What are the critical groove geometry requirements to prevent 'rolling' of a spiral retaining ring under thrust load?

'Rolling' or 'dishing' of a spiral ring occurs when the thrust load causes the ring to twist, leading to premature ejection. To prevent this, the groove must have a sharp corner (maximum radius of $10\%$ of material thickness $t$) and a sufficiently deep wall. The 'Groove Deformation' load $P_g$ is often the limiting factor rather than the 'Ring Shear' load $P_r$. $P_g$ is calculated using $P_g = \frac{D \pi G S_y}{K}$, where $G$ is groove depth, $D$ is shaft/bore diameter, $S_y$ is the yield strength of the groove material, and $K$ is a safety factor (usually 2.0). If the housing is a soft material like aluminum, a wider groove and thicker ring are mandatory.