Patent Publication Number: US-7586217-B1

Title: High performance motor and magnet assembly therefor

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
   This application is a divisional of U.S. patent application Ser. No. 11/381,648, filed May 4, 2006, entitled HIGH PERFORMANCE MOTOR AND MAGNET ASSEMBLY THEREFOR, which is a continuation-in-part of U.S. patent application Ser. No. 11/151,152, filed Jun. 13, 2005, entitled HIGH PERFORMANCE LINEAR MOTOR AND MAGNET ASSEMBLY THEREFOR, which issued as U.S. Pat. No. 7,145,271, on Dec. 5, 2006, which is a divisional application of U.S. patent application Ser. No. 10/889,384, filed Jul. 12, 2004, entitled HIGH PERFORMANCE LINEAR MOTOR AND MAGNET ASSEMBLY THEREFOR, issued as U.S. Pat. No. 6,919,653, on Jul. 19, 2005, which is a divisional application of U.S. patent application Ser. No. 10/369,161, filed Feb. 19, 2003, entitled HIGH PERFORMANCE LINEAR MOTOR AND MAGNET ASSEMBLY THEREFOR, which issued as U.S. Pat. No. 6,803,682, on Oct. 12, 2004, which claims the benefit of U.S. Provisional Patent Application Ser. No. 60/358,654, filed on Feb. 21, 2002, and entitled HIGH PERFORMANCE LINEAR MOTOR MAGNET ASSEMBLY THEREFOR. The entireties of these applications are incorporated by reference herein. 

   TECHNICAL FIELD 
   The present invention relates to motors and, more particularly, to a magnet assembly and to a motor incorporating the magnet assembly. 
   BACKGROUND OF THE INVENTION 
   Linear motors are used in various types of systems, such as for positioning and moving applications, including machining and gantry type systems. The high performance systems often require moving elements subjected to high acceleration levels. In order to achieve such high acceleration, the linear motor must exert large forces upon the elements to be moved. 
   There are various configurations of linear motors, including flat motors, U-channel motors and tubular shaped motors. Different types of linear motors. Common to most linear motors is a moving assembly, usually called a forcer or stage, which moves relative to a stationary platen (or path) according to magnetic fields generated by application of current through one or more associated windings. The windings can be on the forcer or at the platen depending on the type of motor. For example, in a permanent magnet linear motor, a series of armature windings can be mounted within a forcer that is movable relative to a stationary path. The path can include an array of permanent magnets configured to interact with the coils in the stage when energized with an excitation current. 
   Alternatively, in another type of conventional linear motor, permanent magnets can be part of a moveable stage with the coils situated in the platen. Usually, the permanent magnets are attached to a back iron plate above the coils, which are oriented along a path of travel. The magnets usually are rectangular in shape. The magnets are arranged along the back iron so that adjacent pairs of magnets have opposite magnetic pole orientations. The magnets can be oriented generally normal to the direction of travel or inclined at a slight angle from normal to an axis of the direction of travel for the linear motor. The inclined angle creates a flux distribution along the axis of movement, which is generally sinusoidal in nature. Such a resulting distribution due to the optimized motor geometry tends to reduce cogging during operation of the linear motor, which would otherwise occur if the magnets were aligned, normal to the axis of movement. 
   Although an inclined angle of the magnets can reduce some cogging, it presents a disadvantage in that a larger area typically must be covered by the rectangular magnets in order to sufficiently cover and interact with the coils of the armature. When the magnets are implemented with a larger area so as to reduce cogging effects, a larger footprint for the back iron also is required. This tends to increase the overall weight and size of the stage. Such increases in size and weight can present additional obstacles, such as in applications where there are size constraints and low mass is desirable. For example, as the mass of the stage increases, the available acceleration experiences a corresponding reduction, and the ability to stop the motor accurately also reduces because of the increased power dissipation needed to stop the motor. 
   As the use of linear motors in manufacturing equipment continues to increase, nominal increases in the speed of operation translate into significant savings in the cost of production. Accordingly, it is desirable to provide a magnet assembly that can be part of a high performance linear motor. 
   SUMMARY 
   The following presents a simplified summary of the invention in order to provide a basic understanding of some aspects of the invention. This summary is not an extensive overview of the invention. It is intended to neither identify key or critical elements of the invention nor delineate the scope of the invention. Its sole purpose is to present some concepts of the invention in a simplified form as a prelude to the more detailed description that is presented later. 
   One aspect of the present invention provides a magnet assembly that can be employed as part of a linear motor stage to form a high performance linear motor. The magnet assembly includes a plurality of magnets operatively associated with magnetically conductive plate, commonly known as a back iron. The magnets extend from a common side of the back iron. The back iron is dimensioned and configured to substantially conform to magnetic flux that travels through the back iron when the magnet assembly is exposed to a magnetic field, such as from windings of a motor path. In one particular aspect of the present invention, a cross-sectional dimension of the back iron varies between opposed ends of the back iron as a function of the position and/or orientation of the magnets. For example, a thickness of the back iron is greater at locations between adjacent pairs of the magnets than at locations generally centered with the respective magnets. As a result of such back iron geometry, force output to moving mass ratio of a motor incorporating the magnet assembly is improved over conventional configurations of magnet assemblies. Also, the back iron geometry reduces leakage flux. 
   Another aspect of the present invention provides a linear motor system that includes a path having a plurality of windings, which can be energized to produce desired magnetic fields. The linear motor system also includes a magnet assembly, such as described above. The linear motor system achieves high performance because the magnet assembly has a reduced mass, which substantially conforms to magnet flux lines that travel through the magnet assembly during energization of path windings. The mass further can be reduced by employing generally elongated octagonal magnets, such as by removing corner portions from rectangular magnets. 
   According to yet another aspect, a magnet assembly can be used in a linear motor arrangement in such a way so as to generate a Halbach array. A Halbach array can be achieved by a special formation of magnets using 90-degree angles to direct each individual magnet&#39;s field in alternating vertical and horizontal orientations, such that half of the magnets are vertically polarized (e.g., perpendicular to a direction of motion of the linear motor), while the other half of the magnets are horizontally polarized, permitting maximization of the magnetic field produced thereby in a desired direction. Additionally, remnant fields that do not contribute to force output in a horizontal direction can be cancelled. This magnet arrangement can be formed as a reduced mass magnet assembly as described above, and can further concentrate magnetic flux in a desired direction while simultaneously mitigating the effects of stray magnetic fields. 
   According to another aspect, a platen and forcer system is provided. The system employs the reduced mass magnet assembly as previously described. Additionally or independently, other features of the forcer system are modified so as to further optimize magnetic flux capacity in a desired direction. For example, the system can comprise magnetically conductive backing materials fashioned from solid stock, laminations, and/or combinations of smaller stock, or by other known means, such as as sintering, etc., with a varied cross-sectional thickness comprising peaks and valleys, and a plurality of magnets associated therewith such that the center of each magnet is generally aligned with a valley (e.g., a relatively thinner region of the metal backing). The plurality of magnets can be arranged to generate a Halbach array that maximizes output force in a desired horizontal direction and minimizes and/or cancels magnetic fields that do not contribute to force output in the desired horizontal direction. Furthermore, the platen and forcer system mitigates shielding requirements when employed in conjunction with the Halbach array magnet arrangement, making the system highly suitable for manufacturing applications such as e-beam lithography, focused ion beam systems, and the like. For instance, an electron beam employed to etch, inspect, and/or otherwise fabricate a semiconductor wafer can be adversely affected by stray static and alternating magnetic fields, which results in intricate shielding requirements and its complex design when traditional platen and forcer systems are employed. To mitigate a need for elaborate shielding, the subject systems and methods can employ the Halbach magnet arrangement, which can facilitate reducing costs and improving throughput in such fabrication environments. It will be appreciated that any type of linear motor (e.g., iron core motors, ironless motors, can be utilized in conjunction with the various aspects set forth herein. 
   According to still another aspect, a reduced-mass magnet assembly is described for a rotary motor to facilitate performance improvement and/or enhancement. For example, various aspects can be employed in conjunction with a moving-magnet rotary motor, such as an interior rotor brushless permanent magnet motor, wherein a stator has a core and houses a plurality of coils and magnets are deployed on a rotor. Said stator and rotor may be constructed of laminations or solid magnetically conductive material. Additionally and/or alternatively, such aspects can be employed in conjunction with a moving-coil rotary motor, such as an exterior-rotor brushless permanent magnet motor, wherein a rotor houses a plurality of coils and magnets are deployed on a stator. According to related aspects, any combination of rotating and stationary coils and magnets can be employed. For instance, the motor can be fashioned with rotating magnets and stationary coils and/or stationary magnets and rotating coils. In one aspect, an annular ring with magnets mounted thereon can be modified to optimize magnetic flux in a given direction. For example, a plurality of magnets can be operatively associated with a magnetically conductive annular ring with a varied cross-sectional thickness such that peaks and valleys are formed generally throughout the cross-sectional dimension. The plurality of magnets can be dispersed such that each magnet generally aligns with a valley region of the annular ring to facilitate aligning the valleys with magnetic flux lines generated by the magnets. 
   To the accomplishment of the foregoing and related ends, certain illustrative aspects of the invention are described herein in connection with the following description and the annexed drawings. These aspects are indicative, however, of but a few of the various ways in which the principles of the invention may be employed and the present invention is intended to include all such aspects and their equivalents. Other advantages and novel features of the invention will become apparent from the following detailed description of the invention when considered in conjunction with the drawings. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
       FIG. 1  is an isometric view of a moving magnet assembly in accordance with an aspect of the present invention. 
       FIG. 2  is a top elevation of the magnet assembly of  FIG. 1 . 
       FIG. 3  is a side sectional view of the magnet assembly taken along line  3 - 3  of  FIG. 2 . 
       FIG. 4  is side sectional view of part of a linear motor in accordance with an aspect of the present invention. 
       FIG. 5  is a side sectional view similar to  FIG. 4 , illustrating magnetic flux lines for an energized linear motor in accordance with an aspect of the present invention. 
       FIG. 6  is a side sectional view of a motor magnet assembly in accordance with another aspect of the present invention. 
       FIG. 7  is a side sectional view of a motor magnet assembly in accordance with another aspect of the present invention. 
       FIG. 8  is a side sectional view of a motor magnet assembly in accordance with another aspect of the present invention. 
       FIG. 9  is a side section view of a motor magnet assembly in accordance with various aspects set forth herein, showing a typical orientation, such as in a Halbach array. 
       FIG. 10  illustrates a platen and forcer motor system in accordance with various aspects. 
       FIG. 11  illustrates an interior-rotor brushless permanent magnet motor that can be utilized in conjunction with a backing of varied cross-section, in accordance with various aspects described herein. 
       FIG. 12  is an illustration of an exterior-rotor brushless permanent magnet motor that can be utilized in conjunction with a backing of varied cross-sectional width as described herein, in accordance with various aspects. 
       FIG. 13  illustrates a portion of a rotary motor with a backing of varied cross-section, in accordance with various aspects. 
   

   DETAILED DESCRIPTION OF THE INVENTION 
   The present invention provides a magnet assembly for use in a linear motor. The magnet assembly includes a back iron and an array of magnets. The back iron is in the form of a plate having opposed surfaces of the back iron. The magnets are arranged in a generally linear array along one of the surfaces. The other surface of the back iron plate is dimensioned and configured according to the magnetic field distribution and/or localized regions of saturation associated with the motor geometry/topology. For example, the surface of the back iron plate opposite to which the magnets are attached can be scalloped, such that a dimension between the opposed surfaces at locations generally aligned with the magnet centers is less than a dimension between the opposed surfaces at locations between adjacent magnets. 
   Additionally, the subject invention can be employed in conjunction with a rotary motor, a platen and forcer arrangement, and/or any other suitable arrangement in which the various aspects described herein. . . . 
     FIGS. 1 ,  2  and  3  illustrate a magnet assembly  10  in accordance with an aspect of the present invention. The magnet assembly  10  includes an array of permanent magnets  12 ,  14 ,  16 ,  18 ,  20 ,  22 ,  24 , and  26  of alternating magnetic polarity (see  FIG. 2 ). The magnets  12 - 26  are arranged in a substantially parallel relationship to each other and mounted to a generally rigid and magnetically conductive plate  30 , commonly referred to (and hereinafter referred to) as a back iron. The alternating polarity facilitates the flow of magnetic flux through the magnets  12 - 26  and the back iron  30 . The assembly  10  also includes an outer support structure  32  of a suitable non-conducting material, such as an epoxy or a polymer material. The support structure  32  helps hold the magnets  12 - 26  and back iron  30  in a desired relationship. 
     FIG. 2  is a top elevation of the magnet assembly of  FIG. 1  in which the support structure  32  has been removed. As shown in  FIG. 2 , the magnets  12 - 26  have a generally rectangular geometry and are spaced apart from each other by a predetermined distance. The magnets  12 - 26  have long axes, which are oriented generally perpendicular to a desired direction of travel for the assembly  10 , indicated at  34 , and which are aligned substantially parallel to each other. To provide desired flux distribution, the corners of each of the magnets  12 - 26  have been chamfered to form magnets having elongated octagonal geometries, such as shown in  FIG. 2 . The precise configuration can vary depending on the size of the magnets  12 - 26 , the size of the motor in which the assembly is to be employed as well as the desired characteristics for the motor. In this example, the illustrated magnet geometry also helps reduce the mass of the magnet assembly  10 . By way of example, the magnets are formed of a NdFeB material or other type of high performance permanent magnetic materials. 
   Referring to the side-sectional view of  FIG. 3 , the  12 - 26  magnets are mounted to and extend from a common side  36  of the back iron  30 . The back iron  30  also includes another side  38  opposite the side  36  to which the magnets  12 - 26  are mounted. In particular, the magnets  12 - 26  are positioned in slots or receptacles on the side  36 , which are dimensioned and configured to receive a portion of the respective magnets therein. Adjacent pairs of the slots define notches  40 ,  42 ,  44 ,  46 ,  48 ,  50 , and  52  of the back iron material that extend between adjacent pairs of magnets. The notches  40 - 52  operate to separate adjacent pairs of the magnets  12 - 26  by a predetermined distance, indicated at  56 , which corresponds to the width of the respective notches. For example, less than one-half the width of the magnets  12 - 26  are recessed into the back iron  30 , such that more than one-half the width of the magnets extend outwardly from the side  36  of the back iron  30 . The notches  40 - 52  and remaining surface of the side  36  are generally coplanar, although other shapes and configurations could be used in accordance with an aspect of the present invention. Also, the notches  40 - 52  act as retainers locking the magnets in place providing the desired stiffness. However, it will be appreciated by those skilled in the art that the back iron  30  may be designed without notches  40 - 52  (e.g., in a scenario in which the magnets  12 - 26  are affixed to back iron  30  with an adhesive or other suitable means), in order to further reduce the weight of the magnet assembly. 
   In accordance with an aspect of the present invention, a cross-sectional dimension of the back iron  30  varies along its length between spaced apart ends  58  and  60  so as to substantially conform to the magnetic flux generated during operation of a motor that includes the magnet assembly  10 . In the example of  FIG. 3 , the thickness of the back iron  30  between the opposed sides  36  and  38  is greater at locations between adjacent pairs of the magnets  12 - 26  than at locations generally aligned with centers of the respective magnets. The back iron  30  can be formed of substantially any generally rigid material capable of conducting a magnetic field, so as to help form a magnetic circuit formed of the magnets  12 - 26  of different polarities and associated motor windings (not shown). 
   For example, the back iron  30  is formed of a non-linear material having a high magnetic permeability and desired saturation characteristics. In a particular aspect of the present invention, the back iron is formed of vanadium permeadur (e.g., cobalt—48.75%, Vanadium—2%, Carbon—0.004%, Manganese—0.05%, Silicon—0.05%, Iron—balance), which has particularly high saturation characteristics compared to other non-linear materials. While such material is considerably more expensive than steel, its superior magnetic properties are desirable in ultra-high performance motors according to the present invention. It is to be understood and appreciated that a high performance magnet assembly, in accordance with an aspect of the present invention, could employ other types of non-linear materials (e.g., M19 steel) than vanadium permeadur. 
   By way of illustration, the back iron  30  has a maximum thickness, indicated at  62 , at its ends  38  and  30  and at locations  64 ,  66 ,  68 ,  70 ,  72 ,  74 , and  76  between adjacent pairs of magnets  12 - 26 . In the example of  FIG. 3 , the locations  64 - 76  having the maximum thickness  62  are substantially coextensive with the notches  40 - 52 . Additionally, the side  38  of the back iron  30  at the ends  58  and  60  and at the locations  64 - 76  are generally coplanar and substantially parallel to the other side  36  of the back iron. It is to be appreciated, however, that back iron other shapes (e.g., curved in the direction of travel) also could be utilized in accordance with an aspect of the present invention. Thus, as shown in  FIGS. 1 and 2 , the side  38  defines generally rectangular and coplanar strips extend between side edges  80  and  82  of the back iron  30  at the ends  58  and  60  and at the locations  64 - 76 . 
   The back iron  30  further has a minimum thickness, indicated at  84 , at locations  86 ,  88 ,  90 ,  92 ,  94 ,  96 ,  98 , and  100  substantially centered with the long axes of the respective magnets  12 - 26 . In the example of  FIG. 3 , the locations  86 - 100  have the minimum thickness  84 , which define generally rectangular planes or strips in the side surface  38  spaced from and substantially parallel to the magnets  12 - 26  over which the respective locations are positioned. The locations generally rectangular strips, which can be coplanar, extend between the side edges  80  and  82  of the back iron  30 . 
   The portions of the side  38  extending between the locations of maximum thickness (e.g., the ends  58  and  60  and the locations  64 - 76 ) and the locations of minimum thickness  86 - 100  slope upwardly and downwardly to provide a desired scalloped or sawtooth cross section, as illustrated in  FIG. 3 . That is, the locations (or strips)  64 - 76  and  86 - 100  respectively provide alternating peaks and valleys along the surface  38  of the back iron. 
   Referring to  FIG. 2 , each of the locations  64 - 76  of maximum back iron thickness has a width  104  in the direction  34 , which width is greater than or equal to zero. Similarly, each of the locations  86 - 100  of minimum back iron thickness has a width  106  in the direction  34 , which width is greater than or equal to zero. Accordingly, while the locations of maximum and minimum thickness are illustrated as generally planar and parallel to the side  36 , those skilled in the art will understand and appreciated that virtually any widths  104  and  106  can be employed to provide different varying cross-sectional configurations for the back iron in accordance with an aspect of the present invention. Additionally or alternatively, while the locations  64 - 76 , the locations  86 - 100  and the portion of the side surface extending therebetween are illustrated as generally planar surfaces, it is to be appreciated that one or more of such surface portions could be curved in accordance with an aspect of the present invention. 
     FIG. 4  illustrates a cross-sectional view of a linear motor system  130  in accordance with an aspect of the present invention. The system  130  includes a moving magnet assembly (or stage)  132  that is moveable in a direction of travel, indicated at  134 , relative to a path  136 . For example, the magnet assembly  132  is supported relative to the path  136  for movement in the direction  134 , such as by low or no friction bearings (e.g., air bearings, not shown) to provide a desired air gap between the magnet assembly and the path. 
   The magnet assembly  132  includes a plurality of magnets  138 ,  140 ,  142 ,  144 ,  146 ,  148 ,  150 , and  152 , which are attached to and extend from a common side  156  of a back iron  158 . An opposite side  160  of the back iron  158  is dimensioned and configured to conform to flux lines of a magnetic circuit formed between the magnet assembly and the path when the path is energized. That is, the thickness of the back iron  158  between the opposed sides  156  and  160  is greater at locations between adjacent pairs of the magnets  138 - 152  than at locations generally aligned with centers of the respective magnets. As a result, the side surface  160  has a generally scalloped or ribbed appearance between its ends; e.g., it is formed of alternating peaks and valleys between spaced apart ends of the back iron. The particular cross-sectional configuration of the back iron can vary, such as described herein. 
   The path  136  includes a plurality of spaced apart teeth  162  that extend from a base portion  164  toward the magnet assembly  132  located above the path  136 . Typically, the teeth  162  are oriented substantially parallel relative to each other and to the magnets  138 - 152 . The path  136  also includes windings  166  disposed around selected teeth. The windings  166  could be pre-wound coil assemblies or wound in-situ around the teeth  162 . 
   Those skilled in the art will understand and appreciate that the linear motor system typically includes a motor controller programmed and/or configured to control operation of the motor system  130 . For example, an encoder or other positioning system provides the controller with position information, based on which the controller controls energization of the associated windings  166  to effect desired movement of the magnet assembly  132  relative to the path. Those skilled in the art further will understand and appreciate various configurations of paths  136  and coil windings that could be utilized in combination with a magnet assembly in accordance with an aspect of the present invention. 
     FIG. 5  depicts a graphical representation of part of linear motor system  200 , similar to that shown in  FIG. 4 , illustrating magnetic flux lines  202  for magnet circuits formed by a magnet assembly  204  and energized windings of a motor path  206  in accordance with an aspect of the present invention. The magnet assembly  204  includes a plurality of permanent magnets  208 ,  210 ,  212 ,  214 ,  216 ,  218 ,  220 , and  222  that are operatively coupled to a back iron  226 . 
   In accordance with an aspect of the present invention, as shown in  FIG. 5 , the back iron  226  is dimensioned and configured to conform to the magnet flux lines that travel through the magnetic circuits formed of the magnet assembly and the path  206 . The back iron  226  has a greater cross-sectional dimension at locations at ends of the magnet assembly  204  and between adjacent pairs of magnets than at the locations generally centered with the respective magnets. Consequently, the overall mass of the moveable magnet assembly  204  is less than if such portions had not been removed. Additionally, because the selected portions have been removed according to the magnetic flux lines during energization of the path windings, the forces generated between the assembly  204  and the path remain substantially unchanged from a back plane that would include a substantially planar surface opposite the magnets. 
   To further reduce the mass of the magnet assembly, the magnets can be configured to have chamfered corners, so as to provide a generally elongated octagonal geometry. The particular dimensions and configuration of magnets and back iron can be further optimized based on magnetic finite element analysis. As a result, under Newton&#39;s law, the acceleration of the magnet assembly  204  relative to the path  206  is increased by an amount proportional to the reduced mass of the magnet assembly. Additionally, the geometry further provides flux distribution that is substantially sinusoidal distribution, which mitigates total harmonic distortion (THD). A lower THD corresponds to a more efficient motor. 
   As mentioned above, it is to be appreciated that various configurations of magnet assemblies can be implemented in accordance with an aspect of the present invention.  FIGS. 6-8  illustrate some examples of other configurations of magnet assemblies that can be utilized. It will be understood and appreciated that such examples are solely for illustrative purposes and that numerous other possible configurations exist, all of which are within the scope of the appended claims. 
     FIG. 6  illustrates a magnet assembly  240  for use in a linear motor in accordance with an aspect of the present invention. The assembly  240  includes a plurality of elongated permanent magnets  242  operatively coupled to a back iron  244 . As shown in  FIG. 6 , a cross-sectional dimension of the back iron  244  varies along its length between spaced apart end portions  246  and  248  of the back iron. In particular, a side surface  250  of the back iron  244  opposite a side  252  to which the magnets  242  are attached has a substantially triangular or sawtooth geometry having alternating peaks  254  and valleys  256 . The other side  252  is generally planar, although it includes slots or receptacles in which a portion of the respective magnets  242  is received. As a result of such back iron  244  configuration, the thickness of the back iron at locations between adjacent pairs of magnets  242  and at the end portions  246  and  248  is greater than its thickness at locations generally centered with the long axes of the respective magnets. 
   The geometry of the back iron  244  substantially conforms to magnetic flux lines that travel through the back iron from the magnets so as to provide extremely high flux densities. The geometry further enables the back iron  244  to have a reduced mass. The magnets also can be configured to have chamfered corners, so as to provide a generally elongated octagonal geometry, such that the mass of the magnet assembly is further reduced. The combination of high flux densities and reduce back iron mass result in a high performance motor capable of achieving rapid acceleration compared to conventional linear motors of similar size. 
     FIG. 7  illustrates a magnet assembly  260  for use in a linear motor in accordance with another aspect of the present invention. The assembly  260  includes a plurality of elongated permanent magnets  262  operatively coupled at a side surface  264  of a back iron  266 . The back iron  266  has a cross-sectional dimension that varies along its length between spaced apart end portions  268  and  270  in accordance with an aspect of the present invention. In particular, a side surface  272  of the back iron  244  opposite the side  264  to which the magnets  262  are attached has a plurality of substantially elongated rectangular peaks (or protrusions)  276 . The peaks  276  extend between side edges of the back iron. That is, the side  272  has alternating rectangular peaks  276  and valleys  278  to provide a generally square wave cross-sectional geometry between the end portions  268  and  270 . The peaks  276  are generally centered over spaces between adjacent pairs of the magnets  262  and the valleys are generally centered over the long axes of the respective magnets. The side  264  is generally planar, although it includes slots or receptacles in which a portion of the respective magnets  262  is received. 
   As a result of such geometry for the back iron  266 , the thickness of the back iron at locations between adjacent pairs of magnets  262  and at the end portions  268  and  270  is greater than its thickness at locations generally centered with the magnets. This geometry substantially conforms to magnetic flux lines that travel through the back iron  266  from the magnets  262  so as to provide extremely high flux densities, such as when associated windings of a motor incorporating the magnet assembly  260  are energized. The geometry further enables the back iron  266  to have a reduced mass. The combination of high flux densities and reduced back iron mass result in a high performance motor capable of achieving rapid acceleration compared to conventional linear motors of similar size. 
     FIG. 8  depicts yet another magnet assembly  280  in accordance with an aspect of the present invention. The magnet assembly includes a plurality of permanent magnets  282  operatively connected to a generally planar side surface  284  of a back iron  286 . Specifically, a portion of the magnets  282  can be received in associated slots or receptacles formed in the side  284 , although the magnets could be attached to the back iron in the absence of such slots. 
   In accordance with an aspect of the present invention, a side surface  288  of the back iron  286  opposite the side  284  to which the magnets are connected is dimensioned and configured to substantially conform to magnetic flux lines associated with the magnet assembly when exposed to magnetic fields from energized windings of an associated motor path (not shown). In the example of  FIG. 8 , the side surface  288  has alternating peaks  290  and valleys  292  to provide a generally sinusoidal cross-sectional configuration between spaced apart end portions  294  and  296  of the back iron  286 . The peaks  290  are generally centered over spaces located between adjacent pairs of magnets  282  and the valleys  292  are generally centered over corresponding centers of the respective magnets. 
   As a result of the back iron geometry shown in  FIG. 8 , the magnet assembly  280  is able to complete magnetic circuits in an associated linear motor so as to provide extremely high flux densities, such as when associated windings of the motor incorporating the magnet assembly are energized. The geometry further provides the back iron  286  with a reduced mass. To further reduce the mass of the magnet assembly, the magnets  282  can be configured as a generally elongated octagon, such as by removing corner portions of the magnets. The combination of high flux densities and reduced back iron mass result in a high performance motor capable of achieving rapid acceleration compared to conventional linear motors of similar size. 
     FIG. 9  illustrates yet another magnet assembly for use in a motor in accordance with various aspects. A plurality of magnets  302  can be arranged on side  304  of back iron  306  in such a way so as to generate a Halbach array. The back iron  306  consists of peaks  310  and valleys  312  on side  308  between spaced apart end portions  314  and  316 . The plurality of magnets  302  are shown with directional arrows indicating the polarization of each of the respective magnets. The arrangement shown facilitates concentration of the magnetic field below the magnets  302  and cancels out any remnant magnetic field above the magnets  302  resulting in a low stray magnetic field. Cancellation of magnetic field effects in undesired locations prevents interference to the overall force output of the magnet assembly  300 . 
   With further reference to  FIG. 9 , side  308  of back iron  306  consists of peaks  310  and valleys  312  so as to reduce the mass of the magnet assembly while at the same time optimizing magnetic flux through the back iron  306 . Peaks  310  and valleys  312  provide a generally sinusoidal cross-sectional configuration between spaced apart end portions  314  and  316  of the back iron  306 . However, it will be appreciated that the cross-sectional shape of the peaks  310  and valleys  312  can be triangular, saw-toothed, shaped as a square-wave, etc., or any other suitable shape that facilitates reducing mass while retaining sufficient rigidity. The peaks  310  are positioned over spaces located between adjacent pairs of magnets  302  of the Halbach array, while valleys  312  are generally centered over corresponding centers of the respective magnets  302 . It will further be appreciated that, in accordance with various other aspects, the back iron can be designed to have a fixed thickness, and magnets positioned therein can have varied thicknesses to reduce mass associated with the assembly. 
     FIG. 10  is an illustration of a platen and forcer linear motor system  340 . Forcer  342  includes magnet assembly  344 , which comprises a plurality of magnets  346  arranged in spaced relation to each other on side  360  of conductive metal backing  348 . Side  350  of metal backing  348  shows peaks  352  and valleys  354  in between ends  356  and  358 . This modification to backing  348  allows for a reduction in total mass of the forcer  342 , thus permitting optimized acceleration capabilities along platen  374 . Platen  374  can be, for example, a solid platen, a laminated platen, or any other suitable platen configuration, as will be appreciated by one skilled in the art. It is further to be appreciated that the plurality of magnets  346  can additionally be adapted to possess polarization characteristics such that a Halbach array is formed. According to this aspect, the magnetic field generated by the Halbach array would be optimally concentrated in air gap  372  between the forcer  342  and platen  374 . This arrangement allows for maximal efficiency with respect to strength of the magnetic field in a vertical direction because remnant magnetic fields in an undesired location (e.g. horizontally) will be cancelled. 
   The system  340  comprises a forcer  342  and associated magnet assembly  344  that is moveable in multiple directions of travel. For example, the magnet assembly  344  can be supported for movement in various directions about the platen, such as by low or no friction bearings (e.g., air bearings, not shown) to provide a desired air gap  372  between the magnet assembly  344  and the platen  374 . The magnet assembly  344  can comprise a plurality of magnets  346 , which are attached to and extend from a common side  360  of a metal backing  348 . An opposite side  350  of the metal backing  348  is dimensioned and configured to conform to flux lines of a magnetic circuit formed between the magnet assembly  344  and the platen  374  when the platen  374  is energized. That is, the thickness of the metal backing  348  between the opposed sides is greater at locations between adjacent pairs of the magnets  346  than at locations generally aligned with centers of the respective magnets. As a result, the top surface  350  has a generally scalloped or ribbed appearance between its ends; e.g., it is formed of alternating peaks  352  and valleys  354  between spaced apart ends of the backing  344 . The particular cross-sectional configuration of the backing can vary, such as described herein. Furthermore, in accordance with various other aspects, the forcer  342  can be designed to have a fixed thickness, and magnets  346  positioned therein can have varied thicknesses, varied lengths, and/or varied widths, to reduce mass associated with the assembly  344 . 
   The platen  374  comprises a plurality of spaced apart teeth  362  that extend from a base portion toward the magnet assembly  344  located above the platen  374 . Typically, the teeth  362  are oriented substantially parallel relative to each other and to the magnets  346 . The platen  374  also comprises windings  364  disposed around selected teeth  362 . The windings  364  can be pre-wound coil assemblies or wound in-situ around the teeth  362 . Moreover, in order to further reduce mass of the system  340 , a plurality of notches  376  can be provided in the bottom of the platen  374 . Those skilled in the art will understand and appreciate that the platen and forcer system  340  can additionally comprise a motor controller programmed and/or configured to control operation of the system  340 . For example, an encoder or other positioning system can provide the controller with position information, based on which the controller controls energization of the associated windings  364  to effect desired movement of the forcer  342  relative to the platen  374 . Those skilled in the art further will understand and appreciate various configurations of platens  374  and coil windings  364  that can be utilized in combination with a magnet assembly in accordance with various other aspects. 
   In another aspect, the platen and forcer linear motor system  340  can, for example, be utilized in a semiconductor fabrication process. The system  340  can be used to move a plurality of wafers along an assembly line and/or about an assembly area. By canceling stray magnetic fields using the Halbach array arrangement, shielding requirements associated with conventional platen and forcer systems can be greatly reduced. It is to be appreciated that any known lithography process can be utilized in accordance with the present invention, such as, for instance, electron beam (E-beam) lithography. E-beam lithography is a method that employs an electron beam to form patterns on a wafer. The direction of the electron beam can be altered by stray magnetic fields that are present around the platen and forcer linear motor system  340 . Stray magnetic fields can be produced by nearby unattached equipment, magnets and current-carrying coils. Stray magnetic fields can be AC or DC. For instance, local uncoupled stray magnetic fields are generated due to a magnetic field of a permanent magnet and a coil carrying current, such that the sinusoidal excitation of motor phases, magnet motion, the magnetic system, etc., cause magnetic spikes. DC fields are typically non-varying, or slowly varying, and are caused by a permanent magnet. To mitigate the effects of stray magnetic fields, magnets  346  can be arranged such that a Halbach array is generated. This arrangement cancels remnant magnetic fields in undesired directions and concentrates the strength of the magnetic field in the air gap  372  between the forcer  342  and platen  374 . It will be appreciated that the air gap  372  is illustrated with an exaggerated width for ease of viewing, and that in practice the air gap  372  may be approximately 0.5 to 1.7 mm wide. Thus, by varying the cross-section of the backing  344  and arranging magnets  346  in a forcer portion  342  of a platen and forcer system  340  to generate a Halbach array, platen and forcer system  340  can be made for use in conjunction with, while facilitating reducing shielding requirements associated with, sensitive static and/or varying leakage components, such as an electron-beam component. 
     FIG. 11  illustrates an interior-rotor brushless permanent magnet motor  380  that can be utilized in conjunction with a backing of varied cross-section, in accordance with various aspects described herein. Rotary motor systems consisting of a stator and a rotor are well known in the art and are not discussed in detail herein for the sake of brevity. The motor  380  comprises stators  384  with windings and rotor assemblies  386  having a plurality of magnets disposed therein, as illustrated by a cross-sectional view  388  of a rotor  386 . A plurality of notches  396  can be provided to facilitate providing a “scalloped” rotor plate  398 , in order to reduce mass of the motor  380 . Within rotor assembly  386  resides a plurality of magnets  382  positioned in spaced relation to each other, as illustrated in the enlarged view  390  of the rotor assembly cross-section  388 . It is to be appreciated that any desired number of magnets can be employed in motor  380 . Rotor assembly  386  further comprises a plurality of scalloped rotors  392 , which can be arranged in a one-to-one configuration with magnets  382 , as well as in any other suitable or desired configuration. 
   Magnets  382  can be arranged in alternating polarities (e.g., north and south, . . . ). Additionally, it is to be appreciated that magnets  382  can be polarized so as to produce a Halbach array. The Halbach array arrangement of magnets  382  can facilitate canceling remnant magnetic fields in an angular direction (e.g., along the circumference of the rotor assembly) that would detract from the overall force output of the rotary motor. One with skill in the art will additionally appreciate that a core material that makes up the central core  394  of the rotary motor can be composed of any suitable conductive metal, in particular, non-oriented electrical steel. This material is capable of supporting high magnetic flux density and low core losses in high rate of acceleration change applications typical in linear and rotary motor systems. In this example, the utilization of both the Halbach array arrangement and non-oriented electrical steel core material maximizes the concentration of the magnetic field in the core of the motor and further prevents current loss and non-contributory magnetic field effects. 
     FIG. 12  is an illustration of an exterior-rotor brushless permanent magnet motor  400  that can be utilized in conjunction with a backing of varied cross-sectional width as described herein, in accordance with various aspects. The motor  400  comprises a pair of stators  402  and a pair of rotor assemblies  404  that are positioned exterior to the stators  402 , as opposed to the interior rotor configuration of  FIG. 11 . A cross-sectional view  406  of a rotor  404  is presented and illustrates a plurality of arc magnets  408  disposed upon an annular ring  410 , such that the magnets  408  are positioned in an air gap  412  in the rotor assembly. The annular ring  410  can have a variable thickness, such that the annular ring  410  is thicker in areas generally aligned with gaps between magnets  408 , and relatively thinner in areas generally aligned with the centers of magnets  408 . In this manner, mass of the motor  400  can be reduced. Additionally, to further reduce motor mass, a plurality of notches  414  can be formed at the interior of the assembly. The arc magnets  408  can be arranged in alternating polarities (e.g., north and south) and/or can be arranged to generate a Halbach array as described above. In accordance with various other aspects, the annular ring  410  can be designed to have a fixed thickness, and magnets  408  affixed thereto can have varied thicknesses to reduce mass associated with the assembly. According to still other aspects, magnets  408  can be designed to have a rounded edge  413  to further reduce mass and/or weight of the motor assembly. Alternatively, the motor topologies described with regard to  FIGS. 11 and 12  can be employed in conjunction with a variable cross-section backing, as described below with regard to  FIG. 13 . 
     FIG. 13  illustrates a portion of a rotary motor  420 , such as the motors described with regard to  FIGS. 11 and 12 , with a backing of varied cross-section, in accordance with various aspects. The motor  420  comprises a stator with windings  422 , and a rotor portion  424  comprising a magnetically conductive annular ring  428  that has a plurality of magnets  426  disposed thereon. The magnets  426  can be arranged to have alternating north-south polarity or arranged in any other suitable orientation, as will be appreciated by those skilled in the art. 
   The annular ring  428  can additionally have a varied cross-sectional dimension. For example, the annular ring  428  can be thinner in areas generally aligned with the centers of magnets  426 , and thicker, relatively, in areas generally aligned with the ends of the magnets  426  (e.g., the spaces between magnets  426 , In this configuration, the annular ring  428  exhibits a plurality of peaks  430  and valleys  432 , similar to those described above with regard to various linear motors and/or aspects related thereto. It will be appreciated that the orientation of the peaks  430  and valleys  432  can be generally sinusoidal, crenate, saw-toothed, triangular, square, etc., or any other suitable shape that facilitates reducing mass while retaining rigidity. As previously discussed with respect to magnet assemblies for linear motors, this arrangement of magnets  426  allows for reduction in the overall size of the rotor assembly  424 , and further allows the magnets  426  to conform to the magnetic flux lines that travel through annular ring  428  and which are produced by windings associated with a stator  422  of the rotary motor  420 . The reduced size of the annular ring still further facilitates increasing acceleration capabilities of the rotor  420 . Acceleration capabilities can further be increased by reducing mass on an inner side of the motor  420 , which can be achieved by providing a plurality of notches  434  to scallop the inner side of the motor  420 . 
   What has been described above includes exemplary implementations of the present invention. It is, of course, not possible to describe every conceivable combination of components or methodologies for purposes of describing the present invention, but one of ordinary skill in the art will recognize that many further combinations and permutations of the present invention are possible. For example, a magnet assembly, in accordance with an aspect of the present invention can have different numbers of magnets from that shown and described herein. Additionally, the magnet assembly can have a different contour from the substantially flat configuration shown herein, such as to conform to the contour of the path with which the magnet assembly is to be utilized. Accordingly, the present invention is intended to embrace all such alterations, modifications and variations that fall within the spirit and scope of the appended claims.