Abstract:
An electromagnetic actuator generates electromagnetic forces across large radial gaps to support a body. The actuator has an actuator target having a rotational axis, and a target magnetic element arranged circumferentially around the rotational axis that has inner and outer magnetic poles. A cylindrical soft-magnetic target pole is magnetically coupled to the outer cylindrical magnetic pole of the target magnetic element. An actuator base includes radial poles arranged circumferentially around and radially spaced apart from the cylindrical soft-magnetic target pole. The radial poles and the cylindrical soft-magnetic target pole are magnetically coupled and define a plurality of magnetic control circuits. Control coils around the radial poles are configured to produce magnetic fluxes in the magnetic control circuits. The target magnetic element, the cylindrical soft-magnetic target pole, and the radial poles are magnetically coupled and define a magnetic bias circuit, the magnetic element producing magnetic flux in the magnetic bias circuit.

Description:
TECHNICAL FIELD 
     This disclosure relates to generating electromagnetic forces and supporting a body, at least in part, by a magnetic field. 
     BACKGROUND 
     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 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. In such magnetic bearings, the clearance between the stationary and moving parts can have an effect on the magnitude of the supporting force established by the magnetic field. 
     SUMMARY 
     An electromagnetic actuator includes an actuator target with a rotational axis. A target magnetic element is arranged circumferentially around the rotational axis and has inner and outer magnetic poles. The inner magnetic pole of the target magnetic element can be located closer to the rotational axis than the outer magnetic pole. A cylindrical soft-magnetic target pole piece can be magnetically coupled to the outer cylindrical magnetic pole of the target magnetic element. An actuator base includes a plurality of radial poles arranged circumferentially around and radially spaced apart from the cylindrical soft-magnetic target pole piece. The plurality of radial poles and the cylindrical soft-magnetic target pole piece may define radial gaps therebetween. A plurality of control coils may be around the plurality of radial poles. The plurality of radial poles and the cylindrical soft-magnetic target pole may be magnetically coupled and define a plurality of magnetic control circuits. The plurality of control coils may be configured to produce control magnetic fluxes in the plurality of magnetic control circuits. The target magnetic element, the cylindrical soft-magnetic target pole, and the plurality of radial poles may be magnetically coupled and define a magnetic bias circuit. The target magnetic element may be configured to produce bias magnetic flux in the magnetic bias circuit. 
     The electromagnetic actuator may further include a target bias magnetic flux return element magnetically coupled to the inner magnetic pole of the target magnetic element. The target bias magnetic flux return element may further define the magnetic bias circuit. The target bias magnetic flux return element of the electromagnetic actuator may also include a soft-magnetic structure. The target magnetic element of the electromagnetic actuator may be a first target magnetic element and the cylindrical soft-magnetic target pole piece may be a first cylindrical soft-magnetic target pole piece. A second target magnetic element may have inner and outer cylindrical magnetic poles arranged circumferentially around the rotational axis, the inner magnetic pole of the second target magnetic element may be located closer to the rotational axis than the outer magnetic pole of the second target magnetic element and the polarities of the inner and outer magnetic poles of the second target magnetic element may be opposite to polarities of the inner and outer magnetic poles of the first target magnetic element. A second cylindrical soft-magnetic target pole may be proximate the outer cylindrical magnetic pole of the second target magnetic element. A third target magnetic element may be located axially between the first and the second target magnetic elements and having a first disk-shaped magnetic pole and a second disk-shaped magnetic pole arranged circumferentially around the rotational axis. The first disk-shaped pole may be adjacent the first target magnetic element and may have the same polarity as the outer cylindrical pole of the first target magnetic element. The second disk-shaped pole may be adjacent the second target magnetic element and may have the same polarity as the outer cylindrical pole of the second target magnetic element. 
     The actuator base may include a base bias magnetic flux return element magnetically coupled to the plurality of radial poles and further defining the magnetic bias circuit. The base bias magnetic flux return element may include a stationary soft-magnetic cylindrical pole. 
     The electromagnetic actuator may also include a base magnetic element having a first pole and a second pole, the first pole may be magnetically coupled to the plurality of radial poles and may have a polarity opposite to a polarity of the outer pole of the target magnetic element. The second pole may be magnetically coupled to the base bias magnetic flux return element. 
     Alternatively, the electromagnetic actuator may include a soft-magnetic spacer installed between and magnetically coupled to the plurality of the radial poles and the base bias magnetic flux return element. 
     The plurality of radial poles may be a first plurality of radial poles, the plurality of control coils may be a first plurality of control coils, and the plurality of magnetic control circuits may be a first plurality of magnetic control circuits. The base bias magnetic flux return element may further include a second plurality of radial poles arranged circumferentially around and radially spaced apart from the second cylindrical soft-magnetic target pole piece, the second plurality of radial poles and the second cylindrical soft-magnetic target pole piece may define radial gaps therebetween. A second plurality of control coils may be around the second plurality of radial poles. The second plurality of radial poles and the second cylindrical soft-magnetic target pole piece may be magnetically coupled and define a second plurality of magnetic control circuits, the second plurality of control coils may be configured to produce control magnetic fluxes in the second plurality of magnetic control circuits. 
     A method for exerting a radial force on a body, where the body may be configured to rotate about a rotational axis, includes generating a bias magnetic flux using a target magnetic element mounted on the body circumferentially around the rotational axis and having inner and outer magnetic poles, the inner magnetic pole located closer to the rotational axis than the outer magnetic pole. The method further includes communicating the bias magnetic flux between a first radial pole assembly, the body, and a second radial pole assembly. The first and second radial pole assemblies may be magnetically coupled and spaced apart from one another along the rotational axis. The first and second radial pole assemblies may each be circumferentially arranged around the rotational axis. The first and second radial pole assemblies may be separated from the body by an air gap. The bias magnetic flux may propagate through the body in a direction parallel to the rotational axis. The bias magnetic flux generated by the target magnetic element may further be the first bias magnetic flux, and there may be a second bias magnetic flux generated by a base magnetic element added to the first bias magnetic flux. The base magnetic element may be located between the first and the second radial pole assemblies. The method may further include communicating a radial control magnetic flux between the first radial pole assembly and a first body pole coupled to the body, the first radial control magnetic flux may propagate between a first radial pole of the first pole assembly, the body pole, and a second pole of the first radial pole assembly. The first radial control magnetic flux may propagate in a radial direction orthogonal to the rotational axis. The method also may include communicating a second radial control magnetic flux between the second radial pole assembly and a second body pole coupled to the body and spaced apart from the first body pole along the rotational axis. The second radial control magnetic flux may propagate between a first radial pole of the second pole assembly, the second body pole, and a second pole of the second pole assembly. The second radial control magnetic flux may propagate in a radial direction orthogonal to the rotational axis opposite from the first radial control magnetic flux. The net magnetic flux, which is a superposition of the bias and control magnetic fluxes, may exert an electromagnetic force on the actuator target. Generating the first and the second radial control magnetic fluxes may include energizing a control coil around each of the first and second radial poles of the first and second radial pole assemblies with a control current. The method may further include varying the control current to affect a total magnetic flux in the air gaps between the first and second radial pole assemblies and the body. 
     An electric machine system includes a rotor and a stator; the rotor having a rotational axis configured to move relative to the stator. An electromagnetic actuator sub-assembly includes an actuator target coupled to the rotor and an actuator base coupled to the stator. The actuator target includes a target magnetic element arranged circumferentially around the rotational axis and having inner and outer magnetic poles. The inner magnetic pole may be located closer to the rotational axis than the outer magnetic pole. A cylindrical, soft-magnetic target pole piece may be magnetically coupled to the outer cylindrical magnetic pole of the target magnetic element. An actuator base includes a plurality of radial poles arranged circumferentially around and radially spaced apart from the cylindrical soft-magnetic target pole piece. The plurality of radial poles and the cylindrical soft-magnetic target pole piece may define radial gaps therebetween. A plurality of control coils may be around the plurality of radial poles. The plurality of radial poles and the cylindrical soft-magnetic target pole may be magnetically coupled and define a plurality of magnetic control circuits. The plurality of control coils may be configured to produce control magnetic fluxes in the plurality of magnetic control circuits. The target magnetic element, the cylindrical soft-magnetic target pole, and the plurality of radial poles may be magnetically coupled and define a magnetic bias circuit, the target magnetic element may be configured to produce bias magnetic flux in the magnetic bias circuit. The system further may include at least one control electronics package configured to control the magnetic flux in the plurality of magnetic control circuits by controlling currents in the control coils. The net magnetic flux, which is a superposition of the bias and control magnetic fluxes, may exert an electromagnetic force on the actuator target. The system may further include one or more position sensors configured to sense a position of the rotor and the control electronic package may energize the control coils around each of the plurality of radial poles with control currents in response to changes of signals from the position sensors so that the rotor is supported by electromagnetic forces without a mechanical contact with the stator. The rotor of the electric machine system may be coupled to a driven load where the driven load may include at least one of a flywheel, a compressor, a generator, or an expander. Alternatively, the rotor of the electric machine system may be coupled to a driver, the driver including at least one of a motor, an engine, or a turbine. The system may further include a can separating the body from the base configured to prevent access of a working fluid to at least the control coils. 
    
    
     
       DESCRIPTION OF DRAWINGS 
         FIG. 1A  is a side cross-sectional view of an embodiment of a homopolar actuator for generating electromagnetic forces in large air gaps. 
         FIGS. 1B-C  are axial cross-sectional views of the homopolar actuator of  FIG. 1A . 
         FIG. 2A  is a side cross-sectional view illustrating the operational principles of the embodiment of the homopolar actuator of  FIG. 1A-C . 
         FIGS. 2B-C  are axial cross-sectional views of  FIG. 2A  illustrating the operational principles of the embodiment of the homopolar actuator of  FIG. 1A-C . 
         FIG. 3A  is a side cross-sectional view of an embodiment of a homopolar actuator incorporating a continuous flux return pole. 
         FIGS. 3B-C  are axial cross-sectional views of the homopolar actuator of  FIG. 3A . 
         FIG. 4A  is a side cross-sectional view of an embodiment of a homopolar actuator with the bias flux being generated by the magnets mounted on the rotor. 
         FIGS. 4B-C  are axial cross-sectional views of the homopolar actuator of  FIG. 4A . 
         FIG. 5  is a side cross-sectional view of an electrical machine equipped with an Active Magnetic Bearing (AMB) system incorporating an embodiment of the homopolar actuator of the present disclosure. 
     
    
    
     DETAILED DESCRIPTION 
     Some applications of magnetic bearings involve large clearances between the stationary and moving parts of the bearings. Large clearances may arise in applications where the moving part is submerged in some sort of a liquid or a gas that should be isolated from the stationary part of a machine by means of a hermetically sealed can. The thickness of this can may add to the clearance between the stationary and moving parts of the magnetic bearing and, thus, may significantly increase it. Alternatively, it may not be required to isolate stationary parts of the motor/generator and magnetic bearings from processing gases or fluids, but large clearances between the stationary and rotating parts may be needed if large particles are present in the processing gases or fluids which may cause a machine seizure if stuck in small clearances. Increasing clearances between the stationary and rotating parts of the bearing may result in increasing magnetic reluctance of the air gap defined by the clearance. The increasing reluctance, in turn, decreases the total magnetic flux communicated between the stationary and rotating members, which results in a decrease of the magnitude of the supporting force. 
       FIG. 1A  is a side cross-sectional schematic of an embodiment of the magnetic actuator of the present disclosure. The magnetic actuator  100  shown in  FIG. 1A  can produce controllable forces on an object  102  in the radial plane defined by X axis  128  and Y axis  129  (as shown in  FIGS. 1B-C ). The magnetic interaction takes place between the actuator target  127  (defined by the object  102  and movable magnetic circuit components  103  firmly affixed to the object  102 ) and the stationary magnetic circuit components. The stationary magnetic circuit components may be referred to collectively as the stationary assembly  104 . As described further below, the movable magnetic circuit components  103  and the stationary assembly  104  define a magnetic circuit. In  FIG. 1A , the actuator target  127  is shown to have a rotational symmetry about the axis Z  130 ; this, however, is not necessary. 
     The stationary assembly  104  includes two sets of radial poles  105   a - d  (shown in  FIG. 1B) and 106   a - d  (shown in  FIG. 1C ) situated around the actuator target  127 . Radial poles  105   a - d  and  106   a - d  may be made of a soft-magnetic material, in particular they may be assembled of soft-magnetic conductive laminations stacked axially and electrically isolated from each other. Each of the radial poles  105   a - d  and  106   a - d  has one of the control coils  107   a - d  or  108   a - d  around it. For example, radial pole  105   a  has control coil  107   a  around it; and radial pole  106   a  has control coil  108   a  around it. The radial stationary poles within each group  105   a - d  and  106   a - d  are magnetically linked to each other. The movable magnetic circuit components  103  may include radially magnetized magnets  111  and  113 , axially magnetized magnet  112 , soft-magnetic sleeves  116  and  117 , soft-magnetic target poles  118  and  119  and soft-magnetic target backiron  125 . If the object  102  is soft-magnetic, the soft-magnetic target backiron  125  may not be necessary. Target poles  118  and  119  may be made of a soft-magnetic material; in particular, they may be assembled of soft-magnetic conductive laminations stacked axially and electrically isolated from each other. Further, the target poles  118  and  119  may have a chamfered surface, which may focus the magnetic flux radially into the poles. The radial poles  105   a - d  have surfaces adjacent to the surface of the target poles  118 , and separated from it by radial air gaps  109   a - d . Similarly, the radial magnetic stationary poles  106   a - d  have surfaces adjacent to the surface of the soft magnetic target poles  119 , and separated from it by radial air gaps  110   a - d . In some implementations, a fewer or greater number of radial magnetic stationary poles  105   a - d  and  106   a - d  may be utilized. 
     Sleeves  116  and  117  are between the target poles  118  and  119  and the magnets  111  and  113 , respectively. The sleeves  116  and  117  help to compress the magnets to protect them from breaking during high rotational speeds. The sleeves  116  and  117  may be steel tubes sized in such a way that the magnets remain at compression during high rotational speeds. For example, they may be steel tubes applied at high temperatures around the magnets  111  and  113 , and then allowed to cool. Sleeves  116  and  117  may be, for example, magnetic steel tubes to conduct magnetic flux between the magnets  111  and  113  and the air gaps  109   a - d  and  110   a - d , respectively. The pole areas of the magnets  111  and  113  can be made larger than the net area of all the surfaces of the stator radial magnetic poles  105   a - d  or  106   a - d  facing the gaps  109   a - d  or  110   a - d  by extending the magnets  111  and  113  axially without sacrificing the cross-section of the object  102 . Sleeve  124  supports magnet  112  such that magnet  112  remains at compression at high rotational speeds. Sleeve  124  may be non-magnetic material such as stainless steel or may be brass, Inconel®, or any strong non-magnetic material known in the art. 
       FIG. 2  explains the operational principle of the device  100 . The radial poles  105   a - 105   d ,  106   a - 106   d , the target poles  118  and  119 , radially magnetized magnets  111  and  113 , axially magnetized magnet  112 , stationary permanent magnet  114 , and the soft-magnetic sleeves  116  and  117  form a magnetic bias circuit. Permanent magnets  111 - 113  within the moveable portion of the magnetic circuit  103  and the stationary permanent magnet  114  within the stationary portion of the magnetic circuit (i.e., within the stationary assembly  104 ) generate bias magnetic flux  115 . Beginning hypothetically at magnet  114 , bias flux  115  propagates from the magnet  114  radially through the radial poles  106   a - d , across the air gaps  110   a - d , into the target pole  119 , and into the backiron  125 . The bias flux  115  then propagates axially, e.g., in the positive Z direction in  FIG. 2A , and is then directed radially through target pole  118 , across the air gaps  109   a - d , and radially through the radial poles  105   a - 105   d  and back to magnet  114 . The bias flux  115  flows radially within each set of the radial control poles  105   a - d  and  106   a - d : outward in the poles  105   a - d  and inward in the poles  106   a - d . Because the polarity of the bias fluxes within each set of the radial magnetic stationary poles  105   a - d  or  106   a - d  is the same, the proposed electromagnetic actuator can be classified as homopolar. Using two sets of magnets mounted on both the stationary part of the magnetic circuit (magnet  114  of stationary assembly  104 ) and the moveable part of the magnetic circuit (magnets  111 - 113  of the movable magnetic circuit components  103 ) may result in a smaller magnetic flux leakage between two sets of radial magnetic stationary poles  105   a - d  and  106   a - d  than if magnets were only installed on the stationary part of the magnetic circuit. Minimizing the magnetic flux leakage between two sets of radial magnetic stationary poles  105   a - d  and  106   a - d  increases the useful flux that can be accommodated in these poles before magnetic saturation is reached, resulting in a higher load capacity of the bearing. Two sets of magnets as such may also result in a smaller amount of magnetic material on the moveable portion of the magnetic circuit than if magnets were installed only on the moveable part of the magnetic circuit. Minimizing the amount of the magnetic material on the moveable portion of the magnetic circuit is beneficial in applications where the moveable portion of the magnetic circuit is subjected to high stresses because of a low mechanical strength of the magnetic materials. An example of such application is when the object  102  spins about the Z axis  130  and the stresses in the moveable portion of the magnetic circuit are caused by centrifugal forces. Using radially magnetized magnets  111  and  113  in the moveable portion of the magnetic circuit  103  allows one to obtain the desired bias flux  115  in the air gaps  109   a - d  and  110   a - d  even when these gaps are very large by making these magnets sufficiently long axially without having to make the cross-section of the object  102  under these magnets unacceptably small. Keeping this cross-section sufficiently large is critical in applications where the strength and the rigidity of the actuator target are of high importance, particularly in applications where the actuator target  127  spins about the Z axis  130 , because most of the strength and the rigidity may come from the object  102  whereas magnets  111 - 113  typically are the mechanically weakest components. The soft-magnetic poles  118  and  119  serve to collect the fluxes from the entire axial spans of the magnets  111  and  113  and direct them to the air gaps  109   a - d  and  110   a - d . This allows obtaining high bias flux densities in the in the air gaps  109   a - d  and  110   a - d  even when these gaps are very large. Tapered shapes of the soft-magnetic poles  118  and  119  further increase bias flux densities in the air gaps  109   a - d  and  110   a - d  by reducing magnetic flux leakages between the poles  118 ,  119  and the outwards faces of the radial magnetic stationary poles  105   a - d  and  106   a - d . The axially magnetized magnet  112  reduces internal magnetic flux leakage inside the moveable magnetic circuit portion  103  resulting in higher bias magnetic flux densities in the radial air gaps  109   a - d  and  110   a - d  and may not be necessary. It also may be substituted for a non-magnetic material, such as stainless steel, or may be brass, Inconel®, or any strong non-magnetic material known in the art. A non-magnetic sleeve  124  on top of the magnet  112  keeps the magnet  112  in compression, thus preventing it from breaking apart under the influence of centrifugal forces. 
     When the object  102  is centrally positioned and there are no currents in the radial control windings  107   a - d  or  108   a - d , the bias flux densities under each pole  105   a - d  and  106   a - d  are equal because of the symmetrical nature of the system. Therefore, there is no radial force produced on the object  102 . By energizing some of the radial control windings,  107   a - d  and  108   a - d , the flux distribution may be altered so as to develop a radial force. For example,  FIGS. 2B and 2C  show windings  107   a ,  107   c  and  108   a ,  108   c  energized with control currents  120   a ,  120   c  and  121   a ,  121   c  respectively. These currents produce radial control fluxes  122  and  123 . Note that the paths of the radial control fluxes  122  and  123  lie entirely in the soft-magnetic parts of the stationary portion of the magnetic circuit (i.e., of stationary assembly  104  and a movable magnetic circuit components  103 ). In particular, in the movable portion of the magnetic circuit  103  the radial control fluxes  122  and  123  travel within the soft-magnetic poles  118  and  119  and do not cross permanent magnets  111 - 113  which would otherwise significantly increase the reluctances of the magnetic paths due to their low permeability, and, consequently, would result in much larger currents  120   a ,  120   c  and  121   a ,  121   c  needed to produce the same radial control fluxes  122  and  123 . 
     In the radial air gaps  109   a  and  110   a  control fluxes  122  and  123  add to the magnetic bias flux  115 , whereas in the radial air gaps  109   c  and  110   c , radial control fluxes  122  and  123  subtract from the magnetic bias fluxes  115 . Due to the higher resulting net magnetic flux densities in the radial air gaps  109   a  and  110   a  compared to the radial air gaps  109   c  and  110   c , radial electromagnetic force F Y    126  acts on the actuator target poles  118 ,  119  and, consequently, on the object  102 . In  FIG. 2  this force F Y    126  is directed upward. 
     Continuing with  FIG. 2 , the portion of the electromagnetic force F Y    126  exerted on either actuator target pole  118  or  119  by the upper poles  105   a  or  106   a  associated with winding  107   a  and  108   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 bias flux  115  in radial gaps  109   a  or  110   a , B 1   rad  is the density of the radial control fluxes  122  or  123  in the radial gap  109   a  or  110   a  associated with windings  107   a  or  108   a , and A rad  is the projection of the pole surface adjacent to the radial air gap  109   a  or  110   a  on a plane normal to the pole axis (Y axis as illustrated in  FIG. 2 ).
 
     Similarly, the electromagnetic force exerted on either actuator target pole  118  or  119  by the lower poles  105   c  or  106   c  associated with windings  107   c  and  108   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 either actuator target pole  118  or  119  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       -     B   ⁢           ⁢     1   rad         )     2       }       =     2   ⁢       A   rad       μ   0       ⁢   B   ⁢           ⁢     0   rad     ⁢   B   ⁢           ⁢     1   rad                 
If radial control currents  120   a  and  120   c  ( 121   a  and  121   c ) are equal to a radial control current I rad , the radial control magnetic flux density B 1   rad  will be proportional to the radial control current I rad , and consequently, the radial force F rad  will be proportional to I rad . Although illustrated and described above in the Y direction, the same features apply in the X direction. Therefore, this implementation allows the electromagnetic actuator  100  to produce bidirectional electromagnetic forces along two radial axes, designated in  FIG. 2  as X  128  and Y  129 .
 
     The soft-magnetic poles  118  and  119  can be composed of electrical steel laminations electrically isolated from each other and stacked together in the axial direction in order to minimize eddy currents that can be induced if the object  102  rotates about its axis Z  130 . The soft-magnetic sleeves  116  and  117  may provide additional structural integrity if the soft-magnetic poles  118  and  119  are composed of electrical steel laminations. 
       FIGS. 3A-C  illustrate another embodiment of the actuator of the present disclosure. The difference from  FIG. 1  is that the second set of radial magnetic stationary poles  106   a - 106   d  is replaced with a single continuous stator flux return pole  331  separated from the actuator target pole  319  by a continuous air gap  332 . The stator flux return pole  331  may not produce a controllable force on the actuator target pole  319 , but provides a return path for the bias flux  315 . 
       FIG. 3A  is a side cross-sectional schematic of an embodiment of the magnetic actuator of the present disclosure. The magnetic actuator  300  shown in  FIG. 3  can produce controllable forces on an object  302  in the radial plane defined by X axis  328  and Y axis  329  (as shown in  FIGS. 3B-C ). The magnetic interaction takes place between the actuator target  327 , defined by the object  302  and movable magnetic circuit components  303  firmly affixed to the object  302 , and a stationary magnetic circuit components. The stationary magnetic circuit components may be referred to collectively as the stationary assembly  304 . As described further below, the movable magnetic circuit components  303  and the stationary assembly  304  define a magnetic circuit. In  FIG. 3A , the actuator target  327  is shown to have a rotational symmetry about the axis Z  330 ; this, however, is not necessary. 
     The stationary assembly  304  includes radial poles  305   a - d  (shown in  FIG. 3B ) and a continuous stator flux return pole  331  (shown in  FIG. 3C ) situated around the actuator target  327 . Radial poles  305   a - d  and stator flux return pole  331  may be made of a soft-magnetic material, in particular they may be assembled of soft-magnetic conductive laminations stacked axially and electrically isolated from each other. Each of the radial poles  305   a - d  has one of the control coils  307   a - d  around it. For example, radial pole  305   a  has control coil  307   a  around it. The radial stationary poles  305   a - d  are magnetically linked to each other. The movable magnetic circuit components  303  may include radially magnetized magnets  311  and  313 , axially magnetized magnet  312 , soft-magnetic sleeves  316  and  317 , soft-magnetic target poles  318  and  319  and soft-magnetic target backiron  325 . If the object  302  is soft-magnetic, the soft-magnetic target backiron  325  may not be necessary. Target poles  318  and  319  may be made of a soft-magnetic material; in particular, they may be assembled of soft-magnetic conductive laminations stacked axially and electrically isolated from each other. Further, the target poles  318  and  319  may have a chamfered surface, which may focus the direction of the magnetic flux radially into the poles. The radial poles  305   a - d  have surfaces adjacent to the surface of the target poles  318 , and separated from it by radial air gaps  309   a - d . Similarly, the radial magnetic stationary pole  331  has a surface adjacent to the surface of the soft magnetic target poles  319 , and separated from it by radial air gaps  332 . In some implementations, a fewer or greater number of radial magnetic stationary poles  305   a - d  may be utilized. 
     Sleeves  316  and  317  are between the target poles  318  and  319  and the magnets  311  and  313 , respectively. The sleeves  316  and  317  help to compress the magnets to protect them from breaking during high rotational speeds. The sleeves  316  and  317  may be steel tubes sized in such a way that the magnets remain at compression during high rotational speeds. For example, they may be steel tubes applied at high temperatures around the magnets  311  and  313 , and then allowed to cool. Sleeves  316  and  317  may be, for example, magnetic steel tubes to conduct magnetic flux between the magnets  311  and  313  and the air-gaps  309   a - d  and  332 , respectively. Sleeve  324  supports magnet  312  such that magnet  312  remains at compression at high rotational speeds. Sleeve  324  may be non-magnetic material such as stainless steel or may be brass, Inconel®, or any strong non-magnetic material known in the art. 
     As illustrated in  FIGS. 3A-C , the radial poles  305   a - 305   d  and  331 , the target poles  318  and  319 , magnets  311 - 314 , and the soft-magnetic sleeves  316  and  317  form a magnetic bias circuit. Magnets  311 - 314  produce bias magnetic flux  315  in the bias magnetic circuit. In the embodiment of  FIG. 3A , beginning hypothetically at magnet  314 , bias flux  315  propagates from the magnet  314  radially through the radial pole  331 , across the air gap  332 , into the target pole  319 , and into the backiron  325 . The bias flux  315  then propagates axially, e.g., in the positive Z direction in  FIG. 3A , and is then directed radially through target pole  318 , across the air gaps  309   a - 309   d , and radially through the radial poles  305   a - 305   d  and back to magnet  314 . The axially magnetized magnet  312  reduces internal magnetic flux leakage inside the moveable magnetic circuit portion  303  resulting in higher bias magnetic flux densities in the radial air gaps  309   a - d  and may not be necessary. It also may be substituted for a non-magnetic material, such as stainless steel, or may be brass, Inconel®, or any strong non-magnetic material known in the art. 
       FIG. 4A  illustrates an embodiment of the actuator of the present disclosure where the stationary portion of the actuator lacks a permanent magnet.  FIG. 4A  is a side cross-sectional schematic of an embodiment of the magnetic actuator replacing the permanent magnetic in the stationary portion  404  with a soft-magnetic spacer  433 . The magnetic actuator  400  shown in  FIG. 4A  can produce controllable forces on an object  402  in the radial plane defined as the plane normal to the Z axis  430 . The magnetic interaction takes place between the actuator target  427 , defined by the object  402  and movable magnetic circuit components  403  firmly affixed to the object  402 , and stationary magnetic circuit components. The stationary magnetic circuit components may be referred to collectively as the stationary assembly  404 . As described further below, the movable magnetic circuit components  403  and the stationary assembly  404  define a magnetic circuit. In  FIG. 4 , the actuator target  427  is shown to have a rotational symmetry about the axis Z  430 ; this, however, is not necessary. In  FIG. 4 , the bias flux is generated only by magnets  411 - 413  mounted on the actuator target  427  whereas the magnet installed in the stationary portion of the magnetic circuit  404  of the apparatus in  FIG. 4A  is replaced with a soft-magnetic spacer  433 . 
     The stationary assembly  404  includes two sets of radial poles  405   a - d  (shown in  FIG. 4B) and 406   a - d  (shown in  FIG. 4C ) situated around the actuator target  427 . Radial poles  405   a - d  and  406   a - d  may be made of a soft-magnetic material, in particular they may be assembled of soft-magnetic conductive laminations stacked axially and electrically isolated from each other. Each of the radial poles  405   a - d  and  406   a - d  has one of the control coils  407   a - d  or  408   a - d  around it. For example, radial pole  405   a  has control coil  407   a  around it; and radial pole  406   a  has control coil  408   a  around it. The radial stationary poles within each group  405   a - d  and  406   a - d  are magnetically linked to each other. The movable magnetic circuit components  403  may include radially magnetized magnets  411  and  413 , axially magnetized magnet  412 , soft-magnetic sleeves  416  and  417 , soft-magnetic target poles  418  and  419  and soft-magnetic target backiron  425 . If the object  402  is soft-magnetic, the soft-magnetic target backiron  425  may not be necessary. Target poles  418  and  419  may be made of a soft-magnetic material, in particular they may be assembled of soft-magnetic conductive laminations stacked axially and electrically isolated from each other. Further, the target poles  418  and  419  may have a chamfered surface, which may focus the direction of the magnetic flux radially into the poles. The radial poles  405   a - d  have surfaces adjacent to the surface of the target poles  418 , and separated from it by radial air gaps  409   a - d . Similarly, the radial magnetic stationary poles  406   a - d  have surfaces adjacent to the surface of the soft magnetic target poles  419 , and separated from it by radial air gaps  410   a - d . In some implementations, a fewer or greater number of radial magnetic stationary poles  405   a - d  and  406   a - d  may be utilized. 
     Sleeves  416  and  417  are adjacent the target poles  418  and  419  and the magnets  411  and  413 , respectively. The sleeves  416  and  417  help to compress the magnets to protect them from breaking during high rotational speeds. The sleeves  416  and  417  may be steel tubes sized in such a way that the magnets remain at compression during high rotational speeds. For example, they may be steel tubes applied at high temperatures around the magnets  411  and  413 , and then allowed to cool. Sleeves  416  and  417  may be, for example, magnetic steel tubes to conduct magnetic flux between the magnets  411  and  413  and the air gaps  409   a - d  and  410   a - d , respectively. Sleeve  424  supports magnet  412  such that magnet  412  remains at compression at high rotational speeds. Sleeve  424  may be a non-magnetic material, such as a stainless steel, brass, Inconel®, or any strong non-magnetic material known in the art. 
     As illustrated in  FIG. 4 , the radial poles  405   a - d  and  406   a - d , the target poles  418  and  419 , magnets  411 - 413 , and the soft-magnetic sleeves  416  and  417  form a magnetic bias circuit. Magnets  411 - 413  produce bias magnetic flux  415  in the bias magnetic circuit. In the embodiment of  FIG. 4 , beginning hypothetically at spacer  433 , bias flux  415  propagates from the spacer  433  radially through the radial poles  406   a - d , across the air gaps  410   a - d , into the target pole  419 , and into the backiron  425 . The bias flux  415  then propagates axially, e.g., in the positive Z direction in  FIG. 4 , and is then directed radially through target pole  418 , across the air gaps  409   a - d , and radially through the radial poles  405   a - d  and back to spacer  433 . The axially magnetized magnet  412  reduces internal magnetic flux leakage inside the moveable magnetic circuit portion  403  resulting in higher bias magnetic flux densities in the radial air gaps  409   a - d  and  410   a - d  and may not be necessary. It also may be substituted for a non-magnetic material such as a stainless steel or may be brass, Inconel®, or any strong non-magnetic material known in the art. 
     The embodiment shown in  FIGS. 1A-C  uses magnets in both the moveable portion of the magnetic circuit  103  and a stationary assembly  104 , which allows for the reduction in the amount of the magnetic material in the moveable portion of the magnetic circuit  103  while also allowing for a reduction in the leakage flux between two sets of the stator radial magnetic poles  105   a - d  and  106   a - d . The latter point is illustrated, for example, in  FIG. 2A .  FIG. 2A  shows that both magnet  114  mounted on the stationary portion of the magnetic circuit  104  and magnets  111 - 113  mounted on the moveable portion of the magnetic circuit  103  produce leakage fields  240  and  242 , respectively, in the axial gap  137  between the two sets of the stator radial magnetic poles  105   a - d  and  106   a - d , respectively. However, since these fields are directed oppositely in the axial gap  137  they weaken or cancel each other. Note that in the design shown in  FIG. 4 , magnets  411 - 413  produce a low leakage fields in the axial gap  437  because this gap is shunted by the soft-magnetic spacer  433 , which has much smaller magnetic reluctances. In contrast, in the design shown in  FIGS. 1A-C  and  FIGS. 2A-C , the magnet  114  has a large magnetic reluctance and the magnetic field generated by magnets  111 - 113  will be present in the axial gap  137 , between the two sets of the stator radial magnetic poles  105   a - d  and  106   a - d.    
     In some aspects, the proposed radial homopolar permanent-magnet-biased electromagnetic actuator  100  may be utilized as a part of an Active Magnetic Bearing (AMB) system to support an object without a mechanical contact.  FIG. 5  shows an example of using an AMB system in a rotational electric machine  500 . The rotational electric machine  500  can be, for example, an electric compressor including an electric motor  550  driving an impeller  552  mounted directly on the motor shaft  554 . The electric motor  550  shown in  FIG. 5  has a rotor  556  and a stator  558 . Alternatively, the impeller  552  can be driven by a flow of gas or liquid and spin the rotor  556  attached to it through the shaft  554 . In this case, the motor  550  can be used as a generator. In embodiments, the rotor  556  of the electric machine  500  can be supported without mechanical contact by means of front and rear radial AMBs  560  and  562  in combination with axial AMB  564 . When the AMBs  560 ,  562 , and  564  are not working, the rotor rests on the mechanical backup bearings  570  and  572 . The front backup bearing  570  provides the axial support of the entire rotor  556  and a radial support of the rotor front end, whereas the rear backup bearing  572  provides only radial support of the rear end of the rotor  556 . There are sufficient radial clearances between the inner diameters of the mechanical backup bearings  570 ,  572  and the outer diameters of the rotor portions interfacing with those bearings to allow the rotor  556  to be positioned radially without touching the backup bearings  570 ,  572  when the AMBs  560  and  562  are activated. Similarly, there are sufficient axial clearances between the backup bearings  570 ,  572  and the portions of the rotor  556  interfacing with those bearings to allow the rotor  556  to be positioned axially without touching the backup bearings  570  and  572  when the axial AMB  564  is activated. 
     The axial AMB  564  may include an electromagnetic actuator  580 , axial position sensor  582  and control electronics  510 . The electromagnetic actuator  580  serves to exert forces on the axial actuator target  584  firmly mounted on the rotor  556  in the direction of the Z-axis  530  (axial direction). The front radial AMB  560  may include an electromagnetic actuator  586  per present disclosure, front radial position sensors  588  and control electronics  510 . The electromagnetic actuator  586  is capable of exerting radial forces on the actuator target  590  firmly mounted on the front end of the rotor  556 . The rear radial AMB  562  may include an electromagnetic actuator  592  per present disclosure, rear radial position sensors  594  and control electronics  510 . The electromagnetic actuator  592  is capable of exerting radial forces on the actuator target  596  firmly mounted on the rear end of the rotor  556 . 
     Signals from the axial position sensor  582  and radial position sensors  588  and  594  are input into the control electronics  510 , which generates currents in the control coils of the electromagnetic actuators  580 ,  586  and  592  whenever it finds that the rotor is deflected from the desired position such that these currents produce forces pushing the rotor back to the desired position. 
     In some applications it is desirable to prevent access of the working gas or fluid to the windings and other stationary parts of the motor/generator and magnetic bearings. In  FIG. 5 , this is achieved by using a can  598  separating a cavity with the rotor  556  from the stationary parts of the motor/generator  550  and radial AMBs  560  and  562 . Because the thickness of the can is added to radial gaps separating stationary portions of the radial AMBs  560  and  562  from the corresponding actuator targets  590  and  596 , the system shown in  FIG. 5  would benefit from the actuator of the present disclosure, which allows increasing the forces produced by AMBs  560  and  562  in case of large air gaps without increasing their footprints. 
     In other applications it may not be required to isolate stationary parts of the motor/generator and magnetic bearings from processing gases or fluids, but large clearances between the stationary and rotating parts may be needed if large particles are present in the processing gases or fluids which may cause a machine seizure if stuck in small clearances. These applications would also benefit from the actuator of the present disclosure. 
     A number of embodiments have been described. Nevertheless, it will be understood that various modifications may be made without departing from the concepts described herein. Accordingly, other embodiments are within the scope of the following claims.