This work describes a foundation of sophisticated diagnostic techniques for the detection of shaft cracks in rotordynamic systems, considering the dynamical behavior of a rotating cracked shaft under the application of external loads. The response is modeled as a modified Jeffcott rotor, while the crack is assumed to induce a time-varying stiffness in the model. The focus of this work is the development of external loading strategies to create damage sensitive measures of vibration response and then analyze that using advanced technologies such as wavelet analysis. This will enable the detection of the crack depth, as represented by the magnitude of the damage-induced time-varying stiffness, from vibration measurements. This entails developing external forcing functions for which features of the vibration response are sensitive to the presence of the damage. The development of such inputs is based on a multiple-scales analysis of the full equations of motion, including the time-varying stiffness. From this, a resonance (called combination resonance) is identified between the operating speed of the shaft, the fundamental frequency of the shaft, and the frequency of the external forcing. When the system is operated at this resonant condition, the translational vibrations of the shaft contain a spectral component near the fundamental shaft frequency that is proportional to the amplitude of the time-varying stiffness. The resonance bandwidth, obtained from this analysis, enables us to build a framework for the development of damage detection techniques for rotating machinery. Continuous Wavelet Transform (CWT) is applied to the vibration response of a rotordynamic system that utilizes harmonic forcing satisfying combination resonance. The variation of wavelet coefficients with respect to the variation of different system parameters is examined. Attention is focused on how the resonant bandwidth affects the variation of wavelet coefficients as crack grows.

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