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Pinned shaft with four grooves

Pinned_shaft_with_four_grooves
Pinned shaft with four grooves

Values for calculation

$T$ $\mathrm{Nm}$
$r$ $\mathrm{mm}$
$a$ $\mathrm{mm}$
$L$ $\mathrm{mm}$
$G$ $\mathrm{MPa}$

Calculation

Coefficient $ C $

$$C=0.7854-0.0409\cdot\cfrac{a}{r}-6.2371\cdot\left(\cfrac{a}{r}\right)^2+7.2538\cdot\left(\cfrac{a}{r}\right)^3$$

Coefficient $ B $

$$B=1.2135-2.9697\cdot\cfrac{a}{r}+33.713\cdot\left(\cfrac{a}{r}\right)^2-99.506\cdot\left(\cfrac{a}{r}\right)^3+130.49\cdot\left(\cfrac{a}{r}\right)^4$$

Polar moment of inertia

$$K=2\cdot C\cdot r^4$$

Angle of twist

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

Torsion stress at $ M $

$$τ_{max-at-M}=\cfrac{10^3\cdot T\cdot B}{r^3}$$

Requirements

$$0.1 \le\cfrac{a}{r} \le 0.5$$