Explain the phenomenon of radial expansion in wave springs during compression and its impact on housing bore clearance.

As a wave spring is compressed from its free height $H$ to a working height $H_w$, the waves flatten, causing the mean diameter $D_m$ to expand. The expansion $\Delta D$ can be approximated by $\Delta D = \frac{0.051(h^2 - t^2)N^2}{D_m}$. If the clearance between the spring's Outer Diameter (OD) and the housing bore is insufficient, the spring will bind, leading to an exponential increase in spring rate and potential permanent deformation. Engineers must specify a bore diameter $D_{bore} > OD_{max} + \Delta D$ to ensure the spring functions as a simple beam without secondary radial constraints.