Heteropolar null-flux electrodynamic bearings for the passive radial suspension of rotors

Magnetic bearings allow to support a rotating object without contact. This makes them more suitable than mechanical bearings for applications where removing the wear and/or the lubrication is highly sought-after, for example. Nowadays, the magnetic bearings used in the industry are controlled actively. This requires the use of sensors, controllers and power electronics. However, the complexity, cost and overall dimensions associated with this control system can become prohibitive, especially for small rated power applications. A way to overcome these disadvantages could be the use of magnetic bearings that do not require external control means, i.e. passive bearings. Electrodynamics bearings (EDBs) belong to this category. Electrodynamic bearings are based on the electromagnetic interaction forces between permanent magnets and currents flowing in a conductor. These currents are induced by the relative speed between the magnets and the conductors. For efficiency purposes, electrodynamic bearings are designed in such a way that there is no net variation in the permanent magnet flux linked by the winding when the rotor spins in a centered position. As a result, there are no induced currents, no forces, and above all no losses in the bearing when the rotor spins in a centered position. This characteristic is referred to as null-flux. It is found in all the designs of electrodynamic bearings that are studied nowadays. In contrast, when the rotor spins in an off-centered position, currents are induced in the winding. This creates a force on the rotor that tends to restore its centered position. In this case, the energy dissipated in the windings comes from the drive torque on the rotor that keeps the spin speed constant. On the one hand, this prevents the operation at zero spin speed. On the other hand, it eliminates the need for an additional electrical power supply to feed the bearing, as is the case for the existing active magnetic bearings. Finally, the absence of control system induces gains in compactness, simplicity, costs and reliability. As a result, electrodynamic bearings could be well suited for applications where these aspects are critical. Despite these advantages, electrodynamic bearings have not made their way out of the labs yet due to their lowstiffness and stability issues. In this context, this thesis aims at taking one further step toward the implementation of heteropolar electrodynamic bearings in practical applications. To this end, new design guidelines and models are proposed, validated, and applied to different case studies. Indeed, the design of a new electrodynamic bearing is usually based on the intuition and experience of its inventor. This work proposes guidelines to ease this design process. The guidelines are deduced by imposing the null-flux characteristic to a bearing comprising magnets with radial magnetic field and a winding with an arbitrary shape. This yields the identity q = p +/- 1, where q and p are the number of pole pairs of the winding and permanent magnets, respectively. Based on these guidelines, new bearing topologies are also introduced. Regarding the modeling, recent years have seen the emergence of a new kind of model of electrodynamic bearings. As opposed to the previous ones, this model is dynamic, i.e. obtained without making any assumption on the kinematics of the rotor axis. This opened the possibility of performing stability analyses in a rigorous way. Furthermore, the stability can be analyzed using conventional system analysis tools, because the model takes the form of a linear state-space representation. This thesis proposes a dynamic model with an enlarged scope, i.e. suitable for a wider range of bearing geometries. Thanks to this model, the performance and stability of various EDBs can be optimized and compared to find the most appropriate solution for a given application. Although various embodiments of heteropolar bearings have been proposed, very few efforts have been dedicated to the evaluation and optimization of their performance, and the actual potential of heteropolar EDBs still needs to be evaluated. In this aim, a graphical method based on the analysis of the root locus of the system is proposed. It is then applied to the comparison of bearings with different winding yoke permeabilities. Based on the dynamic model developed in this thesis, the optimization of the stability and stiffness of a yokeless bearing is also carried out, yielding a Pareto front of optimal bearings. These optimal bearings are finally compared to existing homopolar and heteropolar embodiments in terms of stiffness to magnet volume ratio, showing that similar ratios can be obtained. Lastly, the bearing dynamic model is applied to the prediction of balancing radial electrodynamic forces due to rotor eccentricities in permanent magnet machines. The main assumptions of the model are validated to show its applicability in this case, and the forces from the model are compared to finite element simulation results, showing a good agreement between both predictions.