Abstract
A method is presented that enables collocated and noncollocated magnetic bearing models on flexible supports to be included into the transfer matrix method for rotor stability analyses. The linear magnetic bearing model is represented as an open-loop stiffness, an actuator gain, and a frequency-dependent transfer function relating the sensed rotor displacement to the perturbation currents in the coils of the bearing actuator. The open-loop stiffness is handled in the same way that an ordinary hydrodynamic bearing is handled, while the bearing actuator gain and transfer function combination is treated as a complex-valued frequency-dependent stiffness that acts between the actuator location and the sensor position. The flexible support is modeled as a lumped mass with linear principal and cross-coupled stiffness and damping coefficients. The singularities introduced into the eigenvalue search surface from representing degrees of freedom from the main line of the rotor as transfer functions are canceled. This enables eigenvalues to be found in the vicinity of singular points. The stability of a specific rotor-bearing system is studied as a function of support flexibility and damping thus demonstrating the proposed method.
