Official Answer
Answer
The spring rate $k$ for a multi-turn Crest-to-Crest wave spring is derived from the beam theory applied to curved segments. The standard formula is $k = \frac{E b t^3 N^4}{4 D_m^3 n}$, where $E$ is the Modulus of Elasticity, $b$ is the radial wall width, $t$ is the material thickness, $N$ is the number of waves per turn, $D_m$ is the mean diameter, and $n$ is the number of turns. In this configuration, the turns act as springs in series, which is why the rate is inversely proportional to $n$. Engineers must ensure the deflection does not exceed the linear range, typically defined as $80\%$ of the available travel to avoid wave nesting or 'bottoming out' which causes a non-linear spike in force.
