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Sphere on a plate

Sphere on a plate D 2 2a P
Sphere on a plate

Values for calculation

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

Calculation

Material coefficient

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

Dimensional coefficient

$$K_D=D_2$$
$K_D=D_2$
Equations in LaTeX code
K_D=D_2

Radius of circular contact area

$$a=0.721\cdot\sqrt[3]{P\cdot K_D\cdot C_E}$$
$a=0.721\cdot\sqrt[3]{P\cdot K_D\cdot C_E}$
Equations in LaTeX code
a=0.721\cdot\sqrt[3]{P\cdot K_D\cdot C_E}

Contact stress

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

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