Answer
The process of edge-coiling a spiral ring involves significant plastic deformation, which leaves high residual tensile stresses on the outer edges and compressive stresses on the inner edges. Without stress relieving, these residual stresses can lead to 'warping' or dimensional instability over time. Stress relieving carbon steel at $650^{\circ}F$ to $750^{\circ}F$ for 30 minutes allows for the relaxation of these internal stresses without significantly reducing the hardness achieved during the previous heat treatment. This ensures that the ring maintains its free diameter and flatness, which are critical for proper seating in the groove and for achieving the calculated 'cling' force.