Week 2 Bevel Gear Challenge

OBJECTIVE

To run an analysis on a bevel gear pair and solve for von mises equivalent stress, equivalent elastic strain and total deformation. In addition to that, to also perform a grid dependency test for mesh sizes 6mm, 5mm and 4mm.

WHAT IS GRID DEPENDENCY?

Finite element preprocessors have come a long way over the years—to the point where users with minimal training can create meshes that appear good enough based on their element density and distribution. Balance is essential. The mesh must be complete enough to provide an accurate solution, without being so large that it takes too long to run.

The graph plateaus and approaches the actual result the more we refine the mesh as shown

The grid dependence test is a process used to find the optimal grid condition that has the smallest number of grids without generating a difference in the numerical results based on the evaluation of various grid conditions. This test incorporates the most basic and accurate way to evaluate mesh quality, which is to refine the mesh until a critical result such as the maximum stress in a specific location converges: meaning that it doesn’t change significantly as the mesh is refined. 

With this concept in mind, we shall carry out this analysis to see which mesh size would be 'good enough' to provide an accurate enough result, without compromising on computational time. The mesh sizes to be used are 6mm, 5mm and 4mm.

MODEL IMAGE

PROCEDURE

This challenge has 3 cases but we only need to follow a single general procedure and alter the mesh size in the end (before initiating the analysis). The procedure is as follows:

1. After opening ANSYS Workbench, we are met with the Project Schematic window. Here, we can select the 'System Structural' analysis system on the left. Doing so creates a new project. Here, we can rename the project and also change the material if needed. We will need to right-click 'Geometry' and select 'import'. The STP file provided for this project should be selected. 

Since the material is to be structural steel (which is the default), we needn't worry about applying any for this challenge.

2. The model requires editing and this is done by right-clicking 'Geometry' and clicking 'Edit Geometry in SpaceClaim'. With SpaceClaim open, we need to work on each of the gear faces. To do that, we simply need to click on them and select the tool that needs to be used. In this case, we will be requiring a larger hole in both gears. We are to create a circle of 45mm on the large gear face and 25mm on the small gear's face.

After that, using the pull tool, they are pulled towards the other side of the gear to create the hole.

We can then close SpaceClaim and right-click 'Model' and select 'edit'. This will bring the model up in the Mechanical interface.

3. To avoid confusion, we can rename the gears in the geometry section of the outline. Then we can right-click 'Contacts' under Connections and select 'Rename based on definition', so the contacts will be named according to the updated gear names.

The type of contact is to be defined as Frictional. For contact bodies and target bodies, we need to select the faces on either side of each tooth on each gear as shown. The other options are selected as shown in the below screenshot. After the selection of surfaces for each entity, please click apply.

The contact body would be the body on which the contact faces exist (small gear) and the same goes for the target body (large gear). For formulation, Augmented Lagrange is selected to reduce vibration and stabilize the simulation.

4. The next step is to add revolute joint properties to each of the gears. The following procedure will therefore be repeated for each gear. Right-clicking the Contact entity again, we can then go to Insert > Joint.

The type is going to be revolute and the connection type will be body-ground. For 'body', we shall be selecting the inner face(s) of the gear as shown. As stated before, this same process is followed for the other gear as well. Therefore, there will be two joints.

5. Next, we shall define the analysis settings. For that, we go to Static Structural > Analyses Settings. We shall be editing this entity in the window on the bottom left as shown. The number of steps will be 6 and after that, we will be selecting all the steps in the graph window by ctrl+clicking each manually.

THEN, we can work on the other options. They are edited as per the above screenshot, with the initial time step being 0.2s, minimum time step being 0.1s and maximum time step being 1s.

6. Now, we need to right-click static structural > Insert > Joint Load. This process will be carried out for each gear with some differences. In this case, we shall be working on the large gear first.

For the large gear, we shall be selecting 'moment' for the type. The magnitude would be defined using tabular data again. The values may need to be positively or negatively assigned and this would depend on the axis direction when defining the joint. This is because either of them will decide the direction of rotation. Care must be taken to ensure the moment values are entered as per the set units.

For the small gear, the joint type would be 'rotation' and the magnitude would be defined using tabular data, at which point ANSYS will let us define values using a table with the other variable being the time step. The values will increase by 20* on each step.

7. Now we can generate the outputs. To do this, we can right-click Solution > Insert > Deformation > Total (for maximum deformation), right-click Solution > Insert > Stress > Equivalent (Von-Mises) (for stress) and finally, right-click Solution > Insert > Strain> Equivalent (Von Mises) (for strain). This creates three new entries in the tree below 'Solution'.

Now, all we need to do is right-click solution again and click 'Evaluate all results'. But before that, it is here we define the mesh. To provide better results on the teeth, we can selectively refine the mesh in those regions using the 'sizing' option (right-click Mesh in outline > insert > sizing). The teeth are selected as shown and a mesh size of 2mm is assigned.

After this, we can go back to 'mesh' in the outline and edit the entity in its window on the bottom left. Going to the 'Defaults' section, here we can change the mesh size to 6mm. The idea is to evaluate and analyse the results, save the project as a separate case, then come back here and change the mesh size to one of the remaining sizes (5mm/4mm), run the analysis and repeat the process again. This way, we will have 3 project files for the 3 different cases.

Finally, when the analysis is done, we can view the results by simply clicking each of these solution entities we created, in the Outline menu.

OUTPUTS

Case 1: 6mm Mesh

Equivalent Von-Mises Stress

Maximum & Minimum

Equivalent Von-Mises Strain

Maximum & Minimum

Total Deformation

Maximum & Minimum

Case 2: 5mm Mesh

Equivalent Von-Mises Stress

Maximum & Minimum

Equivalent Von-Mises Strain

Maximum & Minimum

Total Deformation

Maximum & Minimum

Case 3: 4mm Mesh

Equivalent Von-Mises Stress

Maximum & Minimum

Equivalent Von-Mises Strain

Maximum & Minimum

Total Deformation

Maximum & Minimum

OBSERVATIONS

Tabulation of output values:

As part of the grid dependency test, the numbers to look out for are the maximum stress values. As we can see, the maximum stress value increases with an increase in mesh density (decrease in mesh size). Even though the maximum stress is almost similar in cases 2 & 3, it is safe to assume that these cases have optimal meshes, with refined meshes not changing these values drastically (as it does between cases 1 & 2).

The deformation values do not change at all, barring the average values, which do have a linear decrease as the mesh size decreased in each case. The maximum strain values jumped between 1.6e-05 and 1.4e-05. If we were to consider these results as well, there is no conclusion that the mesh was at optimal refinement. So, to be sure, it's best to further refine the mesh so as to obtain results that would favour grid independence.

Again, if the stress values are to be solely considered, I believe the mesh size is optimal at 4mm since the stress values seem to plateau at that point.

RESULTS

Static structural analysis was carried out on the given pair of bevel gears with the required outputs of Von-Mises stress, Equivalent elastic strain and Total Deformation being generated. In addition to that, a gear dependency test was carried out through different mesh sizes of 6mm, 5mm and 4mm to find out the optimal mesh size that is both time-saving and as accurate as possible.

It was established that further mesh refinement may be required to be absolutely sure that gear independence has been achieved. But going by the stress values alone, it did seem like the maximum stress values plateaued between mesh sizes 5mm and 4mm, suggesting that those sizes may be more than enough to ensure an optimal mesh.