Abstract:
An electromagnetic actuator includes a body having a rotational axis, a first pole adjacent an end facing surface of the body, and a second pole adjacent a lateral facing surface of the body. The poles are adapted to communicate magnetic flux with the body. The body, the first pole, and the second pole define an axial magnetic control circuit. The actuator includes a plurality of radial poles adjacent the lateral facing surface of the body and adapted to communicate magnetic flux with the body. The body and the plurality of radial poles define a plurality of radial magnetic control circuits. The plurality of radial poles are adapted to communicate magnetic fluxes with the body and at least one of the first pole or the second pole. The body, the plurality of radial poles, and at least one of the first pole or the second pole define a magnetic bias circuit.

Description:
BACKGROUND 
   This disclosure relates to generating electromagnetic forces and supporting a body, at least in part, by a magnetic field. 
   Equipment and machinery often contain moving (e.g. rotating) members, which require support during operation. A bearing, or similar device, may be used to support the moving member. Although many types of bearings require direct contact with the member to provide the necessary support, some applications benefit from or require non-contact, or nearly non-contact support for the member. A magnetic bearing uses a magnetic field to apply force to, and thereby support, the moving member in a non-contact, or nearly non-contact, manner. The non-contact or nearly non-contact support provided by the magnetic bearing can provide frictionless or nearly frictionless movement of the member. Should a machine include a member with varying dimensions, the bearing used for support, regardless of its type, may require a custom design or additional construction considerations in order to assemble the machine with the bearing. Therefore, the manufacture of the machine utilizing such a magnetic bearing may be inefficient due to the unique bearing design. 
   SUMMARY 
   This disclosure relates to generating electromagnetic forces and supporting a body, at least in part by a magnetic field. 
   In one implementation, an electromagnetic actuator includes a body having a rotational axis, a first pole adjacent an end facing surface of the body and adapted to communicate magnetic flux with the end facing surface of the body, and a second pole adjacent a lateral facing surface of the body and adapted to communicate magnetic flux with the lateral facing surface of the body. The body, the first pole, and the second pole are magnetically coupled and define an axial magnetic control circuit. The electromagnetic actuator also includes a plurality of radial poles adjacent the lateral facing surface of the body and adapted to communicate magnetic fluxes with the lateral facing surface of the body. The body and the plurality of radial poles are magnetically coupled and define a plurality of radial magnetic control circuits. Also, the plurality of radial poles are adapted to communicate magnetic fluxes with the lateral facing surface of the body and at least one of the first pole or the second pole. The body, the plurality of radial poles, and at least one of the first pole or the second pole define a magnetic bias circuit. 
   Implementations can include one or more of the following features. For example, three or more radial poles can be provided. The magnetic bias circuit can include a radial magnetic bias circuit and an axial magnetic bias circuit. The first pole can be oriented towards the end facing surface of the body, and the second pole can be oriented towards the lateral facing surface of the body. The end facing surface of the body can be orthogonal to the rotational axis. The body can include a low reluctance target adapted to communicate magnetic flux. An axial coil can be provided that is adapted to produce a magnetic flux in the axial magnetic control circuit and a plurality of radial coils can be provided that are adapted to produce magnetic fluxes in the plurality of radial magnetic control circuits. The magnetic flux entering the end facing surface of the body can exert an axial force on the body and the magnetic fluxes entering the lateral surface of the body can exert radial forces on the body. A plurality of corresponding radial control currents can generate the magnetic fluxes in the plurality of radial magnetic control circuits, and the radial forces can be linearly proportional to the plurality of corresponding radial control currents. At least one of the first pole or the second pole can include a circular ring. One or more permanent magnets can be provided that are adapted to produce a magnetic flux in the magnetic bias circuit. The permanent magnets can include at least one of a neodymium iron boron magnet a samarium cobalt magnet, or other magnetic material. The permanent magnets can include at least one of an axially magnetized permanent magnet or a radially magnetized permanent magnet. 
   In another implementation, a rotating machine system includes a body having a rotational axis, an electromagnetic actuator sub-assembly, one or more position sensors, and at least one control electronics package. The electromagnetic actuator sub-assembly includes a first pole adjacent an end facing surface of the body and adapted to communicate an axial control magnetic flux with the end facing surface of the body, a second pole adjacent a lateral facing surface of the body and adapted to communicate the axial control magnetic flux with the lateral facing surface of the body, and a plurality of radial poles adjacent the lateral facing surface of the body. The plurality of radial poles are adapted to communicate a plurality of radial control magnetic fluxes with the lateral facing surface of the body and also adapted to communicate bias magnetic flux with the lateral facing surface of the body and at least one of the first pole or the second pole. The body, the first pole, and the second pole are magnetically coupled and define an axial magnetic control circuit. The body and the plurality of radial poles are magnetically coupled and define a plurality of radial magnetic control circuits. Additionally, the body, the plurality of radial poles, and at least one of the first pole or the second pole define a magnetic bias circuit. 
   Implementations can include one or more of the following features. For example, a second electromagnetic actuator sub-assembly can be provided. The first electromagnetic actuator sub-assembly can be adapted to produce an axial force on the body in a first direction as a function of a first control current, and the second electromagnetic actuator sub-assembly can be adapted to produce an opposing axial force on the body as a function of a second control current. The second control current can be substantially equal in magnitude and opposite in direction to the first control current. The axial force and the opposing axial force may produce a net axial force on the body. Furthermore, the net axial force may be linearly proportional to the magnitude of the first and second control currents. The body can be coupled to a driven load. The driven load may include at least one of a flywheel, a compressor, a generator, or an expander. In additional aspects, the body is coupled to a driver. The driver may include at least one of a motor, an engine, or a turbine. 
   All or some or none of the described implementations may have one or more of the following features or advantages. For example, the electromagnetic actuator may produce the required force with minimal power consumption. In addition, the required force produced by the electromagnetic actuator is linearly proportional to a corresponding control current, which may simplify the control of the electromagnetic actuator and achieve a better system dynamic and higher control quality. Furthermore, the electromagnetic actuator may possess low rotational losses. As another example, the electromagnetic actuator may have a compact and low weight design. The rotating body should have components mounted on it with minimal size and weight in order to increase the frequency of the first natural bending mode of the body, which, in some aspects, limits vibrations caused by the body&#39;s imbalance as it rotates at a high rotational speed. Finally, the electromagnetic actuator may allow the construction of the body in the form of a rotor that has a gradually decreasing rotor diameter from the rotor center of gravity toward the rotor ends; this also may increase the frequency of the first natural bending mode of the body, which limits vibrations caused by the body&#39;s imbalance as it rotates at a high rotational speed. 
   Additionally, all or some or none of the described implementations may have one or more of the following features or advantages. For example, the electromagnetic actuator can be assembled to the rotating body without substantial disassembly of the electromagnetic actuator by sliding the electromagnetic actuator over the target of the rotating body (or the target of the rotating body into the electromagnetic actuator). This reduces manufacturing and repair costs of machines using the electromagnetic actuator, because the machine may be more easily assembled and disassembled. Two of the same electromagnetic actuators can be used in supporting the rotating body, thus also reducing manufacturing and repair costs. The rotating body need not include a reduction in transverse dimension inboard of the target to accommodate an inboard axial control pole of the electromagnetic actuator. Accordingly, any impact on dynamic performance caused by the reduction in transverse dimension can be reduced or eliminated. Additionally, the electromagnetic actuator can produce axial and radial forces with only one feature, the target, installed on the rotating body and using only one bias field, thus minimizing the weight and size of components mounted on the rotating body. A portion of the magnetic field required to produce electromagnetic force can be generated by permanent magnets, rather than electromagnets, thus reducing power consumption of the electromagnetic actuator. Furthermore, the electromagnetic actuator may utilize modern rare-earth permanent magnets with high energy densities, thus allowing for a compact and low weight design. Also, the electromagnetic actuator may introduce a bias magnetic field, which allows for the produced force to be controlled in proportion to a corresponding current. Finally, the magnetic field around the target can be uniform or nearly uniform, in the absence or radial loading, thus reducing eddy current losses induced by rotation of the rotating body, even if the target is conductive, as in some aspects. In the presence of radial loadings, the electromagnetic actuator may exhibit minimal rotational losses, which can be further reduced by making at least a portion of the target laminated. 
   These general and specific aspects may be implemented using a device, system or method, or any combinations of devices, systems, or methods. The details of one or more implementations are set forth in the accompanying drawings and the description below. Other features, objects, and advantages will be apparent from the description and drawings, and from the claims. 

   
     DESCRIPTION OF DRAWINGS 
       FIG. 1  illustrates a rotating machine system incorporating one implementation of an electromagnetic actuator; 
       FIG. 2A  illustrates one implementation of the electromagnetic actuator; 
       FIG. 2B  illustrates an additional view of an actuator target; 
       FIG. 2C  illustrates an alternate implementation of the actuator target; 
       FIG. 3  illustrates one implementation of a radial pole assembly and control windings; 
       FIG. 4  illustrates another implementation of the radial pole assembly and control windings; 
       FIG. 5  illustrates another implementation of the electromagnetic actuator; 
       FIG. 6  illustrates an example system to support a rotating body through the use of one or more implementations in accordance with the concepts described herein; and 
       FIG. 7  illustrates another example system to support the rotating body through the use of one or more implementations in accordance with the concepts described herein. 
   

   DETAILED DESCRIPTION 
   This disclosure provides various implementations for generating electromagnetic forces and supporting a body, at least in part by a magnetic field. In certain implementations, electromagnetic force may be exerted on a rotating body by an electromagnetic actuator, alone or in combination with other electromagnetic actuators or other types of bearings, bushings, or other mechanisms. The electromagnetic actuator utilizes a magnetic field to, for example, exert force on the body. The force may be used in supporting the body. In certain applications, the electromagnetic actuator is part of an active magnetic bearing. The magnetic bearing is active in that a system of sensors and feedback control electronics operate to vary currents in the electromagnetic actuator to control the supporting forces applied to the rotating body and maintain the rotating body in position under various loading conditions. The position of the rotating body, or portion of the rotating body, may be constantly monitored through the use of position sensors in some aspects. In certain implementations, the electromagnetic actuator is controlled to support the rotating body as the body rotates about an axis. However, the concepts described can be applied to systems that allow other types of movement besides rotation. 
     FIG. 1  illustrates an example rotating machine system. Rotating machine  110  includes a rotating body  120  and one or more electromagnetic actuators  130 . Although illustrated as a single body here, it is contemplated that rotating machine  110  may include multiple rotating bodies  120 . Furthermore, although two electromagnetic actuators  130  are illustrated in  FIG. 1 , fewer or greater than two actuators  130  may be utilized as appropriate in the application. In certain implementations, one or more electromagnetic actuators  130  can be used together with one or more other types of bearings, bushings or other support mechanisms. Although electromagnetic actuators  130  are shown internal to the rotating machine  110 , these systems may be implemented within the structural enclosure of the rotating machine  110  or exterior to the structure, as required by the particular application. 
   Position sensors  140 , as illustrated, sense displacement of the body  120 . In  FIG. 1 , three position sensors  140  are located at each end of body  120  to sense displacement in three dimensions. In other implementations, a fewer or greater number of position sensors  140  may be utilized. Position sensors  140  are coupled to control electronics  150  by signal paths  160 . Control electronics  150  receive signals from position sensors  140  and control the operation of electromagnetic actuators  130  relative to the signals. Control electronics  150  communicate with electromagnetic actuators  130  through signal paths  170 . Although shown exterior to the structure of rotating machine  110 , position sensors  140 , signal paths  160  and  170 , and control electronics  150  may be internal to rotating machine  110 . An active magnetic bearing may include an electromagnetic actuator  130 , control electronics  150 , and associated position sensors  140 . 
   The rotating machine  110  may be, for example, a motor, a generator, or a motor-generator, which as a motor receives electricity and produces kinetic energy (movement) or as a generator produces electricity from kinetic energy. Another example of rotating machine  110  is a motor-compressor set, which operates to compress any appropriate gas for a number of applications. For instance, the motor-compressor set may compress a petroleum by-product, refrigerant vapor, or ammonia, to name only a few. In another example, rotating machine  110  may be a turbine (or expander)-generator set, which expands a gas to drive a generator and produce electricity. In yet another example, rotating machine  110  is a flywheel device that stores kinetic energy. 
   Rotating body  120 , as illustrated in  FIG. 1 , is supported by one or more electromagnetic actuators  130  to rotate about its longitudinal axis. Although shown as a shaft, or cylindrical body in  FIG. 1 , the present disclosure contemplates that rotating body  120  may be one of a variety of shaped structural members. In some implementations, the shaft diameter may be variable along the length of the shaft. Furthermore, for example, rotating body  120  may be a hollow shaft, with both a circular inner and outer diameter. Although illustrated as internal to rotating machine  110 , rotating body  120  may reside external to the structural enclosure of the machine. 
     FIG. 2A  illustrates one implementation of the electromagnetic actuator  130  described in the present disclosure. The electromagnetic actuator  130  is structurally enclosed by an axial control pole  206   a , a passive radial pole  206   b , and an axial back iron  220 . In this implementation, rotating body  120  is a shaft  222  with a reduced diameter outboard stub  223 . The stub  223 , however, may be omitted in other implementations. A magnetic axial control flux  218 , produced by axial control winding  216 , is illustrated as conducting through various components within the electromagnetic actuator  130 , for example, axial control pole  206   a , passive radial pole  206   b , axial back iron  220 , and an actuator target  212 . 
   Electromagnetic actuator  130  utilizes at least two independent magnetic control circuits such that unidirectional axial forces and bidirectional radial forces are applied to actuator target  212 . For example, an axial magnetic control circuit and a radial magnetic control circuit may be used to produce such forces. The axial magnetic control circuit includes actuator target  212  and a stationary portion  221 , which includes axial control pole  206   a  and passive radial pole  206   b . The axial control pole  206   a  and passive radial pole  206   b  may be magnetically linked through axial back iron  220 . Axial control pole  206   a  has a surface  209  concentric with actuator target  212  and separated from target  212  by axial air gap  208 . Passive radial pole  206   b  also has a surface  207  concentric with actuator target  212  and separated from target  212  by radial air gap  211 . In some aspects, axial air gap  208  and radial air gap  211  may be uniform or substantially uniform circumferentially. Referring briefly to  FIG. 2B , the concentric surface  209  of axial control pole  206   a  is adjacent to an axial target surface  232 . Axial target surface  232  yields a non-zero projection on any plane normal to symmetry axis  228 . Furthermore, the concentric surface  207  of passive radial pole  206   b  is adjacent to a radial target surface  230 . Radial target surface  230  yields a non-zero projection on any plane encompassing symmetry axis  228 . Concentric surfaces  207  and  209  may be substantially planar, or for example, may be conical or any other rotational shape. Magnetic forces may develop on the axial target surface  232  and radial target surface  230 . The axial magnetic control circuit is energized by axial control coil  216  wound around the actuator target axis  228  and encompassed by the axial magnetic control circuit, such that magnetic axial control flux  218  is induced in the axial magnetic control circuit upon a flow of current through coil  216 . 
   The radial magnetic control circuit includes actuator target  212  and a stationary portion  214 , including radial control poles  225  and associated radial control coils  224 . Radial control poles  225  (shown in  FIG. 3 ) are separated from actuator target  212  by radial air gap  210 . In some aspects, radial air gap  210  may be uniform or substantially uniform circumferentially. 
   Bias permanent magnets  204   a  and  204   b  produce a difference in scalar magnetic potentials between the stationary portions of the axial and radial magnetic control circuits,  221  and  214 , respectively. Furthermore, permanent magnets  204   a  and  204   b  may have a high reluctance for magnetic flux. For example, magnets  204   a  and  204   b  may be modern high-energy rare-earth magnets, such as Neodymium Iron Boron (NdFeB) or Samarium Cobalt (SmCo). Therefore, the stationary portions of the axial and radial magnetic control circuits remain magnetically isolated from each other. Thus, axial magnetic control flux  218  cannot leak into the stationary portion of the radial magnetic control circuit  214 , and radial control flux (shown in  FIG. 3 ) cannot leak into the stationary portion of the axial magnetic control circuit  221 . In other implementations, the difference in scalar magnetic potentials between the stationary portions of the axial and radial control circuits,  221  and  214  respectively, may be produced by other devices, for example, electromagnetic coils. 
   Upon introduction of actuator target  212 , the difference in scalar magnetic potentials results in two constant magnetic bias fluxes  202   a  and  202   b . Bias fluxes  202   a  and  202   b  pass through various components of electromagnetic actuator  130 . For example, bias magnetic flux  202   a  travels through axial control pole  206   a  towards axial air gap  208  and crosses gap  208  to enter actuator target  212  from axial target surface  232  (as illustrated in  FIG. 2B ). From target  212 , magnetic bias flux  202   a  travels through radial air gap  210  and enters the stationary portion of radial magnetic control circuit  214 . Bias magnetic flux  202   a  travels then to permanent magnet  204   a  to close the loop. Similarly, bias magnetic flux  202   b  travels through passive radial pole  206   b , crosses radial air gap  211 , and enters actuator target  212  from the radial target surface  230  (as illustrated in  FIG. 2B ). From target  212 , magnetic bias flux  202   b  travels across radial air gap  210  and enters the stationary portion of radial magnetic control circuit  214 , where it propagates within it towards permanent magnet  204   b , where it closes the loop. Radial air gaps  210  and  211  and axial air gap  208  provide for non-contact or nearly non-contact (and correspondingly frictionless or near-frictionless) support of shaft  222  during operation of electromagnetic actuator  130 . 
   In some implementations, actuator target  212  is separately constructed and rigidly attached to shaft  222 . In other implementations, some or all of the actuator target  212  can be integral to or integrally formed with the shaft  222 . The actuator target  212  and, in some implementations, at least a portion of the shaft  222  adjacent the actuator target  212  are a low reluctance material, for conducting bias fluxes  202   a  and  202   b . If there are no currents in the radial control coils  224 , the bias magnetic fluxes  202   a  and  202   b , as well as the axial control flux  218 , are uniform or substantially uniform circumferentially within actuator target  212 . Therefore, any point of the actuator target  212  does not experience a magnetic flux variation upon rotation, which, in certain aspects with a conductive target, may otherwise induce eddy-current losses, producing an equivalent of the friction in mechanical bearings. The eddy currents are induced when there are currents in the radial control coils  224  producing radial force on the actuator target  212 , since the radial control magnetic flux (illustrated in  FIG. 3 ) may not be substantially uniform circumferentially. At least a portion,  212   a , of the actuator target  212  magnetically linked with the stationary radial magnetic control circuit  214  may be composed of thin electrically-isolated laminates stuck together axially as shown in  FIG. 2C . Another portion  212   b  of actuator target  212  magnetically linked with passive radial pole  206   b  may be non-laminated but magnetically permeable. This portion  212   b  may be integral to the shaft  222  if, for example, shaft  222  is magnetically permeable. 
   Axial control winding  216  carries the axial control current. This current produces magnetic axial control flux  218 , which either adds to or subtracts from the bias magnetic flux  202   a  in axial air gap  208 . Magnetic axial control flux  218  passes through the axial control pole  206   a , passive radial pole  206   b , axial back iron  220 , axial air gap  208 , actuator target  212 , and radial air gap  211 . As there is only one axial air gap  208 , the magnetic force F ax1    226  can be produced only in one direction, aiming to reduce the gap  208 . 
   Continuing further with  FIG. 2A , the axial force  226  acting on actuator target  212  is proportional to the second power of the net magnetic flux density in the axial air gap  208 . If the density of the bias flux  202   a  in axial air gap  208  is designated as B 0   ax , and the density of control flux  218  in axial air gap  208  is designated as B 1   ax , then axial force F ax1    226  may be calculated as: 
   
     
       
         
           
             
               F 
               
                 ax 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 1 
               
             
             = 
             
               
                 1 
                 
                   2 
                   ⁢ 
                   
                     μ 
                     0 
                   
                 
               
               ⁢ 
               
                 
                   
                     ( 
                     
                       
                         B 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           0 
                           ax 
                         
                       
                       + 
                       
                         B 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           1 
                           ax 
                         
                       
                     
                     ) 
                   
                   2 
                 
                 · 
                 
                   A 
                   ax 
                 
               
             
           
           , 
         
       
     
   
   where μ 0 =4π·10 −7  H/m is the permeability of a vacuum in SI units and A ax  is the area of the axial projection of axial control pole  206   a  on the surface of actuator target  212 . Because the density of the control flux B 1   ax  is linearly proportional to the axial control current in axial control coil  216 , the axial force  226  is a quadratic function of the axial control current. 
   Magnetic bias fluxes  202   a  and  202   b , as well as magnetic control flux  218 , do not yield a net radial force when the actuator target  212  is centered radially, because these fluxes are distributed uniformly or substantially uniformly around the circumference of actuator target  212 . By varying the axial control current in axial control winding  216 , and, consequently, the axial control flux  218 , the magnitude of the axial force F ax1    226  may be varied, and thus controlled. With the actuator target  212  rigidly mounted on or integral to shaft  222 , all forces exerted on the target  212  are directly transferred to shaft  222 . Electromagnetic actuator  130  may produce controllable radial forces through the introduction of radial control magnetic fluxes produced by radial control windings  224  and the stationary portion of the radial magnetic control circuit  214 , as described in  FIG. 3 . 
     FIG. 3  illustrates an example implementation of the stationary portion of the radial magnetic control circuit  214  utilizing four radial control windings  224   a  through  224   d , as viewed axially. The radial control poles  225   a  through  225   d , around which the windings  224   a  through  224   d  are wound, are situated evenly around actuator target  212  and magnetically linked to each other. Furthermore, the radial control poles  225   a  through  225   d  have surfaces concentric with actuator target  212 , adjacent to radial target surface  230  (as shown in  FIG. 2B ), and separated from target  212  by radial air gap  210 . In some implementations, a fewer or greater number of radial control poles  225  may be utilized. The magnetic bias fluxes  202   a  and  202   b  generated by permanent magnets  204   a  and  204   b  add in the stationary portion of the radial magnetic control circuit  214  and flow radially. When the actuator target  212  is centrally positioned and there are no currents in the radial control windings  224   a  through  224   d , the bias flux density under each pole  225   a  through  225   d  associated with windings  224   a  through  224   d  is equal because of the symmetrical nature of the system. Therefore, there is no radial force produced on actuator target  212  by the stationary portion of the radial magnetic control circuit  214 . 
   Continuing with  FIG. 3 , by energizing some of the radial control windings,  224   a  through  224   d , the flux distribution may be altered so as to develop a radial force. For example,  FIG. 3  shows windings  224   a  and  224   c  energized with control currents  302   a  and  302   c , respectively. These currents produce radial control flux  304 . In the portion of radial air gap  210  located between the pole  225   a  and actuator target  212 , control flux  304  adds to the combined magnetic bias fluxes  202   a  and  202   b . Conversely, radial control flux  304  subtracts from the combined magnetic bias fluxes  202   a  and  202   b  within the portion of radial air gap  210  located between the radial control pole  225   c  and actuator target  212 . Due to the higher magnetic flux density between actuator target  212  and radial control pole  225   a  as compared to the magnetic flux density between target  212  and radial control pole  225   c , radial electromagnetic force F Y    306  acts on actuator target  212 . As shown in  FIG. 3 , this force F Y    306  is directed upward. 
   Continuing with  FIG. 3 , the portion of the electromagnetic force F Y    306  exerted on the actuator target  212  by the upper pole  225   a  associated with winding  224   a can be calculated as 
               f     rad   ⁢           ⁢   1       =       1     2   ⁢     μ   0         ⁢         (       B   ⁢           ⁢     0   rad       +     B   ⁢           ⁢     1   rad         )     2     ·     A   rad           ,         
where B 0   rad  is the density of the combined bias fluxes  202   a  and  202   b  in radial gap  210 , B 1   rad  is the density of the radial control flux  304  in the portions of the radial gap  210  associated with windings  224   a  and  224   c , and A rad  is the projection of the upper (or lower) pole surface adjacent to the radial air gap  210  on a plane normal to the pole axis (Y axis as illustrated in  FIG. 3 ).
 
   Similarly, the electromagnetic force exerted on the actuator target  212  by the lower pole  225   c  associated with winding  224   c  can be calculated as: 
   
     
       
         
           
             F 
             
               rad 
               ⁢ 
               
                   
               
               ⁢ 
               2 
             
           
           = 
           
             
               1 
               
                 2 
                 ⁢ 
                 
                   μ 
                   0 
                 
               
             
             ⁢ 
             
               
                 
                   ( 
                   
                     
                       B 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         0 
                         rad 
                       
                     
                     - 
                     
                       B 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         1 
                         rad 
                       
                     
                   
                   ) 
                 
                 2 
               
               · 
               
                 
                   A 
                   rad 
                 
                 . 
               
             
           
         
       
     
   
   The net radial force on the shaft  222  will then be: 
   
     
       
         
           
             
               
                 
                   F 
                   rad 
                 
                 = 
                 
                   
                     F 
                     
                       rad 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       1 
                     
                   
                   - 
                   
                     F 
                     
                       rad 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       2 
                     
                   
                 
               
             
           
           
             
               
                 = 
                 
                   
                     
                       A 
                       rad 
                     
                     
                       2 
                       ⁢ 
                       
                         μ 
                         0 
                       
                     
                   
                   ⁢ 
                   
                     { 
                     
                       
                         
                           ( 
                           
                             
                               B 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 0 
                                 rad 
                               
                             
                             + 
                             
                               B 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 1 
                                 rad 
                               
                             
                           
                           ) 
                         
                         2 
                       
                       - 
                       
                         
                           ( 
                           
                             
                               B 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 0 
                                 rad 
                               
                             
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                               B 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 1 
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                           ) 
                         
                         2 
                       
                     
                     } 
                   
                 
               
             
           
           
             
               
                 = 
                 
                   2 
                   ⁢ 
                   
                     
                       A 
                       rad 
                     
                     
                       μ 
                       0 
                     
                   
                   ⁢ 
                   B 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     0 
                     rad 
                   
                   ⁢ 
                   B 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     1 
                     rad 
                   
                 
               
             
           
         
       
     
   
   If both radial control currents  302   a  and  302   c  are equal to a radial control current I rad , the radial control magnetic flux density B 1   rad  will be linearly proportional to the radial control current I rad , and consequently, the radial force F rad  will be linearly proportional to I rad . Although illustrated and describe above in the Y direction, the same features apply in the X direction. Therefore, this implementation allows the electromagnetic actuator  130  to produce bidirectional electromagnetic forces along two radial axes, designated in  FIG. 3  as X and Y. 
     FIG. 4  illustrates another example implementation of the stationary portion of the radial magnetic control circuit  214  utilizing three radial control windings  224 , as viewed axially. The radial forces are produced in a substantially similar manner to the implementation described in  FIG. 3 . For example, one radial control winding  224   a  may be energized with a control current, thereby producing a radial control flux. The control flux adds to the combined bias fluxes  202   a  and  202   b  in the portion of radial air gap  210  under radial control pole  225   a , while subtracting from the combined bias fluxes  202   a  and  202   b  in the portions of radial air gap  210  under radial control poles  225   b  and  225   c . This results in a radial force  306  directed towards the pole  225   a  associated with winding  224   a . Referring to  FIGS. 3 and 4 , while these implementations may affect the radial axes control and the radial pole construction, they do not affect the axial pole system and its control, nor the permanent magnet bias system and its construction. 
     FIG. 5  illustrates another implementation of the electromagnetic actuator described in the present disclosure. This implementation  530  differs from the implementation shown and described in  FIG. 2A , however, this disclosure contemplates that electromagnetic actuator  530  may be utilized in any application suitable for electromagnetic actuator  130 , including, for example, the rotating machine  110  illustrated in  FIG. 1 . For example, the generation of magnetic bias and control flux may be accomplished differently in  FIG. 5 . Referring to  FIG. 2A , bias fluxes  202   a  and  202   b  are generated, for example, by axially magnetized permanent magnets  204   a  and  204   b , while the control flux  218  is generated by the axial control winding  216 . Conversely, as illustrated in  FIG. 5 , the magnetic bias fluxes  202   a  and  202   b  are generated by a radially magnetized permanent magnet  502 . Although illustrated as a single radially magnetized permanent magnet  502 , multiple radially magnetized permanent magnets  502  may be utilized. Furthermore, axial control winding  216 , as illustrated in  FIG. 2A , is substituted with axial control coils  504   a  and  504   b , which may utilize space more efficiently. Although illustrated in  FIG. 5  as two coils,  504   a  and  504   b , one coil  504   a  or  504   b  may be utilized. Although the component arrangements differ between electromagnetic actuators  130  and  530 , the operation of the two electromagnetic actuators ( 130  and  530 ) is substantially similar. 
     FIG. 6  illustrates an example system to support the rotating member through the use of one or more implementations of the present disclosure. As shown, this system includes electromagnetic actuators  130   a  and  130   b  coupled to both ends of the continuous shaft  222 . When one or more position sensors (not shown) and one or more control electronics (not shown) are utilized, these actuators form an active magnetic bearing system capable of providing non-contact or nearly non-contact, and thus frictionless or nearly frictionless, support for shaft  222 . The position sensors detect deflection of the shaft  222  from a required position and provide the deflection information to the control electronics, which generate electrical currents for electromagnetic actuators  130   a  and  130   b  in order to produce forces necessary to keep the shaft  222  in the required position. Electromagnetic actuator  130 , as described in the present disclosure, may be coupled to shaft  222  as shown; however, electromagnetic actuator  530  may also be utilized. 
   The system in  FIG. 6  allows for axial force to be applied to shaft  222  in either direction through the use of two or more electromagnetic actuators  130  (or  530 , as appropriate). For example, if the magnitudes and the directions of the axial control currents in the electromagnetic actuators  130   a  and  130   b  in  FIG. 6  are such that the force F ax1    226   a  produced by electromagnetic actuator  130   a  is higher than the force F ax2    226   b  produced by electromagnetic actuator  130   b , there will be a net axial force directed as F ax1    226   a . Conversely, should the force F ax2    226   b  produced by electromagnetic actuator  130   b  be greater than force F ax1    226   a , there will be net axial force directed as F ax2    226   b . Furthermore, should equal axial control currents flow in the electromagnetic actuators  130   a  and  130   b  and their parameters are identical, a net axial force of zero acts on shaft  222 , since the forces F ax1  and F ax2  counteract each other. 
   Continuing with  FIG. 6 , the axial force F ax1  exerted by electromagnetic actuator  130   a  can be calculated as: 
   
     
       
         
           
             F 
             
               ax 
               ⁢ 
               
                   
               
               ⁢ 
               1 
             
           
           = 
           
             
               1 
               
                 2 
                 ⁢ 
                 
                   μ 
                   0 
                 
               
             
             ⁢ 
             
               
                 
                   ( 
                   
                     
                       B 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         0 
                         ax 
                       
                     
                     + 
                     
                       B 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         1 
                         ax 
                       
                     
                   
                   ) 
                 
                 2 
               
               · 
               
                 
                   A 
                   ax 
                 
                 . 
               
             
           
         
       
     
   
   If electromagnetic actuator  130   b  has an identical design and is supplied with axial control current of the same magnitude as actuator  130   a  but the opposite direction, the electromagnetic axial force F ax2  that actuator  130   b  exerts on the shaft  222  can be calculated as: 
   
     
       
         
           
             F 
             
               ax 
               ⁢ 
               
                   
               
               ⁢ 
               2 
             
           
           = 
           
             
               1 
               
                 2 
                 ⁢ 
                 
                   μ 
                   0 
                 
               
             
             ⁢ 
             
               
                 
                   ( 
                   
                     
                       B 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         0 
                         ax 
                       
                     
                     - 
                     
                       B 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         1 
                         ax 
                       
                     
                   
                   ) 
                 
                 2 
               
               · 
               
                 
                   A 
                   ax 
                 
                 . 
               
             
           
         
       
     
   
   Therefore, the net force, F ax , that the two actuators,  130   a  and  130   b , exert on shaft  222  can be calculated as: 
   
     
       
         
           
             
               
                 
                   F 
                   ax 
                 
                 = 
                 
                   
                     F 
                     
                       ax 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       1 
                     
                   
                   - 
                   
                     F 
                     
                       ax 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       2 
                     
                   
                 
               
             
           
           
             
               
                 = 
                 
                   
                     
                       A 
                       ax 
                     
                     
                       2 
                       ⁢ 
                       
                         μ 
                         0 
                       
                     
                   
                   ⁢ 
                   
                     { 
                     
                       
                         
                           ( 
                           
                             
                               B 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 0 
                                 ax 
                               
                             
                             + 
                             
                               B 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 1 
                                 ax 
                               
                             
                           
                           ) 
                         
                         2 
                       
                       - 
                       
                         
                           ( 
                           
                             
                               B 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 0 
                                 ax 
                               
                             
                             - 
                             
                               B 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 1 
                                 ax 
                               
                             
                           
                           ) 
                         
                         2 
                       
                     
                     } 
                   
                 
               
             
           
           
             
               
                 = 
                 
                   2 
                   ⁢ 
                   
                     
                       A 
                       ax 
                     
                     
                       μ 
                       0 
                     
                   
                   ⁢ 
                   B 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     0 
                     ax 
                   
                   ⁢ 
                   B 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     
                       1 
                       ax 
                     
                     . 
                   
                 
               
             
           
         
       
     
   
   Although the axial force produced by each individual actuator,  130   a  or  130   b , is a quadratic function of the control flux density B 1   ax , the net axial force on the rotor is linearly proportional to B 1   ax , which is also linearly proportional to the axial control current in the electromagnetic actuators  130   a  and  130   b . Together, electromagnetic actuators  130   a  and  130   b  may produce net axial force in any direction, as well as a torque about any axis except for the rotation axis of shaft  222 . Therefore, all degrees of freedom of the shaft  222  except for the rotation about its axis may be controlled, while the rotation about the axis is frictionless or nearly frictionless. 
     FIG. 7  illustrates another example system to support a rotating member through the use of one or more implementations of the present disclosure. Electromagnetic actuator  130 , as described in the present disclosure, may be coupled to shaft  222  as shown; however, electromagnetic actuator  530  may also be utilized. Furthermore, another type of electromagnetic actuator  730  may be coupled to shaft  222  opposite to the presently disclosed electromagnetic actuator. Electromagnetic actuator  730  operates to provide radial support of the corresponding end of shaft  222  and produce a force F ax2    726 . This force can be counteracted by the controllable force F ax1    226  generated by electromagnetic actuator  130  or  530 . If the magnitude of F ax1    226  is less than that of F ax2    726 , the net force would be directed as F ax2    726 . Conversely, if the magnitude of F ax1    226  exceeds that of F ax2    726 , the net force will be directed as F ax1    226 . The system of  FIG. 7  is also applicable to instances where another type of bearing, bushing, or other support mechanism, including those without provisions to control the axial force exerted by the support mechanism (e.g. ball bearing systems, thin fluidic film bearing systems, and others), can be substituted for electromagnetic actuator  730 . 
   As illustrated in  FIGS. 6 and 7 , electromagnetic actuator  130  or  530  may slide on or off of shaft  222  without disassembly. Thus, assembly (or disassembly) of rotating machine  110  utilizing electromagnetic actuators  130  or  530  may be accomplished by sliding the stationary portions of electromagnetic actuators  130  or  530  over shaft  222  without any disassembly or further modification to electromagnetic actuators  130  or  530 . Additionally, although  FIGS. 6 and 7  illustrate electromagnetic actuators  130  or  530  as external to shaft  222 , actuators  130  or  530  may operate inside the support structure. 
   A number of implementations have been described. Nevertheless, it will be understood that various modifications may be made. Accordingly, other implementations are within the scope of the following claims.