Week 1 Spur Gear Challenge
Objective:
The aim of the challenge isto perform the simulation to know the total deformation and equivalent stresses and strains in the spur gear pair provided.
Case setup and execution:
Case 1:
First the "Static structural" module was opened in Ansys Workbench. In the "Engineering data", "Egineering data sources" tab was opened to select the material. Cast iron was added to the material library.
Then the geometrical model was imported. Then the "model" was opened. In the "Ansys Mechanical", first both the spur gears were assigned Cast iron as the material, by selecting them individually from the geometry tab in model tree.
Then the contact between the two gears was defined by selecting the faces of the teeth of the gears. The contact was made "frictional", the behaviour was "symmetric", the "Augmented Lagrange" formulation was used and the for the interface "adjust to touch" option was used.
Then the both the gears were provided with the revolute joint. In the Connections, joint-revolute was inserted and "body-to-ground" connection was specified. The inner faces of the gears were selected to define the respective joints.
Then the model was meshed using the element size of 1 mm.
In the analysis settings, the number of load steps was chosen as 6. The auto stepping was turned on. The substeps were defined using time. THe initial timestep was input as 0.2 sec., the minimum timestep was 0.05 sec. and maximum timestep was 1 sec.
The "large deflection" option was turned on.
Then by right clicking on "analysis settings", "joint-load" was inserted. Using this, one gear was provided the rotation about local z-axis. The rotation was provided in tabular form. It was 0 degrees at 0 seconds and increased by 30 degrees in each load step upto 180 degrees.
The other gear was provided the moment of -10 N-mm about the local z-axis using the joint-load option. It was ensured that the rotations of the two gears are in opposite directions.
The the "Solution" tab was right clicked to insert the desired outputs of total deormation, equivalent elastic strain and equivalent von mises stress.
Then the model was run using the solve button.
However the model failed to converge due to some elements getting highly distorted. To rectify this, the moment was provided in N-m instead of N-mm, by changing the units.
This time also, the model failed to converge. Hence, in the analysis settings, for the 1st load step, the initial timestep was changed to 0.001 sec and the minimum timestep was changed to 5e-05 sec.
For rest of the load steps, the "carry-over time step" was turned on and the minimum timestep was changed to 5e-05 sec.
For each loadstep, maximum timestep was kept at 1 sec.
Then the model was run. This time it ran smoothly and converged. The results are explained below.
Case 2:
For Case 2 the material was to be "Cast steel". As the material was not available in the "Engineering data sources", the material was created by using the data provided in the question.
The gears were assigned the "Cast steel" material. Rest of the setup was similar to case 1.
The model was run. The results are explained below.
Case 3:
For Case 2 the material was to be "Cast bronze". As the material was not available in the "Engineering data sources", the material was created by using the data provided in the question.
The gears were assigned the "Cast bronze" material. Rest of the setup was similar to case 1.
The model was run. The results are explained below.
Results:
Case 1:
Equivalent stress
Equivalent strain:
Total deformation:
Case 2:
Equivalent stress:
Equivalent strain:
Total deformation
Case 3:
Equivalent stress
Equivalent strain
Total deformation
The results are presented below in a tabular format
| Case | Material | Max. Total deformation | Max. Equivalent stress | Max. Equivalent strain |
| Case 1 | Cast iron | 29.996 mm | 352.96 MPa | 0.00401 |
| Case 2 | Cast steel | 29.996 mm | 350.18 MPa | 0.00175 |
| Case 3 | Cast bronze | 29.997 mm | 353.68 MPa | 0.0045 |
It is clear from the abopve tabole, that the strain and stress values are lowest in Case 2, which used Cast steel as material. This is because the cast steel has a higher Young's modulus, almost 2.5 times of both the cast iron and cast bronze, as can be seen from below image:
Also the strain and stress values are higher in Case 3 involving cast bronze, which has lower Young's modulus (80 GPa) than the Cast iron (89 GPa).
Stress intensity:
Stress intensity is the modification in the local stress values in the vicinity of a crack or a notch, which increases the probability of the failure of the specimen at that particular location. It is measured using the stress intensity factor (SIF), which indicates the extent to which local stress is modified due to presence of a crack or a notch.
In the present challenge, the location of the maximum stress, at the base of the teeth of the gear, is the most prone to developing a crack due to the bending stresses developed because of action of the teeth of the other gear. At this location, the stress intensity would be maximum. Hence this location would be a possible location for fracture.
Conclusion:
Thus, the stress and strain values, stress intensity and the possibility of fracture are lowest in case 2, involving the Cast steel material. Hence the Cast steel would be the preferred material.