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Circular shaft with two flattened

Circular shaft with two flattened r W
Circular shaft with two 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 $

$$C=0.7854-0.4053\cdot\cfrac{h}{r}-3.581\cdot\left(\cfrac{h}{r}\right)^2+5.2708\cdot\left(\cfrac{h}{r}\right)^3-2.0772\cdot\left(\cfrac{h}{r}\right)^4$$
$C=0.7854-0.4053\cdot\cfrac{h}{r}-3.581\cdot\left(\cfrac{h}{r}\right)^2+5.2708\cdot\left(\cfrac{h}{r}\right)^3-2.0772\cdot\left(\cfrac{h}{r}\right)^4$
Equations in LaTeX code
C=0.7854-0.4053\cdot\cfrac{h}{r}-3.581\cdot\left(\cfrac{h}{r}\right)^2+5.2708\cdot\left(\cfrac{h}{r}\right)^3-2.0772\cdot\left(\cfrac{h}{r}\right)^4

Coefficient $ B $

$$B=0.6366+2.5303\cdot\cfrac{h}{r}-11.157\cdot\left(\cfrac{h}{r}\right)^2+49.568\cdot\left(\cfrac{h}{r}\right)^3-85.886\cdot\left(\cfrac{h}{r}\right)^4+69.849\cdot\left(\cfrac{h}{r}\right)^5$$
$B=0.6366+2.5303\cdot\cfrac{h}{r}-11.157\cdot\left(\cfrac{h}{r}\right)^2+49.568\cdot\left(\cfrac{h}{r}\right)^3-85.886\cdot\left(\cfrac{h}{r}\right)^4+69.849\cdot\left(\cfrac{h}{r}\right)^5$
Equations in LaTeX code
B=0.6366+2.5303\cdot\cfrac{h}{r}-11.157\cdot\left(\cfrac{h}{r}\right)^2+49.568\cdot\left(\cfrac{h}{r}\right)^3-85.886\cdot\left(\cfrac{h}{r}\right)^4+69.849\cdot\left(\cfrac{h}{r}\right)^5

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

$$0\le\cfrac{h}{r}\le 0.6$$
$0\le\cfrac{h}{r}\le 0.6$
Equations in LaTeX code
0\le\cfrac{h}{r}\le 0.6
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