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Helical torsion spring round (given the deflection of spring)

Helical torsion spring round D d φ r F
Helical torsion spring round

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} $
$ \{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} $
$ \{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} $
$ \{φ\in\mathbb{R}\mid φ>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.
$ φ $ $ \mathrm{°} $
$ \{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

Bending stress

$$σ_B=\cfrac{φ\cdot\cfrac{π}{180}\cdot E\cdot 10^3\cdot d}{2\cdot D\cdot π\cdot n}$$
$σ_B=\cfrac{φ\cdot\cfrac{π}{180}\cdot E\cdot 10^3\cdot d}{2\cdot D\cdot π\cdot n}$
Equations in LaTeX code
σ_B=\cfrac{φ\cdot\cfrac{π}{180}\cdot E\cdot 10^3\cdot d}{2\cdot D\cdot π\cdot n}
$$σ_B\le σ_{adm}$$
$σ_B\le σ_{adm}$
Equations in LaTeX code
σ_B\le σ_{adm}

Safety factor

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

Force

$$F=\cfrac{π\cdot d^3\cdot σ_B}{32\cdot r}$$
$F=\cfrac{π\cdot d^3\cdot σ_B}{32\cdot r}$
Equations in LaTeX code
F=\cfrac{π\cdot d^3\cdot σ_B}{32\cdot r}

Applied torque moment

$$M=F\cdot r\cdot 10^{-3}$$
$M=F\cdot r\cdot 10^{-3}$
Equations in LaTeX code
M=F\cdot r\cdot 10^{-3}

Spring stiffness

$$k=\cfrac{F}{r\cdot 10^{-3}\cdot φ\cdot\cfrac{π}{180}}$$
$k=\cfrac{F}{r\cdot 10^{-3}\cdot φ\cdot\cfrac{π}{180}}$
Equations in LaTeX code
k=\cfrac{F}{r\cdot 10^{-3}\cdot φ\cdot\cfrac{π}{180}}

Energy stored

$$E_p=\cfrac{F\cdot r\cdot 10^{-3}\cdot φ\cdot\cfrac{π}{180}}{2}$$
$E_p=\cfrac{F\cdot r\cdot 10^{-3}\cdot φ\cdot\cfrac{π}{180}}{2}$
Equations in LaTeX code
E_p=\cfrac{F\cdot r\cdot 10^{-3}\cdot φ\cdot\cfrac{π}{180}}{2}
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