Official Answer
Answer
The number of waves $N$ is inversely proportional to the deflection and directly proportional to the cube of the load capacity. Specifically, the load $P$ is proportional to $N^4$. However, increasing $N$ reduces the arc length between peaks, which increases the stiffness but can lead to manufacturing difficulties and higher stress concentrations at the peaks. For stability, $N$ should be an integer or half-integer to ensure uniform load distribution. In applications with rotating shafts, an odd number of waves is often preferred to avoid harmonic resonance with the shaft's rotational frequency, especially when the operating speed approaches the spring's natural frequency $f_n = \frac{1}{2π}\sqrt{\frac{k}{m}}$.
