Stress Rotation Disc Ring Body

The stress ( $\sigma_z$ ) induced in a solid rotating disc is given by: $\sigma_z = \frac{\omega^2 r^2 \rho}{3} = \frac{v^2 \rho}{3} = \frac{(2 \pi n / 60)^2 r^2 \rho}{3}$

Variables:

$\sigma_z$ : Stress (Pa, N/m²)
$\omega$ : Angular velocity (rad/s)
$r$ : Radius of the disc (m)
$\rho$ : Density of the material (kg/m³)
$v$ : Tangential velocity ( $v = \omega r$ , m/s)
$n$ : Rotational speed (revolutions per minute, rpm)

Stress in a Rotating Ring

For a rotating ring with an inner radius $r_2$ and outer radius $r_1$ , the stress ( $\sigma_z$ ) is: $\sigma_z = \frac{\omega^2 \rho (r_1^2 + r_1 r_2 + r_2^2)}{3}$

For a thin ring, where the wall thickness is small compared to the mean radius $r = (r_1 + r_2)/2$ , this simplifies to: $\sigma_z = \omega^2 \rho r^2$

Variables:

$r_1$ : Outer radius of the ring (m)
$r_2$ : Inner radius of the ring (m)
$r$ : Mean radius of a thin ring (m)

Interactive Charts

References

Original Source