Analytical modelling and numerical experiment for simultaneous identification of unbalance and rolling-bearing coefficients of the continuous single-disc and single-span rotor-bearing system with Rayleigh beam model

Abstract This study proposes an algorithm for the simultaneous identification of residual unbalance and bearing dynamic coefficients of a single-disc and single-span rotor based on the unbalance response. The rotor is modelled as a homogeneous and continuous Rayleigh beam. A fourth-order non-homogeneous partial differential equation set with a homogeneous boundary condition is solved to obtain the analytical solution, which expresses the unbalance response as a function of position, rotor unbalance, and bearing stiffness and damping coefficients. Accordingly, the inverse problem is studied. A novel algorithm that can be applied to both a rolling-bearing rotor and an oil journal bearing rotor is proposed to identify the rotor unbalance during operation. Another novel algorithm is developed to identify the bearing stiffness and damping coefficients for a rolling-bearing rotor. Only four measured unbalance responses are required in the two above-mentioned algorithms. Thus, a simultaneous identification of the rotor unbalance and the roll-bearing dynamic coefficients can be achieved. Furthermore, only a measured response registered for the disc, the two bearings and any other selected cross-section of the rotor shaft under steady-state operating conditions is required. Numerical simulation shows that the proposed identification algorithms have excellent detection capabilities. In summary, the proposed algorithms provide an efficient means for rotor parameter identification without test runs or external excitations.