Vibration Behavior of Misaligned Rotor with the Asymmetric Shaft Using Theory of Timoshenko Beam

Abstract

In the present study, an accurate model is used for analyzing an asymmetric shaft with misalignment and under unbalance forces in rotating coordinates verified by developing an experimental test.The asymmetric rotor modeled by the Timoshenko beam theory is coupled to a motor.The differential equations of motion are discretized by Rayleigh-Ritz method and derived from Hamilton's principle. Thereafter, According to the results, a frequency range is detected in which,resonance and instability will occur. The dynamic behavior of the rotor is investigated near the boundary of the instability region. Various parameters, including unbalanced and misalignment induced forces, and the dimensions of the cross-section of the shaft are taken into account.Finally,vibration responses of the system and their Fast Fourier Transform (FFT) are presented graphically to determine the frequencies of the harmonic responses. It is concluded that the asymmetry of the shaft and misalignment fault severely affect the dynamic response of the rotor.Moreover, the accuracy of the results is increased by applying the Timoshenko beam theory.By developing an experimental test for the rotor system connected to an electric motor with misalignment fault, verifying this model has been done.The experimental results obviously obtained the unstable operating area as acquired by the differential equations of motion.