What are the critical bore and shaft clearance requirements to prevent 'binding' during wave spring compression?

As a wave spring is compressed, its mean diameter $D_m$ expands. The theoretical expansion $\Delta D$ can be estimated as $\Delta D = \frac{0.05 f^2}{D_m Z^2}$, where $f$ is the deflection. If the clearance between the spring's Outer Diameter ($OD$) and the housing bore is insufficient, the spring will bind, leading to an erratic spring rate and potential localized buckling. For a standard internal application, the bore diameter should be at least $102-105\%$ of the spring's free $OD$. Similarly, for external applications over a shaft, the shaft diameter should be at most $95-98\%$ of the spring's free $ID$. These clearances also provide the necessary volume for lubricants in high-speed rotating assemblies like clutch packs.