Answer
Fatigue failure in wave springs is analyzed by evaluating the alternating stress $\sigma_a$ and the mean stress $\sigma_m$. Using the Modified Goodman equation: $\sigma_a / S_e + \sigma_m / S_{ut} = 1/n$, where $S_e$ is the endurance limit and $S_{ut}$ is the ultimate tensile strength. In a clutch application, the spring cycles between a preload height $H_1$ and an operating height $H_2$. If the calculated stress at $H_2$ exceeds the fatigue limit of the material (e.g., SAE 9254 or 17-7PH), micro-cracks initiate at the inner diameter where tensile stresses are highest during compression. Failure analysis usually reveals 'beach marks' or striations indicative of cyclic loading. Mitigation involves increasing the number of waves $n$ to reduce the stress per wave or utilizing a shot-peening process to induce compressive residual stresses on the surface.
