A rotor unbalance response based approach to the identification of the closed-loop stiffness and damping coefficients of active magnetic bearings

The stiffness and damping coefficients of active magnetic bearings (AMBs) have direct influence on the dynamic response of a rotor bearing system, including the bending critical speeds, modes of vibrations and stability. Rotor unbalance response is informative in the identification of these bearing support parameters. In this paper, we propose a method for identifying closed-loop AMB stiffness and damping coefficients based on the rotor unbalance response. We will use a flexible rotor-AMB test rig to help describe the proposed method as well as to validate the identification results. First, based on a rigid body model of the rotor, a formula is derived that computes the nominal values of the bearing stiffness and damping coefficients at a given rotating speed from the experimentally measured rotor unbalance response at the given speed. Then, based on a finite element model of the rotor, an error response surface is constructed for each parameter to estimate the identification errors induced by the rotor flexibility. The final identified values of the stiffness and damping coefficients equal the sums of the nominal values initially computed from the unbalance response and the identification errors determined by the error response surfaces. The proposed identification method is carried out on the rotor-AMB test rig. In order to validate the identification results, the identified values of the closed-loop AMB stiffness and damping coefficients are combined with the finite element model of the rotor to form a full model of the rotor-AMB test rig, from which the model unbalance responses at various rotating speeds are determined through simulation and compared with the experimental measurements. The close agreements between the simulation results and the measurements validate the proposed identification method. (C) 2015 Elsevier Ltd. All rights reserved.