Answer
If the operating frequency of a compressor matches the natural frequency of the wave spring, resonance occurs, leading to amplitude magnification and stresses far exceeding the design limit. The first natural frequency $f_n$ of a wave spring is $f_n = \frac{1}{2 \pi} \sqrt{\frac{k}{m_{eff}}}$, where $k$ is the spring rate and $m_{eff}$ is the effective mass. Failure is typically characterized by a clean, 45-degree fatigue fracture at the peak or valley of the wave. To troubleshoot, one must either change the spring rate (by altering $t$ or $Z$) to shift the $f_n$ away from the operating frequency or introduce damping into the system. Crest-to-Crest springs have lower natural frequencies than single-turn springs and are more susceptible to this in high-speed machinery.
