Ball and socket contact stresses

[cabellos6]

I am familiar with Hertzian contact mechanics for spheres in contact with a falt surface or a sphere in contact with another sphere. However, I am unsure on how to model a ball and socket contact? Could anyone help me with this idea please?

Thanks

 

[FredGarvin]

Sorry it took so long on this. I apparently forgot how to read.

According to the bible, Roark's, for a ball and socket:

The max compressive stress is:

$$\sigma_c = .918\left[ \sqrt[3]{\frac{P}{K_D^2 C_E^2}}\right]$$

Where:
$$P$$=the compressive load applied
$$K_D$$= Load condition factor = $$\frac{D_1D_2}{D_1-D_2}$$
$$D_1$$= Diameter of the socket
$$D_2$$= Diameter of the ball
$$C_E$$= $$\left[\frac{1-\nu_1^2}{E_1}\right]+\left[\frac{1-\nu_2^2}{E_2}\right]$$
$$E, \nu$$ = Modulus of elasticity and Poisson's Ratio

Also, don't forget that the maximums for Hertzian stresses do not occur at the surface of the bodies.