Estimation of the internal and external damping from the forward and backward spectrum of a rotor with a fatigue crack

Abstract

Both internal and external damping are concurrently present in a rotor system. However, the internal damping that originates from various sources often leads to instability in the rotor system, and hence its accurate estimation is crucial. The goal of the present paper is to distinctly estimate both external and internal damping in a Jeffcott rotor containing transverse crack. The modelling of the fatigue crack is based on the assumption of a switching crack, which additionally provides the internal damping due to rubbing on crack faces, which is hardly addressed in literature. Moreover, the fatigue crack leads to the forward and backward whirls due to asymmetry in the rotor. In the process of development of the identification procedure in the form of the regression equation for the estimation of internal damping, other important unknown rotor system parameters, like the external damping, unbalance and loss of stiffness of the shaft due to the crack, are also identified. This reduces the estimation error of the internal damping due to reduction in deviations of other model parameters. Numerically simulated responses are obtained from equations of motion of the rotor system in the form of a closed-form expression and by the Runge-Kutta integration method. The full-spectrum response data (both magnitude and phase) are utilized during the testing of the proposed identification procedure. Phase corrections have been incorporated in the full-spectrum. Measurement noise is added in numerical responses during identification of parameters to check the robustness of the algorithm and found to be working satisfactorily. Keywords: Internal damping, External damping, Switching crack, Unbalance, Full spectrum