Frequency dependent impedance model for heteropolar magnetic bearings

Accurate analytical models are fundamental to design and optimise high performance magnetic bearings. Understanding the bearing’s dynamic behaviour over its operational envelope is essential to this task and is performed through frequency response analyses. This work formulates an integrated frequency dependent model of a radial heteropolar active magnetic bearing (AMB) in which terms for the stray capacitance, winding resistance, and winding leakage inductance are included. The model is based on a lumped parameter model frequently used for high frequency laminated inductor applications. Two magnetic core models are evaluated. The first comprises a reluctance network approach and incorporates eddy-current, fringing, and leakage correction terms, while the second constitutes a single gapless magnetic core of equivalent length and effective permeability. The accuracy of the latter is improved by intuitively adjusting two parameters in the analytical model. The magnetic bearing parameters calculated as functions of frequency are compared with practical measurements. The integrated single core model demonstrates superior correlation with experimental results for frequencies up to 1 MHz.