Patent Publication Number: US-2013229078-A1

Title: Control for rotating electrical machinery

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This patent application is a continuation-in-part of U.S. patent application Ser. No. 13/280,314, filed Oct. 24, 2011, which is incorporated herein by reference. 
    
    
     FIELD 
     The present invention generally relates to rotating electrical machinery. More particularly, some example embodiments relate to improved and simplified control of rotating electrical machinery. 
     BACKGROUND 
     A common and essentially universal feature of rotating electrical machinery is the use of electromagnetic effectors or actuators to produce rotational movement as required by a particular application. These electromagnetic effectors or actuators commonly consist of electrically conductive wire that is wound into multiconductor bundles of widely varying topologies, sometimes referred to as coils. Electrical currents are passed through these coils, producing magnetic fields that interact with other magnetic fields and/or magnetic components so as to rotate a portion of a machine sometimes referred to as a rotor. Commonly, these coils have a single function in that they are employed only in producing rotation (as in an electric motor) or changing rotation into electric power (as in a generator). 
     Examples of rotating electrical machinery that use such electromagnetic effectors or actuators include electric motors and electric generators, which convert electrical energy into mechanical motion and mechanical motion into electrical energy, respectively. In electric motors, currents are driven through one or more electromagnetic coils to create magnetic fields that react against other magnetic fields and/or magnetic materials so as to rotate a portion of the machine commonly called a rotor. In electric generators, a rotor that is caused to rotate by mechanical means interacts with magnetic fields or magnetic elements to induce currents to flow in electromagnetic coils, thereby changing mechanical energy into electrical energy. The electromagnetic coils that are employed in producing rotation or changing rotation into electric power may be referred to as a first category of electromagnetic actuators. 
     A second category of electromagnetic actuators may be present in some rotating electrical machinery in the form of components that employ electrical power to stabilize the position of a rotor. Common examples include machines that incorporate magnetic bearings in which all or a portion of the magnetic actuator forces are generated by electromagnetic coils. It is often the case that such electromagnetic actuators are dedicated components, that is, they perform no other function beyond their use in rotor position control. 
     Rotating electrical machinery with magnetic bearings are often referred to as “bearingless” systems. On inspection, these bearingless systems are seen to exhibit the most basic function of a bearing, and are thus not truly bearingless. In this regard, the basic function of bearings and some of the detrimental aspects of their use in rotating machinery will now be described. 
     It is common with rotating electrical machinery to constrain the rotor within particular position limits during operation. For example, mechanical, magnetic, and/or other bearings are commonly used to support rotors in motors and generators so that the rotor is separated from stationary components at all times during machine operation. 
     A rotor exhibits a principal axis of rotation, defined by the rotor design and by the particular distribution of mass in the components and materials that make up the rotor. This axis of rotation may be termed the inertial axis of rotation, and is the axis about which the rotor would spin in the absence of any perturbing outside force. Bearings operate by confining a rotor to a particular axis of rotation determined by the bearing design and construction, and by the interaction of the bearings with the rotor they support. This axis, termed the geometric axis of rotation, often differs from the rotor&#39;s inertial axis of rotation. 
     To the extent that a rotor&#39;s inertial axis of rotation differs from its geometric axis of rotation, forces are developed that are resolved at the bearings, which are the mechanical interface between the spinning rotor and the stationary environment. Non-identity between inertial and geometric axes may occur as instances of three conditions or combinations thereof: simple displacement in which the two axes are parallel and therefore not intersecting, an angular displacement in which the two axes are not parallel but do intersect at one point, or an angular displacement in which the two axes are not parallel and do not intersect at any point. In the art of rotating machinery, such differences are commonly termed as “imbalance” of the rotor. To the extent that the rotor is imbalanced, that is, to the extent that its inertial rotational axis differs from a bearing-imposed geometric axis, forces are developed at the bearings that cause wear, destructive resonances, and other detrimental effects known in the art of rotating machinery. 
     Bearings comprise a wide range of technologies: they may be fabricated from rigid materials (e.g., sleeve, journal, and rolling element bearings), or they may employ fluids (e.g., film bearings, air bearings), or they may employ magnetic forces to preclude physical contact between moving and stationary components. Magnetic bearings may be passive or actively controlled. Different bearing technologies may be mixed within a single system to place a rotor or rotors at position(s) required for successful device operation. 
     While bearings comprise a great variety of technologies, they all share a common characteristic: when the rotational axis of the rotating assembly which they support becomes non-coincident with the geometric rotational axis imposed by a bearing, bearings exert a force on the rotating assembly to maintain the inertial axis within an acceptable deviation from the geometric axis. This is the fundamental commonality among bearings of widely differing technologies. In solid material bearings, counterforces are generated when the bearing materials are deformed by rotational forces, and the magnitudes of counterforces are controlled by the degree of noncoincidence between inertial and geometric rotational axes, the rotational rate, and the properties of the bearing materials. In film bearings, counterforces are generated by compression of a thin lubricating fluid, and the magnitude of these forces are determined in part by the particulars of the fluid in addition to rotational rate and the disparity between inertial and geometric rotational axes. In passive magnetic bearings, counterforces are generated by the change in distance between magnetic elements, which may mediate a change in the force between two permanent magnets, or a change in the force between a magnet and a moving conductor. In active magnetic bearings, counterforces may be generated by changing the magnitude and/or direction of electric currents through conductive elements in response to drive signals computed from sensors that detect departures of a rotor from its desired position. In all these cases, the counterforces developed by bearings are (a) synchronous with rotation of the rotor and (b) increase and decrease according to the degree of departure of the rotor from its desired position. 
     The prior art in rotating electrical machinery demonstrates the long use of bearings despite the significant disadvantages and limitations they confer. The prior art also demonstrates the use of active magnetic bearings that require effector components such as actuator coils that do not contribute to the primary function of the rotating electrical machine of which they are a part. 
       FIG. 1A  schematically illustrates an example rotating electrical machine  100 A (hereinafter “machine  100 A”) including mechanical bearings  102 A,  102 B (collectively “mechanical bearings  102 ”). In the illustrated embodiment, the machine  100 A is implemented as an electrical motor including an electrical drive source  104  (hereinafter “drive source  104 ”). Alternately, the machine  100 A may be implemented as an electrical generator by substituting an electrical load for the drive source  104 , in which case magnets within a rotor of the machine  100 A may induce electrical currents in stator windings, thereby converting the rotor&#39;s kinetic energy into electrical energy. 
     The machine  100 A includes a stator assembly  106 A with a shaft  106 B extending from both ends thereof and fixing the stator assembly  106 A to a stationary stator mounting plate  108 . The stator assembly  106 A includes two electromagnetic coils or sets of windings. More generally, the stator assembly  106 A may include N electromagnetic coils. The electromagnetic coils may be energized according to drive currents generated by per-coil drivers  104 A of the drive source  104  in response to control signals generated by a controller  104 B of the drive source  104 . The controller  104 B may be coupled to an electrical input  110 . 
     The stator assembly  106 A includes a long axis  112  that is parallel to a Z axis of an arbitrarily-defined coordinate system  114 . The coordinate system  114  includes mutually perpendicular X, Y and Z axes. 
     The machine  100 A additionally includes a rotor  116 A that may be substantially cylindrical or more generally may have any shape that is substantially radially symmetric. The rotor  116 A includes an axis of rotation  118  that is substantially concentric with the long axis  112  of the stator assembly  106 A. The rotor  116 A is configured to rotate or spin about its axis of rotation  118  around the stator assembly  106 A during normal operation, as generally denoted at  120 . 
     The rotor  116 A includes magnets  122  implemented as permanent magnets, electromagnets, or any combination thereof. The magnets  122  provide a magnetic field. In operation, the magnetic field of the magnets  122  interacts with magnetic fields generated by energizing the electromagnetic coils of the stator assembly  106 A, thereby generating a torque on the rotor  116 A and causing the rotor  116 A to rotate or spin about the stator assembly  106 A. 
     The spinning rotor  116 A is stabilized in space and rotatably supported by the mechanical bearings  102 , including an upper bearing  102 A and a lower bearing  102 B that are attached to the shaft  106 B. The mechanical bearings  102  constrain the rotor  116 A in translation along the X, Y, and Z axes, and constrain the rotor in tilt about the X and Y axes (often referred to, respectively, as θ x  and θ w ). The mechanical bearings  102  additionally permit rotation of the rotor  116 A about the Z axis in either direction. An example of a class of mechanical bearings that may accomplish such functions is referred to as a double angular contact ball bearing, which may sustain loads against movement in three axes simultaneously. As explained above, counterforces developed by the mechanical bearings  102  are (a) synchronous with rotation of the rotor  116 A and (b) increase and decrease according to the degree of departure of the rotor  116 A from its desired position. 
       FIG. 1B  schematically illustrates an example rotating electrical machine  100 B (hereinafter “machine  100 B”) including active magnetic bearings (AMBs)  124 A,  124 B (collectively “AMBs  124 ”). The machine  100 B of  FIG. 1B  is similar in many respects to the machine  100 A of  FIG. 1A  and includes many of the same or identical components, as denoted by the use of identical reference numbers. For example, similar to the machine  100 A of  FIG. 1A , the machine  100 B of  FIG. 1B  includes a drive source  104 , a stator assembly  106 A including electromagnetic coils, a shaft  106 B, a stationary stator mounting plate  108 , and magnets  122 . Moreover, although illustrated as an electrical motor, the machine  100 B may instead be implemented as an electrical generator by substituting an electrical load for the drive source  104 . 
     The machine  100 B additionally includes a rotor  116 B that is generally similar to the rotor  116 A of  FIG. 1A , except that the rotor  116 B includes upper and lower magnets  126 A,  126 B (collectively “magnets  126 ”) or magnet assemblies coupled thereto which respectively form a part of an upper AMB  124 A and a lower AMB  124 B. The upper AMB  124 A additionally includes two X axis upper bearing coils  128 A,  128 B extending radially from the shaft  106 B in opposite directions parallel to the X axis and two Y axis upper bearing coils  130 A,  130 B (only one is depicted in  FIG. 1B ) extending radially from the shaft  106 B in opposite directions parallel to the Y axis. Analogously, the lower AMB  124 B additionally includes two X axis lower bearing coils  128 C,  128 D extending radially from the shaft  106 B in opposite directions parallel to the X axis and two Y axis lower bearing coils  130 C,  130 D (only one is depicted in  FIG. 1B ) extending radially from the shaft  106 B in opposite directions parallel to the Y axis. The four X axis bearing coils  128 A- 128 D are collectively referred to hereinafter as X axis bearing coils  128 , while the four Y axis bearing coils  130 A- 130 D are collectively referred to hereinafter as Y axis bearing coils  128 . 
     The machine  100 B further includes upper AMB drive electronics  132 A and lower AMB drive electronics  132 B (collectively “drive electronics  132 ”). The upper AMB drive electronics  132 A may be communicatively coupled to the upper AMB  124 A, while the lower AMB drive electronics  132 B may be communicatively coupled to the lower AMB  124 B. One or more sensors, processors, and/or other components associated with the AMBs  124  may also be included in the machine  100 B, although they have been omitted from  FIG. 1B  for clarity. The machine  100 B may additionally include one or more components for constraining the Z axis positioning of the rotor  116 B, which components have similarly been omitted from  FIG. 1B  for clarity. The use of AMBs  124  in the machine  100 B of  FIG. 1B  may substantially eliminate mechanical wear associated with mechanical bearings, such as the mechanical bearings  102  of  FIG. 1A . 
     In operation, the drive electronics  132  selectively energize the X axis bearing coils  128  and the Y axis bearing coils  130  to generate magnetic fields that interact with magnetic fields of the magnets  126  to ultimately constrain the rotor  116 B in translation along the X and Y axes, and to constrain the rotor  116 B in tilt about the X and Y axes, e.g., θ x  and θ y . For example, when energized, each of the X axis bearing coils  128  and/or Y axis bearing coils  130  may attract the magnets  126  attached to the rotor  116 B and thereby cause the rotor  116 B to move in the X or Y axis with respect to the stationary stator assembly  106 A, depending on which of the X axis bearing coils  128  and/or Y axis bearing coils  130  are energized. Thus, in the embodiment of  FIG. 1B , two coils are required to effect bidirectional translation on the X axis and two coils are required to effect bidirectional translation on the Y-axes. Moreover, two sets of four coils, including one at each end of the stator assembly  106 A (e.g., one set of four coils in the upper AMB  124 A and one set of four coils in the lower AMB  124 B), are required to control tilt, or θ x  and θ y , of the rotor  116 B. Thus, the machine  100 B of  FIG. 1B  requires a total of 8 bearing coils  128 ,  130 , along with drive electronics  132  and/or other associated components to provide rotor position control in only four degrees of freedom, e.g., X, Y, θ x , and θ y . 
     Thus, in the machine  100 B of  FIG. 1B , the AMBs  124 , the drive electronics  132 , and/or other associated components are provided in addition to the electromagnetic coils of the stator assembly  106 A and the drive source  104  and do not contribute to the primary function of the machine  100 B, which is the conversion of electrical energy to kinetic energy (in the case of an electrical motor) or the conversion of kinetic energy to electrical energy (in the case of an electrical generator). Moreover, the two AMBs  124 , drive electronics  132 , and/or other associated components can significantly increase the cost and complexity of the machine  100 B, and/or are subject to failure, thereby reducing the reliability of the machine  100 B compared to other machines in which such components are not necessary. 
     The subject matter claimed herein is not limited to embodiments that solve any disadvantages or that operate only in environments such as those described above. Rather, this background is only provided to illustrate one exemplary technology area where some embodiments described herein may be practiced. 
     BRIEF SUMMARY OF SOME EXAMPLE EMBODIMENTS 
     The embodiments discussed herein generally relate to improved and simplified control of rotating electrical machinery. Some example embodiments reduce and/or eliminate the need for bearings to maintain the position of a rotor, and do so without requiring additional current-carrying coils to accomplish this function, instead employing coils that are already incorporated into a rotating electrical machine to effect its rotary operation. 
     Accordingly, an example embodiment includes a rotating electrical machine including a stator assembly, a rotor, and a controller. The stator assembly has two or more stator control coils and is centered on a Z axis that is perpendicular to an XY plane defined by mutually perpendicular X and Y axes. The rotor is configured to rotate about a rotational axis that is nominally collinear with the Z axis and has a magnet array that provides a magnetic field configured to pass through the two or more stator control coils. The controller is configured to control the two or more stator control coils to selectively generate magnetic fields that interact with the magnetic field of the magnet array to: control rotation of the rotor about the second axis; and one or both of: control translation of the rotor in the XY plane; and control rotation of the rotor about the X axis and the Y axis. 
     Another example embodiment includes a method of providing multi-axis control in a rotating electrical machine. The method includes providing a rotating electrical machine including a stator assembly having multiple stator control coils and a rotor having a magnet that provides a magnetic field that passes through the stator control coils. The rotor has at least two degrees of freedom, including a first degree of freedom including rotation about a Z axis, and any one or more of: a second degree of freedom including translation along the Z axis; a third degree of freedom including rotation about an X axis perpendicular to the Z axis; a fourth degree of freedom including translation along the X axis; a fifth degree of freedom including rotation about a Y axis perpendicular to each of the X and Z axes; and a sixth degree of freedom including translation along the Y axis axes. The method also includes operating the stator control coils to control the rotor with respect to the first degree of freedom, including increasing or decreasing a rotational rate of the rotor about the Z axis, wherein the rotating electrical machine functions as an electrical motor or an electrical generator by rotation of the rotor about the Z axis. The method also includes operating at least some of the same stator control coils that control the rotor with respect to the first degree of freedom to control the rotor with respect to any one or more of the first, second, third, fourth, fifth, or sixth degrees of freedom. 
     This Summary is provided to introduce a selection of concepts in a simplified form that are further described below in the Detailed Description. This Summary is not intended to identify key features or essential characteristics of the claimed subject matter, nor is it intended to be used as an aid in determining the scope of the claimed subject matter. 
     Additional features and advantages of the invention will be set forth in the description which follows, and in part will be obvious from the description, or may be learned by the practice of the invention. The features and advantages of the invention may be realized and obtained by means of the instruments and combinations particularly pointed out in the appended claims. These and other features of the present invention will become more fully apparent from the following description and appended claims, or may be learned by the practice of the invention as set forth hereinafter. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       To further clarify the above and other advantages and features of the present invention, a more particular description of the invention will be rendered by reference to specific embodiments thereof which are illustrated in the appended drawings. It is appreciated that these drawings depict only typical embodiments of the invention and are therefore not to be considered limiting of its scope. The invention will be described and explained with additional specificity and detail through the use of the accompanying drawings in which: 
         FIG. 1A  schematically illustrates an example rotating electrical machine including mechanical bearings; 
         FIG. 1B  schematically illustrates an example rotating electrical machine including active magnetic bearings; 
         FIG. 2  schematically illustrates an example two-phase rotating electrical machine (hereinafter “machine”) according to some embodiments described herein; 
         FIG. 3A  is an overhead view of an example embodiment of the magnet array that may be included in the machine of  FIG. 2 ; 
         FIG. 3B  is a perspective view of a magnet that may be included in the magnet array of  FIG. 3A ; 
         FIG. 3C  is a graph of magnetic field intensity as a function of distance from a center C of the magnet array of  FIG. 3A  in an XZ plane; 
         FIGS. 4A-4B  depict a front view and a side view, respectively, of an example embodiment of a stator control coil that may be included in the stator assembly of  FIG. 2 ; 
         FIG. 5A  is a schematic view along a Z axis of an example embodiment of the stator assembly of  FIG. 2 ; 
         FIG. 5B  is a schematic side view illustrating a relative orientation of two of the stator control coils in the stator assembly of  FIG. 5A ; 
         FIG. 5C  illustrates example electrical interconnections of the stator control coils of the stator assembly of  FIG. 5A ; 
         FIGS. 6A and 6B  include cross-sectional views of the machine of  FIG. 2  in a plane parallel to an XY plane; and 
         FIG. 7  illustrates a perspective view of a stator coil with a nonplanar stator coil geometry. 
     
    
    
     DETAILED DESCRIPTION 
     Some embodiments described herein include rotating electrical machinery that employs electromagnetic actuator coils for multiple functions. For example, electromagnetic coils that impart rotation to a rotor are also used to position the rotor. This confers at least two important, independent benefits: it reduces the number of coils required to rotate and control the position of a rotor, and it enables control of the rotor without use of bearings. Reduction of the number of control coils to effect rotation and position control confers additional benefits in reducing the number of electrical drive subsystems needed, simplifies mechanical construction of the machine, and improves reliability through reduction of component count. 
     In an example embodiment, electrical coils already present in the machine are employed to provide up to 6 axes of position and attitude control of the rotor in addition to being employed for their normal function of effecting changes in rotation rate of the electrical machine. Specifically, the machine may include a rotating portion, such as a rotor, that rotates about the Z axis, where the rotation is driven by electrical coils that deliver energy to the rotating portion, or where the electrical coils extract energy from the rotating portion. The electrical coils, together with one or more other components, may cooperate to perform two or more of the following functions: (1) effect translational positioning of the rotating portion along at least one of up to three mutually perpendicular X, Y, and/or Z axes and/or effect increases, (2) effect tilting of the rotating portion in either or both of the X and Y axes, and (3) effect normal operation of the rotating portion, including increases and/or decreases in the rate of rotation about the Z axis of the rotating portion. The foregoing functions may be achieved without the use of dedicated electrical coils beyond those used to effect changes in the rate of rotation about the Z axis. 
     Although some embodiments will be described in terms of an electrical motor or generator that has a stationary set of electrical coils surrounded by a moving magnetic field that is generated by moving permanent magnets, it will be appreciated that the principles described herein are applicable to rotating electrical machines in which electrical coils are rotating rather than stationary, and/or in which changing magnetic fields are provided by appropriately driven electromagnets alone or in combination with permanent magnets. 
     An example embodiment will be described in terms of a two-phase electrical motor or generator that employs a bipolar cylindrical magnetic field. However, the invention is not limited to two-phase rotating electrical machinery. Indeed, the invention may be applied in single-phase motors or generators. The invention may also be applied in electrical motors or generators exhibiting three or more electrical phases. 
     Reference will now be made to the drawings to describe various aspects of example embodiments of the invention. It is to be understood that the drawings are diagrammatic and schematic representations of such example embodiments, and are not limiting of the present invention, nor are they necessarily drawn to scale. 
       FIG. 2  schematically illustrates an example two-phase rotating electrical machine  200  (hereinafter “machine  200 ”) according to some embodiments described herein. While various components are illustrated in  FIG. 2 , the machine  200  may alternately or additionally include similar but different components than those illustrated and/or other components not illustrated in  FIG. 2 . Although depicted as an electrical motor, the machine  200  may alternately be implemented as an electrical generator. 
     The machine  200  includes a stator assembly  202  with a shaft  204  extending from both ends thereof and fixing the stator assembly  202  to stationary upper and lower stator mounting plates  206 A,  206 B. The stator assembly  202  includes four electromagnetic coils or stator control coils. More generally, the stator assembly  202  may include N stator control coils. The stator control coils may be energized according to drive currents generated by percoil drivers  208  of a drive source  210  in response to control signals generated by a controller  212  of the drive source  210 . 
     The machine  200  additionally includes a rotor  213  configured to rotate about the stator assembly  202 . The rotor  213  includes a rotor tube  214  and, although not shown, may also include one or more additional masses coupled to the rotor tube  214  to increase the amount of kinetic energy that may be developed by rotation of the rotor  213  within the machine  200 . In some embodiments, the rotor tube  214  includes 6061 T6 aluminum alloy and has a nominal overall length (e.g., in the Z direction) of 12 inches, an inner diameter of three inches, and an outer diameter of 3.5 inches. The rotor tube  214  is aligned with its long axis parallel to and coincident with the Z axis. The Z axis is the principal axis of rotation of the rotor tube  213  in the present example. 
     Fixed to an inner surface  214 A of the rotor tube  214  is a magnet array  216 . The magnet array  216  includes an eight segment dipolar permanent magnet Halbach array in some embodiments, an example of which is described in more detail below. It will be understood by those skilled in the art that other configurations of permanent magnets may be employed to meet particular requirements, and that such operable configurations do not limit this invention. 
     At the upper (+Z axis) end of the rotor tube  214 , the machine  200  includes a means  218  for suspending the rotor  213  (hereinafter “suspending means  218 ”), including the rotor tube  214 , against the force of gravity. In the present example, the suspending means  218  includes a conventional magnetic levitator as is known in the art of magnetically suspended rotating machinery. Other means of supporting the rotor  213 , such as radially compliant mechanical means, may be employed, and such operable suspension means do not limit this invention. 
     The stator assembly  202  including the four stator control coils is positioned within a hollow interior of the rotor tube  214  so that the stator control coils substantially intersect a magnetic field created by the magnet array  216 , and so that the center of force of the magnetic field created by the magnet array  216  does not coincide with the center of force of the stator control coils when the stator control coils are energized. The shaft  204  or other mechanical means are provided which support the stator assembly  202  radially concentric to the interior of the rotor tube  214  and fix the stator assembly  202  with respect to rotation about and translation along the Z axis. 
     The machine  200  additionally includes one or more upper rotor position sensors  220  and/or one or more lower rotor position sensors  222 . Each of the upper and lower rotor position sensors  220 ,  222  may include, but is not limited to an optical, inductive, capacitive, acoustic and/or other position sensor. In the present example, the upper and lower rotor position sensors  220 ,  222  each include one or more Hall sensors to sense the magnitude and direction of a rotating magnetic field produced by the magnet array  216 . For example, the upper rotor position sensors  220  may include four Hall sensors mounted at or near an upper Z axis extreme of the shaft  204  coupled to the upper stator mounting plate  206 A, while the lower rotor position sensors  222  may similarly include four Hall sensors mounted at or near a lower Z axis extreme of the shaft  204  coupled to the lower stator mounting plate  206 B. 
     The upper rotor position sensors  220  and the lower rotor position sensors  222  are positioned such that the local magnetic field is simultaneously measured in the +X, −X, +Y, and −Y directions at each end of the stator assembly  202 . The upper rotor position sensors  220  and the lower rotor position sensors  222  generate and provide data to the controller  212  from which the controller  212  may determine the position of the rotor  213  with respect to the X, Y, and Z axes, and the angular excursion of the rotor  213  about the X and Y axes, and the rotational position of the rotor  213  in its rotation about the Z axis. The data generated by the upper rotor position sensors  220  and the lower rotor position sensors  222  may be made available to the controller  212  at sufficiently frequent intervals to enable the controller  212  to compute the state of the rotor  213  and to compute corrective signals, if required. The corrective signals may be applied to the stator control coils of the stator assembly  202  to adjust the state of the rotor  213 , as needed, which may include one or more of increasing or decreasing a rotational rate of the rotor  213  about the Z axis, translating the rotor  213  with respect to the stationary components of the machine  200  in the X, Y, and/or Z directions, and tilting the rotor  213  about the X and/or Y axes. 
     It will be apparent that no particular data acquisition interval may be specified, as the interval will vary with the rotor&#39;s rotational speed, the rapidity with which computation of the rotor&#39;s state may be made, and the magnitude of control authority available to the rotor positioning system, as well as the requirement, if any, that the system maintain rotor position in the presence of exceptional disturbances that may arise during operation of the rotor. An example of exceptional disturbances would be the imposition of forces on an operating flywheel due to earth movements (e.g., earthquakes) that couple to the machine  200 . 
       FIG. 3A  is an overhead view of an example embodiment of the magnet array  216  that may be included in the machine  200  of  FIG. 2 , and  FIG. 3B  is a perspective view of a magnet  302 A that may be included in the magnet array  216  of  FIG. 3A , all arranged in accordance with at least some embodiments described herein. With combined reference to  FIGS. 3A-3B , the magnet array  216  includes eight individual magnets  302 A- 302 H (collectively “magnets  302 ”). The magnets  302  are arranged to form a hollow cylinder having an inner diameter of 2R i  each magnet  302  having the form illustrated in  FIG. 3B . Magnetization vectors within each magnet  302  are shown in  FIG. 3A  by arrows that lie within the outline of each magnet  302 , the arrowhead corresponding to magnetic north. Curved lines with solid arrowheads within the hollow interior of the magnet array  216  array indicate the configuration of the magnetic field within this region as projected onto the XY plane. The configuration of the magnet array  216  is sometimes referred to as a dipolar cylindrical Halbach array. 
     In some embodiments, each of the magnets  302  has a length L (e.g., parallel to the Z axis) of four inches, an inner semi-cylindrical surface  304  having a radius of curvature of R i , which may be equal to 25.4 millimeters (mm), and an out semi-cylindrical surface  306  having a radius of curvature of 43.4 mm. In the magnet array  216 , the inner semi-cylindrical surfaces  304  of all of the magnets  302  form an inner cylindrical surface of the magnet array  216  including a minimum radius of the rotor  213  of the machine  200  of  FIG. 2 . It will be apparent, with the benefit of the present disclosure, that a central volume of cylindrical shape is left open by this construction. The magnets  302  may be fabricated from C8 or equivalent grade ceramic magnetic material, and/or may be fabricated from different magnetic materials as may be determined by particular engineering needs. 
       FIG. 3C  is a graph of magnetic field intensity as a function of distance from a center C of the magnet array  216  of  FIG. 3A  in the XZ plane, arranged in accordance with at least some embodiments disclosed herein. As illustrated, magnetic field intensity is substantially zero at the center of the magnet array  216 , and rises along any radius from the center outward to a local free space maximum at the inner cylindrical surface of the magnet array  216  that is collectively formed by the inner semi-cylindrical surfaces  304  of all of the magnets  304 . This pattern is also observed in the YZ plane.  FIG. 3C  additionally illustrates a diameter D of the stator assembly  202 . 
       FIGS. 4A-4B  depict a front view and a side view, respectively, of an example embodiment of a stator control coil  400  that may be included in the stator assembly  202  of  FIG. 2 , arranged in accordance with at least some embodiments described herein. For example, the stator assembly  202  may include four stator control coils  400 . The stator control coil  400  of  FIGS. 4A-4B  includes electrically conducting material such as copper wire that allows the flow of electrical current when its leads are connected to an external source of power, such as the drive source  210  of  FIG. 2 , and which allows the flow of electrical current when subjected to a changing magnetic field and when its leads are connected to an external electrical load (not shown). 
     The stator control coil  400  has a major length L major  parallel to the Z axis and minor length L minor  parallel to the XY plane. Generally, the stator control coil  400  comprises multiple turns of conducting material whose number and physical disposition vary according to the requirements of its particular use. 
     More particularly, while the stator control coil  400  illustrated in  FIGS. 4A-4B  is constructed by winding a coil of copper wire less than three turns in order to simply illustrate how the stator control coil  400  is formed, in one embodiment, the stator control coil  400  is constructed by forming 39 turns of #22 gauge copper wire having a thin insulating layer into a coil wound as tightly as is practical. The coil may have a major length L major  of approximately five inches, a minor length L minor  of approximately 0.75 inches, and of wire cross section dimensions of approximately 0.5 inches wide x approximately 0.25 inches deep. These dimensions are determined by electrical requirements and are not limiting to the practice of the invention. 
     The stator control coil  400  is substantially rectangular and planar in overall form. That is, the stator control coil  400  does not exhibit a substantial overall twist apart from those functionally insignificant departures from topological perfection that are incident to practical fabrication of an electrical coil. 
     In an example embodiment, four stator control coils  400  are mounted on a stator assembly that provides mechanical support for the stator control coils  400  and which allows electrical connections to be made to each stator control coil  400 . The four stator control coils  400  may be disposed upon the stator assembly according to the schematic views presented in  FIGS. 5A and 5B . The stator control coils  400  may be controllably electrically energized, and/or controllably connected to electrical loads singly or in combination in order to exert control forces on a rotor. 
       FIG. 5A  is a schematic view along the Z axis of an example embodiment of the stator assembly  202  of  FIG. 2 , arranged in accordance with at least some embodiments described herein. In the illustrated embodiment, the stator assembly  202  includes four stator control coils A 1 , A 2 , B 1 , and B 2  that may each correspond to the stator control coil  400  of  FIGS. 4A-4B .  FIG. 5B  is a schematic side view illustrating a relative orientation of two of the stator control coils A 1  and B 1  in the stator assembly  202  of  FIG. 5A , arranged in accordance with at least some embodiments described herein. The stator control coils A 1 , A 2 , B 1 , B 2  may be affixed to a supporting core or form which has been omitted form  FIGS. 5A-5B  for clarity. 
       FIG. 5C  illustrates example electrical interconnections  500  of the stator control coils A 1 , A 2 , B 1 , B 2 , arranged in accordance with at least some embodiments described herein. In these and other embodiments, the drive current of each of the stator control coils A 1 , A 2 , B 1 , B 2  may be controlled in magnitude, polarity, frequency, and relative phase, or any combination thereof. 
       FIGS. 6A and 6B  include cross-sectional views of the machine  200  of  FIG. 2  in a plane parallel to the XY plane, arranged in accordance with at least some embodiments described herein. The relative positioning of the stator assembly  202 —including the stator control coils A 1 , A 2 , B 1 , and B 2 —and the rotor  213 —including the rotor tube  214  and the magnet array  216 —is illustrated in  FIGS. 6A-6B . 
     Operation of the machine  200  will next be described with respect to FIGS.  2  and  6 A- 6 B. The following description assumes that the rotor  213  is initially centered radially on the Z axis and is levitated at its desired location along the Z axis, but is at rest with respect to spin, and that the upper rotor position sensors  220  and the lower rotor position sensors  222  each include four Hall sensors mounted at opposite extrema of the shaft  204 . A command to spin the rotor  213  is delivered by the controller  212  to the per-coil drivers  208 . 
     The position and stationary state of the rotor  213  are computed by the controller  212  from Hall sensor magnetic field data received from the upper and lower rotor position sensors  220 ,  222 . The controller  212  generates and provides control signals to the per-coil drivers  208  to cause the per-coil drivers  208  to generate drive currents that energize the stator control coils A 1 , A 2 , B 1 , B 2  so as to expose the rotor  213  to a substantially pure torque  602  ( FIG. 6A ), with substantially no net radial translation or tilt forces. In particular, electrical currents of equal magnitude flow through each of the four stator control coils A 1 , A 2 , B 1 , B 2 , ensuring that each stator control coil develops a magnetic field substantially equal in magnitude to that of each of the other stator control coils A 1 , A 2 , B 1 , B 2 . A magnitude of the torque  602  may vary from a minimum to a maximum as the magnetic field of the magnet array spins about the stator assembly  202  as the rotor  213  spins. 
     Example waveforms corresponding to the drive currents that drive the stator control coils A 1 , A 2 , B 1 , and B 2  to generate magnetic fields with substantially equal magnitude are denoted at  604  in  FIG. 6A . It is apparent, with the benefit of the present disclosure, that under this condition, force vectors that resolve onto the rotor  213  as radial translation forces sum to zero when integrated around the rotor, while force vectors that have nonzero components tangential to the rotor are additive and result in rotation of the rotor  213  with respect to the stator assembly  202 . In this instance, the stator control coils A 1 , A 2 , B 1 , B 2  function much the same as simple spin-up coils in electric motors known to the art and have no effect on rotator state of the rotor  213  other than rotation about the Z axis. 
     As the rotor  213  spins about the stator assembly  202 , the dipolar magnetic field provided by the magnet array  216  and passing through the stator assembly  202  completes two apparent revolutions for each full rotation of the rotor  213 . That is, any given location of the stator assembly  202  will be exposed to opposing poles of the dipolar magnetic field twice for each single rotation of the rotor  213 . The Hall sensor magnetic field data generated by the upper and lower rotor position sensors  220 ,  222  thus varies at twice the rotation rate of the rotor  213  and may be readily used to compute the rotation rate of the rotor  213 . In addition, the upper and lower rotor position sensors  220 ,  222  measure substantially simultaneous values of the local magnetic field along both directions of the X and Y axes at each Z end of the stator assembly  202 . Because of the radial variation of magnetic field strength within the magnet array  216  as depicted in  FIG. 3C , radial displacement of the rotor  213  may be calculated for two different positions along the Z axis (the two locations occupied by the upper and lower rotor position sensors  220 ,  222 ), and therefore radial position and tilt of the rotor  213  may be calculated in the following manner. 
     Radial motion of the rotor  213  causes a corresponding radial displacement of the magnetic field provided by the magnet array  216 . This in turn will change the local magnetic field magnitude measured by the upper and/or lower rotor position sensors  220 ,  222  in which the radial motion has a vector projection. Thus, if the rotor  213  translates purely along the X axis, the two pairs of Hall sensors (one pair at each end of the stator assembly  202 ) within the upper and lower rotor position sensors  220 ,  222  that respond to X axis components of the local magnetic field will measure different values from those measured prior to the translation along the X axis. In particular, Hall sensors that are brought into closer proximity with the magnet array  216  will measure greater magnetic field strength, while those Hall sensors that are positioned further away from the magnet array  216  will measure a lower magnetic field strength. This magnetic field strength data, when combined with known positions of the Hall sensors, can be used to compute the magnitude and direction of a radial translation of the rotor  213 , and can also be used to computer whether the rotor  213  is tilting about the X and/or Y axes. In the latter case, the change in magnitudes of Hall sensor signals may differ between the two sets of Hall sensors at the two Z ends of the stator assembly  202 . The variation may indicate different magnitudes of radial translation at the corresponding Z axis positions of the rotor  213 , which defines a tilt of the rotor  213  about the X and/or Y axis. Further, temporal analysis of position states of the rotor  213  as calculated from Hall sensor data can quantify velocity and acceleration of the rotor  213 , which may be incorporated into position control algorithms as part of computation of position correction commands. 
     Rotor radial motion without torque can be produced by interactions of the magnetic fields generated by one or more of the stator control coils A 1 , A 2 , B 1 , B 2  by driving selected ones of the stator control coils A 1 , A 2 , B 1 , B 2  with unequal drive currents. An example will be described in which one pair of stator coils (A 1  and A 2 ) are driven to produce radial force on the rotor. Example waveforms corresponding to the drive signals that drive the stator control coils A 1  and A 2  to generate magnetic fields effective to impart radial motion, e.g., rotor translation  606 , to the rotor  213  are denoted at  608  in  FIG. 6B . 
     In particular, stator control coils A 1  and A 2  may be driven by sinusoidal current waveforms  608  having a frequency twice that of the rotation frequency of the rotor  213 . This constraint is imposed by the use of a magnet array  216  with a dipolar magnetic field rotating about the stator assembly  202 . If both stator control coils A 1  and A 2  are driven in phase, and with equal currents, no net radial force is developed on the rotor  213 . If the stator control coils A 1  and A 2  are driven in a fixed phase relationship but with different current magnitudes, a radial force is generated in a fixed direction whose magnitude is substantially proportional to the degree of difference in the magnitude of currents that drive the stator control coils A 1  and A 2 . If the phase relationship between the two drive currents is then varied, the direction of the radial force may be selected and directed towards any direction in the XY plane. 
     It will be apparent that although the direction of this radial force is fixed by the phase relationship between the drive currents, and while the maximum magnitude of this radial force is determined by the difference between the drive current magnitudes, the instantaneous radial force magnitude will vary between zero and its maximum as the rotor  213  spins around the stator assembly  202 . The number of times that the radial force will vary from its minimum to its maximum during a single rotation of the rotor  213  is determined by the number of poles of the magnetic field employed. In the present embodiment, the number of magnetic poles is two (a dipolar field), and the radial force therefore reaches its maximum and minimum twice for each rotation of the rotor  213 . A similar relationship holds for drive currents in stator control coils B 1  and B 2 , thereby enabling all stator control coils A 1 , A 2 , B 1 , B 2  capable of radially positioning the rotor  213  in addition to modifying its rate of rotation. It will be apparent that this additional capability requires no additional electronic components beyond those used to effect changes in rotation rate of the rotor  213 . 
     Referring again to  FIG. 2 , reference line  224  denotes a location along the Z axis of the center of mass of the rotor  213  and the center of the magnetic field provided by the magnet array  216  (hereinafter “Z axis rotor center of mass and magnetic field center  224 ”), and reference line  226  denotes a location along the Z axis of the center of the magnetic fields generated by the stator control coils A 1 , A 2 , B 1 , B 2  (hereinafter “Z axis of stator control coil magnetic field center  226 ). It will be further apparent, with the benefit of the present disclosure, that tilt about the X and/or Y axes may be achieved as well using the same set of stator control coils A 1 , A 2 , B 1 , B 2 . In particular, because of noncoincidence of the Z axis rotor center of mass and magnetic field center  224  with respect to the Z axis of stator control coil magnetic field center  226 , a translation force exerted on the rotor  213  by one of the stator control coils A 1 , A 2 , B 1 , B 2  individually will develop a torque about the X and/or Y axis, depending on the phase relationship between the stator control coil A 1 , A 2 , B 1 , B 2  and the position of the rotor  213 , resulting in a controllable rotor tilt. 
     Embodiments described herein can also provide independent tilt control of a rotor even in the circumstance in which the Z axis center of mass of the rotor and the Z axis center of the stator coil magnetic fields are in fact coincident, in which case a minimal degree of rotor tilt would be afforded. In these and other embodiments, the rotor  213  may include stator control coils each with a nonplanar stator coil geometry in which at least one opposed stator control pair comprises coils that occupy substantially one plane above the midpoint of the stator assembly along the Z axis, and whose construction rotates approximately 90 degrees below said stator midpoint, the two such coils together comprising an assembly that may be electrically excited to provide rotor tilt substantially without rotor translation. 
       FIG. 7  illustrates a perspective view of a stator coil  700  with such nonplanar stator coil geometry, arranged in accordance with at least some embodiments described herein. The stator control coil  700  may be referred to hereinafter as a “type C coil  700 .” As illustrated, the type C coil  700  can generally be divided into a lower loop and an upper loop that is rotated about the Z axis 90 degrees with respect to the lower loop. It will be apparent that the upper loop of the type C coil  700  produces a magnetic field that is rotated about the Z axis by 90° with respect to the lower loop, and that the electromagnetic forces which the upper and lower loops produce in reaction upon the rotor&#39;s rotating magnetic field therefore differ in their magnitude and direction. In particular, when the local rotor magnetic field is oriented such that, for example, drive current through the upper loop of the type C coil  700  produces a minimum of electromagnetic force, the drive current through the lower loop of the type C coil  700  will be at a maximum. Because the type C coils  700  are placed on the stator assembly so that they are substantially or mostly symmetric about the center of mass of the rotor and the magnetic field of the rotor along the Z axis, a radial force will be exerted by the lower coil loop on the rotor, and substantially no force will be exerted by the upper coil loop on the rotor. This will result in a torque of the rotor about the X and/or Y axis, according to the particular placement of the type C coil with respect to the local X and Y coordinate axes. Two such coils mounted in opposition on the stator thereby provide independent control of rotor tilt without developing net translational or rotational forces. 
     It will be apparent that although the above embodiment is described in terms of supplying drive currents to stator control coils A 1 , A 2 , B 1 , B 2  to operate the rotor  213  as a motor, the invention may be equally well practiced through controllably connecting the stator control coils A 1 , A 2 , B 1 , B 2  to electrical loads, in the case of a flywheel energy storage device, whereby energy may be extracted from the flywheel&#39;s rotational kinetic energy while the flywheel rotor&#39;s position is controlled as described herein. 
     It will be apparent that a full six degrees of rotor position control may be achieved by employing a magnetic field configuration that provides a component of divergence along the Z axis as well as the X and Y axes. In this configuration, stator control coils may be configured to provide force components in the + and −Z directions, providing rotor translation along the Z axis. Accordingly, separate dedicated suspending means, such as the suspending means  218  of  FIG. 2 , may be omitted. 
     It will be apparent that the invention is operable with rotating electrical machinery that does not employ bearings (as discussed earlier) in which a machine&#39;s rotor, which rotates substantially about an inertial axis of rotation, may be controllably positioned using stator control coils that would be incapable of such positioning but for this invention. 
     The embodiments described herein may include the use of a special purpose or general-purpose computer including various computer hardware or software modules, as discussed in greater detail below. 
     Embodiments described herein may be implemented using computer-readable media for carrying or having computer-executable instructions or data structures stored thereon. Such computer-readable media may be any available media that may be accessed by a general purpose or special purpose computer. By way of example, and not limitation, such computer-readable media may include tangible or non-transitory computer-readable storage media including RAM, ROM, EEPROM, CD-ROM or other optical disk storage, magnetic disk storage or other magnetic storage devices, or any other storage medium which may be used to carry or store desired program code in the form of computer-executable instructions or data structures and which may be accessed by a general purpose or special purpose computer. Combinations of the above may also be included within the scope of computer-readable media. 
     Computer-executable instructions comprise, for example, instructions and data which cause a general purpose computer, special purpose computer, or special purpose processing device to perform a certain function or group of functions. Although the subject matter has been described in language specific to structural features and/or methodological acts, it is to be understood that the subject matter defined in the appended claims is not necessarily limited to the specific features or acts described above. Rather, the specific features and acts described above are disclosed as example forms of implementing the claims. 
     As used herein, the term “module” or “component” can refer to software objects or routines that execute on the computing system. The different components, modules, engines, and services described herein may be implemented as objects or processes that execute on the computing system (e.g., as separate threads). While the system and methods described herein are preferably implemented in software, implementations in hardware or a combination of software and hardware are also possible and contemplated. In this description, a “computing entity” may be any computing system as previously defined herein, or any module or combination of modulates running on a computing system. 
     The present invention may be embodied in other specific forms without departing from its spirit or essential characteristics. The described embodiments are to be considered in all respects only as illustrative and not restrictive. The scope of the invention is, therefore, indicated by the appended claims rather than by the foregoing description. All changes which come within the meaning and range of equivalency of the claims are to be embraced within their scope.