Week 2 Bevel Gear Challenge

Grid dependency test: It is a type of parametric study of a finite element model where the variation of the analysis results is observed with respect to changing mesh refinement (i.e. reducing mesh element sizes). In other words, the dependency of the FE analysis on the mesh applied is studied. At the point where the FE results stop depending on the mesh element size, mesh convergence is observed. After mesh convergence, the analysis results no longer depend (or change very negligibly) on the decreasing mesh element size i.e. the FE model becomes grid independent. Mesh convergence has several uses. It can be used to accurately predict the actual solution to the FE problem, as the result approaches it as the number of nodes increase in the model. It can be also used as a tool to identify the appropriate mesh size. Once mesh convergence is reached, further refinement of mesh is of no use as the computation power required and the computation time increase significantly for a very insignificant and often negligible change in the results. Thus, the mesh size at which mesh convergence is achieved is often the correct mesh size to use.

Model parameters for the bevel gears:
Material used for the gears: Structural steel
Mesh properties:
Element type: Tetrahedral, order controlled by the program
Element Size: Varying (6mm,5mm,4mm)
Face sizing applied at the tooth face of both the gears as they are the critical regions in contact with each other
Element size in face sized mesh: 1.75 mm (constant for all cases)
Smoothing: Low
Contact Properties:
Type: Frictional
Behaviour: Symmetric
Formulation: Augmented Lagrange
Interface Treatment: Adjust to touch
Joints: Body to ground revolute joints for each gear
Joint Loads:
Moment to the larger gear (driving gear) = 100 N-mm
Rotational motion of the smaller gear (driven gear) = 0-120 degrees angular displacement in 6 load steps
Analysis settings:
Initial time step= 0.05 seconds
Minimum time step = 0.001 seconds
Maximum time step = 0.1 seconds
Large deflections = ON

Mesh refinement of the bevel gear FE model is carried out by reducing the global mesh element size (the face sized mesh element size of 1.75mm remains constant) from 6mm to 4mm. In the parametric study in ANSYS, the input parameter is the mesh global element size, with the output parameters being the minimum, maximum and average total deformation, equivalent elastic strain, equivalent von mises stress. Note that all these results will be for the last timestamp of the simulation i.e. at t=6s, thus the maximum von mises stress over time (over the 6 loadsteps) is also parametrized. For the grid dependency test, the maximum von mises stress, the maximum equivalent strain and the maximum total deformation are compared with respect to the changing mesh element size (6mm,5mm,4mm).

Mesh global element size = 6mm

Joint Load

Von Mises Stress distribution

Maximum Von Mises stress distribution wrt loadsteps and substeps

Maximum Von Mises stress over the whole simulation (=3.7966 MPa) occurs in the 3rd load step at t=3.75 seconds.

Total deformation

Maximum total deformation distribution wrt loadsteps and substeps

The green curve represents the maximum total deformation values, the blue curve represents the average total deformation values and the red curve represents the minimum total deformation values.
Maximum total deformation of 47.873 mm over the whole simulation occurs at the end of the last loadstep at t = 6 seconds

Equivalent elastic strain distribution

Maximum equivalent elastic strain distribution wrt loadsteps and substeps

Maximum equivalent elastic strain over the entire simulation (=2.3842 e-5) occurs in the 3rd loadstep at t = 3.75 seconds.

Below is the animation of the simulation carried out for mesh size = 6mm

https://drive.google.com/file/d/1-zKC1RtNLh-1V9RocQSuFJBA3L2S4-ld/view?usp=sharing

Parametric study:
1^st design point (DP0): Mesh global element size = 6mm
2^nd design point (DP1): Mesh global element size = 5mm
3^rd design point (DP2): Mesh global element size = 4mm

Input and output parameters:

Results:
Maximum von mises stress for DP0 = 3.7966 MPa
Maximum von mises stress for DP1 = 5.5369 MPa
Maximum von mises stress for DP2 = 4.8329 MPa

Maximum equivalent elastic strain for DP0 = 2.3077 e-05 mm/mm
Maximum equivalent elastic strain for DP1 = 2.9564 e-05 mm/mm
Maximum equivalent elastic strain for DP2 = 2.6902 e-05 mm/mm

Average total deformation for DP0 = 37.646 mm
Average total deformation for DP1 = 37.463 mm
Average total deformation for DP2 = 37.121 mm

As can be seen, the results of the FE model are quite sensitive to the mesh global element size, especially for the case of the von mises stress, where we observe significant difference in the obtained values for varying mesh sizes. Both the maximum von mises stress and the maximum elastic strain show a simiar kind of variation for the varying mesh element sizes. The average total deformation also varies significantly but the maximum total deformation values are same for all mesh sizes.

NOTE: The equivalent elastic strain values obtained in the parametric study are the maximum strain values at the last load step (t=6s), while the stress and total deformation values are the global maximum values for the whole simulation over all the loadsteps.