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Round wire helical spring (given the deflection of spring)

Round wire helical spring D d
Round 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

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

Force

$$F=\cfrac{f\cdot d^4\cdot G\cdot 10^3}{64\cdot n\cdot\left(\cfrac{D}{2}\right)^3}$$
$F=\cfrac{f\cdot d^4\cdot G\cdot 10^3}{64\cdot n\cdot\left(\cfrac{D}{2}\right)^3}$
Equations in LaTeX code
F=\cfrac{f\cdot d^4\cdot G\cdot 10^3}{64\cdot n\cdot\left(\cfrac{D}{2}\right)^3}

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}

Spring index

$$C=\cfrac{D}{d}$$
$C=\cfrac{D}{d}$
Equations in LaTeX code
C=\cfrac{D}{d}

Wahl factor

$$K_W=\cfrac{4\cdot C-1}{4\cdot C-4}+\cfrac{0.615}{C}$$
$K_W=\cfrac{4\cdot C-1}{4\cdot C-4}+\cfrac{0.615}{C}$
Equations in LaTeX code
K_W=\cfrac{4\cdot C-1}{4\cdot C-4}+\cfrac{0.615}{C}

Shear stress

$$τ_S=\cfrac{8\cdot F\cdot D\cdot K_W}{π\cdot d^3}$$
$τ_S=\cfrac{8\cdot F\cdot D\cdot K_W}{π\cdot d^3}$
Equations in LaTeX code
τ_S=\cfrac{8\cdot F\cdot D\cdot K_W}{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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