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. It is expressed as $K = \frac{E b t^3 N}{D_m^3 n} \times \frac{ID}{OD}$, where $E$ is the Young's Modulus, $b$ is the radial wall, $t$ is the thickness, $N$ is the number of waves per turn, $n$ is the number of turns, and $D_m$ is the mean diameter. To ensure structural integrity, the operating stress $S$ must be calculated using $S = \frac{3 \pi P D_m}{4 N b t^2}$, where $P$ is the applied load. In aerospace applications, we typically target an operating stress below 80 percent of the minimum tensile strength for 17-7PH CH900 to prevent premature fatigue failure.
