Coupled Lateral and Torsional Vibrations of a Cracked Rotor

Rotor crack problems present a significant safety and loss hazard in nearly every application of modern turbomachinery, particularly in the power generation industry. However, early crack detection is not easily achieved during the operation of machinery. The difficulty is based on the fact that a crack produces an undetectable change in the overall structural response. This paper analyzes the coupling of torsional and lateral vibrations for an unbalanced cracked rotor. The rotor equations of motion for a system with cracked shaft, obtained using Lagrangian dynamics, show coupling and nonlinear interaction between the torsional and lateral vibrations. To investigate the effect of a transverse surface crack on the dynamic rotor response the breathing crack model was employed. By applying an external torsional excitation together with the excitation due to unbalance, signature responses were observed in the rotor vibration spectrum at sum and difference frequencies. These signature responses were due to the nonlinear effect of the crack. The observed phenomena, analytically defined here, offers a new methodology concerning crack detection and prognosis in rotors.Copyright © 2004 by ASME