Answer
A tapered mandrel is used to expand an external spiral ring so it can be slid over a shaft and into a groove. The mandrel's major diameter should be approximately $1\%$ to $2\%$ larger than the shaft diameter, and the 'taper' or angle should be shallow (typically $10^\circ$ to $15^\circ$) to prevent over-stressing the ring. The ring is pushed down the mandrel using a plunger or sleeve. The critical design parameter is the 'Maximum Expansion Limit.' The ring should never be expanded such that the ID exceeds $D_{free} + (\sigma_y D_f^2 / E b)$, where $\sigma_y$ is the yield strength. Exceeding this limit will cause the ring to take a permanent set, resulting in a loose fit in the groove. For automated assembly, the mandrel surface must be hardened and polished to minimize friction and prevent scratching the ring's surface.
