Answer
Parallelism between the two surfaces compressing a wave spring is critical for uniform load distribution. If the surfaces are non-parallel by an angle $\theta$, the waves on one side of the spring will be compressed more than those on the opposite side. This creates an eccentric load, leading to a tilting moment $M = P \cdot e$. The peak stress on the 'high' side can be calculated as $\sigma_{max} = \sigma_{nominal} \cdot (1 + (6 \cdot e / D_m))$, where $e$ is the eccentricity. This non-uniform loading leads to premature fatigue failure and can cause the spring to shift radially, potentially scuffing the shaft or housing. For critical applications, mating surfaces should be ground to a parallelism within $0.05$ mm.