Answer
The coiling process introduces significant internal stresses into the flat wire. Without stress relieving, the ring will exhibit 'creep' or dimensional instability, potentially expanding or contracting in storage or service. Stress relieving is typically performed at temperatures between $600^{\circ}F$ and $900^{\circ}F$ depending on the alloy. This thermal cycle stabilizes the microstructure, ensures the ring maintains its specified free diameter, and optimizes the elastic limit. For multi-turn rings, it also ensures that the layers stay tightly nested without gaps.