Super-harmonic responses analysis for a cracked rotor system considering inertial excitation

In this paper, an investigation on the nonlinear vibration, especially on the super-harmonic resonances, in a cracked rotor sys- tem is carried out to provide a novel idea for the detection of crack faults in rotor systems. The motion equations of the system are formulated with the consideration of the additional excitation from an inertial environment as well as the forced excitation of the rotor unbalance. By using the harmonic balance method, the analytical solutions of the equations with four orders of harmonic exponents are obtained to analyze the nonlinear response of the system. Then through numerical calculations, the vi- bration responses affected by system parameters including the inertial excitation, the forced excitation, the crack and damping factors are investigated in detail. The results show that the occurrence of the super-harmonic resonances of the rotor system is due to the interaction between crack breathing and the inertial excitation. Correspondingly, the super-harmonic responses are significantly affected by the inertial excitation and the crack stiffness （or depth）. The rotor unbalance, however, does not make apparent effects on the super-harmonic responses. Consequently, the super-harmonic resonances peaks can be viewed as an identification signal of the crack fault due to the application of the inertial excitation. By utilizing the inertial excitation, the super-harmonic response signals in rotor systems with early crack faults can be amplified and detected more easily.