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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

$$h=r-W$$

Coefficient $ C $

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

Coefficient $ B $

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

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

$$τ_{max}=\cfrac{T\cdot10^3\cdot B}{r^3}$$

Requirements

$$ 0\le\cfrac{h}{r}\le 0.293 $$