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Flat wire helical spring (given the deflection of spring)

Flat wire helical spring D d
Flat wire helical 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\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} $
$ \{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{mm} $
$ \{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}}

Force

$$F=\cfrac{f\cdot d^4\cdot G\cdot 10^3}{44.9\cdot n\cdot\left(\cfrac{D}{2}\right)^3}$$
$F=\cfrac{f\cdot d^4\cdot G\cdot 10^3}{44.9\cdot n\cdot\left(\cfrac{D}{2}\right)^3}$
Equations in LaTeX code
F=\cfrac{f\cdot d^4\cdot G\cdot 10^3}{44.9\cdot n\cdot\left(\cfrac{D}{2}\right)^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

$$τ_S=\cfrac{4.8\cdot F\cdot\cfrac{D}{2}}{d^3}$$
$τ_S=\cfrac{4.8\cdot F\cdot\cfrac{D}{2}}{d^3}$
Equations in LaTeX code
τ_S=\cfrac{4.8\cdot F\cdot\cfrac{D}{2}}{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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