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Ball and socket contact stresses

  1. Dec 28, 2007 #1
    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
     
  2. jcsd
  3. Jan 3, 2008 #2

    FredGarvin

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    Science Advisor

    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:

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

    Where:
    [tex]P[/tex]=the compressive load applied
    [tex]K_D[/tex]= Load condition factor = [tex]\frac{D_1D_2}{D_1-D_2}[/tex]
    [tex]D_1[/tex]= Diameter of the socket
    [tex]D_2[/tex]= Diameter of the ball
    [tex]C_E[/tex]= [tex]\left[\frac{1-\nu_1^2}{E_1}\right]+\left[\frac{1-\nu_2^2}{E_2}\right][/tex]
    [tex]E, \nu[/tex] = 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.
     
    Last edited: Jan 3, 2008
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