How does the 'Expansion and Contraction' of a wave spring diameter during compression affect the housing and shaft clearances?

When a wave spring is compressed from its free height to an operating height, the waves flatten, causing the mean diameter $D_m$ to expand. This expansion follows the geometric relationship where the developed length of the wave must be conserved. For a spring in a bore, the expansion $\Delta D$ can be approximated. If the clearance between the spring $D_{out}$ and the housing $D_{bore}$ is insufficient, the spring will bind, leading to an unpredictable increase in spring rate and potential scoring of the housing walls. In high-speed rotating equipment, this binding can also cause thermal expansion issues. Designers must ensure that $D_{out(max)} + \text{expansion} < D_{bore(min)}$ at the minimum operating height.