What is the relationship between 'Wave Number' ($n$) and the 'Bending Stress' for a constant load $P$?

The bending stress $\sigma$ in a wave spring is given by $\sigma = (6 \cdot P \cdot D_m) / (n^2 \cdot b \cdot t^2)$. This formula shows that the stress is inversely proportional to the square of the number of waves $n$. By increasing the number of waves, the load $P$ is distributed across more points of contact, which significantly reduces the stress in the material for a given deflection. However, increasing $n$ also increases the spring rate $k$ by the fourth power ($k \propto n^4$), making the spring much stiffer. Designers must optimize $n$ to achieve the required force while keeping the stress level below the yield strength (for static) or the fatigue limit (for dynamic) of the material.