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Cylinder on a cylinder

Cylinder on a cylinder D 2 D 1 L b P P
Cylinder on a cylinder

Values for calculation

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

Calculation

Load per unit length

$$p=P/L$$
$p=P/L$
Equations in LaTeX code
p=P/L

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

$$K_D=\cfrac{D_1\cdot D_2}{D_1+D_2}$$
$K_D=\cfrac{D_1\cdot D_2}{D_1+D_2}$
Equations in LaTeX code
K_D=\cfrac{D_1\cdot D_2}{D_1+D_2}

Width of rectangular contact area

$$b=1.60\cdot\sqrt{p\cdot K_D\cdot C_E}$$
$b=1.60\cdot\sqrt{p\cdot K_D\cdot C_E}$
Equations in LaTeX code
b=1.60\cdot\sqrt{p\cdot K_D\cdot C_E}

Contact stress

$$σ_c=0.798\cdot\sqrt{\cfrac{p}{K_D\cdot C_E}}$$
$σ_c=0.798\cdot\sqrt{\cfrac{p}{K_D\cdot C_E}}$
Equations in LaTeX code
σ_c=0.798\cdot\sqrt{\cfrac{p}{K_D\cdot C_E}}
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