Answer
The Goodman Diagram correlates the mean stress ($\sigma_m$) and alternating stress ($\sigma_a$) to the material's ultimate tensile strength ($S_u$) and endurance limit ($S_e$). For a wave spring, $\sigma_m = _x000c_rac{\sigma_{max} + \sigma_{min}}{2}$ and $\sigma_a = _x000c_rac{\sigma_{max} - \sigma_{min}}{2}$. The spring is considered safe for infinite life if $_x000c_rac{\sigma_a}{S_e} + _x000c_rac{\sigma_m}{S_u} < 1$. In high-frequency applications, such as fuel injectors, failure often occurs due to surface micro-cracks at the wave peaks. Shot peening is frequently employed to introduce compressive residual stresses on the surface, effectively shifting the operating point lower on the Goodman Diagram and extending the number of cycles before crack initiation.
