78410
3-5.03810
3-6.35410
3-6.52810
3-5.59510
3-3.80510
3-1.54710
755.559
32.73710
34.15410
34.92110
35.06910
34.71610
34.01410
33.10510
32.09610
31.05210
0
3-1.05310
3-2.110
3-3.11310
3-4.03310
3-4.74710
3-5.11810
3-5.00810
3-4.29910
3-2.9410
3-1.07410
31.110
33.06810
34.67510
35.3310
34.75810
33.48310
31.81910
0
3-1.48110
31.97810
= Mr.III
0
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
35.06910
31.93210
3-1.02410
3-3.24910
3-4.43210
3-4.54310
3-3.80510
3-2.610
3-1.34410
-376.463
120.5
173.48
-48.864
-291.784
-285.055
164.848
31.02210
32.15210
33.06810
33.62310
33.23110
31.64410
-550.716
3-2.92810
3-5.11810
3-6.48910
3-2.32110
3-7.4210
3-6.05110
3-3.1510
220.192
34.01810
36.81710
38.06710
38.12910
37.10510
35.36810
33.45710
36.16310
= Mr.IV
0
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
-48.864
3-3.07610
3-5.32310
3-6.18910
3-5.50510
3-3.44310
-737.075
32.07610
33.98610
34.38110
33.60310
31.99310
-48.864
3-1.77310
31.69310
3-4.31510
3-3.95510
3-2.09810
220.192
32.96510
34.71810
34.95410
34.09610
32.35710
250.036
3-1.55110
31.86410
3-4.19510
3-3.87610
3-2.05910
220.192
32.94110
34.68410
34.92710
34.09610
32.4110
324.312
3-1.43510
32.04110
=
-
7/26/2019 P644L (2)
4/62
77
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
390
400
410
420
430
440
450
460
470
480
490
500
510
520
530
540
550
560
570
580
590
600
610
620
630
640
650
660
670
680
690
700
710
720
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
3-4.47910
3-4.97810
3-4.2510
3-2.84810
-657.479
31.48710
33.3110
34.64710
35.28510
35.36810
34.93810
34.18510
33.22510
32.17510
31.0910
0
3-1.07710
3-2.13410
3-3.14110
3-4.03410
3-4.69510
3-5.04310
3-4.89210
3-4.12210
3-2.710
-733.783
31.56810
33.8110
35.59910
36.53110
36.35710
35.0410
32.78410
0
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
3-1.25510
3-2.80310
3-3.15910
3-2.84810
3-1.73510
-646.4
169.417
612.967
590.947
324.312
45.614
62.82
525.347
31.44110
32.65910
33.8110
34.52210
34.39810
33.21610
31.00610
3-1.9110
3-5.04310
3-6.37310
3-2.14510
3-7.17910
3-5.71110
3-2.68110
961.919
34.94210
38.01910
39.66710
39.68710
38.0710
35.36810
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
6869
70
71
72
3-3.95410
3-3.53710
3-1.59110
961.919
33.86410
35.88510
36.52610
35.65310
33.37510
324.312
3-1.43510
32.04110
3-3.95410
3-3.53710
3-1.59110
961.919
33.86410
35.88510
36.52610
35.65310
33.37510
324.312
3-1.43510
32.04110
3-3.95410
3-3.53710
3-1.59110
961.919
33.86410
35.8851036.52610
35.65310
33.37510
324.312
0
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
0
10
20
30
40
50
60
70
80
90
100
110
120
130
140
150
160
170
180
0
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
3-3.85410
3-4.62210
3-4.56710
3-3.45210
3-1.35110
31.47810
34.33210
36.79210
3810
37.48610
35.69910
33.04410
-48.864
3-2.82510
-406.861
3-7.42810
3-7.98910
3-6.84510
3-4.89710
-
7/26/2019 P644L (2)
5/62
78
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
200
210
220
230
240
250
260
270
280
290
300
310
320
330
340
350
360
370
380
390
400
410
420
430
440
450
460
470
480
490
500
510
520
530
540
550
560
570
580
590
600
610
620
630
640
650
660
670
680
690
700
710
720
= Mr.V
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
- .
418.713
32.01410
33.02210
33.45710
33.31810
33.12410
37.19410
562.787
-393.806
-240.082
220.192
31.4610
36.66210
447.545
-882.059
3-1.83910
3-2.52410
3-2.09310
33.52810
-644.111
31.1110
33.69510
36.3310
38.80210
41.00710
39.75110
37.82810
34.46510
324.312
3-2.51310
-93.09
3-7.09510
3-7.5710
3-6.28510
3-4.08110
3-1.02810
31.76310
33.82710
34.91910
34.94410
34.13410
34.16410
38.57210
32.40310
31.50310
31.19310
961.919
32.38310
37.86310
32.04710
675.088
-874.455
3-2.52410
=
-
7/26/2019 P644L (2)
6/62
79
Pentru verificarea la oboseala fusurilor palier, au fost calculeate ini ial momentele de rsucire ale acestorai au fost apoi calculate valorile extreme i amplitudinea:Mr.II.max Mr.II.max 0
Mr.II.max max Mr.IIj 1+Mr.IIj
, Mr.II.max max Mr.IIj 1+Mr.IIj
,
-
7/26/2019 P644L (2)
7/62
80
Mr.V.min Mr.V.min Mr.V.max
Mr.V.min min Mr.Vj 1+Mr.Vj
, Mr.V.min min Mr.Vj 1+Mr.Vj
,if
j 0 71..for
Mr.V.min
:=
AMr.V Mr.V.max Mr.V.min-:=
Mr.II.max 6.531 103
= Mr.II.min 6.528- 103
= AMr.II 1.306 104
=
Mr.III.max 9.687 103
= Mr.III.min 7.42- 103
= AMr.III 1.711 104
=
Mr.IV.max 6.526 103
= Mr.IV.min 6.189- 103
= AMr.IV 1.272 104
=
Mr.V.max 1.007 104
= Mr.V.min 7.989- 103
= AMr.V 1.806 104
=
Modulul de rezistenpolar al seciunii transversale a fusului palier are valoare:
WpP
dp3
16:= WpP 2.682 10
5-= m
3
Rezultvalorile extreme ale efortului unitar de rsucire:
P.max
Mr.V.max
WpP10
5-:= P.max 3.755 10
3=
daN
cm2
P.min
Mr.V.min
WpP 10
5-
:= P.min 2.979- 10
3
=
daN
cm2
Amplitudinea i media acestor eforturi sunt:
Pv
P.max P.min+
2:= Pv 388.047=
daN
cm2
Pm
P.max P.min-
2:= Pm 3.367 10
3=
daN
cm2
Conform indicaiilor din manual pentru materialul de construcie al arborelui cotit (OLC45), se adoptrezistena la obosealprecum i valorile coeficienilor de calcul astfel:
1.4:=_1 2100:=
daN
cm2
0.09:=R.
k
=
R. 2.5:=
-
7/26/2019 P644L (2)
8/62
81
Cu ajutorul lor se determincoeficientul de siguranla obosealpentru fusul palier:
cP
_1
R.
Pv Pm+
:=cP 2.109=
Valoarea obinuteste superioarcelei minim admisibile indicatmai jos:
cp 2...3:=
Verificarea la oboseala pentru fusul maneton
Pentru verificarea la oboseala fusului maneton este necesardeterminarea iniiala forei radiale Zj,normallameneton. Aceasta se obine prin nsumarea algebrica forei radiale Zcu forele de inerie alefusului maneton i ale masei bielei aferentacestuia calculate anterior. Rezultatele vor fi prezentatecentralizat in tabelul de mai jos.
ZjZjj
ZBjFibm+ FR+
j 0 72..for
Zj
:=kN
Rezultastfel reaciunea din reazemul stng al fusului, rezultatele find cuprinse n tabelul de mai jos:
Zsj
Zsjj
1
2Zjj
Fbr+ Fcg+
j 0 72..for
Zsj
:=
kN
Totodats-a calculat momentul de ncovoiere n planul cotului, cu relaia de mai jos, rezultatele findcuprinse centralizat n tabel.
MZ
MZj
l Zsjj l lp-( ) Fbr Fcg-( )+
2
j 0 72..for
MZ
:=
kN
0
0
1
2
3
4
5
6
7
8
9
0
10
20
30
40
50
60
70
80
90
0
0
1
2
3
4
5
6
7
8
9
5-3.40110
5-3.30510
5-3.03410
5-2.64410
5-2.21110
5-1.81310
5-1.51410
5-1.35210
5-1.33410
5-1.43610
5-
0
0
1
2
3
4
5
6
7
8
9
5-1.70110
5-1.65310
5-1.51710
5-1.32310
5-1.10610
4-9.06810
4-7.57510
4-6.76710
4-6.67410
4-7.18710
4-
0
0
1
2
3
4
5
6
7
8
9
3-9.21510
3-8.95710
3-8.23510
3-7.19710
3-6.04210
3-4.9810
3-4.18410
3-3.75410
3-3.70410
3-3.97810
3-
-
7/26/2019 P644L (2)
9/62
82
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
3435
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
110
120
130
140
150
160
170
180
190
200
210
220
230
240
250
260
270
280
290
300
310
320
330
340350
360
370
380
390
400
410
420
430
440
450
460
470
480
490
500
510
520
530
540
= Zj
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
3435
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
.
5-1.8410
5-2.05710
5-2.24410
5-2.38810
5-2.48710
5-2.54910
5-2.58110
5-2.59110
5-2.58210
5-2.55110
5-2.4910
5-2.39310
5-2.2510
5-2.06410
5-1.84910
5-1.6310
5-1.44510
5-1.33810
5-1.34510
5-1.47710
5-1.73310
5-2.04810
5-2.31310
5
-2.506105-2.61910
5-2.61610
5-2.37810
4-6.54310
5-2.25510
5-2.00110
5-1.69510
5-1.46610
5-1.33710
5-1.34310
5-1.4610
5-1.65510
5-1.87810
5-2.110
5-2.28710
5-2.43310
5-2.53210
5-2.59510
5-2.62710
5-2.62910
5-
= Zsj
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
.
4-9.20310
5-1.02910
5-1.12210
5-1.19410
5-1.24410
5-1.27510
5-1.29110
5-1.29610
5-1.29210
5-1.27610
5-1.24610
5-1.19710
5-1.12510
5-1.03210
4-9.24910
4-8.15510
4-7.22810
4-6.69310
4-6.72710
4-7.39210
4-8.66710
5-1.02510
5-1.15710
5
-1.254105-1.3110
5-1.30810
5-1.1910
4-3.27610
5-1.12810
5-1.00110
4-8.48210
4-7.33710
4-6.68810
4-6.71710
4-7.30310
4-8.27910
4-9.39410
5-1.0510
5-1.14410
5-1.21710
5-1.26710
5-1.29810
5-1.31410
5-1.31510
5-
= MZ
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
3435
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
.
3-5.05210
3-5.63110
3-6.12910
3-6.51210
3-6.778103-6.94310
3-7.02810
3-7.05510
3-7.03210
3-6.94810
3-6.78710
3-6.52610
3-6.14510
3-5.64910
3-5.07710
3-4.49410
3-410
3-3.71410
3-3.73310
3-4.08710
3-4.76710
3-5.60910
3-6.31310
3
-6.829103-7.12810
3-7.12110
3-6.48710
3-1.89310
3-6.15910
3-5.48110
3-4.66810
3-4.05810
3-3.71210
3-3.72710
3-4.0410
3-4.5610
3-5.15410
3-5.74610
3-6.24410
3-6.63310
3-6.89810
3-7.06510
3-7.15110
3-7.15610
3-
=
-
7/26/2019 P644L (2)
10/62
83
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
560
570
580
590
600
610
620
630
640
650
660
670
680
690
700
710
720
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
.
5-2.57110
5-2.50110
5-2.39310
5-2.23910
5-2.05310
5-1.83710
5-1.61810
5-1.43510
5-1.33410
5-1.35310
5-1.51410
5-1.81310
5-2.21110
5-2.64510
5-3.03510
5-3.30510
5-3.40110
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
.
5-1.28610
5-1.25110
5-1.19710
5-1.1210
5-1.02710
4-9.18810
4-8.09210
4-7.17910
4-6.67310
4-6.76910
4-7.57610
4-9.0710
5-1.10610
5-1.32310
5-1.51810
5-1.65310
5-1.70110
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
.
3-7.00110
3-6.81410
3-6.52610
3-6.11810
3-5.62110
3-5.04410
3-4.4610
3-3.97310
3-3.70410
3-3.75510
3-4.18510
3-4.98110
3-6.04310
3-7.19810
3-8.23710
3-8.95710
3-9.21510
Pentru determinarea momentului de ncovoiere din planul tangenial se utilizeazvalorile forei tangenialeTj. Pe baza lao a fost determinata variaia reaciunii tangeniale.
TjTjj
Tj
j 0 72..for
Tj
:= Tsj
Tsjj
Tjj
2
j 0 72..for
Tsj
:=
kN kN
Aceste reaciuni determinmomentul de ncovoiere.
MT
MTj
l Tsjj
2
j 0 72..for
MT
:=
kNm
0
0
1
2
3
4
5
6
7
8
9
0
10
20
30
40
50
60
70
80
90
0
0
1
2
3
4
5
6
7
89
0
4-4.38410
4-7.93410
5-1.00110
5-1.02810
4-8.81110
4-5.99210
4-2.43610
4
1.191044.3110
0
0
1
2
3
4
5
6
7
8
9
0
4-2.19210
4-3.96710
4-5.00310
4-5.1410
4-4.40510
4-2.99610
4-1.21810
35.94910
42.15510
4
0
0
1
2
3
4
5
6
7
8
9
0
3-1.16810
3-2.11410
3-2.66710
3-2.7410
3-2.34810
3-1.59710
-649.184
317.112
31.14910
3
-
7/26/2019 P644L (2)
11/62
84
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
110
120
130
140
150
160
170
180
190
200
210
220
230
240
250
260
270
280
290
300
310
320
330
340
350
360
370
380
390
400
410
420
430
440
450
460
470
480
490
500
510
520
530
540
= Tj
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
.
47.74910
47.98210
47.42710
46.32110
44.8910
43.30110
41.65610
0
4-1.65810
4-3.30610
4-4.90310
4-6.35210
4-7.47610
4-8.05910
4-7.88610
4-6.7710
4-4.6310
4-1.69110
41.73210
44.83210
47.36310
48.39410
47.49210
45.48510
42.86510
0
4-2.33210
43.11510
4-7.05410
4-7.83910
4-6.69210
4-4.48510
4-1.03510
42.34210
45.21210
47.31810
48.32410
48.45310
47.77610
46.59110
45.07910
43.42510
4
1.71710
0
= Tsj
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
.
43.87510
43.99110
43.71310
43.16110
42.44510
41.6510
38.28110
0
3-8.2910
4-1.65310
4-2.45110
4-3.17610
4-3.73810
4-4.0310
4-3.94310
4-3.38510
4-2.31510
3-8.45410
38.66110
42.41610
43.68110
44.19710
43.74610
42.74210
41.43210
0
4-1.16610
41.55710
4-3.52710
4-3.91910
4-3.34610
4-2.24210
3-5.17710
41.17110
42.60610
43.65910
44.16210
44.22710
43.88810
43.29510
42.53910
41.71210
38.58510
0
= MT
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
.
32.06510
32.12710
31.97910
31.68510
31.30310
879.737
441.424
0
-441.857
-881.183
3-1.30710
3-1.69310
3-1.99210
3-2.14810
3-2.10210
3-1.80410
3-1.23410
-450.594
461.658
31.28810
31.96210
32.23710
31.99710
31.46210
763.535
0
-621.554
830.06
3-1.8810
3-2.08910
3-1.78410
3-1.19510
-275.947
624.199
31.38910
31.9510
32.21810
32.25310
32.07210
31.75610
31.35310
912.781
457.604
0
=
-
7/26/2019 P644L (2)
12/62
85
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
550
560
570
580
590
600
610
620
630
640
650
660
670
680
690
700
710
720
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
- .
4-3.3610
4-4.94610
4-6.35210
4-7.39310
4-7.94210
4-7.70410
4-6.49210
4-4.25110
4-1.15610
42.4710
4610
48.81710
51.02910
51.00110
47.93710
44.38510
0
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
-8.48410
4-1.6810
4-2.47310
4-3.17610
4-3.69610
4-3.97110
4-3.85210
4-3.24610
4-2.12610
3-5.77810
41.23510
4310
44.40910
45.14310
4
5.0051043.96810
42.19210
0
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
-452.219
-895.496
3-1.31810
3-1.69310
3-1.9710
3-2.11710
3-2.05310
3-1.7310
3-1.13310
-307.972
658.266
31.59910
32.3510
32.74110
3
2.6681032.11510
31.16910
0
Fusul maneton fiind prevzut cu orificiu de ungere, momentul rezultant se determincu ajutorul relaiei:
MoMoj
MZjcos deg( ) MTj
sin deg( )-
j 0 72..for
Mo
:= M17
:=
Rezultatele calculelor sunt cuprinse n tabelul de mai jos, rezultnd cvaloarea maxima momentuluincovoietor total se nregistreazn cazul prezeei contragreutii.
Mo.max Mo.max 0
Mo.max max Moj 1+Moj
, Mo.max max Moj 1+Moj
,
-
7/26/2019 P644L (2)
13/62
86
Mo
0
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
3-1.610
-404.608
652.293
31.37710
31.64910
31.44810
846.156
-12.533
-955.573
3-1.82210
3-2.49310
3-2.91110
3-3.07310
3-3.01410
3-2.7910
3-2.4610
3-2.07210
3-1.65510
3-1.22510
-785.911
-338.69
108.381
533.889
895.147
31.13410
31.18810
996.631
520.752
-201.254
3-1.10310
3-1.97810
3-2.7610
3-3.17710
3-3.06310
3-2.62510
3-1.9910
3-1.23710
-514.4
3-1.14610
781.875
31.10610
945.893
472.482
=
-
7/26/2019 P644L (2)
14/62
87
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
- .
3-1.26210
3-2.0710
3-2.71210
3-3.0810
3-3.21610
3-3.12510
3-2.88210
3-2.53110
3-2.12610
3-1.69210
3-1.24310
-789.352
-333.809
114.897
533.985
878.068
31.10910
31.14610
929.306
425.798
-339.868
3-1.310
3-2.30110
3-3.179103-3.74910
3-3.87810
3-3.51310
3-2.70610
3-1.610
Conform celor prezentate se considerun ciclu simetric de ncrcare, n care Mmin=- Mmax. n aceste condiii,modulul de rezistenpolar al seciunii transversale a fusului manetor.
WpM
d
M
3
16:= WpM 4.634 105-= m3
Rezulteforturile unitare extreme.
max
Mo.max
WpM10
5-:= max 355.806=
daN
cm2
min
Mo.min
WpM10
5-:= min 836.677-=
daN
cm2
-
7/26/2019 P644L (2)
15/62
88
Amplitudinea i media acestor eforturi sunt:
v
max min-
2:= v 596.242=
daN
cm
2
m
max min+
2:= m 240.436-=
daN
cm2
Pe baza indicaiilor de mai sus pentru fusuri din OLC45 se adopt:
_1 3500:=daN
cm2
Totodatse adopt i parametrii:
1.4= k 2:= 0.8:= 0.1:=
Rezultcoeficientul de siguranla obosealpentru solicitarea de ncovoiere a manetonului.
c
_1
k
v m+
:= c 3.363=
Pentru verificarea solicitarii de torsiune este luat n consideraie fusul maneton al celui mai solicitat cot al arborelucotit. Pe baza datelor calculate au fost utilizate valorile momentului de intrare i ale forei tangeniale. Cu ajutorul lorfi calculat momentul de torsiune al fusului maneton.
M5
M5jMr.Vj
R
Ti5j
2+
j 0 72..for
M5
:=
M5.max M5.max 0
M5.max
max M5j 1+
M5j
, M5.max
max M5j 1+
M5j
,
-
7/26/2019 P644L (2)
16/62
89
M5
0
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
3-2.3210
3-2.28510
3-1.90210
3-1.07410
389.981
32.38710
34.33210
36.05210
38.98910
35.24610
33.2110
919.669
3-1.473103-3.15410
336.755
3-5.77310
3-5.66510
3-4.20210
3-2.21410
426.17
32.51110
33.62610
34.1110
34.00210
33.31810
32.58610
36.12710
3-1.00710
3-2.41110
3-2.58710
3-2.30110
-986.4
34.610
-902.206
3-1.24910
3-1.05510
-618.648
706.716
36.79310
32.53410
33.6310
35.08710
3
=
-
7/26/2019 P644L (2)
17/62
90
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
.
38.06110
41.10610
37.51210
35.33910
32.34110
3-1.110
3-2.84210
650.527
3-5.4410
3-5.24710
3-3.64310
3-1.39810
31.44110
33.85510
35.43910
36.00610
35.48910
34.13410
33.62510
37.50510
832.696
-513.711
3-1.15410
3-1.5610
-62.86
35.80210
697.269
308.197
-90.254
-618.648
Se calculeazeforturile unitare corespunztoare momentelor de torsiune extreme.
max
M5.maxWpM
10 6-:= max 238.626= daNcm
2
min
M5.min
WpM10
6-:= min 124.567-=
daN
cm2
Amplitudinea i media acestor eforturi sunt:
v
max min-
2:= v 181.597=
daN
cm2
m
max min+
2:= m 57.03=
daN
cm2
-
7/26/2019 P644L (2)
18/62
91
Prin urmare meninndu-se valorile adoptate la verificarea fusului palier, coeficientul de siguranlaobosealpentru solicitarea de torsiune va fi:
c
_1
R.
v m+
:= c
6.375=
Rezultastfel coeficientul global de siguranla oboseala fusului maneton:
cM
c c
c2
c2
+
:=cM 2.975=
Pentru verificarea la rezistena braului arborelui cotit, se pleacde la valorile maxim i minimaleeforturilor unitare de ncovoiere i compresiune. Pe baza valorilor extreme ale reaciunii radiale rezult
eforturile unitare:
Zsj.max Zsj.max 0
Zsj.max max Zsjj 1+Zsjj
, Zsj.max max Zsjj 1+Zsjj
,
-
7/26/2019 P644L (2)
19/62
92
Cu ajutorul acestor valori anterior adoptate (n cadrul verificrii fusului maneton), rezultcoeficientul desiguranla obosealpentru solicitrile de ncovoiere i compresiune:
cbr.
_1
k
br.v br.m+
:= cbr. 13.55=
Pentru verificarea solicitrii de torsiune a braului este necesar sse determine mai nti modulul derezistenal acestuia. n acest scop avem:Tj.max Tj.max 0
Tj.max max Tjj 1+Tjj
, Tj.max max Tjj 1+Tjj
,
-
7/26/2019 P644L (2)
20/62
93
VII. CALCULUL PRELIMINAR AL VIBRAIILOR TORSIONALE
Pe baza calculelor anterioare i a documentaiei tehnice a motorului de referin, poate fi stabilit sistemul osculantechivalent din figura de mai jos.
Pentru determinarea momentului de inerie al unui cot al arborelui cotit, se calculeaziniial momentul de inerie al fuspalier.
Jp
32dp
4 lp OLC45 1.248 10
4-=:= Nms
2
La rndul su, momentul de inerie al fusului maneton redus la axa de rotaie al arborelui cotit arevaloarea:
JM0 JM mM R2
+:=
JM0
32dM
2 lM dM 8 R
2+ 1.839 10
9-=:=
Nms2
Sistemul oscilant echivalent al instalaiei de propulsie
Momentul de inerie al braelor frcontragreuti:
Jb 503:= Nms2
J'b 158:= Nms2
Momentul de inertie al bratului fara contragreutate, redus la axa de rotate este:
J'b0 J'b mbr rGbr103-
2
+ 158=:= Nms2
Pentru braul cu contragreutate, centrul de masal ansamblului bra- contragreutate va fi amplasat ladistana urmtoare fade axa de rotaie:
-
7/26/2019 P644L (2)
21/62
94
mrbrcg
mbrrGbr mcg rGcg-
mbr mcg+4.243 10
4-=:=
Prin urmare, pentru acest tip de bra, momentul de inerie redus la axa de rotaie este:
Jb0 Jb mbr mcg+( ) rbrcg2
+ 503=:= Nms2
Rezulta astfel momentele de inertie ale coturilor arborelui cotit:
-pentru coturile 1, 3 prevazute cu contragreutati:
Jcot Jp JM0+ 2 Jb0+ 1.006 103
=:= Nms2
-pentru coturile 2, 4 prevazute fara contragreutati:
J'cot
Jp
JM0
+ 2 J'b0
+ 316=:= Nms2
Pentru stabilirea momentelor de inertie ale discurilor (volantilor) arborelui cotit, se mai determinasi momentul de inertie al maselor in miscare, redus la axa de rotatie:
Jm0 mbm 0.5 mit+( ) R2
0.149=:= Nms2
n consecin, momentele de inertie ale discurilor oscilant vor fi:J1=J3 si J2=J4
J1 Jcot Jm0+ 1.006 103
=:= Nms2
J2 J'cot Jm0+ 316.149=:= Nms
2
Pentru volantul motorului, plecand de la dimensiunile sale principale, rezulta momentul deinertie:Dv 1:= m
hv 0.22:= m
Jv
32Dv
4 hv OLC45 168.468=:= Nms
2
Pentru determinarea momentului de inerie al elicei, se recurge la o metodsimplificatde
calcul. Prin prelucrarea diagramelor Troost, diametrul elicei este dat de relaia:
Del 15.25Pef
0.210
3
n0.6
1.307 103
=:= mm
Grosimea celor patru pale ale elicei variazntre 0.3 i 2.8% din diametrulDel. Substituimelicea cu un disc cu urmtoarea grosime:
hel 1.2 102-
Del 15.688=:= mm
Avnd n vedere celicea este confecionatdin bronz cu o densitate mai mare, avem:
-
7/26/2019 P644L (2)
22/62
95
el 8160:=Kg
m3
Jel
32Del
4 hel el 10
15- 36.709=:= Nms
2
Arborele echivalent are diametrul egal cu cel al fusului palier, iar arborele port-elice are diametruldel=90 mm. Rezultastfel i rigiditile poriunilor de arbore ale sistemului de mai sus: k12=k23=k34
del 0.090:= m
G 8.4 1010
:= -modulul de elasticitate k12
32
G
l dp
4 5.442 10
5=:= Nm
Pentru a determina lungimile liniei de arbori se adopturmtoarele mrimi:
-lungimea unui cot ntre mijloacele a 2 paliere adiacente:
y 1.365:= m -calculat n proiectul anterior
y2 y 1.365=:= m
y3 0.75 y 1.024=:= m
y4 y 1.365=:= m
y5 6.5y 8.873=:= m
m
y6 5.3y 7.234=:=Calculm urmtoarele valori:
lv y2y
2- y3+ 1.706=:= m
le y5 y6+ 16.107=:= m
k4v
32
G
lv dp
4 3.4 10
4=:= Nm
kvel
32
G
le
del4
3.359 104
=:= Nm
J2 J1 1.006 103
=:= Nms2
k12 5.442 105
= Nm
J3 J1 1.006 103
=:= Nms2
k23 k12 5.442 105
=:= Nm
J4 J1 1.006 103
=:= Nms2
k34 k12 5.442 105
=:= Nm
n aceste condiii, sunt cunoscute toate caracteristicile dinamiceale sistemului oscilant echivalent i pot fi determinatepulsaiile sale proprii. n acest scop, se utilizeazmetodologia bazatpe aa numita metoda resturilor i organizatncadrul tabelei lui Holzer. n calculele de mai jos sunt cuprinse valorile estimate ale pulsaiilor proprii, mpreuncu valo
corespunztoare ale momentelor reziduale, pentru fiecare pulsaie n parte. Adoptm valori ale pulsaiei pnavemvaloriminime ale momentului rezidual.
-
7/26/2019 P644L (2)
23/62
96
0I 12.379984:=
J1 1.006 103
= a1 1:= M12 a1 J1 0I2
1.542 105
=:=
J2 1.006 103
= a2 a1
M12
k12- 0.717=:= M23 M12 J2 0I
2 a2+ 2.647 10
5=:=
a3 a2
M23
k23- 0.23=:=
J3 1.006 103
= M34 M23 J3 0I2
a3+ 3.002 105
=:=
J4 1.006 103
= a4 a3
M34
k34- 0.322-=:= M4v M34 J4 0I
2 a4+ 2.506 10
5=:=
Jv 168.468= av a4
M4v
k4v- 7.693-=:= Mvel M4v Jv0I
2 av+ 5.199 10
4=:=
Jel 36.709= ael av
Mvel
kvel- 9.241-=:= MrI Mvel Jel0I2 ael+ 0.014=:=
0II 18.51862358:=
J1 1.006 103
= a1 1:= M12 a1 J1 0II2
3.45 105
=:=
J2 1.006 103
= a2 a1
M12
k12- 0.366=:= M23 M12 J2 0II
2 a2+ 4.713 10
5=:=
a3 a2
M23
k23- 0.5-=:=J3 1.006 103= M34 M23 J3 0II2 a3+ 2.987 105=:=
-
7/26/2019 P644L (2)
24/62
97
J4 1.006 103
= a4 a3
M34
k34- 1.049-=:= M4v M34 J4 0II
2 a4+ 6.329- 10
4=:=
Jv 168.468= av a4
M4v
k4v-0.812=:= Mvel M4v Jv0II
2
av+ 1.636- 104
=:=
Jel 36.709= ael av
Mvel
kvel- 1.299=:= MrII Mvel Jel0II
2 ael+ 0.011-=:=
0III 32.950578:=
J1 1.006 103
= a1 1:= M12 a1 J1 0III2
1.092 106
=:=
J2 1.006 103= a2 a1 M12k12
- 1.008-=:= M23 M12 J2 0III2 a2+ 8.204- 10
3=:=
a3 a2
M23
k23- 0.992-=:=
J3 1.006 103
= M34 M23 J3 0III2
a3+ 1.092- 106
=:=
J4 1.006 103
= a4 a3
M34
k34- 1.015=:= M4v M34 J4 0III
2 a4+ 1.641 10
4=:=
Jv 168.468= av a4
M4v
k4v
- 0.532=:= Mvel M4v Jv0III2
av+ 1.138 105
=:=
Jel 36.709= ael av
Mvel
kvel- 2.855-=:=
MrIII Mvel Jel0III2
ael+ 0.03-=:=
Conform datelor din calculele anterioare, pentru valorile minime ale momentelor reziduale
(resturilor), pot fi stabilite pulsaiile proprii ale sistemului oscilant echivalent:
0I 12.38= s1-
0II 18.519= s1-
0III 32.951= s1-
-
7/26/2019 P644L (2)
25/62
98
In ncheierea acestui calcul preliminar la vibraiilor torsionale, s-a realizat stabilirea regimurilor de rezonan, respectivprecizarea turaiilor critice corespunztoare acestor regimuri. n acest scop, n figura de mai jos a fost trasatdiagramapulsaie-turaie. Astfel, pulsaiile proprii fiind independente de turaie, ele sunt reprezentate prin drepte paralele cu abcidiagramei. Pe de altparte, pulsaiile excitaiei de diverse ordine v variazliniar cu turaia.n continuare se stabilesc
valorile turaiilor critice pentru diverse grade ale pulsaiei i diverse ordine v ale excitaiei. Se folosesc urmtoareleexpresii:
v 1 30..:=
nmin 0.5 n 1.2 103
=:=
nmax 1.1 n 2.64 103
=:=
ncrI v( )300I
v:= min
1-
ncrII v( )30 0II
v:= min
1-
ncrIII v( )300III
v:= min
1-
Turaile critice pentru diverse grade (I, II, III) ale pulsaiei i diverse ordine v ale excitaiei.
ncrI v( )
118.22
59.11
39.407
29.555
23.644
19.703
16.889
14.778
13.136
11.822
10.747
9.852
9.094
8.444
7.881
7.389
6.954
6.568
6.222
5.911
5.63
= ncrII v( )
176.84
88.42
58.947
44.21
35.368
29.473
25.263
22.105
19.649
17.684
16.076
14.737
13.603
12.631
11.789
11.052
10.402
9.824
9.307
8.842
8.421
= ncrIII v( )
314.655
157.327
104.885
78.664
62.931
52.442
44.951
39.332
34.962
31.465
28.605
26.221
24.204
22.475
20.977
19.666
18.509
17.481
16.561
15.733
14.984
=
-
7/26/2019 P644L (2)
26/62
99
.
5.14
4.926
4.729
4.547
4.379
4.222
4.077
3.941
.
7.689
7.368
7.074
6.802
6.55
6.316
6.098
5.895
.
13.681
13.111
12.586
12.102
11.654
11.238
10.85
10.488
k 1 10, nmax 50+..:= v 1 30..:= n k( ) k 1:=
0I k( ) 0I:=
0II k( ) 0II:=
0III k( ) 0III:=
v k,( )v n k( )
9.55:= pulsatia excitatiei de ordin v
0 1000 2000
50
100
150
v k,( )
0I k( )
0II k( )
0III k( )
nmin nmax
n k( )
Diagrama pulsaie - turaie pentru stabilirea turaiilor critice
-
7/26/2019 P644L (2)
27/62
100
ANALIZA ARMONICA A EXCITATIEI
Calculul momentului produs de forta de presiune a gazelor
pj0
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
7.35
7.85
8.012
7.75
7.17
6.26
5.33
4.51
3.76
3.18
2.67
2.27
1.95
1.7
1.5
1.33
1.2
1.09
0.99
0.91
0.85
0.79
0.75
0.71
0.67
0.64
0.6
0.54
0.47
0.39
0.34
0.29
0.29
0.25
:= pcart0
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
:=0
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
0
10
20
30
40
50
60
70
80
90
100
110
120
130
140
150
160
170
180
190
200
210
220
230
240
250
260
270
280
290
300
310
320
330
0
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
0
2.488
4.905
7.181
9.247
11.041
12.504
13.587
14.253
14.478
14.253
13.587
12.504
11.041
9.247
7.181
4.905
2.488
0
-2.488
-4.905
-7.181
-9.247
-11.041
-12.504
-13.587
-14.253
-14.478
-14.253
-13.587
-12.504
-11.041
-9.247
-7.181
-
7/26/2019 P644L (2)
28/62
101
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
0.22
0.2
0.19
0.2
0.2
0.2
0.2
0.2
0.21
0.22
0.22
0.23
0.24
0.25
0.26
0.28
0.3
0.32
0.35
0.38
0.42
0.46
0.52
0.59
0.67
0.78
0.91
1.08
1.3
1.58
1.94
2.41
3
3.73
4.67
5.52
6.46
7.35
7.56
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
340
350
360
370
380
390
400
410
420
430
440
450
460
470
480
490
500
510
520
530
540
550
560
570
580
590
600
610
620
630
640
650
660
670
680
690
700
710
720
=
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
-4.905
-2.488
0
2.488
4.905
7.181
9.247
11.041
12.504
13.587
14.253
14.478
14.253
13.587
12.504
11.041
9.247
7.181
4.905
2.488
0
-2.488
-4.905
-7.181
-9.247
-11.041
-12.504
-13.587
-14.253
-14.478
-14.253
-13.587
-12.504
-11.041
-9.247
-7.181
-4.905
-2.488
0
=
pT pj pcart-( )sin +( )
cos ( ):=
-
7/26/2019 P644L (2)
29/62
102
pT
pTjpj( )j
pcart( )j-
sin deg ( )j
deg ( )j
+
cos deg ( )[ ]j
j 0 72..for
pT
:=
MPa
-
7/26/2019 P644L (2)
30/62
103
pT
0
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
0
1.677
3.344
4.66
5.426
5.491
5.109
4.509
3.766
3.08
2.418
1.86
1.397
1.025
0.725
0.481
0.288
0.13
0
-0.106
-0.196
-0.27
-0.337
-0.391
-0.43
-0.463
-0.47
-0.44
-0.381
-0.296
-0.234
-0.169
-0.146
-0.091
-0.051
-0.022
0
0.022
0.042
0.061
0.077
0.089
=MPa
-
7/26/2019 P644L (2)
31/62
104
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
.
0.123
0.123
0.13
0.132
0.129
0.121
0.115
0.104
0.086
0.065
0.037
0
-0.047
-0.11
-0.192
-0.295
-0.436
-0.612
-0.84
-1.129
-1.48
-1.893
-2.362
-2.833
-3.236
-3.508
-3.301
-2.688
-1.569
-15-3.65410
Pe baza calculelor anterioare calculam valoarea medie a presiunii tangentiale echivalente
pTechiv1
720
72
j
pTj=
0.221=:= MPa
pTechiv
pTechivj
1
720
72
j
pTj=
j 0 72..for
pTechiv
:=
MPa
-
7/26/2019 P644L (2)
32/62
105
0 100 200 300 400 500 600 700 800
4-
3.375-
2.75-
2.125-
1.5-
0.875-
0.25-
0.375
1
1.625
2.25
2.875
3.5
4.125
4.75
5.375
6
pT
pTechiv
Variatia presiunii tangentiale echivalente a presiunii gazelor din cilindru
Se vor calcula coeficientii dezvoltarii in serie trigonometrica a presiunii tangentiale echivalente
Ordinul armonicii v
A0
180 0
72
j
pTj=
3.981=:= MPa
v 0:=
Av
180 0
72
j
pTjcos v( )
=
3.981=:= MPa
Bv
90 0
72
j
pTjsin v( )
=
0=:= MPa
MPaCv Av
2Bv
2+ 3.981=:=
0 atan
Bv
Av
0=:= rad
-
7/26/2019 P644L (2)
33/62
106
v 1:=
Av
180 0
72
j
pTjcos v( )
=
2.382-=:=
Bv
90 0
72
j
pTjsin v( )
=
6.379-=:=
Cv Av2
Bv2
+ 6.809=:=
1 atanBv
Av
1.213=:=
v 2:=
Av
180 0
72
j
pTjcos v( )
=
1.129-=:=
Bv
90 0
72
j
pTjsin v( )
=
7.635=:=
Cv Av2
Bv2
+ 7.718=:=
2 atanBv
Av
1.424-=:=
v 3:=
Av
180 0
72
j
pTjcos v( )
=
3.734=:=
Bv
90 0
72
j
pTjsin v( )
=
2.76-=:=
Cv Av2 Bv2+ 4.643=:=
3 atanBv
Av
0.636-=:=
v 4:=
Av
180 0
72
j
pTjcos v( )
=
3.34-=:=
Bv
90 0
72
jpTj sin v( )= 4.332-=:=
-
7/26/2019 P644L (2)
34/62
107
Cv Av2
Bv2
+ 5.47=:=
4 atanBv
Av
0.914=:=
v 5:=
Av
180 0
72
j
pTjcos v( )
=
0.264=:=
Bv
90 0
72
j
pTjsin v( )
=
7.945=:=
Cv Av2
Bv2
+ 7.949=:=
5 atanBv
Av
1.538=:=
v 6:=
Av
180 0
72
j
pTjcos v( )
=
3.025=:=
Bv
90
0
72
j
pTjsin v( )
=
5.177-=:=
Cv Av2
Bv2
+ 5.996=:=
6 atanBv
Av
1.042-=:=
v 7:=
Av
180
0
72
j
pTjcos v( )
=
3.884-=:=
Bv
90 0
72
j
pTjsin v( )
=
1.748-=:=
Cv Av2
Bv2
+ 4.259=:=
7 atanBv
Av
0.423=:=
v 8:=
-
7/26/2019 P644L (2)
35/62
108
Av
180 0
72
j
pTjcos v( )
=
1.624=:=
Bv 90 0
72
j
pTjsin v( )
=
7.269=:=
Cv Av2
Bv2
+ 7.449=:=
8 atanBv
Av
1.351=:=
v 9:=
Av
180 0
72
j
pTj cos v( )= 1.94=:=
Bv
90 0
72
j
pTjsin v( )
=
6.953-=:=
Cv Av2
Bv2
+ 7.218=:=
9 atanBv
Av
1.299-=:=
v 10:=
Av
180 0
72
j
pTjcos v( )
=
3.946-=:=
Bv
90 0
72
j
pTjsin v( )
=
1.053=:=
C
v
A
v
2B
v
2+ 4.084=:=
10 atanBv
Av
0.261-=:=
v 11:=
Av
180 0
72
j
pTjcos v( )
=
2.783=:=
Bv
90 0
72
j
pTj
sin v( )
= 5.693=:=
-
7/26/2019 P644L (2)
36/62
109
Cv Av2
Bv2
+ 6.337=:=
11 atanBv
Av
1.116=:=
v 12:=
Av
180 0
72
j
pTjcos v( )
=
0.615=:=
Bv
90 0
72
j
pTjsin v( )
=
7.867-=:=
Cv Av2
Bv2
+ 7.891=:=
12 atanBv
Av
1.493-=:=
MPapTtrig0 A0
0
0
v
Av cos v deg ( ) Bv sin v deg ( )+( )=
+:=
pTtrig1 A0
1
1
v
Av cos v deg ( ) Bv sin v deg ( )+( )=
+:=
pTtrig2 A0
2
2
v
Av cos v deg ( ) Bv sin v deg ( )+( )=
+:=
pTtrig3 A0
3
3
v
Av cos v deg ( ) Bv sin v deg ( )+( )=
+:=
pTtrig4 A0
4
4
v
Av cos v deg ( ) Bv sin v deg ( )+( )=
+:=
pTtrig5 A0
5
5
v
Av cos v deg ( ) Bv sin v deg ( )+( )=+:=
pTtrig6 A0
6
6
v
Av cos v deg ( ) Bv sin v deg ( )+( )=
+:=
pTtrig7 A0
7
7
v
Av cos v deg ( ) Bv sin v deg ( )+( )=
+:=
pTtrig8 A08
8
vAv cos v deg ( ) Bv sin v deg ( )+( )=+:=
-
7/26/2019 P644L (2)
37/62
110
pTtrig9 A0
9
9
v
Av cos v deg ( ) Bv sin v deg ( )+( )=
+:=
pTtrig10 A010
10
vAv cos v deg ( ) Bv sin v deg ( )+( )=+:=
pTtrig11 A0
11
11
v
Av cos v deg ( ) Bv sin v deg ( )+( )=
+:=
pTtrig12 A0
12
12
v
Av cos v deg ( ) Bv sin v deg ( )+( )=
+:=
0
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
2829
4.596
4.596
4.596
4.596
4.596
4.596
4.596
4.596
4.596
4.596
4.596
4.596
4.596
4.596
4.596
4.596
4.596
4.596
4.596
4.596
4.596
4.596
4.596
4.596
4.596
4.596
4.596
4.596
4.5964.596
0
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
2829
4.596
3.22
1.868
0.58
-0.605
-1.65
-2.524
-3.201
-3.659
-3.886
-3.873
-3.621
-3.139
-2.44
-1.546
-0.485
0.713
2.01
3.366
4.742
6.094
7.382
8.567
9.612
10.486
11.163
11.621
11.848
11.83511.583
0
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
2829
4.596
1.868
-0.605
-2.524
-3.659
-3.873
-3.139
-1.546
0.713
3.366
6.094
8.567
10.486
11.621
11.835
11.101
9.509
7.249
4.596
1.868
-0.605
-2.524
-3.659
-3.873
-3.139
-1.546
0.713
3.366
6.0948.567
0
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
2829
4.596
0.58
-2.524
-3.886
-3.139
-0.485
3.366
7.382
10.486
11.848
11.101
8.447
4.596
0.58
-2.524
-3.886
-3.139
-0.485
3.366
7.382
10.486
11.848
11.101
8.447
4.596
0.58
-2.524
-3.886
-3.139-0.485
-
7/26/2019 P644L (2)
38/62
111
pTtrig0
31
32
33
34
35
36
37
38
39
40
41
42
43
4445
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
.
4.596
4.596
4.596
4.596
4.596
4.596
4.596
4.596
4.596
4.596
4.596
4.596
4.596
4.5964.596
4.596
4.596
4.596
4.596
4.596
4.596
4.596
4.596
4.596
4.596
4.596
4.596
4.596
4.596
4.596
4.596
4.596
4.596
4.596
4.596
4.596
4.596
4.596
4.596
4.596
4.596
4.596
= pTtrig1
31
32
33
34
35
36
37
38
39
40
41
42
43
4445
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
.
10.402
9.509
8.447
7.249
5.952
4.596
3.22
1.868
0.58
-0.605
-1.65
-2.524
-3.201
-3.659-3.886
-3.873
-3.621
-3.139
-2.44
-1.546
-0.485
0.713
2.01
3.366
4.742
6.094
7.382
8.567
9.612
10.486
11.163
11.621
11.848
11.835
11.583
11.101
10.402
9.509
8.447
7.249
5.952
4.596
= pTtrig2
31
32
33
34
35
36
37
38
39
40
41
42
43
4445
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
.
11.621
11.835
11.101
9.509
7.249
4.596
1.868
-0.605
-2.524
-3.659
-3.873
-3.139
-1.546
0.7133.366
6.094
8.567
10.486
11.621
11.835
11.101
9.509
7.249
4.596
1.868
-0.605
-2.524
-3.659
-3.873
-3.139
-1.546
0.713
3.366
6.094
8.567
10.486
11.621
11.835
11.101
9.509
7.249
4.596
= pTtrig3
31
32
33
34
35
36
37
38
39
40
41
42
43
4445
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
.
7.382
10.486
11.848
11.101
8.447
4.596
0.58
-2.524
-3.886
-3.139
-0.485
3.366
7.382
10.48611.848
11.101
8.447
4.596
0.58
-2.524
-3.886
-3.139
-0.485
3.366
7.382
10.486
11.848
11.101
8.447
4.596
0.58
-2.524
-3.886
-3.139
-0.485
3.366
7.382
10.486
11.848
11.101
8.447
4.596
=
-
7/26/2019 P644L (2)
39/62
112
pTtrig4
0
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
4.596
-0.605
-3.659
-3.139
0.713
6.094
10.486
11.835
9.509
4.596
-0.605
-3.659
-3.139
0.713
6.094
10.486
11.835
9.509
4.596
-0.605
-3.659
-3.139
0.713
6.094
10.486
11.835
9.509
4.596
-0.605
-3.659
-3.139
0.713
6.094
10.486
11.835
9.509
4.596
-0.605
-3.659
-3.139
0.713
6.094
= pTtrig5
0
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
4.596
-1.65
-3.873
-0.485
6.094
11.163
11.101
5.952
-0.605
-3.886
-1.546
4.742
10.486
11.583
7.249
0.58
-3.659
-2.44
3.366
9.612
11.835
8.447
1.868
-3.201
-3.139
2.01
8.567
11.848
9.509
3.22
-2.524
-3.621
0.713
7.382
11.621
10.402
4.596
-1.65
-3.873
-0.485
6.094
11.163
= pTtrig6
0
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
4.596
-2.524
-3.139
3.366
10.486
11.101
4.596
-2.524
-3.139
3.366
10.486
11.101
4.596
-2.524
-3.139
3.366
10.486
11.101
4.596
-2.524
-3.139
3.366
10.486
11.101
4.596
-2.524
-3.139
3.366
10.486
11.101
4.596
-2.524
-3.139
3.366
10.486
11.101
4.596
-2.524
-3.139
3.366
10.486
11.101
= pTtrig7
0
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
4.596
-3.201
-1.546
7.382
11.835
5.952
-2.524
-2.44
6.094
11.848
7.249
-1.65
-3.139
4.742
11.621
8.447
-0.605
-3.621
3.366
11.163
9.509
0.58
-3.873
2.01
10.486
10.402
1.868
-3.886
0.713
9.612
11.101
3.22
-3.659
-0.485
8.567
11.583
4.596
-3.201
-1.546
7.382
11.835
5.952
-
=
-
7/26/2019 P644L (2)
40/62
113
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
.
11.835
9.509
4.596
-0.605
-3.659
-3.139
0.713
6.094
10.486
11.835
9.509
4.596
-0.605
-3.659
-3.139
0.713
6.094
10.486
11.835
9.509
4.596
-0.605
-3.659
-3.139
0.713
6.094
10.486
11.835
9.509
4.596
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
.
5.952
-0.605
-3.886
-1.546
4.742
10.486
11.583
7.249
0.58
-3.659
-2.44
3.366
9.612
11.835
8.447
1.868
-3.201
-3.139
2.01
8.567
11.848
9.509
3.22
-2.524
-3.621
0.713
7.382
11.621
10.402
4.596
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
.
-2.524
-3.139
3.366
10.486
11.101
4.596
-2.524
-3.139
3.366
10.486
11.101
4.596
-2.524
-3.139
3.366
10.486
11.101
4.596
-2.524
-3.139
3.366
10.486
11.101
4.596
-2.524
-3.139
3.366
10.486
11.101
4.596
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
.
-2.44
6.094
11.848
7.249
-1.65
-3.139
4.742
11.621
8.447
-0.605
-3.621
3.366
11.163
9.509
0.58
-3.873
2.01
10.486
10.402
1.868
-3.886
0.713
9.612
11.101
3.22
-3.659
-0.485
8.567
11.583
4.596
0
0
1
2
3
4
5
6
7
8
9
10
11
4.596
-3.659
0.713
10.486
9.509
-0.605
-3.139
6.094
11.835
4.596
-3.659
0.713
0
0
1
2
3
4
5
6
7
8
9
10
11
4.596
-3.886
3.366
11.848
4.596
-3.886
3.366
11.848
4.596
-3.886
3.366
11.848
0
0
1
2
3
4
5
6
7
8
9
10
11
4.596
-3.873
6.094
11.101
-0.605
-1.546
10.486
7.249
-3.659
3.366
11.835
1.868
0
0
1
2
3
4
5
6
7
8
9
10
11
4.596
-3.621
8.567
8.447
-3.659
4.742
11.101
-1.65
0.713
11.848
1.868
-2.44
-
7/26/2019 P644L (2)
41/62
114
pTtrig8
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
10.486
9.509
-0.605
-3.139
6.094
11.835
4.596
-3.659
0.713
10.486
9.509
-0.605
-3.139
6.094
11.835
4.596
-3.659
0.713
10.486
9.509
-0.605
-3.139
6.094
11.835
4.596
-3.659
0.713
10.486
9.509
-0.605
-3.139
6.094
11.835
4.596
-3.659
0.713
10.486
9.509
-0.605
-3.139
6.094
11.835
4.596
-3.659
= pTtrig9
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
4.596
-3.886
3.366
11.848
4.596
-3.886
3.366
11.848
4.596
-3.886
3.366
11.848
4.596
-3.886
3.366
11.848
4.596
-3.886
3.366
11.848
4.596
-3.886
3.366
11.848
4.596
-3.886
3.366
11.848
4.596
-3.886
3.366
11.848
4.596
-3.886
3.366
11.848
4.596
-3.886
3.366
11.848
4.596
-3.886
3.366
11.848
= pTtrig10
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
-3.139
8.567
9.509
-2.524
0.713
11.621
4.596
-3.873
6.094
11.101
-0.605
-1.546
10.486
7.249
-3.659
3.366
11.835
1.868
-3.139
8.567
9.509
-2.524
0.713
11.621
4.596
-3.873
6.094
11.101
-0.605
-1.546
10.486
7.249
-3.659
3.366
11.835
1.868
-3.139
8.567
9.509
-2.524
0.713
11.621
4.596
-3.873
= pTtrig11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
10.486
5.952
-3.873
7.382
9.509
-3.201
3.366
11.583
-0.605
-0.485
11.621
3.22
-3.139
9.612
7.249
-3.886
6.094
10.402
-2.524
2.01
11.835
0.58
-1.546
11.163
4.596
-3.621
8.567
8.447
-3.659
4.742
11.101
-1.65
0.713
11.848
1.868
-2.44
10.486
5.952
-3.873
7.382
9.509
-3.201
3.366
11.583
=
-
7/26/2019 P644L (2)
42/62
115
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
.
10.486
9.509
-0.605
-3.139
6.094
11.835
4.596
-3.659
0.713
10.486
9.509
-0.605
-3.139
6.094
11.835
4.596
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
.
-3.886
3.366
11.848
4.596
-3.886
3.366
11.848
4.596
-3.886
3.366
11.848
4.596
-3.886
3.366
11.848
4.596
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
.
11.101
-0.605
-1.546
10.486
7.249
-3.659
3.366
11.835
1.868
-3.139
8.567
9.509
-2.524
0.713
11.621
4.596
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
- .
-0.485
11.621
3.22
-3.139
9.612
7.249
-3.886
6.094
10.402
-2.524
2.01
11.835
0.58
-1.546
11.163
4.596
0
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
4.596
-3.139
10.486
4.596
-3.139
10.486
4.596
-3.139
10.486
4.596
-3.139
10.486
4.596
-3.139
10.486
4.596
-3.139
10.486
4.596
-3.139
10.486
4.596
-3.139
10.486
4.596
-3.139
-
7/26/2019 P644L (2)
43/62
116
pTtrig12
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
.
4.596
-3.139
10.486
4.596
-3.139
10.486
4.596
-3.139
10.486
4.596
-3.139
10.486
4.596
-3.139
10.486
4.596
-3.139
10.486
4.596
-3.139
10.486
4.596
-3.139
10.486
4.596
-3.139
10.486
4.596
-3.139
10.486
4.596
-3.139
10.486
4.596
-3.139
10.486
4.596
-3.139
10.486
4.596
-3.139
10.486
4.596
-3.139
=
-
7/26/2019 P644L (2)
44/62
117
71
72
10.486
4.596
0 200 400 600 8005-
0
5
10
15
pTtrig1
pTtrig2
pTtrig3
pTtrig4
Variatia componentelor armonice
-
7/26/2019 P644L (2)
45/62
118
0 200 400 600 8005-
0
5
10
15
pTtrig5
pTtrig6
pTtrig7
pTtrig8
pTtrig9
Variatia componentelor armonice
-
7/26/2019 P644L (2)
46/62
119
0 200 400 600 8005-
0
5
10
15
pTtrig10
pTtrig11
pTtrig12
Variatia componentelor armonice
pTtrigtotal pTtrig0 pTtrig1+ pTtrig2+ pTtrig3+ pTtrig4+ pTtrig5+ pTtrig6+ pTtrig7+ pTtrig8+ pTtrig9+ pTtrig10+ pTtrig11+:=
0
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
59.746
-15.893
20.344
52.368
33.022
42.09
52.368
40.455
47.965
52.368
43.774
50.996
52.368
45.874
53.069
-
7/26/2019 P644L (2)
47/62
120
pTtrigtotal
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
52.368
47.507
54.774
52.368
48.994
56.401
52.368
50.551
58.189
52.368
52.446
60.487
52.368
55.215
64.12
52.368
60.582
72.255
52.368
80.451
125.793
59.746
-15.893
20.344
52.368
33.022
42.09
52.368
40.455
47.965
52.368
43.774
50.996
52.368
45.874
53.069
52.368
47.507
54.774
52.368
48.994
56.401
52.368
50.551
= MPa
-
7/26/2019 P644L (2)
48/62
121
60
61
62
63
64
65
66
67
68
69
70
71
72
.
52.368
52.446
60.487
52.368
55.215
64.12
52.368
60.582
72.255
52.368
80.451
125.793
59.746
0 200 400 600 800
0
50
100
150
pTtrigtotal
Insumarea componentelor armonice
Calculul valorii momentului motor produs de forta de presiune a gazelor
Momentul motor mediu
Mpm 10
6
R
D2
4
1
721
72
jpTj= 117.02=:= Nm
-
7/26/2019 P644L (2)
49/62
122
D1 1.4:= D5 0.3:= D9 0.7:=
D2 1.3:=daN
cm2
D6 0.2:=daN
cm2
D10 0.7:=daN
cm2
D3 0.9:= D7 1.5:= D11 0.6:=
D4 0.6:= D8 1.1:= D12 0.4:=
Mp1 106
D2
RD1
4 740.741=:= Mp9 10
6 D
2 R
D9
4 370.37=:=
Mp2 106
D2
RD2
4 218.943=:= Mp10 10
6D
2 R
D10
4 117.893=:=
Nm
Mp3 106
D2
RD3
4 151.576=:= Mp11 10
6D
2 R
D11
4 101.051=:=
Nm
Mp4
106
D2
RD4
4 101.051=:= M
p1210
6D
2 R
D12
4 67.367=:=
Mp5 106
D2
RD5
4 158.73=:=
Mp6 106
D2
RD6
4 33.684=:=
Nm
Mp7 106
D2
RD7
4 252.627=:=
Mp8 10
6
D
2
R
D8
4 185.26=:=
Deci valoarea momentului motor este
Mp Mpm Mp1 sin 1 0+( )+ Mp2 sin 2 0+( )+ Mp3 sin 3 0+( )+ Mp4 sin 4 0+( )+ Mp5 sin 5 0+( )+ +:=
Mp 117.02= Nm
Calculul momentului produs de forta de inertie a maselor cu miscare de translatie
Valorile coeficientilor armonici se determina astfel
E1 14 d 116
d3+ 15512 d5+ 0.064=:=
E21-
2
1
32 d
4-
1
32 d
6- 0.5-=:=
E33-
4 d
9-
32 d
3+
81-
512 d
5+ 0.192-=:=
E41-
4 d
2
1-
8 d
4+
1-
16 d
6+ 0.016-=:=
E55
32 d
3
75
512 d
5+ 2.584 10
3-=:=
E6 332 d4 332
d6+ 3.891 10 4-=:=
-
7/26/2019 P644L (2)
50/62
123
Amplitudinea momentului produs de forta de inertie a maselor cu miscare de translatie
Mit1 mit R2
2
E1 673.861=:= Nm
Mit2 mit R2 2 E2 5.307- 103=:= Nm
Mit3 mit R2
2
E3 2.038- 103
=:= Nm
Mit4 mit R2
2
E4 171.142-=:= Nm
Mit5 mit R2
2
E5 27.424=:= Nm
Mit6 mit R2
2
E6 4.129=:= Nm
Calculul momentului total de excitatie
1 0:= 5 0:= 6 0:= 2 := 3 := 4 :=
M1 Mp1 sin1( ) Mit1 sin 1( )+( )2
Mp1 cos 1( ) Mit1 cos 1( )+( )2
+ 1.163 103
=:=
NmM2 Mp2 sin2( ) Mit2 sin 2( )+( )
2Mp2 cos 2( ) Mit2 cos 2( )+( )
2+ 5.343 10
3=:=
M3 Mp3 sin3( ) Mit3 sin 3( )+( )2
Mp3 cos 3( ) Mit3 cos 3( )+( )2
+ 2.162 103
=:=
M4 Mp4 sin4( ) Mit4 sin 4( )+( )2
Mp4 cos 4( ) Mit4 cos 4( )+( )2
+ 246.214=:=
NmM5 Mp5 sin5( ) Mit5 sin 5( )+( )
2Mp5 cos 5( ) Mit5 cos 5( )+( )
2+ 161.976=:=
M6 Mp6 sin6( ) Mit6 sin 6( )+( )2
Mp6 cos 6( ) Mit6 cos 6( )+( )2
+ 35.944=:=
M7 Mp7 sin7( )( )2
Mp7 cos 7( )( )2
+ 252.627=:=
NmM8 Mp8 sin8( )( )
2Mp8 cos 8( )( )
2+ 185.26=:=
M9 Mp9 sin9( )( )2
Mp9 cos 9( )( )2
+ 370.37=:=
M10 Mp10 sin 10( )( )2
Mp10 cos 10( )( )2
+ 117.893=:=
M11 Mp11 sin 11( )( )2
Mp11 cos 11( )( )2
+ 101.051=:= Nm
M12 Mp12 sin 12( )( )2
Mp12 cos 12( )( )2
+ 67.367=:=
-
7/26/2019 P644L (2)
51/62
124
Avand in vedere ordinea de aprindere a motorului, 1-3-4-2, avem rangul aprinderii din cilindrii.
j1 1:=
j2 4:=
j3 2:=
j4 3:=
c 720:=
180 n
301.44 10
4=:=
RAC
s
Determinam valorile momentului total de excitatie
Mv1 Mvsin v ( ):= Nm
Mv2 Mvsin v j2 1-( )
c
i-
:= Nm
M11 M1 sin 1 ( ) 2.483- 103
=:=M12 M1
sin 1 j2 1-( )c
i-
1.892- 103
=:=
M21 M2 sin 2 ( ) 4.065 10
3=:=
M22 M2sin 2 j2 1-( )
c
i-
5.023 10
3=:=
M31 M3sin 3 ( ) 1.027 10
3=:=
M32 M3sin 3 j2 1-( )
c
i-
4.975- 10
3=:=
M41 M4sin 4 ( ) 6.222- 10
3=:=
M51 M5 sin 5 ( ) 3.921 10
3=:= M42 M4 sin 4 j2 1-( )
c
i-
989.204=:=
M61 M6 sin 6 ( ) 1.214 103=:= M52 M5 sin 5 j2 1-( )ci
-
3.137 103=:=
M71 M7sin 7 ( ) 1.531- 10
3=:=
M62 M6sin 6 j2 1-( )
c
i-
3.706- 10
3=:=
M81 M8sin 8 ( ) 435.524-=:=
M72 M7sin 7 j2 1-( )
c
i-
1.343 10
3=:=
M91 M9sin 9 ( ) 1.281- 10
3=:=
M82 M8sin 8 j2 1-( )
c
i-
226.347=:=
M101 M10sin 10 ( ) 4.153 10
3=:=
M111 M11 sin 11 ( ) 2.149- 103=:= M92 M9 sin 9 j2 1-( )
ci-
1.173 103=:=
M121 M12sin 12 ( ) 3.065- 10
3=:=
M102 M10sin 10 j2 1-( )
c
i-
3.857- 10
3=:=
M112 M11sin 11 j2 1-( )
c
i-
4.593 10
3=:=
M122 M12sin 12 j2 1-( )
c
i-
2.234- 10
3=:=
-
7/26/2019 P644L (2)
52/62
125
Mv3 Mvsin v j3 1-( )
c
i-
:= Nm Mv4 Mv sin v j4 1-( )
c
i-
:= Nm
M13 M1sin 1 j3 1-( )
c
i
-
2.495 103
=:= M14 M1 sin 1 j4 1-( )c
i
-
503.478-=:=
M23 M2sin 2 j3 1-( )
c
i-
4.006- 10
3=:= M24 M2 sin 2 j4 1-( )
c
i-
1.792- 10
3=:=
M33 M3sin 3 j3 1-( )
c
i-
1.21- 10
3=:= M34 M3 sin 3 j4 1-( )
c
i-
3.297- 10
3=:=
M43 M4sin 4 j3 1-( )
c
i-
6.295 10
3=:= M44 M4 sin 4 j4 1-( )
c
i-
4.341- 10
3=:=
M53 M5sin 5 j3 1-( )
c
i-
3.722- 10
3=:= M54 M5 sin 5 j4 1-( )
c
i-
4.415- 10
3=:=
M63 M6 sin 6 j3 1-( )
c
i-
1.423- 10
3=:= M64 M6 sin 6 j4 1-( )
c
i-
3.376- 10
3=:=
M73 M7sin 7 j3 1-( )
c
i-
1.542 10
3=:= M74 M7 sin 7 j4 1-( )
c
i-
1.479- 10
3=:=
M83 M8sin 8 j3 1-( )
c
i-
386.004=:= M84 M8 sin 8 j4 1-( )
c
i-
750.482=:=
M93 M9sin 9 j3 1-( )
c
i-
1.488 10
3=:= M94 M9 sin 9 j4 1-( )
c
i-
2.731 10
3=:=
M103 M10sin 10 j3 1-( )
c
i-
4.126- 103
=:= M104 M10 sin 10 j4 1-( )c
i-
4.027 103
=:=
M113 M11 sin 11 j3 1-( )
c
i-
1.662 10
3=:= M114 M11 sin 11 j4 1-( )
c
i-
4.474 10
3=:=
M123 M12sin 12 j3 1-( )
c
i-
3.516 10
3=:= M124 M12 sin 12 j4 1-( )
c
i-
4.15 10
3=:=
Decalajul dintre aprinderi
vj v- j 1-( )
ci:=
1j1 1- j1 1-( )
ci
0=:= 1j2 1- j2 1-( )
ci
540-=:=
1j3 1- j3 1-( )c
i 180-=:= 1j4 1- j4 1-( )
c
i 360-=:=
VERIFICAREA LA REZONANTA A ARBORELUI COTIT
Pentru determinarea amplitudinii momentului de torsiune la rezonanta se pleaca de la regimurile de rezonanta, respecturatiile critice corespunzatoare acestor regimuri. Obesrvam ca regimurile de rezonanta nu se inregistreaza pentru nic
pulsatie.Totusi vom efectua calcule pentru armonica 1 pentru pulsatia