Critical Speed

A shaft whirls when it is turned at its own natural frequency, and that frequency follows directly from how much it sags under its own load: Nc ≈ 946/√δ with δ in mm. Stay below about 0.75× or above 1.4× — and if you run supercritical, remember the machine has to pass through resonance every start and stop.

Static deflection
—
First critical speed
—
Natural frequency
—
Speed ratio N/Nc
—
Operating zone
—
Dynamic magnification
—

Rayleigh’s method treats the shaft as a single spring-mass system, so it gives the FIRST critical speed only and assumes the rotor mass dominates the shaft’s own mass. Multiple discs, stepped shafts and gyroscopic effects need Dunkerley’s method or a rotordynamic model. The magnification factor is undamped and therefore infinite at resonance; real damping limits it, but not enough to make running there acceptable. Get I from Section Properties. Default is a 25 mm shaft.

A helper, not a substitute for engineering judgment. Verify against the governing standard and your own hand calculations before anything is built.