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Torsion of a shaft with a shoulder fillet

Torsion of a shaft with a shoulder fillet D r t d T T
Torsion of a shaft with a shoulder fillet

Values for calculation

$T$ $\mathrm{Nm}$
$D$ $\mathrm{mm}$
$d$ $\mathrm{mm}$
$r$ $\mathrm{mm}$

Calculation

Depth of groove, notch

$$t=\cfrac{D-d}{2}$$
$t=\cfrac{D-d}{2}$
Equations in LaTeX code
t=\cfrac{D-d}{2}
$$0.25\le t/r\le 4.0$$
$0.25\le t/r\le 4.0$
Equations in LaTeX code
0.25\le t/r\le 4.0

Coefficient $ C_1 $

$$C_1=0.905+0.783\cdot\sqrt{t/r}-0.075\cdot t/r$$
$C_1=0.905+0.783\cdot\sqrt{t/r}-0.075\cdot t/r$
Equations in LaTeX code
C_1=0.905+0.783\cdot\sqrt{t/r}-0.075\cdot t/r

Coefficient $ C_2 $

$$C_2=-0.437-1.969\cdot\sqrt{t/r}+0.553\cdot t/r$$
$C_2=-0.437-1.969\cdot\sqrt{t/r}+0.553\cdot t/r$
Equations in LaTeX code
C_2=-0.437-1.969\cdot\sqrt{t/r}+0.553\cdot t/r

Coefficient $ C_3 $

$$C_3=1.557+1.073\cdot\sqrt{t/r}-0.578\cdot t/r$$
$C_3=1.557+1.073\cdot\sqrt{t/r}-0.578\cdot t/r$
Equations in LaTeX code
C_3=1.557+1.073\cdot\sqrt{t/r}-0.578\cdot t/r

Coefficient $ C_4 $

$$C_4=-1.061+0.171\cdot\sqrt{t/r}+0.086\cdot t/r$$
$C_4=-1.061+0.171\cdot\sqrt{t/r}+0.086\cdot t/r$
Equations in LaTeX code
C_4=-1.061+0.171\cdot\sqrt{t/r}+0.086\cdot t/r

Stress concentration factor

$$K_t=C_1+C_2\cdot\left(\cfrac{2\cdot t}{D}\right)+C_3\cdot\left(\cfrac{2\cdot t}{D}\right)^2+C_4\cdot\left(\cfrac{2\cdot t}{D}\right)^3$$
$K_t=C_1+C_2\cdot\left(\cfrac{2\cdot t}{D}\right)+C_3\cdot\left(\cfrac{2\cdot t}{D}\right)^2+C_4\cdot\left(\cfrac{2\cdot t}{D}\right)^3$
Equations in LaTeX code
K_t=C_1+C_2\cdot\left(\cfrac{2\cdot t}{D}\right)+C_3\cdot\left(\cfrac{2\cdot t}{D}\right)^2+C_4\cdot\left(\cfrac{2\cdot t}{D}\right)^3

Nominal or reference normal stress

$$σ_{nom}=\cfrac{16\cdot T\cdot 10^3}{π\cdot d^3}$$
$σ_{nom}=\cfrac{16\cdot T\cdot 10^3}{π\cdot d^3}$
Equations in LaTeX code
σ_{nom}=\cfrac{16\cdot T\cdot 10^3}{π\cdot d^3}

Maximum normal stress

$$σ_{max}=K_t\cdot σ_{nom}$$
$σ_{max}=K_t\cdot σ_{nom}$
Equations in LaTeX code
σ_{max}=K_t\cdot σ_{nom}
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