Meshing concentration for Contact stress study between two solids
 

I'm studying the stress and the deformation at the contact area for the following bodies.

The Ring under bearing load, moment and velocity from the shaft connected to it throw its hole. (Check attachment)

In order to refine the mesh for the contact area, do I have to refine it along the entire circumference since it's rotating (red color)?
Or refining only the contact area (marked with yellow)?

Only contact area. You can hand calc width of contact surface (Hertz Formula) and select element size as 1/10 or 1/20 of contact area width, for beginning, then you should refine mesh further until contact pressure stop changing.

Thank you.


One more question regarding the Hertz Formula.
I've found the attached formula to calculate the stress and the width for solid cylinder against a plane. However, my case as you saw is a hollow ring and the bearing load is against the inner surface.
Would be fine to calculate (outer radius - inner radius) and move on or there is different equation for hollow cylinder?

I don’t know formula for hollow cylinder.
If you want to make everything fine then you can start with simple test problem. Elastic brick vs elastic solid cylinder. This problem can be reduced into 2D. Refine mesh until you get results close to the formula. Now you are sure that you do everything right.
Then move to your problem with hollow cylinder and use mesh size from previous case for beginning. Remesh model if needed. Although the exact solution is unknown (I`m not sure that analytical formula for your cylinder exist) you verify your numerical approach with simple test problem. Right approach guarantees good results.
That’s how engineering FEA works. There are no formula for gearbox housing or turbine blade but you can make simple test problem like plate with hole and extrapolate approach into real structure.
If you are diligent enough you can achieve amazing accuracy, less than 0.5% with fine mesh.
With these results, you will be absolutely sure of the correctness of your approach.

Aha, okay.
Appreciate your tips :)