Answer
Fatigue life estimation for wave springs involves calculating the alternating stress $\sigma_a$ and the mean stress $\sigma_m$. For a wave spring, the maximum stress occurs at the wave peaks and is given by $\sigma = \frac{3 \cdot π \cdot E \cdot t \cdot N^2 \cdot f}{4 \cdot D_m^2 \cdot n}$. Using the Goodman relation $\frac{\sigma_a}{\sigma_e} + \frac{\sigma_m}{\sigma_{ut}} = 1$, where $\sigma_e$ is the endurance limit and $\sigma_{ut}$ is the ultimate tensile strength (approx. 1650 MPa for 17-7PH CH900), engineers can determine if the spring will survive $10^6$ cycles. In high-cycle applications like medical pumps, we aim for a safety factor $S_f > 1.2$. Residual stresses from the coiling process must be relieved via heat treatment at $480^∘C$ to ensure the mean stress does not shift during service.
