Week 1 Spur Gear Challenge

OBJECTIVE

To carry out a static structural analysis on the given spur gear pair using ANSYS Workbench. The analysis is to be carried out on 3 cases wherein each case, different materials would be applied to these gears. Through the analysis, the maximum deformation, stress intensity, and stresses formed in the model are to be derived and compared.

Materials to be applied: Cast Iron, Cast Steel and Cast Bronze

IMAGE OF MODEL

PROCEDURE

Preface: After setting up and running the analysis in the first case, all we need to do is change the material and run them again for the next two cases.

IMPORTING THE MODEL AND MATERIAL CREATION

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.

2. Now, we can add the materials right here and make our job easier for later. To do that, we need to double-click Engineering Data'. This opens up the list of inserted materials. We then need to click on the Engineering Data Source tab as shown by the red arrow below then click on the 'click here' to add a new library to ‘create your own material library’ as shown in the red box.

Then, we can type in our new material library name and press enter. There will be a save window that appears where we can enter the .xml file name as shown by the red arrow below, then click on 'Save' to create a new material library in ANSYS.

After doing so, we can go ahead and create new materials within this library. We just need to select the checkbox as shown by the green box below. To create your new material inside this library, click on ‘Click here to add a new material’ as shown in the red box.

Then, it is just a matter of dragging material properties from the left sidebar into the outline section of the material. We shall be adding those that have been specified for this project - for cast bronze and cast steel. The values outlined should be entered.

After that, we simply need to click the yellow '+' symbol on each material's corresponding 'add' column to add these specific materials to the project. In addition to this, we can add 'cast iron', which is already in the ANSYS Granta library in the Engineering Data Sources. Once we are done, we can simply close the tab - the program may ask if you want to save - you can respond in the affirmative.

3. Once we return to the project schematic window, we can right-click geometry and select 'edit'. This will bring the model up in the Mechanical interface.

MESHING THE MODEL

By default, the algorithm would have meshed the model using hexahedrons and the mesh size may not be ideal. To fix this, we simply need to select the mesh and edit the entity in its window on the bottom left. Going to the 'Defaults' section and change the mesh to a preferable size (the finer the mesh, the more accurate the final results - at the cost of time).

As you can see, I went with a mesh size of 1 mm. Make sure adaptive sizing is turned off and smoothing is set to low. After that, we can press 'enter' and then right-click 'Mesh' from the outline and click 'generate'.

SETTING UP AND RUNNING THE ANALYSIS

1. First thing we need to do is set up the contact between the two gears. To do this, we can right-click 'Connections' from the outline > Insert > Manual Contact Region.

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. Care must be taken to only select the flatter surfaces. The peaks and troughs are to be ignored. 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 (left gear) and the same goes for the target body (right gear). For formulation, Augmented Lagrange is selected to reduce vibration and stabilize the simulation.

2. 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.

3. 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 5e-2s and maximum time step being 0.5s.

4. 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 left gear first.

For 'Joint', we shall be selecting the joint contact created for the left gear as shown. The 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 30* on each step. After they're filled in as shown, we can go ahead and create another joint load.

For the right gear, we shall be selecting 'moment' for the type. The magnitude would be defined using tabular data again. The negative moment values are so the gear rotates in the anti-clockwise direction (since the left gear is rotating in a clockwise direction). Care must be taken to ensure the moment values are entered as per the set units.

5. 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 > Stress > Intensity. 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 doing that, at this juncture, it is important to take note of the material applied, and hence the case in which this analysis will be carried out. We can go to the Geometry section in the outline and check the details of both gears:

As we can see, we have cast iron here. Taking note of this, we can evaluate and analyse the results, save the project as a separate case, then come back here and change the material to one of the remaining (cast steel/cast bronze), 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 - CAST IRON

Equivalent Von Mises Stress

Minimum and maximum stress locations and values

Stress Intensity

Minimum and maximum stress intensity locations and values

Deformation

Minimum and maximum deformation locations and values

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CASE 2 - CAST STEEL

Equivalent Von Mises Stress

Minimum and maximum stress locations and values

Stress Intensity

Minimum and maximum stress intensity locations and values

Deformation

Minimum and maximum deformation locations and values

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CASE 3 - CAST BRONZE

Equivalent Von Mises Stress

Minimum and maximum stress locations and values

Stress Intensity

Minimum and maximum stress intensity locations and values

Deformation

Minimum and maximum deformation locations and values

OBSERVATIONS

Tabulation of output values:

As we can see, the stresses generated in the cast steel case is comparably higher than those generated in the other two cases. The locations of the maximum and minimum stresses generated are similar in all cases, probably due to the same conditions of the simulation.

Coming to deformations, again, all three cases have the same values due to the aforementioned reason.

Stress intensity results also showcase the same ordering as that of equivalent stress, with cast steel experiencing a higher maximum stress intensity. It must be noted that cast bronze experiences a slightly higher average stress intensity than cast steel, but the difference is very minute. In fracture mechanics, a stress intensity factor is calculated as a function of applied stress, crack size, and part geometry. Failure occurs once the stress intensity factor exceeds the material's fracture toughness. At this point the crack will grow in a rapid and unstable manner until fracture. 

With that in mind, it is highly likely that cast steel will experience crack development and fractures first. Regarding where it is likely to fracture, when looking at all the stress intensity simulations, we will see that the region of maximum stress intensity is the same in all 3 cases:

It's the base of tooth on the right gear that is undergoing direct impact with the left gear. This is the region that is most likely to fracture first.

RESULT

Structural analysis was carried out on the given spur gear model and the analysis was compared between 3 cases of different materials as requested.

With cast iron having the lowest stress intensity numbers and lower stress generation in general from all the three cases (even though its maximum stress value is slightly higher than that of cast bronze), I would recommend cast iron. Due to these low numbers, cast iron gears would have a longer life compared to the other two.