# How can I draw a free body diagram of a rotating wheel?

Gevorg
I am currently performing failure analysis on an A356 Aluminum alloy wheel subjected to rotational loading, with a maximum load of 650 kgf and a torque of 4600 Nm. Cracks formed in the wheel after 1.3*10^6 rotations.

My job is to perform a stress analysis to determine the regions of maximum stress concentration under such loading conditions. I figured it is first necessary to draw a free body diagram of the entire wheel and then apply the method of sections, in which I would make cuts along specific regions of the wheel and determine the forces acting on them.

Below I've drawn a free body diagram of the wheel. The sum of the forces acting on the 5 holes should equal 650 kgf. The up pointing arrow is equal in magnitude to their sum. The applied torque, shown in blue, should be equal in magnitude to the torque generated by the left pointing force of friction in order for the wheel to rotate at a constant angular velocity.

I still feel that something is missing and can't quite put my finger on it. Could someone provide some insight?

#### Attachments

35.6 KB · Views: 1,898

Your diagram looks good for a metal wheel running on a hard (steel or concrete) surface. The moment could be applied as five forces on the bolt holes, each force in a circumferential direction. If that wheel has a pneumatic tire on it, the vertical and tangential forces are applied around the rim.

After further thought, the cracks tell you the location(s) of the maximum fatigue stresses. And the total number of load cycles until cracks appear tells you the magnitude of the stresses.

If this wheel is on a motor vehicle, then the maximum stresses may come from cornering forces. That would require a completely different free body diagram.

The complexity of the wheel make hand calculations difficult, and of questionable accuracy. This problem is best solved using FEA. It does not need a high end FEA package, the SolidWorks Premium package will easily handle this job.

Gevorg
Gevorg
After further thought, the cracks tell you the location(s) of the maximum fatigue stresses. And the total number of load cycles until cracks appear tells you the magnitude of the stresses.

If this wheel is on a motor vehicle, then the maximum stresses may come from cornering forces. That would require a completely different free body diagram.

The complexity of the wheel make hand calculations difficult, and of questionable accuracy. This problem is best solved using FEA. It does not need a high end FEA package, the SolidWorks Premium package will easily handle this job.

You are right, JRMichler; cracks form at the locations of maximum stress. To the best of my knowledge, the wheel was not subject to cornering forces. I unfortunately don't have any background in FEA; however, simple calculations should be enough to prove that stress concentrations occur where the cracks formed and allow me to suggest design modifications.