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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 $ $ \mathrm{mm} $
$ D $ $ \mathrm{mm} $
$ n $
$ E $ $ \mathrm{GPa} $
$ G $ $ \mathrm{GPa} $
$ f $ $ \mathrm{mm} $
$ S_y $ $ \mathrm{MPa} $

Calculation

Shear admissible stress

$$τ_{adm}=\cfrac{S_y}{\sqrt{3}}$$

Force

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

Spring stiffness

$$k=\cfrac{F}{f\cdot 10^{-3}}$$

Energy stored

$$E_p=\cfrac{F\cdot f\cdot 10^{-3}}{2}$$

Shear stress

$$τ_S=\cfrac{4.8\cdot F\cdot\cfrac{D}{2}}{d^3}$$

$$τ_S\le τ_{adm}$$

Safety factor

$$S_F=\cfrac{τ_{adm}}{τ_S}$$