Answer
The maximum tensile stress $\sigma$ at the crest of a wave spring is expressed by $\sigma = _x000c_rac{3 imes au imes P imes D_m}{b imes t^2 imes N^2}$ where $P$ is the load. However, standard linear beam theory often under-predicts stress due to the curvature of the ribbon. A correction factor $K$, derived from the ratio of $D_{out}/D_{in}$, is applied. As the $D_{out}/D_{in}$ ratio increases, the stress concentration at the inner diameter of the wave crest increases. In high-cycle fatigue applications (e.g., automotive transmissions), if the calculated stress exceeds the minimum tensile strength of the material (e.g., $200,000$ PSI for Carbon Steel SAE 1070), the spring will suffer from permanent set or fatigue failure. We typically design for a maximum stress of 80% of yield for static applications and 50% for dynamic applications.
