Explain the calculation for the expansion/contraction limit of a spiral ring during installation.

Spiral rings are installed by winding them into a groove. The stress during expansion (for external rings) or contraction (for internal rings) must remain below the material's yield strength to avoid permanent deformation. The maximum fiber stress during installation is $\sigma_{inst} = \frac{E imes t imes (D_g - D_f)}{D_g imes D_f}$, where $D_g$ is the groove diameter and $D_f$ is the free diameter. If $\sigma_{inst} > S_y$, the ring will not return to its original shape, resulting in a loose fit. For 302 Stainless Steel rings, the maximum allowable expansion is typically limited to $1\%$ to $2\%$ of the diameter to maintain a 'snug' fit.