Abstract:
Conductive lap windings are interleaved with conventional loops in the stator of a motor-generator. The rotor provides magnetic induction lines that, when rotated, cut across the lap windings and the loops. When the rotor is laterally displaced from its equilibrium axis of rotation, its magnetic lines of induction induce a current in the interleaved lap windings. The induced current interacts with the magnetic lines of induction of the rotor in accordance with Lenz&#39;s law to generate a radial force that returns the rotor to its equilibrium axis of rotation.

Description:
The United States Government has rights in this invention pursuant to Contract No. W-7405-ENG-48 between the United States Department of Energy and the University of California for the operation of Lawrence Livermore National Laboratory. 

   BACKGROUND OF THE INVENTION 
   1. Field of the Invention 
   The present invention relates to magnetic bearings and, more particularly, to a passive magnetic bearing used to support and stabilize the rotor of a motor-generator. 
   2. Description of Related Art 
   An armature and a field winding comprise the primary elements of motors, generators and alternators. In low power applications, the armature rotates through the magnetic lines of induction provided by the stationary field winding. In this configuration, the armature composes the rotor part of the assembly, while the field winding is the stator. This is the design used in automobile alternators because the stator is on the outside of the rotor, and thus can be incorporated into a protective casing to facilitate replacement of the assembly. In high-power industrial applications, the field winding usually rotates while the armature composes the stator. 
   Regardless of the configuration, the rotor requires a degree of freedom to rotate about is longitudinal axis. Mechanical bearings, such as journal bearings, ball bearings, and roller bearings are commonly used for this purpose. Such bearings necessarily involve friction between the rotating element and the bearing components. This reduces the efficiency of the unit, and the designer must also contend with the attendant problems of heat and wear. 
   Even non-contact bearings, such as air bearings, involve frictional losses that can be appreciable and, in addition, are sensitive to dust particles. Furthermore, mechanical bearings, and especially air bearings, are poorly adapted for use in a vacuum. 
   The use of magnetic forces to provides an attractive alternative because, as it provides for rotation without contact, it avoids the aforementioned drawbacks. One such approach uses position sensors to detect incipient unstable motion of the rotating element and then uses magnetic coils in conjunction with electronic servo amplifiers to provide stabilizing forces to restore it to its (otherwise unstable) position of force equilibrium. The foregoing is usually designated as an “active” magnetic bearing, in reference to the active involvement of electronic feedback circuitry in maintaining stability. 
   Less common than the servo-controlled magnetic bearings just described are magnetic bearings that use superconductors to provide a repelling force acting against a permanent magnet element in such a way as to levitate that magnet. These bearing types utilize the flux-excluding property of superconductors to maintain a stable state by appropriately shaping the superconductor and the magnet to provide restoring forces for displacements in any direction from the position of force equilibrium. Obviously, magnetic bearings that employ superconductors must keep the superconductor at cryogenic temperatures, and this comprises a significant consideration for any design incorporating this type of bearing. 
   As may be seen from the foregoing, there presently exists a need in the art for a bearing that avoids the shortcomings and problems attendant to using mechanical bearings, but does so without the drawbacks and design limitations associated with active or superconducting magnetic bearings. The present invention fulfills this need in the art. 
   SUMMARY OF THE INVENTION 
   Conductive lap windings are interleaved with conventional loops in the stator of a motor-generator. The rotor provides magnetic induction lines that, when rotated, cut across the lap windings and the loops. When the rotor is laterally displaced from its equilibrium axis of rotation, its magnetic lines of induction induce a current in the interleaved lap windings. The induced current interacts with the magnetic lines of induction of the rotor in accordance with Lenz&#39;s law to generate a radial force that returns the rotor to its equilibrium axis of rotation. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
       FIG. 1  is a section front view of a motor-generator that includes the passive magnetic bearing of the present invention. 
       FIG. 2  is a section side view of the motor-generator that includes the passive magnetic bearing of the present invention, taken along line  2 — 2  of  FIG. 1 . 
       FIG. 3  is a front view of the motor-generator that includes the passive magnetic bearing of the present invention, showing only the lap windings and connecting wire of the passive magnetic bearing for the top and bottom quadrants of the stator. 
       FIG. 4  is a front view of the motor-generator that includes the passive magnetic bearing of the passive magnetic bearing showing only the lap windings and connecting wire of the passive magnetic bearing for the side quadrants of the stator. 
       FIG. 5  is a top view of the stator showing only the loops and interleaved lap winding of the passive magnet bearing for the top quadrant of the stator. 
       FIG. 6  is a schematic drawing showing the top and bottom quadrants of the passive magnetic bearing when the rotor is in the equilibrium position. 
       FIG. 7  is a schematic drawing showing the top and bottom quadrants of the passive magnetic bearing when the rotor is displaced downward from the equilibrium positions. 
   

   DETAILED DESCRIPTION OF THE INVENTION 
   Turning to the drawings,  FIG. 1  is a section front view of motor-generator  11  including conductive lap windings  12 ,  13 ,  14  and  15  of the present invention. Motor-generator  11  also includes rotor  17  rotating its longitudinal axis of symmetry  19  and around stator  21 . As shown in  FIG. 1 , when rotor  17  is in equilibrium, axis  19  is collinear with longitudinal axis of symmetry  22  of stator  21 . Radial gap  23  separates rotor  17  and stator  21 . Gap  23  is uniform and cylindrical when rotor  17  is in its equilibrium position, and becomes asymmetrical when rotor  17  is displaced therefrom. 
   As also shown in  FIG. 2 , a section view taken along line  2 — 2  of  FIG. 1 , stator  21  includes conductive rectangular loops  25 . Rotor  17  includes annular Halbach magnet array  27  that generates a magnetic field radially inward towards axis  19 , having lines of induction that intersect lap windings  12 ,  13 ,  14  and  15 , and loops  25 . A discussion of Halbach magnet arrays is provided in K. Halbach, “Application of Permanent Magnets in Accelerators and Electron Storage Rings,”  Journal of Applied Physics,  Vol. 57, Apr. 15, 1985, pp. 3605–3608, which is hereby incorporated by reference. 
   Omitted from the drawings is the structure of stator  21  that supports loops  25 , and the circuitry of stator  21  connecting loops  25  to either an external circuit to apply the voltage output generated by motor-generator  15 , or to a voltage source to drive motor-generator  15 . The foregoing structure and circuitry are well known to those skilled in the electromechanical arts. 
   Lap windings  12 ,  13 ,  14 , and  15  are interleaved with loops  25 .  FIG. 3  shows a front view of motor-generator  11  with lap windings  12  and  13 , and wires  29  shown with solid lines, and the outline of stator  21  shown in phantom. Lap winding  12  is interleaved across the top quadrant of stator  21  and lap winding  13  is interleaved across the bottom quadrant of stator  21 . Wires  29  electrically connect lap windings  12  and  13  to form a closed circuit.  FIG. 4  shows a front view of motor-generator  11  with lap windings  14  and  15 , and wires  31  shown with solid lines, and the outline of stator  21  shown in phantom. Lap winding  14  is interleaved across the quadrant on one side of stator  21 , and lap winding  15  is interleaved across the quadrant on the other side. Wires  31  electrically connect lap windings  14  and  15  to form a closed circuit. 
     FIG. 5  is a top view of lap winding  12  interleaved with loops  25  across the top quadrant of stator  21 . Lap winding  12  is composed of parallel lateral sections  33  and longitudinal sections  35 . Longitudinal sections  35  space lateral sections  33  azimuthally apart from one another by one-half of the wavelength, λ, of the lines of induction emanating from the multiple poles of Halbach array  27 . Lap winding  13  is aligned with lap winding  12 ; that is, each singular lateral section  33  and longitudinal section  35  for lap winding  12  lies in a vertical plane containing the same respective section for lap winding  13 . Similarly, lap winding  14  is aligned with lap winding  15 . 
     FIG. 6  is a schematic drawing showing the interaction between the lines of induction of Halbach array  27  and lap windings  12  and  13 , to induce vertical centering forces that act upon the top and bottom quadrants of stator  21 . More particularly, as Halbach array  27  rotates counterclockwise around axis of symmetry  19  at angular velocity ω, a current, i, is induced in both lap winding  12  in the top quadrant of stator  21  and in lap winding  13  in the bottom quadrant. 
   When rotor  17  is rotating in equilibrium, axis of symmetry  19  is collinear with axis of symmetry  22  of stator  21  and gap  23  is uniform about the inner circumference of Halbach array  27 . The magnetic fields moving across lap windings  12  and  13  are of equal strength, and are phased so as to induce an equal time-varying current, i, in lap winding  12  and lap winding  13 . Since lap windings  12  and  13  are connected in opposing series to form a circuit by wires  29 , the net current flowing through the circuit is zero and thus the net induced force is zero. 
   However, if rotor  17  is transversely displaced relative to axis  22  of stator  21 , gap  23  will become asymmetrical. The strength of the magnetic field of Halbach array  27  increases exponentially as gap  23  decreases. Thus the field strength acting on lap windings  12  and  13  will differ, and this will induce a net current, i, through the circuit comprised of lap windings  12  and  13 , and wires  29 . In accordance with Lenz&#39;s law, the cross product of the net current, i, and the lines of induction will result in a radial force F 12  acting on lap winding  12  and a radial force F 13  acting on lap winding  13 . Both F 12  and F 13  will be in the same direction as the displacement of rotor  17 . Equal and opposing reactive forces will act against rotor  17 , i. e., in the opposite direction as the displacement of rotor  17 , until gap  23  becomes symmetrical, i. e., when rotor  17  reaches its equilibrium position. 
   Referring to the example shown in  FIG. 7 , if rotor  17  is displaced downward relative to stator  22 , gap  23  will be less for the top quadrant of stator  21  than for the bottom quadrant. As the strength of the magnetic field affecting lap winding  12  will be greater than that affecting lap winding  13 , a clockwise current, i, will be induced throughout the closed circuit. The cross product of i and the lines of induction acting on lap windings  12  and  13  will induce forces F 12  and F 13  acting downwardly against lap windings  12  and  13 , respectively. Equal and opposing reactive forces will act upwardly on rotor  17  until it is returned to its equilibrium position, with axis  19  lying collinear with axis  22 . 
   The same analysis is applicable to lap windings  14  and  15 . They will interact in an identical manner with the magnetic field of Halbach array  27  to generate a centering force to restore rotor  17  to its equilibrium position when it undergoes a horizontal transverse displacement therefrom. 
   By making the angular width in the azimuthal direction of lap windings  14  and  15  unequal to the angular width of lap windings  12  and  13 , anisotropic stiffness could be introduced. That is, because of the difference in the azimuthal extent of the windings, the magnitude of the reactive force, or stiffness, for restoring a horizontal displacement to the equilibrium position, would be different from that of restoring a vertical displacement to the equilibrium position. Anisotropic stiffness is known to provide a stabilizing effect against rotor-dynamic instabilities. 
   It is to be understood, of course, that the foregoing description relates only to an embodiment of the invention, and that modification to that embodiment may be made without departing from the spirit and scope of the invention as set forth in the following claims.