Nonlinear Breathing Behavior Study of Transverse Crack on a Jeffcott Rotor Under Torsional Excitation

Abstract

In this paper, Jeffcott rotor model is employed to explore the vibration response of breathing cracked system with unbalance mass. Based on the energy method and Lagrange principle, 6 degree-of-freedom equation of motion is derived in fixed coordinate system. The crack model is established using strain energy release theory of facture mechanics. The stiffness matrix induced by the crack is changing with the variation of crack open area. Zero stress intensity factor (SIF) method is used to determine the crack closure line by computing the SIF for opening mode. By integrating compliant coefficients over newly determined crack open area, the stiffness matrix is updated and vibration response is solved for every time step by Gear’s method. In addition, the breathing behavior of the crack is studied for multiple eccentricity phases and rotation speeds in order to provide effective guidance for damage detection. The paper explores the effect of external torsional loading on the crack breathing behavior. Finally, the coupling of lateral and torsional vibration is investigated to be used as an indicator of damage detection and health monitoring.