Answer
To prevent rolling failure, the groove depth $d$ must be sufficient to ensure the ring remains seated even when subjected to the maximum expected thrust load. The rule of thumb is that the ring should be seated at least $1/3$ to $1/2$ of its radial wall thickness $b$ into the groove. Mathematically, the stability is governed by the ratio of the groove depth to the ring's thickness. For a standard safety factor of $2.0$, the minimum groove depth $d_{min}$ is calculated based on the groove material's yield strength $\sigma_y$ and the thrust load $P$: $d_{min} = (P \cdot S) / (D \cdot \pi \cdot \sigma_y)$. In soft materials like plastics or aluminum, the groove must be significantly deeper than in hardened steel to prevent the material from shearing or 'plowing' under the ring's edge.
