Fatigue Analysis of a Wheel Rim

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Fatigue Analysis of a Wheel Rim

During the development of safety critical components like a car wheel rim, making sure fatigue cracks do not occur is one of the most important tasks. When a final prototype is available this is ensured by testing, but prototype production and testing are time consuming and expensive activities. Good predictions from simulations can keep down the number the number of prototypes to a minimum.

In this example, you do a fatigue evaluation on a model of a wheel rim, subjected to the load history from a simulated test.

Model Definition

For a definition of geometry, loads and boundary conditions, see the documentation for the model Submodel in a Wheel Rim in the Structural Mechanics Module Application Library.

The fatigue limit (in terms if the stress amplitude) is known for two cases with pure axial loading. For pure tension it is 95 MPa, and for fully reversed loading it is 125 MPa. In this model, you use the Findley criterion, so the Findley parameters have to be derived from these data.

In pure tension, the Findley criterion can be written as

This means that you have to solve the simultaneous equations

to get the Findley parameters f and k. The result is f = 84 MPa and k = 0.30.

Results and Discussion

The fatigue usage factor distribution is shown in Figure 1. The maximum value is about 0.67, which should indicate that the design is good when taking into account that the required safety factor has been included in the load. In Figure 2 the stress histories in the critical point are displayed. The loading is slightly nonproportional, and has a compressive mean stress, which is captured by the Findley criterion.

Figure 1: Fatigue usage factor using the Findley criterion.

Figure 2: Stress histories in the critical point.

Notes About the COMSOL Implementation

In this example, you perform the fatigue analysis as an additional study step in a model which already contains the results from a stress analysis. Since the critical points for fatigue crack initiation is on the free surface of the body, it is sufficient to do the fatigue evaluation on the boundary, and not in the domain. This reduces CPU and memory requirements significantly.

Fatigue_Module/Stress_Based/rim_fatigue

Modeling Instructions

In this example you will start from an existing model which is an example in the Structural Mechanics Module.

1

From the menu, choose .

2

From the Application Libraries root, browse to the folder Structural_Mechanics_Module/Tutorials and double-click the file rim_submodel.mph.

Stress in Submodel

If the model was stored without solutions, you will now have to run and before continuing.

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In the toolbar, click

to open the window.

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Go to the window.

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In the tree, select .

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Find the subsection. In the table, clear the check boxes for and .

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Click in the window toolbar.

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In the toolbar, click

to close the window.

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Right-click and choose the boundary evaluation .

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Select Boundaries 2–5 only.

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In the window for , locate the section.

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From the list, choose .

Material 3 (mat3)

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In the window, expand the node.

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Right-click and choose .

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In the window for , locate the section.

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From the list, choose .

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From the list, choose .

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Locate the section. In the table, enter the following settings:


Property	Variable	Value	Unit	Property group
Normal stress sensitivity coefficient	k_Findley	0.30	1	Findley
Limit factor	f_Findley	84[MPa]	Pa	Findley

1

In the toolbar, click

to open the window.

2

Go to the window.

3

Find the subsection. In the table, clear the check boxes for and .

4

Find the subsection. In the tree, select .

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Click in the window toolbar.

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In the toolbar, click

to close the window.

Step 1: Fatigue

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In the window for , locate the section.

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Find the subsection. From the list, choose .

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From the list, choose .

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From the list, choose .

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In the toolbar, click

.

Max/Min Surface 1

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In the toolbar, click

and choose .

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In the window for , locate the section.

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In the text field, type ftg.fus.

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Click to expand the section. Locate the section. From the list, choose .

5

Locate the section. In the text field, type 2.

The maximum value of fatigue usage factor may be outside the expected area because a singularity can be present on the edge of the boundary where the fixed constraint is applied. Add a selection to ensure to display the maximum value of the surface of interest.

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In the toolbar, click

.

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Select Boundary 5 only.

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In the toolbar, click

.

Fatigue Usage Factor (ftg)

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In the window, click .

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In the window for , locate the section.

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From the list, choose .

In order to get the location of the point with maximum fatigue usage, zoom in on the maximum marker and click on it in the graphics window. You will then see the value and the coordinates in the Table window. The location will be approximately (0.016, 0.092, 0.088). Use these coordinates to create a Cut Point 3D dataset for detailed evaluation of the stress history in the critical point.

1

In the toolbar, click

.

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In the window for , locate the section.

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From the list, choose .

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Locate the section. In the text field, type 0.0164.

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In the text field, type 0.0924.

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In the text field, type 0.0884.

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Select the check box.

1D Plot Group 5

In the toolbar, click

.

1

Right-click and choose .

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In the window for , locate the section.

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From the list, choose .

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Click in the upper-right corner of the section. From the menu, choose .

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Locate the section. From the list, choose .

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Click to expand the section. Find the subsection. From the list, choose .

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Locate the section. From the list, choose .

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Locate the section. In the text field, type 3.

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Click to expand the section. Select the check box.

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From the list, choose .

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In the table, enter the following settings:


Legends
sx

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Right-click and choose .

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In the window for , locate the section.

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In the text field, type solid2.sy.

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Locate the section. In the table, enter the following settings:


Legends
sy

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Right-click and choose .

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In the window for , locate the section.

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In the text field, type solid2.sz.

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Locate the section. In the table, enter the following settings:


Legends
sz

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Right-click and choose .

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In the window for , locate the section.

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In the text field, type solid2.sxy.

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Locate the section. In the table, enter the following settings:


Legends
sxy

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Right-click and choose .

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In the window for , locate the section.

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In the text field, type solid2.syz.

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Locate the section. In the table, enter the following settings:


Legends
syz

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Right-click and choose .

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In the window for , locate the section.

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In the text field, type solid2.sxz.

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Locate the section. In the table, enter the following settings:


Legends
sxz

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In the window, under click .

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In the window for , type Stress History in the text field.

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Click to expand the section. From the list, choose .

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In the text area, type Stress history in critical point.

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In the toolbar, click

.