Week 2 Bevel Gear Challenge
Grid Dependency Test
Mesh Size and Refinement is one of the most important considerations taken during Finite Element Analysis and the quality of Mesh depends on it. It directly effects the accuracy of any simulation, the higher the mesh density(or lower the mesh size) the higher the accuracy of the results. This would suggest that every simulation should be run with the lowest mesh size available but a lower mesh size increases the computation time of the simulation.
Practicality suggests to reduce the mesh size until there is very negligible variation in between to results or the results converge. This process is known as Grid Dependency Test or Mesh Refinement Test. As mesh size approaches 0, the approximate solution and the actual solution converge. The main goal of this test is to achieve an efficient mesh size which isn’t coarse enough to provide inaccurate results yet not fine enough that computation time is low.
GDT on Bevel Gears
To perform this test we run the simulation with the same exact analysis settings and parameters for 6mm, 5mm and 4mm.
The assigned material is Structural Steel whose density is 7850kg/m^3, Young’s Modulus is 200GPa, Poisson’s Ratio is 0.3, Yield Strength is 250MPa and Ultimate tensile strength is 460MPa.
The following steps were applied for analysis:
No. of steps-6
Auto Time Setting-ON
Defined By-Time
Initial Time Step-0.2s
Maximum Time Step-1s
Minimum Time Step-0.1s
Large Deflection is turned on
Contact Type is Frictional
Behavior is Symmetric
Interface is Adjusted to Touch
Simulation is formulated using Augmented Lagrange
Revolute Ground to body Joints are used on both the driver and pinion gears
Rotational Load in increments of 20deg is given on the pinion starting from 0 and increasing up to 120deg
Moment of -100N is applied on Driver Gear
A local face sizing of 1.75mm mesh is applied on all faces that come in contact(i.e. Teeth Faces) since that is the area of interest from which we wish to generate results. This is to obtain accurate results.
6mm
|
Total Deformation Max 47.883mm |
|||
|
Time (sec) |
Minimum (mm) |
Maximum (mm) |
Average (mm) |
|
0.2 |
0.87249 |
1.8939 |
1.4275 |
|
0.4 |
1.7439 |
3.7856 |
2.8578 |
|
0.7 |
3.0467 |
6.6136 |
5.0089 |
|
1 |
4.3412 |
9.4236 |
7.1134 |
|
1.2 |
5.1978 |
11.283 |
8.5133 |
|
1.4 |
6.048 |
13.129 |
9.9186 |
|
1.7 |
7.3093 |
15.866 |
12.023 |
|
2 |
8.5505 |
18.561 |
14.078 |
|
2.2 |
9.3652 |
20.329 |
15.428 |
|
2.4 |
10.168 |
22.073 |
16.777 |
|
2.6 |
10.959 |
23.79 |
18.116 |
|
2.9 |
12.12 |
26.31 |
20.114 |
|
3 |
12.5 |
27.134 |
20.754 |
|
3.2 |
13.248 |
28.758 |
22.035 |
|
3.4 |
13.98 |
30.346 |
23.293 |
|
3.505 |
14.357 |
31.166 |
23.955 |
|
3.61 |
14.73 |
31.975 |
24.609 |
|
3.7675 |
15.28 |
33.168 |
25.583 |
|
4 |
16.07 |
34.883 |
27.01 |
|
4.2 |
16.728 |
36.312 |
28.186 |
|
4.4 |
17.366 |
37.698 |
29.343 |
|
4.7 |
18.284 |
39.689 |
31.042 |
|
5 |
19.151 |
41.572 |
32.699 |
|
5.2 |
19.7 |
42.764 |
33.773 |
|
5.4 |
20.225 |
43.904 |
34.798 |
|
5.7 |
20.967 |
45.855 |
36.291 |
|
5.835 |
21.282 |
46.771 |
36.946 |
|
5.9175 |
21.468 |
47.332 |
37.343 |
|
6 |
21.651 |
47.883 |
37.733 |
|
Equivalent Elastic strain Max 3.47*10^-5 |
|||
|
Time |
minimum (mm/mm) |
maximum (mm/mm) |
Average (mm/mm) |
|
0.2 |
2.27E-13 |
1.75E-05 |
6.94E-08 |
|
0.4 |
5.07E-13 |
2.24E-05 |
8.06E-08 |
|
0.7 |
2.15E-13 |
1.52E-05 |
7.00E-08 |
|
1 |
2.35E-13 |
1.41E-05 |
5.66E-08 |
|
1.2 |
1.39E-12 |
1.61E-05 |
7.12E-08 |
|
1.4 |
3.98E-13 |
1.69E-05 |
6.92E-08 |
|
1.7 |
2.76E-13 |
1.62E-05 |
6.37E-08 |
|
2 |
1.26E-13 |
2.73E-05 |
6.16E-08 |
|
2.2 |
1.83E-12 |
1.93E-05 |
7.47E-08 |
|
2.4 |
1.58E-13 |
1.69E-05 |
7.09E-08 |
|
2.6 |
2.68E-13 |
2.11E-05 |
8.29E-08 |
|
2.9 |
2.10E-13 |
1.75E-05 |
6.90E-08 |
|
3 |
1.17E-12 |
1.80E-05 |
7.59E-08 |
|
3.2 |
7.97E-13 |
1.03E-05 |
5.52E-08 |
|
3.4 |
1.40E-12 |
1.70E-05 |
7.56E-08 |
|
3.505 |
1.53E-12 |
1.01E-05 |
5.66E-08 |
|
3.61 |
7.30E-13 |
1.90E-05 |
7.19E-08 |
|
3.7675 |
2.47E-13 |
2.45E-05 |
8.31E-08 |
|
4 |
4.13E-13 |
1.56E-05 |
6.66E-08 |
|
4.2 |
1.24E-12 |
1.86E-05 |
7.45E-08 |
|
4.4 |
3.86E-13 |
1.87E-05 |
7.65E-08 |
|
4.7 |
2.18E-13 |
2.05E-05 |
7.26E-08 |
|
5 |
1.22E-12 |
2.44E-05 |
8.60E-08 |
|
5.2 |
1.37E-13 |
9.85E-06 |
4.82E-08 |
|
5.4 |
4.73E-13 |
6.40E-06 |
4.53E-08 |
|
5.7 |
1.54E-12 |
7.01E-06 |
5.04E-08 |
|
5.835 |
1.68E-13 |
2.22E-05 |
6.98E-08 |
|
5.9175 |
1.75E-13 |
2.25E-05 |
7.02E-08 |
|
6 |
1.67E-13 |
3.47E-05 |
8.11E-08 |
|
Equivalent Stress Max 5.45Pa |
|||
|
Time(MPa) |
Minimum (Mpa) |
Maximum (Mpa) |
Average (Mpa) |
|
0.2 |
1.97E-08 |
2.79E+00 |
1.13E-02 |
|
0.4 |
6.05E-08 |
4.14E+00 |
1.33E-02 |
|
0.7 |
2.01E-08 |
2.92E+00 |
1.17E-02 |
|
1 |
2.47E-08 |
1.32E+00 |
9.02E-03 |
|
1.2 |
9.16E-08 |
2.59E+00 |
1.17E-02 |
|
1.4 |
4.33E-08 |
2.68E+00 |
1.12E-02 |
|
1.7 |
2.96E-08 |
2.36E+00 |
1.01E-02 |
|
2 |
2.30E-08 |
2.73E+00 |
9.45E-03 |
|
2.2 |
1.86E-07 |
3.20E+00 |
1.22E-02 |
|
2.4 |
2.46E-08 |
2.67E+00 |
1.15E-02 |
|
2.6 |
4.22E-08 |
3.61E+00 |
1.36E-02 |
|
2.9 |
2.21E-08 |
2.60E+00 |
1.16E-02 |
|
3 |
1.05E-07 |
3.22E+00 |
1.28E-02 |
|
3.2 |
7.12E-08 |
1.71E+00 |
9.00E-03 |
|
3.4 |
1.02E-07 |
2.82E+00 |
1.25E-02 |
|
3.505 |
1.56E-07 |
1.80E+00 |
9.20E-03 |
|
3.61 |
6.86E-08 |
2.96E+00 |
1.19E-02 |
|
3.7675 |
3.74E-08 |
4.45E+00 |
1.38E-02 |
|
4 |
2.04E-08 |
2.57E+00 |
1.08E-02 |
|
4.2 |
1.80E-07 |
3.54E+00 |
1.25E-02 |
|
4.4 |
3.48E-08 |
3.14E+00 |
1.26E-02 |
|
4.7 |
1.34E-08 |
3.19E+00 |
1.19E-02 |
|
5 |
1.12E-07 |
4.33E+00 |
1.43E-02 |
|
5.2 |
2.32E-08 |
1.01E+00 |
7.85E-03 |
|
5.4 |
6.97E-08 |
8.54E-01 |
7.53E-03 |
|
5.7 |
1.66E-07 |
1.02E+00 |
8.31E-03 |
|
5.835 |
2.33E-08 |
3.35E+00 |
1.15E-02 |
|
5.9175 |
2.36E-08 |
3.39E+00 |
1.16E-02 |
|
6 |
2.17E-08 |
5.45E+00 |
1.33E-02 |
5mm
|
Total Deformation Max 47.883mm |
|||
|
Time (sec) |
Minimum (mm) |
Maximum (mm) |
Average (mm) |
|
0.2 |
0.87249 |
1.8939 |
1.4201 |
|
0.4 |
1.7439 |
3.7856 |
2.843 |
|
0.7 |
3.0467 |
6.6136 |
4.9827 |
|
1 |
4.3412 |
9.4236 |
7.0765 |
|
1.2 |
5.1978 |
11.283 |
8.4691 |
|
1.4 |
6.048 |
13.129 |
9.867 |
|
1.7 |
7.3093 |
15.866 |
11.96 |
|
2 |
8.5505 |
18.561 |
14.004 |
|
2.2 |
9.3652 |
20.329 |
15.347 |
|
2.4 |
10.168 |
22.073 |
16.688 |
|
2.6 |
10.959 |
23.79 |
18.02 |
|
2.9 |
12.12 |
26.31 |
20.007 |
|
3 |
12.5 |
27.134 |
20.644 |
|
3.2 |
13.248 |
28.758 |
21.917 |
|
3.4 |
13.98 |
30.346 |
23.168 |
|
3.505 |
14.357 |
31.166 |
23.825 |
|
3.61 |
14.73 |
31.975 |
24.475 |
|
3.7675 |
15.28 |
33.168 |
25.444 |
|
4 |
16.07 |
34.883 |
26.862 |
|
4.2 |
16.728 |
36.312 |
28.031 |
|
4.4 |
17.366 |
37.698 |
29.181 |
|
4.7 |
18.284 |
39.689 |
30.868 |
|
5 |
19.151 |
41.572 |
32.514 |
|
5.2 |
19.7 |
42.764 |
33.58 |
|
5.4 |
20.225 |
43.904 |
34.599 |
|
5.4525 |
20.359 |
44.194 |
34.863 |
|
5.505 |
20.491 |
44.521 |
35.123 |
|
5.5838 |
20.686 |
45.06 |
35.512 |
|
5.7019 |
20.971 |
45.867 |
36.09 |
|
5.8791 |
21.382 |
47.07 |
36.941 |
|
6 |
21.651 |
47.883 |
37.511 |
|
Equivalent Elastic strain Max 2.71*10^-5 |
|||
|
time |
minimum (mm/mm) |
maximum (mm/mm) |
Average (mm/mm) |
|
0.2 |
1.77E-13 |
1.95E-05 |
6.76E-08 |
|
0.4 |
4.67E-13 |
2.21E-05 |
7.93E-08 |
|
0.7 |
7.33E-13 |
1.62E-05 |
7.25E-08 |
|
1 |
2.00E-13 |
1.52E-05 |
5.72E-08 |
|
1.2 |
1.58E-12 |
1.81E-05 |
7.24E-08 |
|
1.4 |
3.06E-13 |
1.64E-05 |
6.92E-08 |
|
1.7 |
2.22E-13 |
1.57E-05 |
6.35E-08 |
|
2 |
1.87E-13 |
3.29E-05 |
6.23E-08 |
|
2.2 |
1.45E-12 |
1.99E-05 |
7.29E-08 |
|
2.4 |
1.73E-13 |
1.77E-05 |
6.98E-08 |
|
2.6 |
2.75E-13 |
2.05E-05 |
8.19E-08 |
|
2.9 |
7.87E-14 |
1.38E-05 |
6.63E-08 |
|
3 |
1.06E-12 |
1.51E-05 |
7.25E-08 |
|
3.2 |
7.37E-13 |
1.09E-05 |
5.59E-08 |
|
3.4 |
6.53E-13 |
2.12E-05 |
7.27E-08 |
|
3.505 |
9.50E-14 |
1.13E-05 |
5.82E-08 |
|
3.61 |
1.28E-12 |
1.99E-05 |
6.94E-08 |
|
3.7675 |
3.67E-13 |
2.13E-05 |
7.91E-08 |
|
4 |
4.27E-13 |
1.47E-05 |
6.40E-08 |
|
4.2 |
1.11E-12 |
1.88E-05 |
7.60E-08 |
|
4.4 |
4.00E-13 |
2.02E-05 |
7.86E-08 |
|
4.7 |
2.80E-13 |
1.95E-05 |
7.42E-08 |
|
5 |
1.10E-12 |
2.44E-05 |
8.84E-08 |
|
5.2 |
2.33E-13 |
9.25E-06 |
4.96E-08 |
|
5.4 |
4.45E-13 |
6.68E-06 |
4.70E-08 |
|
5.4525 |
7.54E-13 |
8.24E-06 |
6.11E-08 |
|
5.505 |
2.27E-13 |
7.82E-06 |
4.90E-08 |
|
5.5838 |
2.04E-13 |
1.52E-05 |
6.26E-08 |
|
5.7019 |
1.52E-12 |
8.76E-06 |
5.44E-08 |
|
5.8791 |
1.12E-12 |
2.04E-05 |
7.30E-08 |
|
6 |
6.05E-13 |
2.71E-05 |
8.25E-08 |
|
Equivalent Stress Max 4.599 Pa |
|||
|
Time(MPa) |
Minimum (Mpa) |
Maximum (Mpa) |
Average (Mpa) |
|
0.2 |
2.16E-08 |
3.1156 |
1.11E-02 |
|
0.4 |
8.66E-08 |
4.1567 |
1.31E-02 |
|
0.7 |
7.84E-08 |
2.7742 |
1.21E-02 |
|
1 |
2.30E-08 |
1.4687 |
9.28E-03 |
|
1.2 |
1.37E-07 |
3.0634 |
1.20E-02 |
|
1.4 |
5.27E-08 |
2.6743 |
1.15E-02 |
|
1.7 |
3.31E-08 |
2.4184 |
1.03E-02 |
|
2 |
1.68E-08 |
3.7493 |
9.80E-03 |
|
2.2 |
1.08E-07 |
3.4962 |
1.21E-02 |
|
2.4 |
1.65E-08 |
2.6215 |
1.14E-02 |
|
2.6 |
3.91E-08 |
3.5146 |
1.34E-02 |
|
2.9 |
1.39E-08 |
2.2557 |
1.11E-02 |
|
3 |
8.94E-08 |
2.691 |
1.22E-02 |
|
3.2 |
6.35E-08 |
1.8647 |
9.09E-03 |
|
3.4 |
5.23E-08 |
3.832 |
1.21E-02 |
|
3.505 |
1.89E-08 |
1.8709 |
9.43E-03 |
|
3.61 |
1.13E-07 |
3.1722 |
1.15E-02 |
|
3.7675 |
3.79E-08 |
3.9502 |
1.32E-02 |
|
4 |
1.99E-08 |
2.5521 |
1.04E-02 |
|
4.2 |
1.99E-07 |
3.5666 |
1.28E-02 |
|
4.4 |
3.50E-08 |
3.6348 |
1.31E-02 |
|
4.7 |
3.50E-08 |
3.116 |
1.23E-02 |
|
5 |
8.58E-08 |
4.3371 |
1.48E-02 |
|
5.2 |
1.20E-08 |
1.1571 |
8.10E-03 |
|
5.4 |
5.50E-08 |
0.97341 |
7.73E-03 |
|
5.4525 |
6.66E-08 |
1.3298 |
1.02E-02 |
|
5.505 |
1.25E-08 |
0.99601 |
8.07E-03 |
|
5.5838 |
1.09E-08 |
2.8109 |
1.05E-02 |
|
5.7019 |
1.40E-07 |
1.2563 |
8.95E-03 |
|
5.8791 |
1.03E-07 |
3.3151 |
1.21E-02 |
|
6 |
2.44E-08 |
4.5991 |
1.37E-02 |
4mm
|
Total Deformation Max 47.883 |
|||
|
Time (sec) |
Minimum (mm) |
Maximum (mm) |
Average (mm) |
|
0.2 |
0.87249 |
1.8939 |
1.406 |
|
0.4 |
1.7439 |
3.7856 |
2.8149 |
|
0.7 |
3.0467 |
6.6136 |
4.9335 |
|
1 |
4.3412 |
9.4236 |
7.0065 |
|
1.2 |
5.1978 |
11.283 |
8.3853 |
|
1.4 |
6.048 |
13.129 |
9.7694 |
|
1.7 |
7.3093 |
15.866 |
11.842 |
|
2 |
8.5505 |
18.561 |
13.866 |
|
2.2 |
9.3652 |
20.329 |
15.195 |
|
2.4 |
10.168 |
22.073 |
16.524 |
|
2.6 |
10.959 |
23.79 |
17.843 |
|
2.9 |
12.12 |
26.31 |
19.811 |
|
3 |
12.5 |
27.134 |
20.441 |
|
3.2 |
13.248 |
28.758 |
21.702 |
|
3.4 |
13.98 |
30.346 |
22.941 |
|
3.505 |
14.357 |
31.166 |
23.593 |
|
3.61 |
14.73 |
31.975 |
24.237 |
|
3.7675 |
15.28 |
33.168 |
25.196 |
|
4 |
16.07 |
34.883 |
26.601 |
|
4.2 |
16.728 |
36.312 |
27.759 |
|
4.4 |
17.366 |
37.698 |
28.898 |
|
4.7 |
18.284 |
39.689 |
30.57 |
|
5 |
19.151 |
41.572 |
32.202 |
|
5.2 |
19.7 |
42.764 |
33.259 |
|
5.4 |
20.225 |
43.904 |
34.268 |
|
5.7 |
20.967 |
45.855 |
35.737 |
|
5.805 |
21.213 |
46.568 |
36.24 |
|
5.91 |
21.452 |
47.281 |
36.737 |
|
6 |
21.651 |
47.883 |
37.156 |
|
Equivalent Elastic strain Max 2.76*10^-5 |
|||
|
time |
minimum (mm/mm) |
maximum (mm/mm) |
Average (mm/mm) |
|
0.2 |
1.81E-13 |
1.77E-05 |
6.54E-08 |
|
0.4 |
4.94E-13 |
2.02E-05 |
7.70E-08 |
|
0.7 |
2.29E-13 |
1.53E-05 |
6.85E-08 |
|
1 |
2.58E-13 |
1.40E-05 |
5.54E-08 |
|
1.2 |
1.35E-12 |
1.83E-05 |
6.93E-08 |
|
1.4 |
4.13E-13 |
1.83E-05 |
6.73E-08 |
|
1.7 |
2.64E-13 |
1.74E-05 |
6.32E-08 |
|
2 |
1.47E-13 |
2.20E-05 |
5.75E-08 |
|
2.2 |
1.40E-12 |
1.82E-05 |
6.84E-08 |
|
2.4 |
1.50E-13 |
1.79E-05 |
6.58E-08 |
|
2.6 |
2.59E-13 |
2.41E-05 |
7.59E-08 |
|
2.9 |
1.83E-13 |
1.37E-05 |
6.50E-08 |
|
3 |
1.21E-12 |
1.73E-05 |
7.08E-08 |
|
3.2 |
7.66E-13 |
1.19E-05 |
5.56E-08 |
|
3.4 |
1.26E-12 |
2.23E-05 |
7.18E-08 |
|
3.505 |
2.07E-13 |
1.05E-05 |
5.70E-08 |
|
3.61 |
8.46E-13 |
2.24E-05 |
6.88E-08 |
|
3.7675 |
3.21E-13 |
2.77E-05 |
7.84E-08 |
|
4 |
4.57E-13 |
1.44E-05 |
6.24E-08 |
|
4.2 |
1.10E-12 |
2.16E-05 |
7.35E-08 |
|
4.4 |
3.89E-13 |
2.02E-05 |
7.44E-08 |
|
4.7 |
2.92E-13 |
1.79E-05 |
7.09E-08 |
|
5 |
1.09E-12 |
2.40E-05 |
8.35E-08 |
|
5.2 |
2.35E-13 |
8.41E-06 |
4.69E-08 |
|
5.4 |
4.53E-13 |
6.54E-06 |
4.44E-08 |
|
5.7 |
1.58E-12 |
7.76E-06 |
5.11E-08 |
|
5.805 |
2.15E-13 |
2.23E-05 |
6.88E-08 |
|
5.91 |
1.51E-12 |
2.27E-05 |
6.94E-08 |
|
6 |
2.02E-13 |
2.76E-05 |
7.81E-08 |
|
Equivalent Stress Max 5.3814 Pa |
|||
|
Time(MPa) |
Minimum (Mpa) |
Maximum (Mpa) |
Average (Mpa) |
|
0.2 |
2.28E-08 |
2.8532 |
1.08E-02 |
|
0.4 |
8.55E-08 |
3.5548 |
1.28E-02 |
|
0.7 |
1.65E-08 |
2.6502 |
1.16E-02 |
|
1 |
2.21E-08 |
1.4284 |
9.05E-03 |
|
1.2 |
9.77E-08 |
3.0293 |
1.15E-02 |
|
1.4 |
5.14E-08 |
2.9816 |
1.11E-02 |
|
1.7 |
4.01E-08 |
2.6611 |
1.01E-02 |
|
2 |
1.33E-08 |
1.6379 |
9.05E-03 |
|
2.2 |
8.03E-08 |
3.271 |
1.15E-02 |
|
2.4 |
1.74E-08 |
2.8703 |
1.11E-02 |
|
2.6 |
4.07E-08 |
4.3711 |
1.27E-02 |
|
2.9 |
9.72E-09 |
2.5086 |
1.10E-02 |
|
3 |
1.07E-07 |
2.9693 |
1.20E-02 |
|
3.2 |
6.06E-08 |
2.0233 |
9.08E-03 |
|
3.4 |
6.03E-08 |
3.8622 |
1.20E-02 |
|
3.505 |
9.91E-09 |
1.5548 |
9.25E-03 |
|
3.61 |
4.79E-08 |
3.6083 |
1.13E-02 |
|
3.7675 |
3.78E-08 |
5.4024 |
1.31E-02 |
|
4 |
7.13E-08 |
2.1919 |
1.02E-02 |
|
4.2 |
1.70E-07 |
4.0232 |
1.23E-02 |
|
4.4 |
3.72E-08 |
3.4233 |
1.23E-02 |
|
4.7 |
2.88E-08 |
2.885 |
1.16E-02 |
|
5 |
1.56E-07 |
4.068 |
1.39E-02 |
|
5.2 |
2.69E-08 |
1.0498 |
7.77E-03 |
|
5.4 |
5.55E-08 |
0.87461 |
7.42E-03 |
|
5.7 |
1.04E-07 |
1.2277 |
8.46E-03 |
|
5.805 |
2.46E-08 |
3.545 |
1.14E-02 |
|
5.91 |
9.98E-08 |
3.6087 |
1.15E-02 |
|
6 |
2.24E-08 |
5.3814 |
1.29E-02 |
There is no change in Total deformation across the 3 tests
The Equivalent Stress Generated reduces from 6mm to 5mm before increasing again for 4mm tests
The Equivalent Elastic Stress Generated Decreases significantly from 6mm to 5mm before marginally increasing for the 4mm test
This change in the trend of decreasing values from 6-5 mm and the subsequent increase from 5-4 mm tests is due to the relatively coarse nature of the mesh as we decrease the mesh size even further the trend of increase or decrease in values will also become far more consistent as well as the accuracy of the results generated