Answer
The number of waves $n$ is a primary determinant of both the spring rate and the stability of the contact interface. The spring rate $k$ scales with $n^4$, meaning small changes in the wave count result in significant load variations. In subsea actuators where consistent seal preload is required, a minimum of $n=3$ is necessary for 3-point stability. Increasing $n$ reduces the individual wave amplitude required for a given total height, which minimizes the bending stress per wave $\sigma_w$. However, a very high $n$ results in a very stiff spring that is sensitive to manufacturing tolerances. The stability against buckling for multi-turn springs is assessed by the ratio of free height to mean diameter ($H_f/D_m$); if this ratio exceeds 1.5, internal or external guidance (a shaft or bore) is mandatory to prevent lateral shifting during the $P = k \cdot x$ linear range.
