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Circular shaft with four flattened

Circular shaft with four flattened r W
Circular shaft with four flattened

Values for calculation

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

Calculation

Height of the segment

$$h=r-W$$
$h=r-W$
Equations in LaTeX code
h=r-W

Coefficient $ C $

$$C=0.7854-0.7\cdot\cfrac{h}{r}-7.7982\cdot\left(\cfrac{h}{r}\right)^2+14.578\cdot\left(\cfrac{h}{r}\right)^3$$
$C=0.7854-0.7\cdot\cfrac{h}{r}-7.7982\cdot\left(\cfrac{h}{r}\right)^2+14.578\cdot\left(\cfrac{h}{r}\right)^3$
Equations in LaTeX code
C=0.7854-0.7\cdot\cfrac{h}{r}-7.7982\cdot\left(\cfrac{h}{r}\right)^2+14.578\cdot\left(\cfrac{h}{r}\right)^3

Coefficient $ B $

$$B=0.6366+2.6298\cdot\cfrac{h}{r}-5.6147\cdot\left(\cfrac{h}{r}\right)^2+30.853\cdot\left(\cfrac{h}{r}\right)^3$$
$B=0.6366+2.6298\cdot\cfrac{h}{r}-5.6147\cdot\left(\cfrac{h}{r}\right)^2+30.853\cdot\left(\cfrac{h}{r}\right)^3$
Equations in LaTeX code
B=0.6366+2.6298\cdot\cfrac{h}{r}-5.6147\cdot\left(\cfrac{h}{r}\right)^2+30.853\cdot\left(\cfrac{h}{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

$$τ_{max}=\cfrac{T\cdot10^3\cdot B}{r^3}$$
$τ_{max}=\cfrac{T\cdot10^3\cdot B}{r^3}$
Equations in LaTeX code
τ_{max}=\cfrac{T\cdot10^3\cdot B}{r^3}

Requirements

$$0\le\cfrac{h}{r}\le 0.293$$
$0\le\cfrac{h}{r}\le 0.293$
Equations in LaTeX code
0\le\cfrac{h}{r}\le 0.293
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