Official Answer
Answer
The expansion limit for an external ring is the maximum diameter it can be stretched to without permanent set. The maximum stress during expansion is $\sigma_{exp} = (E \cdot t \cdot (D_s - D_i)) / (D_i^2)$, where $D_s$ is the shaft diameter and $D_i$ is the ring's free inner diameter. If $\sigma_{exp}$ exceeds the yield strength $\sigma_y$ of the material (e.g., SAE 1070), the ring will not return to its original shape and will lose its grip on the groove. This is why spiral rings are often manufactured with multiple turns; two or three thinner turns can provide the same total thickness $T$ as a single heavy turn but with significantly lower individual stress $t$ during installation, allowing for much greater expansion ratios.
