Menu

Helical torsion spring round (given the force on 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} $
$ \{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

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}

Bending stress

$$σ_B=\cfrac{32\cdot M\cdot 10^3}{π\cdot d^3}$$
$σ_B=\cfrac{32\cdot M\cdot 10^3}{π\cdot d^3}$
Equations in LaTeX code
σ_B=\cfrac{32\cdot M\cdot 10^3}{π\cdot d^3}
$$σ_B\le σ_{adm}$$
$σ_B\le σ_{adm}$
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}

Spring angular deflection

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

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}
On this page