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Spiral torsion springs (given the force on spring)

Spiral torsion springs F r f d
Spiral torsion springs

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} $
$ \{r\in\mathbb{R}\mid r>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.
$ r $ $ \mathrm{mm} $
$ \{L\in\mathbb{R}\mid L>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.
$ L $ $ \mathrm{mm} $
$ \{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} $
$ \{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} $
$ \{σ_{adm}\in\mathbb{R}\mid σ_{adm}>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.
$ σ_{adm} $ $ \mathrm{MPa} $

Calculation

Tensile stress

$$σ=\cfrac{32\cdot r\cdot F}{π\cdot d^3}$$
$σ=\cfrac{32\cdot r\cdot F}{π\cdot d^3}$
Equations in LaTeX code
σ=\cfrac{32\cdot r\cdot F}{π\cdot d^3}
$$σ\le σ_{adm}$$
$σ\le σ_{adm}$
Equations in LaTeX code
σ\le σ_{adm}

Safety factor

$$S_F=\cfrac{σ_{adm}}{σ}$$
$S_F=\cfrac{σ_{adm}}{σ}$
Equations in LaTeX code
S_F=\cfrac{σ_{adm}}{σ}

Spring deflection

$$f=\cfrac{2\cdot r\cdot L}{E\cdot 10^3\cdot d}\cdot σ$$
$f=\cfrac{2\cdot r\cdot L}{E\cdot 10^3\cdot d}\cdot σ$
Equations in LaTeX code
f=\cfrac{2\cdot r\cdot L}{E\cdot 10^3\cdot d}\cdot σ

Spring angular deflection

$$φ=\cfrac{f}{r}\cdot\cfrac{180}{π}$$
$φ=\cfrac{f}{r}\cdot\cfrac{180}{π}$
Equations in LaTeX code
φ=\cfrac{f}{r}\cdot\cfrac{180}{π}

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}}
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