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Cone compression springs (given the force on spring)

Cone compression spring D 0 d D 1
Cone compression spring

Values for calculation

$ \{d\in\mathbb{R}\mid d>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 $ $ \mathrm{mm} $
$ \{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} $
$ \{D_0\in\mathbb{R}\mid D_0>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_0 $ $ \mathrm{mm} $
$ \{n\in\mathbb{R}\mid n>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.
$ n $
$ \{E\in\mathbb{R}\mid E>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 $ $ \mathrm{GPa} $
$ \{G\in\mathbb{R}\mid G>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.
$ G $ $ \mathrm{GPa} $
$ \{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} $
$ \{S_y\in\mathbb{R}\mid S_y>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 $ $ \mathrm{MPa} $

Calculation

Shear admissible stress

$$τ_{adm}=\cfrac{S_y}{\sqrt{3}}$$
$τ_{adm}=\cfrac{S_y}{\sqrt{3}}$
Equations in LaTeX code
τ_{adm}=\cfrac{S_y}{\sqrt{3}}

Spring deflection

$$f=\cfrac{16\cdot n\cdot\left(\cfrac{D_1}{2}+\cfrac{D_0}{2}\right)\cdot\left(\left(\cfrac{D_1}{2}\right)^2+\left(\cfrac{D_0}{2}\right)^2\right)\cdot F}{d^4\cdot G\cdot 10^3}$$
$f=\cfrac{16\cdot n\cdot\left(\cfrac{D_1}{2}+\cfrac{D_0}{2}\right)\cdot\left(\left(\cfrac{D_1}{2}\right)^2+\left(\cfrac{D_0}{2}\right)^2\right)\cdot F}{d^4\cdot G\cdot 10^3}$
Equations in LaTeX code
f=\cfrac{16\cdot n\cdot\left(\cfrac{D_1}{2}+\cfrac{D_0}{2}\right)\cdot\left(\left(\cfrac{D_1}{2}\right)^2+\left(\cfrac{D_0}{2}\right)^2\right)\cdot F}{d^4\cdot G\cdot 10^3}

Spring stiffness

$$k=\cfrac{F}{f\cdot 10^{-3}}$$
$k=\cfrac{F}{f\cdot 10^{-3}}$
Equations in LaTeX code
k=\cfrac{F}{f\cdot 10^{-3}}

Energy stored

$$E_p=\cfrac{F\cdot f\cdot 10^{-3}}{2}$$
$E_p=\cfrac{F\cdot f\cdot 10^{-3}}{2}$
Equations in LaTeX code
E_p=\cfrac{F\cdot f\cdot 10^{-3}}{2}

Shear stress

$$τ_S=\cfrac{16\cdot F\cdot\cfrac{D_1}{2}}{π\cdot d^3}$$
$τ_S=\cfrac{16\cdot F\cdot\cfrac{D_1}{2}}{π\cdot d^3}$
Equations in LaTeX code
τ_S=\cfrac{16\cdot F\cdot\cfrac{D_1}{2}}{π\cdot d^3}
$$τ_S\le τ_{adm}$$
$τ_S\le τ_{adm}$
Equations in LaTeX code
τ_S\le τ_{adm}

Safety factor

$$S_F=\cfrac{τ_{adm}}{τ_S}$$
$S_F=\cfrac{τ_{adm}}{τ_S}$
Equations in LaTeX code
S_F=\cfrac{τ_{adm}}{τ_S}
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