Answer
The natural frequency $
u$ of a wave spring is critical to avoid resonance. It is calculated as $
u_n = \frac{1}{2 \pi} \sqrt{\frac{k g}{W}}$, where $k$ is the spring rate and $W$ is the weight of the active portion of the spring. In high-speed valve-trains, if the valve's operating frequency or any of its harmonics match $
u_n$, the spring will undergo 'resonance surging'. This results in a drastic loss of load and high-amplitude oscillations that can cause the waves to clash and fail via rapid fatigue. To increase the natural frequency, a designer can increase the spring rate (by increasing $t$ or $b$) or decrease the mass. Wave springs are often preferred over coil springs in these applications because they can achieve the same rate with significantly less mass, resulting in a higher $
u_n$.
