Shaft Calculation Base.pdf
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Transilvania University of Brasov Program
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Shaft calculation base
This program allows to prove the bearing ability for shafts and axes. The calculation base is provided by DIN 743, edition of December 2012. The proof of the bearing ability for shafts an axes is produced by defining a calculated safety. This safety is divided in the safety against fatigue fracture and the residual deformation (and flaw or forced break). When calculating the avoidance of fatigue fracture, constant stress amplitudes being equivalent to damaging loads are taken as a basis. These ones are resulting from the predetermined loads. When proving against the residual deformation or forced break, designated as a safety against yielding, only the maximum occurring load is determinant. This one is resulting from the predetermined loads, too. The calculation of safeties is related only to the point of a clear notch effect. For it, 9 calculable notches are at your disposal due to the graphical selection, principally. The scope is limited to steels. Welded members should be calculated separately. But the utilized standard or the present program is ineffective for this purpose! The calculation base for the module Shaft Calculation is provided by DIN 743, edition of December 2012, part 1-4 “ Tragfähigkeitsberechnung von Wellen and Achsen” (“Calculation of bearing capacity of shafts and axes”).
Input data: Shaft calculation in accordance with DIN 743 - standard version Geometry scheme Calculation process
General shaft geometry Dynamic and static strength proof
Type of loading: tension-pressure
Dynamically pure cyclic
Type of loading: bending
Dynamically pure cyclic
Type of loading: torsion
Dynamically pure cyclic
Factor for maximum loading (tension-pressure)
1
Factor for maximum loading (bending)
1
Factor for maximum loading (torsion)
1
Specifications about the material Strength values according to
MDESIGN database (DIN 743)
Material designation
15CrMoV59
Material number
1.8521
Gage diameter
dB = 100
mm
For the gage diameter Tensile strength
B (Rm) = 900
N/mm²
Yield stress
S (Re) = 750
N/mm²
Cyclic fatigue strength under bending stress
bW = 450
N/mm²
Cyclic tension and pressure fatigue strength
zdW = 360
N/mm²
tW = 270
N/mm²
Cyclic torsional fatigue strength
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Young's modulus
E = 215000
N/mm²
Shear modulus
G = 83000
N/mm²
Density
= 7850
kg/m³
Apply surface hardening to
Total shaft
Material group
Nitrated steel
Heat treatment
quenched and tempered
Surface hardening
no
Shaft geometry
Shaft geometry Nr. Da l Di l Da r Di r mm mm mm mm
L mm
Rz µm
r mm
d: mm
t: mm
zd:
b:
t: nzd: nb:
nt:
dBK: zddB bdBK dBK: K: :
1
30
0
30
0
40
6
15
0
0
0
0
0
0
0
0
0
0
0
0
2
50
0
50
0
48
6,3
25
0
0
0
0
0
0
0
0
0
0
0
0
3
40
0
40
0
8
6
20
0
0
0
0
0
0
0
0
0
0
0
0
4
50
0
50
0
10
6,3
25
0
0
0
0
0
0
0
0
0
0
0
0
5
60
0
60
0
80
6
30
0
0
0
0
0
0
0
0
0
0
0
0
6
40
0
40
0
20
1,6
20
0
0
0
0
0
0
0
0
0
0
0
0
7
30
0
30
0
25
3,2
25
0
0
0
0
0
0
0
0
0
0
0
0
Predetermine the diameter determinant for the heat treatment ?
no
Calculation of the deflection for point
x=0
Shaft speed
n:0
Consideration of dead weight
Bearing Nr.
mm 1/min
no
Type =
Position x = mm
Radial bearing stiffness c r = N/m
Torsional bearing stiffness c = N*m
Bending bearing stiffness c = N*m
Radial bearing stiffness c r = N/m
Torsional bearing stiffness c = N*m
Bending bearing stiffness c = N*m
1
Locating bearing ->
16
1e+015
0
0
1e+015
0
0
2
Locating bearing <-
215
1e+015
0
0
1e+015
0
0
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Specifications about loadings Axial forces Fax Nr.
Position x = mm
Amount = N
Radius = mm
Angle = °
1
85
30,088
33
90
2
135
109,91
25
0
Radial forces Fr Nr.
Position x = mm
Amount = N
Angle = °
1
12,5
383,379
90
2
72,5
1257,489
0
3
153
383,379
90
4
231
1257,489
0
Torsion Nr.
Position x = mm
Torsion moments Mt: N*mm
Power P: kW
Transition part =
1
85
134135,48
0
takeoff
2
160
134135,48
0
drive
Specifications about the load/loadings Loading case
Constant mean stress (loading case 1)
Change the limit number of loading cycles ?
no
Minimum safety against fatigue fracture
SDmin = 1,2
Minimum safety against residual deformation
SFmin = 1,2
Results: Calculation process: Total shaft length
Dynamic and static strength proof L
=
231
mm
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Total shaft mass
m
=
3,306
Mass moment of inertia of the shaft
J
=
0,00117
kg*m²
Geometrical moment of inertia of the shaft
I
=
158,061
cm4
Position of the centre of gravity in the X-axis
xs
=
121,833
mm
Angle of torsion
=
-0,009
Additional shaft data: Shaft fillet number
l mm
Ip cm4
Wt cm³
m kg
1
40
7,952
5,301
0,222
2
48
61,359
24,544
0,74
3
8
25,133
12,566
0,079
4
10
61,359
24,544
0,154
5
80
127,235
42,412
1,776
6
20
25,133
12,566
0,197
7
25
7,952
5,301
0,139
Supporting forces: No. Type
Position x mm
Radial force in the Y-axis Ry N
kg
°
J kg*m² 0 0,0002 0 0
I cm4
Wb cm³
3,976
2,651
30,68
12,272
12,566
6,283
30,68
12,272
63,617
21,206
0
12,566
6,283
0
3,976
2,651
0,0008
Radial force in the Z-axis Rz N
Result. radial force R N
Axial force in the X-axis Rax N
1
Locating bearing ->
16
-813,166
-514,556
962,293
0
2
Locating bearing <-
215
-1701,812
-252,202
1720,398
-139,998
Resulting maximum bending moment: Position
x
=
72,5
mm
Amount
Mbmax
=
46,343
N*m
Position
x
=
85
mm
Amount
Mtmax
=
134,135
N*m
Position
x
=
135
mm
Amount
Fzdmax
=
Position
x
=
Amount
zdmax
=
Position
x
=
Amount
bmax
=
Position
x
=
88
mm
Amount
tmax
=
10,674
N/mm²
x
=
88
mm
Resulting maximum torsional moment:
Resulting maximum tension-pressure-force: -139,998
N
Resulting maximum tension-pressure-stress: 206 -0,198
mm N/mm²
Resulting maximum bending stress: 215 7,59
mm N/mm²
Resulting maximum torsional stress:
Resulting maximum compartable stress: Position
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vmax
=
19,53
N/mm²
Position
x
=
90,42
mm
Amount
ymax
=
0,00203
mm
Position
x
=
15,84
mm
Amount
=
0,003259
Position
x
=
88
Amount
SF
=
46,042
Position
x
=
92,4
Amount
SD
=
18,316
deff
=
60
Amount Resulting maximum deflection:
Angle of the maximum deflection: °
Minimum safety against yielding: mm
Minimum safety against fatigue fracture:
Material parameter for Material designation
15CrMoV59
Material number
1.8521
mm
mm
Tensile strength
B
=
900
N/mm²
Yield stress
S
=
750
N/mm²
Cyclic tension and pressure fatigue strength
zdW
=
360
N/mm²
Cyclic fatigue strength under bending stress
bW
=
450
N/mm²
Cyclic torsional fatigue strength
tW
=
270
N/mm²
Technological dimension factor (tensile strength)
K1Bdeff
=
1
Technological dimension factor (yield stress)
K1Sdeff
=
1
Parameter of cross-sections:
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Tension-pressure force Fzd and tension/pressure stress zd No. Type Position Result. Amplitude Mean x Fzdx Fzda Fzdm mm N N N 1
Shaft fillet
40
2
Shaft fillet
88
-30,088
-30,088
0
-30,088
-0,024
0
-0,024
3
Shaft fillet
96
-30,088
-30,088
0
-30,088
-0,024
0
-0,024
4
Shaft fillet
106
-30,088
-30,088
0
-30,088
-0,015
0
-0,015
5
Shaft fillet
186
-139,998
-139,998
0
-139,998
-0,111
0
-0,111
6
Shaft fillet
206
-139,998
-139,998
0
-139,998
-0,198
0
-0,198
7
Calculation results for point x
0
0
0
0
0
0
Bending moment Mb and bending stress b No. Type Position Result. x Mbx mm N*m
0
0
Maximum Amplitude Mean Maximum Fzdmax zda zdm zdmax N N/mm² N/mm² N/mm²
Amplitude Mean Mba Mbm N*m N*m
0
0
0
0
0
0
0
Maximum Amplitude Mean Maximum Mbmax ba bm bmax N*m N/mm² N/mm² N/mm²
1
Shaft fillet
40
19,599
19,599
0
19,599
7,394
0
7,394
2
Shaft fillet
88
39,699
39,699
0
39,699
6,318
0
6,318
3
Shaft fillet
96
36,428
36,428
0
36,428
5,798
0
5,798
4
Shaft fillet
106
32,471
32,471
0
32,471
2,646
0
2,646
5
Shaft fillet
186
10,287
10,287
0
10,287
1,637
0
1,637
6
Shaft fillet
206
16,28
16,28
0
16,28
6,142
0
6,142
7
Calculation results for point x
0
0
0
0
0
0
0
0
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Torsional moment Mt und Torsional stress t No. Type Position Result. x Mtx mm N*m
Amplitude Mean Mta Mtm N*m N*m
0
0
0
Maximum Amplitude Mean Maximum Mtmax ta tm tmax N*m N/mm² N/mm² N/mm²
1
Shaft fillet
40
0
0
0
2
Shaft fillet
88
134,135
134,135
0
134,135
10,674
0
10,674
3
Shaft fillet
96
134,135
134,135
0
134,135
10,674
0
10,674
4
Shaft fillet
106
134,135
134,135
0
134,135
5,465
0
5,465
5
Shaft fillet
186
0
0
0
0
0
0
0
6
Shaft fillet
206
0
0
0
0
0
0
0
7
Calculation results for point x
0
0
0
0
0
0
0
0
Calculation results for point
x
=
0
mm
Trend of curve of the transverse force
Qx
=
0
N
deflection
yx
=
0,00091
mm
Angle of deflection
=
0,003257
°
0
Critical shaft speed values: Critical bending shaft speed values No. Critical shaft speed values nb 1/min
Eigenfrequencies rad/s
1
134410,41
2
431436,25
45179,9
3
786687,24
82381,69
4
1273347,82
133344,67
5
1637701,84
171499,74
Critical torsional shaft speed values No. Critical shaft speed values nb 1/min
14075,42
Eigenfrequencies rad/s
1
584513,65
61210,13
2
1080949,83
113196,8
3
1246844,45
130569,25
4
1514360,39
158583,45
5
2035515,15
213158,65
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Strength proof: K2(d) - Geometrical dimension factor KF - Influence factor of surface roughness , - Form factors No. Type Position Tension- Bending Tensionx pressure and pressure, mm K2(d) torsion bending K2(d) KF
Torsion KF
1
Shaft fillet
40
1
0,91
0,89
0,94
2
Shaft fillet
88
1
0,89
0,89
3
Shaft fillet
96
1
0,89
0,89
4
Shaft fillet
106
1
0,87
5
Shaft fillet
186
1
0,89
6
Shaft fillet
206
1
7
Calculation results for point x
0
1
G - Relative stress drop n, - Bearing factor No. Type
Position x mm
Tensionpressure Gzd 1/mm
Tension- Bending pressure b zd
Torsion
1,26
1,2
1,11
0,94
1,2
1,13
1,08
0,94
1,25
1,17
1,1
0,89
0,93
1,24
1,15
1,09
0,97
0,98
1,17
1,13
1,07
0,91
0,93
0,96
1,19
1,14
1,08
0,91
0,89
0,94
-
-
-
Bending Gb 1/mm
Torsion Gt 1/mm
Tensionpressure nzd
Bending nb
Torsion n
1
Shaft fillet
40
0,15
0,15
0,08
1,02
1,02
1,01
2
Shaft fillet
88
0,12
0,12
0,05
1,01
1,01
1,01
3
Shaft fillet
96
0,14
0,14
0,06
1,02
1,02
1,01
4
Shaft fillet
106
0,12
0,12
0,05
1,01
1,01
1,01
5
Shaft fillet
186
0,08
0,08
0,04
1,01
1,01
1,01
6
Shaft fillet
206
0,14
0,14
0,06
1,02
1,02
1,01
7
Calculation results for point x
-
-
-
-
-
-
0
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zddBK, bdBK, dBK - Stress concentration factor at dBK zd, b, - Stress concentration factors Kv - Influence factor of surface hardening No. Type Positio Tension Bendin Torsio Tension Bending Torsion Tension Bendin Torsio n g n b g n x pressur dBK pressur pressur Kvb Kv mm e bdBK e e zd Kvzd zddBK 1
Shaft fillet
40
-
-
-
1,24
1,18
1,1
1
1
1
2
Shaft fillet
88
-
-
-
1,18
1,11
1,07
1
1
1
3
Shaft fillet
96
-
-
-
1,23
1,15
1,09
1
1
1
4
Shaft fillet
106
-
-
-
1,22
1,13
1,08
1
1
1
5
Shaft fillet
186
-
-
-
1,16
1,12
1,06
1
1
1
6
Shaft fillet
206
-
-
-
1,17
1,12
1,07
1
1
1
7
Calculation results for point x
0
-
-
-
1
1
1
1
1
1
K, K - Total influence factor zdWK, bWK, tWK - Cyclic fatigue strength of the notched part K2F - Static bearing effect No. Type Positio Tension Bendin Torsion Tension Bendin Torsion Tension Bendin Torsio n g K g s g n x pressur K pressur bWK tWK pressur K2Fb K2Ft mm e e N/mm² N/mm² e K zdWK K2Fzd N/mm² 1
Shaft fillet
40
1,36
1,43
1,28
263,81
314,8 5
211,23
1
1,2
1,2
2
Shaft fillet
88
1,31
1,38
1,27
275,18
326,1 8
211,99
1
1,2
1,2
3
Shaft fillet
96
1,35
1,42
1,29
266,08
317,0 6
208,71
1
1,2
1,2
4
Shaft fillet
106
1,35
1,42
1,31
265,81
316,1 6
205,78
1
1,2
1,2
5
Shaft fillet
186
1,19
1,29
1,21
303,34
349,6
222,4
1
1,2
1,2
6
Shaft fillet
206
1,25
1,31
1,22
288,17
343,3 4
221,3
1
1,2
1,2
7
Calculation results for point x
0
1,13
1,23
1,17
319,74
366,4 8
230,63
1
1,2
1,2
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F - Yield point rise zdFK, bFK, tFK - Yield point of the part No. Type Position x mm
Tensionpressure Fzd
Bending Fb
Torsion Ft
Tensionpressure zdFK N/mm²
Bending bFK N/mm²
Torsion tFK N/mm²
1
Shaft fillet
40
1
1
1
750
900
519,62
2
Shaft fillet
88
1
1
1
750
900
519,62
3
Shaft fillet
96
1
1
1
750
900
519,62
4
Shaft fillet
106
1
1
1
750
900
519,62
5
Shaft fillet
186
1
1
1
750
900
519,62
6
Shaft fillet
206
1
1
1
750
900
519,62
7
Calculation results for point x
0
1
1
1
750
900
519,62
Static safety No.
Type
Position x mm
SF
In Point1 SF1
in Point2 SF2
1
Shaft fillet
40
121,72
-
-
2
Shaft fillet
88
46,04
-
-
3
Shaft fillet
96
46,43
-
-
4
Shaft fillet
106
91,52
-
-
5
Shaft fillet
186
508,19
-
-
6
Shaft fillet
206
141,08
-
-
7
Calculation results for point x
-
-
0
- Influence factor of the mean stress sensitivitz mv, mv - Comparative mean stress No. Type Positio Tension Bending Torsion n bK K x pressur mm e zdK
10000
mv mv mv1 mv1 mv2 mv2 N/mm² N/mm² N/mm² N/mm² N/mm² N/mm²
1
Shaft fillet
40
-
0,21
-
0
0
-
-
-
-
2
Shaft fillet
88
0,18
0,22
0,13
0
0
-
-
-
-
3
Shaft fillet
96
0,17
0,21
0,13
0
0
-
-
-
-
4
Shaft fillet
106
0,17
0,21
0,13
0
0
-
-
-
-
5
Shaft fillet
186
0,2
0,24
-
0
0
-
-
-
-
6
Shaft fillet
206
0,19
0,24
-
0
0
-
-
-
-
7
Calculation results for point x
0
-
-
-
0
0
-
-
-
-
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Alternating fatigue strength of the part (rated fatigue limit) No. Type Positio Tension Bending Torsion Tension Bendin Torsio n bADK tADK g n x pressur N/mm² N/mm² pressur in in mm e e Point1 Point1 in zdADK Point1 bADK1 tADK1 N/mm² N/mm² N/mm² zdADK1 N/mm² 1
Shaft fillet
40
2
Shaft fillet
88
275,18
326,18
3
Shaft fillet
96
266,08
317,06
4
Shaft fillet
106
265,81
316,16
5
Shaft fillet
186
303,34
349,6
-
6
Shaft fillet
206
288,17
343,34
7
Calculation results for point x
0
Dynamic safety No.
-
-
Type
314,85
-
-
Tension pressur e in Point2 zdADK2 N/mm²
Bendin g in Point2 bADK2 N/mm²
Torsio n in Point2 tADK2 N/mm²
-
-
-
-
-
-
211,99
-
-
-
-
-
-
208,71
-
-
-
-
-
-
205,78
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
Position x mm
SD
in Point1 SD1
in Point2 SD2
1
Shaft fillet
40
42,58
-
-
2
Shaft fillet
88
18,53
-
-
3
Shaft fillet
96
18,4
-
-
4
Shaft fillet
106
35,89
-
-
5
Shaft fillet
186
198
-
-
6
Shaft fillet
206
53,83
-
-
7
Calculation results for point x
-
-
0
10000
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Unnotched (part dimension) for point x N/mm˛ 900
720
540
Material Number
= 15CrMoV59 = 1.8521
B(deff) zdF bF tF zdW bW tW
= = = = = = =
900 750 900 520 360 450 270
N/mm˛ N/mm˛ N/mm˛ N/mm˛ N/mm˛ N/mm˛ N/mm˛
360
Tension-pressure Bending Torsion
180
0
-180
-360
-540
N/mm˛ 180
360
540
720
900
Notched (part dimension) for point x N/mm˛ 900
720
540
Material Number
= 15CrMoV59 = 1.8521
B(deff) zdFK bFK tFK zdWK bWK tWK
= = = = = = =
900 750 900 520 320 366 231
N/mm˛ N/mm˛ N/mm˛ N/mm˛ N/mm˛ N/mm˛ N/mm˛
360
Tension-pressure Bending Torsion
180
0
-180
-360
-540
N/mm˛ 180
360
540
720
900
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Trend of curve of the transverse force in the Y-X-plane
Qy, N 1257,5
838,3
419,2
0,0
-419,2
-838,3
- 1257,5 0
L, mm
25
50
75
100
125
150
175
200
225
Trend of curve of the transverse force in the Z-X-plane
Qz, N 383,4
255,6
127,8
0,0
-127,8
-255,6
-383,4 0
L, mm
25
50
75
100
125
150
175
200
225
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Trend of curve of the transverse force (combined characteristic)
Q, N 1257,5
838,3
419,2
0,0
-419,2
-838,3
- 1257,5 0
L, mm
25
50
75
100
125
150
175
200
225
Bending moment in the Y-X-plane
Mby, Nm 45,9
30,6
15,3
0,0
-15,3
-30,6
-45,9 0
L, mm
25
50
75
100
125
150
175
200
225
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Trend of curve of the bending moment curve in the Z-X plane
Mbz, Nm 15,6
10,4
5,2
0,0
- 5,2
-10,4
-15,6 0
L, mm
25
50
75
100
125
150
175
200
225
Trend of curve of the bending moment (combined characteristic)
Mb, Nm 46,3
30,9
15,4
0,0
-15,4
-30,9
-46,3 0
L, mm
25
50
75
100
125
150
175
200
225
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Trend of curve of the torsional moment
Mt, Nm 134,1
89,4
44,7
0,0
-44,7
-89,4
-134,1 0
L, mm
25
50
75
100
125
150
175
200
225
Trend of curve of the tension-pressure forces
Fzd, N 140,0
93,3
46,7
0,0
-46,7
-93,3
-140,0 0
L, mm
25
50
75
100
125
150
175
200
225
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Deflection and angle of deflection in the Y-X-plane
Angle Deflection
0
L, mm
25
50
75
100
125
150
175
200
y, mm
5,90e- 3
3,23e- 3
3,93e- 3
2,15e- 3
1,97e- 3
1,08e- 3
0.00
0.00
- 1,97e- 3
- 1,08e- 3
- 3,93e- 3
- 2,15e- 3
- 5,90e- 3
- 3,23e- 3
225
Deflection and angle of deflection in the Z-X-plane
Angle Deflection
0
L, mm
25
50
75
100
125
150
175
200
y, mm
1,60e- 3
6,56e- 4
1,07e- 3
4,38e- 4
5,34e- 4
2,19e- 4
0.00
0.00
- 5,34e- 4
- 2,19e- 4
- 1,07e- 3
- 4,38e- 4
- 1,60e- 3
- 6,56e- 4
225
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Deflection and angle of deflection (combined characteristic)
Angle Deflection
0
L, mm
25
50
75
100
125
150
175
200
y, mm
6,09e- 3
3,26e- 3
4,06e- 3
2,17e- 3
2,03e- 3
1,09e- 3
0.00
0.00
- 2,03e- 3
- 1,09e- 3
- 4,06e- 3
- 2,17e- 3
- 6,09e- 3
- 3,26e- 3
225
Comparative mean stress (normal stress)
mv, N/mm˛ 0,0
0,0
0,0
0,0
- 0,0
- 0,0
- 0,0 0
L, mm
25
50
75
100
125
150
175
200
225
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Comparative mean stress (shear stress)
mv, N/mm˛ 0,0
0,0
0,0
0,0
- 0,0
- 0,0
- 0,0 0
L, mm
25
50
75
100
125
150
175
200
225
Safety factor against yielding (diagram section up to 5*minimum safety)
SF 230,2
191,8
153,5
115,1
76,7
38,4
0,0 0
L, mm
25
50
75
100
125
150
175
200
225
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Safety against fatigue fracture (diagram section up to 5*minimum safety)
SF 91,6
76,3
61,1
SF6=53,8
45,8
SF1=42,6
30,5
SF4=35,9
15,3 SF2=18,5 SF3=18,4
0,0 0
L, mm
25
50
75
100
125
150
175
200
225
Maximum value of the tension-pressure stress (combined characteristic)
max, N/mm˛ 0,2
0,1
0,1
0,0
- 0,1
- 0,1
- 0,2 0
L, mm
25
50
75
100
125
150
175
200
225
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Maximum value of the bending stress (combined characteristic)
max, N/mm˛ 7,6
5,1
2,5
0,0
- 2,5
- 5,1
- 7,6 0
L, mm
25
50
75
100
125
150
175
200
225
Maximum value of the torsional stress (combined characteristic)
max, N/mm˛ 10,7
7,1
3,6
0,0
- 3,6
- 7,1
-10,7 0
L, mm
25
50
75
100
125
150
175
200
225
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Compartable stress development (resultant)
v, N/mm˛ 19,5
16,3
13,0
9,8
6,5
3,3
0,0 0
L, mm
25
50
75
100
125
150
175
200
225
Amplitude value of the tension-pressure stress (combined characteristic)
zda, N/mm˛ 0,2
0,1
0,1
0,0
- 0,1
- 0,1
- 0,2 0
L, mm
25
50
75
100
125
150
175
200
225
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Amplitude value of the bending stress (combined characteristic)
ba, N/mm˛ 7,6
5,1
2,5
0,0
- 2,5
- 5,1
- 7,6 0
L, mm
25
50
75
100
125
150
175
200
225
Amplitude value of the torsional stress (combined characteristic)
ta, N/mm˛ 10,7
7,1
3,6
0,0
- 3,6
- 7,1
-10,7 0
L, mm
25
50
75
100
125
150
175
200
225
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Mean value of the tension-pressure stress (combined characteristic)
zdm, N/mm˛ 0,0
0,0
0,0
0,0
- 0,0
- 0,0
- 0,0 0
L, mm
25
50
75
100
125
150
175
200
225
Mean value of the bending stress (combined characteristic)
bm, N/mm˛ 0,0
0,0
0,0
0,0
- 0,0
- 0,0
- 0,0 0
L, mm
25
50
75
100
125
150
175
200
225
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Mean value of the torsional stress (combined characteristic)
tm, N/mm˛ 0,0
0,0
0,0
0,0
- 0,0
- 0,0
- 0,0 0
L, mm
25
50
75
100
125
150
175
200
225
Safety factor against yielding
L1
L2
> 1,20
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Safety against fatigue fracture
L1
L2
> 1,20
Resultant graphic Y-X-plane y Fr2 Fr4 Fax2 T1
T2
Fax1
L1
L2
x, mm 0
23,100
46,200
69,300
92,400
115,500
138,600
161,700
184,800
207,900
231,000
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Resultant graphic Z-X-plane z
Fr3
Fr1
Fax1
T1
T2 Fax2
L1
L2
x, mm 0
23,100
46,200
69,300
92,400
115,500
138,600
161,700
184,800
207,900
231,000
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This program allows to prove the bearing ability for shafts and axes. The calculation base is provided by DIN 743, edition of December 2012. The proof of the bearing ability for shafts an axes is produced by defining a calculated safety. This safety is divided in the safety against fatigue fracture and the residual deformation (and flaw or forced break). When calculating the avoidance of fatigue fracture, constant stress amplitudes being equivalent to damaging loads are taken as a basis. These ones are resulting from the predetermined loads. When proving against the residual deformation or forced break, designated as a safety against yielding, only the maximum occurring load is determinant. This one is resulting from the predetermined loads, too. The calculation of safeties is related only to the point of a clear notch effect. For it, 9 calculable notches are at your disposal due to the graphical selection, principally. The scope is limited to steels. Welded members should be calculated separately. But the utilized standard or the present program is ineffective for this purpose! The calculation base for the module Shaft Calculation is provided by DIN 743, edition of December 2012, part 1-4 “ Tragfähigkeitsberechnung von Wellen and Achsen” (“Calculation of bearing capacity of shafts and axes”).
Input data: Shaft calculation in accordance with DIN 743 - standard version Geometry scheme Calculation process
General shaft geometry Dynamic and static strength proof
Type of loading: tension-pressure
Dynamically pure cyclic
Type of loading: bending
Dynamically pure cyclic
Type of loading: torsion
Dynamically pure cyclic
Factor for maximum loading (tension-pressure)
1
Factor for maximum loading (bending)
1
Factor for maximum loading (torsion)
1
Specifications about the material Strength values according to
MDESIGN database (DIN 743)
Material designation
15CrMoV59
Material number
1.8521
Gage diameter
dB = 100
mm
For the gage diameter Tensile strength
B (Rm) = 900
N/mm²
Yield stress
S (Re) = 750
N/mm²
Cyclic fatigue strength under bending stress
bW = 450
N/mm²
Cyclic tension and pressure fatigue strength
zdW = 360
N/mm²
tW = 270
N/mm²
Cyclic torsional fatigue strength
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Young's modulus
E = 215000
N/mm²
Shear modulus
G = 83000
N/mm²
Density
= 7850
kg/m³
Apply surface hardening to
Total shaft
Material group
Nitrated steel
Heat treatment
quenched and tempered
Surface hardening
no
Shaft geometry
Shaft geometry Nr. Da l Di l Da r Di r mm mm mm mm
L mm
Rz µm
r mm
d: mm
t: mm
zd:
b:
t: nzd: nb:
nt:
dBK: zddB bdBK dBK: K: :
1
30
0
30
0
40
6
15
0
0
0
0
0
0
0
0
0
0
0
0
2
50
0
50
0
48
6,3
25
0
0
0
0
0
0
0
0
0
0
0
0
3
40
0
40
0
8
6
20
0
0
0
0
0
0
0
0
0
0
0
0
4
50
0
50
0
10
6,3
25
0
0
0
0
0
0
0
0
0
0
0
0
5
60
0
60
0
80
6
30
0
0
0
0
0
0
0
0
0
0
0
0
6
40
0
40
0
20
1,6
20
0
0
0
0
0
0
0
0
0
0
0
0
7
30
0
30
0
25
3,2
25
0
0
0
0
0
0
0
0
0
0
0
0
Predetermine the diameter determinant for the heat treatment ?
no
Calculation of the deflection for point
x=0
Shaft speed
n:0
Consideration of dead weight
Bearing Nr.
mm 1/min
no
Type =
Position x = mm
Radial bearing stiffness c r = N/m
Torsional bearing stiffness c = N*m
Bending bearing stiffness c = N*m
Radial bearing stiffness c r = N/m
Torsional bearing stiffness c = N*m
Bending bearing stiffness c = N*m
1
Locating bearing ->
16
1e+015
0
0
1e+015
0
0
2
Locating bearing <-
215
1e+015
0
0
1e+015
0
0
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Specifications about loadings Axial forces Fax Nr.
Position x = mm
Amount = N
Radius = mm
Angle = °
1
85
30,088
33
90
2
135
109,91
25
0
Radial forces Fr Nr.
Position x = mm
Amount = N
Angle = °
1
12,5
383,379
90
2
72,5
1257,489
0
3
153
383,379
90
4
231
1257,489
0
Torsion Nr.
Position x = mm
Torsion moments Mt: N*mm
Power P: kW
Transition part =
1
85
134135,48
0
takeoff
2
160
134135,48
0
drive
Specifications about the load/loadings Loading case
Constant mean stress (loading case 1)
Change the limit number of loading cycles ?
no
Minimum safety against fatigue fracture
SDmin = 1,2
Minimum safety against residual deformation
SFmin = 1,2
Results: Calculation process: Total shaft length
Dynamic and static strength proof L
=
231
mm
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Total shaft mass
m
=
3,306
Mass moment of inertia of the shaft
J
=
0,00117
kg*m²
Geometrical moment of inertia of the shaft
I
=
158,061
cm4
Position of the centre of gravity in the X-axis
xs
=
121,833
mm
Angle of torsion
=
-0,009
Additional shaft data: Shaft fillet number
l mm
Ip cm4
Wt cm³
m kg
1
40
7,952
5,301
0,222
2
48
61,359
24,544
0,74
3
8
25,133
12,566
0,079
4
10
61,359
24,544
0,154
5
80
127,235
42,412
1,776
6
20
25,133
12,566
0,197
7
25
7,952
5,301
0,139
Supporting forces: No. Type
Position x mm
Radial force in the Y-axis Ry N
kg
°
J kg*m² 0 0,0002 0 0
I cm4
Wb cm³
3,976
2,651
30,68
12,272
12,566
6,283
30,68
12,272
63,617
21,206
0
12,566
6,283
0
3,976
2,651
0,0008
Radial force in the Z-axis Rz N
Result. radial force R N
Axial force in the X-axis Rax N
1
Locating bearing ->
16
-813,166
-514,556
962,293
0
2
Locating bearing <-
215
-1701,812
-252,202
1720,398
-139,998
Resulting maximum bending moment: Position
x
=
72,5
mm
Amount
Mbmax
=
46,343
N*m
Position
x
=
85
mm
Amount
Mtmax
=
134,135
N*m
Position
x
=
135
mm
Amount
Fzdmax
=
Position
x
=
Amount
zdmax
=
Position
x
=
Amount
bmax
=
Position
x
=
88
mm
Amount
tmax
=
10,674
N/mm²
x
=
88
mm
Resulting maximum torsional moment:
Resulting maximum tension-pressure-force: -139,998
N
Resulting maximum tension-pressure-stress: 206 -0,198
mm N/mm²
Resulting maximum bending stress: 215 7,59
mm N/mm²
Resulting maximum torsional stress:
Resulting maximum compartable stress: Position
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vmax
=
19,53
N/mm²
Position
x
=
90,42
mm
Amount
ymax
=
0,00203
mm
Position
x
=
15,84
mm
Amount
=
0,003259
Position
x
=
88
Amount
SF
=
46,042
Position
x
=
92,4
Amount
SD
=
18,316
deff
=
60
Amount Resulting maximum deflection:
Angle of the maximum deflection: °
Minimum safety against yielding: mm
Minimum safety against fatigue fracture:
Material parameter for Material designation
15CrMoV59
Material number
1.8521
mm
mm
Tensile strength
B
=
900
N/mm²
Yield stress
S
=
750
N/mm²
Cyclic tension and pressure fatigue strength
zdW
=
360
N/mm²
Cyclic fatigue strength under bending stress
bW
=
450
N/mm²
Cyclic torsional fatigue strength
tW
=
270
N/mm²
Technological dimension factor (tensile strength)
K1Bdeff
=
1
Technological dimension factor (yield stress)
K1Sdeff
=
1
Parameter of cross-sections:
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Tension-pressure force Fzd and tension/pressure stress zd No. Type Position Result. Amplitude Mean x Fzdx Fzda Fzdm mm N N N 1
Shaft fillet
40
2
Shaft fillet
88
-30,088
-30,088
0
-30,088
-0,024
0
-0,024
3
Shaft fillet
96
-30,088
-30,088
0
-30,088
-0,024
0
-0,024
4
Shaft fillet
106
-30,088
-30,088
0
-30,088
-0,015
0
-0,015
5
Shaft fillet
186
-139,998
-139,998
0
-139,998
-0,111
0
-0,111
6
Shaft fillet
206
-139,998
-139,998
0
-139,998
-0,198
0
-0,198
7
Calculation results for point x
0
0
0
0
0
0
Bending moment Mb and bending stress b No. Type Position Result. x Mbx mm N*m
0
0
Maximum Amplitude Mean Maximum Fzdmax zda zdm zdmax N N/mm² N/mm² N/mm²
Amplitude Mean Mba Mbm N*m N*m
0
0
0
0
0
0
0
Maximum Amplitude Mean Maximum Mbmax ba bm bmax N*m N/mm² N/mm² N/mm²
1
Shaft fillet
40
19,599
19,599
0
19,599
7,394
0
7,394
2
Shaft fillet
88
39,699
39,699
0
39,699
6,318
0
6,318
3
Shaft fillet
96
36,428
36,428
0
36,428
5,798
0
5,798
4
Shaft fillet
106
32,471
32,471
0
32,471
2,646
0
2,646
5
Shaft fillet
186
10,287
10,287
0
10,287
1,637
0
1,637
6
Shaft fillet
206
16,28
16,28
0
16,28
6,142
0
6,142
7
Calculation results for point x
0
0
0
0
0
0
0
0
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Shaft calculation base
Torsional moment Mt und Torsional stress t No. Type Position Result. x Mtx mm N*m
Amplitude Mean Mta Mtm N*m N*m
0
0
0
Maximum Amplitude Mean Maximum Mtmax ta tm tmax N*m N/mm² N/mm² N/mm²
1
Shaft fillet
40
0
0
0
2
Shaft fillet
88
134,135
134,135
0
134,135
10,674
0
10,674
3
Shaft fillet
96
134,135
134,135
0
134,135
10,674
0
10,674
4
Shaft fillet
106
134,135
134,135
0
134,135
5,465
0
5,465
5
Shaft fillet
186
0
0
0
0
0
0
0
6
Shaft fillet
206
0
0
0
0
0
0
0
7
Calculation results for point x
0
0
0
0
0
0
0
0
Calculation results for point
x
=
0
mm
Trend of curve of the transverse force
Qx
=
0
N
deflection
yx
=
0,00091
mm
Angle of deflection
=
0,003257
°
0
Critical shaft speed values: Critical bending shaft speed values No. Critical shaft speed values nb 1/min
Eigenfrequencies rad/s
1
134410,41
2
431436,25
45179,9
3
786687,24
82381,69
4
1273347,82
133344,67
5
1637701,84
171499,74
Critical torsional shaft speed values No. Critical shaft speed values nb 1/min
14075,42
Eigenfrequencies rad/s
1
584513,65
61210,13
2
1080949,83
113196,8
3
1246844,45
130569,25
4
1514360,39
158583,45
5
2035515,15
213158,65
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Strength proof: K2(d) - Geometrical dimension factor KF - Influence factor of surface roughness , - Form factors No. Type Position Tension- Bending Tensionx pressure and pressure, mm K2(d) torsion bending K2(d) KF
Torsion KF
1
Shaft fillet
40
1
0,91
0,89
0,94
2
Shaft fillet
88
1
0,89
0,89
3
Shaft fillet
96
1
0,89
0,89
4
Shaft fillet
106
1
0,87
5
Shaft fillet
186
1
0,89
6
Shaft fillet
206
1
7
Calculation results for point x
0
1
G - Relative stress drop n, - Bearing factor No. Type
Position x mm
Tensionpressure Gzd 1/mm
Tension- Bending pressure b zd
Torsion
1,26
1,2
1,11
0,94
1,2
1,13
1,08
0,94
1,25
1,17
1,1
0,89
0,93
1,24
1,15
1,09
0,97
0,98
1,17
1,13
1,07
0,91
0,93
0,96
1,19
1,14
1,08
0,91
0,89
0,94
-
-
-
Bending Gb 1/mm
Torsion Gt 1/mm
Tensionpressure nzd
Bending nb
Torsion n
1
Shaft fillet
40
0,15
0,15
0,08
1,02
1,02
1,01
2
Shaft fillet
88
0,12
0,12
0,05
1,01
1,01
1,01
3
Shaft fillet
96
0,14
0,14
0,06
1,02
1,02
1,01
4
Shaft fillet
106
0,12
0,12
0,05
1,01
1,01
1,01
5
Shaft fillet
186
0,08
0,08
0,04
1,01
1,01
1,01
6
Shaft fillet
206
0,14
0,14
0,06
1,02
1,02
1,01
7
Calculation results for point x
-
-
-
-
-
-
0
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Shaft calculation base
zddBK, bdBK, dBK - Stress concentration factor at dBK zd, b, - Stress concentration factors Kv - Influence factor of surface hardening No. Type Positio Tension Bendin Torsio Tension Bending Torsion Tension Bendin Torsio n g n b g n x pressur dBK pressur pressur Kvb Kv mm e bdBK e e zd Kvzd zddBK 1
Shaft fillet
40
-
-
-
1,24
1,18
1,1
1
1
1
2
Shaft fillet
88
-
-
-
1,18
1,11
1,07
1
1
1
3
Shaft fillet
96
-
-
-
1,23
1,15
1,09
1
1
1
4
Shaft fillet
106
-
-
-
1,22
1,13
1,08
1
1
1
5
Shaft fillet
186
-
-
-
1,16
1,12
1,06
1
1
1
6
Shaft fillet
206
-
-
-
1,17
1,12
1,07
1
1
1
7
Calculation results for point x
0
-
-
-
1
1
1
1
1
1
K, K - Total influence factor zdWK, bWK, tWK - Cyclic fatigue strength of the notched part K2F - Static bearing effect No. Type Positio Tension Bendin Torsion Tension Bendin Torsion Tension Bendin Torsio n g K g s g n x pressur K pressur bWK tWK pressur K2Fb K2Ft mm e e N/mm² N/mm² e K zdWK K2Fzd N/mm² 1
Shaft fillet
40
1,36
1,43
1,28
263,81
314,8 5
211,23
1
1,2
1,2
2
Shaft fillet
88
1,31
1,38
1,27
275,18
326,1 8
211,99
1
1,2
1,2
3
Shaft fillet
96
1,35
1,42
1,29
266,08
317,0 6
208,71
1
1,2
1,2
4
Shaft fillet
106
1,35
1,42
1,31
265,81
316,1 6
205,78
1
1,2
1,2
5
Shaft fillet
186
1,19
1,29
1,21
303,34
349,6
222,4
1
1,2
1,2
6
Shaft fillet
206
1,25
1,31
1,22
288,17
343,3 4
221,3
1
1,2
1,2
7
Calculation results for point x
0
1,13
1,23
1,17
319,74
366,4 8
230,63
1
1,2
1,2
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F - Yield point rise zdFK, bFK, tFK - Yield point of the part No. Type Position x mm
Tensionpressure Fzd
Bending Fb
Torsion Ft
Tensionpressure zdFK N/mm²
Bending bFK N/mm²
Torsion tFK N/mm²
1
Shaft fillet
40
1
1
1
750
900
519,62
2
Shaft fillet
88
1
1
1
750
900
519,62
3
Shaft fillet
96
1
1
1
750
900
519,62
4
Shaft fillet
106
1
1
1
750
900
519,62
5
Shaft fillet
186
1
1
1
750
900
519,62
6
Shaft fillet
206
1
1
1
750
900
519,62
7
Calculation results for point x
0
1
1
1
750
900
519,62
Static safety No.
Type
Position x mm
SF
In Point1 SF1
in Point2 SF2
1
Shaft fillet
40
121,72
-
-
2
Shaft fillet
88
46,04
-
-
3
Shaft fillet
96
46,43
-
-
4
Shaft fillet
106
91,52
-
-
5
Shaft fillet
186
508,19
-
-
6
Shaft fillet
206
141,08
-
-
7
Calculation results for point x
-
-
0
- Influence factor of the mean stress sensitivitz mv, mv - Comparative mean stress No. Type Positio Tension Bending Torsion n bK K x pressur mm e zdK
10000
mv mv mv1 mv1 mv2 mv2 N/mm² N/mm² N/mm² N/mm² N/mm² N/mm²
1
Shaft fillet
40
-
0,21
-
0
0
-
-
-
-
2
Shaft fillet
88
0,18
0,22
0,13
0
0
-
-
-
-
3
Shaft fillet
96
0,17
0,21
0,13
0
0
-
-
-
-
4
Shaft fillet
106
0,17
0,21
0,13
0
0
-
-
-
-
5
Shaft fillet
186
0,2
0,24
-
0
0
-
-
-
-
6
Shaft fillet
206
0,19
0,24
-
0
0
-
-
-
-
7
Calculation results for point x
0
-
-
-
0
0
-
-
-
-
12/12/2018 11:43:49 Page 10/27
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Alternating fatigue strength of the part (rated fatigue limit) No. Type Positio Tension Bending Torsion Tension Bendin Torsio n bADK tADK g n x pressur N/mm² N/mm² pressur in in mm e e Point1 Point1 in zdADK Point1 bADK1 tADK1 N/mm² N/mm² N/mm² zdADK1 N/mm² 1
Shaft fillet
40
2
Shaft fillet
88
275,18
326,18
3
Shaft fillet
96
266,08
317,06
4
Shaft fillet
106
265,81
316,16
5
Shaft fillet
186
303,34
349,6
-
6
Shaft fillet
206
288,17
343,34
7
Calculation results for point x
0
Dynamic safety No.
-
-
Type
314,85
-
-
Tension pressur e in Point2 zdADK2 N/mm²
Bendin g in Point2 bADK2 N/mm²
Torsio n in Point2 tADK2 N/mm²
-
-
-
-
-
-
211,99
-
-
-
-
-
-
208,71
-
-
-
-
-
-
205,78
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
Position x mm
SD
in Point1 SD1
in Point2 SD2
1
Shaft fillet
40
42,58
-
-
2
Shaft fillet
88
18,53
-
-
3
Shaft fillet
96
18,4
-
-
4
Shaft fillet
106
35,89
-
-
5
Shaft fillet
186
198
-
-
6
Shaft fillet
206
53,83
-
-
7
Calculation results for point x
-
-
0
10000
12/12/2018 11:43:49 Page 11/27
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Shaft calculation base
Unnotched (part dimension) for point x N/mm˛ 900
720
540
Material Number
= 15CrMoV59 = 1.8521
B(deff) zdF bF tF zdW bW tW
= = = = = = =
900 750 900 520 360 450 270
N/mm˛ N/mm˛ N/mm˛ N/mm˛ N/mm˛ N/mm˛ N/mm˛
360
Tension-pressure Bending Torsion
180
0
-180
-360
-540
N/mm˛ 180
360
540
720
900
Notched (part dimension) for point x N/mm˛ 900
720
540
Material Number
= 15CrMoV59 = 1.8521
B(deff) zdFK bFK tFK zdWK bWK tWK
= = = = = = =
900 750 900 520 320 366 231
N/mm˛ N/mm˛ N/mm˛ N/mm˛ N/mm˛ N/mm˛ N/mm˛
360
Tension-pressure Bending Torsion
180
0
-180
-360
-540
N/mm˛ 180
360
540
720
900
12/12/2018 11:43:49 Page 12/27
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Shaft calculation base
Trend of curve of the transverse force in the Y-X-plane
Qy, N 1257,5
838,3
419,2
0,0
-419,2
-838,3
- 1257,5 0
L, mm
25
50
75
100
125
150
175
200
225
Trend of curve of the transverse force in the Z-X-plane
Qz, N 383,4
255,6
127,8
0,0
-127,8
-255,6
-383,4 0
L, mm
25
50
75
100
125
150
175
200
225
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Trend of curve of the transverse force (combined characteristic)
Q, N 1257,5
838,3
419,2
0,0
-419,2
-838,3
- 1257,5 0
L, mm
25
50
75
100
125
150
175
200
225
Bending moment in the Y-X-plane
Mby, Nm 45,9
30,6
15,3
0,0
-15,3
-30,6
-45,9 0
L, mm
25
50
75
100
125
150
175
200
225
12/12/2018 11:43:49 Page 14/27
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Trend of curve of the bending moment curve in the Z-X plane
Mbz, Nm 15,6
10,4
5,2
0,0
- 5,2
-10,4
-15,6 0
L, mm
25
50
75
100
125
150
175
200
225
Trend of curve of the bending moment (combined characteristic)
Mb, Nm 46,3
30,9
15,4
0,0
-15,4
-30,9
-46,3 0
L, mm
25
50
75
100
125
150
175
200
225
12/12/2018 11:43:49 Page 15/27
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Trend of curve of the torsional moment
Mt, Nm 134,1
89,4
44,7
0,0
-44,7
-89,4
-134,1 0
L, mm
25
50
75
100
125
150
175
200
225
Trend of curve of the tension-pressure forces
Fzd, N 140,0
93,3
46,7
0,0
-46,7
-93,3
-140,0 0
L, mm
25
50
75
100
125
150
175
200
225
12/12/2018 11:43:49 Page 16/27
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Shaft calculation base
Deflection and angle of deflection in the Y-X-plane
Angle Deflection
0
L, mm
25
50
75
100
125
150
175
200
y, mm
5,90e- 3
3,23e- 3
3,93e- 3
2,15e- 3
1,97e- 3
1,08e- 3
0.00
0.00
- 1,97e- 3
- 1,08e- 3
- 3,93e- 3
- 2,15e- 3
- 5,90e- 3
- 3,23e- 3
225
Deflection and angle of deflection in the Z-X-plane
Angle Deflection
0
L, mm
25
50
75
100
125
150
175
200
y, mm
1,60e- 3
6,56e- 4
1,07e- 3
4,38e- 4
5,34e- 4
2,19e- 4
0.00
0.00
- 5,34e- 4
- 2,19e- 4
- 1,07e- 3
- 4,38e- 4
- 1,60e- 3
- 6,56e- 4
225
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Deflection and angle of deflection (combined characteristic)
Angle Deflection
0
L, mm
25
50
75
100
125
150
175
200
y, mm
6,09e- 3
3,26e- 3
4,06e- 3
2,17e- 3
2,03e- 3
1,09e- 3
0.00
0.00
- 2,03e- 3
- 1,09e- 3
- 4,06e- 3
- 2,17e- 3
- 6,09e- 3
- 3,26e- 3
225
Comparative mean stress (normal stress)
mv, N/mm˛ 0,0
0,0
0,0
0,0
- 0,0
- 0,0
- 0,0 0
L, mm
25
50
75
100
125
150
175
200
225
12/12/2018 11:43:49 Page 18/27
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Comparative mean stress (shear stress)
mv, N/mm˛ 0,0
0,0
0,0
0,0
- 0,0
- 0,0
- 0,0 0
L, mm
25
50
75
100
125
150
175
200
225
Safety factor against yielding (diagram section up to 5*minimum safety)
SF 230,2
191,8
153,5
115,1
76,7
38,4
0,0 0
L, mm
25
50
75
100
125
150
175
200
225
12/12/2018 11:43:49 Page 19/27
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Safety against fatigue fracture (diagram section up to 5*minimum safety)
SF 91,6
76,3
61,1
SF6=53,8
45,8
SF1=42,6
30,5
SF4=35,9
15,3 SF2=18,5 SF3=18,4
0,0 0
L, mm
25
50
75
100
125
150
175
200
225
Maximum value of the tension-pressure stress (combined characteristic)
max, N/mm˛ 0,2
0,1
0,1
0,0
- 0,1
- 0,1
- 0,2 0
L, mm
25
50
75
100
125
150
175
200
225
12/12/2018 11:43:49 Page 20/27
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Maximum value of the bending stress (combined characteristic)
max, N/mm˛ 7,6
5,1
2,5
0,0
- 2,5
- 5,1
- 7,6 0
L, mm
25
50
75
100
125
150
175
200
225
Maximum value of the torsional stress (combined characteristic)
max, N/mm˛ 10,7
7,1
3,6
0,0
- 3,6
- 7,1
-10,7 0
L, mm
25
50
75
100
125
150
175
200
225
12/12/2018 11:43:49 Page 21/27
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Shaft calculation base
Compartable stress development (resultant)
v, N/mm˛ 19,5
16,3
13,0
9,8
6,5
3,3
0,0 0
L, mm
25
50
75
100
125
150
175
200
225
Amplitude value of the tension-pressure stress (combined characteristic)
zda, N/mm˛ 0,2
0,1
0,1
0,0
- 0,1
- 0,1
- 0,2 0
L, mm
25
50
75
100
125
150
175
200
225
12/12/2018 11:43:49 Page 22/27
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:
Shaft calculation base
Amplitude value of the bending stress (combined characteristic)
ba, N/mm˛ 7,6
5,1
2,5
0,0
- 2,5
- 5,1
- 7,6 0
L, mm
25
50
75
100
125
150
175
200
225
Amplitude value of the torsional stress (combined characteristic)
ta, N/mm˛ 10,7
7,1
3,6
0,0
- 3,6
- 7,1
-10,7 0
L, mm
25
50
75
100
125
150
175
200
225
12/12/2018 11:43:49 Page 23/27
Transilvania University of Brasov Program
: MDESIGN
Module v ersion : 15.0.9
U ser :
C ustomer :
Date : 12.12.2018
Project
:
Shaft calculation base
Mean value of the tension-pressure stress (combined characteristic)
zdm, N/mm˛ 0,0
0,0
0,0
0,0
- 0,0
- 0,0
- 0,0 0
L, mm
25
50
75
100
125
150
175
200
225
Mean value of the bending stress (combined characteristic)
bm, N/mm˛ 0,0
0,0
0,0
0,0
- 0,0
- 0,0
- 0,0 0
L, mm
25
50
75
100
125
150
175
200
225
12/12/2018 11:43:49 Page 24/27
Transilvania University of Brasov Program
: MDESIGN
Module v ersion : 15.0.9
U ser :
C ustomer :
Date : 12.12.2018
Project
:
Shaft calculation base
Mean value of the torsional stress (combined characteristic)
tm, N/mm˛ 0,0
0,0
0,0
0,0
- 0,0
- 0,0
- 0,0 0
L, mm
25
50
75
100
125
150
175
200
225
Safety factor against yielding
L1
L2
> 1,20
12/12/2018 11:43:49 Page 25/27
Transilvania University of Brasov Program
: MDESIGN
Module v ersion : 15.0.9
U ser :
C ustomer :
Date : 12.12.2018
Project
:
Shaft calculation base
Safety against fatigue fracture
L1
L2
> 1,20
Resultant graphic Y-X-plane y Fr2 Fr4 Fax2 T1
T2
Fax1
L1
L2
x, mm 0
23,100
46,200
69,300
92,400
115,500
138,600
161,700
184,800
207,900
231,000
12/12/2018 11:43:49 Page 26/27
Transilvania University of Brasov Program
: MDESIGN
Module v ersion : 15.0.9
U ser :
C ustomer :
Date : 12.12.2018
Project
:
Shaft calculation base
Resultant graphic Z-X-plane z
Fr3
Fr1
Fax1
T1
T2 Fax2
L1
L2
x, mm 0
23,100
46,200
69,300
92,400
115,500
138,600
161,700
184,800
207,900
231,000
12/12/2018 11:43:49 Page 27/27
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