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Trapezoid

Trapezoid
Trapezoid

Values for calculation

$T$ $\mathrm{Nm}$
$m$ $\mathrm{mm}$
$n$ $\mathrm{mm}$
$b$ $\mathrm{mm}$
$D$ $\mathrm{mm}$
$r$ $\mathrm{mm}$
$ϕ$ $\mathrm{rad}$
$L$ $\mathrm{mm}$
$G$ $\mathrm{MPa}$

Calculation

Profile area

$$A=\cfrac{m+n}{2}\cdot b$$

Coefficient $ s $

$$s=\cfrac{m-n}{b}$$

Coefficient $ V_L $

$$V_L=0.10504-0.1\cdot s+0.0848\cdot s^2-0.06746\cdot s^3+0.0515\cdot s^4$$

Coefficient $ V_s $

$$V_s=0.10504+0.1\cdot s+0.0848\cdot s^2+0.06746\cdot s^3+0.0515\cdot s^4$$

Coefficient $ C $

$$C=\cfrac{D}{1+\cfrac{π^2\cdot D^4}{16\cdot A^2}}\cdot\left[1+\left[0.118\cdot\ln{\left(1+\cfrac{D}{2\cdot r}\right)+0.238\cdot\cfrac{D}{2\cdot r}}\right]\cdot \tanh\left(\cfrac{2\cdotϕ}{π}\right)\right]$$

Polar moment of inertia

$$K=\cfrac{1}{12}\cdot b\cdot\left(m+n\right)\cdot\left(m^2+n^2\right)-V_L\cdot m^4-V_s\cdot n^4$$

Angle of twist

$$θ=\cfrac{T\cdot 10^3\cdot L}{K\cdot G}$$

Torsion stress

$$τ_{max}=\cfrac{10^3\cdot T}{K}\cdot C$$