Answer
The natural frequency $f_n$ of a wave spring is critical in high-speed automotive transmissions to avoid resonance-induced fatigue. The fundamental frequency is given by $f_n = \frac{1}{2 \pi} \sqrt{\frac{K g}{W}}$, where $K$ is the spring rate, $g$ is the gravitational constant, and $W$ is the weight of the spring. Because wave springs have a much lower mass than traditional coil springs, their natural frequency is significantly higher, often moving the resonance point outside the operating range of the machinery. However, for multi-turn springs, the individual turns can also exhibit local vibration modes. Engineers use Finite Element Analysis (FEA) to verify that the excitation frequency of the system does not align with the first or second harmonic of the spring, which would otherwise cause 'wave jumping' and premature failure.
