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Sphere in a spherical socket

Sphere in a spherical socket P D 2 D 1 2a
Sphere in a spherical socket

Values for calculation

$ P $ $ \mathrm{N} $
$ D_1 $ $ \mathrm{mm} $
$ D_2 $ $ \mathrm{mm} $
$ ν_1 $
$ ν_2 $
$ E_1 $ $ \mathrm{MPa} $
$ E_2 $ $ \mathrm{MPa} $

Calculation

Material coefficient

$$C_E=\cfrac{1-ν_1^2}{E_1}+\cfrac{1-ν_2^2}{E_2}$$

Dimensional coefficient

$$K_D=\cfrac{D_1\cdot D_2}{D_1-D_2}$$

Radius of circular contact area

$$a=0.721\cdot\sqrt[3]{P\cdot K_D\cdot C_E}$$

Contact stress

$$σ_c=0.918\cdot\sqrt[3]{\cfrac{P}{K_D^2\cdot C_E^2}}$$

Relative motion of approach along the axis of loading of two points, one in each of the two contact bodies, remote from the contact zone

$$y=1.040\cdot\sqrt[3]{\cfrac{P^2\cdot C_E^2}{K_D}}$$