Official Answer
Answer
As a Crest-to-Crest wave spring is compressed toward its solid height, the mean diameter $D_m$ increases due to the flattening of the waves. The standard spring rate formula $k = \frac{E b t^3 N^4}{1.23 D_m^3 Z}$ assumes a constant diameter. In reality, the increased $D_m$ leads to a non-linear softening effect initially, followed by a sharp hardening as the waves approach the solid state. Engineers must account for this by using an adjusted mean diameter $D_{adj} = D_m + (f \cdot \tan(\theta))$ where $f$ is deflection and $\theta$ is the wave angle. Failure to account for this in precision aerospace valves can lead to incorrect cracking pressures.
