Whirling Speed Calculator

About this calculator

Every rotating shaft has a natural bending frequency, and if it spins at that speed the small, unavoidable imbalance in the shaft gets amplified into a large, self-reinforcing bow called whirling or whipping — left unchecked, it can bend or snap the shaft. Rayleigh’s approximation puts the critical speed at Nc = (60/2π) × √(g/δ) rpm, where δ is the shaft’s static deflection under its own weight (or an equivalent load) and g is gravitational acceleration.

The formula shows that a stiffer, less-deflecting shaft has a higher, safer critical speed, while a longer or more flexible one whirls at a lower, more dangerous one. Mechanical and rotating-equipment engineers — designing turbine rotors, pump shafts, motor spindles and generator shafts — use this estimate to keep the normal operating speed safely away from the critical speed, or to plan for rapid pass-through if the machine must cross it during start-up.