Answer
Installation stress occurs when the ring is expanded over a shaft or contracted into a bore. The stress is calculated as $\sigma_{inst} = _x000c_rac{4 imes E imes t imes ext{Expansion}}{D_m^2}$. This stress must not exceed the yield strength of the material to avoid permanent deformation. The 'Modulus of Resilience' ($U_r = _x000c_rac{\sigma_y^2}{2E}$) represents the material's ability to absorb energy elastically. A material with a high $U_r$, like 17-7PH, can be expanded significantly more than a material with a lower $U_r$, like 316 Stainless, before taking a set. If the required expansion for installation exceeds the material's elastic limit, the ring must be designed with a larger free diameter or a multi-turn configuration to distribute the strain.
