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Pinned shaft with two grooves

Pinned shaft with two grooves M r a
Pinned shaft with two grooves

Values for calculation

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

Calculation

Coefficient $ C $

$$C=0.7854-0.0147\cdot\cfrac{a}{r}-3.0649\cdot\left(\cfrac{a}{r}\right)^2+2.5453\cdot\left(\cfrac{a}{r}\right)^3$$
$C=0.7854-0.0147\cdot\cfrac{a}{r}-3.0649\cdot\left(\cfrac{a}{r}\right)^2+2.5453\cdot\left(\cfrac{a}{r}\right)^3$
Equations in LaTeX code
C=0.7854-0.0147\cdot\cfrac{a}{r}-3.0649\cdot\left(\cfrac{a}{r}\right)^2+2.5453\cdot\left(\cfrac{a}{r}\right)^3

Coefficient $ B $

$$B=1.0055+1.5427\cdot\cfrac{a}{r}-2.9501\cdot\left(\cfrac{a}{r}\right)^2+7.0534\cdot\left(\cfrac{a}{r}\right)^3$$
$B=1.0055+1.5427\cdot\cfrac{a}{r}-2.9501\cdot\left(\cfrac{a}{r}\right)^2+7.0534\cdot\left(\cfrac{a}{r}\right)^3$
Equations in LaTeX code
B=1.0055+1.5427\cdot\cfrac{a}{r}-2.9501\cdot\left(\cfrac{a}{r}\right)^2+7.0534\cdot\left(\cfrac{a}{r}\right)^3

Polar moment of inertia

$$K=2\cdot C\cdot r^4$$
$K=2\cdot C\cdot r^4$
Equations in LaTeX code
K=2\cdot C\cdot r^4

Angle of twist

$$θ=\cfrac{T\cdot 10^3\cdot L}{K\cdot G}$$
$θ=\cfrac{T\cdot 10^3\cdot L}{K\cdot G}$
Equations in LaTeX code
θ=\cfrac{T\cdot 10^3\cdot L}{K\cdot G}

Torsion stress at $ M $

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

Requirements

$$0.1 \le\cfrac{a}{r} \le 0.5$$
$0.1 \le\cfrac{a}{r} \le 0.5$
Equations in LaTeX code
0.1 \le\cfrac{a}{r} \le 0.5
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