Explain the influence of the number of waves $N$ on the load capacity and stability of a nested wave spring.

In nested wave springs, the total load $P_{total}$ is the sum of the loads of individual turns, but the number of waves $N$ per turn dictates the stability and the spring rate $k$. A higher $N$ increases the spring rate proportionally to $N^4$, allowing for very high loads in small axial spaces. However, a high $N$ also reduces the wave amplitude, which can lead to manufacturing tolerances having a greater percentage impact on load accuracy. For stability, $N$ must be an integer or a half-integer (e.g., 3.5, 4.5) to ensure proper crest-to-crest alignment and prevent 'shingling' where the turns slide over one another.