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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

$$τ_{adm}=\cfrac{S_y}{\sqrt{3}}$$
$τ_{adm}=\cfrac{S_y}{\sqrt{3}}$
Equations in LaTeX code
τ_{adm}=\cfrac{S_y}{\sqrt{3}}

Force

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

$$k=\cfrac{F}{f\cdot 10^{-3}}$$
$k=\cfrac{F}{f\cdot 10^{-3}}$
Equations in LaTeX code
k=\cfrac{F}{f\cdot 10^{-3}}

Energy stored

$$E_p=\cfrac{F\cdot f\cdot 10^{-3}}{2}$$
$E_p=\cfrac{F\cdot f\cdot 10^{-3}}{2}$
Equations in LaTeX code
E_p=\cfrac{F\cdot f\cdot 10^{-3}}{2}

Shear stress

$$τ_S=\cfrac{16\cdot F\cdot\cfrac{D_1}{2}}{π\cdot d^3}$$
$τ_S=\cfrac{16\cdot F\cdot\cfrac{D_1}{2}}{π\cdot d^3}$
Equations in LaTeX code
τ_S=\cfrac{16\cdot F\cdot\cfrac{D_1}{2}}{π\cdot d^3}
$$τ_S\le τ_{adm}$$
$τ_S\le τ_{adm}$
Equations in LaTeX code
τ_S\le τ_{adm}

Safety factor

$$S_F=\cfrac{τ_{adm}}{τ_S}$$
$S_F=\cfrac{τ_{adm}}{τ_S}$
Equations in LaTeX code
S_F=\cfrac{τ_{adm}}{τ_S}
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