Answer
Nested wave springs are produced by coiling multiple layers of the same wire in parallel, whereas Crest-to-Crest springs are coiled in series. The primary advantage of a nested spring is that the spring rate $K$ increases linearly with the number of turns $n$ (layers), expressed as $K_{total} = n \times K_{single}$. This allows for extremely high loads in very tight axial spaces where a single-turn spring would fail due to over-stressing. Mathematically, while a Crest-to-Crest spring increases deflection for a given load, a nested spring increases load for a given deflection. In subsea valve actuators, nested springs are used to provide thousands of Newtons of force with a stack height that is a fraction of what a traditional coil spring would require, though they are more susceptible to internal friction and galling between layers.
