Abstract:
An electrical machine is provided. The electrical machine includes a rotor comprising an inner rotor having a plurality of inner rotor poles and an outer rotor having a plurality of outer rotor poles. The electrical machine further comprises a stator configured to modulate a magnetic flux and to transmit torque to inner rotor and the outer rotor, the stator comprising a stator core interposed concentrically between the inner rotor and the outer rotor; a multiple of stator windings disposed in a plurality of stator slots, the stator windings configured to form a multiple of stator poles. The stator further comprises a plurality of stator teeth interposed between the plurality of stator slots, wherein an arithmetic sum or difference of twice number of stator teeth and a number of the stator poles equals a number of rotor poles.

Description:
BACKGROUND 
       [0001]    The invention relates generally to electrical machines and in particular, to high torque density electrical machines. 
         [0002]    Electrical machines, such as motors and generators are typically capable of delivering high torque and power at high speeds. However, certain applications require high torque and power at low speeds. Generally, electrical machines that deliver higher torque at lower speeds are expensive. Alternatively, a high torque at low speeds may be achieved by incorporating mechanical gearing for speed reduction. However, certain undesirable factors such as additional cost, acoustic noise, and mechanical wear and tear lead to a need for continuous lubrication and maintenance of such mechanical equipment. 
         [0003]    Magnetic gears offer significant benefits as compared to their mechanical counterparts. These benefits include accurate position control on a drive shaft, higher torque at very low speed, and a lack of physical contact between an input shaft and an output shaft, to name only a few. However magnetic gearing is of a relatively complex design, and provides relatively low torque density. 
         [0004]    More recently, planetary-like magnetic gear arrangements using rare-earth permanent magnets have been proposed, which result in favorable torque transmission capabilities between an inner rotor and an outer rotor. However, such systems require additional stationary windings resulting in a complex construction. 
         [0005]    Therefore, it is desirable to provide a high torque density electrical machine that addresses the aforementioned issues. 
       BRIEF DESCRIPTION 
       [0006]    According to an embodiment of the invention, an electrical machine is provided. The electrical machine includes a rotor comprising an inner rotor having a plurality of inner rotor poles and an outer rotor having a plurality of outer rotor poles. The electrical machine further comprises a stator configured to modulate a magnetic flux and to transmit torque to the inner rotor and the outer rotor, the stator comprising a stator core interposed concentrically between the inner rotor and the outer rotor; a multiple of stator windings disposed in a plurality of stator slots, the stator windings configured to form a multiple of stator poles. The stator further comprises a plurality of stator teeth interposed between the plurality of stator slots, wherein an arithmetic sum or difference of twice a number of stator teeth and a number of the stator poles equals a number rotor poles. 
         [0007]    According to another embodiment, an electrical machine is provided. The electrical machine includes a stator comprising an inner stator having a plurality of inner stator poles and an outer stator having a plurality of outer stator poles. The stator further includes a stator core comprising a plurality of stator teeth interposed between a plurality of stator slots and defining an inner stator and an outer stator. The stator core is configured to modulate a magnetic flux and transmit torque and a plurality of stator windings disposed in the plurality of stator slots, the plurality of stator windings configured to form a plurality of stator poles. The electrical machine further includes a rotor comprising a rotor core interposed concentrically between the inner stator and the outer stator and a plurality of rotor poles disposed on an inner surface of the rotor core and an outer surface of the rotor core; wherein the number of rotor poles equals an arithmetic sum or difference of twice the number of stator teeth and the number of stator poles. 
         [0008]    According to another embodiment, an electrical machine is provided. The electrical machine includes at least one pair of rotors having a plurality of rotor poles and at least one stator comprising a stator core having a plurality of stator teeth defining a plurality of stator slots there between. The stator core further being interposed axially between the at least one pair of rotors, and a plurality of stator windings disposed in the plurality of stator slots, the stator windings configured to form a plurality of stator poles; wherein an arithmetic sum or difference of twice the number of stator teeth and the number of the stator poles equals an arithmetic sum of the number of rotor poles. 
         [0009]    According to another embodiment, an electrical machine is provided. The electrical machine includes at least one pair of stators having a plurality of stator poles, the at least one pair of stators comprising plurality of stator windings disposed around a plurality of stator teeth, the stator windings configured to form the plurality of stator poles. The electrical machine further includes a rotor comprising at least one rotor core interposed axially between the at least one pair of stators and a plurality of rotor poles disposed on either side of the rotor core; wherein an arithmetic sum of the number of rotor poles equals an arithmetic sum or difference of twice the number of stator teeth and the number of the stator poles. 
         [0010]    According to another embodiment, an electrical machine is provided. The electrical machine includes a rotor comprising a rotor core and a plurality of permanent magnets embedded radially within the rotor core to form a plurality of rotor poles. The electrical machine further includes a stator comprising a stator core disposed concentrically outside the rotor and including a plurality of stator teeth defining a plurality of stator slots there between; wherein an arithmetic sum or difference of twice the number of stator teeth and the number of the stator poles equals the number of rotor poles. 
     
    
     
       DRAWINGS 
         [0011]    These and other features, aspects, and advantages of the present invention will become better understood when the following detailed description is read with reference to the accompanying drawings in which like characters represent like parts throughout the drawings, wherein: 
           [0012]      FIG. 1  is a schematic representation of an electromechanical energy conversion system employing magnetic gearing; 
           [0013]      FIG. 2  is a diagrammatical cross sectional view of an electrical machine with a rotor-stator-rotor arrangement indicating radial flux linkage and configured to operate as a double-sided machine according to an aspect of the present technique; 
           [0014]      FIG. 3  is a further diagrammatical cross sectional view of the electrical machine in  FIG. 2 ; 
           [0015]      FIG. 4  is a diagrammatical cross sectional view of an electrical machine with a stator-rotor-stator arrangement indicating radial flux linkage and configured to operate as a magnetic gear according to an aspect of the present technique; 
           [0016]      FIG. 5  is a further diagrammatical cross sectional view of the electrical machine in  FIG. 4 ; 
           [0017]      FIG. 6  is a diagrammatical cross sectional view of an axial electrical machine with a rotor-stator-rotor arrangement and configured to operate as a magnetic gear according to an aspect of the present technique; 
           [0018]      FIG. 7  is a further diagrammatical cross sectional view of an axial electrical machine as depicted in  FIG. 6 ; 
           [0019]      FIG. 8  is a further diagrammatical cross sectional view of an axial electrical machine as depicted in  FIG. 6  with a rotor-stator-rotor arrangement indicating the circumferential flux in the stator; 
           [0020]      FIG. 9  is a diagrammatical cross sectional view of another axial electrical machine with a stator-rotor-stator arrangement and configured to operate as a magnetic gear according to an aspect of the present technique; 
           [0021]      FIG. 10  is a further diagrammatical cross sectional view of an axial electrical machine as depicted in  FIG. 9 ; 
           [0022]      FIG. 11  is a further diagrammatical cross sectional view of an axial electrical machine as depicted in  FIG. 9  with a stator-rotor-stator arrangement indicating the circumferential flux in the rotor; 
           [0023]      FIG. 12  is a diagrammatical cross sectional view of a further axial electrical machine with a multiple rotor-stator-rotor arrangement and configured to operate as a magnetic gear according to an aspect of the present technique; 
           [0024]      FIG. 13  is a diagrammatical cross sectional view of an electrical machine with permanent magnets embedded on rotor core and configured to form rotor poles; 
           [0025]      FIG. 14  is a diagrammatical sectional view of the rotor poles including field coils; 
           [0026]      FIG. 15  is a diagrammatical sectional view of the rotor poles including rotor slots and teeth; and 
           [0027]      FIG. 16  is a diagrammatical sectional view of the rotor poles including axial laminations to produce reluctance torque. 
       
    
    
     DETAILED DESCRIPTION 
       [0028]    In accordance with embodiments of the present invention, systems and methods for high torque density electrical machines are described herein. In the following detailed description, numerous specific details are set forth in order to provide a thorough understanding of various embodiments of the present invention. However, those skilled in the art will understand that embodiments of the present invention may be practiced without these specific details, that the present invention is not limited to the depicted embodiments, and that the present invention may be practiced in a variety of alternative embodiments. In other instances, well known methods, procedures, and components have not been described in detail. 
         [0029]    Furthermore, various operations may be described as multiple discrete steps performed in a manner that is helpful for understanding embodiments of the present invention. However, the order of description should not be construed as to imply that these operations need be performed in the order they are presented, nor that they are even order dependent. Moreover, repeated usage of the phrase “in one embodiment” does not necessarily refer to the same embodiment, although it may. Lastly, the terms “comprising”, “including”, “having”, and the like, as used in the present application, are intended to be synonymous unless otherwise indicated. 
         [0030]      FIG. 1  represents a block diagram of an electromechanical system  10  that includes a mechanical load/prime mover  20 , a magnetic gearing  16  and a motor/generator  12 . The mechanical prime mover  20  is coupled via a low speed rotation shaft  18  to the magnetic gearing  16  having a gear ratio of 1:X, wherein X is a whole number. The magnetic gearing is coupled via a high speed rotation shaft  14  to the generator  12 . In a generator configuration (mechanical energy to electrical energy), the low speed rotation of the prime mover  20  is converted to high speed rotation by the magnetic gearing  16  in the gear ratio 1:X. By way of example, if the low speed rotation shaft  18  turns at 90 rotations per minute (rpm) and the gear ratio is 1:20, then the high speed rotation shaft turns at 1800 rpm. 
         [0031]    Conversely, in a motor configuration (electrical energy to mechanical energy) the motor is powered by an electrical source (not shown) driving the motor (e.g. 1800 rpm). The magnetic gearing  16  converts the high speed rotation shaft  14  to a low speed rotation shaft  18  (e.g. 90 rpm). According to an embodiment of the invention, the construction of the magnetic gearing is presented that may be implemented in system  10 . 
         [0032]    Turning now to  FIG. 2 , an exemplary configuration of a magnetic gearing electrical machine  22  is illustrated. The magnetic gearing electrical machine  22  includes a rotor  24 . The rotor  24  includes an outer rotor  26  having multiple outer rotor poles  36 ,  38  and an inner rotor  28  having multiple inner rotor poles  40 ,  42 . In a particular embodiment, the inner rotor poles  36 ,  38  and the outer rotor poles  40 ,  42  include at least one of a multiple permanent magnets, wound rotors or field coils. In the illustrated embodiment, the inner rotor poles  36 ,  38  and the outer rotor poles  40 ,  42  are permanent magnets. A stator is provided to modulate magnetic flux and transmit torque. The stator includes a stator core interposed concentrically between the outer rotor  26  and the inner rotor  28 . A number of stator teeth  30  and stator slots  32  are disposed on the stator core. The stator slots  32  are configured to accommodate stator windings  34 . The stator windings  34  are further interconnected to form a number of stator poles. 
         [0033]    In an exemplary embodiment, the inner rotor poles of the outer rotor  26  may be permanent magnets  36 ,  38  disposed on its inner surface and the outer rotor poles of the inner rotor  28  may be permanent magnets  40 ,  42  disposed in its outer surface. The permanent magnets  36 ,  38 ,  40  and  42  are together configured to form a number of rotor poles. The number of the rotor poles, the number stator poles and the stator teeth are configured to satisfy: 
         [0000]      2 *S   TEETH   ±S   POLE   =R   POLE    (1) 
         [0000]    wherein S TEETH  refers to the number of stator teeth  30 , S POLE  refers to the number of stator poles and R POLE  refers to the number of rotor poles. It may be appreciated that, in one embodiment, the equation (1) applies for the air gap that includes the inner rotor poles and the stator teeth. In another embodiment, the equation (1) applies for the air gap that includes outer rotor poles and the stator teeth. 
         [0034]    The outer rotor  26  may be configured to operate at a lower speed than the inner rotor  28 . During operation of the electrical machine  22 , stator windings  34  are energized. Torque is transmitted by way of interaction between magnetic flux excited by stator windings  34  and magnetic flux excited by permanent magnet rotor poles  36 ,  38 ,  40  and  42 . It may be noted that the orientation of magnetic flux depends on the alignment of the outer rotor poles  40 ,  42  and the inner rotor poles  36 ,  38 . In one embodiment, the permanent magnet  38 ,  40  corresponds to a north pole and the permanent magnet  36 ,  42  corresponds to a south pole. In such a configuration magnetic flux propagates radially inward or outward with respect to an axis of rotation of the rotor indicated by the dashed lines  44  and  46 . 
         [0035]      FIG. 3  illustrates another exemplary embodiment of a magnetic gearing electrical machine  25  having rotor-stator-rotor configuration with a fractional shift in alignment of the inner rotor poles  40 ,  42  of the inner rotor as referenced in  FIG. 2  and the outer rotor poles  36 ,  38  of the outer rotor as referenced in  FIG. 2 . The fractional shift in alignment results in propagation of a magnetic flux  48 ,  50 ,  52 ,  54  along a direction parallel to an axis of rotation of the rotor  24 . The permanent magnets  36 ,  38 ,  40  and  42  are configured to form a number of rotor poles. The number of the rotor poles, the number of stator poles and the stator teeth are chosen to satisfy equation (1). In a particular embodiment, the permanent magnet  36 ,  42  corresponds to a south pole and the permanent magnet  38 ,  40  corresponds to a north pole, resulting in the magnetic flux propagating along a circumferential direction with respect to an axis of rotation of the rotor indicated by the dashed lines  48 ,  50 ,  52  and  54 . 
         [0036]      FIG. 4  is a diagrammatic representation of cross sectional view of a magnetic gearing electrical machine  56  having stator-rotor-stator configuration. The magnetic gearing electrical machine  56  includes a stator  58 . The stator  58  includes an outer stator  60  and an inner stator  62 . The outer stator  60  and the inner stator  62  include multiple stator teeth  66  and stator slots  68  disposed on respective stator cores. The stator  58  is configured to modulate a magnetic flux and transmit torque. The stator slots  68  are configured to accommodate stator windings (not shown) that are further interconnected to form a number of stator poles. A rotor having a rotor core  64  is interposed concentrically between the outer stator and the inner stator. The rotor core  64  includes multiple rotor poles  70 ,  72  disposed on its outer surface and multiple rotor poles  74 ,  76  disposed on its inner surface. In a particular embodiment, the rotor poles  70 ,  72 ,  74  and  76  include at least one of multiple permanent magnets, wound rotors or field coils. In the illustrated embodiment, the inner rotor poles  74 ,  76  and the outer rotor poles  70 ,  72  are permanent magnets. These permanent magnets  70 ,  72 ,  74  and  76  are together configured to form a number of rotor poles. The number of the rotor poles, the number stator poles and the stator teeth are chosen to satisfy equation (1). 
         [0037]    During operation of the electrical machine  56 , stator windings are energized. Torque is transmitted by way of interaction between magnetic flux excited by stator windings and magnetic flux excited by permanent magnet rotor poles  70 ,  72 ,  74  and  76 . It may be noted that the orientation of magnetic flux depends on the alignment of the rotor poles  70 ,  72 ,  74  and  76 . In one embodiment, the permanent magnet  70 ,  76  corresponds to a south pole and the permanent magnet  72 ,  74  corresponds to a north pole. In such a configuration magnetic flux propagates radially inward or outward with respect to an axis of rotation of the rotor indicated by the dashed lines  78  and  80 . 
         [0038]      FIG. 5  illustrates another exemplary embodiment of a magnetic gearing electrical machine  59  having stator-rotor-stator configuration with a fractional shift in alignment of the rotor poles  70 ,  72  as referenced in  FIG. 4  and the rotor poles  74 ,  76  as referenced in  FIG. 4 . The fractional shift in alignment results in propagation of a magnetic flux  82 ,  84 ,  86 , and  88  along a circumferential direction with respect to an axis of rotation of the rotor core  64 . The permanent magnets  70 ,  72 ,  74  and  76  are configured to form a number of rotor poles. The number of the rotor poles, the number of stator poles and the stator teeth are chosen to satisfy equation (1). In a particular embodiment, the permanent magnet  70 ,  76  corresponds to a south pole and the permanent magnet  72 ,  74  corresponds to a north pole, resulting in the magnetic flux propagating along a circumferential direction with respect to an axis of rotation of the rotor indicated by the dashed lines  82 ,  84 ,  86  and  88 . 
         [0039]    Turning now to  FIG. 6 , an axial electrical machine with a rotor-stator-rotor configuration is illustrated. The axial electrical machine  90  includes at least a pair of rotors that include rotor core  92  and  94  disposed on a central non-magnetic shaft  102 . Rotor poles  96  are disposed adjacent to the rotor core  92  and  94 . At least one stator  98  is disposed on the non-magnetic shaft  102  via bearing  104  and interposed axially between the rotor core  92  and  94 . The stator includes stator teeth (not shown) and stator slots (not shown) to accommodate stator windings  100  that are further interconnected to form stator poles. The stator winding configurations may include but are not limited to a lapped or toroidal winding. The number of the rotor poles, the number of stator poles and the stator teeth are chosen to satisfy equation (1). Magnetic flux propagation is illustrated below in  FIGS. 7 and 8 . 
         [0040]      FIG. 7  is a diagrammatical representation of cross sectional view of axial electrical machine of  FIG. 6  illustrating the magnetic flux. The rotor-stator-rotor configuration of axial electrical machine  106  includes at least a pair of rotors  108 ,  110 . The rotors  108 ,  110  include multiple rotor poles  112 ,  114  respectively. In a particular embodiment, the rotor poles  112 ,  114  include at least one of multiple permanent magnets, wound rotors or field coils. In the illustrated embodiment, the rotor poles  112 ,  114  are permanent magnets. A stator  115  is provided to modulate magnetic flux and transmit torque. The stator includes a stator core  116  interposed axially between the rotors  108 ,  110 . A number of stator teeth  118  and stator slots  120  are disposed on the stator core. The stator slots  120  are configured to accommodate stator windings (not shown) that are further interconnected to form a number of stator poles. The stator winding configurations may include but not limited to a lapped or toroidal winding. As an exemplary embodiment, the rotors  108 ,  110  include permanent magnets  112 ,  114  disposed on a surface as illustrated. These permanent magnets  112 ,  114  are configured to form a number of rotor poles. The number of the rotor poles, the number stator poles and the stator teeth are chosen to satisfy equation (1). 
         [0041]    The rotor  108  may be configured to operate at a lower speed than the rotor  110 . During operation of the electrical machine  106 , stator windings are energized. Torque is transmitted by way of interaction between magnetic flux excited by stator windings and magnetic flux exited by permanent magnet rotor poles  112  and  114 . It may be noted that the orientation of magnetic flux depends on the alignment of the rotor poles on the rotors  108  and  110 . In one embodiment, the permanent magnet  112  corresponds to a north pole and the permanent magnet  114  corresponds to a south pole. In such a configuration magnetic flux propagates in the stator core  116  along a direction parallel to an axis of rotation of the rotor indicated by the dashed lines  122  and  124 . 
         [0042]      FIG. 8  illustrates another exemplary embodiment of an axial electrical machine  126  having rotor-stator-rotor configuration with a fractional shift in alignment of the rotor poles  112 ,  114  as referenced in  FIG. 7 . The fractional shift in alignment results in propagation of a magnetic flux  122  and  124  in the stator core  116  along the circumferential direction with respect to an axis of rotation of the rotors  108 ,  110 . The permanent magnets  112  and  114  are configured to form a number of rotor poles. The number of the rotor poles, the number of stator poles and the stator teeth are chosen to satisfy equation (1). In a particular embodiment, the permanent magnet  112  corresponds to a north pole and the permanent magnet  114  corresponds to a south pole, resulting in the magnetic flux propagating along a direction parallel to an axis of rotation of the rotor indicated by the dashed lines  122  and  124 . 
         [0043]      FIG. 9  illustrates an axial electrical machine with a stator-rotor-stator configuration. The axial electrical machine  128  includes at least a pair of stators. The stators include stator cores  130 ,  132  and are disposed on a central non-magnetic shaft  148  via bearings  146 . The stator  130 ,  132  cores include stator teeth  138  to accommodate stator windings  140  that are further interconnected to form stator poles. At least one rotor  134  is interposed axially between the stators  130  and  132  to form air gaps  150 . The rotor  134  is disposed on the non-magnetic shaft  148 . Multiple rotor poles  136  are disposed on the rotor  134 . The number of rotor poles, the number of stator poles and the stator teeth are chosen to satisfy equation (1). It may be noted that the equation applies to each of the air gaps  150 . Magnetic flux propagation is illustrated below in  FIGS. 10 and 11 . 
         [0044]      FIG. 10  is a diagrammatical representation of cross sectional view of axial electrical machine of  FIG. 9  illustrating the magnetic flux. The stator-rotor-stator configuration of axial electrical machine  156  includes at least a pair of stators  158 ,  160 . The stators  158 ,  160  include multiple stator teeth  162  and stator slots  164 , the stators further configured to modulate magnetic flux and transmit torque. The stator slots  164  are configured to accommodate stator windings (not shown) further interconnected to form stator poles. The stator winding configurations may include but are not limited to a lapped or toroidal winding. A rotor  176  is interposed axially between the stators  158 ,  160 . Rotor poles  168 ,  170  are disposed on a rotor core  166 . In a particular embodiment, the rotor poles  168 ,  170  include at least one of multiple permanent magnets, wound rotors or field coils. In the illustrated embodiment, the rotor poles  168 ,  170  are permanent magnets. These permanent magnets  168 ,  170  are configured to form a number of rotor poles. The number of the rotor poles, the number stator poles and the stator teeth are chosen to satisfy equation (1). 
         [0045]    During operation of the electrical machine stator windings are energized. Torque is transmitted by way of interaction between magnetic flux excited by stator windings and magnetic flux excited by permanent magnet rotor poles  168 ,  170 . It may be noted that the orientation of magnetic flux depends on the alignment of the rotor poles. In one embodiment, the permanent magnet  168  corresponds to a north pole and the permanent magnet  170  corresponds to a south pole. In such a configuration magnetic flux propagates in the rotor  116  along a direction parallel to an axis of rotation of the rotor indicated by the dashed lines  172  and  174 . 
         [0046]      FIG. 11  illustrates another exemplary embodiment of an axial electrical machine  178  having stator-rotor-stator configuration with a fractional shift in alignment of the rotor poles  168 ,  170  as referenced in  FIG. 10 . The fractional shift in alignment results in propagation of a magnetic flux  172  and  174  in the rotor  166  along a circumferential direction with respect to an axis of rotation of the rotor  176 . The permanent magnets  168  and  170  are configured to form a number of rotor poles. The number of the rotor poles, the number of stator poles and the stator teeth are chosen to satisfy equation (1). In a particular embodiment, the permanent magnet  168  corresponds to a north pole and the permanent magnet  170  corresponds to a south pole, resulting in the magnetic flux propagating in the rotor  166  along a circumferential direction with respect to an axis of rotation of the rotor indicated by the dashed lines  172  and  174 . 
         [0047]      FIG. 12  is a further diagrammatic representation of the axial electrical machine  90  in  FIG. 6  illustrating an exemplary axial electrical machine  182  employing a stator  98 , as referenced in  FIG. 6  between each pair of multiple rotors  92 ,  184 . The axial electrical machine  182  includes rotors  92 ,  184  and  94 , and stators  98  and  188  that are disposed on a central non-magnetic shaft  192 . In the illustrated embodiment, stator  188  is interposed between rotors  184  and  94 . It may be noted that multiple stators may be disposed between two rotors as illustrated by reference numeral  194 . Furthermore, the rotors  92 ,  94  include rotor poles  96  disposed on a surface of the rotors. Similarly, rotor poles  186  are disposed on a surface of the rotor  184 . The rotors  92 ,  94  and  184  are fixed on to the non-magnetic shaft. Stators  98  and  188  include stator windings  100  and  190  respectively. According to one embodiment of the invention, the stators are fixed on to the non-magnetic shaft  192  via bearings  196 . The stator windings are interconnected to form stator poles. 
         [0048]    Turning now to  FIG. 13 , a sectional view of an electrical machine with embedded permanent magnets configured as rotor poles is illustrated. The electrical machine  200  includes rotor  208 , rotor core  210 , and permanent magnets  212  and  214  embedded radially within the rotor core  210 . The rotor core  210  is further disposed around a support shaft  216 . Moreover, a stator  201  includes a stator core  202  disposed concentrically outside the rotor core  210 . Multiple stator teeth  204  are configured to form stator slots  206  between respective stator teeth  204 . The permanent magnets  212 ,  214  are configured to form a number of rotor poles. The stator slots are configured to accommodate stator windings (not shown) that are further interconnected to form stator poles. In an exemplary embodiment, the stator windings may include coils made from super conducting material. The number of the rotor poles, the number stator poles and the stator teeth are chosen to satisfy equation (1). In the illustrated embodiment, the electrical machine  200  employs a conventional design. However, it will be appreciated that the electrical machine  200  may be designed in an inside-out configuration, wherein the rotor  208  is disposed outside circumferentially around the stator  201 . In an exemplary embodiment, in the inside-out configuration, the rotor poles may include structures such as, but not limited to, embedded magnets or surface mounted permanent magnets. 
         [0049]    During operation of the electrical machine  200  stator windings are energized. Torque is transmitted by way of interaction between magnetic flux excited by stator windings and magnetic flux exited by permanent magnet rotor poles  212 ,  214 . In one embodiment, the permanent magnet  212  corresponds to a north pole and the permanent magnet  214  corresponds to a south pole. 
         [0050]      FIG. 14  is a diagrammatical cross sectional view of an exemplary rotor pole  220  (also referred as field coil configuration) including a field winding  224 . The construction of the rotor pole  220  includes a rotor core  222  that may be made of magnetic material and includes slots configured to accommodate field windings  224  around the rotor core  222 . The field windings may be energized by a direct current source. The configuration of the rotor pole  220  is determined by the direction of current through the field windings  224 . Such configuration of rotor pole  220  may be incorporated in rotor poles of machines illustrated in  FIGS. 2 ,  4 ,  6 ,  9  and  12 . 
         [0051]      FIG. 15  is a diagrammatical representation of an exemplary rotor pole  230  including a wound rotor configuration. The rotor pole  230  includes rotor teeth  234  and rotor slots  236  that are formed alternatively on the rotor core  232 . Such teeth and slot configuration of rotor poles  230  (sometimes referred to as reluctance rotor poles) as illustrated herein may be incorporated in rotor poles of machines illustrated in  FIGS. 2 ,  4 ,  6 ,  9  and  12 . 
         [0052]      FIG. 16  is a diagrammatical representation of an exemplary rotor pole  240  including axial laminations  242 . Such axial laminations  242  may be incorporated in electrical machines that require reluctance torque. Multiple axial laminations such as  240  are stacked one above the other to form a core upon which magnetic flux propagation may be facilitated. Axial laminations  242  include three faces  244 ,  246  and  248 . A radial width of each of the axial lamination  242  varies along a direction illustrated by reference numeral  250 . However, a width  252  remains constant to provide support that may facilitate disposing the axial laminations  242  and  254  on a base (not shown). Such a configuration of the rotor pole  240  may be incorporated in rotor poles of the electrical machines illustrated in  FIGS. 2 ,  4 ,  6 ,  9  and  12 . 
         [0053]    Advantageously, the foregoing system provides a cost effective and convenient means of construction of electrical machines that may be employed in a magnetic gearing. Such constructions also facilitate a higher torque density. Further, a selective number of stator teeth, stator poles and rotor poles satisfying equation (1) provide a desirable stator flux pattern across a rotor. Higher torque densities enable substantial reduction in machine size. Rotating machine with reduced construction mass have other numerous advantages such as reduced mechanical wear and tear, easier handling, and economical for increased torque requirement. Furthermore, direct drive applications find numerous advantages incorporating higher torque density machines. 
         [0054]    While only certain features of the invention have been illustrated and described herein, many modifications and changes will occur to those skilled in the art. It is, therefore, to be understood that the appended claims are intended to cover all such modifications and changes as fall within the true spirit of the invention.