Week 2 Bevel Gear Challenge

Objective:

The objective of this project is to perform a grid dependency test for the bevel gear simulation for the mesh sizes of 4 mm, 5 mm, 6 mm, and solve for Von-Mises stress, Equivalent elastic strain, and Total deformation for the same mesh sizes.

Introduction:

Grid Dependency Test:

Grid dependency test is the test used to know and evaluate how different meshes (grid) weighs in to give an accurate solution. The solutions are more accurate when the mesh size is less or when the mesh is fine. The disadvantage of a finer mesh is that the simulation demands longer computational time to converge to the solution. Hence we try to find the mesh generation that gives a solution that is applicable, accurate enough, and takes reasonable time to converge concerning the complexity of the project.

A grid dependency test helps us evaluate how much the accuracy of the solution is dependent on the meshing (coarse to fine).

Setup Environment:

The material used for the bevel gears is Structural Steel. Two bevel gears are setup to mesh and analyze the mechanism with different mesh sizes for the grid dependency test. Mesh sizes used to perform the grid dependency test are 4 mm, 5 mm, 6 mm. The outputs on which the grid dependency evaluated in this project are Total Deformation, Von-Mises stress, and Equivalent elastic strain.

The teeth of the bevel gears are set to 1.75 mm. The overall mesh sizes will be varying for the grid dependency test. The rotation of the bevel gears is set with a rotation of 20 degrees each second on the smaller gear and moment of 100 N-mm on the large gear. The simulation is done for 6 seconds.

Figure 1. The Geometric Model of the Meshing Bevel Gears.

Figure 2. The Meshing of the Bevel Gear Model.

Figure 3. The Rotational Arrangement of the Bevel Gear Model

Simulation Results:

The following are the results obtained after performing the simulation.

Total Deformation:

Figure 4. Total deformation(in mm) Result of the Bevel Gear Model

Figure 5. Minimum, Average and Maximum Total deformation(in mm) variation of the Bevel Gear Model

Equivalent Stress (Von-Mises):

Figure 6. Equivalent Stress Result of the Bevel Gear Model

Figure 7. Minimum, Average and Maximum Equivalent Stress variation of the Bevel Gear Model

Equivalent Elastic Strain (Von-Mises):

Figure 8. Equivalent Elastic Strain Result of the Bevel Gear Model

Figure 9. Minimum, Average and Maximum Equivalent Elastic Strain variation of the Bevel Gear Model

Grid Dependency Result:

Here the parameter feature is utilized to compare results with varying mesh sizes. The following table depicts the results obtained with the input parameter: mesh size, 4 mm, 5 mm, 6 mm. The output parameters are set to Total Deformation, Equivalent Stress (Von-Mises), Equivalent Elastic Strain.

Table 1. Total Deformation, Equivalent Stress (Von-Mises), Equivalent Elastic Strain, Safety Factor Variance with Mesh Sizes of 4 mm, 5 mm, 6 mm.

Table 2. (Continued...) Total Deformation, Equivalent Stress (Von-Mises), Equivalent Elastic Strain, Safety Factor Variance with Mesh Sizes of 4 mm, 5 mm, 6 mm.

Conclusion:

From the table, the Total deformation values are consistently similar irrespective of the mesh sizing. The equivalent stress and equivalent elastic strain values decrease when the mesh size decrease from 6 mm to 5 mm. When the mesh becomes finer, i.e., from 5 mm to 4 mm there is no significant change in the values of equivalent Stress and equivalent elastic strain. The minimum safety factor value in all the cases is found to be 15.

Hence, we can say that the values of total deformation, equivalent stress, and equivalent elastic strain are headed to a convergence point. Also, further refinement or making the mesh finer will only increase the computation time and will not lead to a better result.