Here is more information on my problem:
Yeah, I tried to type in the equation and it didn't work so well. Thank you for your reply.
To give more info, the semi-spherical ball (about half of the sphere) sits in a semi spherical socket and there is a hole in the center of the spherical socket. Thus, my potential bearing area is essentially a radial ring. I have found some information on Roark's ball and socket stress equations. I've attached the equations to this post.
I'm getting a higher value using this equation than I did using Hertz' equation for concave to convex contact. I would have expected better results. I do not have the actual reference with text, so I'm not sure what the assumptions are.
I have a static load condition and I'm trying to determine the actual stresses on the ball and socket. I would like to specify equal radii, but as dhengr pointed out, I should use some tolerance in my calculations to cover the machining tolerances.
The materials will either be grade 50 steel or ductile iron.