What is the 'centrifugal capacity' and how is it calculated for high-speed shaft rings?

Centrifugal force acts to expand a spiral retaining ring, which can cause it to lift out of its groove at high RPMs. The limiting speed is calculated by $N = \sqrt{\frac{4.48 \cdot 10^{12} E t^2}{\gamma D_m^4}}$, where $t$ is the material thickness and $\gamma$ is the density. If the operating RPM exceeds this value, the ring's 'cling' on the groove is lost. To counter this, engineers specify 'self-locking' rings, which feature a small tab that mechanically locks the layers of the spiral together, preventing expansion. This is standard in aerospace turbine assemblies where rotational speeds can exceed 50,000 RPM.