Week 2 Bevel Gear Challenge
Grid Dependency Test
Grid dependency test is to investigate how the solution depends on the grid size by running the simulation with refined mesh that is finer the mesh, higher is the accuracy of the result but with additional cost on computation time and computational power. We start off with a default mesh and move forth with refined meshing in the areas of interest. Refining continues until we see no more change in the results we obtain and this we call convergence. So, the grid dependency test helps in determining optimal mesh size where the accurate result could be obtained keeping in the mind the cost of time and power. Refining mesh further would result in negligible per cent change is the result but only increase the computational cost.
Aim:
To perform a grid dependency test for the Bevel gear simulation for mesh sizes of 6,5 and 4 mm and solve for Von-Mises stress, Equivalent elastic strain and Total Deformation.
Model:
The model shown here is the basis on which the test is conducted. There is a total of 40 teeth(16 small gear, 24 big gear). The gears have been given Body-Ground Revolute joints with Z axis as the axis of rotation. A face sizing option of element size 1.75mm have been given to the area of contact(teeth).
Simulation:
a) Case I :- 6 mm mesh
Element Size: 6 mm
Face Sizing at contacts: 1.75mm
No. of Nodes: 25970
No. of elements: 13879
Mesh Quality:
Observations
i) Von-Mises(Equivalent) Stress
Max Stress - 3.6162 MPa Min Stress - 2.3171e^-8 MPa
ii) Total Deformation
Max Deformation - 47.866 mm Min Deformation - 21.651 mm
iii) Equivalent Elastic Strain
Max Strain - 2.2564e^-5 mm Min Strain - 1.6829e^-13 mm
b) Case II :- 5 mm Mesh
Element Size: 5 mm
Face Sizing at contacts: 1.75mm
No. of Nodes: 20734
No. of elements: 10970
Mesh Quality
Observation
i) Von-Mises(Equivalent) Stress
Max Stress - 3.3005 MPa Min Stress - 2.1115e^-8 MPa
ii) Total Deformation
Max Deformation - 47.866 mm Min Deformation - 21.651 mm
iii) Equivalent Elastic Strain
Max Strain - 1.8436e^-5 mm Min Strain - 1.8617e^-13 mm
c) Case III :- 4 mm Mesh
Element Size: 4 mm
Face Sizing at contacts: 2 mm
No. of Nodes: 21494
No. of elements: 11406
Mesh Quality
Observation
i) Von-Mises(Equivalent) Stress
Max Stress - 3.23 MPa Min Stress - 2.0903e^-8 MPa
ii) Total Deformation
Max Deformation - 47.866 mm Min Deformation - 21.651 mm
iii) Equivalent Elastic Strain
Max Strain - 1.7968e^-5 mm Min Strain - 1.4972e^-13 mm
Comparison Table
| Total | Deformation | Equivalent | Stress | Elastic | Strain | |
| Max | Min | Max | Min | Max | Min | |
| 6 mm | 47.866 | 21.651 | 3.6162 | 2.3171e^-8 | 2.2564e^-5 | 1.6829e^-13 |
| 5 mm | 47.866 | 21.651 | 3.3005 | 2.1115e^-8 | 1.8436e^-5 | 1.8617e^-13 |
| 4 mm | 47.866 | 21.651 | 3.23 | 2.0904e^-8 | 1.7968e^-5 | 1.4972e^-13 |
Conclusion
From the table we see that the Total Deformation is same in all cases.
The rest of the values changes with change in mesh size but by only a small fraction.
The face sizing mesh was taken as 2mm to get results quicker ( 1.75 mm is recommended)
Thus Grid Dependency test is conducted.