Magnetic bearings are electromechanical systems. From a mechanical point of view, their modeling is plainly related to general rotor dynamics modeling. But the forces acting between the rotor and the stator are of an electromagnetic nature. This paper presents the analysis of the potentially unstable dynamical behavior of magnetic bearings. It adopts an electromechanical point of view and represents the forces acting on the system by dampers, springs, and an electrical phase shift. The coefficients of the model are found by parameter identification with a finite-element model of the system.

Topologies of electrodynamic thrust bearings (EDTB) and axial flux permanent magnet (AFPM) machines exhibit a significant number of similarities. Starting from this observation, the present paper introduces a new self-bearing motor combining, within a single armature winding and through the same permanent magnets, both the passive electrodynamic axial levitation and motor functions. The rotor axial stabilisation being achieved through passively induced currents, no sensor, controller and power electronics related to the bearing function are required. In addition, an electromechanical model describing both the axial and spin dynamics of such a motor is presented. This set of six equations depends on twelve parameters whose determination can be performed through static finite element simulations or quasi-static experimental measurements. The model is linearised allowing us to study the local stability of this passive self-bearing motor around an operation point characterised by the rotor spin speed as well as the external force and torque. The dynamic and quasi-static behaviours as well as the stable spin speed ranges are analysed through a case study. Finally, a first experimental investigation dedicated to the validation of the operation principle as well as the dynamical model is performed.

Eddy-current forces may play a significant role in magnetic bearings. They generate losses and unpredicted forces, which may lead to a malfunction of the bearing. But eddy currents in magnetic bearings may also be used positively, to generate desired forces, like in electrodynamic bearings. This paper presents a model able to predict, analyze, or simulate the dynamical behavior of any rotating magnetic bearing in which classical eddy-current forces arise. This model integrates the mechanical aspects linked to the rotor dynamics and the electrical aspects linked to the electromagnetic nature of the forces. This paper explains how the parameters of the model can be identified on the basis of quasi-static finite element method (FEM) or experiments. The validation of the model is done by comparison with FEM results on an electrodynamic radial bearing.

This paper aims to give a description of a passively levitated self-bearing permanent magnet motor principle. The windings of a permanent magnet motor are connected in such a way that they are also coupled to the p ± 1 harmonics due to a rotor off-centering. They allow for eddy currents to flow inside a short-circuit path when the rotor is out-centered, and in consequence to generate radial force according to the principle of radial heteropolar electrodynamic bearings. The general principles are described, and a 2-D-FE time-dependent model illustrates those principles on two application cases. The theoretical feasibility of this passively levitated permanent magnet motor is shown on a slotless application case.

Recent researches have revealed that electrodynamic thrust bearings can gather, within one single armature winding, both the passive axial restoring force and the driving torque, thus yielding a new passively levitated electrodynamic thrust self-bearing (EDTSB) motor. Although their operation principle as well as the model describing their axial and spin dynamics have already been corroborated, experimental results still lack to properly characterise these machines. In this context, this paper is devoted to an in-depth experimental investigation of an EDTSB motor. Measurements performed on the prototype endorse the assumptions regarding the linearisation of the flux linkages as well as the negligible impact of the magnetic field harmonic content. They also disclose that suspension currents are induced even when the rotor is centred. Finally, the thrust bearing and self-bearing motor behaviours are studied in quasi-static and dynamic conditions, validating the dynamical model.

The design of a new electrodynamic bearing is often based on the intuition and experience of its inventor. This paper proposes general guidelines for the design of null-flux electrodynamic centering bearings based on the interaction between a short circuited winding and permanent magnets. These design guidelines are deduced from an analytical analysis of the magnetic flux, and forces in a bearing with a radial magnetic field and an arbitrary winding. Considering that the electromotive force (EMF) in the winding should cancel when the rotor is centered and should appear as the rotor is off-centered, inducing a current in the winding and therefore a centering force on it, the design guideline is to have q = p ± 1 where q and p are the number of pole pairs of the winding and permanent magnets, respectively. This guideline is validated by finite element simulations and some additional comments are made on the phase shift between the induced EMF and current that maximizes the centering force on the bearing.