Week 2 Bevel Gear Challenge

Objective :

To Understand the concept of Grid Dependency test and run the simulation on the bevel gear using three different mesh sizes i.e. 4mm, 5mm and

6mm and solving the simulation cases to evaluate Von-Mises stress, Equivalent elastic strain and Total Deformation on the bevel gear using Ansys

Workbench.

Theory on Grid Dependency Test :

Grid Dependency Test is used to find out how the solution depends on the grid size by running the simulation with refined mesh i.e. finer

the mesh, higher is the accuracy of the result but with additional cost on consumption time and consumption power.

As, solutions are interpolated at the nodes to get an approximate result, higher the no. of nodes and elements higher is the

computational time and power required to complete the simulation.

With the help of Grid Dependency Test, we can determine the optimal mesh size, where accurate results are obtained keeping in the

mind the cost of time and power. The optimal mesh size obtained is neither too coarse nor fine and further refining the mesh would result in

negligible percent change in the result but will increase the computational cost.

SETUP :

1. Static Structural Analysis on Spur Gear is carried out in Ansys Workbench.
2. Select Static Structural analysis from the Analysis System drop down menu.
3. Select the type of material required from the Engineering Data. In this case Structural Steel is used.
   
   
   Fig. 1 : Properties of Structural Steel
   
   
4. Import the given geometry (Bevel Gear Model) and Open the model in SpaceClaim.
   
   Fig. 2 : Importing Geometry and Opening in SpaceClaim
   
   
5. After opening the model in SpaceClaim, edit the model by removing the unwanted extra surface which is not required for the simulation process by cutting down a circle with dia. 47mm for the big gear and another circle with dia. 27mm for the small gear.
   
   Fig. 3 : Model after unnecessary surfaces are removed
   
   
6. Open the model in Design Modeler

   
   
   Fig. 4: Model as observed in Design Modeler

7. Rename the Gears as Big and Small Gears and Assign the material.
   
   

   Fig. 5 : Gears Renamed and Material assigned
   
8. Contacts are established between the small gear and big gear.
   
   1. Contact Type is defined as Frictional.
   2. The mating surfaces of the Gears are selected as Contact and Target. The small gear is selected as Contact Body and big gear is selected as Target body.
   3. Behaviour is defined to as Symmetric.
   4. Formulation Type used in Augmented Lagrange.
   5. Interface Treatment is changed to Adjust to Touch.
      
      
      
      Fig. 6 : Contact establishment between the gears
      
      
   6. After Creating Contacts between the gears, Revolute type Joints are assigned for both the gears having a Body – Ground Connection.
      
      
      Fig. 7 : Revolute Joint For Big Gear
      

      
      

      Fig. 8 : Revolute Joint for Small Gear
      
      ANALYSIS SETTINGS :

      10. The simulation runs for 6 Steps, So the no. of steps is set to as 6.
      11. The 6 Steps that are created are selected and hence we get the Current Step Number as Multi Step.
      12. Due to convergence issues, change the Auto Time Stepping to Program controlled.
      
      
      
      Fig. 9 : Analysis Setup for the Bevel gear simulation
      
      13. After Setting up the Analysis Setting, Joint loads are given to the gears. Small Gear is given a Revolution Join Load for six-time steps and Large Gear is given a constant Moment Joint Load.
      
      
      
      Fig. 10 : Joint Moment Load for Big Gear
      
      
      
      Fig. 11 : Joint Revolution Load for Small Gear
      
      14. Make sure that the gears are rotating in opposite direction. If the gears are found to be rotating in the same direction, change the direction of rotation of either one of the gears by changing the Reference Coordinate System.
      
      MESH :
      
      15. After the Analysis Setup is done, Generate a Mesh using the default conditions. We can observe that the mesh generated is coarse and needs refinement as it will result in convergence issues.
      
      16. To prevent the mesh from being too coarse, we use mesh face sizing. Right click in Mesh, select Insert and click on Sizing.
      
      
      
      Fig. 14 : Mesh Face Sizing
      
      17. Select the faces of the gear that come in contact. A Total of 40 faces is observed. Keep the face sizing element size as 1.75mm.
      
      
      
      Fig. 15 : Mesh Setup
      
      18. The Mesh generated using Face Sizing is observed to be much better than the previously generated Mesh.
      
      
      
      Fig. 16 : Mesh developed using face sizing feature
      
      RESULTS :
      
      Case - 1: For element size - 4mm and Facing size - 1.75mm
      
      
      Fig. 17 : Element Size 6mm mesh statistics
      
      a. Equivalent Stress (Von-Mises stress) :
      
      
      
      
      Fig. 18 : Equivalent Stress
      
      b. Equivalent Strain (Equivalent elastic strain) :
      
      
      
      Fig. 19 : Equivalent Strain
      
      c. Total Deformation :
      
      
      Fig. 20 : Total Deformation
      
      Case - 2: For element size - 5mm and Facing size - 1.75mm
      
      
      
      Fig. 21 : Element Size 5mm mesh statistics
      
      a. Equivalent Stress (Von-Mises stress) :
      Fig. 22 : Equivalent Stress
      
      b. Equivalent Strain (Equivalent elastic strain) :
      
      
      Fig. 23 : Equivalent Strain
      
      c. Total Deformation :
      
      
      Fig. 24 : Total Deformation
      
      Case - 3: For element size - 6mm and Facing size - 1.75mm
      
      
      
      Fig. 25 : Element Size 4mm mesh statistics
      
      a. Equivalent Stress (Von-Mises stress) :
      
      Fig. 26 : Equivalent Stress
   7. 
      b. Equivalent Strain (Equivalent elastic strain) :
      
      
      Fig. 27 : Equivalent Strain
      
      c. Total Deformation :
      
      
      Fig. 28 : Total Deformation
      
      RESULT COMPARISON :
      
      

      Mesh Size	Min. Equivalent Stress ( MPa )	Max. Equivalent Stress ( MPa )	Min.Equivalent Strain	Max. Equivalent Strain	Min. Deformation ( mm )	Max. Deformation ( mm )
      6mm	0	0.94	0	5.5361E-6	0.32986	16.516
      5mm	5.9265E-5	21.926	6.5388E-10	0.00011382	23.383	47.83
      4mm	2.0578E-7	19.53	1.0289E-12	0.00012757	23.383	47. 83

      
      Table 1 : Result Comparison
      
      CONCLUSION :
      
      Comparing the results for Equivalent Stress, it is observed that as the mesh size decreased, a finer mesh is generated resulting in a higher no. of elements thereby providing accurate results. From the data available, the optimal results are observed for the mesh size of 4mm having a Equivalent Stress from 2.0578E-7 (min.) to 19.53 (max.).
      
      Comparing the results for Equivalent Strain, as observed from the data, for mesh size 4mm Equivalent strain values are ranging from 1.0289E-12 (min.) to 0.00012757 (max.) which evaluates that finer mesh provides much accurate results of strain.
      
      Comparing the results for Deformation, it is observed that the results obtained are similar for all the three mesh sizes. Hence, from the results we can conclude that Grid Dependency Test doesn't seem to change for all the three mesh sizes.