Unified modelling of passive homopolar and heteropolar electrodynamic bearings

A model of passive electrodynamic bearings based on the R–L dynamics of the eddy currents inside a conductor is presented. The model is derived from an analytical solution of the magnetic field in the air region surrounding the rotor for electrodynamic bearings having an even number of magnetic pole pairs. It allows homopolar and heteropolar electrodynamic bearings to be considered in a single unified way that accounts for the electromechanical interactions between the rotating conductor and the magnetic field of the stator. The model of the bearings is then coupled to a Jeffcott rotor model using complex coordinates in a state-space representation, allowing the dynamics of rotors supported by electrodynamic bearings to be studied. The number of magnetic pole pairs is found to influence rotordynamic stability, unbalance responses and frequency responses. The results demonstrate that homopolar electrodynamic bearings have a unique characteristic of passively filtering the transmission of forces due to residual unbalance of the rotor to the machine supports. The models are also used to perform a stability analysis of a case study presented in literature, and results from experimental observation are compared to those obtained analytically.