Answer
In a single-turn overlap wave spring, the number of waves $N$ significantly affects the spring constant $k$ and the stress distribution. According to the formula $k ∝ N^4$, small changes in $N$ lead to exponential changes in stiffness. For high-precision applications, a higher wave count (e.g., $N=5$ or $7$) produces a more stable and linear rate because it increases the number of contact points, thereby reducing the span between waves and minimizing the bending moment $M = \frac{P D_m}{4 N}$. However, as $N$ increases, the allowable deflection before the waves begin to interfere with each other (clashing) decreases. Designers must balance $N$ to achieve the required load while maintaining a safe operating stress below the elastic limit $\sigma_e = \frac{3 π P D_m}{4 b t^2 N^2}$.
