Abstract:
A ferromagnetic shield in contact with a magnet bar at the opposite end from the working surfaces of the bar eliminates the field canceling effects that arise from the Amperian currents at that end. The optimum polarization direction for such bars is one that is parallel to the azimuthal coordinate of the bar. The field at the working surface of the bar approaches that of a bar of infinite length because the shield, located on the side opposite to that of the working surface, completely eliminates, or at least substantially reduces, the field cancellation effect that normally would occur. The magnet bars with shields can be assembled on rotors and stators in flywheel storage systems and other rotating machinery.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
       [0001]    This application claims the benefit of U.S. Provisional Patent Application No. 62/191,885 titled “Improved Levitating Passive Magnetic Bearing Configurations,” filed Jul. 13, 2015, incorporated herein by reference. 
     
    
     STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT 
       [0002]    The United States Government has rights in this invention pursuant to Contract No DE-AC52-07NA27344 between the U.S. Department of Energy and Lawrence Livermore National Security, LLC, for the operation of Lawrence Livermore National Laboratory. 
     
    
     BACKGROUND OF THE INVENTION 
       [0003]    Field of the Invention 
         [0004]    The present invention relates to the design of levitating magnetic bearings of the annular or conical-annular configuration, and more specifically, it relates to the use of alternative polarization and Amperian current directions in levitating passive magnetic bearing configurations. 
         [0005]    Description of Related Art 
         [0006]    Levitating magnetic bearings of the annular or conical-annular configuration are typically made using rectangular blocks that are assembled in a ring the radius of which is large compared to the dimensions of the bars so that the gaps at the outer edge are small compared to their dimensions. Key elements in the passive magnetic bearing systems developed at Lawrence Livermore National Laboratory (LLNL) are the permanent-magnet arrays that levitate the rotating system, e.g., the rotor of a flywheel energy storage system (EMB). It is therefore of value to consider designs of these systems that minimize the amount of magnet material required (reduces the weight added to the rotor), and reduce the material cost of the bearing, both from reducing the amount of permanent magnet material required to fabricate the bearing and/or to allow the use of less expensive magnet material. For example, the high-field permanent magnet material such as SmCo (Br=1.3 Tesla) and NdFeB (Br=1.4 Tesla) are very expensive ($100/lb for SmCo and $50/lb for NdFeB). Ferrite magnets (Br=0.4 Tesla) cost only $2/lb, and are also non-conducting, so that eddy-current losses are zero. New designs are desirable that improve the lift per unit area of levitating bearings, as compared to former designs, sufficiently as to allow the use of ferrite magnets for levitation of EMBs rotors in most cases. The present invention provides such designs 
       SUMMARY OF THE INVENTION 
       [0007]    The invention consists in adding a ferromagnetic shield at the opposite end from the working surfaces of the magnet bars to eliminate the field cancelling effects that arise from the Amperian currents at that end. It is shown that the optimum polarization direction for such bars is one that is parallel to the azimuthal coordinate of the bar, as opposed to polarization in the radial direction or axial direction. In the present invention, the field at the working surface of the bar approaches that of a bar of infinite length because a shield, located on the side opposite to that of the working surface, completely eliminates the field cancellation effect that normally would occur. The invention has a variety of uses including in flywheel storage systems and other rotating machinery. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0008]    The accompanying drawings, which are incorporated into and form a part of the disclosure, illustrate embodiments of the invention and, together with the description, serve to explain the principles of the invention. 
           [0009]      FIG. 1A  shows rectangular permanent magnet block  10  oriented so that its polarization  12  is horizontal with respect to the page. 
           [0010]      FIG. 1B  shows a conventional bearing having a permanent magnet block  20  and a polarization  22  that is vertical with respect to the page. 
           [0011]      FIG. 1C  shows a manner in which the element  8  of  FIG. 1A  can be arranged in a circular pattern for use in a circular bearing. 
           [0012]      FIG. 2A  shows plots of the levitation force/m 2  for horizontally polarized ferrite permanent magnet bars as a function of the length of the magnets. 
           [0013]      FIG. 2B  shows plots of the levitation force/m 2  for vertically polarized ferrite permanent magnet bars as a function of the length of the magnets. 
           [0014]      FIG. 3  shows a cross-sectional view of a passive bearing system that utilizes embodiments of the bearing elements of the present such that the system is stable against vertical (axial) and radial displacements. 
           [0015]      FIG. 4  shows an embodiment of an electro-mechanical battery that utilizes the magnetic elements and shields of the present invention in its levitation and stabilizer systems. 
       
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
       [0016]    The new designs described in this document improve the lift per unit area of levitating bearings, as compared to former designs, sufficiently as to allow the use of ferrite magnets for levitation of EMBs rotors in most cases. Levitating magnet arrays employed in the LLNL passive magnetic bearing systems have consisted of annular or conical-annular arrays of permanent magnets for vertical-axis systems or arc or conical arc arrays for horizontal-axis systems. This document describes an improved form of these arrays that results in a substantial increase in the levitating force per unit magnet weight. As noted above, the improvement is such that in many cases it will allow the replacement of an expensive permanent magnet material, e.g., SmCo, by a much less expensive one, e.g., ferrite. 
         [0017]    In the design of the levitating components of a passive magnetic bearing there are two general classes of magnet arrays from which to choose, namely, annular uniformly polarized arrays or Halbach arrays with radially directed periodicity. The Halbach array makes the most efficient use of the magnetic material but at the price of complexity of the individual magnet elements from which it is assembled. They also have very high stiffness per unit area. This feature can make it more difficult to stabilize the entire passive bearing system against Earnshaw-Theorem-related instability. 
         [0018]    The new invention achieves typical levitation per unit magnet weight factors that fall short of Halbach array bearings by about a factor of two, but are nevertheless better than previous designs by a factor of two or more, and at the same time involve far simpler magnet elements than do Halbach array bearings. 
         [0019]    Returning to the topic of designing annular levitating bearings, it is first of all important to note that there are two generically different approaches that might be taken. These two differ in the polarization direction of the magnets. An annular ring levitation magnet array is typically constructed by assembling small square-ended magnet bars into a circular pattern, having a radial width that is much smaller than the radius of the ring. When this is the case, the gaps between the magnets at the outer edge of the ring are very small compared to the end-on dimension of the blocks so that the effect of these gaps on the magnetic field configuration is minimal. When radially wider rings are required, they can be made up by nesting rings of increasing radius, with small radial gaps between each ring. Conical annular rings can also be assembled in the same manner, as can annular rings located on the inner surface of the rotor that exert an inward force when matched against a cylindrical array of stator magnets. 
         [0020]    At this point in the design there are two choices of magnet polarization that can be chosen. The conventional choice of polarizations are ones that are perpendicular to the working surface of the ring, i.e., either “out-out” (repelling), or “out-in” (attracting). The invention described herein consists in choosing the alternative polarization, i.e., parallel or anti-parallel to the azimuthal coordinate of the annular bearing. By making this choice it will be shown that it is possible to double the repulsion or attraction of the bearing relative to the “out-out” or “in-out” polarizations with the same magnet volume and weight of magnets as used in the conventional magnet polarization orientations. 
         [0021]    In order to explain the electromagnetic origin of the above-cited advantage (of using a non-conventional choice of magnet polarizations) it is very useful to introduce the “Amperian current” model of a permanent magnet bar. According to this model, any permanent magnet can be represented by a pattern of equivalent current sheets on their surface. For rectangular bars these currents on the surface of the bar are constant in magnitude, closing on themselves to form rectangular current loops. For a magnet bar that is polarized so that the emerging B vector is perpendicular to an end of the bar, the Amperian currents flow around the body of the bar represented by the sides of the bar, just as they would flow in a solenoidal coil with rectangular cross section. The above polarization direction is the one conventionally used to create an attracting or a repelling annular bearing out of small rectangular blocks. 
         [0022]      FIG. 1A  shows a bearing element  8  comprising a rectangular permanent magnet block  10  oriented so that its B-field polarization  12  is horizontal with respect to the page. Amperian currents flowing around the block are represented by arrows  14 . The Amperian currents flowing on the bottom and back side of the block are not shown because they are obscured by the block itself. In this configuration, surface  16  is the working surface of the bearing element. The opposite end of block  10  is located within a trough  18  of a shield  16 , which could be made of ferromagnetic material (e.g., soft iron or other high permeability material). 
         [0023]      FIG. 1B  shows a conventional hearing element  19  having a permanent magnet block  20  and a polarization  22  that is vertical with respect to the page. Amperian currents are represented by arrows  24 . In this bearing element, surface  26  is the working surface.  FIG. 1C  shows a manner in which the element  8  of  FIG. 1A  can be arranged in a circular pattern for use in a circular bearing. The figure shows a view from above the working surface  16 . Although only one of these bearing elements is shown, in a complete bearing, a series of these elements would be placed such that the working surfaces  16  are arranged side-by-side with all of the Amperian currents pointing in the same direction. In the case of  FIG. 1C , all of the Amperian current directions are pointed away from the central axis of the circle. If Although not to scale, notice that the thickness of the working surface is small compared to the radius of the circle. Notice also that the magnetic polarization  12  is pointed such that it is parallel with the azimuthal direction of the circle. 
         [0024]    The non-conventional polarization choice (i.e., polarization that is perpendicular to two opposing sides of the bar and is parallel to the working surface) has an Amperian current distribution that runs up one side of the bar, across its upper surface and down the opposite side, closing on itself at the other end of the bar. As is the case with parallel wires carrying currents, the Amperian currents on the upper surface of that bar in the rotating annular bearing are repelled by anti-parallel (vectors that lie along parallel lines but point in opposite directions) currents on the surface of a bar element of the stationary annular bearing. Similarly, when the Amperian currents on the upper surface of the bar elements in the rotating annular bearing are parallel to those in the stator annular bearing ring, the force is attractive when the annuli are coaxial. 
         [0025]    Based on this disclosure, those skilled in the art will recognize that the non-conventional bearings and the object being supported (e.g., a rotor) can be configured in a variety of ways. For example, a circular bearing can be configured with its Amperian current pointed in one direction and another set of bearing elements can be located on a rotor to be supported by the bearing, the rotor bearings having Amperian current directions anti-parallel to that of the stator bearing. In another embodiment, the support bearing can be located such that its Amperian current direction is parallel to that of the rotor magnetic elements such that the support bearing pulls the rotor upward. 
         [0026]    In both cases, but for different reasons, if the above magnet blocks are lengthened or shortened, the strength of the magnetic field above their upper edge will increase or decrease. For the vertically polarized block of  FIG. 1B , this variation comes from the fact that the equivalent solenoid has fewer ampere-turns when shortened and vice-versa. For the horizontally polarized bar of FIG.  1 A, the magnitude of the Amperian current does not depend on the length of the magnet. However, in this case, where the Amperian current on the bottom edge is oppositely directed to the current across the top edge, the oppositely directed magnetic field produced by that current partially cancels the magnetic field above the bar coming from the top edge, and the cancellation effect is greater the shorter the bar. Note that the Amperian currents that run longitudinally in the bar have no influence on the levitation force since they are orthogonal to the end currents and are also oppositely directed to each other. 
         [0027]    The above-described difference in the origin of the length dependence of the magnetic field above the two different magnet blocks opens up an opportunity for a major increase in the magnetic field at the upper surface of one of the bars (the horizontally polarized bar on the left), without increasing its length. As will be described, this means that we can assemble a repelling or attracting annular bearing that, for the same length of magnet bars (and thus the same weight of magnets) can produce levitation forces that in typical cases are approximately a factor of two larger than those achievable with conventional annular magnetic bearings made up of either horizontally or vertically polarized bars. 
         [0028]    As the above discussion makes clear, in the case of the horizontally polarized bar, any technique that can shield the field from the transverse Amperian current at the other end of the bar from its effect at the working end of the bar will be nearly equivalent to using a double length bar in the array. One way this shielding could be done would be to locate a trough (e.g., a cylindrical trough) of ferromagnetic material (e.g., soft iron or other high permeability material) at the back end of the annular bearing. This will trap the flux emerging from the rear end of the bars making the bars to appear to be “infinite” in length. An alternative shield design would consist of individual thin-walled ferromagnetic rectangular cross-section “cups” fitted on the rear end of each bar. 
         [0029]    To insure that the shielding does not appreciably perturb the field at the working surface of the annular bearing, the length of the bars needs to be large compared to the working gap between the rotor and stator of the annular bearing. This is not a serious constraint, since the working gaps are of order 2.0 mm so that magnet lengths greater than about 2.0 cm should satisfy this constraint. 
         [0030]    To summarize, the invention consists of the use of magnet bars with a transverse polarization in constructing an annular bearing or conical-angular rotor or stator bearing element and then surrounding the bars at their back edges with a ferromagnetic shield (or shields). As discussed later, use of the shielding concept to increase the levitation forces will also work with vertically polarized magnet bars (e.g., the bar in  FIG. 1B ), but the gain in force is substantially less than the gain with horizontally polarized bars. 
         [0031]    Computer codes based on the Mathematica® platform were written in order to quantify the improvement in levitation force over conventional designs made possible by the invention. Comparisons were made of the values of the calculated levitation force per m 2  for an annular levitation bearing made up from transversely polarized rectangular ferrite magnet bars (Br=0.39 Tesla) with a width in the radial direction of 0.05 meters and a length in the axial direction of 0.025 m. The mean radius of the bearing was assumed to be 0.25 m so that the gaps between the magnets at their outer edges arising from assembling them in a circular pattern would be small enough to create a minimal effect on the magnetic field at their working surface. 
         [0032]    To illustrate the effect of the length of a magnet bar on the levitation force per unit area, calculations were performed for magnet bars with working surface dimensions of 0.025 m×1.0 m for both horizontally polarized bars (see e.g.,  FIG. 1A ), and vertically polarized bars (see e.g.,  FIG. 1B ). The magnet material in both cases is ferrite (Br=0.39 T). Graphs of the results of these calculations are shown in  FIGS. 2A and 2B . The bars had no shielding at their ends in these calculations.  FIG. 2A  shows plots of the levitation force/m 2  for horizontally polarized ferrite permanent magnet bars as a function of the length of the magnets.  FIG. 2B  shows plots of the levitation force/m 2  for vertically polarized ferrite permanent magnet bars as a function of the length of the magnets. 
         [0033]    As can be seen from the plots, the two polarizations have essentially identical force per unit area as a function of their length. As can also be seen, the lifting force per unit area for typical magnet thicknesses of 0.025 m is approximately a factor of two weaker than that for an equivalent bar reflecting the effect of the magnetic field at the infinite thickness. This factor is the grim that results in the example bars described above from the use of the ferromagnetic shield at the rear end of the magnets as described above. Because of edge effects from the relatively narrow bar width (0.025 m.) used in the calculations shown in  FIGS. 2A and 2B , if wider-dimensioned bars (or stacked smaller dimension bars) are employed, the gain factors were found to be substantially increased. As an example, a magnet set made up of a close-packed stack of 7 of the bars gave a force per unit area of 46,540 N/m 2  with using a ferromagnetic shield, but gave only 16,830 N/m 2  without the shield, representing a gain factor of 2.8. For this case, the ratio of levitated weight to the weight of the rotor magnets was calculated to be 39:1, again a factor of 2.8 larger than for the case of no shield. Finally, the calculations showed that the gain factor achieved if vertically polarized bars are used instead of horizontally polarized ones is less than that for horizontally polarized ones (being limited to the gain achieved by only doubling the effective length of the bar). Thus the optimum polarization in terms of gain in force is the horizontal one. 
         [0034]      FIG. 3  shows a cross-sectional view of a passive bearing system that utilizes the bearing elements of the present invention such that the system is stable against vertical (axial) and radial displacements. As shown in the figure, a vertical axis rotor  110  is being levitated by two conical repelling bearings. One bearing magnet  112  is located at the bottom of rotor  110 , and the other opposing bearing magnet  118  is located on the stator  116 . Bearing magnet  112  is configured such that its working surface  114  faces working surface  120  of bearing  118 . The surface of bearing magnet  112  that is opposite to the working surface  114  is located in a high permeability cup (comprised e.g., of soft iron)  116  according to the present invention. Likewise, the surface of bearing magnet  118  that is opposite to the working surface  120  is located in a high permeability cup  122  according to the principles of the present invention. In this system, tilt motion is stabilized with a stabilizer located near the top of rotor  110 , which stabilizer can be a conventional stabilizer as known in the art, or can be a stabilizer according to the teachings of the present invention. In one configuration, magnets  130  and  140  are arranged so that their respective working surfaces  132  and  142  (facing each other) have Amperian currents that are antiparallel, which causes them to repel each other. Similarly, in one configuration, magnets  112  and  118  are arranged so that their respective working surfaces  114  and  120  (facing each other) have Amperian currents that are antiparallel, which causes them to repel each other. The Amperian currents on the faces are perpendicular to the central axis of rotation  150 . Note that the soft iron material can be substituted with other suitably high permeability materials. In one embodiment, the two facing elements have Amperian currents flowing in antiparallel directions that are perpendicular to the central axis of the system. This example will make clear to those skilled in the art that the passive magnetic bearing configurations having alternative polarization and Amperian current direction can be utilized in a variety of useful ways to provide stabilization and levitation. Note that the bearing elements and high permeability cups, as well as the stabilizer elements, are not drawn to scale and they can, e.g., be much larger to provide greater forces. 
         [0035]      FIG. 4  shows an embodiment of an electro-mechanical battery (EMB)  200  and includes a vacuum chamber  202 . The system includes conventional touchdown bearings  204 . The system includes an electrostatic generator/motor  206 , a description of which can be found in U.S. patent application Ser. No. 13/796,678, titled “An Improved Electrode Geometry for Electrostatic Generators and Motors” incorporated herein by reference. In that application, see  FIGS. 11A and 11B  and the associated description. In the present  FIG. 4 , there is shown a stator  208  and a rotor/carbon fiber flywheel  210 . The lower levitation magnet pair comprises magnet ring  212  and magnet ring  214  which both utilize the bearing elements shown in  FIG. 1A  and as configured in a circle as shown in  FIG. 1C . To achieve levitation, magnet ring  212  must have its Amperian current direction pointing radially either toward or away from the central axis of the stationary system and magnet ring  214  which is attached to rotor  210  must be pointing radially with respect to the central axis of rotation of the rotor and most importantly, it must be pointed in the opposite direction from that of magnet ring  212 . Thus, the two ring will repel one another. 
         [0036]    The upper levitation magnet pair of  FIG. 4  comprises magnet ring  216  and magnet ring  218  which both utilize the bearing elements shown in  FIG. 1A  and as configured in a circle as shown in  FIG. 1C . To achieve levitation, magnet ring  216  must have its Amperian current direction pointing radially either toward or away from the central axis of the stationary system and magnet ring  218  which is attached to rotor  210  must be pointing radially with respect to the central axis of rotation of the rotor and most importantly, it must be pointed in the same direction as that of magnet ring  216 . Thus, the two ring will attract one another. 
         [0037]    The system of  FIG. 4  also employs a magnetic stabilizer, which can be achieved through methods known in the art, such as the use of a Halbach array magnetic stabilizer. Embodiments of the present invention can be utilized to form the stabilizer, with the advantages over the use of a Halbach array, as discussed supra. In this case, a ring  220  of magnets are attached to the stationary system. Another ring  222  of magnets, also configured as shown in  FIG. 1C , are attached to rotor  210 . The Amperian current directions on the working surfaces of the magnets of rings  220  and  222  are in the same direction, thus producing an attractive force between the two rings. If the rotor moves out of rotation, the upper ring  220  exerts a restoring force on ring  222 . 
         [0038]    The foregoing description of the invention has been presented for purposes of illustration and description and is not intended to be exhaustive or to limit the invention to the precise form disclosed. Many modifications and variations are possible in light of the above teaching. The embodiments disclosed were meant only to explain the principles of the invention and its practical application to thereby enable others skilled in the art to best use the invention in various embodiments and with various modifications suited to the particular use contemplated. The scope of the invention is to be defined by the following claims.