Official Answer
Answer
The total axial displacement $\delta_{total}$ is the sum of the initial clearance, the ring deflection, and the groove deformation. $\delta_{total} = (W - t) + \frac{P}{k_{ring}} + \frac{P}{k_{groove}}$, where $W$ is the groove width and $t$ is the ring thickness. If the groove is too wide, the ring can 'tilt', which increases the effective clearance and reduces the contact area. This tilting leads to a non-uniform pressure distribution $p(x)$, which can exceed the yield strength of the housing at the outer edge. For precision assemblies, 'end-play' is minimized by using thicker rings or shims to achieve a 'snug' fit.
