Patent Publication Number: US-10312782-B2

Title: Double stator permanent magnet machine

Description:
CROSS REFERENCE TO RELATED APPLICATION 
     This application claims priority to U.S. Provisional Application No. 61/867,381 filed Aug. 19, 2013. This application is a continuation in part of U.S. application Ser. No. 13/169,233 filed Jun. 27, 2011, which claims priority to U.S. Provisional Application No. 61/358,583 filed Jun. 25, 2010. Each of the above identified patent applications is incorporated herein by reference in its entirety to provide continuity of disclosure. 
    
    
     FIELD OF THE INVENTION 
     This invention relates generally to double stator machines, and more particularly to a double stator permanent magnet machine having structural geometries that optimize the distribution of magnetic flux. 
     BACKGROUND OF THE INVENTION 
     Conventional switched reluctance machines provide a generally robust structure and low manufacturing cost. However, the majority of the electromagnetic forces used by a conventional switched reluctance machine do not contribute to useful work. Rather, these forces create undesirable vibrations that are a major drawback. Thus, conventional switched reluctance machines have limited industrial applicability. Surface mount permanent magnet synchronous machines offer higher torque density than conventional switched reluctance machines. However, rare earth permanent magnet material is expensive and ineffective placement of the rare earth permanent magnets results in high cost and wasteful use of the permanent magnet material. 
     For example, U.S. Pat. No. 5,304,882 to Lipo et al discloses a variable reluctance motor with permanent magnet excitation having a single set of stators and a single rotor having permanent magnets. However, the motor in Lipo requires a significant amount of permanent magnet material, thereby making the manufacture of such a motor expensive. Further, the motor is limited by the amount of electromagnetic forces which contribute to rotational motion, thereby limiting the torque density of the motor and its overall efficiency. 
     Therefore, there is a need for intelligent hybridization of rare earth permanent magnets and effective placement to increase power density at a reduced cost to manufacture. Further, there is a need in the art for a double stator permanent magnet machine in which a higher proportion of the electromagnetic forces generated contributes to motion with a reduced amount of permanent magnet material, thereby lowering the overall cost of manufacture. 
     SUMMARY 
     In one embodiment, a double stator permanent magnet machine includes an inner stator, a rotor adjacent the inner stator and rotatively coupled to the inner stator, and an outer stator adjacent the rotor and rotatively coupled to the rotor. The inner stator includes, a back iron, and a set of inner stator poles connected to the back iron. The rotor includes a shaft, and a set of segments, each segment having a permanent magnet. The outer stator includes a set of outer stator poles. A set of inner stator windings are disposed between each of the inner stator poles and a set of outer stator windings are disposed between each of the outer stator poles. A set of phases, each phase including a subset of the set of inner stator windings and a subset of the set of outer stator windings selectively energize the set of phases with a current to rotate the rotor with respect to the inner stator and the outer stator. 
     In one embodiment, the double stator permanent magnet machine operates as a motor generating a reluctance torque and a reaction torque at a ratio of at least 1:3. 
     In another embodiment, the double stator permanent magnet machine operates as a generator by connecting a load to the shaft of the rotor. 
     In another embodiment, a method for operating a double stator permanent magnet machine is disclosed. In this embodiment, the method includes the steps of energizing each phase of the set of phases with a first current as a flux linkage of each phase increases and energizing each phase of the set of phases with a second current, opposite in polarity from the first current, as the flux linkage of each phase decreases. Reaction torque produced by each phase is maximized and reluctance torque produced by each phase is minimized, only contributing to torque ripple. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The disclosed embodiments will be described with reference to the accompanying drawings. Like pieces in different drawings are designated by same number. 
         FIG. 1  is a perspective view of a preferred embodiment. 
         FIG. 2  is an exploded isometric view of a preferred embodiment. 
         FIG. 3  is a cross-sectional view of a preferred embodiment. 
         FIG. 4  is a schematic of a drive circuit of a preferred embodiment. 
         FIG. 5  is a cross-sectional view of a preferred embodiment in use. 
         FIG. 6  is a graph of the inductance and the flux linkage of phase a with respect to a rotor position of a preferred embodiment. 
         FIG. 7  is a graph of the torque of phase a with respect to a rotor position of a preferred embodiment. 
         FIG. 8  is a graph of the flux linkage of phase a with respect to a rotor position of a preferred embodiment. 
         FIG. 9  is a graph of the current and flux linkage for each phase, and the torque for all phases of a preferred embodiment. 
     
    
    
     DETAILED DESCRIPTION 
     The structure of a double stator permanent magnet machine according to some embodiments of the present invention will be described with reference to  FIGS. 1-5 . 
     Referring to  FIGS. 1 and 2 , double stator permanent magnet machine  1000  includes inner stator  950 , rotor  800 , and outer stator  900 . In a preferred embodiment, each of inner stator  950 , rotor  800 , and outer stator  950  is cylindrical in shape. Inner stator  950  is disposed at the axis of double stator permanent magnet machine  1000  and rotor  800  is generally cylindrical and coaxial with inner stator  950 . Outer stator  900  is generally cylindrical and is coaxial with inner stator  950 . Each of inner stator  950 , rotor  800 , and outer stator  900  are coaxial. 
     In other embodiments, additional layers comprising pairs of rotors and stators may be added to the above-described stator-rotor-stator configuration. 
     Referring to  FIG. 2 , inner stator  950  is attached to inner stator shaft  1001 . End cap  1002  is attached to inner stator shaft  1001  at end  1015 . Bearings  1003  attach to inner stator shaft  1001  at end  1015  between end cap  1002  and inner stator  950 . Bearings  1004  attach to inner stator shaft  1001  at end  1014 . 
     Outer stator  900  is attached to inside surface  1016  of housing  1005 . End cap  1015  is attached to housing  1005  at end  1012 . 
     Rotor  800  includes outer cage  819  and a set of segments, each segment is attached to outer cage  819  as will be further described below in  FIG. 3 . Rotor  800  is attached to rotor end cap  1007 . Rotor end cap  1007  has opening  1008  and shaft  1009 . Bearings  1010  attach to shaft  1009 . End cap  1011  has hole  1017  and attaches to housing  1005  at end  1013  and to bearings  1010  with hole  1017 . Shaft  1009  inserts through hole  1017 . 
     Bearings  1004  are connected to opening  1008  of rotor end cap  1007  and bearings  1003  are connected to opening  1006  of rotor  800  enabling rotor  800  to rotatively couple to inner stator shaft  1001  and to end cap  1011 . Rotor  800  rotates relative to inner stator  950  and outer stator  900  about axis  1018  while inner stator  950  and outer stator remain stationary as will be further described below. 
     End portion  1019  of housing  1005  is used to house portions of wiring, which are selectively energized in operation of double stator permanent magnet machine  1000 , as will be further described below. End portion  1020  of housing  1005  is adapted for connecting a load to rotor  800  with shaft  1009 . Either end portion  1019  or  1020  may be used for either of these functions. 
     In a preferred embodiment, each of bearings  1003 ,  1004 , and  1010  is a needle bearing. Other suitable bearings known in the art may be employed. 
     Referring to  FIG. 3 , outer stator  900 , rotor  800 , and inner stator  950  will be described in further detail. Double stator permanent magnet machine  1000  includes outer stator  900 , rotor  800 , and inner stator  950  coaxial with center axis  976 . Outer stator  900  has outer stator poles  901 ,  902 ,  903 ,  904 ,  905 ,  906 ,  907 , and  908  spaced at equal outer angular intervals. Outer stator pole  901  has outer pole head  909  and outer pole surface  910 . Outer stator pole  902  has outer pole head  911  and outer pole surface  912 . Outer stator pole  903  has outer pole head  913  and outer pole surface  914 . Outer stator pole  904  has outer pole head  915  and outer pole surface  916 . Outer stator pole  905  has outer pole head  917  and outer pole surface  918 . Outer stator pole  906  has outer pole head  919  and outer pole surface  920 . Outer stator pole  907  has outer pole head  921  and outer pole surface  922 . Outer stator pole  908  has outer pole head  923  and outer pole surface  924 . 
     Each outer stator pole is aligned opposite a corresponding inner stator pole. Inner stator  950  includes back iron  975  and inner stator poles  951 ,  952 ,  953 ,  954 ,  955 ,  956 ,  957 , and  958  spaced at equal inner angular intervals, each connected to and radially extending from back iron  975 . Inner stator pole  951  has inner pole head  959  and inner pole surface  960 . Inner stator pole  952  has inner pole head  961  and inner pole surface  962 . Inner stator pole  953  has inner pole head  963  and inner pole surface  964 . Inner stator pole  954  has inner pole head  965  and inner pole surface  966 . Inner stator pole  955  has inner pole head  967  and inner pole surface  968 . Inner stator pole  956  has inner pole head  969  and inner pole surface  970 . Inner stator pole  957  has inner pole head  971  and inner pole surface  972 . Inner stator pole  958  has inner pole head  973  and inner pole surface  974 . 
     Rotor  800  includes segments  801 ,  802 ,  803 ,  804 ,  805 , and  806  attached to outer cage  819  and evenly spaced with respect to each other in outer cage  819 . Outer cage  819  includes cage segments  821 ,  822 ,  823 ,  824 ,  825 , and  826  to which segments  801 ,  802 ,  803 ,  804 ,  805 , and  806  attach as will be further described below. Segment  801  has permanent magnet  807  centered within segment  801 . Permanent magnet  807  has polarity  813 . Segment  801  is attached to cage segments  826  and  821 . Segment  802  has permanent magnet  808  centered within segment  802 . Permanent magnet  808  has polarity  814 . Segment  802  is attached to cage segments  821  and  822 . Segment  803  has permanent magnet  809  centered within segment  803 . Permanent magnet  809  has polarity  815 . Segment  803  is attached to cage segments  822  and  823 . Segment  804  has permanent magnet  810  centered within segment  804 . Permanent magnet  810  has polarity  816 . Segment  804  is attached to cage segments  823  and  824 . Segment  805  has permanent magnet  811  centered within segment  805 . Permanent magnet  811  has polarity  817 . Segment  805  is attached to cage segments  824  and  825 . Segment  806  has permanent magnet  812  centered within segment  806 . Permanent magnet  812  has polarity  818 . Segment  806  is attached to cage segments  825  and  826 . Each of permanent magnets  807 ,  808 ,  809 ,  810 ,  811 , and  812  has a tangential magnetization. Each of polarities  813 ,  814 ,  815 ,  816 ,  817 , and  818  is a north pole. 
     In preferred embodiments, rotor  800  is a shell-type or drum rotor. Segments  801 ,  802 ,  803 ,  804 ,  805 , and  806  are formed so as not to project radially outward or inward from outer cage  819 , i.e., are formed as arcuate portions of rotor  800 . The radially outer surface of each segment is flush or substantially flush with the radially outer surface of outer cage  819 . The radially inner surface of each segment is flush or substantially flush with the radially the inner surface of outer cage  819 . 
     In a preferred embodiment, each of inner stator poles  951 ,  952 ,  953 ,  954 ,  955 ,  956 ,  957 , and  958 , outer stator poles  901 ,  902 ,  903 ,  904 ,  905 ,  906 ,  907 , and  908 , and segments  801 ,  802 ,  803 ,  804 ,  805 , and  806  is formed as a portion extended in the direction of center axis  976 . In this regard, the terms “stack length” or “axial length,” used with reference to center axis  976  of double stator permanent magnet machine  1000 , inner stator  950 , rotor  800 , or outer stator  900 , refer herein to the length of the portion of double stator permanent magnet machine  1000 , inner stator  950 , outer stator  900 , or rotor  800  that participates in electromechanical energy conversion, not the entire length of double stator permanent magnet machine  1000 , inner stator  950 , outer stator  900 , or rotor  800 . The term “length” will be used to refer to the entire length of double stator permanent magnet machine  1000 , inner stator  950 , outer stator  900 , or rotor  800 . 
     Each of inner stator poles  951 ,  952 ,  953 ,  954 ,  955 ,  956 ,  957 , and  958 , outer stator poles  901 ,  902 ,  903 ,  904 ,  905 ,  906 ,  907 , and  908 , and segments  801 ,  802 ,  803 ,  804 ,  805 , and  806  is formed as a single portion extending along the entire stack length of double stator permanent magnet machine  1000 . The respective cross-sections of inner stator poles  951 ,  952 ,  953 ,  954 ,  955 ,  956 ,  957 , and  958 , outer stator poles  901 ,  902 ,  903 ,  904 ,  905 ,  906 ,  907 , and  908 , and segments  801 ,  802 ,  803 ,  804 ,  805 , and  806  remain the same throughout the respective stack lengths of inner stator  950 , outer stator  900  and rotor  800 . The stack lengths of double stator permanent magnet machine  1000 , inner stator  950 , outer stator  900 , and rotor  800  extend most of the lengths of double stator permanent magnet machine  1000 , inner stator  950 , outer stator  900 , and rotor  800 , respectively. 
     Rotor  800  is positioned between outer stator  900  and inner stator  950  forming air gap  827  between rotor  800  and outer pole surfaces  910 ,  912 ,  914 ,  916 ,  918 ,  920 ,  922 , and  924 , and forming air gap  828  between rotor  800  and inner pole surfaces  960 ,  962 ,  964 ,  966 ,  968 ,  970 ,  972 , and  974 . 
     Double stator permanent magnet machine  1000  includes four phases, a, b, c, and d. Phase a includes windings a 3 , a′ 3 , a 4 , and a′ 4  connected in series. Phase b includes windings b 3 , b′ 3 , b 4 , and b′ 4  connected in series. Phase c includes windings c 3 , c′ 3 , c 4 , and c′ 4  connected in series. Phase d includes windings d 3 , d′ 3 , d 4 , and d′ 4  connected in series. 
     In a preferred embodiment, double stator permanent magnet machine  1000  has four phases. In other embodiments, double stator permanent magnet machine  1000  can have any number of phases depending on the desired design. 
     Windings a 3  are disposed between outer stator poles  903  and  902  having a proximal-distal current flow. Windings b 3  are disposed between outer stator poles  902  and  901  having a proximal-distal current flow. Windings c 3  are disposed between outer stator poles  901  and  908  having a proximal-distal current flow. Windings d 3  are disposed between outer stator poles  908  and  907  having a proximal-distal current flow. Windings a′ 3  are disposed between outer stator poles  907  and  906  having a distal-proximal current flow. Windings b′ 3  are disposed between outer stator poles  906  and  905  having a distal-proximal current flow. Windings c′ 3  are disposed between outer stator poles  905  and  904  having a distal-proximal current flow. Windings d′ 3  are disposed between outer stator poles  904  and  903  having a distal-proximal current flow. 
     Windings a 4  are disposed between inner stator poles  957  and  956  having a proximal-distal current flow. Windings b 4  are disposed between inner stator poles  956  and  955  having a proximal-distal current flow. Windings c 4  are disposed between inner stator poles  955  and  954  having a proximal-distal current flow. Windings d 4  are disposed between inner stator poles  954  and  953  having a proximal-distal current flow. Windings a′ 4  are disposed between inner stator poles  953  and  952  having a distal-proximal current flow. Windings b′ 4  are disposed between inner stator poles  952  and  951  having a distal-proximal current flow. Windings c′ 4  are disposed between inner stator poles  951  and  958  having a distal-proximal current flow. Windings d′ 4  are disposed between inner stator poles  958  and  957  having a distal-proximal current flow. As shown, the general direction of current flow of windings a 3 , a′ 3 , a 4 , and a′ 4 , b 3 , b′ 3 , b 4 , and b′ 4 , c 3 , c′ 3 , c 4 , and c′ 4 , d 3 , d′ 3 , d 4 , and d′ 4  is a positive current flow. Reversing the current flows in windings a 3 , a′ 3 , a 4 , and a′ 4 , b 3 , b′ 3 , b 4 , and b′ 4 , c 3 , c′ 3 , c 4 , and c′ 4 , d 3 , d′ 3 , d 4 , and d′ 4  is a negative current flow. 
     In a preferred embodiment, the windings of each phase are electrically isolated from each other. In this embodiment, windings a 3 , a′ 3 , a 4 , and a′ 4  are electrically isolated from windings b 3 , b′ 3 , b 4 , and b′ 4 , windings c 3 , c′ 3 , c 4 , and c′ 4  and windings d 3 , d′ 3 , d 4 , and d′ 4 . In this embodiment, windings b 3 , b′ 3 , b 4 , and b′ 4 , are electrically isolated from windings a 3 , a′ 3 , a 4 , and a′ 4 , windings c 3 , c′ 3 , c 4 , and c′ 4 , and windings d 3 , d′ 3 , d 4 , and d′ 4 . In this embodiment, windings c 3 , c′ 3 , c 4 , and c′ 4  are electrically isolated from windings a 3 , a′ 3 , a 4 , and a′ 4 , windings b 3 , b′ 3 , b 4 , and b′ 4 , and windings d 3 , d′ 3 , d 4 , and d′ 4 . In this embodiment, windings d 3 , d′ 3 , d 4 , and d′ 4  are electrically isolated from windings a 3 , a′ 3 , a 4 , and a′ 4 , windings b 3 , b′ 3 , and b′ 4 , and windings c 3 , c′ 3 , c 4 , and c′ 4 . 
     In a preferred embodiment, rotor position θ is measured positively in the clockwise direction from x-axis  1200 . 
     In a preferred embodiment, the number of inner stator poles is an even number and spaced at equal angular intervals about center axis  976 . 
     In a preferred embodiment, the number of segments is an even number and spaced at equal angular intervals about center axis  976 . 
     In a preferred embodiment, the number of outer stator poles is an even number and spaced at equal angular intervals about center axis  976 . 
     In a preferred embodiment, given that the number of inner and outer stator poles is even and that inner and outer stator poles are spaced at equal angular or circumferential intervals, it follows that for any given pole of a given stator there will be another pole of the given stator at a position diametrically opposed to the given pole. That is, if a given pole of a given stator is positioned at, for example, 0 degrees, another pole of the given stator will be positioned at 180 degrees. 
     In a preferred embodiment, double stator permanent magnet machine  1000  has an 8/6/8 configuration, i.e., eight outer stator poles, six rotor segments, and eight inner stator poles, spaced at even intervals. In another embodiment, double stator permanent magnet machine  1000  has a 6/4/6 configuration. In another embodiment, double stator permanent magnet machine  1000  has a 10/8/10 configuration. In another embodiment, double stator permanent magnet machine  1000  has a 12/8/12 configuration. In another embodiment, double stator permanent magnet machine  1000  has a 16/12/16 configuration. Other configurations may be employed having the outer stator poles equal the number of inner stator poles. 
     In a preferred embodiment, segments  801 ,  802 ,  803 ,  804 ,  805 , and  806  are positioned at intervals of 60° on center with respect to each other. In other configurations, other intervals are employed. 
     In a preferred embodiment, outer stator poles  901 ,  902 ,  903 ,  904 ,  905 ,  906 ,  907 , and  908  are positioned at equal outer angular intervals of 45° with respect to each other. In other configurations, other outer angular intervals are employed. 
     In a preferred embodiment, each of outer pole surfaces  910 ,  912 ,  914 ,  916 ,  918 ,  920 ,  922 , and  924  has an arc length of approximately 25°. In other configurations, other arc lengths are employed. 
     In a preferred embodiment, inner stator poles  951 ,  952 ,  953 ,  954 ,  955 ,  956 ,  957 , and  958  are positioned at equal inner angular intervals of 45° with respect to each other. In other configurations, other inner angular intervals are employed. 
     In a preferred embodiment, each of inner pole surfaces  960 ,  962 ,  964 ,  966 ,  968 ,  970 ,  972 , and  974  has an arc length of approximately 25°. In other configurations, other arc lengths are employed. 
     In a preferred embodiment, outer stator  900  is made of M-19 laminated electric silicon steel. Other grades of laminated electric silicon steel not exceeding M-49 may be employed. 
     In a preferred embodiment inner stator  950  is made of M-19 laminated electric silicon steel. Other grades of laminated electric silicon steel not exceeding M-49 may be employed. 
     In a preferred embodiment, each of segments  801 ,  802 ,  803 ,  804 ,  805 , and  806  is made of M-19 laminated electric silicon steel. Other grades of laminated electric silicon steel not exceeding M-49 may be employed. 
     In a preferred embodiment, each of permanent magnets  807 ,  808 ,  809 ,  810 ,  811 , and  812  is a rare earth magnet having a relative permeability approximately close to that of air having a relative permeability of approximately 1.00000037. In one embodiment, each of the permanent magnets  807 ,  808 ,  809 ,  810 ,  811 , and  812  is made of neodymium having a relative permeability of approximately 1.05. In another embodiment, each of permanent magnets  807 ,  808 ,  809 ,  810 ,  811 , and  812  is made of samarium-cobalt having a relative permeability of approximately 1.05. In another embodiment, each of permanent magnets  807 ,  808 ,  809 ,  810 ,  811 , and  812  is made of a ceramic. In another embodiment, each of permanent magnets  807 ,  808 ,  809 ,  810 ,  811 , and  812  is made of a ferrite. In another embodiment, each of permanent magnets  807 ,  808 ,  809 ,  810 ,  811 , and  812  is a non-rare earth magnet. 
     In a preferred embodiment, windings a 3 , a′ 3 , a 4 , and a′ 4 , b 3 , b′ 3 , b 4 , and b′ 4 , c 3 , c′ 3 , c 4 , and c′ 4 , d 3 , d′ 3 , d 4 , and d′ 4  are made of copper. Other suitable conductive materials known in the art may be employed. 
     In a preferred embodiment, each of air gaps  827  and  828  is approximately 1.0 mm. 
     Referring to  FIG. 4 , circuit  1100  drives double stator permanent magnet machine  1000 . Circuit  1100  includes bridge converters  1101 ,  1102 ,  1103 , and  1104  controlling phases a, b, c, and d, respectively. 
     In a preferred embodiment, each of bridge converters  1101 ,  1102 ,  1103 , and  1104  is a full bridge converter providing both positive and negative current. 
     In another embodiment, each of bridge converters  1101 ,  1102 ,  1103 , and  1104  is a half bridge converter, each having independent control of each phase current magnitude and direction. 
     The operation of a double stator permanent magnet machine according to preferred embodiments will be described with reference to  FIGS. 5-9 . 
     In a preferred embodiment, double stator permanent magnet machine  1000  is configured to operate with three or more separately excitable phases. 
     Referring to  FIG. 5 , double stator permanent magnet machine  1000  is configured to operate with four separately excitable phases a, b, c, and d. Electromagnetic torque is generated by the tendency of the magnetic circuit to realize the configuration of minimum magnetic reluctance (resistance). When a given phase is excited by causing a current to flow through the windings of that phase, a set of opposed segments nearest the energized windings are attracted thereto, and thus align themselves respectively with the pairs of stator poles between which the windings are disposed into an aligned position. In this aligned position, the reluctance is at a minimum. Since the number of segments is not equal to the number of poles of either stator, when the set of opposed segments are aligned with pairs of stator poles, a second set of opposed segments will be in an unaligned position. Exciting the phase adjacent to the unaligned segments will cause those segments to align themselves respectively with the pairs of stator poles of that adjacent phase, since reluctance is at a maximum in the unaligned position. By successively energizing adjacent phases, rotor  800  is caused to rotate while generating torque. The successive energizing of different phases involves the switching of current into different stator windings as reluctance varies. When reluctance is at a minimum, inductance is at a maximum, and vice versa. Multiphase excitation can be implemented by currents injected in multiple phases simultaneously to increase torque production. 
     Still referring to  FIG. 5  by way of example, when the windings of phase a are energized, segments  802  and  805  are pulled into alignment with a stator pole set of phase a including inner stator poles  953  and  952  and outer stator poles  903  and  902  by rotating clockwise into the aligned position as shown. Phase a generates magnetic flux paths  1501 ,  1502 ,  1503 , and  1504 . Phase b is then excited. When the excitation of phase b begins, segments  804  and  801  will be in the half-aligned position as shown. When the windings of phase b are energized segments  804  and  801  are pulled clockwise into alignment with a stator pole set of phase b including inner stator poles  955  and  956  and outer stator poles  905  and  906 . By continuing to energize each adjacent phase in counterclockwise succession, rotor  800  is made to rotate in the clockwise direction. 
     In another embodiment, energizing adjacent phases in a clockwise succession will cause rotor  800  to rotate counterclockwise. 
     In a preferred embodiment, the phases of double stator permanent magnet machine  1000  are sequentially energized. In this embodiment, double stator permanent magnet machine  1000  is operated as a motor, generating positive torque. In this embodiment, a given phase is energized when the opposing segments nearest the windings to be energized, are in an unaligned position or shortly thereafter, and the given phase is turned off, i.e., the windings corresponding to the phase are deenergized, just before the segments align with the set of inner and outer stator poles surrounding the phase. 
     In order to operate as a motor, stator phase excitation needs to be synchronized with the rotor position. A discrete encoder or resolver will perform the functionality. However, as the position information is also encoded in the inductance profile and induced back EMF, a position sensorless method can be developed as long as there is access to the applied phase current and voltage. 
     In another embodiment, double stator permanent magnet machine  1000  is operated as a generator. In this embodiment, external torque is applied. In this embodiment, a given phase produces a current pulse while the segments nearest the windings to be energized are brought into an aligned position or shortly thereafter. The given phase may then be deenergized, i.e., the windings corresponding to the phase may be switched off, just before the segments reach a fully unaligned position relative to the stator pole set surrounding the given phase. 
     In a preferred embodiment, θ=0° is defined as the aligned position, θ=15° is defined as the half-aligned position, and θ=30° is defined as the unaligned position for double stator permanent magnet machine  1000 . 
     The geometry of double stator permanent magnet machine  1000  enables shortened magnetic flux paths  1501 ,  1502 ,  1503 , and  1504  generated by the energizing of the phases as compared to a switched reluctance machine of the prior art. 
     In use, torque is generated by double stator permanent magnet machine  1000  through selectively energizing the windings disposed between inner stator poles and outer stator poles of phases a, b, c, and d with current using circuit  1100 , thereby causing rotor  800  to rotate with respect to outer stator  900  and inner stator  950 . The energizing of the windings disposed between inner stator poles of inner stator  950  and outer stator poles of outer stator  900  for a phase is synchronized with the position, θ, of rotor  800 . 
     For each given phase, the terminal voltage is defined by: 
                     V   a     =         Ri   a     +     E   a       =       Ri   a     +       d   ⁢           ⁢     ϕ   a       dt                 (   1   )               
where, R is the resistance for the given phase, i a  is current for the given phase, E a  is the induced back EMF for the given phase, and ϕ a  is the flux linkage for the given phase. The flux linkage ϕ a  for the given phase is defined as:
 
ϕ a   =L   aa (θ r ) i   a +ψ pm   _   a (θ r )+ M   ab (θ r ) i   b   +M   ac (θ r ) i   c   +M   ad (θ r ) i   d   (2)
 
where L aa  is the self inductance in the given phase, ψ pm  is the flux linkage caused by the permanent magnet, M ab , M ac , M ad  are the mutual inductances between the phases, i b , i c , i d  are the phase currents for phases b, c, d, respectively, and θ r  is the angular position of rotor  800  for the given phase. Because the mutual inductance between each phase is an order of magnitude smaller than the self inductance, the interaction between each phase is neglected resulting in the flux linkage for the given phase defined as:
 
ϕ a   =L   aa (θ r ) i   a +ψ pm   _   a (θ r )  (3)
 
     As a result, the induced back EMF for the given phase is defined as: 
     
       
         
           
             
               
                 
                   
                     
                       
                         
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                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 
                                   ψ 
                                   pm_a 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     θ 
                                     r 
                                   
                                   ) 
                                 
                               
                             
                             
                               d 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               t 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                         ⁢ 
                         
                           
                             
                               i 
                               a 
                             
                             ⁢ 
                             
                               
                                 d 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 
                                   
                                     L 
                                     aa 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     
                                       θ 
                                       r 
                                     
                                     ) 
                                   
                                 
                               
                               
                                 dθ 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 r 
                               
                             
                             ⁢ 
                             
                               ω 
                               r 
                             
                           
                           + 
                           
                             
                               
                                 L 
                                 aa 
                               
                               ⁡ 
                               
                                 ( 
                                 
                                   θ 
                                   r 
                                 
                                 ) 
                               
                             
                             ⁢ 
                             
                               
                                 di 
                                 a 
                               
                               
                                 
                                     
                                 
                                 ⁢ 
                                 dt 
                               
                             
                           
                           + 
                           
                             
                               
                                 d 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 
                                   
                                     ψ 
                                     pm_a 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     
                                       θ 
                                       r 
                                     
                                     ) 
                                   
                                 
                               
                               
                                 d 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 θ 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 r 
                               
                             
                             ⁢ 
                             
                               
                                 ω 
                                 r 
                               
                               ( 
                               5 
                               ) 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
           
         
       
     
     Using equation (5), the electromagnetic power for the given phase is defined by: 
                         P   =       ⁢       i   a     ⁢     E   a                   =       ⁢       i   a     ⁡     (         i   a     ⁢       d   ⁢           ⁢       L   aa     ⁡     (     θ   r     )           d   ⁢           ⁢   θ   ⁢           ⁢   r       ⁢     ω   r       +         L   aa     ⁡     (     θ   ⁢           ⁢   r     )       ⁢       di   a     dt       +         d   ⁢           ⁢       ψ   pm_a     ⁡     (     θ   r     )           d   ⁢           ⁢   θ   ⁢           ⁢   r       ⁢     ω   r         )                   =       ⁢         i   a   2     ⁢       d   ⁢           ⁢       L   aa     ⁡     (     θ   r     )           d   ⁢           ⁢   θ   ⁢           ⁢   r       ⁢     ω   r       +       i   a     ⁢       L   aa     ⁡     (     θ   r     )       ⁢       di   a     dt       +       i   a     ⁢       d   ⁢           ⁢       ψ   pm_a     ⁡     (     θ   r     )           d   ⁢           ⁢   θ   ⁢           ⁢   r       ⁢     ω   r                     =       ⁢         1   2     ⁢     (         i   a   2     ⁢       d   ⁢           ⁢       L   aa     ⁡     (     θ   r     )           d   ⁢           ⁢     θ   r         ⁢     ω   r       +       i   a   2     ⁢       d   ⁢           ⁢       L   aa     ⁡     (     θ   r     )         dt       +     2   ⁢     i   a     ⁢       L   aa     ⁡     (     θ   r     )       ⁢       d   ⁢           ⁢     i   a       dt         )       +       i   a     ⁢       d   ⁢           ⁢       ψ   pm_a     ⁡     (     θ   r     )           d   ⁢           ⁢   θ   ⁢           ⁢   r       ⁢     ω   r                     =       ⁢         d   ⁢           ⁢     (       1   2     ⁢       L   aa     ⁡     (     θ   r     )       ⁢     i   a   2       )       dt     +       (         1   2     ⁢     i   a   2     ⁢       d   ⁢           ⁢       L   aa     ⁡     (     θ   r     )           d   ⁢           ⁢     θ   r           +       i   a     ⁢       d   ⁢           ⁢       ψ   pm_a     ⁡     (     θ   r     )           d   ⁢           ⁢     θ   r             )     ⁢     ω   r                       (   6   )               
where ω r  is the angular frequency of rotor  800 , and
 
               d   ⁡     (       1   2     ⁢       L   aa     ⁡     (     θ   r     )       ⁢     i   a   2       )       dt         
in equation (6) is the reactive power because
 
               d   ⁡     (       1   2     ⁢       L   aa     ⁡     (     θ   r     )       ⁢     i   a   2       )       dt         
refers to variation of the energy stored in the field. The reactive power is not consumed by double stator permanent magnet machine  1000 . The reactive power cycles between the power supply and double stator permanent magnet machine  1000 . The second term,
 
                 (         1   2     ⁢     i   a   2     ⁢       d   ⁢           ⁢       L   aa     ⁡     (     θ   r     )           d   ⁢           ⁢     θ   r           +       i   a     ⁢       d   ⁢           ⁢       ψ   pm_a     ⁡     (     θ   r     )           d   ⁢           ⁢     θ   r             )     ⁢     ω   r       ,         
is the active power converted to mechanical energy by double stator permanent magnet machine  1000 . Dividing the active power by the angular frequency of rotor  800 , the torque for the given phase is defined by:
 
     
       
         
           
             
               
                 
                   T 
                   = 
                   
                     
                       
                         1 
                         2 
                       
                       ⁢ 
                       
                         i 
                         a 
                         2 
                       
                       ⁢ 
                       
                         
                           d 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             
                               L 
                               aa 
                             
                             ⁡ 
                             
                               ( 
                               
                                 θ 
                                 r 
                               
                               ) 
                             
                           
                         
                         
                           d 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             θ 
                             r 
                           
                         
                       
                     
                     + 
                     
                       
                         i 
                         a 
                       
                       ⁢ 
                       
                         
                           d 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             
                               ψ 
                               pm_a 
                             
                             ⁡ 
                             
                               ( 
                               
                                 θ 
                                 r 
                               
                               ) 
                             
                           
                         
                         
                           d 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             θ 
                             r 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   7 
                   ) 
                 
               
             
           
         
       
     
     The total torque generated by double stator permanent magnet machine  1000  includes two sources of torque: reluctance torque, 
                 1   2     ⁢     i   a   2     ⁢       d   ⁢           ⁢       L   aa     ⁡     (     θ   r     )           d   ⁢           ⁢     θ   r           ,         
and reaction torque,
 
               i   a     ⁢         d   ⁢           ⁢       ψ   pm_a     ⁡     (     θ   r     )           d   ⁢           ⁢     θ   r         .           
These two sources of torque can be either additive or subtractive depending on the operation mode.
 
     The reluctance torque is determined by the magnitude of the current and the inductance variation over rotor position. The direction of the reluctance torque is determined by the differentiation of inductance over rotor position. 
     The reaction torque direction depends on the flux linkage variation and the current direction. The reaction torque magnitude is linearly related to the current magnitude and the flux variation of the permanent magnet provided that no saturation is present. If the flux linkage differentiation is positive, positive current will result in positive torque. If the flux linkage differentiation is negative, negative current will result in positive torque. The positive reaction torque is generated regardless of inductance slope. Positive torque can be produced over the entire electrical cycle. 
     In a preferred embodiment, the total torque generated by double stator permanent magnet machine  1000  is a ratio of at least 1:3, reluctance torque to reaction torque. 
     Referring to  FIG. 6 , inductance profile  1106  and flux linkage profile  1107  of phase a are overlaid as two plots in graph  1105  which plots the profiles between the rotor positions of −30° to 30°. Phases b, c, and d have the same waveform of inductance profile over rotor position with a fixed angle shift between each phase. Flux linkage profile  1107  is the same as the flux linkage profile plotted in  FIG. 8  as will be described below, viewed over a narrow window of rotational positions. 
     Inductance profile  1106  has an inductance dip when the permanent magnet aligns with the center of the phase a windings at 0°. When the rotor moves from a completely unaligned position near −30° to where first half of rotor segment aligns with the stator at about −12°, the inductance increases to a maximum at about −12°. Since the permanent magnet material has a relative permeability very close to air, the equivalent airgap length will increase until about −5° after which it remains constant, the inductance decreases to a minimum at about −5° where the permanent magnet is between stator poles. The equivalent airgap length remains constant and the inductance remains constant between about −5° and +5°. The inductance increases to the maximum value at about 12° since the second half of rotor segment is fully aligned with stator at about +12°. The inductance will decrease again when the second half of rotor segment rotates away from the aligned position, towards +30°. 
     Referring to  FIG. 7 , graph  1108  of torque versus rotor position is provided. Curve  1109  is the torque profile produced by a first applied current and curve  1110  is the torque profile produced by a second applied current with a polarity opposite to the first applied current. The torque is only plotted for rotational positions between −30° and +30°. The profiles shown are periodically repeated every 60° throughout the remainder of the rotational positions. 
       FIG. 7  indicates that when positive torque is desired, the machine can be excited by an appropriate polarity of current for half of the electrical cycle. By switching the polarity of the current at −30°, 0°, +30° and so forth, positive torque can be generated in the entire electrical cycle. This effectively boosts the torque generated by a factor of two. The net reluctance torque is approximately zero, contributing only to torque ripple. 
     Referring to  FIG. 8  by way of example, flux linkage variation  1111  versus the position of rotor  800  for phase a is shown. This relationship of flux linkage variation  1111  versus rotor position is the same for each phase, with a fixed angle shift between each phase, and thereby current is applied to the windings of each phase in the same manner. 
     In one embodiment, current is applied to the windings of each phase when the flux linkage for each phase increases and decreases, fully utilizing reaction torque. In this embodiment, for a period beginning at point  1112  a first current is applied to the windings of each phase as the flux linkage increases through points  1113  and  1114 , until the flux linkage peaks at point  1115 . During this half-period from point  1112  to point  1115 , the reluctance torque is positive and the first current applied is positive. As the flux linkage peaks at point  1115  and decreases through points  1116  and  1117  until the flux linkage bottoms out at point  1116 , a second current, opposite in polarity from the first current, is applied to the windings of each phase. During this half-period from point  1115  to point  1118 , the reluctance torque is negative and the second current applied is negative. During a full period, the net reluctance torque is zero, only contributing to torque ripple. 
     In another embodiment, current is only applied to the windings of each phase as the flux linkage increases. In this embodiment, for a period beginning at point  1112  a first current is applied to the windings of each phase as the flux linkage increases through points  1113  and  1114 , until the flux linkage peaks at point  1115 . During this half-period from point  1112  to point  1115 , the reluctance torque is positive and the first current applied is positive. As the flux linkage peaks at point  1115  and decreases through points  1116  and  1117  until the flux linkage bottoms out at point  1118 , no current is applied to the windings of each phase. 
     Referring to  FIG. 9  in one embodiment, the current sequence in relation to the flux linkage for each phase of double stator permanent magnet machine  1000  is shown. Curve  1119  is the flux linkage for phase a. Curve  1120  is the current applied in phase a. Curve  1121  is the flux linkage in phase b. Curve  1122  is the current applied in phase b. Curve  1123  is the flux linkage in phase c. Curve  1124  is the current applied in phase c. Curve  1125  is the flux linkage in phase d. Curve  1126  is the current applied in phase d. In this embodiment, as the flux increases for each phase, a first positive current is applied to the respective phase windings. For each phase, as the flux linkage decreases a second negative current is applied to the respective phase windings. When the flux linkage plateaus for each phase, no current is applied. 
     In this embodiment, when phases a, b, c, and d are excited, torque curve  1127  is produced that includes torque ripples  1128  in flat areas of flux linkage due to reluctance torque. 
     In another embodiment, a first positive current is applied to the respective phase windings only as the flux increases for each phase. No negative current is applied. In this embodiment, curves  1120 ,  1122 ,  1124 , and  1126 , will only have a positive portion. 
     In one embodiment, approximately 6 A is applied to the windings of each phase when the flux linkage increases in each phase and approximately −6 A is applied to the windings of each phase when the flux linkage decreases in each phase. Other amounts of current are applied for other configurations and torque requirements. 
     In another embodiment, approximately 6 A is applied to the windings of each phase only when the flux linkage increases in each phase. Other amounts of current are applied for other configurations and torque requirements. 
     It will be appreciated by those skilled in the art that modifications can be made to the embodiments disclosed and remain within the inventive concept. Therefore, this invention is not limited to the specific embodiments disclosed, but is intended to cover changes within the scope and spirit of the claims.