What is the impact of the 'radial expansion' phenomenon on the design of a wave spring operating in a tight bore?

As a wave spring is compressed from its free height $H_f$ toward its solid height $H_s$, the waves flatten, causing the mean diameter $D_m$ to expand. This radial expansion can be approximated by $ riangle OD = 0.045 imes _x000c_rac{w^2 imes f}{D_m}$, where $w$ is the wave height and $f$ is the deflection per wave. In high-precision aerospace valves, ignoring this expansion leads to 'bore binding,' where the spring OD interferes with the housing ID. This creates parasitic friction, hysteresis in the load-deflection curve, and potential mechanical galling. Engineers must specify a clearance ratio, typically ensuring the housing $ID > OD_{max}$ at the full work height.