# Split hollow shift

## Values for calculation

$T$ $\mathrm{Nm}$
$r_o$ $\mathrm{mm}$
$r_i$ $\mathrm{mm}$
$h$ $\mathrm{mm}$
$L$ $\mathrm{mm}$
$G$ $\mathrm{MPa}$

## Calculation

### Coefficient $C_1$

$$C_1=0.4427+0.0064\cdot\cfrac{h}{r_i}-0.0201\cdot\left(\cfrac{h}{r_i}\right)^2$$

### Coefficient $C_2$

$$C_2=-0.8071-0.4047\cdot\cfrac{h}{r_i}+0.1051\cdot\left(\cfrac{h}{r_i}\right)^2$$

### Coefficient $C_3$

$$C_3=-0.0469+1.2063\cdot\cfrac{h}{r_i}-0.3538\cdot\left(\cfrac{h}{r_i}\right)^2$$

### Coefficient $C_4$

$$C_4=0.5023-0.9618\cdot\cfrac{h}{r_i}+0.3639\cdot\left(\cfrac{h}{r_i}\right)^2$$

### Coefficient $C$

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

### Coefficient $B_1$

$$B_1=2.0014-0.14\cdot\cfrac{h}{r_i}-0.3231\cdot\left(\cfrac{h}{r_i}\right)^2$$

### Coefficient $B_2$

$$B_2=2.9047+3.0069\cdot\cfrac{h}{r_i}-4.05\cdot\left(\cfrac{h}{r_i}\right)^2$$

### Coefficient $B_3$

$$B_3=-15.721-6.5077\cdot\cfrac{h}{r_i}-12.496\cdot\left(\cfrac{h}{r_i}\right)^2$$

### Coefficient $B_4$

$$B_4=29.553+4.1115\cdot\cfrac{h}{r_i}+18.845\cdot\left(\cfrac{h}{r_i}\right)^2$$

### Coefficient $B$

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

### Polar moment of inertia

$$K=2\cdot C\cdot r_o^4$$

### Angle of twist

$$θ=\cfrac{T\cdot 10^3\cdot L}{K\cdot G}$$

### Torsion stress at $M$

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

## Requirements

$$0.2 \le\cfrac{r_i}{r_o} \le 0.6$$$$0.1 \le\cfrac{h}{r_i} \le 1$$