Tribology calculations 1

[Student095]

Hello fellow engineers,

I am trying to calculate the maximum contact pressure, the contact radius and the elastic deformation between a sphere and a cylinder base as illustrated:

I have been given the following equations:

What gets me confused is the choice of the radius value which should be substituted in the equations. Should it be the sphere radius or the composite radius?

I have run the simulation in Abaqus, measuring the contact radius using the Distance tool under Query by looking at the deformed model with a scale factor of 1.
I observe a large % difference between my calculations of the contact radius and the Abaqus results.
I have checked for common mistakes, units, and still haven't managed to bring this difference down.

Any help would be greatly appreciated.

 

[FEA way]

It’s a sphere radius. Check "Roark’s Formulas for Stress and Strain" book. There you will also find equations for such a case.