Answer
In high-speed rotating shafts, centrifugal force acts on the mass of the retaining ring, attempting to expand it radially. If the centrifugal force exceeds the 'cling' or radial grip of the ring on the groove bottom, the ring will lift out of the groove, leading to catastrophic assembly failure. The maximum RPM ($N_{max}$) is calculated by balancing the centrifugal force against the ring's elastic grip: $N_{max} = _x000c_rac{70.4}{D_m} imes _x000c_rac{E imes I imes ext{Grip}}{_x000d_ho imes A imes R_m^3}$, where $_x000d_ho$ is the material density and $I$ is the moment of inertia. For ultra-high RPMs, engineers specify a 'self-locking' feature where a tab on the inner turn interlocks with a slot on the outer turn, mechanically preventing the ring from expanding.
