Menu

Contact stress two sphere

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

Values for calculation

$ \{F\in\mathbb{R}\mid F>0\} $
This set includes all real numbers that are greater than zero. Therefore, it contains only positive numbers. Zero and negative numbers are not included in this set.
$ F $ $ \mathrm{N} $
$ \{D_1\in\mathbb{R}\mid D_1>0\} $
This set includes all real numbers that are greater than zero. Therefore, it contains only positive numbers. Zero and negative numbers are not included in this set.
$ D_1 $ $ \mathrm{mm} $
$ \{E_1\in\mathbb{R}\mid E_1>0\} $
This set includes all real numbers that are greater than zero. Therefore, it contains only positive numbers. Zero and negative numbers are not included in this set.
$ E_1 $ $ \mathrm{MPa} $
$ \{ν_1\in\mathbb{R}\mid ν_1>0\} $
This set includes all real numbers that are greater than zero. Therefore, it contains only positive numbers. Zero and negative numbers are not included in this set.
$ ν_1 $
$ \{HB_1\in\mathbb{R}\mid HB_1>0\} $
This set includes all real numbers that are greater than zero. Therefore, it contains only positive numbers. Zero and negative numbers are not included in this set.
$ HB_1 $ $ \mathrm{HB} $
$ \{S_{y-1}\in\mathbb{R}\mid S_{y-1}>0\} $
This set includes all real numbers that are greater than zero. Therefore, it contains only positive numbers. Zero and negative numbers are not included in this set.
$ S_{y-1} $ $ \mathrm{MPa} $
$ \{D_2\in\mathbb{R}\mid D_2>0\} $
This set includes all real numbers that are greater than zero. Therefore, it contains only positive numbers. Zero and negative numbers are not included in this set.
$ D_2 $ $ \mathrm{mm} $
$ \{E_2\in\mathbb{R}\mid E_2>0\} $
This set includes all real numbers that are greater than zero. Therefore, it contains only positive numbers. Zero and negative numbers are not included in this set.
$ E_2 $ $ \mathrm{MPa} $
$ \{ν_2\in\mathbb{R}\mid ν_2>0\} $
This set includes all real numbers that are greater than zero. Therefore, it contains only positive numbers. Zero and negative numbers are not included in this set.
$ ν_2 $
$ \{HB_2\in\mathbb{R}\mid HB_2>0\} $
This set includes all real numbers that are greater than zero. Therefore, it contains only positive numbers. Zero and negative numbers are not included in this set.
$ HB_2 $ $ \mathrm{HB} $
$ \{S_{y-2}\in\mathbb{R}\mid S_{y-2}>0\} $
This set includes all real numbers that are greater than zero. Therefore, it contains only positive numbers. Zero and negative numbers are not included in this set.
$ S_{y-2} $ $ \mathrm{MPa} $
$ C_c $
$ \{S_F\in\mathbb{R}\mid S_F>0\} $
This set includes all real numbers that are greater than zero. Therefore, it contains only positive numbers. Zero and negative numbers are not included in this set.
$ 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}$
$\text{if }\ \text{Hardened }$$\text{material }$$\text{1}= \text{yes}\wedge\text{Hardened }$$\text{material }$$\text{2}= \text{yes}$
Equations in LaTeX code
\text{if }\ \text{Hardened }$$\text{material }$$\text{1}= \text{yes}\wedge\text{Hardened }$$\text{material }$$\text{2}= \text{yes}
$$σ_H=\min\left(\cfrac{4.2\cdot S_{y-1}}{S_F}\cdot C_c, \cfrac{4.2\cdot S_{y-2}}{S_F}\cdot C_c\right)$$
$σ_H=\min\left(\cfrac{4.2\cdot S_{y-1}}{S_F}\cdot C_c, \cfrac{4.2\cdot S_{y-2}}{S_F}\cdot C_c\right)$
Equations in LaTeX code
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}$
$\text{else if }\ \text{Hardened }$$\text{material }$$\text{1}= \text{yes}\wedge\text{Hardened }$$\text{material }$$\text{2}= \text{no}$
Equations in LaTeX code
\text{else if }\ \text{Hardened }$$\text{material }$$\text{1}= \text{yes}\wedge\text{Hardened }$$\text{material }$$\text{2}= \text{no}
$$σ_H=\min\left(\cfrac{4.2\cdot S_{y-1}}{S_F}\cdot C_c, \cfrac{7\cdot HB_2}{S_F}\cdot C_c\right)$$
$σ_H=\min\left(\cfrac{4.2\cdot S_{y-1}}{S_F}\cdot C_c, \cfrac{7\cdot HB_2}{S_F}\cdot C_c\right)$
Equations in LaTeX code
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}$
$\text{else if }\ \text{Hardened }$$\text{material }$$\text{1}= \text{no}\wedge\text{Hardened }$$\text{material }$$\text{2}= \text{no}$
Equations in LaTeX code
\text{else if }\ \text{Hardened }$$\text{material }$$\text{1}= \text{no}\wedge\text{Hardened }$$\text{material }$$\text{2}= \text{no}
$$σ_H=\min\left(\cfrac{7\cdot HB_1}{S_F}\cdot C_c, \cfrac{7\cdot HB_2}{S_F}\cdot C_c\right)$$
$σ_H=\min\left(\cfrac{7\cdot HB_1}{S_F}\cdot C_c, \cfrac{7\cdot HB_2}{S_F}\cdot C_c\right)$
Equations in LaTeX code
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)
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$σ_H=\min\left(\cfrac{7\cdot HB_1}{S_F}\cdot C_c, \cfrac{4.2\cdot S_{y-2}}{S_F}\cdot C_c\right)$$
$σ_H=\min\left(\cfrac{7\cdot HB_1}{S_F}\cdot C_c, \cfrac{4.2\cdot S_{y-2}}{S_F}\cdot C_c\right)$
Equations in LaTeX code
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

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

Diameter of sphere contact area

$$b=1.442\cdot\sqrt[3]{F\cdot K_D \cdot C_E}$$
$b=1.442\cdot\sqrt[3]{F\cdot K_D \cdot C_E}$
Equations in LaTeX code
b=1.442\cdot\sqrt[3]{F\cdot K_D \cdot C_E}

Contact stress

$$σ_c=0.918\cdot\sqrt[3]{\cfrac{F}{K_D^2\cdot C_E^2}}$$
$σ_c=0.918\cdot\sqrt[3]{\cfrac{F}{K_D^2\cdot C_E^2}}$
Equations in LaTeX code
σ_c=0.918\cdot\sqrt[3]{\cfrac{F}{K_D^2\cdot C_E^2}}
$$σ_c\le σ_H$$
$σ_c\le σ_H$
Equations in LaTeX code
σ_c\le σ_H
On this page