Answer
The number of waves $N$ is inversely proportional to the operating stress for a given deflection. The bending stress $\sigma$ is calculated by $\sigma = \frac{3 \pi P D}{4 N^2 b t^2}$, where $P$ is the load and $D$ is the mean diameter. Increasing $N$ reduces the stress at a specific load point because the total deflection is distributed across more contact points, effectively shortening the beam length between peaks. However, increasing $N$ also increases the spring rate $K$ exponentially ($N^4$), which can lead to a very stiff spring. For fatigue-critical applications, such as automotive clutch packs, $N$ is optimized to keep the alternating stress amplitude below the endurance limit of the material, typically $SAE 1070-1090$ carbon steel, while maintaining the required clamp force.
