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.(FSA - Sciences de l'ingénieur) -- UCL, 201

Null Flux Radial Electrodynamic Bearing

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 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=ppm 1 where q and p are the number of pole pairs of the winding and permanent magnets, respectively. This guideline is validated by FE simulations and some additional comments are made on the phase shift between the induced emf and current which maximizes the centering force on the bearing

Linear State-Space Representation of Heteropolar Electrodynamic Bearings with Radial Magnetic Field

Electrodynamic bearings can operate without active control means. In that case, the dynamic behavior of the bearing relies solely on passive electromagnetic phenomena which can be studied using specific models. In recent years, linear state-space representations linking the forces and the relative motion between the stationary and moving parts of such a bearing were obtained without making any assumption on the kinematics of the rotor axis. However, significant limitations remain regarding the topology of the bearing. As regards heteropolar bearings with radial magnetic field, the latter refers to: 1) the number of winding phases; 2) the number of pole pairs of the permanent magnets (PMs) and winding; 3) the presence of PMs at the rotor or at the stator; and 4) the presence of a ferromagnetic yoke attached to the winding. This paper presents a model free of these limitations. Compared with existing models, few additional complexities are introduced in the state-space representation. As a result, the dynamics of a wider range of heteropolar electrodynamic bearings can now be studied with a linear model

Performance of Yokeless Heteropolar Electrodynamic Bearings

Electrodynamic bearings (EDBs) are a promising way to support rotors passively with no friction. In particular, heteropolar EDBs could allow for combining the motor and guiding functions, thereby optimizing the use of permanent magnets. Despite this advantage, few efforts have been dedicated to the evaluation and optimization of the performance of heteropolar EDBs. In this paper, the performance of a yokeless topology of heteropolar EDB is evaluated and optimized. This is done by evaluating the parameters of a parametric dynamical model of the EDB using a two-dimensional analytical model of the field distribution in the bearing. Compared to existing EDBs, the present one is shown to achieve a reasonable stiffness to permanent magnet volume ratio at high speeds

Yokeless radial electrodynamic bearing

When null-flux, passive electrodynamic bearings include a ferromagnetic yoke in front of the permanent magnets, the stiffness associated with the radial centering force becomes negative under a critical speed. This yields a strong instability and the necessity of using mechanical launch bearings at low speeds. In this paper, an electrodynamic bearing without ferromagnetic yoke is proposed. An analytical 2D model of the bearing is presented and some hypotheses are validated. The model is then used to perform a first analysis of the bearing performance. The force predictions correspond to expectations: the stiffness never reaches negative values. It is also shown that for given geometrical parameters, the performance of the studied bearing can be improved by choosing the appropriate number of phases and number of pole pairs of the winding

Description of an Electrodynamic Self-Bearing Permanent Magnet Machine

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

Yokeless radial electrodynamic bearing

Due to the presence of a ferromagnetic yoke in passive electrodynamic magnetic bearings, the stiffness associated with their radial centering force becomes negative under a critical speed. This leads to instability problems and to the necessity of using mechanical launch bearings at low speed. In this paper, an electrodynamic bearing without ferromagnetic yoke is proposed. An analytical 2D model of the bearing is presented and used to perform a first analysis of the bearing. The force predictions correspond to expectations: the stiffness never reaches negative values. It is also shown that for given geometrical dimensions, the performance of the studied bearing can be significantly improved by choosing the appropriate number of phases and number of pole pairs of the winding

radial electrodynamic bearing

The invention provides a radial bearing for supporting a shaft of a rotating device comprising an inductor having an inductor axis, generating a magnetic field radial to said inductor axis having p pole pairs, a winding having loops disposed around a winding axis, magnetically coupled to said radial magnetic field, and connected in a closed circuit in such a manner that the net flux variation intercepted by said winding when said inductor and said winding are in rotation with respect to each other is zero when said inductor axis and said winding axis coincide, and a gap between said inductor and said winding. According to the invention, said armature winding comprises p-1 or p+1 pole pairs when p is larger than or equal to 1 and said armature winding comprises one pole pair when p is equal to 0

Performance of yokeless heteropolar electrodynamic bearings

Electrodynamic bearings (EDBs) are a promising way to support rotors passively with no friction. In particular, heteropolar EDBs could allow for combining the motor and guiding functions, thereby optimizing the use of permanent magnets. Despite this advantage, few efforts have been dedicated to the evaluation and optimization of the performance of heteropolar EDBs. In this paper, the performance of a yokeless topology of heteropolar EDB is evaluated and optimized. This is done by evaluating the parameters of a dynamical model of the EDB using a two-dimensional analytical model

Semi-analytical determination of inductances in windings with axial and azimuthal wires

Purpose - Optimizing an electromechanical device often requires a significant number of evaluations of the winding inductance. In order to reduce drastically the computing costs associated with the calculation of inductances, the purpose of this paper is to propose a semi-analytical toolbox to calculate inductances in any winding made of axial and azimuthal wires and lying in the air. Design/methodology/approach - First, this paper presents a typical rectangular, spiral winding and the way its geometry is approximated for inductance calculations. Second, the basic formulas to calculate inductances of various windings arrangements are provided. The analytical model of the inductances is exposed, and the formulas for the inductances are derived. Finally, a validation is proposed by comparing analytical predictions to 3D FE simulations results and experimental measurements. Findings - The semi-analytical predictions agree with the finite element methods (FEM) and experimental data. Furthermore, the calculation of the inductances was done using much fewer resources with the semi-analytical model than with FEM. Research limitations/implications - The analytical formula for the mutual inductance between coaxial circular arcs is a series with an infinite number of terms which should be truncated appropriately. This is necessary because the term are found using a recurrence formula which may be unstable for a high number of terms. Practical implications - The paper includes implications for the optimization of electromechanical devices comprising windings made of axial and azimuthal pieces of wires. Originality/value - The main original result resides in the analytical expression of Neumann's integral for the inductance between two coaxial circular arcs