Answer
The spring rate $k$ for a crest-to-crest wave spring is governed by the number of turns $N$, the number of waves per turn $n$, and the material properties. The standard formula for the rate is $k = \frac{E \cdot b \cdot t^3 \cdot n^4}{I_d \cdot D_m^3 \cdot N}$, where $E$ is the Modulus of Elasticity, $b$ is the radial wall, $t$ is the material thickness, and $D_m$ is the mean diameter. The factor $I_d$ is a correction factor for the curvature. In high-precision applications, the addition of shim ends increases the rate and provides a 360-degree contact surface, reducing the effective active number of waves. The designer must account for the transition from the inactive shim to the active wave, which typically involves a linearity correction of 5-10% in the load-deflection curve as the spring approaches its solid height.
