Official Answer
Answer
The radial expansion $\Delta r$ of a retaining ring due to rotation is given by $\Delta r = \frac{\rho \cdot \omega^2 \cdot R^3}{E}$, where $\rho$ is the density, $\omega$ is the angular velocity, and $R$ is the mean radius. The ring will fail when $\Delta r$ exceeds the groove depth $d$. More specifically, the maximum speed $N$ (in RPM) is calculated as $N = \sqrt{\frac{440 \times 10^6 \cdot E \cdot I}{w \cdot \rho \cdot R^4}}$, assuming the ring is made of steel. If the application requires a speed higher than this limit, a 'Self-Locking' ring or a heavier cross-section ring must be used. Additionally, the fit must be tight; a loose ring will start to expand at a lower RPM than a ring with high initial 'cling' (interference).
