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Contact stress two sphere

Contact stress two sphere F F D 2 D 1 b
Contact stress two sphere

Values for calculation

$ F $ $ \mathrm{N} $
$ D_1 $ $ \mathrm{mm} $
$ E_1 $ $ \mathrm{MPa} $
$ ν_1 $
$ HB_1 $ $ \mathrm{HB} $
$ S_{y-1} $ $ \mathrm{MPa} $
$ D_2 $ $ \mathrm{mm} $
$ E_2 $ $ \mathrm{MPa} $
$ ν_2 $
$ HB_2 $ $ \mathrm{HB} $
$ S_{y-2} $ $ \mathrm{MPa} $
$ C_c $
$ S_F $

Calculation

Allowable Hertz pressure

$\text{if }\ \text{Hardened }$$\text{material }$$\text{1}= \text{yes}\wedge\text{Hardened }$$\text{material }$$\text{2}= \text{yes}$
$$σ_H=\min\left(\cfrac{4.2\cdot S_{y-1}}{S_F}\cdot C_c, \cfrac{4.2\cdot S_{y-2}}{S_F}\cdot C_c\right)$$
$\text{else if }\ \text{Hardened }$$\text{material }$$\text{1}= \text{yes}\wedge\text{Hardened }$$\text{material }$$\text{2}= \text{no}$
$$σ_H=\min\left(\cfrac{4.2\cdot S_{y-1}}{S_F}\cdot C_c, \cfrac{7\cdot HB_2}{S_F}\cdot C_c\right)$$
$\text{else if }\ \text{Hardened }$$\text{material }$$\text{1}= \text{no}\wedge\text{Hardened }$$\text{material }$$\text{2}= \text{no}$
$$σ_H=\min\left(\cfrac{7\cdot HB_1}{S_F}\cdot C_c, \cfrac{7\cdot HB_2}{S_F}\cdot C_c\right)$$
$\text{else}$
$$σ_H=\min\left(\cfrac{7\cdot HB_1}{S_F}\cdot C_c, \cfrac{4.2\cdot S_{y-2}}{S_F}\cdot C_c\right)$$

Material coefficient

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

Dimensional coefficient

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

Diameter of sphere contact area

$$b=1.442\cdot\sqrt[3]{F\cdot K_D \cdot C_E}$$

Contact stress

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

$$σ_c\le σ_H$$