Patent Publication Number: US-8120223-B2

Title: Permanent magnet machine with offset pole spacing

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is a divisional of application Ser. No. 12/881,694, filed Sep. 14, 2010, which is a divisional of application Ser. No. 12/268,592, filed Nov. 11, 2008, both of which are incorporated by reference herein in their entirety. 
    
    
     BACKGROUND 
     1. Field 
     This disclosure relates to an interior permanent magnet machine having a rotor with multiple laminations in axially stacked relationship. 
     2. Background Discussion 
     An interior permanent magnet machine typically includes a stator with a ferrous metal core comprising stacked laminations, stator coil windings that carry excitation current and a rotor with circumferentially spaced permanent magnets on the rotor periphery that cooperate with circumferentially spaced stator poles. The stator poles are separated from the periphery of the rotor by a calibrated air gap. When the machine is acting as a motor, the coils are energized by an electrical current to provide rotor torque. The current has an alternating, multiple-phase waveform of sinusoidal shape. The interaction of an electromagnetic flux flow path created by the stator windings with the flux flow path created by the permanent magnets typically is accompanied by harmonic waveform components that induce motor torque fluctuations. Harmonic flux waveform components are created because the stator has windings contained in slots rather than in a uniform sinusoidal distribution along the inner circumference of the stator. The rotor flux also has harmonic flux because of discrete permanent magnet shapes and sizes. These features are manifested by a motor torque ripple, or torque oscillation, accompanied by vibration and noise. Further, operating efficiency of the motor is affected adversely. High order frequencies can be filtered out by the limited bandwidth of the mechanical system of a traction drive of a hybrid electric vehicle, but low frequencies will cause unacceptable oscillations. 
     The biggest components of the stator and rotor fluxes are called the fundamental components. In normal operation, both the stator and rotor fundamental fluxes rotate in the same direction and at the same speed, and the interaction between the stator and rotor fundamental fluxes generate rotor torque. The stator and rotor harmonic fluxes have different pole numbers, rotation speeds and directions. As a result, the interactions between rotor and stator harmonic fluxes generate torque fluctuation, which is called torque ripple. The torque ripple has different components with different frequencies. The order of a torque ripple component is defined as the ratio of the frequency of the torque ripple component to the speed of the rotor in revolution per second. 
     A conventional way to reduce motor torque ripple comprises skewing axially placed sections of the rotor ripple, one section with respect to the other. The rotor typically is connected drivably to a rotor shaft using a keyway and slot driving connection. In order to offset or skew a rotor section with respect to an adjacent section, the sections are relatively rotated, usually about one-half of the stator slot pitch. If it is assumed that the rotor is divided into a given number of axial sections (k), the sections are rotated with respect to adjacent sections by an angle equal to:
 
Skew angle ( k )=360/( k×N   s ) in mechanical degrees,
 
where N s  is the number of slots.
 
The maximum rotation between any two axial sections of the rotor is:
 
     Max relative skew angle (k)=(k−1)×360/(k×NN s ) in mechanical degrees. For example, in the case of a two section, 48 slot stator, a typical value of the skew angle is 3.75°. The skewing of the rotor is intended to produce a smoother mechanical torque than would otherwise be achieved using a straight rotor. This will eliminate certain undesirable oscillations or ripple of the torque caused by harmonics present in the air gap flux and in the air gap permeance. 
     For permanent magnet machines it is also common practice to skew the permanent magnets rather than the sections. However, the skewing method cannot eliminate all the torque ripple components because it cannot be designed to be effective to reduce all the torque ripple components. Another disadvantage of the skewing technique is that the average torque is also reduced, resulting in a de-rating with respect to the non-skewed design. Also, from a manufacturing perspective, skewing of either stator or rotor cores results in added complexity and cost. 
     SUMMARY 
     An objective of the invention is to minimize a so-called torque ripple with minimal reduction in average torque. This differs from the invention of copending application Ser. No. 11/839,928, filed Aug. 16, 2007 entitled “Permanent Magnet Machine,” which is assigned to the assignee of the present invention, in which an objective is to improve motor efficiency during operation in a motoring mode by using asymmetry in rotor design features of the motor while allowing an acceptable decrease in regenerative energy recovery during operation in a generating mode. 
     The present invention will break the symmetry of the rotor laminations, so that at a given instant the torque contributions of the multiple sections will be altered to reduce torque ripple. 
     In a first embodiment of the invention, torque ripple can be attenuated by using radial skewing. This is done by offsetting the magnetic axis of a rotor magnetic pole with respect to the axis of the adjacent rotor magnetic pole. 
     In a second embodiment of the invention, the rotor magnets are arranged in a “V” configuration. The shape of the torque ripple is a function of the shape of the “V” configuration. By using at least two different, properly designed “V” configurations in the laminations, the total machine ripple can be reduced in amplitude. 
     In a third embodiment of the invention, the laminations in a multiple section rotor are arranged in at least three rotor sections, which are relatively rotated in small increments, one section with respect to the other. This can be done by using at least two pairs of key slot positions. In this way, the axis of a magnetic pole of one section is displaced angularly with respect to the pole axis of the adjacent section. 
     In a fourth embodiment of the invention, pole arc angles for separate pairs of magnets are different (i.e., not equal), unlike a design in which the arc angles between magnets of each pair of magnets on the rotor periphery are the same. The rotor design of this embodiment will reduce the magnitude of the torque ripple while maintaining the average torque almost unchanged when compared to a conventional rotor. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1   a  is a plan view of a rotor lamination; 
         FIG. 1   b  is a side view of the rotor lamination; for the motor shown in  FIG. 1   a;    
         FIG. 2   a  is a diagrammatic view of a motor with a rotor comprised of multiple sections, each section being comprised of multiple laminations wherein flux lines are generated solely by the permanent magnet; 
         FIG. 2   b  is a view similar to the view of  FIG. 2   a  wherein the stator has energized windings with electrical current, but wherein the magnets are not included, the flux lines being generated solely by the stator windings; 
         FIG. 3  is a schematic representation of a prior art two-section rotor in which the sections are skewed, one with respect to the other, according to a known skewing technique; 
         FIG. 4  shows a symmetric lamination for a prior art eight pole rotor design for use in the electric motor rotor seen in  FIG. 3 ; 
         FIG. 5  shows a rotor lamination with a magnetic axis skewing arrangement in accordance with a first embodiment of the present invention; 
         FIG. 6  is a plot of rotor rotation angle in mechanical degrees versus motor torque in Newton meters showing the effect on motor instantaneous torque using the magnet arrangement of  FIG. 5 ; 
         FIG. 7  is a view of a skewing arrangement that may be used rather than the skewing arrangement of  FIG. 5 ; 
         FIG. 8  is an illustration of a magnet distribution that has a different separation between the interpolar axes compared to the interpolar axes separation of  FIGS. 5 and 7 ; 
         FIG. 9  is a plot of motor torque versus rotation angle in mechanical degrees for the rotor design illustrated in  FIG. 8 ; 
         FIG. 10  shows a rotor configuration of a permanent magnet motor together with some of the variables that can be used to manipulate the harmonic content of the motor torque; 
         FIG. 11  is a view of a portion of a laminated rotor with two angular positions of the magnets for adjacent rotor sections; 
         FIG. 12  shows a view of a laminated rotor in which adjacent magnets are arranged with a different angle theta at alternate rotor locations; 
         FIG. 13  is a schematic representation in three-dimensional form showing the axial alignment of the magnetic poles in a four pole structure; 
         FIG. 14  shows a skewing of rotor laminations of a permanent magnet rotor of the type shown in  FIG. 3 ; 
         FIG. 15  shows the effect of flipping a second section of a rotor with respect to a first section; 
         FIG. 16  is an illustration of a final skewing technique after adjacent sections of the rotor have been aligned along a key slot for the sections shown in  FIGS. 14 and 15 ; 
         FIG. 17  is an illustration of an embodiment of the invention wherein two key slots are placed relative to each other at approximately 90° to allow construction of a four-section rotor; 
         FIG. 18  is a view similar to  FIG. 17 , but which illustrates the first two sections of a four section rotor; 
         FIG. 19  is a combined view of the rotor sections of  FIGS. 17 and 18 ; 
         FIG. 20  is an illustration of the final assembly of the four sections of  FIGS. 17-19 ; 
         FIG. 21  is an enlarged view of the final assembly of the four sections seen in  FIG. 20 ; 
         FIG. 22  is a view similar to the views of  FIGS. 18-21  with key slots to improve balancing; 
         FIG. 23  is a final assembly view of the rotor laminations shown in  FIG. 22 ; 
         FIG. 24  is a view of a rotor design seen in  FIG. 23 , but which is provided with built-in keys instead of key slots; 
         FIG. 25  is a plot showing a reduction in torque ripple for a conventional skewed design for the present invention and for a rotor that is unskewed; and 
         FIGS. 26 ,  27  and  28  show examples of hybrid electric vehicle powertrain architectures capable of using the motor of the present invention. 
     
    
    
     PARTICULAR DESCRIPTION OF EMBODIMENTS OF THE INVENTION 
     For the purpose of describing typical operating environments for the permanent magnet machine of the invention, reference first will be made to  FIGS. 26 ,  27  and  28 , which respectively illustrate a power-split hybrid electric vehicle powertrain, a detailed power-split hybrid electric vehicle powertrain corresponding to the powertrain of  FIG. 26  and a series hybrid electric vehicle powertrain. In the case of the powertrain schematically illustrated in  FIG. 28 , an engine  10  is mechanically connected to a generator  12 , which in turn is electrically coupled to an electric motor  14 . Typically, the electrical coupling includes a DC link comprising an AC/DC inverter  16  and a DC/AC inverter  16 ′. A high-voltage traction battery  18  is coupled to the DC link through a DC/DC converter  20 . The motor is mechanically coupled to a geared transmission mechanism  22 , which may have multiple-ratio gearing or single-ratio gearing. 
     Traction wheels  24  are driven by torque output elements of the transmission mechanism. All of the mechanical energy of the engine, except for power losses, is transferred to the generator, which converts mechanical energy to electrical energy for driving the motor  14 . Any electrical energy not required to drive the motor is used to charge the battery  18 . When the vehicle is braking, all or part of the vehicle mechanical kinetic energy transferred from the transmission to the motor  14 , except for losses, is used to charge the battery as the motor  14  acts as a generator. 
     In contrast to the series arrangement of  FIG. 28 , the series-parallel arrangement of  FIG. 26  includes a direct mechanical connection between the engine and the transmission, as shown at  26 . The series-parallel gearing of the hybrid powertrain of  FIG. 26  is shown in more detail in  FIG. 27 . Components that are counterparts for components in the series arrangement of  FIG. 28  have been indicated by common reference numerals, although prime notations are added to the numerals in  FIGS. 26 and 27 . 
     The mechanical connection between the transmission  22 ′ and the engine  10 ′ includes a planetary gear system  26 . The planetary gear system, seen in  FIG. 27 , includes a ring gear  28 , which acts as a power output member for driving a power input element of the transmission mechanism  22 ′. A sun gear  30  is mechanically connected to generator  12 ′. The carrier for the planetary gear unit  26 , shown at  32 , is connected to the power output shaft or crankshaft of the engine  10 ′. As the engine delivers torque through the planetary gear unit  26 , to the transmission. The sun gear acts as a reaction element since it is mechanically connected to the generator. The load on the generator thus will determine the speed of the engine. During forward drive, torque of motor  14 ′ complements engine torque and provides a second power input to the transmission. During reverse drive, the torque direction of the motor  14 ′ is changed so that it will operate in a reverse direction. The engine is inactive at this time. 
     When the vehicle is in a braking mode, regenerative energy is delivered from the wheels through the transmission to the motor. The motor at this time acts as a generator to charge the battery. A portion of the regenerative energy is distributed through the transmission to the engine in a mechanical torque flow path, shown in part at  26 ′ in  FIG. 26 . In this respect, the regenerative energy flow path of the powertrain of  FIG. 26  differs from the energy flow path for the powertrain of  FIG. 28 , where no mechanical energy during regenerative braking is distributed to the engine. 
     The rotor and the stator for the disclosed embodiments of the invention may be comprised of ferrous alloy laminations. A rotor and stator construction of this type is shown in the partial radial cross-sectional view of  FIG. 1   b . A stator lamination is shown at  36  in  FIGS. 2   a  and  2   b , and a rotor lamination is shown at  38 . A small air gap  40 , seen in  FIGS. 1   c  and  2 , is located between the inner periphery of the stator laminations  36  and the outer periphery of the rotor laminations  38 . Radially extending openings  37  are formed in the stator laminations and symmetrically positioned magnet openings  42  are formed near the outer periphery of each rotor lamination  38 . Each magnet opening receives a magnet  44 . Any number of laminations in a given design may be used, depending on design choice. The laminations are arranged in a stack. Multiple stacks (e.g., one, two or three) may be used. 
       FIG. 1   a  and  FIG. 1   b  illustrate a rotor section construction with multiple laminations arranged in stacked relationship. The magnet openings are shown in  FIG. 1   a , but this figure omits an illustration of the magnets. 
     The center of the rotor laminations has a circular central opening  60  for accommodating a driveshaft with a keyway that may receive a drive key  62 . 
     The openings  42  are symmetrically disposed with respect to adjacent pairs of magnet openings  42 , one of the axes of symmetry being shown in  FIG. 1   a.    
       FIG. 2   a  is a partial view of a rotor lamination  38 . The stator  36  has stator windings in the openings  37 , but they are not illustrated in  FIG. 2   a  because it is assumed that in the case of  FIG. 2   a , the stator windings do not carry electrical current. The stator windings with current, however, are shown in  FIG. 2   b.    
     A magnetic rotor flux flow path is shown at  65  in  FIG. 2   a . A magnetic stator flux flow path is shown at  65  and  66  in  FIG. 2   b . The rotor flux and the stator flux interact, as shown in part at  68 , to develop rotor torque in known fashion. 
     A known way to reduce motor torque ripple is to skew the sections of the rotor, one with respect to the other, by offsetting one half of the rotor lamination stack with respect to the other half. This is seen in  FIG. 3 , where the X-axis  90  for rotor section  92  is skewed relative to the Y-axis shown at  94  for an adjacent rotor section  96 . The amount of rotation of one section relative to the other is usually one half of the stator key or slot pitch. This is expressed as follows:
 
skew angle=180 °/N   s  in mechanical degrees,
 
     where N s  is the number of slots. 
     Magnet openings in rotor section  92  are shown at  98 . The magnet openings are evenly spaced in the case of the rotor of  FIG. 3 . Magnet openings similar to openings  98  are located in rotor section  96 . The rotor spacing about the Z-axis  102  in  FIG. 3  is uniform. Reference may be made to U.S. Pat. No. 7,170,209 for an illustration of a motor rotor with skewed rotor sections. 
     Magnet openings in the rotors of the embodiments of the invention that are disclosed need not be shaped as shown in the figures of the drawings. The shape of the magnet openings is a design choice. 
       FIG. 4  shows a plan view of a typical lamination for the sections illustrated in  FIG. 3 . As in the case of  FIG. 2 , rotor sections having laminations of the type shown in  FIG. 4  may include a key-and-slot connection with a rotor driveshaft, although the key-and-slot connection is not shown in  FIG. 4 . 
     The rotor design having sections, as illustrated in  FIG. 4 , is divided into a generic number of axial sections K, each section being rotated with respect to an adjacent section by an angle equal to: 
     skew angle(k)=360/(k*N s ) in mechanical degrees, 
     where N s  is the number of slots, 
     The maximum rotation between any two axial sections of the rotor is:
 
max relative skew angle( k )=( k− 1)*360/( k*N   s ) in mechanical degrees.
 
     The magnet poles are located as shown in  FIG. 4 . The angle between the magnetic axes of adjacent poles is 45° for an eight pole design. The angle between the magnetic axes and the interpolar axes is one half of the angle between the magnetic axes of adjacent poles for an eight pole design. 
     The disclosed embodiments of the invention have eight magnetic poles, but the scope of the invention is not limited to the use of eight magnetic poles. The number of poles used is a matter of design choice. 
     A first embodiment of the invention is shown in  FIG. 5 , where a rotor lamination has poles that are radially skewed. The skewing is realized within each lamination itself by offsetting the magnetic axis of a magnet pole with respect to an adjacent pole. 
     Manufacture of the rotor is simplified by the absence of several steps usually needed to create multiple, axially-stacked rotor sections. This manufacturing method is especially valuable in the case of an integrated starter-generator type motor, where the stacked length of the sections is normally short and the known skewing method described with reference to  FIG. 3  is not feasible. The embodiment of the invention, however, is not limited to short stack motors and generators, but it can be applied to any permanent magnet machine. It can exceed the performance of an electric machine with known skewing and it may be made using simpler manufacturing processes. The performance improvement is due to a further reduction of the torque ripple previously described. Further, the embodiment of the invention of  FIG. 5  is not limited by the number of axial segments in the rotor design. It has as many pole-spacing possibilities as the number of rotor poles. 
     In the design of  FIG. 5 , the spacing between the axis of symmetry of two adjacent magnets is not constant. It can be either one of two values:
         i.e., Alpha 1 =360/poles+skew angle; or
           Alpha 2 =360/poles−skew angle.   
               

     For an eight pole, 48-slot motor and a skew angle of 3.75°, Alpha 1  and Alpha 2  are 48.75 and 41.25 mechanical degrees, respectively. Other values of skew angle can be chosen according to design choice. The effect of this magnet arrangement on the motor torque for a typical inner permanent magnet machine is shown in  FIG. 6 . A typical rotor torque ripple plot for a non-skewed rotor is shown at  110  in  FIG. 6  and a corresponding rotor torque ripple plot for a skewed rotor, according to the invention, is shown at  112 . The amplitude of the ripple of plot  112  is significantly lower than the amplitude of plot  110 . 
     This rotor design is also suitable for other arrangements for the rotor poles, such as the one shown in  FIG. 7 , where poles  1 - 8  are separated by an angle alpha=45+skew angle/7, and poles  8  and  1  are separated by angle beta=45−skew angle. In contrast, for the design shown in  FIG. 5 , the skew angle is arbitrarily set to be equal to 3.5°, alpha=45.5° and beta=41.5°. 
     An effect on torque ripple, similar to the effect on torque ripple for the design of  FIG. 5 , can be obtained by the distribution pattern for the magnets seen in  FIG. 8 . In  FIG. 8 , for any given pole, the offset with respect to the original magnetic axis remains the same as the one shown in  FIG. 7  (i.e., pole number  2  has a magnetic axis that is displaced 22.00° from one interpolar axis and 23° from the adjacent interpolar axis), but pole number  3  has taken the place of pole number  8 , and pole number  4  has been moved to the location of pole number  3 , etc. This distribution has a more uniform spacing between the poles than in the case of the design of  FIG. 7 . 
     A plot of the motor torque versus rotation angle for the design of  FIG. 8  is seen in  FIG. 9 . The torque ripple seen in  FIG. 9  is identified by numeral  106 . For purposes of comparison, the torque ripple for a rotor having sections using the known design with no skew is shown at  108 . 
     A plot of motor torque versus rotation angle for the design of  FIG. 5 , as previously mentioned, is seen in  FIG. 6  where a conventional design with no skew is plotted at  110  and the plot corresponding to the design of  FIG. 5  is shown at  112 . The amplitude of the ripple seen at  106  in  FIG. 9  has a lower amplitude than the amplitude seen at  112  in  FIG. 6  for the design of  FIG. 5 . 
     The invention is not limited to the use of flat magnets. It may have “V” shape magnets or other shapes. 
       FIG. 10  shows a magnet configuration in which the rotor magnets, seen at  114  and  116 , are arranged in a “V” shape. In the case of the design of  FIG. 10 , the shape and the amplitude of the torque ripple is a function of the shape and amplitude of the angle theta between the magnets  114  and  116 . Parameters that affect this shape and the magnitude of each are identified in  FIG. 10 , where the width of each magnet may be 19.25 mm and the distance between a point of engagement of the magnets  114  and  116  and the air gap may be 10.75 mm. The specific parameters, of course, can be different than those illustrated in  FIG. 10 . 
       FIG. 11  shows how the angle theta is adjusted to obtain smoother torque production. Although the average values for the torque will not be greatly affected, the harmonic components of the torque can be manipulated by properly designing the different “V” shapes. For purposes of illustration, magnets  118  and  120  for laminations of one section are shown overlapped with respect to magnets for laminations of an adjacent section. Magnets  118  and  120  for one section are separated by an angle theta 1 , whereas the angle for an adjacent section is theta 2 . Further, the shape, length and width of magnets of one section may differ from the shape, length and width of magnets of another section. 
     In addition to the implementation of the invention seen in  FIG. 11 , the multiple magnetic poles on the rotor can be designed with at least two different arrangements. For example, the eight pole rotor of  FIG. 12  may have poles  1 ,  3 ,  5 , and  7  of laminations of one section arranged according to the design of  FIG. 11 , in which the angle is theta 1 , and the other four poles may have a design in which the angle is theta 2 . Further, to avoid low frequency torque oscillations, the rotor can be divided into two axial segments for the design shown in  FIG. 11 , which are rotated with respect to each other, so that poles  1 ,  3 ,  5  and  7  of one section of the rotor are aligned with poles  2 ,  4 ,  6  and  8  of an adjacent section. This arrangement is shown in  FIG. 13 , where the magnetic axis of a set of poles A for one section is aligned with the axis of a set of magnetic poles B for an adjacent section. 
     The concept illustrated in  FIG. 13  can be extended to include rotor configurations that are different from the “V” shaped configuration seen in  FIGS. 11 and 12 . For example, pole type A in  FIG. 13  could include “V” shaped magnets and pole type B could be flat or surface mounted magnets, as in the case of  FIGS. 5 ,  7  and  8 . The torque harmonics can be manipulated in this fashion to create an attenuated total torque ripple. Further, more than two types of magnet configurations can be used, and variations can be made in the proximity of the magnets to the air gap to manipulate torque harmonics. 
     A third embodiment of the invention makes it possible to form the laminations of multiple axial sections in a manufacturing process using a single rotor lamination stamping die in order to avoid multiple lamination types in the same rotor. 
       FIG. 14  shows a skewing arrangement for a permanent magnet motor using a single lamination type where the first section of the rotor is assembled by stacking half of the rotor laminations and inserting the magnets in their magnet openings. The laminations have a key slot  124 , where key slot axis  130  is rotated with respect to the nearest pole axis  126  by a certain angle. To create the second section of the rotor, the rest of the laminations are flipped around axis  130 , as shown in  FIGS. 14 and 15 . Because of the flip, the pole axis shown at  126  in  FIG. 14  becomes pole axis  128  in  FIG. 15  and is rotated by Gamma with respect to axis  130  in the counter-clockwise direction. The optimum angle would be determined based on the harmonic content of the air gap flux and the air gap permeance. When the two rotor sections are aligned using the key slot as the common aligning device, the pole axes of the two rotor sections are displaced by 2×Gamma with respect to each other. 
     Performance of the rotor shown in  FIG. 16  can be improved to approximate a continuous skewing effect by increasing the number of rotor sections and rotating them in smaller incremental steps. The present invention is aimed at accomplishing this task using a single lamination die. This is illustrated in  FIG. 17 , which shows laminations with a first key slot at  132  and a second key slot at  134 . The key axis for slot  132  is shown at  136 , and the key axis for slot  134  is shown at  138 . 
     The first section of the rotor is obtained by axial stacking one quarter of the rotor laminations and then aligning them along the first key slot. The second section is similarly made by flipping the laminations and stacking them, as in the design of  FIGS. 14-16 . This will result in the partial assembly shown in  FIG. 18 , which illustrates the first two stages of a four section rotor. The angle formed by  136  (Gamma 1 ) and the nearest pole axis  142  is different from the angle  138  (Gamma 2 ) and the nearest pole axis  144 . The magnetic axes shown at  140  and  142  in  FIG. 18  in one example of the invention are separated by 2×Gamma 1 . The key slot axis is shown at  136  for the slot  132 . 
     The included angle created by the intersection of axes  136  and  138  for key slots  132  and  134 , respectively, may be referred to as angle Delta, expressed as:
 
Delta= N* 360 /P+ 2Gamma1,
 
where P is the number of poles, and N is any number in the number set of 1, 2, 3, . . . P−1.
 
     In  FIG. 19 , the third section of the rotor assembly for the third embodiment of the invention is created from the non-flipped laminations, as in the case of the first section, but it is rotated to the angle Delta clockwise so that it is aligned with the first two sections using the second key slot  134 . In  FIG. 19 , numeral  154  designates the key slot axis. The third section in the design of  FIG. 19  is offset by theta 2 −theta 1  from the first section.  FIG. 20  shows the final assembly of all four sections. 
       FIG. 21  is an enlargement of a portion of the four sections illustrated in  FIG. 20 . It shows the axis of the magnetic poles of the different sections relative to the key slot axes. 
     The fourth section of  FIGS. 20 and 21  is created from flipped laminations, which are rotated counter-clockwise by the angle delta and aligned on the second key slot. The resulting structure shown in  FIGS. 20 and 21  has four sections, which have the following rotations with respect to the shaft key: The first is shown at  158 , which is rotated theta 1  in a counter-clockwise direction; the second section shown at  160  is rotated theta 1  in a clockwise direction; the third section shown at  162  is rotated theta 2  in a counter-clockwise direction; and the fourth section shown at  164  is rotated theta 2  in a clockwise direction. The key slot axis is shown at  166 . 
     It is possible with this embodiment of the invention to arrange the laminations so that the second key slot is aligned with the magnet axis. In this case, the third and fourth rotor sections will have zero rotation and a balanced symmetrical three section rotor thus becomes possible. 
     Rotor balancing can be improved in the design of the third embodiment with the adoption of a second set of key slots placed at 180° from the other two, as illustrated in  FIG. 22 , where key slots  168  and  170  are spaced 180°, respectively, from key slots  172  and  174 . Following the procedure described previously with respect to  FIG. 21 , the resulting design is illustrated in  FIG. 23  where two keys are used to secure the rotor to the rotor shaft to achieve improved rotor balance. This is seen at  176  and  178  in  FIG. 23 . 
     It is possible in the case of the configuration according to the third embodiment of the invention to use a pole number count other than a pole count of eight. A four pole rotor can be treated in the same way as a rotor with a pole count of eight poles. Also, the assembly technique can be applied to rotors that do not use a key slot, but rather use a tab or other alignment device, such as a cleat. Further, built-in keys can be used as illustrated in  FIG. 24 . In the case of the design of  FIG. 24 , the rotor shaft will have two key slots  180  and  182  that are as wide as the keys, and two larger key slots  184  and  186  that accommodate a misalignment of the keys, shown at  188  and  190 , respectively. 
       FIG. 25  is a plot of torque ripple obtained by the embodiments of the invention using a finite element simulation technique. A conventional method of skewing will result in a ripple plot as shown at  192 . A plot using three lamination sections according to the present invention is shown at  194 . For purposes of comparison, an unskewed rotor plot is shown at  196 . 
     Although embodiments of the invention have been disclosed, it will be apparent to persons skilled in the art that modifications may be made without departing from the scope of the invention.