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Spiral torsion springs (given the deflection of spring)

Spiral torsion springs F r f d
Spiral torsion springs

Values for calculation

$d$ $\mathrm{mm}$
$r$ $\mathrm{mm}$
$L$ $\mathrm{mm}$
$E$ $\mathrm{GPa}$
$φ$ $\mathrm{°}$
$σ_{adm}$ $\mathrm{MPa}$

Calculation

Spring deflection

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

Tensile stress

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

Force

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

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 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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