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

In summary, the conversation discusses a failure analysis of an A356 Aluminum alloy wheel subjected to rotational loading, with a maximum load of 650 kgf and a torque of 4600 Nm. The cracks formed after 1.3*10^6 rotations and the main goal is to determine the regions of maximum stress concentration. A free body diagram is drawn and further calculations are needed to analyze the stress distribution. It is suggested that FEA be used for more accurate results, but simple calculations can still provide insight for design modifications.
  • #1
Gevorg
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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?
upload_2017-11-12_18-42-27.png
 

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  • #2
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.
 
  • #3
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.
 
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  • #4
JRMichler said:
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.
 

1. What is a free body diagram?

A free body diagram is a visual representation of all the forces acting on an object. It helps to simplify complex systems and understand the net force and direction of motion of the object.

2. How do I draw a free body diagram of a rotating wheel?

To draw a free body diagram of a rotating wheel, first identify the object or system you want to analyze. Then, draw the object as a point or a simple shape, and label all the forces acting on it, including weight, normal force, friction, and any other external forces. Finally, draw arrows to represent the magnitude and direction of each force.

3. What are the forces acting on a rotating wheel?

The forces acting on a rotating wheel include its weight, which is directed downwards towards the center of the earth, a normal force from the ground, which is perpendicular to the surface of the wheel, and any frictional forces that may be present due to the contact between the wheel and the ground.

4. How can I determine the direction of rotation in a free body diagram of a rotating wheel?

The direction of rotation in a free body diagram of a rotating wheel can be determined by the direction of the net torque acting on the wheel. If the net torque is clockwise, the wheel will rotate in a clockwise direction, and if the net torque is counterclockwise, the wheel will rotate in a counterclockwise direction.

5. Can I use a free body diagram to calculate the angular acceleration of a rotating wheel?

Yes, a free body diagram can be used to calculate the angular acceleration of a rotating wheel. By summing up the net torque acting on the wheel and using Newton's second law of motion for rotational motion, the angular acceleration can be determined.

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