Official Answer
Answer
The number of waves $N$ has a dramatic effect on the spring's performance. The spring rate $k$ is proportional to $N^4$ ($k \propto \frac{E \cdot b \cdot t^3 \cdot N^4}{D_m^3}$). Adding waves significantly increases the stiffness. However, as $N$ increases, the allowable deflection $f$ decreases because the physical distance between wave crests becomes smaller, leading to steeper wave angles and higher bending stresses for the same amount of deflection. The stress $S$ is proportional to $1/N^2$. Therefore, a spring with more waves can carry a higher load $P$ but at the cost of reduced travel. Engineers must balance $N$ to achieve the required force $P$ within the available axial space without exceeding the material's yield strength.
