Answer
Wave springs in transmission systems or actuators undergo dynamic cyclic deflection between a minimum stress ($\%S_{min}$) and a maximum stress ($\%S_{max}$). The Goodman Fatigue Diagram plots Mean Stress ($S_m$) on the X-axis against Alternating Stress ($S_a$) on the Y-axis:
$$S_m = \frac{S_{max} + S_{min}}{2}$$
$$S_a = \frac{S_{max} - S_{min}}{2}$$
Fatigue Life Estimation Steps:
1. Plot the point $(S_m, S_a)$ on the modified Goodman Diagram for the specific material (e.g., carbon steel wire or 17-7PH).
2. If the operating stress point lies comfortably below the material-specific Goodman endurance limit boundary line, the spring is calculated to achieve infinite life ($> 10^6$ cycles).
3. If the point lies above the boundary line, fatigue failure is highly probable, requiring engineers to either adjust the minimum preload (reducing alternating stress $S_a$) or select a thicker, multi-turn design to distribute load and lower localized peak stresses.
