Critical Speed of a Rotating Shaft - Rayleigh–Ritz method

Description

In solid mechanics, in the field of rotordynamics, the critical speed is the theoretical angular velocity that excites the natural frequency of a rotating object, such as a shaft, propeller, leadscrew, or gear.

The equation illustrated here is the Rayleigh–Ritz method applied to a shaft. The static deflection expresses the relationship between rigidity of the shaft and inertial forces; it includes all the loads applied to the shaft when placed horizontally.However, the relationship is valid no matter what the orientation of the shaft is.

Critical speed depends upon the magnitude and location of the shaft unbalance, the length of the shaft, its diameter, and the kind of bearing support. Good practice suggests that the maximum operating speed should not exceed 75% of the critical speed.