What is the governing equation for the 'Thrust Capacity' of a spiral retaining ring based on groove material shear?

The thrust capacity is often limited by the shear strength of the groove material rather than the ring itself. The allowable thrust load $P_g$ is given by $P_g = \frac{D imes d imes ext{\pi} imes S_y}{K}$, where $D$ is the shaft/bore diameter, $d$ is the groove depth, $S_y$ is the yield strength of the groove material, and $K$ is a safety factor (typically 2). If the groove material is soft (e.g., aluminum), the groove wall will yield and deform ('dish'), causing the ring to 'pop out' under load. In such cases, increasing the groove depth or using a harder housing material is necessary to meet the axial load requirements.