Patent Publication Number: US-10784727-B2

Title: Salient pole, wound field, synchronous machine with enhanced saliency

Description:
BACKGROUND 
     Permanent magnet (PM) machines are used in today&#39;s hybrid and electric vehicles due to their ideal performance characteristics. With the uncertainty associated with the cost and overseas sourcing of PM materials, other types of machines are being explored to determine if they can offer similar performance without the need for permanent magnets. Salient pole, wound field, synchronous machines (WFSMs) have similar torque characteristics relative to PM machines, but are free of permanent magnet material because a rotor winding generates the field flux instead of the permanent magnet material. Although WFSMs and PM machines share the same operating principles, WFSMs operate with a small saliency and a minimal reluctance torque. Saliency relates to a variation of an inductance at a machine terminal as a function of a relative position on a rotor. 
     SUMMARY 
     In an example embodiment, a rotor of a salient pole, wound field, synchronous machine is provided that includes, but is not limited to, a rotor core, a plurality of pole bodies, and a field winding. The rotor core includes, but is not limited to, a rotor shaft face configured to mount to a shaft for rotation of the rotor about a first axis. Each pole body of the plurality of pole bodies includes, but is not limited to, a pole core, a pole shoe, and a single flux barrier. The pole core includes, but is not limited to, a first pole core face and a second pole core face extending from the rotor core. The pole shoe is mounted to the pole core and includes, but is not limited to, an arc face, a first tip extending from a first edge of the arc face, a second tip extending from a second edge of the arc face opposite the first edge, a first pole shoe face extending between the first tip and the first pole core face, and a second pole shoe face extending between the second tip and the second pole core face. The single flux barrier forms an enclosed space filled with a material having a magnetic permeability between approximately zero and approximately 1000 relative to a magnetic permeability of a vacuum. The single flux barrier includes, but is not limited to, a top wall, a shaft mounting wall configured to mount adjacent the shaft when the rotor is mounted to the shaft, and a plurality of interior walls connected between the top wall and the shaft mounting wall. The plurality of interior walls extend parallel to and centered between the first pole core face and the second pole core face. The field winding is wound around each pole core of the plurality of pole bodies. 
     In another example embodiment, a salient pole, wound field, synchronous machine is provided that includes, but is not limited to, a stator and a rotor. The rotor includes, but is not limited to, a rotor core, a plurality of pole bodies, and a field winding. The rotor core includes, but is not limited to, a rotor shaft face configured to mount to a shaft for rotation of the rotor relative to the stator about a first axis. Each pole body of the plurality of pole bodies includes, but is not limited to, a pole core, a pole shoe, and a single flux barrier. The pole core includes, but is not limited to, a first pole core face and a second pole core face extending from the rotor core. The pole shoe is mounted to the pole core and includes, but is not limited to, an arc face, a first tip extending from a first edge of the arc face, a second tip extending from a second edge of the arc face opposite the first edge, a first pole shoe face extending between the first tip and the first pole core face, and a second pole shoe face extending between the second tip and the second pole core face. The single flux barrier forms an enclosed space filled with a material having a magnetic permeability between approximately zero and approximately 1000 relative to a magnetic permeability of a vacuum. The single flux barrier includes, but is not limited to, a top wall, a shaft mounting wall configured to mount adjacent the shaft when the rotor is mounted to the shaft, and a plurality of interior walls connected between the top wall and the shaft mounting wall. The plurality of interior walls extend parallel to and centered between the first pole core face and the second pole core face. The field winding is wound around each pole core of the plurality of pole bodies 
     Other principal features of the disclosed subject matter will become apparent to those skilled in the art upon review of the drawings described below, the detailed description, and the appended claims. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Illustrative embodiments of the disclosed subject matter will hereafter be described referring to the accompanying drawings, wherein like numerals denote like elements. 
         FIG. 1  depicts a front view of a four pole, salient pole, wound field, synchronous machine (WFSM) in accordance with an illustrative embodiment. 
         FIG. 2  depicts a zoomed portion of one pole of the front view of the salient pole WFSM of  FIG. 1  in accordance with an illustrative embodiment. 
         FIG. 3  depicts a back view of a rotor of the salient pole WFSM in accordance with an illustrative embodiment. 
         FIG. 4  depicts a front view of the rotor of the salient pole WFSM with windings in accordance with an illustrative embodiment. 
         FIG. 5  depicts a phasor diagram of the salient pole WFSM at one per unit speed in accordance with an illustrative embodiment. 
         FIG. 6  depicts a total output torque versus a torque angle for different saliency designs using the salient pole WFSM of  FIG. 1  in accordance with an illustrative embodiment. 
         FIG. 7  depicts a comparison of a maximum torque for the different saliency designs as back electromotive force varying using the salient pole WFSM of  FIG. 1  in accordance with an illustrative embodiment. 
         FIG. 8  depicts a stator current, a stator ohmic loss, and an optimum torque angle comparison for a given output torque using the salient pole WFSM of  FIG. 1  in accordance with an illustrative embodiment. 
         FIG. 9  depicts a front view of a rotor of a four pole, salient pole WFSM with a flux barrier in accordance with a first illustrative embodiment. 
         FIG. 10  depicts a perspective view of the rotor of  FIG. 9  in accordance with a first illustrative embodiment. 
         FIG. 11  depicts a front view of a salient pole, wound field, synchronous machine (WFSM) with the rotor of  FIG. 10  in accordance with an illustrative embodiment. 
         FIG. 12  depicts a perspective view of the salient pole WFSM of  FIG. 11  in accordance with an illustrative embodiment. 
         FIG. 13  depicts a q-axis flux density distribution using the salient pole WFSM of  FIG. 11  in accordance with an illustrative embodiment. 
         FIG. 14  depicts a d-axis flux density distribution using the salient pole WFSM of  FIG. 11  in accordance with an illustrative embodiment. 
         FIG. 15  depicts an air gap centerline d-axis flux density distribution for a rotor pole aligned to stator teeth using the salient pole WFSM of  FIG. 11  with two different barrier widths in comparison to a conventional salient pole WFSM of  FIG. 1  in accordance with an illustrative embodiment. 
         FIG. 16  depicts air gap centerline d-axis flux density distribution for a rotor pole aligned to stator slots using the salient pole WFSM of  FIG. 11  with two different barrier widths in comparison to the conventional salient pole WFSM of  FIG. 1  in accordance with an illustrative embodiment. 
         FIG. 17  depicts a d-axis stator winding flux linkage using the salient pole WFSM of  FIG. 11  with two different barrier widths in comparison to the conventional salient pole WFSM of  FIG. 1  in accordance with an illustrative embodiment. 
         FIG. 18  depicts an air gap centerline q-axis flux density distribution for a rotor pole aligned to stator teeth using the salient pole WFSM of  FIG. 11  with two different barrier widths in comparison to a conventional salient pole WFSM of  FIG. 1  in accordance with an illustrative embodiment. 
         FIG. 19  depicts an air gap centerline q-axis flux density distribution for a rotor pole aligned to stator slots using the salient pole WFSM of  FIG. 11  with two different barrier widths in comparison to the conventional salient pole WFSM of  FIG. 1  in accordance with an illustrative embodiment. 
         FIG. 20  depicts a q-axis stator winding flux linkage using the salient pole WFSM of  FIG. 11  with two different barrier widths in comparison to the conventional salient pole WFSM of  FIG. 1  in accordance with an illustrative embodiment. 
         FIG. 21  depicts the average output torque using the salient pole WFSM of  FIG. 11  with three different barrier widths in comparison to the conventional salient pole WFSM of  FIG. 1  in accordance with an illustrative embodiment. 
         FIG. 22  depicts a zoomed back view of a portion of a rotor of a salient pole WFSM with a flux barrier in accordance with a second illustrative embodiment. 
         FIG. 23  depicts a zoomed back view of a portion of a rotor of a salient pole WFSM with a flux barrier in accordance with a third illustrative embodiment. 
         FIG. 24  depicts a perspective view of the rotor of  FIG. 23  in accordance with an illustrative embodiment. 
         FIG. 25  depicts a front view of a salient pole WFSM with the rotor of  FIG. 23  in accordance with an illustrative embodiment. 
         FIG. 26  depicts a perspective view of the salient pole WFSM of  FIG. 23  in accordance with an illustrative embodiment. 
     
    
    
     DETAILED DESCRIPTION 
     Salient permanent magnet (PM) machines have a built-in saliency structure due to the presence of magnets on a rotor d-axis, wherein the magnet effectively acts as a large air gap to the stator flux. Studies have suggested that a peak output torque is improved with the addition of motor saliency over that obtainable from a non-salient pole structure. For example, in a salient pole PM traction motor, it was shown that about 40% of peak output torque is made up of reluctance torque arising from the saliency. 
     A salient pole synchronous machine has a non-uniform air gap as understood by a person of skill in the art. For example, referring to  FIG. 1 , a front view of a salient pole, wound field, synchronous machine (WFSM)  100  is shown in an illustrative embodiment. In general, salient pole WFSM  100  may be used as a motor or a generator dependent on the driving mechanism. Salient pole WFSM  100  illustrates a conventional design. Salient pole WFSM  100  may include a stator  102  and a rotor  104 . If salient pole WFSM  100  is utilized as a motor, stator  102  causes rotor  104  to rotate utilizing electrical energy thereby rotating a shaft mounted to rotor  104  to provide mechanical energy; whereas, if salient pole WFSM  100  is utilized as a generator, the shaft is rotated by an external mechanical force/torque that causes rotor  104  to rotate thereby causing stator  102  to generate electrical energy. In the illustrative embodiment of  FIG. 1 , rotor  104  is mounted in a center of stator  102  that is generally cylindrical though other arrangements may be used. 
     In the illustrative embodiment of  FIG. 1 , stator  102  includes a stator core  106  and a plurality of teeth  108 . Each tooth of the plurality of teeth  108  includes a slot wall of a plurality of slot walls  110  and a tooth face of a plurality of tooth faces  111 . The plurality of teeth  108  are mounted to project from stator core  106  towards rotor  104 . In the illustrative embodiment of  FIG. 1 , stator  102  includes 36 teeth. In alternative embodiments, salient pole WFSM  100  may have a fewer or a greater number of teeth. Each tooth face of the plurality of tooth faces  111  faces rotor  104 . One or more armature windings, also referred to as stator windings, are wound through slots formed by the plurality of slot walls  110  in various manners, as understood by a person of skill in the art, to carry one or more phases of electrical current. A number of stator poles is the same as a number of rotor poles. The plurality of teeth  108  determine whether the winding configuration is concentrated or distributed. For illustration, the one or more armature windings may be wound full pitched, concentrated or distributed or short pitched, distributed as understood by a person of skill in the art. 
     In the illustrative embodiment of  FIG. 1 , rotor  104  includes a rotor core  112  and a plurality of pole bodies  116 . An interior of rotor core  112  is defined by a rotor shaft face  114  that is configured to mount to the shaft for rotation of rotor  104  with the shaft. In the illustrative embodiment of  FIG. 1 , rotor  104  includes four pole bodies though any even number of pole bodies may be used. The plurality of pole bodies  116  includes a first pole body  116   a , a second pole body  116   b , a third pole body  116   c , and a fourth pole body  116   d . The plurality of pole bodies  116  are mounted to project from rotor core  112  toward the plurality of tooth faces  111  of stator  102 . The plurality of pole bodies  116  act as salient magnetic poles. Rotor  104  may have a greater or a fewer number of pole bodies and include pole bodies having different shapes. The plurality of pole bodies  116  extend from rotor core  112  opposite rotor shaft face  114  at equal angular intervals and have a common arc length dimension. Each pole body of the plurality of pole bodies  116  may include a pole core  118  and a pole shoe  120  that generally form a “T” shape. Pole core  118  mounts between rotor core  112  and pole shoe  120 . 
     First pole body  116   a  of the plurality of pole bodies  116  includes a first pole core  118   a  and a first pole shoe  120   a . Second pole body  116   b  of the plurality of pole bodies  116  includes a second pole core  118   b  and a second pole shoe  120   b . Third pole body  116   c  of the plurality of pole bodies  116  includes a third pole core  118   c  and a third pole shoe  120   c . Fourth pole body  116   d  of the plurality of pole bodies  116  includes a fourth pole core  118   d  and a fourth pole shoe  120   d.    
     Referring to  FIGS. 2 and 9 , a zoomed portion of a front view of salient pole WFSM  100  is shown in accordance with an illustrative embodiment. First pole core  118   a  may include a first pole core front face  202   a , a first pole core right face  204   a , a first pole core back face  300   a  (shown referring to  FIG. 3 ), and a first pole core left face  206   a . Each of first pole core front face  202   a , first pole core right face  204   a , first pole core back face  300   a , and first pole core left face  206   a  may be generally flat and rectangular. First pole core  118   a  may be formed of a conductive material such as iron or steel. First pole core  118   a  may be formed of a solid section of conductive material or of a plurality of laminations stacked together. The plurality of laminations may be stacked parallel to each other from first pole core front face  202   a  to first pole core back face  300   a  such that first pole core right face  204   a  and first pole core left face  206   a  are not solid, but are formed of a stack of laminations. In an alternative embodiment, the plurality of laminations may be stacked parallel to each other from first pole core right face  204   a  to first pole core left face  206   a  such that first pole core front face  202   a  and first pole core back face  300   a  are not solid, but are formed of a stack of laminations. 
     Second pole core  118   b , third pole core  118   c , and fourth pole core  118   d  may be formed in a similar manner. Second pole core  118   b  may include a second pole core front face  202   b , a second pole core right face  204   b , a second pole core back face  300   b  (shown referring to  FIG. 3 ), and a second pole core left face  206   b . Third pole core  118   c  may include a third pole core front face  202   c , a third pole core right face  204   c , a third pole core back face  300   c  (shown referring to  FIG. 3 ), and a third pole core left face  206   c . Fourth pole core  118   d  may include a fourth pole core front face  202   d , a fourth pole core right face  204   d , a fourth pole core back face  300   d  (shown referring to  FIG. 3 ), and a fourth pole core left face  206   d.    
     First pole shoe  120   a  may include a first pole shoe front face  208   a , a first pole shoe right face  210   a , a first pole shoe arc face  212   a , a first pole shoe back face  302   a  (shown referring to  FIG. 3 ), and a first pole shoe left face  214   a . First pole shoe front face  208   a  and first pole shoe back face  302   a  may be generally flat. First pole shoe arc face  212   a  may be arced and face the plurality of tooth faces  111  of stator  102 . First pole shoe right face  210   a  and pole shoe left face  214   a  may be generally flat or curved. First pole shoe right face  210   a  mounts between first pole core right face  204   a  and first pole shoe arc face  212   a . First pole shoe left face  214   a  mounts between first pole core left face  206   a  and first pole shoe arc face  212   a.    
     First pole shoe right face  210   a  and first pole shoe arc face  212   a  are joined at a first tip  220   a . First pole shoe left face  214   a  and first pole shoe arc face  212   a  are joined at a second tip  222   a . First tip  220   a  and second tip  222   a  may have different shapes. For example, in the illustrative embodiment of  FIG. 2 , first tip  220   a  and second tip  222   a  form a first point shape that is generally pointed. In the illustrative embodiment of  FIG. 3 , first tip  220   b  and second tip  222   b  form a second point shape that is truncated. In the illustrative embodiment of  FIG. 4 , first tip  220   c  and second tip  222   c  form a third point shape that is further truncated. 
     First pole shoe  120   a  may be formed of a magnetic material such as iron or steel. First pole shoe  120   a  may be formed of a plurality of laminations stacked together. The plurality of laminations may be stacked parallel to each other from first pole shoe front face  208   a  to first pole shoe back face  302   a  such that first pole shoe right face  210   a  and first pole shoe left face  214   a  are not solid, but are formed of a stack of laminations. In an alternative embodiment, the plurality of laminations may be stacked parallel to each other from first pole shoe right face  210   a  to first pole shoe left face  214   a  such that first pole shoe front face  208   a  and first pole shoe back face  302   a  are not solid, but are formed of a stack of laminations. 
     Second pole shoe  120   b , third pole shoe  120   c , and fourth pole shoe  120   d  may be formed in a similar manner. Second pole shoe  120   b  may include a second pole shoe front face  208   b , a second pole shoe right face  210   b , a second pole shoe arc face  212   b , a second pole shoe back face  302   b  (shown referring to  FIG. 3 ), and a second pole shoe left face  214   b . Third pole shoe  120   c  may include a third pole shoe front face  208   c , a third pole shoe right face  210   c , a third pole shoe arc face  212   c , a third pole shoe back face  302   c  (shown referring to  FIG. 3 ), and a third pole shoe left face  214   c . Fourth pole shoe  120   d  may include a fourth pole shoe front face  208   d , a fourth pole shoe right face  210   d , a fourth pole shoe arc face  212   d , a fourth pole shoe back face  302   d  (shown referring to  FIG. 3 ), and a fourth pole shoe left face  214   d.    
     As stated previously, stator  102  and rotor  104  are separated by a non-uniform air gap. For example, a first air gap  216  is formed between the plurality of tooth faces  111  of stator  102  and each pole shoe arc face  212  of the plurality of pole bodies  116  of rotor  104 . Different air gaps result between tooth faces  111  that are not opposite pole shoe arc face  212  of the plurality of pole bodies  116 . As rotor  104  rotates, a position of first air gap  216  and the different air gaps rotates relative to the plurality of teeth  108  of stator  102 . 
     Referring to  FIG. 3 , a back view of a second rotor  104   a  is shown in accordance with an illustrative embodiment. Second rotor  104   a  is similar to rotor  104  except that second rotor  104   a  includes a second rotor core  112   a  instead of rotor core  112 . Second rotor core  112   a  includes a connecting face between each pole body of the plurality of pole bodies  116 . A rotor back face  304  of second rotor  104   a  may include first pole core back face  300   a , first pole shoe back face  302   a , second pole core back face  300   b , second pole shoe back face  302   b , third pole core back face  300   c , third pole shoe back face  302   c , fourth pole core back face  300   d , fourth pole shoe back face  302   d , a first core back face portion  306 , a second core back face portion  308 , a third core back face portion  310 , and a fourth core back face portion  312 . The dashed lines included in  FIG. 3  are intended to illustrate face boundaries for descriptive purposes though it should be understood that rotor back face  304  may be formed of a continuous surface of a common material. The continuous surface may be a lamination of steel or iron, for example. Additionally different face boundaries may be defined as a transition between the plurality of pole bodies  116  and rotor core  112 ,  112   a.    
     Though not shown, a rotor front face of second rotor  104   a  may be identical to rotor back face  304 .  FIG. 9  shows a rotor back face  926  identical to rotor back face  304  except with a flux barrier formed in each pole body of the plurality of pole bodies. First core back face portion  306  may extend between rotor shaft face  114  and a first rotor core face  314 . Second core back face portion  308  may extend between rotor shaft face  114  and a second rotor core face  316 . Third core back face portion  310  may extend between rotor shaft face  114  and a third rotor core face  318 . Fourth core back face portion  312  may extend between rotor shaft face  114  and a fourth rotor core face  320 . 
     First rotor core face  314  may be generally flat and rectangular and extend between first core back face portion  306  and a first core front face portion  918  (shown in  FIG. 9  except with a flux barrier as described further below). Second rotor core face  316  may be generally flat and rectangular and extend between second core back face portion  308  and a second core front face portion  920  (shown in  FIG. 9  except with a flux barrier as described further below). Third rotor core face  318  may be generally flat and rectangular and extend between third core back face portion  310  and a third core front face portion  922  (shown in  FIG. 9  except with a flux barrier as described further below). Fourth rotor core face  320  may be generally flat and rectangular and extend between fourth core back face portion  312  and a fourth core front face portion  924  (shown in  FIG. 9  except with a flux barrier as described further below). In alternative embodiments, first rotor core face  314 , second rotor core face  316 , third rotor core face  318 , and fourth rotor core face  320  may not be flat or rectangular. For example, first rotor core face  314 , second rotor core face  316 , third rotor core face  318 , and fourth rotor core face  320  may be arced. 
     First rotor core face  314  also extends between first pole core right face  204   a  of first pole body  116   a  and a fourth pole core left face  206   d  of fourth pole body  116   d . Second rotor core face  316  also extends between a second pole core right face  204   b  of second pole body  116   b  and first pole core left face  206   a  of first pole body  116   a . Third rotor core face  318  also extends between a third pole core right face  204   c  of third pole body  116   c  and a second pole core left face  206   b  of second pole body  116   b . Fourth rotor core face  320  also extends between a fourth pole core right face  204   d  of fourth pole body  116   d  and a third pole core left face  206   c  of third pole body  116   c.    
     First core back face portion  306 , second core back face portion  308 , third core back face portion  310 , and fourth core back face portion  312  may be formed of a magnetically conductive material such as iron or steel. First core back face portion  306 , second core back face portion  308 , third core back face portion  310 , and fourth core back face portion  312  may be formed of a solid block of material or of a plurality of laminations stacked together. The plurality of laminations may be stacked parallel to each other from core back face portions  306 ,  308 ,  310 ,  312  to core front face portions  918 ,  920 ,  922 ,  924  such that rotor shaft face  114  and rotor core faces  314 ,  316 ,  318 ,  320  are not solid, but are formed of a stack of laminations. The plurality of laminations may be stacked parallel to each other from rotor shaft face  114  to rotor core faces  314 ,  316 ,  318 ,  320  such that core back face portions  306 ,  308 ,  310 ,  312  and the core front face portions  918 ,  920 ,  922 ,  924  are not solid, but are formed of a stack of laminations. 
     Referring to  FIG. 4 , a field winding  400  is wound around the plurality of pole cores  118  including first pole core  118   a , second pole core  118   b , third pole core  118   c , and fourth pole core  118   d  in the illustrative embodiment of  FIG. 4 . The plurality of pole shoes  120  including first pole shoe  120   a , second pole shoe  120   b , third pole shoe  120   c , and fourth pole shoe  120   d  in the illustrative embodiment of  FIG. 4 , assist in holding field winding  400  in place. A first end of field winding  400  connects to a first terminal  402 . A second end of field winding  400  connects to a second terminal  404 . First terminal  402  and second terminal  404  supply DC to field winding  400 . A symbol “X” denotes wrapping into the page, and a symbol “●” denotes wrapping out of the page. Solid and dashed connecting lines denote wrapping of field winding  400  between the plurality of pole cores  118 , where the dashed connecting line is behind third pole core  118   c.    
     In a synchronous motor, application of three-phase alternating current (AC) power to the armature windings wound around the plurality of teeth  108  of stator  102  causes a rotating magnetic field to be setup around rotor  104 . The rotating magnetic field attracts a rotor field activated by the DC carried by field winding  400  resulting in a turning force on the shaft or vice versa. The synchronous motor may be provided with or may provide a fewer or a greater number of phases of AC power. 
     Due to the non-uniform air gap, a reactance varies with a rotor position of rotor  104 . As a result, the salient-pole WFSM has two axes of symmetry: (1) a field pole axis  406  (axis of field winding  400  in a direction of the DC field) also called a direct axis or d-axis, and (2) a second axis  408  passing through a center of an interpolar space also called a quadrature axis or q-axis. In the illustrative embodiment of  FIG. 4 , the q-axis is 90 degrees later than the d-axis because there are four salient poles. As rotor  104  rotates, there is a change in the energy stored. Either energy is extracted from the magnetic field and becomes mechanical energy (motor operation), or energy is stored in the magnetic field and flows into an electrical circuit powered from the stator windings of stator  102  (generator operation). 
     A steady state performance of a salient pole, WFSM can be modeled using circuit equations with field flux linkage and armature reaction inductances that are nonlinearly dependent on a flux level. However, insight into saliency effects on steady state behavior can be obtained using a simplified model that ignores resistive voltage drop and magnetic saturation resulting in constant equivalent circuit inductances. Assuming distributed stator windings with sinusoidal excitation, and neglecting space harmonics from the rotor field and armature reaction, the resulting steady-state equivalent circuit model can be derived in a dq-reference frame formed by d-axis  406  and q-axis  408 . 
     Referring to  FIG. 5 , a phasor diagram of a salient pole, WFSM at one per unit (pu) speed is shown in accordance with an illustrative embodiment. In the per unit system, dq-axis voltage equations can be expressed as:
 
 V   q   =n   pu ( E   i   +X   d   I   d )= n   pu ( X   ad   I   f   +X   d   I   d )  (1)
 
 V   d   =−n   pu   X   q   I   q   (2)
 
where:
         n pu =per unit speed;   E i =per unit open circuit voltage (produced by the DC field interacting with the stator winding) at one per unit speed;   I d =per unit d-axis current at one per unit speed;   I f =per unit wound field current in field winding  400  at one per unit speed;   I q =per unit q-axis current at one per unit speed;   X d =per unit d-axis synchronous reactance at one per unit speed;   X ad =per unit d-axis magnetizing reactance at one per unit speed; and   X q =per unit q-axis reactance at one per unit speed.       

     For a given armature current, open circuit voltage E i  can be modeled as proportional to a product of magnetizing reactance X ad  and wound field current I f  as indicated in equation (1). With V s  defined as a stator voltage and stator current I s  as a phase or armature current, the dq-components can be expressed in terms of terminal quantities as:
 
 V   s   ≤δ=V   q   {right arrow over (q)}+V   d   {right arrow over (d)}   (3)
 
 I   s   ≤γ=I   q   {right arrow over (q)}+I   d   {right arrow over (d)}   (4)
 
where δ+γ is a power factor (PF) angle, δ is a first portion of a PF angle (also called a torque or load angle) between the q-axis and the stator voltage, and γ is a second portion of the PF angle (also called a gamma or internal PF angle) between the q-axis and the phase current.
 
     An output power P can be approximated by a terminal input power in a high efficiency motor as: 
     
       
         
           
             
               
                 
                   
                       
                   
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                   ) 
                 
               
             
           
         
       
     
     By dividing per unit speed n pu  from both sides of equation (6), an output torque T at any speed can be calculated as: 
     
       
         
           
             
               
                 
                   T 
                   = 
                   
                     
                       P 
                       
                         n 
                         pu 
                       
                     
                     = 
                     
                       
                         
                           
                             E 
                             i 
                           
                           ⁢ 
                           
                             I 
                             s 
                           
                           ⁢ 
                           cos 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           γ 
                         
                         - 
                         
                           0.5 
                           ⁢ 
                           
                             ( 
                             
                               
                                 X 
                                 d 
                               
                               - 
                               
                                 X 
                                 q 
                               
                             
                             ) 
                           
                           ⁢ 
                           
                             I 
                             s 
                             2 
                           
                           ⁢ 
                           sin 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           2 
                           ⁢ 
                           γ 
                         
                       
                       = 
                       
                         
                           
                             X 
                             ad 
                           
                           ⁢ 
                           
                             I 
                             f 
                           
                           ⁢ 
                           
                             I 
                             s 
                           
                           ⁢ 
                           cos 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           γ 
                         
                         - 
                         
                           0.5 
                           ⁢ 
                           
                             ( 
                             
                               
                                 X 
                                 d 
                               
                               - 
                               
                                 X 
                                 q 
                               
                             
                             ) 
                           
                           ⁢ 
                           
                             I 
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                             2 
                           
                           ⁢ 
                           sin 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           2 
                           ⁢ 
                           γ 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   7 
                   ) 
                 
               
             
           
         
       
     
     The output power can be evaluated by measuring the torque at a given speed. The torque equation is a function of the open circuit voltage, the armature current, and a saliency (X d −X q ). Two components of the torque can be identified, a field torque component, E i I s  cos γ, which is a result of an interaction between stator  102  and the rotor field, and a reluctance torque component, 0.5(X d −-X q )I s   2  sin 2γ, which arises from the saliency of the machine. 
     In general, a polarity of the saliencies X d −X q  of a salient pole WFSM is opposite to that of a salient pole PM design. For a salient pole WFSM, X q  is smaller than X d  because the salient pole structure has more air space at a rotor slot opening. Part of the q-axis flux needs to traverse the rotor interpolar part to make a full flux linkage loop. Hence, the effective air gap on the q-axis flux path is enlarged by having slotting effects both from stator  102  and rotor  104 . On the other hand, the d-axis flux path is made of iron (or other suitable material) on a solid rotor structure, where an effective air gap only needs to consider stator slotting. As a result, the saliency X d −X q  is positive. The reluctance torque is small or sometimes negligible due to the small saliencies of a conventional rotor structure. 
     For a given load condition, reluctance power can potentially be an important output power component of WFSMs as its saliencies increases beyond that normally encountered using WFSM  100 .  FIG. 6  shows curves of an output torque, as a function of current angle γ, and the saliencies X d −X q  (assuming X d  is fixed) for rated speed operation with 1 pu line current and 0.8 pu open circuit voltage (same field current for fixed X d ). A first curve  606  represents the output torque as a function of current angle γ for X d −X q =0.2 pu. A second curve  604  represents the output torque as a function of current angle γ for X d −X q =0.4 pu. A third curve  602  represents the output torque as a function of current angle γ for X d −X q =0.6 pu. A fourth curve  600  represents the output torque as a function of current angle γ for X d −X q =0.8 pu. A maximum output torque can be achieved by choosing an optimum current angle γ′ for the given current amplitude at each saliency level. This peak value increases monotonically as the saliency varies from 0.2 pu to 0.8 pu. At the same time, the optimum current angle, γ′, rotates backward from −12.6° to −30.6°. As a result, more power can be produced in a WFSM by improving the saliency without the need to increase the current or to introduce any additional copper loss in stator  102  or rotor  104 . 
     Considering X d −X q =0.4 pu and X d −X q =0.8 pu, as the field torque varies with cos(γ), it reaches its maximum at γ=0°. For the reluctance torque component, it is proportional to the product of X d −X q  and sin 2γ, since X d −X q  is positive, the reluctance torque is positive for −45°&lt;γ&lt;0°. The larger saliency design has greater amplitude in reluctance torque, while both designs reach their maximum reluctance torque at γ=−45°. As a result, a large saliency design can produce more total output power due to better reluctance power generation capability. As the saliency increases, the reluctance torque weighs more heavily in the total output torque generation. The optimum current angle γ′ also rotates away from where the maximum field torque operating point γ=0° is achieved to that which is close to the maximum reluctance torque operating point γ=−45°. 
     An alternative design approach is shown in  FIG. 7  where different saliency levels are reached as X d  changes. The open circuit voltage varies in accordance with X ad  if the field current is constant. Maximum available torque is compared in this plot between different saliency levels as E i  varies. A first curve  700  represents the output torque as a function of E i  for X d −X q =0.2 pu. A second curve  702  represents the output torque as a function of E i  for X d −X q =0.4 pu. A third curve  704  represents the output torque as a function of E i  for X d −X q =0.6 pu. A fourth curve  706  represents the output torque as a function of E i  for X d −X q =0.8 pu. The results indicate that large saliency and large open circuit voltage E i  are preferred for torque production providing a guideline for saliency enhancement in WFSM design, namely, to maximize torque capability, X ad  or open circuit voltage should be preserved as the saliency increases. 
     In motor operation beyond rated speed, the field current of a WFSM can be reduced as speed increases and torque requirements decrease to maintain good efficiency and satisfactory constant power speed range within the controller voltage limit. A large saliency design can further reduce the losses in the machine and improve the overall efficiency.  FIG. 8  shows a required stator current for different saliency designs (fixed X d =1.2 pu and E i =0.8 pu) to produce the same amount of torque. A first curve  800  shows the stator current I s  as a function of the saliencies. A second curve  802  shows a stator loss I s   2 R as a function of the saliencies. A third curve  802  shows the optimum current angle γ′ as a function of the saliencies. Compared to a design with X d −X q =0.4 pu operating at 1 pu current, first curve  800  suggests that less current is needed as saliency increases. Up to 11% of the stator current could be saved, corresponding to 20% of the stator ohmic losses when the saliency is improved from 0.4 pu to 0.8 pu. Though the stator current is reduced, the optimum current angle γ′ still rotates towards the maximum reluctance torque operating point γ=−45° as saliency increases. 
     The concept of saliency enhancement is, as suggested by its name, to enlarge the difference between the q-axis and the d-axis reactance: X d −X q . For WFSMs, it is desirable to design the magnetic paths to have low permeability on the q-axis, thus further lowering the q-axis reactance, while keeping the d-axis reactance unchanged as much as possible. In this case, the effect on open circuit voltage is minimized. As a result, the total output power can be improved with increasing reluctance power. However, it becomes challenging to design a WFSM with large saliency, because the q-axis and the d-axis flux paths in WFSMs are cross-coupled on stator  102  and rotor  104 . The flux on the q-axis and the d-axis rotate along with the load current based on a stator fundamental frequency. As a result, any design modifications made on rotor  104  tend to affect both the q-axis and the d-axis flux paths. 
     In general, flux barriers on WFSMs can be categorized into three designs: single barrier (SB), multi-layer barrier (MLB), and axial laminated (AL).  FIG. 9  shows a front view of an illustrative rotor pole design for using a SB design.  FIG. 22  shows an illustrative rotor pole design for using a MLB design.  FIG. 23  shows an illustrative rotor pole design for using a AL design. The shape details of first tip  220   a ,  220   b ,  220   c  and second tip  222   a ,  222   b ,  222   c  are ignored herein. Though different in shape, a flux barrier of all three structures is designed to be parallel to the rotor d-axis and perpendicular to the q-axis, so that the flux on the d-axis is kept unaffected as much as possible, and the flux on the rotor q-axis is blocked by a barrier. The barrier may be formed of various materials that are insulators (a low electrical conductivity) having a low magnetic permeability, ideally with a relative magnetic permeability approximately equal to one relative to the permeability of a vacuum though an insulating material with a relative magnetic permeability between approximately zero and approximately 1000 relative to a vacuum has a sufficiently low magnetic permeability. Illustrative materials include plastic such as a polyester film such as a Mylar® film produced by Dupont Teijin Films, a polyimide film such as Kapton® film or paper produced by E. I. du Pont de Nemours, an aromatic polyamide such as Nomex® paper produced by E. I. du Pont de Nemours, polyvinylcloride, air, paint with a similar magnetic permeability, etc. The relative magnetic permeability of these materials is typically between one and two, the relative magnetic permeability being a ratio of the magnetic permeability of the material in question divided by the magnetic permeability of a vacuum. As understood by a person of skill in the art, the permeability of a vacuum is also known as the magnetic permeability of free space and is defined as μ 0 =4π×10 −7  Newtons/Amperes 2 (N/A 2 ). 
     A comparison between the electromagnetic characteristics between the three designs is listed in Table I below. 
     
       
         
           
               
               
               
               
             
               
                   
                 TABLE I 
               
               
                   
                   
               
               
                   
                 Axial Lamination 
                 Multi-layer Barrier 
                 Single Barrier 
               
               
                   
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
            
               
                 Iron Loss 
                 High 
                 Low 
                 Low 
               
               
                 Air gap Flux 
                 Smoothest 
                 Smooth 
                 Least Smooth 
               
               
                   
               
            
           
         
       
     
     Among these three structures, the AL design may be the most difficult to manufacture and assemble because its laminations have many different shapes, although the even spaced lamination insulation barriers can provide the smoothest air gap flux. The AL design may also generate the most iron losses. The MLB and SB both use low permeability slits as the flux barrier. The SB design may be the easiest and cheapest to manufacture based on a uniform lamination design, although it may provide the least smooth air gap flux. 
     Referring to  FIG. 9 , a front view of a third rotor  104   b  is shown in accordance with an illustrative embodiment. Referring to  FIG. 10 , a perspective view of third rotor  104   b  is shown in accordance with an illustrative embodiment. Third rotor  104   b  is mounted to a shaft  900 . For illustration, first core front face portion  918  may include a first dovetail  902  to mount to shaft  900 . Second core front face portion  920  may include a second dovetail  904  to mount to shaft  900 . Third core front face portion  922  may include a third dovetail  906  to mount to shaft  900 . Fourth core front face portion  924  may include a fourth dovetail  908  to mount to shaft  900 . 
     Third rotor  104   b  is identical to second rotor  104   a  except that third rotor  104   b  includes a single flux barrier  904  embedded in a radial center of each of the plurality of pole bodies  116 . First pole body  116   a  may include a first flux barrier  910   a . First flux barrier  910   a  extends through a radial center of first pole core  118   a  and first pole shoe  120   a  between first pole shoe front face  208   a  and first pole shoe back face  302   a . First flux barrier  910   a  is further positioned halfway between first pole shoe right face  210   a  and first pole shoe left face  214   a , halfway between first pole core right face  204   a  and first pole core left face  206   a , and extends from first pole shoe arc face  212   a  to rotor shaft face  114 . 
     First flux barrier  910   a  may include a first plurality of interior walls  912   a , a first top wall  914   a , and a first shaft mounting wall  916   a  that form an enclosed space that may be filled with the insulating material having a low relative magnetic permeability. First shaft mounting wall  916   a  may form a dovetail to mount first flux barrier  910   a  to shaft  900 . Similarly, second pole body  116   b  may include a second flux barrier  910   b ; third pole body  116   c  may include a third flux barrier  910   c ; and fourth pole body  116   d  may include a fourth flux barrier  910   d . Second flux barrier  910   b , third flux barrier  910   c , and fourth flux barrier  910   d  are identical in shape and composition and mounted in an identical position relative to second pole body  116   b , third pole body  116   c , and fourth pole body  116   d , respectively, as first flux barrier  910   a.    
       FIG. 10  shows a first axis  1000  that is parallel to a radial center of first pole body  116   a ; a second axis  1002  that is parallel to a radial center of second pole body  116   b  and perpendicular to first axis  1000 ; and a third axis  1004  that is perpendicular to first axis  1000  and to second axis  1002  and parallel to an axial center of third rotor  104   b.    
     Referring to  FIG. 11 , a front view of a second salient pole WFSM  100   a  is shown in accordance with an illustrative embodiment. Referring to  FIG. 12 , a perspective view of second salient pole WFSM  100   a  is shown in accordance with an illustrative embodiment. Second salient pole WFSM  100   a  may include stator  102  and third rotor  104   b.    
     A flux barrier width W fb  between the first plurality of interior walls  912   a  of first flux barrier  910   a , a second plurality of interior walls  912   b  of second flux barrier  910   b , a third plurality of interior walls  912   c  of third flux barrier  910   c , and a fourth plurality of interior walls  912   d  of fourth flux barrier  910   d  may be selected by keeping the magnetizing reactance X ad  or open circuit voltage E i  unchanged. To avoid introduction of a vulnerability to saturation due to saliency, the rotor pole width should be increased by the same flux barrier width W fb  to keep the core volume the same as a base design. Each rotor pole width extends parallel to either first axis  1000  or second axis  1002 . For illustration, the rotor pole width of first flux barrier  910   a  is parallel to second axis  1002 ; whereas, the rotor pole width of second flux barrier  910   b  is parallel to first axis  1000 . Each of first flux barrier  910   a , second flux barrier  910   b , third flux barrier  910   c , and fourth flux barrier  910   d  extends from shaft  900  through a center of each pole body of the plurality of pole bodies  116  in a radial direction perpendicular to third axis  1004  and in an axial direction parallel to third axis  1004 . 
     Again, third rotor  104   b  may include a fewer or a greater number of the plurality of pole bodies  116 , where each pole body includes an identical flux barrier  910 . Each flux barrier  910  can be made of identical lamination pieces with flux barriers in the center of each rotor pole body  116 , or can be made of solid bars in the axial direction parallel to third axis  1004 . For example, solid bars may be preferable in large high speed generators. The dovetails may assist in stacking and holding laminations together with the flux barriers on shaft  900 . 
     The design parameter W fb  may be tuned by keeping the magnetizing reactance X ad  or open circuit voltage E i  unchanged. To avoid introducing a vulnerability to saturation due to saliency, the rotor pole span should be increased by the same flux barrier width W fb  to keep the core volume the same as a base design. Because
 
λ d   =L   ad   I   f   +L   d   I   d   =L   ad   I   f +( L   ad   +L   ls ) I   d   (8)
 
λ q   =L   q I q   (9)
 
the saliency can be evaluated for different W fb  widths by checking corresponding dq-axis flux plots. L ls , L ad , L d , and L q  are leakage, magnetizing, d-axis and q-axis inductance respectively. L ad , L d , and L q  can be converted to X ad , X d , and X q  easily with the same proportionality constant,
 
       FIG. 13  shows the q-axis flux distribution and flux lines of a single barrier design W fb =0.1 W r_pb , where W r_pb  is a width of each pole core  118  in an initial design. For example, W r_pb  is a width of each pole core  118  in second rotor  104 . A range of relative width values may be selected and performance evaluated to determine an “optimum” width value for flux barrier width W fb . For example, the range may be 3% to 10% of the width of each pole core  118  in second rotor  104 . When third rotor  104   b  is at a position where flux barrier  904  is aligned with a stator tooth, the q-axis flux lines close to the flux barrier tip form a zigzag leakage path. These flux lines find a low reluctance path even by passing through the air gap two more times, which limits the effective amount of flux lines going through the barrier structure. It can be expected that the leakage becomes worse as W fb  increases. 
       FIG. 14  shows a d-axis flux distribution and flux lines of the single barrier design W fb =0.1 W r_pb . The d-axis flux path is also changed to some extent, as less flux passes through the stator teeth when a tooth is directly aligned with flux barrier  910 . If W fb  continues to increase such that W fb  extends a length of the tooth face of the plurality of teeth  108  of stator  102 , the tooth may be short circuited, making the effective d-axis circumferential flux path on the stator side reduced by one tooth in a quarter model. The d-axis flux-linkage may become more prone to saturation and affect X ad  under a high current excitation, which should be avoided. Thus, W fb =0.1 W r_pb  may be defined as an upper boundary, and a reasonable lower boundary may be chosen as W fb =0.03 W r_pb . 
     A summary of two barrier width designs at the selected tuning boundaries: W fb =0.1 W r_pb  and W fb =0.03 W r_pb  are shown in  FIGS. 15-20 .  FIG. 15  shows the d-axis flux density distribution for a rotor pole centered between stator teeth using second salient pole WFSM  100   a  with W fb =0.1 W r_pb  ( 1500 ) and W fb =0.03 W r_pb ( 1502 ) in comparison to salient pole WFSM  100  ( 1504 ) in accordance with an illustrative embodiment. A large dip can be observed on the d-axis flux distribution at the air gap centerline, for W fb =0.1 W r_pb  due a flux partial short circuit. The phenomenon is less prominent for W fb =0.03 W r_pb . 
       FIG. 16  shows the d-axis flux density distribution for a rotor pole centered between stator slots using second salient pole WFSM  100   a  with W fb =0.1 W r_pb  ( 1600 ) and W fb =0.03 W r_pb  ( 1602 ) in comparison to salient pole WFSM  100  ( 1604 ) in accordance with an illustrative embodiment.  FIG. 17  shows the d-axis stator winding flux linkage using second salient pole WFSM  100   a  with W fb =0.1 W r_pb  ( 1700 ) and W fb =0.03 W r_pb  ( 1702 ) in comparison to salient pole WFSM  100  ( 1704 ) in accordance with an illustrative embodiment. 
       FIG. 18  shows the q-axis flux density distribution for a rotor pole centered between stator teeth using second salient pole WFSM  100   a  with W fb =0.1 W r_pb  ( 1800 ) and W fb =0.03 W r_pb  ( 1802 ) in comparison to salient pole WFSM  100  ( 1804 ) in accordance with an illustrative embodiment. The q-axis flux is effectively blocked at the same rotor position except for some leakage flux.  FIG. 19  shows the q-axis flux density distribution for a rotor pole centered between stator slots using second salient pole WFSM  100   a  with W fb =0.1 W r_pb  ( 1900 ) and W fb =0.03 W r_pb  ( 1902 ) in comparison to salient pole WFSM  100  ( 1904 ) in accordance with an illustrative embodiment.  FIG. 20  shows the q-axis stator winding flux linkage using second salient pole WFSM  100   a  with W fb =0.1 W r_pb ( 2000 ) and W fb =0.03 W r_pb  ( 2002 ) in comparison to salient pole WFSM  100  ( 2004 ) in accordance with an illustrative embodiment. 
       FIG. 21  shows the average output torque at rated operating condition using second salient pole WFSM  100   a  with W fb =0.1 and W r_pb  W fb =0.07 W r_pb , W fb =0.03 W r_pb  in comparison to salient pole WFSM  100  (conventional) in accordance with an illustrative embodiment. The average torque improvement becomes apparent as the stator current increases, from a 2.3% percent improvement at 1 pu current to a 15.8% percent improvement at 2.5 pu current for W fb =0.07 W r_pb . Additional torque improvement can be obtained because reluctance torque increases along with I s   2 . 
     The d-axis flux is well preserved when the flux barrier aligns with the stator slot with both width designs. However, a small dip in the center can be observed for design W fb =0.1 W r_pb . The q-axis flux at this rotor position is also effectively blocked as shown in  FIG. 19 . The flux leakage and short circuit phenomena caused by the barrier and stator slots can be quantitatively assessed by looking at the average stator flux-linkage over one electric cycle in  FIG. 17  and  FIG. 20  for d-axis and q-axis respectively. The differentiated slope of flux-linkage along the d-axis or q-axis at certain operating points is an indication of the corresponding inductance. The inhibiting effects of the flux barrier design on the q-axis is easy to capture. The larger W fb  design provides a smaller slope, which means a smaller q-axis inductance. The plots also suggest that the q-axis flux path saturation level is less prone to variations of current, as the flux barrier dominates the magnetic characteristics on this axis. However, though it is difficult to determine the difference between salient pole WFSM  100  and W fb =0.1 W r_pb  and W fb =0.03 W r_pb  for third rotor  104   b , the average d-axis flux-linkage value is most reduced for W fb =0.1 W r_pb . Saturation can be clearly observed as the current increases. 
     W fb =0.07 W r_pb  was determined to be an “optimum” flux barrier width by selecting a parameter to maintain for an existing salient pole WFSM design such as the rated torque at rated speed, and to improve the torque under over rated speed region (rotor field excitation would be reduced according to the speed). The effective core volume should be retained to maintain the magnetizing reactance or open circuit voltage. The design of flux barrier width W fb  may be done based on the choice of rotor pole body width and air gap length to control a magnetic short circuit and flux leakage. Sensitivity of the d-axis flux path saturation to current variation may be controlled with an optimum selection. A variety of widths are selected and evaluated to determine the optimum flux barrier width that maintains the selected performance parameter(s). 
     Within the voltage limit, total losses are reduced due to the fact that a reduced stator current may be used to produce the same amount of torque. For higher speed, total losses are further reduced. In particular, the eddy losses in stator  102  and third rotor  104   b , stator hysteresis loss and stator copper loss are reduced due to the fact that less stator current is needed to produce the required torque. Less current leads to a lower flux level in second salient pole WFSM  100   a , which is helpful in reducing iron losses at high speed. 
     Referring to  FIG. 22 , a back view of a portion of a fourth rotor  104   c  is shown in accordance with an illustrative embodiment. Fourth rotor  104   c  illustrates a MLB design that has a plurality of flux barriers positioned in a manner similar to first flux barrier  910   a . In the illustrative embodiment of  FIG. 22 , fourth rotor  104   c  includes six flux barriers distributed evenly across first pole body  116   a  though a fewer or a greater number of flux barriers may be used. The width of each flux barrier may be determined by determining W fb  for first flux barrier  910   a  of third rotor  104   b  and distributing that width evenly between each of the plurality of flux barriers based on the selected number of flux barrier. The flux barriers further extend across first core back face portion  306 , second core back face portion  308 , third core back face portion  310 , fourth core back face portion  312 , first core front face portion  918 , second core front face portion  920 , third core front face portion  922 , and fourth core front face portion  924 . 
     Referring to  FIG. 23 , a back view of a portion of a fifth rotor  104   d  of a third salient pole WFSM  100   b  (shown with reference to  FIGS. 25 and 26 ) with a plurality of axial flux barriers is shown in accordance with an illustrative embodiment. The plurality of axial flux barriers are shown in dark areas between the plurality of laminations that are stacked parallel to each other from first pole core right face  204   a  to first pole core left face  206   a  such that first pole core front face  202   a  and first pole core back face  300   a  are not solid, but are formed of a stack of laminations between which the plurality of axial flux barriers are formed. First core back face portion  306 , second core back face portion  308 , third core back face portion  310 , fourth core back face portion  312 , first core front face portion  918 , second core front face portion  920 , third core front face portion  922 , and fourth core front face portion  924  are further formed of a stack of laminations between which the plurality of axial flux barriers are formed. 
     Referring to  FIG. 24 , a perspective view of fifth rotor  104   d  is shown in accordance with an illustrative embodiment. Referring to  FIG. 26 , a front view of third salient pole WFSM  100   b  is shown in accordance with an illustrative embodiment. Referring to  FIG. 27 , a perspective view of third salient pole WFSM  100   b  is shown in accordance with an illustrative embodiment. 
     The width of each flux barrier may be determined by determining W fb  for first flux barrier  910   a  of third rotor  104   b  and distributing that width evenly between each of the plurality of flux barriers that are distributed equally across each pole core front face  202   a ,  202   d ,  202   c ,  202   d  and pole core back face  300   a ,  300   d ,  300   c ,  300   d.    
     As used herein, the term “mount” includes join, unite, connect, couple, associate, insert, hang, hold, affix, attach, fasten, bind, paste, secure, hinge, bolt, screw, rivet, solder, weld, glue, form over, form in, layer, mold, rest on, rest against, abut, and other like terms. The phrases “mounted on”, “mounted to”, and equivalent phrases indicate any interior or exterior portion of the element referenced. These phrases also encompass direct mounting (in which the referenced elements are in direct contact) and indirect mounting (in which the referenced elements are not in direct contact, but are connected through an intermediate element) unless specified otherwise. Elements referenced as mounted to each other herein may further be integrally formed together, for example, using a molding or thermoforming process as understood by a person of skill in the art. As a result, elements described herein as being mounted to each other need not be discrete structural elements unless specified otherwise. The elements may be mounted permanently, removably, or releasably unless specified otherwise. 
     Use of directional terms, such as top, bottom, right, left, front, back, upper, lower, horizontal, vertical, behind, etc. are merely intended to facilitate reference to the various surfaces of the described structures relative to the orientations introduced in the drawings and are not intended to be limiting in any manner unless otherwise indicated. 
     As used in this disclosure, the term “connect” includes join, unite, mount, couple, associate, insert, hang, hold, affix, attach, fasten, bind, paste, secure, bolt, screw, rivet, pin, nail, clasp, clamp, cement, fuse, solder, weld, glue, form over, slide together, layer, and other like terms. The phrases “connected on” and “connected to” include any interior or exterior portion of the element referenced. Elements referenced as connected to each other herein may further be integrally formed together. As a result, elements described herein as being connected to each other need not be discrete structural elements. The elements may be connected permanently, removably, or releasably. 
     The word “illustrative” is used herein to mean serving as an example, instance, or illustration. Any aspect or design described herein as “illustrative” is not necessarily to be construed as preferred or advantageous over other aspects or designs. Further, for the purposes of this disclosure and unless otherwise specified, “a” or “an” means “one or more”. Still further, using “and” or “or” in the detailed description is intended to include “and/or” unless specifically indicated otherwise. 
     The foregoing description of illustrative embodiments of the disclosed subject matter has been presented for purposes of illustration and of description. It is not intended to be exhaustive or to limit the disclosed subject matter to the precise form disclosed, and modifications and variations are possible in light of the above teachings or may be acquired from practice of the disclosed subject matter. The embodiments were chosen and described in order to explain the principles of the disclosed subject matter and as practical applications of the disclosed subject matter to enable one skilled in the art to utilize the disclosed subject matter in various embodiments and with various modifications as suited to the particular use contemplated. It is intended that the scope of the disclosed subject matter be defined by the claims appended hereto and their equivalents.