Official Answer
Answer
The maximum rotational speed $N$ at which an external ring will lose its grip on the shaft is given by $N = _x000c_rac{1}{R_m} imes ext{√}(_x000c_rac{4 E I g (D_G - D_I)}{w _x000d_ho A R_m^3})$ where $E$ is the modulus, $I$ is the moment of inertia, $D_G$ is the groove diameter, $D_I$ is the ring inner diameter, $w$ is the material width, $_x000d_ho$ is the density, and $A$ is the cross-sectional area. As the shaft rotates, centrifugal force acts on the ring's mass, causing it to expand. If the expansion exceeds the interference fit (the 'cling'), the ring leaves the groove. For high-speed applications, engineers specify 'Self-Locking' spiral rings, which feature a tab-and-slot mechanism to mechanically prevent expansion.
