Answer
The spring rate $k$ for a multi-turn Crest-to-Crest wave spring is derived from the formula $k = _x000c_rac{E b t^3 N^4}{I D^3 n}$ where $E$ is the Modulus of Elasticity, $b$ is the radial width, $t$ is the material thickness, $N$ is the number of waves per turn, $D$ is the mean diameter, and $n$ is the number of turns. The factor $I$ represents a constant derived from the ratio of the spring diameter to the radial wall. Discrepancies between theoretical and actual rates typically arise from the 'active' versus 'inactive' wave count at the end turns. As the spring is compressed, the contact area at the crests increases, effectively shortening the active length and leading to a non-linear increase in rate, often referred to as the 'bottoming effect' when approaching solid height.
