Bevel Gear: Grid Dependency Test
GRID DEPENDENCY TEST
As per the different sources studied, it is also either said as grid independence or mesh convergence. As the word ‘grid’ looks similar to the word ‘mesh’ which means that to discretize the continuous system but it could be varied from coarser to finer mesh. Based on this mesh, the solutions are evaluated at nodes and rest are interpolated which adds up-to approximation. This approximation can be reduced to some extent through finer mesh (i.e., more element and node count) but it costs computational time to us. Thus, the accuracy of the results gets improved through finer mesh.
Grid dependency test helps to determine the optimum mesh size where more accurate solution for the problem is obtained keeping in mind the computational time as well. Basically, it provides us answer to question i.e., How mesh is good enough for accurate results? Evaluate solution’s percentage difference for successive mesh based on variation of mesh size (finer) in and around the concern region, till negligible percent change is observed. This is point at which we obtain optimum mesh, beyond this (finer mesh) there is not much change observed irrespective of more computational time required for obtaining solution.
OBJECTIVE
The objective of this project is to perform grid dependency test for bevel gear simulation for different mesh sizes, i.e., 6, 5, and 4 mm. Evaluate and comment on their von-mises stress, equivalent elastic strain, and total deformation.
CAD geometry considered for simulation (front and side view shown below):
The nomenclature considered for ease in identification of two bevel gears based on their size, i.e. one on the left side is named as ‘SMALL and vice-verse.
Material and their respective properties considered for simulation (tabulated below):
As here static structural analysis is being performed, density is not required for setting up the simulation.
For all the cases (based on mesh size), the same pre-processing steps has been followed as stated below but different mesh size considered, i.e. 6, 5, and 4 mm in global mesh settings.
Contacts were setup between two bevel gears having 16 faces on ‘SMALL’ and 24 faces on ‘BIG’ (shown below in figure) bevel gear which would be interacting at interface based on touch. Frictionless contact has been defined, i.e., frictional with frictional coefficient ‘ZERO’.
Revolute joints were setup based on connection type ‘body-ground’ for each gear. ‘SMALL’ bevel gear is given the rotation of 120 degree in 6 steps, i.e. increment of 20 degree at ‘SMALL’ joint. While ‘BIG’ bevel gear is provided with constant moment of 100 N.mm in opposite direction at ‘BIG’ joint. The specification of respective gear has been shown below in figure.
Meshing of bevel gears were carried out using tetrahedral element shown below. As the simulation was carried out in academic version, the overall count for elements/nodes were always kept below 32,000 by adjusting the element size (fine upto maximum extent).
The concerned regions, i.e., contact faces are provided with local mesh setting of 1.75 mm as face sizing (40 faces). The element size considered and count for nodes/elements have been tabulated below which is same for all the cases.
Analysis Settings for successful simulation run:
Initial Time Step – 0.10
Min. Time Step – 0.05
Max. Time Step – 0.20
Von-Mises Results for all cases (i.e., 6, 5, and 4 mm)
Total Deformation Results for all cases (i.e., 6, 5, and 4 mm)
Equivalent Strain Results for all cases (i.e., 6, 5, and 4 mm)
Based on Global Mesh Setting,
Case 1: 6 mm Vs. Case 2: 5 mm Vs. Case 3: 4 mm
The comparison table for all cases w.r.t. von-mises, eq. strain, and stress intensity and their respective percentage change has been shown below:
Grid dependency test has been performed on the bevel gear simulation by varying global mesh setting from 6 mm to 4 mm element size with the increment of 1 mm.
Grid dependency test has been performed on the bevel gear simulation by varying global mesh setting from 6 mm to 4 mm element size with the increment of 1 mm. Based on the results as shown above with their respective percentage change (i.e., from 6 mm to 5 mm and 5 mm to 4 mm) states that as the mesh size is reduced in region having coarser mesh effects the accuracy of the results which can be seen through the percentage change. As the mesh is refined to 4 mm, it can be observed that percentage change has been reduced to quite an extent, which states that the results are much accurate than previous coarser mesh. If we reduce the mesh size beyond this, the percentage change may reduce by the factor of 0.1, but would cost the computational time.
Thus, we could say that optimum mesh size (global) in non-critical region is 4 mm. If finer mesh is considered, then there wouldn't be much effect on the result but computational time would rise quite a much.