# Shaft with one keyway

## Values for calculation

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

## Calculation

### Coefficient $C_1$

$$C_1=0.7854$$

### Coefficient $C_2$

$$C_2=-0.0848+0.1234\cdot\cfrac{a}{b}-0.0847\cdot\left(\cfrac{a}{b}\right)^2$$

### Coefficient $C_3$

$$C_3=-0.4318+2.2\cdot\cfrac{a}{b}+0.7633\cdot\left(\cfrac{a}{b}\right)^2$$

### Coefficient $C_4$

$$C_4=-0.078+2.0618\cdot\cfrac{a}{b}-0.5234\cdot\left(\cfrac{a}{b}\right)^2$$

### Coefficient $C$

$$C=C_1+C_2\cdot\cfrac{b}{r}+C_3\cdot\left(\cfrac{b}{r}\right)^2+C_4\cdot\left(\cfrac{b}{r}\right)^3$$

### Coefficient $B_1$

$$B_1=1.169-0.3168\cdot\cfrac{a}{b}+0.049\cdot\left(\cfrac{a}{b}\right)^2$$

### Coefficient $B_2$

$$B_2=0.4349-1.5096\cdot\cfrac{a}{b}+0.8677\cdot\left(\cfrac{a}{b}\right)^2$$

### Coefficient $B_3$

$$B_3=-1.183+4.2764\cdot\cfrac{a}{b}-1.7024\cdot\left(\cfrac{a}{b}\right)^2$$

### Coefficient $B_4$

$$B_4=0.8812-0.2627\cdot\cfrac{a}{b}-0.1897\cdot\left(\cfrac{a}{b}\right)^2$$

### Coefficient $B$

$$B=B_1+B_2\cdot\cfrac{b}{r}+B_3\cdot\left(\cfrac{b}{r}\right)^2+B_4\cdot\left(\cfrac{b}{r}\right)^3$$

### 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 at $M$

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

## Requirements

$$0.2 \le\cfrac{b}{r} \le 0.5$$$$0.5 \le\cfrac{a}{b} \le 1.5$$