Contact mechanics, elastic bedding

[ladil123]

Contact mechanics, "elastic bedding"

Hello!

I need some help regarding my problem.
I have a solid shaft with a mounted ring on it. The has a higher E-modulus than the shaft.
A force F is acting downwards on the ring. As seen in the picture. The force could be assumed to be a point load if its easier than a even distributed one?

I want to calculate the circumferencial and radial stress that is acting in the ring due to the applied force and the fact that the shaft is either made of steel or cast iron which is softer than steel.
I want to make a pretty easy calculation of this, but I want the different lenghts to have an influence on the stress.

I have heard something about "elastic bedding" that takes the fact that the material beneth the ring is softer than the ring, but some contact mechanics could maybe do the trick?
I´ll need some help starting with this.

Thanks
Daniel

 

[Achy47]

Hello Daniel,

As a scientist who specializes in contact mechanics, I can offer some guidance on your problem. Firstly, you are correct in considering the difference in E-modulus between the ring and the shaft. This will have a significant impact on the stress distribution in the ring.

To start, I would recommend using the Hertzian contact theory to calculate the stresses in the ring. This theory takes into account the elastic properties of both materials and the geometry of the contact area. It is commonly used in contact mechanics to analyze the stresses in a contact interface.

Additionally, you can consider using the concept of "elastic bedding" to further refine your calculations. This refers to the deformation of the softer material (in this case, the shaft) under the applied load, which can affect the stress distribution in the ring. By taking into account the elastic properties of both materials and the geometry of the contact, you can use this concept to make a more accurate calculation of the stresses in the ring.

I would recommend consulting a textbook or online resources on Hertzian contact theory and elastic bedding to get a better understanding of the calculations involved. You may also want to consider using a finite element analysis software to model the problem and obtain more precise results.

I hope this helps you get started on your calculations. Good luck!


- Scientist in Contact Mechanics