Abstract:
A permanent magnet assembly is disclosed that utilizes at least two rotating magnet subassemblies, and first and second stationary magnet subassemblies arranged so that their magnetic vectors oppose each other. At a first rotational position of the rotating magnet subassemblies, the magnetic vectors of the rotating magnet subassemblies align with the magnetic vector of the first stationary magnet subassembly and oppose the magnetic vector of the second stationary magnet subassembly. At a second rotational position, the magnetic vectors of the rotating magnet subassemblies are reversed, thereby aligning with the magnetic vector of the second stationary magnet subassembly and opposing the magnetic vector of the first stationary magnet subassembly. By locating air gap portions where the magnetic vectors of the rotating magnetic subassemblies meet the magnetic vectors of the stationary magnetic subassemblies, the air gap portions are subjected to a time-varying magnetic flux density.

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
   This application claims the benefit of provisional patent application 60/476,969, filed Jun. 9, 2003, the disclosure of which is incorporated by reference. 

   FIELD OF THE INVENTION 
   This invention relates generally to magnets, and more particularly to a composite magnet structure specially adapted to provide a time-varying high amplitude magnetic field across an air gap. 
   BACKGROUND OF THE INVENTION 
   Permanent magnets have been used for many years and for many purposes. However, new applications of permanent magnets are driving the development of increasingly sophisticated permanent magnet assemblies. 
   A permanent magnet assembly that can produce a periodic high amplitude magnetic field intensity across a gap is of particular interest. For example, such a permanent magnet assembly can be used to apply a time-varying magnetic field to magnetocaloric materials. Magnetocaloric materials near a transition from a ferromagnetic state to a paramagnetic state will warm when magnetized and cool when demagnetized. This property can be used to provide heating or cooling, for example in a magnetic refrigerator. 
   SUMMARY OF THE INVENTION 
   A permanent magnet assembly according to the present invention preferably utilizes at least two rotating magnet subassemblies and at least two stationary magnet subassemblies wherein the rotary motion of the rotating magnet subassemblies causes them to alternatively align with one stationary magnet subassembly and then with the other stationary magnet subassembly, whereby a time-varying magnetic flux density may be efficiently generated within one or more portions of an air gap. 
   A preferred embodiment of a permanent magnet assembly according to the present invention utilizes two synchronized counter-rotating magnet subassemblies at the midpoint between two stationary magnet subassemblies, where each rotating magnet subassembly includes a rectangular permanent magnet section and two rounded end caps made of magnetically permeable material, and each stationary magnet subassembly includes two permanent magnet sections plus two concave sections and a flux return section made of magnetically permeable material. In this embodiment, the concave sections of the stationary magnet assemblies surround two air gap portions, one air gap portion for each stationary magnet assembly, and the rotary motion of the rotating dipoles causes the intensity of the magnetic field through these air gap portions to oscillate, with the intensity of the magnetic field through one air gap portion maximized when the intensity of the magnetic field through the other air gap portion is minimized. 
   A variety of structures can be used in an apparatus according to the invention. For example, each stationary magnet subassembly may include only a single permanent magnet portion, or it may include more than the two permanent magnet portions found in the preferred embodiment. Instead of the two rotating magnetic subassemblies found in the preferred embodiment, there could be only a single rotating magnet subassembly, or there could be a greater number of rotating magnetic subassemblies. The relative dimensions, shapes, and positions of the rotating magnetic subassemblies and the stationary magnetic subassemblies could be optimized for a particular application. 
   A magnet assembly according to the invention, incorporating rotating dipole magnet blocks to provide a periodic high amplitude magnetic field intensity within an air gap, can have several desirable features. 
   Such a magnet assembly can provide a wide variation in magnetic field intensity in an air gap. Field intensities of at least 1.5 Tesla in a high-field air gap portion concurrent with fields of less than 0.05 Tesla in a low-field air gap portion have been observed through modeling of the assembly in this position. 
   The air gap experiencing the time-varying magnetic field intensity in such a magnet assembly can have a particular shape and structure that makes it especially useful, for example by being well suited for a magnetic refrigerator. The air gap in such a magnet assembly can be, for example, a linear air gap of rectangular cross-section. Such a magnet assembly can allow constant access to the air gap that is subject to the periodic high amplitude magnetic field intensity, and this can enable components of a magnetic refrigerator such as magnetocaloric material and heat transfer fluid plumbing to be stationary and positioned within that air gap. 
   A magnet assembly according to the invention can have relatively low operating costs, for example by minimizing space requirements and by minimizing the mass of any moving parts. 
   Such a magnet assembly can also have relatively low manufacturing costs, for example by avoiding any requirement for precisely machined permanent magnets. Each of the permanent magnet portions of such a magnet assembly can be rectangular in shape with an orthogonal magnetization vector to minimize production costs. This geometry is especially well suited to the manufacture of sintered NdFeB magnets by current pressing methods, and the relatively low number of magnet mating surfaces contributes to a reasonable number of required precision grinding operations. 
   Precisely machined structures can be used in a magnet assembly according to the invention, for example rounded pole caps and concave sections may have rounded surfaces that may benefit from close tolerances to allow these moving pieces to nest closely together, while still providing a continuous flux path with maximum permeance when the rotating dipoles align. However, in such a magnet assembly, these structures can be made of magnetically permeable material that are affixed to rectangular permanent magnet portions, avoiding any precision machining of permanent magnet material. 
   Further objects, features, and advantages of the invention will be apparent from the following detailed description when taken in conjunction with the accompanying drawings. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
     In the drawings: 
       FIG. 1  is a perspective view of an exemplary magnet assembly in accordance with the invention. 
       FIG. 2  is a cross-sectional view of the magnet assembly of  FIG. 1  taken along the line  2 — 2  thereof. 
       FIGS. 3(   a ),  3 ( b ),  3 ( c ), and  3 ( d ) are cross-sectional views of the magnet assembly of  FIG. 1  taken along the line  2 — 2  thereof, with the rotating magnet subassemblies rotated 45°, 90°, 135°, and 180° respectively. 
       FIG. 4  shows the lines of magnetic flux in a cross-section of the magnet assembly of  FIG. 1  taken along the line  2 — 2  thereof, with the rotating magnet subassemblies positioned as in  FIG. 1 . 
       FIG. 5  shows the lines of magnetic flux in a cross-section of the magnet assembly of  FIG. 1  taken along the line  2 — 2  thereof, with the rotating magnet subassemblies positioned as in  FIG. 3(   a ). 
       FIG. 6  shows a cross-sectional view of an alternative magnet assembly according to the invention. 
       FIG. 7  is a graph of the magnetic field intensity in a portion of the air gap having a periodic magnetic field in the magnetic assembly of  FIG. 1 . 
       FIG. 8  is a graph of the magnetic field intensity in a portion of the air gap having a periodic magnetic field in the magnetic assembly of  FIG. 6 . 
       FIG. 9  shows a cross-sectional view of a second alternative magnet assembly according to the invention. 
       FIGS. 10(   a ),  10 ( b ),  10 ( c ), and  10 ( d ) are cross-sectional views of the magnet assembly of  FIG. 9  with the rotating subassemblies rotated 45°, 90°, 135°, and 180° respectively. 
       FIG. 11  shows a cross-sectional view of an exemplary magnet assembly according to another aspect of the invention. 
       FIG. 12  shows a perspective view of an exemplary magnet assembly according to one more aspect of the invention. 
   

   DETAILED DESCRIPTION OF THE INVENTION 
   Referring to the drawings,  FIG. 1  is a perspective view of an exemplary magnet assembly in accordance with the invention, indicated generally at  20 . The magnet assembly  20  includes a first rotating magnet subassembly, indicated generally at  30 , a second rotating magnet subassembly, indicated generally at  31 , a first stationary magnet subassembly, indicated generally at  32 , and a second stationary magnet subassembly, indicated generally at  33 . 
   The magnet assembly  20  at least partially surrounds an air gap, indicated generally at  21 . The air gap  21  includes a first air gap portion  22  at least partially surrounded by portions of the first stationary magnet subassembly  32  and a second air gap portion  24  at least partially surrounded by portions of the second stationary magnet subassembly  33 . The air gap  21  also includes a third air gap portion  23  between the first air gap portion  22  and the second air gap portion  24  and between the first rotating magnetic subassembly  30  and the second rotating subassembly  31 . 
   When the first rotating magnet subassembly  30  and the second rotating magnet subassembly  31  are at the rotational positions shown in  FIG. 1 , the first air gap portion  22  experiences a high magnetic field intensity, the third air gap portion  23  experiences an intermediate magnetic field intensity, and the second air gap portion  24  experiences a low magnetic field intensity. As the first rotating magnet subassembly  30  and the second rotating magnet subassembly  31  rotate through a cycle of rotation, the first air gap portion  22  and the second air gap portion  24  of the air gap  21  alternately experience a high magnetic field intensity and then a low magnetic field intensity. Since the first air gap portion  22  and the second air gap portion  24  thereby experience a time-varying magnetic field, these air gap portions provide areas in which magnetic work may be performed. 
   In the magnet assembly  20 , the first rotating magnet subassembly  30  and second rotating magnet subassembly  31  each include a permanent magnet portion  40  and rounded end caps  43 . The permanent magnet portion  40  may be formed of any suitable permanent magnet material, for example of the type sold by Sumitomo Special Metals of Japan under the trademark Neomax  50 . The rounded end caps  43  may be formed of any suitable magnetically permeable material, for example low-carbon steel such as the material sold by High Temp Metals of California, USA under the trademark Permendur 2V. It may be desirable to employ the permeable material in a laminated form or other form that has low eddy current losses. 
   In the magnet assembly  20 , the first stationary magnet subassembly  32  and the second stationary magnet subassembly  33  preferably each include two permanent magnet portions  50 , two concave sections  53 , and a flux return section  54 . The permanent magnet portions  50  of each stationary magnet subassembly can be formed of any suitable permanent magnetic material, for example of the types discussed above. The permanent magnet portions  50  of each stationary magnet subassembly are preferably shorter in the vertical dimension than the rotary magnet blocks to ensure minimum Gauss levels outside the high field region. The concave sections  53  and flux return section  54  of each stationary magnet subassembly can be formed of any suitable magnetically permeable material, for example of the types discussed above. The concave sections  53  include a concave cutout, preferably in the shape of a circular arc, on the side nearest the rotating magnetic subassemblies to allow for clearance of the swept path of the rotating magnetic subassemblies. 
     FIG. 2  is a cross-sectional view of the magnet assembly  20  of  FIG. 1  taken along the line  2 — 2  thereof. In  FIG. 2 , as in  FIG. 1 , the rotating magnetic subassemblies are positioned such that the first air gap portion  22  experiences a high magnetic field intensity and the second air gap portion  24  experiences a low magnetic field intensity. 
   As perhaps best shown in  FIG. 2 , the permanent magnet portion  40  of each rotating magnet subassembly has a North end  41  (marked “N”) and a South end  42  (marked “S”). The rounded end caps  43  of magnetically permeable material coupled to each end of the permanent magnet portion  40  of each rotating magnet subassembly are preferably designed to nest within the concave sections  53  of the stationary magnetic subassemblies. Each rotating magnet subassembly has a North end  45  and a South end  46 , and each rotating magnet subassembly is adapted to rotate about a rotational axis  44 . 
   Each permanent magnet portion  50  of each stationary magnet subassembly has a North end  51  and a South end  52 . Each stationary magnet subassembly, comprised of the permanent magnet portions  50 , the concave sections  53 , and the flux return section  54 , also has a North end  55  and a South end  56 . 
   The North end  55  of each stationary magnet subassembly includes a North pole face  57 , and the South end  56  of each stationary magnet subassembly includes a South pole face  58 . The first air gap portion  22  lies between the North pole face  57  and the South pole face  58  of the first stationary magnet subassembly  32 , and the second air gap portion  24  lies between the North pole face  57  and the South pole face  58  of the second stationary magnet subassembly  33 . 
     FIG. 2  and  FIGS. 3(   a )–( d ) illustrate one half of a complete cycle of exemplary magnet assembly  20 . When the rotating magnetic subassemblies are at the rotational position shown in  FIG. 2 , all six permanent magnets (the four permanent magnet portions  50  in the first stationary magnet subassembly  32  and second stationary magnet subassembly  33 , plus the two permanent magnet portions  40  in the first rotating magnet subassembly  30  and the second rotating magnet subassembly  31 ), are aligned such that their combined magnetomotive force (“mmf”) passes through the first air gap portion  22 , thereby subjecting the first air gap portion  22  to a high magnetic field intensity. 
     FIGS. 3(   a ),  3 ( b ), and  3 ( c ) show the exemplary magnet assembly  20  with the rotating magnetic subassemblies rotated 45°, 90°, and 135°, respectively, as the rotating magnetic subassemblies travel from their positions in  FIG. 2  to their positions in  FIG. 3(   d ). When the rotating magnetic subassemblies are at the rotational position shown in  FIG. 3(   d ), the permanent magnet portions are aligned such that their combined magnetomotive force (“mmf”) passes through the second air gap  24 , thereby subjecting the second air gap portion  24  to a high magnetic field intensity as shown in  FIG. 3(   d ). After reaching the positions in  FIG. 3(   d ), the rotating magnetic subassemblies continue their rotation and return to the position shown in  FIG. 2 . 
   There is a unique magnetic field distribution within the air gap for each angular position of the magnets during one cycle. The maximum difference in flux density between the high and low field zones occurs whenever the rotary dipole vectors are parallel to the stationary dipole vectors. Furthermore, the difference in flux density between the two zones is at a minimum, essentially zero, when the rotary dipole vectors are perpendicular to the stationary dipole vectors. It is interesting to note that a 45-degree offset of the rotary dipole vectors relative to stationary dipole vectors results in a difference in flux density between the high and low field zones that is greater than half of the maximum difference. Thus the field change in the air gap is non-linear throughout the rotational cycle. This is a characteristic that can be encouraged by relative sizing and positioning of the magnets in an effort to minimize the portion of the cycle during which the high-field zones have a similar flux density. 
   Thus, the rotating magnetic subassemblies  30  and  31  together act as a switch to control which portion of the air gap receives flux contribution from the permanent magnet portions of the rotating magnetic subassemblies  30  and  31  and the stationary magnet subassemblies  32  and  33 . The first air gap portion  22  and the second air gap portion  24  experience alternating high magnetic field intensity and low magnetic field intensity as the rotating magnetic subassemblies  30  and  31  move from their positions shown in  FIG. 2  to their positions shown in  FIG. 3(   d ) and back again with every cycle of the rotating magnetic subassemblies. 
   When the rotating magnetic subassemblies are positioned as shown in  FIG. 2 , the upper and lower concave sections  53  of the first stationary magnet subassembly  32  and the rounded end caps  43  that nest therein are magnetically coupled to the North pole face  57  and the South pole face  58 , respectively, above and below the air gap portion  22 . These concave sections provide a volume of magnetically permeable material in which the lines of flux can change direction and converge before crossing the air gap portion  22  through the North pole face  57  and the South pole face  58 , to concentrate the lines of flux and achieve an air gap flux density higher than the saturation flux density of the permanent magnet portions of the magnet assembly. 
   When the rotating magnetic subassemblies are positioned as shown in  FIG. 2 , the upper and lower concave sections  53  of the second stationary magnet subassembly  33  and the rounded end caps  43  that nest therein provide a low reluctance path for flux lines to travel in a circuit through the second central rotating magnetic subassembly  31 , the second stationary magnet subassembly  33 , and the first central rotating magnetic subassembly  30  (and on through the first air gap portion  22 ) with little disturbance. As shown in  FIG. 2 , one or more tapers or chamfers may also be included in the concave sections  53 , for example to carry flux between magnets with discontinuous vertical positions or to concentrate the lines of flux. 
   Each stationary magnet subassembly in the magnet assembly  20  preferably includes a flux return section  54 , to provide a return path for the lines of magnetic flux. Each flux return section  54  in the magnet assembly  20  is preferably sized to carry an amount of flux at least as great as the flux provided by one stationary magnet subassembly (including two permanent magnet portions  50 ) plus the flux provided by both rotating magnetic subassemblies (including two permanent magnet portions  40 ) without saturating. Each flux return section  54  may include one or more chamfers, for example along the outer corners, to reduce stray flux and assembly weight. 
   As shown in  FIGS. 2 and 3(   a )– 3 ( d ), the air gap portions  22  and  24  that experience a time-varying magnetic field are not swept by the rotation of the rotating magnetic subassemblies, so those areas can be used to incorporate magnetocaloric materials, plumbing, wiring, means of translation, or other implements or objects. However, in the magnet assembly  20  the air gap portion  23  positioned directly between the rotary magnets (that experiences an intermediate magnetic field intensity at the rotational positions shown in  FIGS. 2 and 3(   d )) is occupied by the rotating magnetic subassemblies during rotation, and therefore cannot be used for other purposes. 
     FIG. 4  shows a computer simulation of the lines of magnetic flux in a cross-section of the magnet assembly  20  when the rotating magnet subassemblies are positioned as in  FIG. 2 . At that rotational position, the air gap portion  22  of the air gap contains a high density of line spacing, indicating high magnetic flux density in that area. As shown in  FIG. 4 , the maximum flux density in a flux return section  54  occurs on the side furthest from the high-field zone when all magnets are parallel. Thus, when the rotating magnet subassemblies are positioned as in  FIG. 2 , the flux density through the flux return section  54  in the second stationary magnet subassembly  33  will be at its maximum. 
     FIG. 5  shows a computer simulation of the lines of magnetic flux in a cross-section of the magnet assembly  20  when the rotating magnet subassemblies are positioned at a 45° angle, as in  FIG. 3(   a ). As shown in  FIG. 5 , the direction and distribution of flux has begun to change as the region of high magnetic field intensity moves from the air gap portion  22 , as shown in  FIG. 2 , to the air gap portion  24 , as shown in  FIG. 3(   d ). 
     FIG. 6  shows a cross-sectional view of an alternative magnet assembly  60  according to the invention. The alternative magnet assembly  60  has a similar construction to the magnet assembly  20  of  FIGS. 1–5 . However, a comparison of  FIGS. 2 and 6  shows that the distance between the axes of rotation  44  of the rotating magnetic subassemblies  30  and  31  in the magnet assembly  60  of  FIG. 6  is greater than the distance between the axes of rotation  44  of the rotating magnetic subassemblies  30  and  31  in the magnet assembly  20  of  FIG. 2 . 
   One effect of the greater separation between the rotating magnetic subassemblies in the magnet assembly  60  is to provide greater clearance between the rotating magnetic subassemblies during rotation so that the space directly between the rotating magnetic subassemblies, the third air gap portion  23  in  FIG. 6 , can be used for other purposes, for example to incorporate magnetocaloric materials, plumbing, wiring, means of translation, or other implements or objects. 
   Another effect of the greater separation between the rotating magnetic subassemblies in the magnet assembly  60  is to alter the way the magnetic field intensity through the air gap changes over time.  FIG. 7  is a graph of a simulation of the magnetic field intensity through one full cycle of rotation in the portion of the air gap marked  24  in the magnet assembly of  FIG. 2 .  FIG. 8  is a graph of a simulation of the magnetic field intensity through one full cycle of rotation in the portion of the air gap marked  24  in the magnet assembly of  FIG. 6 . 
   As shown in  FIGS. 7 and 8 , for both the magnet assembly  20  and the magnet assembly  60 , the maximum magnetic field in the portion of the air gap marked  24  in those figures occurs when the rotating magnet subassemblies have been rotated 180° and the minimum magnetic field occurs at 0° (360°). In both cases, the magnetic field intensity changes in an asymmetric fashion across a cycle of rotation of the rotating magnetic subassemblies. 
   However, the magnetized state of the air gap marked  24  in  FIG. 2  is more heavily skewed toward the third quarter of a rotation in the magnet assembly  20  compared to the magnet assembly  60 . The rate of field increase in the second quarter of a rotation is relatively rapid, and the rate of field decrease in the third quarter of a rotation is relatively slow, in the magnet assembly  20  compared to the magnet assembly  60 . Thus, if a particular application should call for a more symmetrical field progression per zone during the rotation, the rotary magnets can each be positioned further from the horizontal centerline of the air gap. 
   However, increasing the distance between the axes of rotation of the rotating magnetic subassemblies can require significantly larger permanent magnet portions to produce the same maximum field differential between the high-field portions  22  and the low-field portions  24  of the air gap  21 . The additional permanent magnet material can be most easily incorporated in the horizontal width of the permanent magnet portions  50  of the stationary magnet subassemblies  32  and  33 , as shown in  FIG. 6 . 
     FIG. 9  shows a cross-sectional view of another alternative magnet assembly  61  according to the invention. The magnet assembly  61  has a similar construction to the magnet assembly  20  of  FIG. 2 . However, while the rotating magnetic subassemblies  30  and  31  in the magnet assembly  20  rotate synchronously but in opposite directions, the rotating magnetic subassemblies  30  and  31  in the magnet assembly  61  rotate synchronously in the same direction. 
     FIG. 9  and  FIGS. 10(   a )–( d ) illustrate one half of a complete cycle of the magnet assembly  61 . Similar to the magnet assembly  20 , when the rotating magnetic subassemblies in the magnet assembly  61  are at the rotational position shown in  FIG. 9 , all six permanent magnets portions are aligned such that their combined magnetomotive force (“mmf”) passes through the first air gap portion  22  shown in  FIG. 9 . 
     FIGS. 10(   a ),  10 ( b ), and  10 ( c ) show the magnet assembly  61  with the rotating magnetic subassemblies rotated 45°, 90°, and 135°, respectively, as the rotating magnetic subassemblies travel from their positions in  FIG. 9  to their positions in  FIG. 10(   d ). Similar to the magnet assembly  20 , when the rotating magnetic subassemblies reach the rotational position shown in  FIG. 10(   d ), the permanent magnet portions are aligned such that their combined magnetomotive force (“mmf”) passes through the second portion  24  shown in  FIG. 10(   d ). After passing through the positions in  FIG. 10(   d ), the rotating magnetic subassemblies continue their rotation and return to the position shown in  FIG. 9 . Similar to the magnet assembly  20 , the first air gap portion  22  and the second air gap portion  24  experience alternating high magnetic field intensity and low magnetic field intensity as the rotating magnetic subassemblies  30  and  31  move from their positions shown in  FIG. 9  to their positions shown in  FIG. 10(   d ) and back again with every cycle of the rotating magnetic subassemblies. 
   One effect of rotating the rotating magnetic subassemblies  30  and  31  in the same direction in the magnet assembly  61  is that the North ends  45  of the rotating magnetic subassemblies  30  and  31  are adjacent at the intermediate rotational position shown in  FIG. 10(   b ). Similarly, in the magnet assembly  61 , the South ends  46  of the rotating magnetic subassemblies  30  and  31  would be adjacent at a rotation of 270° (not shown in the figures). In contrast,  FIGS. 3(   a )– 3 ( d ) show that in the magnet assembly  20  there is no rotational position in which like magnetic poles of the rotating magnetic subassemblies  30  and  31  are adjacent. 
     FIG. 11  shows a cross-sectional view of another embodiment of a magnet assembly  62  according to the invention. The magnet assembly  62  has a similar construction to the magnet assembly  20  of  FIG. 2 . However, the stationary magnetic subassemblies  32  and  33  in the magnet assembly  62  are simpler than the stationary magnetic subassemblies  32  and  33  in the magnet assembly  20 . Each stationary magnet subassembly  32  and  33  in the magnet assembly  62  includes a single permanent magnet portion  50  that replaces the two permanent magnet portions  50  and the flux return section  54  found in the stationary magnetic subassemblies  32  and  33  in the magnet assembly  20 . 
     FIG. 12  shows a cross-sectional view of another embodiment of a magnet assembly  63  according to the invention. The magnet assembly  63  has a similar construction to the magnet assembly  20  of  FIG. 2 . However, the rotating magnetic subassemblies  30  and  31  are oriented so that the axes of rotation  44  of those rotating magnetic subassemblies is parallel to the direction of the magnetic flux through the air gap. In the magnet assembly  63 , the rotating magnetic subassemblies  30  and  31  could rotate in the same direction, or in opposite directions. In the magnet assembly  63  the magnetic poles of the rotating magnetic subassemblies  30  and  31  do not approach each other. Further, the rotating magnetic subassemblies do not sweep through the air gap. 
   There are various possibilities with regard to alternative embodiments and applications of a magnet assembly according to the invention. For example, although the exemplary embodiments of the present invention refer to specific materials, other materials known to those skilled in the art as having suitable properties can be appropriately substituted. Similarly, although the exemplary embodiments of the present invention show particular shapes and relative dimensions, other shapes and dimensions can be used. 
   A variety of structures can be used in a permanent magnet assembly according to the invention. For example, the permanent magnet portions shown in the illustrative embodiments herein may each comprise a single permanent magnet, or one or more of these permanent magnet portions may be a composite structure comprised of one or more permanent magnets, and one or more sections made of magnetically permeable material. The permanent magnet portions shown in the illustrative embodiments may also include one or more sections of magnetically impermeable material, for example to provide structural support, containment, or protection. 
   For example, a rotating magnetic subassembly for use in a magnet assembly according to the invention can be formed by fixing rounded end caps made of magnetically permeable material to a rectangular block of permanent magnet material, as shown in the illustrative embodiments herein. However, a rotating magnetic subassembly could also be formed by machining a block of permanent magnet material to obtain rounded end caps made of permanent magnet material instead of or in addition to rounded end caps formed of magnetically permeable material. If multiple rotating subassemblies are used, it is not necessary that all of the rotating subassemblies include a permanent magnet section. Some, but not all, of the rotating subassemblies may be formed entirely of magnetically permeable material without a permanent magnet section. 
   Similarly, a stationary magnetic subassembly for use in a magnet assembly according to the invention can be formed by fixing concave sections made of magnetically permeable material to one or more rectangular blocks of permanent magnet material, as shown in the illustrative embodiments herein. However, a stationary magnetic subassembly could also be formed by machining a block of permanent magnet material to obtain concave sections made of permanent magnet material instead of or in addition to concave sections formed of magnetically permeable material. 
   To optimize a permanent magnet assembly according the invention for a particular application, additional features known in the art may also be included. For example, tapered pole pieces can be used to concentrate flux across an air gap. Blocking magnets, flux containment jackets, or flux containment sheaths, chamfers, or filled-in corners can also be used, for example to optimize flux return while minimizing stray flux, assembly weight, and rotational moment of inertia. 
   Although permanent magnet portions and composite magnet subassemblies are described herein as having “north” and “south” ends, and may be labeled as “N” or “S” in the drawings, it should be understood that this is by way of convention only and not as a limitation. For example, while a particular embodiment may be shown in the drawings with permanent magnet portions having a particular orientation, it should be understood that an equivalent structure could be formed by substituting an “south” or “S” for every “north” or “N,” and vice-versa. Thus, any claim including “north” or “south” in a limitation should be construed to also cover structures that would meet that claim with the words “north” and “south” reversed. 
   Although the surfaces of the north and south pole faces of the stationary magnetic subassemblies are shown herein as essentially planar, whereby the air gaps subjected to a time-varying magnetic field have a substantially rectangular cross-section, this is not required and other shapes may be used. For example, some applications of a permanent magnet assembly according to the invention could include pole faces having concave or convex shapes. Thus, the cross-section of the air gaps subjected to a time-varying magnetic field can include, but not be limited to, a rectangle (including but not limited to a square), a parallelogram, a trapezoid, a circle, an oval, or nearly any other shape or combination of shapes. 
   The embodiments of a permanent magnet assembly according to the invention described herein are shown in the drawings in exemplary orientations. It is understood that a permanent magnet assembly according to the invention can be used in any orientation. Any particular term such as “vertical” or “horizontal” used herein in reference to a structure does not limit that structure to any particular orientation or frame of reference. 
   The exemplary embodiments herein are described as including rotating subassemblies and stationary subassemblies that subject air gaps to a time-varying magnetic field. However, it should be understood that the “rotating” subassemblies in the exemplary embodiments discussed herein could also be made stationary, with the “stationary” subassemblies adapted to rotate relative to the “rotating” subassemblies, to obtain essentially the same relative motion between the “stationary” and “rotating” subassemblies. 
   This is particularly apparent with respect to the embodiment shown in  FIG. 12 . Since the two “rotating” subassemblies of  FIG. 12  have a common axis of rotation, it would be straightforward to rotate the “stationary” subassemblies relative to the “rotating” subassemblies. Of course, it would also be possible to rotate both the “stationary” and the “rotating” subassemblies relative to each other in opposite directions or in the same direction at different angular velocities, to obtain essentially the same relative motion between the “stationary” and “rotating” subassemblies. 
   Similarly, either or both of the “stationary” and “rotating” subassemblies could be adapted to rotate in an oscillating (back and forth) fashion around a portion of an entire cycle of rotation. Thus, in the claims the term rotate is intended to encompass any form of relative motion between structures that involves rotation about at least a portion of a cycle of rotation, and is not intended to be limited to rotation in a single direction, or through an entire cycle of rotation, or with respect to which of the structures actually rotates. 
   It is understood that the invention is not limited to the particular embodiments described herein, but embraces all such modified forms thereof as come within the scope of the following claims.