Experimental Identification of Internal and External Damping in a Rotor System with a Fatigue-Crack Using Full Spectrum

Abstract

Demand of higher speeds in rotor systems has elevated the possibility of numerous instabilities. Internal damping is one of the key parameters for instability in such machinery. Its studies are generally conducted for a possible range of chosen internal damping values. Hence, experimental estimation of internal damping along with external damping is very vital for an accurate prediction of rotor stability, which is scarcely addressed in the literature. To fill this gap, current paper presents an experimental identification methodology for estimation of the internal and external damping in a cracked rotor system. Other crucial unknown fault parameters of rotor system, like additive crack stiffness and unbalance, have also been identified. In present work, internal damping due to rub between transverse fatigue crack faces has been envisioned for the first time. Hence, internal damping has been considered due to combined effect of material hysteretic, i.e. the rub between transverse fatigue crack faces, and the rub between disc and shaft during shaft rotation. Measurements much below critical speeds ensures the main contribution of crack in internal damping due to weight dominance effect as compared to shaft material damping. In experimental setup, a hairline fatigue crack was artificially developed by three-point bending procedure in a shaft at a notch location. The opening and closure behavior of crack faces during rotation of the shaft leads to the forward and backward whirls of the rotor at multiple frequencies, which are apparent in the full spectrum. Mathematical modeling of the rotor system for development of identification algorithm is based on these behaviors of cracked rotor system. Experimentally measured responses have been converted into the full spectrum (both amplitude and phase) based on regression analysis and fast Fourier transform (FFT). Earlier, amplitudes of full spectrum have been used for qualitative indication of crack. But in the present work, corresponding phase has also been considered in quantitative estimation of crack parameter along with other system fault parameters. With the help of a multi-frequency reference signal, phase anomalies have been removed during processing of full spectrum. The bow effect of shaft has been removed from full spectrum responses with the help of a slow roll measurement. Estimated parameters are consistent for different sets of rotor speeds and for different frequency ranges of excitation forces due to fatigue crack. Validations of identified parameters have been done by comparing experimental responses with numerically generated system responses. The latter was generated using experimentally identified parameters in the mathematical model of cracked rotor system.