Answer
In advanced wave spring design, the linear approximation of load $P = k · f$ fails as deflection $f$ exceeds 80% of the available work stroke. The L-factor, or the non-linearity correction, accounts for the change in the wave geometry and the shifting contact points. As the spring is compressed, the radius of curvature at the crests changes, effectively shortening the moment arm. The revised stress formula becomes $\sigma = \frac{3 · π · P · D_m}{4 · b · t^2 · n^2}$. If the spring is designed near its elastic limit, this non-linearity can lead to permanent set, especially in materials like SAE 1070 carbon steel. Designers must use Finite Element Analysis (FEA) to map the stress distribution across the wave peak and valley to ensure the maximum fiber stress does not exceed the minimum yield strength $\sigma_y$ of the material.
