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Cone compression springs (given the deflection of spring)

Cone compression spring D 0 d D 1
Cone compression spring

Values for calculation

$ d $ $ \mathrm{mm} $
$ D_1 $ $ \mathrm{mm} $
$ D_0 $ $ \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

$$F=\cfrac{f\cdot d^4\cdot G\cdot 10^3}{16\cdot n\cdot\left(\cfrac{D_1}{2}+\cfrac{D_0}{2}\right)\cdot\left(\left(\cfrac{D_1}{2}\right)^2+\left(\cfrac{D_0}{2}\right)^2\right)}$$

Spring stiffness

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

Energy stored

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

Shear stress

$$τ_S=\cfrac{16\cdot F\cdot\cfrac{D_1}{2}}{π\cdot d^3}$$

$$τ_S\le τ_{adm}$$

Safety factor

$$S_F=\cfrac{τ_{adm}}{τ_S}$$