Official Answer
Answer
Centrifugal forces at high RPM can cause a spiral retaining ring to expand and lift out of its groove. The maximum allowable speed $N_{max}$ (in RPM) is calculated using $N_{max} = \sqrt{\frac{4.48 \times 10^{12} E I (D_g - D_i)}{\mu R_m^3 (D_g^2 - D_i^2)}}$, where $D_g$ is the groove diameter, $D_i$ is the free inside diameter, $R_m$ is the mean radius, and $\mu$ is the mass per unit length. This limit is reached when the centrifugal expansion equals the initial interference fit (pre-stress) of the ring in the groove. For high-speed gearbox applications, engineers often specify a 'heavy-duty' ring or a self-locking feature (tab and slot) that mechanically prevents the ring from expanding under these inertial loads.
