Week 2 Bevel Gear Challenge

Objective 1: To define grid independency.

Objective 2: To perform grid independency check on a Bevel gear working for three meshes with element size 4, 5 and 6 mm.

Objective 3: To plot total deformation, equivalent (von-mises ) strains and elastic strains for above three cases.

Solution 1:

The solution of a simulation varies with mesh or grid density. The denser grid leads to better resolution as solution is approximated with shape functions by more nearer nodal points. Otherwise, approximation far from nodal point will be different from true solution.

The grip independency of a solution reaches when solution converges upto an order and said to be grid independent. In other words, even for finer mesh, solution doesn’t change upto a certain order. This order depends upon desired accuracy of the solution.

Grid independency check is required to get most accurate solution upto the desired order with minimal required computatioinal efforts.

Solution 2 :

For the given cases, simulation of bevel gear working with meshes of 4,5 and 6 mm, a grid independency check is performed.

The max. and min. total deformations(47.877 and 21.651mm) are exactly same for all three meshes. This verifies the grid indpendcty of the solution for mesh element size lesser then 6mm as shown in figure 1 and table 1.

Bevel Gear	4mm	5mm	6mm
Max total deformation	47.877	47.877	47.877
Min total deformation	21.651	21.651	21.651
Max eq. stress	1.4034	1.2597	1.4021
Min eq. stress	2.11E-08	2.33E-08	2.36E-08
Max. elastic strain	9.00E-06	9.01E-06	9.38E-06
Min. elastic strain	1.51E-13	1.61E-13	1.20E-13

Table 1 : Grid independency check for meshes with 4,5 and 6 mm

The equivalent (von-mises) stresses and elastic strains are also converged upto order of zero as shown in figure 2 and table1. Hence grid independency can be stated.

Figure 1 Variation of max and min total deformation for the three meshes

Figure 2 Variations of equivalent stresses and elastic strain for three meshes

Solution 3 :

The total deformations for three cases are as follows. The defomation is highest at the tooth faces. From tooth faces it is gradually decreasing upto the base of the gear. The larger gear has more deformation compared to smaller gear.

Mesh element size : 4 mm
Mesh element size : 5 mm
Mesh element size : 6 mm

The equivalent (von-mises) stresses for three cases are as follows :

Mesh element size : 4 mm
Mesh element size : 5 mm
Mesh element size : 6 mm

The eauivalent elastic strains for three cases are as follows :

Mesh element size : 4 mm
Mesh element size : 5 mm
Mesh element size : 6 mm