Answer
The 'cling' force is the radial pressure the ring exerts on the groove bottom, ensuring it doesn't rotate or vibrate. This is a function of the 'Free Diameter' ($D_f$) being smaller than the 'Groove Diameter' ($D_g$). The radial pressure $q$ is given by $q = \frac{E I (D_g - D_f)}{R^2 D_g D_f}$. Since $I = \frac{b t^3}{12}$, the cling force is directly proportional to the cube of the material thickness $t$. For applications with high vibration (e.g., automotive transmissions), a thicker ring or a larger 'under-size' on $D_f$ is required to increase the cling. However, this also increases the installation stress $\sigma = \frac{E t c}{2 R^2}$, where $c$ is the radial expansion required. Designers must solve these coupled equations to ensure the ring stays put without snapping during assembly.
