Week 2 Railwheel and Track
Rail Wheel and Track
We will be simulating the motion of a rail wheel on a track in this exercise to find the deformation on the wheel, Equivalent Stress generated across the system and the fatigue generated in the wheel and it’s subsequent Life Expectancy.
The model is imported to and opened in space claim where we can see that there are 3 different bodies assembled together; The Track, The Wheel and The Axle.
All the bodies are made of structural steel and with Poisson’s Ratio of 0.3, Density of 7850 kg/m^3 and ultimate tensile strength of 460n/mm^2
There are 2 contact regions:
Track and wheel contact(Frictional)
Axle and wheel contact(Frictionless)
The track is fixed to the ground
The axle has translational motion to rotate and move along the track
The wheel has been defined using a planar joint to keep it from moving off the track during the simulation
The simulation is run for 5 steps measured by time. The analysis settings are as follows:
Initial Time step: 1e-2s
Minimum time step: 1e-3s
Maximum time step: 0.1s
2 different simulations are run both of which have an equal displacement of 500mm and 100000N and 500000N in the negative Y direction respectively
Every step has a displacement of 500mm
Results:
Total Deformation(100000N)
|
Time |
Minimum |
Maximum |
Average |
|
1.00E-02 |
0 |
1.1872 |
0.47177 |
|
2.00E-02 |
0 |
3.2445 |
1.2189 |
|
3.50E-02 |
0 |
6.3333 |
2.3404 |
|
5.75E-02 |
0 |
10.97 |
4.0238 |
|
7.44E-02 |
0 |
14.45 |
5.2871 |
|
8.28E-02 |
0 |
16.191 |
5.919 |
|
8.70E-02 |
0 |
17.062 |
6.235 |
|
9.13E-02 |
0 |
19.605 |
7.0803 |
|
9.76E-02 |
0 |
20.915 |
7.5555 |
|
0.10391 |
0 |
22.225 |
8.0308 |
|
0.1134 |
0 |
24.191 |
8.744 |
|
0.12764 |
0 |
27.138 |
9.8135 |
|
0.14899 |
0 |
29.847 |
10.876 |
|
0.17035 |
0 |
34.227 |
12.469 |
|
0.20239 |
0 |
40.828 |
14.865 |
|
0.25044 |
0 |
50.739 |
18.463 |
|
0.32252 |
0 |
65.615 |
23.864 |
|
0.42252 |
0 |
86.193 |
31.339 |
|
0.52252 |
0 |
106.79 |
38.823 |
|
0.62252 |
0 |
127.4 |
46.311 |
|
0.72252 |
0 |
147.95 |
53.783 |
|
0.82252 |
0 |
168.53 |
61.27 |
|
0.92252 |
0 |
189.07 |
68.74 |
|
1 |
0 |
205.02 |
74.538 |
|
1.0775 |
0 |
220.88 |
80.314 |
|
1.155 |
0 |
236.79 |
86.103 |
|
1.255 |
0 |
257.24 |
93.543 |
|
1.355 |
0 |
277.8 |
101.02 |
|
1.455 |
0 |
298.22 |
108.45 |
|
1.555 |
0 |
318.67 |
115.9 |
|
1.655 |
5.68E-14 |
339.1 |
123.35 |
|
1.755 |
6.07E-14 |
359.43 |
130.77 |
|
1.855 |
3.55E-15 |
379.83 |
138.21 |
|
1.955 |
3.55E-15 |
400.11 |
145.62 |
|
2 |
0 |
409.28 |
148.97 |
|
2.045 |
1.78E-15 |
418.43 |
152.31 |
|
2.0901 |
3.55E-15 |
427.5 |
155.63 |
|
2.1577 |
3.55E-15 |
441.22 |
160.64 |
|
2.2577 |
3.55E-15 |
461.39 |
168.03 |
|
2.3577 |
3.18E-14 |
481.62 |
175.43 |
|
2.4577 |
3.18E-14 |
501.73 |
182.8 |
|
2.5577 |
3.18E-14 |
521.89 |
190.19 |
|
2.6577 |
3.18E-14 |
542 |
197.55 |
|
2.7577 |
2.84E-14 |
562.18 |
204.92 |
|
2.8577 |
2.84E-14 |
582.25 |
212.27 |
|
2.9577 |
2.84E-14 |
602.24 |
219.6 |
|
3 |
2.84E-14 |
610.7 |
222.7 |
|
3.0423 |
2.84E-14 |
619.18 |
225.81 |
|
3.0847 |
2.84E-14 |
627.65 |
228.92 |
|
3.127 |
2.84E-14 |
636.02 |
231.99 |
|
3.1905 |
2.84E-14 |
648.77 |
236.66 |
|
3.254 |
2.84E-14 |
661.47 |
241.31 |
|
3.3493 |
2.84E-14 |
680.36 |
248.25 |
|
3.4493 |
2.84E-14 |
700.2 |
255.54 |
|
3.5493 |
6.51E-14 |
719.96 |
262.82 |
|
3.6493 |
6.51E-14 |
739.6 |
270.08 |
|
3.7493 |
8.53E-14 |
759.32 |
277.36 |
|
3.8493 |
1.89E-13 |
778.81 |
284.59 |
|
3.9493 |
1.89E-13 |
798.39 |
291.84 |
|
4 |
1.89E-13 |
808.22 |
295.48 |
|
4.0507 |
1.89E-13 |
818.17 |
299.15 |
|
4.1014 |
1.91E-13 |
828.12 |
302.82 |
|
4.1775 |
1.93E-13 |
842.85 |
308.28 |
|
4.2775 |
1.93E-13 |
862.36 |
315.5 |
|
4.3775 |
1.95E-13 |
881.65 |
322.67 |
|
4.4775 |
1.95E-13 |
901 |
329.85 |
|
4.5775 |
1.95E-13 |
920.3 |
337.01 |
|
4.6775 |
1.95E-13 |
939.48 |
344.14 |
|
4.7775 |
1.89E-13 |
958.71 |
351.29 |
|
4.8775 |
1.93E-13 |
977.73 |
358.39 |
|
4.9388 |
1.93E-13 |
989.48 |
362.76 |
|
5 |
1.93E-13 |
1001.1 |
367.09 |
Total Deformation(500000N)
|
Time |
Minimum |
Maximum |
Average |
|
1.00E-02 |
0 |
1.1856 |
0.47154 |
|
2.00E-02 |
0 |
3.2422 |
1.2185 |
|
3.50E-02 |
0 |
6.3323 |
2.3406 |
|
5.75E-02 |
0 |
10.974 |
4.0254 |
|
9.13E-02 |
0 |
17.944 |
6.555 |
|
1.25E-01 |
0 |
26.56 |
9.6056 |
|
1.76E-01 |
0 |
35.394 |
12.889 |
|
2.26E-01 |
0 |
45.832 |
16.679 |
|
3.02E-01 |
0 |
61.537 |
22.379 |
|
0.40219 |
0 |
82.228 |
29.889 |
|
0.50219 |
0 |
102.8 |
37.363 |
|
0.60219 |
0 |
123.43 |
44.857 |
|
0.70219 |
0 |
144.03 |
52.345 |
|
0.80219 |
0 |
164.57 |
59.818 |
|
0.90219 |
7.11E-15 |
185.18 |
67.311 |
|
1 |
7.11E-15 |
205.23 |
74.605 |
|
1.0978 |
7.11E-15 |
225.29 |
81.906 |
|
1.1956 |
0 |
245.27 |
89.182 |
|
1.2956 |
7.11E-15 |
265.8 |
96.644 |
|
1.3956 |
0 |
286.27 |
104.09 |
|
1.4956 |
0 |
306.71 |
111.54 |
|
1.5956 |
0 |
327.19 |
118.99 |
|
1.6956 |
0 |
347.57 |
126.43 |
|
1.7956 |
0 |
368 |
133.88 |
|
1.8956 |
0 |
388.33 |
141.3 |
|
1.9478 |
7.11E-15 |
398.98 |
145.19 |
|
2 |
0 |
409.48 |
149.03 |
|
2.0522 |
0 |
420.03 |
152.89 |
|
2.1044 |
0 |
430.63 |
156.76 |
|
2.1827 |
0 |
446.47 |
162.55 |
|
2.2609 |
0.00E+00 |
462.36 |
168.36 |
|
2.3609 |
0.00E+00 |
482.49 |
175.74 |
|
2.4609 |
0.00E+00 |
502.63 |
183.11 |
|
2.5609 |
0.00E+00 |
522.72 |
190.48 |
|
2.6609 |
1.78E-15 |
542.88 |
197.86 |
|
2.7609 |
1.78E-15 |
563.05 |
205.23 |
|
2.8609 |
5.33E-15 |
583.08 |
212.56 |
|
2.9609 |
5.33E-15 |
603.1 |
219.9 |
|
3 |
1.78E-15 |
610.9 |
222.76 |
|
3.0391 |
1.78E-15 |
618.66 |
225.61 |
|
3.0781 |
0.00E+00 |
626.45 |
228.48 |
|
3.1367 |
5.33E-15 |
638.19 |
232.77 |
|
3.2246 |
0.00E+00 |
655.67 |
239.19 |
|
3.3125 |
5.33E-15 |
673.21 |
245.62 |
|
3.4125 |
0.00E+00 |
693.01 |
252.9 |
|
3.5125 |
0.00E+00 |
712.78 |
260.18 |
|
3.6125 |
0.00E+00 |
732.42 |
267.43 |
|
3.7125 |
0.00E+00 |
752.1 |
274.7 |
|
3.8125 |
0.00E+00 |
771.65 |
281.94 |
|
3.9125 |
0.00E+00 |
791.15 |
289.18 |
|
4 |
0.00E+00 |
808.29 |
295.51 |
|
4.0875 |
1.42E-14 |
825.39 |
301.83 |
|
4.175 |
5.33E-15 |
842.47 |
308.14 |
|
4.2625 |
0.00E+00 |
859.42 |
314.43 |
|
4.3625 |
0.00E+00 |
878.8 |
321.62 |
|
4.4625 |
0.00E+00 |
898.03 |
328.77 |
|
4.5625 |
0.00E+00 |
917.33 |
335.93 |
|
4.6625 |
0.00E+00 |
936.58 |
343.08 |
|
4.7625 |
0.00E+00 |
955.71 |
350.21 |
|
4.8625 |
0.00E+00 |
974.76 |
357.31 |
|
4.9625 |
0.00E+00 |
993.86 |
364.42 |
|
5 |
0.00E+00 |
1000.9 |
367.07 |
Equivalent Stress Generated(100000N)
|
Equivalent Stress(MPa) |
|||
|
time |
minimum |
maximum |
Average |
|
1.00E-02 |
6.44E-12 |
1.0078 |
1.18E-02 |
|
2.00E-02 |
9.48E-13 |
2.0139 |
2.36E-02 |
|
3.50E-02 |
9.72E-13 |
3.5201 |
4.14E-02 |
|
5.75E-02 |
1.41E-12 |
5.7726 |
6.80E-02 |
|
7.44E-02 |
1.69E-12 |
7.4644 |
8.80E-02 |
|
8.28E-02 |
2.41E-12 |
8.3149 |
9.80E-02 |
|
8.70E-02 |
2.04E-12 |
8.7394 |
0.10302 |
|
9.13E-02 |
1.67E-12 |
9.1771 |
0.1081 |
|
9.76E-02 |
1.06E-12 |
9.8176 |
0.11565 |
|
0.10391 |
1.14E-12 |
10.459 |
0.12321 |
|
0.1134 |
1.37E-12 |
11.423 |
0.13453 |
|
0.12764 |
1.39E-12 |
12.827 |
0.15139 |
|
0.14899 |
1.55E-12 |
13.941 |
0.16862 |
|
0.17035 |
1.73E-12 |
17.282 |
0.19648 |
|
0.20239 |
6.43E-13 |
20.544 |
0.23335 |
|
0.25044 |
3.71E-12 |
25.44 |
0.2886 |
|
0.32252 |
4.30E-12 |
33.859 |
0.36643 |
|
0.42252 |
2.37E-12 |
51.423 |
0.49951 |
|
0.52252 |
4.77E-12 |
93.124 |
0.62613 |
|
0.62252 |
2.65E-12 |
128.14 |
0.76861 |
|
0.72252 |
7.71E-12 |
105.9 |
0.87078 |
|
0.82252 |
9.11E-12 |
133.91 |
0.97576 |
|
0.92252 |
1.31E-11 |
144.08 |
1.0911 |
|
1 |
1.39E-11 |
108.93 |
1.1539 |
|
1.0775 |
1.62E-11 |
168.6 |
1.2007 |
|
1.155 |
1.26E-11 |
161 |
1.1865 |
|
1.255 |
1.70E-11 |
146.54 |
1.2086 |
|
1.355 |
2.11E-11 |
105.79 |
1.1721 |
|
1.455 |
2.31E-11 |
100.82 |
1.2011 |
|
1.555 |
3.94E-11 |
130.82 |
1.1563 |
|
1.655 |
3.91E-11 |
138.8 |
1.1815 |
|
1.755 |
4.66E-11 |
128.64 |
1.1788 |
|
1.855 |
4.98E-11 |
132.87 |
1.155 |
|
1.955 |
5.34E-11 |
109.28 |
1.1438 |
|
2 |
3.98E-11 |
109.75 |
1.1438 |
|
2.045 |
5.15E-11 |
86.375 |
1.1351 |
|
2.0901 |
5.06E-11 |
128.05 |
1.1843 |
|
2.1577 |
5.10E-11 |
129.13 |
1.1808 |
|
2.2577 |
4.90E-11 |
103.06 |
1.1706 |
|
2.3577 |
4.92E-11 |
118.18 |
1.1882 |
|
2.4577 |
4.87E-11 |
118.63 |
1.2243 |
|
2.5577 |
5.34E-11 |
96.687 |
1.177 |
|
2.6577 |
5.48E-11 |
128.56 |
1.2233 |
|
2.7577 |
5.12E-11 |
111.28 |
1.1859 |
|
2.8577 |
5.20E-11 |
119.66 |
1.212 |
|
2.9577 |
5.42E-11 |
125.32 |
1.2199 |
|
3 |
5.69E-11 |
139.38 |
1.2376 |
|
3.0423 |
5.51E-11 |
132.44 |
1.2319 |
|
3.0847 |
7.37E-11 |
117.42 |
1.2065 |
|
3.127 |
6.91E-11 |
148.71 |
1.2497 |
|
3.1905 |
6.94E-11 |
149 |
1.2409 |
|
3.254 |
6.62E-11 |
162.27 |
1.2126 |
|
3.3493 |
7.30E-11 |
166.01 |
1.2426 |
|
3.4493 |
6.76E-11 |
98.312 |
1.1987 |
|
3.5493 |
6.68E-11 |
113.91 |
1.2062 |
|
3.6493 |
6.64E-11 |
109.62 |
1.2477 |
|
3.7493 |
6.74E-11 |
109.87 |
1.2402 |
|
3.8493 |
7.55E-11 |
115.54 |
1.2517 |
|
3.9493 |
8.10E-11 |
99.138 |
1.1887 |
|
4 |
9.33E-11 |
142.34 |
1.1924 |
|
4.0507 |
9.20E-11 |
142.26 |
1.1882 |
|
4.1014 |
9.37E-11 |
112.83 |
1.1459 |
|
4.1775 |
1.22E-10 |
153.44 |
1.1869 |
|
4.2775 |
1.28E-10 |
150.75 |
1.1623 |
|
4.3775 |
1.74E-10 |
136.88 |
1.1621 |
|
4.4775 |
2.13E-10 |
123.54 |
1.1497 |
|
4.5775 |
2.61E-10 |
189.08 |
1.1864 |
|
4.6775 |
3.49E-10 |
112.14 |
1.1791 |
|
4.7775 |
3.41E-10 |
131.22 |
1.1879 |
|
4.8775 |
4.38E-10 |
99.466 |
1.1677 |
|
4.9388 |
4.36E-10 |
95.023 |
1.1523 |
|
5 |
5.21E-10 |
84.781 |
1.1501 |
Equivalent Stress Generated(500000N)
|
Equivalent Stress(MPa) |
|||
|
time |
minimum |
maximum |
Average |
|
1.00E-02 |
4.84E-13 |
5.039 |
5.91E-02 |
|
2.00E-02 |
1.40E-11 |
10.069 |
1.18E-01 |
|
3.50E-02 |
2.04E-11 |
17.6 |
2.07E-01 |
|
5.75E-02 |
3.50E-11 |
28.86 |
3.40E-01 |
|
9.13E-02 |
5.10E-11 |
45.825 |
5.40E-01 |
|
1.25E-01 |
4.61E-11 |
56.739 |
7.22E-01 |
|
1.76E-01 |
5.05E-11 |
81.563 |
0.98232 |
|
2.26E-01 |
5.85E-11 |
113.04 |
1.307 |
|
3.02E-01 |
7.55E-11 |
144 |
1.7246 |
|
0.40219 |
9.30E-11 |
234.47 |
2.3402 |
|
0.50219 |
1.13E-10 |
333.39 |
2.8926 |
|
0.60219 |
7.11E-11 |
449.45 |
3.5696 |
|
0.70219 |
9.27E-11 |
336.75 |
4.0852 |
|
0.80219 |
1.48E-10 |
633.51 |
4.674 |
|
0.90219 |
1.52E-10 |
679.91 |
5.0945 |
|
1 |
1.63E-10 |
397.59 |
5.5833 |
|
1.0978 |
1.69E-10 |
589.03 |
5.6505 |
|
1.1956 |
1.75E-10 |
488.74 |
5.8104 |
|
1.2956 |
1.83E-10 |
569.28 |
5.8024 |
|
1.3956 |
1.87E-10 |
418.34 |
5.7671 |
|
1.4956 |
2.00E-10 |
426.49 |
5.7035 |
|
1.5956 |
1.90E-10 |
500.52 |
5.5269 |
|
1.6956 |
1.92E-10 |
420.33 |
5.4935 |
|
1.7956 |
1.97E-10 |
542.83 |
5.3932 |
|
1.8956 |
1.98E-10 |
550.29 |
5.3987 |
|
1.9478 |
1.94E-10 |
513.72 |
5.3075 |
|
2 |
2.08E-10 |
352 |
5.3176 |
|
2.0522 |
2.09E-10 |
388.92 |
5.4198 |
|
2.1044 |
2.11E-10 |
440.9 |
5.4505 |
|
2.1827 |
2.21E-10 |
467.56 |
5.4488 |
|
2.2609 |
2.19E-10 |
429.47 |
5.411 |
|
2.3609 |
2.36E-10 |
358.96 |
5.4213 |
|
2.4609 |
2.47E-10 |
391.28 |
5.5853 |
|
2.5609 |
2.67E-10 |
417.59 |
5.5475 |
|
2.6609 |
2.59E-10 |
470.78 |
5.5887 |
|
2.7609 |
2.58E-10 |
429.87 |
5.4232 |
|
2.8609 |
2.37E-10 |
407.59 |
5.35 |
|
2.9609 |
2.28E-10 |
428.6 |
5.4606 |
|
3 |
2.38E-10 |
418.88 |
5.4487 |
|
3.0391 |
2.56E-10 |
406.92 |
5.4578 |
|
3.0781 |
2.70E-10 |
418.04 |
5.4703 |
|
3.1367 |
2.89E-10 |
413.22 |
5.3791 |
|
3.2246 |
3.30E-10 |
664.3 |
5.4241 |
|
3.3125 |
3.63E-10 |
667.46 |
5.3784 |
|
3.4125 |
3.94E-10 |
383.3 |
5.3151 |
|
3.5125 |
4.14E-10 |
408.15 |
5.3281 |
|
3.6125 |
4.43E-10 |
414.7 |
5.4678 |
|
3.7125 |
4.31E-10 |
414.56 |
5.4855 |
|
3.8125 |
4.83E-10 |
374.56 |
5.509 |
|
3.9125 |
5.49E-10 |
442.78 |
5.4499 |
|
4 |
6.06E-10 |
444.43 |
5.3204 |
|
4.0875 |
6.85E-10 |
380.1 |
5.3342 |
|
4.175 |
7.57E-10 |
477.56 |
5.2605 |
|
4.2625 |
8.32E-10 |
623.41 |
5.341 |
|
4.3625 |
8.57E-10 |
570.23 |
5.2047 |
|
4.4625 |
9.76E-10 |
428.44 |
5.3013 |
|
4.5625 |
1.01E-09 |
654.12 |
5.3634 |
|
4.6625 |
1.09E-09 |
517.75 |
5.3509 |
|
4.7625 |
1.31E-09 |
348.6 |
5.1739 |
|
4.8625 |
1.55E-09 |
360.02 |
5.2712 |
|
4.9625 |
1.79E-09 |
376.64 |
5.311 |
|
5 |
1.97E-09 |
325.44 |
5.3339 |
Life(100000N)
1000000 Cycles
Life(500000N)
Maximum 1000000 Cycles
Minimum 5116.1 Cycles
User Defined Results:
We can generate certain user defined results using predefined syntax expressions in ansys to create new parameters for design reference. To check the reliability of such results We have generated a user defined result in the above simulation for total deformation by the expression (UX^2+UY^2+UZ^2)^0.5. This is the coordinate geometric Formula for calculating the total displacement of point which has been translated.
The Data generated for both the Deformations is exactly the same
Maximum Deformation 1001.1mm
The Total Deformation Generated in both 100000N and 500000N is similar though undesirable and the stress generated under 100000N Load is lower than the ultimate tensile stress but under 500000N loading the structure will fail as the stress exceeds 460N/mm^2