Answer
The maximum RPM $N$ for a spiral retaining ring is limited by the point where centrifugal forces overcome the ring's radial cling on the groove bottom. The formula is $N = \sqrt{(448 \cdot E \cdot I \cdot g) / (\rho \cdot A \cdot R_m^3 \cdot (R_o - R_i))}$ where $E$ is the modulus, $I$ is the moment of inertia, $g$ is gravity, $\rho$ is material density, and $R_m$ is the mean radius. As the ring rotates, the center of mass generates a radial force $F_c = m \cdot \omega^2 \cdot r$. For external rings, this force acts to expand the ring. Engineering designs must ensure a safety factor of at least $2.0$ relative to the operating RPM. If the calculated limit is exceeded, designers should specify a 'Self-Locking' feature, which utilizes a tab-and-slot mechanism to mechanically prevent diameter expansion under high angular velocity.
