Patent Publication Number: US-2006012263-A1

Title: Axial field electric machine

Description:
RELATED APPLICATIONS  
      The present application is a continuation-in-part of U.S. application Ser. No. 08/763,824, the disclosure of which is hereby incorporated by reference in its entirety. 
    
    
     BACKGROUND OF THE INVENTION  
      1. Field of the Invention  
      The present invention relates generally to electric machines or motor/generators and, more specifically, to permanent magnet, axial field electric machines.  
      2. Description of the Related Art  
      An electric motor/generator, referred to in the art as an electric machine, is a device that converts electrical energy to mechanical energy and/or mechanical energy to electrical energy. Since electric machines appear more commonly as motors the ensuing discussion often assumes that electric energy is being converted to mechanical energy. However, those knowledgeable in the art recognize that the description below applies equally well to both motors and generators.  
      Electric machines generally operate based on Faraday&#39;s law, which can be written as e=BLv, and the Lorentz force equation, which is often written as F=BLi. In electric machines that utilize rotational motion, these equations can be written as e=k 1 BLω and T=k 2 BLi respectively. Faraday&#39;s law describes the speed voltage or back EMF (electromotive force), e, that appears across motor conductors due to the geometrically orthogonal interaction of a magnetic field having flux density B with conductors of length L traveling at a rotational speed ω. The Lorentz force equation describes the torque T generated by the geometrically orthogonal interaction of a magnetic field having flux density, B, with conductors of length L carrying current i. The coefficients k 1  and k 2  are constants that are a function of motor geometry, material properties, and design parameters.  
      A variety of electric machine types exist in the art based on how they generate the magnetic field and on how they control the flow of electrical energy in the conductors exposed to the magnetic field. The present invention pertains to electric machines where the magnetic field B is primarily generated by permanent magnets affixed to the rotating assembly, or rotor of the machine; whereas the conductors are affixed to the stationary assembly, or stator of the machine and electronic circuitry is used to control the flow of electrical energy. In the art this type of machine is commonly called a brushless DC motor or a brushless permanent magnet machine. In addition, such electric machines can be modified to use induction to generate the magnetic field. In this case the machine is commonly called an induction motor.  
      Electric machines that produce rotational motion are classified as either radial field or axial field. Radial field machines have a radially directed magnetic field interacting with axially directed conductors, leading to rotational motion. On the other hand, axial field machines have an axially directed magnetic field interacting with radially directed conductors, leading to rotational motion. Of these two machine topologies, the axial field machine appears much less often. In the art, axial field machines are most often found in applications where: (i) there is insufficient axial length to accommodate a radial field machine, (ii) relatively little torque is needed, and (iii) motor energy conversion efficiency is not a primary concern. The reasons why axial field machines generally appear less often than radial field machines include: (a) more familiarity with radial field machines, (b) the desire to minimize cost by reusing existing radial field machine tooling, and (c) the lack of market incentive to address manufacturing issues unique to axial field machines.  
      In terms of quantity produced, the spindle motor in computer floppy disk drives is the most commonly appearing axial field electric machine. In this application minimizing cost is the most critical design goal. As a result, this motor does not utilize materials, design steps, or construction techniques that lead to high efficiency over a broad range of speeds, high motor constant, or high power density. The floppy disk spindle motor uses an axial field topology solely because there is insufficient axial space available inside the floppy disk housing to use a radial field motor. This motor is typically manufactured with one rotor element and one stator element, with the stator element being constructed from a steel-backed printed circuit board upon which the stator windings and motor electric drive circuitry are connected.  
      The present invention discloses design aspects for axial field machines that offer greater performance than common axial field machines and performance that meets, exceeds, or is competitive with radial field machines. Performance in this case includes the measures of: (i) energy conversion efficiency, (ii) motor constant, (iii) gravimetric power density, (iv) volumetric power density, (v) manufacturing cost, and (vi) construction flexibility due to modular construction.  
      Energy conversion efficiency describes how well an electric machine converts energy. For a motor, efficiency can be written as 
 
η=(Power Out)/(Power In)=( T ω)/( Tω+P   r   +P   c   +P   m )  (Eq. 1) 
 
 where T is torque, ω is rotational speed, P r  is resistive loss i.e., the so called I 2 R loss, which represents power converted to heat by the resistance of the current carrying conductors in the motor, P c  is the core loss, which represents power converted to heat due to hysteresis and eddy current losses in the conductive and magnetic materials used in the motor, and P m  is the mechanical loss, which includes bearing loss, windage, etc. Core and mechanical losses generally increase with the square of speed, so efficiency typically increases from zero at zero speed, to some peak value at some rated speed, then decreases beyond that rated speed. For constant speed applications, achieving high peak efficiency at a constant rated speed is all that is important. For variable speed applications, however, it is important to maximize the range of speeds over which maximum efficiency can be achieved. As defined in Eq. 1, efficiency is unitless and is often expressed as a percentage, where 100% efficiency reflects the ideal electric machine. 
 
      Referring to  FIG. 30 , a graph is presented showing the efficiency of a typical electric machine known in the art at various speeds and torque. The operation of the electric machine is bounded by a peak speed, a peak torque, and a maximum power output. In this example, the electric machine has a peak efficiency of 90% at a particular operating point (i.e., at a particular rated speed and torque). At other operating points, however, the efficiency drops off precipitously as indicated by the contours of constant efficiency. In a traction application, for example, when the electric machine is operated at different operating points on the graph, the average efficiency will be much lower than peak efficiency.  
      In servomotor applications where a motor does not turn continuously but rather starts and stops frequently, efficiency is not a good measure of motor performance because efficiency is zero at zero speed, i.e., ω=0. Under these conditions, the ability to produce torque with minimum losses is important. In the art the term motor constant describes the motor characteristic. Motor constant can be written and simplified as  
               K   m     =       T       P   r         =           K   T     ⁢   I           I   2     ⁢   R         =       K   T       R                   (     Eq   .           ⁢   2     )             
 
 where K T  is the motor torque constant, I is the net motor current, and R is the net motor resistance. Core loss and mechanical loss are not included in the motor constant because these losses are zero at zero speed. The square root of P r  is used in Eq. 2 because it makes the motor constant independent of current, which makes it independent of any motor load and makes it easier to compare the performance of different motors. Based on Eq. 1 and Eq. 2, it is clear that a motor exhibiting high efficiency will generally exhibit a high motor constant. Likewise, if a motor exhibits minimal core loss and mechanical loss, a motor having a high motor constant will also exhibit high efficiency. 
 
      Gravimetric and volumetric power density are defined as the ratio of output power, e.g., Tω for a motor, to the mass and volume of the machine, respectively. As such, gravimetric power density is often specified in terms of watts per pound, horsepower per pound, or kilowatts per kilogram. Likewise, volumetric power density is often specified in terms of watts per cubic inch or kilowatts per cubic meter. In most cases, there is a high degree of correlation between these two measures of power density. That is, given that electric machines are generally constructed from the same types of materials, their mass is directly proportional to their volume, thus a motor having a high gravimetric power density, will also exhibit a high volumetric power density. Given this correlation, it is common to use the term power density to mean either gravimetric or volumetric power density or both. In any case, since output power is the product of torque and speed, power density increases linearly with speed to the point where it is no longer possible to maintain torque production, at which point power density decreases. In addition, given that torque is generally proportional to current as shown in Eq. 2, the ability to produce torque is only limited by the ability to remove the heat created by the resulting I 2 R loss P r  and the speed dependent losses P c  and P m , which decrease efficiency. As a result, power density is generally proportional to efficiency because more power can be safely produced in a more efficient motor. For example, a highly efficient motor generates less heat for a given torque output than a less efficient motor, which in turn implies that the more highly efficient motor can generate more torque and therefore have higher power density, while generating the same amount of heat as the less efficient motor.  
      In the art, electric machines of varying outputs generally require significant unique tooling for each voltage and torque level. For a given diameter it is typical to specify a number of rotor and stator lengths, with similar but different parts and tooling required for each rotor and stator. For example, in a brushless DC motor each stator may be made from the same stator laminations stacked to various lengths, but the windings are unique for every length as well as for every voltage level at any fixed length. As a result, additional cost is incurred in traditional motors due to the additional capital expense and inventory required to support a family of motors at a given diameter.  
      In view of the above, there is a need for an improved axial field-electric machine that provides a high efficiency over a wide variety of speeds and torque and a high gravimetric and volumetric power density over a wide range of speeds and torque. There is also a need for an improved axial field electric machine that allows for easy modification of the rotor and/or stator to increase or decrease the power output of the electric machine.  
     SUMMARY OF THE INVENTION  
      These and other needs are satisfied by the axial field electric machine of the present invention. Based on the above discussion, the present invention discloses design aspects for an axial field electric machine that maximize efficiency, motor constant, power density, as well as offer the benefits of modular construction, and the potential for reduced cost. Efficiency and motor constant are maximized by maximizing the production of torque while incurring minimal losses. In particular, one aspect of the invention eliminates all ferromagnetic material that incurs core loss, thereby essentially eliminating P c  from Eq. 1, above (although eddy current losses in the conductors must be considered). Doing so increases peak efficiency, broadens the range of speeds over which efficiency is high, and increases power density by eliminating the high mass associated with the added stationary ferromagnetic material. In addition, other aspects of the invention minimizes P r , which maximize motor constant and maximizes the peak efficiency. Power density is maximized further according to an embodiment of the present invention by optimum selection of the amount of permanent magnet material relative to stator volume. Modular construction allows a whole family of motors at varying power levels to be constructed by stacking sets of identical rotor components and stator components axially within the same motor. Since each rotor and stator is identical, no duplication of capital cost is incurred to produce a whole family of motors. In addition, other aspects of the invention make it possible to select a variety of voltage levels by simply changing the way individual stators are connected, thereby minimizing the inventory required to support a whole family of motors. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       FIG. 1  is a pictorial view of an exemplary axial field electric machine of the present invention;  
       FIG. 2  is an enlarged sectional view taken on line  2 - 2  of  FIG. 1 ;  
       FIG. 3  is a sectional view taken on line  3 - 3  of  FIG. 2 ;  
       FIG. 4  is a face view of a magnetic element of the axial field electric machine, showing the polarization of the magnet;  
       FIG. 5  is a side elevation view of a magnetic element;  
       FIG. 6  is a graphical illustration of the magnetic flux emanating from a magnetic element;  
       FIG. 7  is a plot showing the demagnetization characteristics of permanent magnets and the operating point of a magnet when used in an electric machine constructed according to the present invention;  
       FIG. 8  is a block diagram showing an air conditioner unit including an axial field electric machine constructed according to an embodiment of the present invention.  
       FIG. 9  is a pictorial view of a shaft for use in the axial field electric machine of the present invention;  
       FIG. 10  is a pictorial view of a hub that can be mounted to the shaft of  FIG. 9 ;  
       FIG. 11  is a pictorial view of a conductor element of the axial field electric machine;  
       FIG. 12  is a cross-sectional view of an axial field electric machine constructed according to an embodiment of the present invention;  
       FIG. 13  is a schematic diagram of the conductor element winding arrangement of  FIG. 11 ;  
       FIG. 14  is a pictorial view of an alternative conductor element winding arrangement having single-turn, rectangular cross-section conductors;  
       FIG. 15  is a flux diagram for a plurality of magnetic elements;  
       FIGS. 16   a - f  are views of a plurality of subassemblies in an alternative conductor element;  
       FIG. 17  is a top plan view of another subassembly in an alternative conductor element illustrating both sides of the subassembly;  
       FIG. 18  is a sectional view taken along line  18 - 18  of  FIG. 17 , showing multiple subassemblies;  
       FIG. 19  is a sectional view taken along line  19 - 19  of  FIG. 17 ;  
       FIG. 20  is a partial top plan view similar to  FIG. 17 , but showing the portion of the conductor element winding arrangement relating to 12 phases of windings of one of the subassemblies;  
       FIG. 21  is a block diagram of a motor controller;  
       FIG. 22  is a timing diagram of the motor signals generated by the motor controller of  FIG. 21 ;  
       FIG. 23  is a schematic diagram of the conductor elements connected to one another in a configuration selected to operate the axial field electric machine at a first voltage;  
       FIG. 24  is a schematic diagram of the conductor elements connected to one another in a configuration selected to operate the axial field electric machine at a second voltage;  
       FIG. 25  is a schematic diagram of the conductor elements connected in a configuration selected to operate the axial field electric machine at a third voltage;  
       FIG. 26  is, in part, a front elevation view of a vehicle having the axial field electric machine disposed within a wheel and, in part, a cross-sectional detail view of an alternative embodiment of the axial, field electric machine suitable for installation within the wheel.  
       FIG. 27  is a plan view of a frame used for a conductor element in an axial field electric machine constructed according to an embodiment of the present invention.  
       FIG. 28  is a view of a connector support element for an axial field electric machine constructed according to an embodiment of the present invention.  
       FIG. 29  is a view of a partially completed axial field electric machine constructed according to an embodiment of the present invention.  
       FIG. 30  is a graph depicting contours of constant efficiency for a typical electric machine known in the art.  
       FIG. 31  is a graph depicting contours of constant efficiency for an electric machine constructed according to an embodiment of the present invention. 
    
    
     DETAILED DESCRIPTION  
      With reference to the drawing figures, a number of embodiments of the present invention are shown that maximize peak efficiency, efficiency over a broad range of speeds, motor constant, and power density. Also with reference to the drawing figures, an axial field electric machine according to embodiments of the present invention will be described that has a modular design that allows for cost effective creation of an entire family of machines for varying applications.  
      Conductor Element  
      As used herein, the term conductor element refers to an element of the axial field electric machine that provides conductors that traverse the magnetic flux generated by an adjacent magnet or magnetic element. In a motor application, the conductors in the conductor element carry electric current in response to a motor controller, and in a generator application, electric voltage is induced across the conductors by the magnet or magnetic element. In the examples given below, the stator of the axial field electric machine includes one or more conductor elements. One skilled in the art will recognize that in an alternative embodiment, the conductor elements could also from the rotor of the axial field electric machine, in which case magnetic elements form the stator of the electric machine.  
      To achieve a high power density, each conductor element is designed so as to maximize the amount of conductive material (e.g., as conductor phases) that traverses the magnetic flux from adjacent magnets or magnetic elements. Conductive material that does not traverse this magnetic flux contributes to the mass and losses of the machine and thereby reduces the efficiency and power density of the machine. To achieve a modular design, it is advantageous if each conductor element is similar in construction.  
      A first embodiment of a conductor element is shown in  FIG. 14 . In this embodiment, the conductor element  121  includes four phase windings  122 ,  124 ,  126 , and  128 , each having a dielectric coating or the like to electrically insulate one phase winding from the other. Each conductor in the phase winding has a generally rectangular cross-sectional shape with a generally constant axial thickness and a width that tapers linearly with the radius of the conductor element. As shown in  FIG. 14 , each phase winding starts at a first terminal point (e.g., first terminal point  126   a  of phase winding  126 ) at the outer periphery of the conductor element  121 , extends in a radial direction as a radial conductor section  126   c  towards the center of the conductor element, extends in an arcuate path at the center (not visible) and extends away from the center as a radial conductor section  126   d  to the outer periphery of the conductor element to form a loop. Each phase winding may include a number of loops around the conductor element. In this example, phase winding  126  includes four such loops and eight radial conductor sections  126   c - 126   j  between first terminal point  126   a  and a second terminal point  126   b  distributed uniformly around the conductor element. The radial conductor sections are connected at the center and periphery by arcuate sections such as outer arcuate section  126   k  and inner arcuate section  126   m.    
      The current path in conductor element  121  of  FIG. 14  is shown in  FIG. 13 . Phase winding  126 , for example is shown as extending between a point labeled φ 3 − and φ 3 + and crosses between the periphery of conductor element  121  and an inner portion of the element eight times.  
      Returning to  FIG. 14 , in this example, each radial section of a conductor winding is offset from another radial section in the same phase winding by radial sections of each of the other phase windings. In other words, radial section  126   c  and radial section  126   d  are offset from each other by a radial section from each of phase windings  122 ,  124 , and  128 . The phase windings define a generally planar or wheel-like structure, with a total of 32 radial sections arranged in a spoke-like manner. In this example, conductive sockets  42  are provided at the terminal points for electrically coupling one conductor element to another.  
      As will be described in further detail below, conductor element  12 . 1  is adapted to be placed axially adjacent to a magnetic element such as a magnetic disk with sector shaped poles. The relationship of one of these poles to conductor element  121  is shown in  FIG. 13  in a dashed outline form as element  100 . To maximize the amount of conductive material in the conductor phases adjacent to the magnetic poles, each radial section is tapered or wedge-shaped, i.e., their widths decrease in a radially inward direction, thereby allowing them to be packed closely together in the spoke-like arrangement. Phase windings  122 ,  124 ,  126  and  128  are made of metal, preferably cast or otherwise formed into the illustrated winding shape, but it may also be suitable to form dielectric coated rectangular tapered metal wire into the illustrated winding shape to reduce eddy currents in the conductors. Packing conductors  122 ,  124 ,  126  and  128  closely together maximizes the amount of their conductive material that passes through the flux. The ratio between the volume of conductive material that passes through the magnetic flux and the volume of the entire conductor element that passes through the flux is known as the “fill factor.” The fill factor for the stator shown in  FIG. 14  is generally greater than 80 percent and is typically between 60% and 90%. Increasing the fill factor maximizes the efficiency and motor constant as given in Eqs. 1 and 2 above by minimizing the resistance R of the conductive material. Power density is also improved by maximizing the fill factor even though the conductive material adds mass to the machine because the added conductive material promotes torque production.  
      In an alternative embodiment of the stator, each conductor element comprises one or more subassemblies, each formed, for example, of printed circuit material that has been suitably etched to form the conductor pattern and electrical interconnections between subassemblies described below. The printed circuit material and etching process may be any such material and process known in the art that is commonly used to manufacture printed circuit boards or flexible printed circuits in the electronics industry. The subassemblies can be bonded together or otherwise attached to one another. The resulting multiple-layer printed circuit conductor element functions in the same manner as conductor element  121  in  FIGS. 13 and 14 , described above. In that regard, this alternative conductor element may have any suitable number of conductor windings and conductor phases. The alternative stator assembly may have a thickness as small as about 0.1 inches, thereby facilitating the construction of smaller axial field electric machines. Nevertheless, a typical alternative conductor element for a small electric machine (e.g., one producing 7.5 HP) may have a thickness of about 0.25 inches. Larger motors may be constructed using an alternative conductor element having a thickness as great as about two inches.  
      This alternative conductor element includes one or more subassemblies such as subassembly  129  in  FIGS. 16   a - b . Subassembly  129  includes a substrate  129   a  having first and second sides, which is made of a suitable dielectric or insulating material. Multiple conductive traces  131  are formed on substrate  129   a  to provide conductor windings in subassembly  129 . For example, substrate  129   a  can be made of a common substrate material such as FR4 or other thin sheet-like plastic material. In this embodiment, subassembly  129  includes a composite material sheet, commonly referred to as “flex PC,” where substrate  129   a  is a thin sheet-like plastic which is bonded to copper. For example, substrate  129   a  can have a thickness less than about 0.010 —inches (10 mils) thick and is preferably 1 to 3 mils thick. The flex PC material includes a dielectric substrate and a 3 mil thick layer of copper on each of the first and second sides of the substrate. Conductive traces  131  are formed on substrate  129   a  by etching away copper between adjacent traces. To increase the amount of conductive material in each subassembly  129 , the thickness of the conductive traces  131  is then increased to six mils on the first and second sides of the substrate. This can be achieved using a well-known mask and sputtering technique. The space between adjacent conductive traces  131  is filled with a dielectric resin. In this embodiment, the dielectric material for substrate  129   a  and for separating adjacent traces  131  is rated to 2000 volts. The spacing between adjacent conductive traces in this example is on the order of ten mils and is preferably about four mils.  
      In this example, each conductive trace has a thickness of six mils, but can be increased to 15 mils. As shown in  FIG. 16   a , each conductive trace  131  includes an outer section  131   b , a radial section  131   c  that extends in a generally radial direction from an outer diameter to an inner diameter of the conductor element, and an inner section  131   d  that extends from the radial section  131   c  towards a center of the conductor element. As with the conductor element  121  of  FIG. 14 , subassembly  129  is designed to maximize the amount of conductive material adjacent to the magnetic poles of an axially adjacent magnetic element (described below). In other words, subassembly  129  is designed to maximize the amount of conductive material in the radial sections  131   c  of each conductive trace  131 . Doing so maximizes the fill factor which in turn contributes to maximizing efficiency, motor constant, and power density.  
      As illustrated in  FIGS. 17 and 18 , each subassembly can have conductive traces on both sides of substrate  129   a , in the manner associated with what is commonly known as a two-sided printed circuit board. In  FIG. 17 , conductive traces  131  on the first side are shown in a solid line, and conductive traces  137  on the second side are shown in a dashed line. Conductive traces  131  and  137  are essentially identical, mirroring one another in size and position. Each end of a conductor  131  is electrically connected to an end of a conductor  137  via an inter-side through-hole  139 . Each inter-side through-hole  139  is plated on its interior to provide a conductive path in a manner well-known in multi-layer printed circuit board manufacture.  
      A first terminal through-hole  141  is disposed at one end of one of conductive traces  131  (i.e., coupled to a terminal portion  131   a  of conductive trace  131 ), and a second terminal through-hole  143  is disposed at one end of another of conductive traces  131 . Terminal through-holes  141  and  143  are plated through-holes similar to inter-side through-holes  139 , but they do not connect conductive trace  131  to conductive trace  137 . Rather, terminal through-holes  141  and  143  form the terminals of an electrical circuit. The conductor path of the circuit, a portion of which is indicated by arrows  145  in  FIG. 17 , begins at terminal  141 , follows one of conductors  131  on the first side of substrate  129   a  changes sides via one of inter-side through-holes  139 , and continues through one of conductors  137  on the second side of the subassembly. The portion of the conductor path indicated by arrows  145  defines a winding. (In this example, the winding has only a single turn of conductor, in a manner similar to the embodiment described above with respect to  FIG. 14 .) The circuit then follows a second winding by again changing sides via another of inter-side through-holes  139 , and continues through another of conductive traces  131 . The connections continue in such a manner (e.g., in a clockwise manner) until bridge portion  145   a . The connections proceed in an opposite direction (e.g., in a counter-clockwise manner) to terminal  143 . The circuit shown in  FIG. 17  includes twelve windings between the two sides of the subassembly.  
      As shown in  FIGS. 16 and 17 , and as stated above, each conductive trace  131  includes an outer section  131   b , a radial section  131   c , and an inner section  131   d . The inner section  131   d  and the inner section  137   d  of a conductive trace on the other side of substrate  129   a  are coupled via an inter-side through-hole  139 . In this embodiment, the inner sections  131   d  and  137   d  form substantially 45° angles with a line  138  tangential to an inner radius of subassembly  129 . Connecting the inner connector portions  131   b  and  137   b  in such a manner minimizes the resistive or I 2 R loss P r  in the electric machine. Likewise, in this embodiment, the outer connector portions  131   b  and  137   b , coupled together by an inter-side through-hole  139 , form substantially 45 angles with a line  140  tangential to an outer radius of subassembly  129  for the same purpose.  
      Although a conductor element may include only the windings of a single subassembly  129 , such as that shown in  FIG. 17 , a conductor element can include windings of multiple subassemblies electrically connected in series or parallel. As illustrated in  FIG. 18 , subassemblies  129  are bonded together to form a conductor element. A plastic sheet  147  (e.g., of a dielectric or insulating material such as the commonly known Prepreg material) between layers  129  bonds the laminations together when heated and subjected to pressure, and also electrically insulates conductive traces  137  of one subassembly from conductive traces  131  of an adjacent subassembly. As illustrated in  FIG. 19 , terminal through-holes  141  of all subassemblies are electrically connected together, and terminal through-holes  143  of all subassemblies are electrically connected together, thereby electrically connecting the windings in parallel to form a conductor element.  
      Referring to  FIGS. 16   a - f , the different subassemblies are connected in serial. One skilled in the art will appreciate that individual-subassemblies can be joined in series and/or parallel, as desired, in a conductor element.  FIGS. 16   a - b  depict the first and second sides of a topmost subassembly,  FIGS. 16   c - d  depict the first and second sides of a second subassembly (i.e., under the subassembly of  FIGS. 16   a - b ), and  FIGS. 16   e - f  depict the first and second sides of the bottom subassembly. In this example, one of the conductor windings begins at a terminal portion  150   a  and extends in a generally radial direction towards the center of the conductor element  129 . In  FIGS. 16   a - f , arrows are used to show a relative direction of current in radial portions of this conductor winding. Conductor  150   a  is coupled to conductor  150   b  on the opposite side of the subassembly as shown in  FIG. 16   b  via an inter-side through hole. Conductor  150   b  is coupled to conductor  150   c  ( FIG. 16   a ) via another inter-side through hole. Accordingly, in  FIGS. 16   a - b , conductors  150   a - 1  are coupled together. Referring to  FIG. 16   b , a bridge portion  151  couples conductor  1501  to  150   m . Conductors  150   m - x  are coupled together in a manner similar to conductors  150   a - 1 . In summary, the conductor winding in the subassembly shown in  FIGS. 16   a - b  starts at terminal portion  150   a  and continues through conductors  150   b - 1 , bridge portion  151 , conductors  150   m - x  and terminal section  152 .  
      In this embodiment, terminal section  152  on an upper side of the subassembly shown in  FIGS. 16   a - b  is coupled to terminal section  153   a  on a bottom side of the subassembly shown in  FIGS. 16   c - d  via a terminal through hole. In a manner similar- to what is described above, the conductor winding in the subassembly shown in  FIGS. 16   c - d  starts at terminal portion  153   a  and continues through conductors  153   b - 1 , bridge portion  154   a , conductors  153   m - x  and terminal section  154 . Terminal section  154  is coupled to another terminal section in the next subassembly not shown via a terminal through hole  155   a  ( FIG. 16   a ). Terminal through holes  155   b - k  likewise couple terminal sections of conductor windings in adjacent subassemblies in the conductor element (as do the other unlabelled terminal through holes). In the conductor assembly of  FIGS. 16   a - f , thirteen subassemblies are coupled together in such a manner. Terminal through hole  155   k  couples a terminal section in the twelfth subassembly (not shown) to the terminal section  156   a  of the thirteenth subassembly shown in  FIGS. 6   e - f . The conductor winding starts at terminal section  156   a  and continues through conductors  156   b - 1 , bridge section  157 , conductors  156   m - x  and terminal section  158 . Terminal section  158  is coupled to the uppermost side of the first subassembly via a terminal through hole  1551 . Accordingly, a serial connection of the conductor windings begins at the terminal section  150   a  and ends at terminal through hole  1551  in  FIG. 16   a.    
      In the example of  FIG. 20 , the conductor element includes twelve conductor phase windings. In the 12-phase conductor element of  FIG. 20 , conductive traces  131  and  137  are arranged at an angular spacing of 2.5 degrees and two conductive traces  131  from one phase are separated by eleven conductive traces  131  from the other phase windings. For purposes of clarity, only a portion of the conductor element is shown in  FIG. 20 , illustrating the pair of terminals for phase-1, labeled “φ 1   + ” and “φ 1   − ” and the pair of terminals for phase-2, labeled “φ 2   + ” and “φ 2   + ” Nevertheless, the completed conductor element would have 12 pairs of terminals for phases 1-12. In the example of  FIGS. 16   a - f , the conductor element includes eight conductor phase windings. In this example, adjacent conductive traces from one phase are separated by one conductive trace from each of the other seven phases.  
      In the embodiments of the conductor element described above with respect to  FIGS. 16-20 , a fill factor for the conductor element can be between 60 and 90% and is typically between 80% and 84%.  
      In view of the embodiments illustrated in  FIGS. 14 , and  16 - 20 , persons of skill in the art will understand that in other embodiments the conductors may have any suitable size, shape, and number of windings and turns. For example, in an embodiment similar to that illustrated in  FIG. 14 , each winding may have two turns of rectangular wire having wedge-shaped elongated portions.  
      Magnetic Element  
      In the axial field electric machine of the present invention, one or more magnetic elements are provided that interact with the conductor elements discussed above with respect to  FIGS. 14 and 16 - 20 . For example, the rotor of the axial field electric machine can include one or more magnetic elements such as the rotor disk  14  shown in  FIG. 4 . Again, to achieve a high efficiency, motor constant, and power density for the axial field electric machine, it is advantageous if the magnetic elements have a low density and a high energy product (as discussed further below).  
      As illustrated in  FIG. 4 , each rotor disk  14  may include an annular magnet  54  mounted on a hub  56 . Hub  56  can have hub ventilation openings  58  with angled, vane-like walls for impelling cooling air through housing  10 . Each magnet  54  may be made from a suitable ferroceramic material, such as M-V through M-VIII, oriented barium ferrite (BaO—6Fe 6 —O), strontium ferrite (SrO—6Fe 6 —O 2 ), or lead ferrite (PbO—6Fe 6 —O 2 ). Alternatively, magnets  54  may be made from a bonded or sintered neodymium-iron-boron (NdFeB) material. Both ferroceramic magnets and NdFeB magnets are known in the art and commercially available. As illustrated in  FIG. 4 , magnet  54  is polarized to provide multiple magnetic poles or sectors  57  uniformly distributed angularly around magnet  54 . Alternatively, each magnetic element or rotor disk can include a plurality of individual sector-shaped magnets that are joined together into an annular shape with an appropriate adhesive or support structure.  
      As illustrated in  FIG. 5 , each sector is polarized through the thickness of magnet  54 . Thus, each sector has opposite poles on opposite faces  60  and  62  of the magnet  54 . In addition, the poles of sectors  57  on face  60  alternate with those of adjacent sectors  57  on face  60 , and the poles of sectors  57  on face  62  alternate with those of adjacent sectors on face  62 . In this embodiment, each rotor disk  14  is to be mounted on a shaft with the poles of its magnet  54  axially aligned with opposite poles of any adjacent magnets  54  (i.e., a North pole on face  62  of a first rotor magnet  54  will be axially aligned with a South pole on face  60  of a second axially adjacent rotor magnet  54 ). Magnetic flux therefore travels axially between such axially aligned poles.  
      As discussed above in this example, magnet  54  is mounted to a hub  56  which in turn is mounted to a shaft. Referring to  FIG. 9 , an example of a shaft  16   a  is shown. Shaft  16   a  is splined and provides a mating surface for the central portion of the hub  56   a  as shown in  FIG. 10 . It is preferable if magnet  54  is mounted to hub  56   a  before being magnetized to ensure proper orientation between adjacent magnets when the hub  56   a  is placed onto shaft  16   a.    
      As illustrated in  FIG. 15 , annular disks or endplates  64  and  66 , made of a suitable high-permeability material such as steel, are mounted to outer faces  60  of the magnet  54  of the endmost two rotor disks  14 . Endplates  64  and  66  contain the magnetic flux between adjacent poles of the rotor magnet  54  adjacent to endplate  64  or  66 . By mounting high permeability endplates to the endmost two rotor disks, the endplates rotate with the rotor magnet thereby eliminating the core loss associated with the high permeability material in the flux path of the magnets. As a result, the efficiency of the electric machine is maximized.  
      As illustrated in  FIG. 15 , conceptually, the magnetic flux only “flows” from a sector  57  of a first one of the two endmost rotor disks  14 , through axially aligned sectors  57  of adjacent magnets  54  until reaching the second one of the two endmost rotor disks  14 , where one of endplates  64  and  66  directs the flux to an angularly adjacent sector  57 . The flux then returns axially through aligned sectors  57  of adjacent magnets  54  until again reaching the first endmost rotor disk  14 , where the other of endplates  64  and  66  directs the flux to an angularly adjacent sector  57 . The magnets  54  other than the two endmost magnets  54  may be referred to herein for convenience as inner rotor disks or magnets  54 . The flux thus follows a serpentine pattern, weaving axially back and forth through aligned sectors  57  of magnets  54 .  
      Magnet  54  has at least one South and one North pole on each side  60  and  62 . The minimum number of magnet poles distributed around each face  60  or  62  of magnet  54  is a function of the demagnetization characteristics of the magnet material used. If the demagnetization characteristic has a “knee” in the second quadrant of its B-H curve at room temperature, the number of magnet poles must be sufficiently large to keep the magnet poles from being irreversibly demagnetized before magnet  54  is assembled into the electric machine.  
       FIG. 6  illustrates the axially-directed flux density B profile emanating from magnet pole faces assembled into the electric machine. The flux density is generally positive over North poles and negative over South poles. Between North and South poles the flux density passes through zero flux density at the midpoint.  70  between poles of magnet  54 . When magnet  54  is formed by a single piece of annular magnet material, the interpolar region  72  between magnet poles represents permanent magnet material that is nonuniformly magnetized due to limitations inherent in the magnetizing process. When magnet  54  is formed from a plurality of sector shaped magnets, the interpolar region  72  represents the unmagnetized adhesive or support structure holding the magnets together. The transition width d shown in  FIG. 6  is the width generally over the midpoint  70  where the axial flux density is significantly diminished with respect to its peak value. As explained in further detail below, this transition width d is used as part of a design algorithm for the electric machine.  
      Electric Machine Design  
      As described in further detail below, two embodiments of an electric machine designed according to embodiments of the present invention will be shown. The first uses the conductor element design shown in  FIG. 14 , the second uses the conductor element design shown in  FIGS. 16-20 . According to an embodiment of the present invention, the magnetic and conductor elements are designed and ihe electric machine is designed so as to maximize the efficiency, motor constant, and power density of the electric machine. The embodiments described below have a modular design allowing a user to select the number of conductor elements and magnetic elements that are needed for a particular application.  
     First Embodiment  
      As illustrated in  FIGS. 1-3 , a first embodiment of the axial field electric machine designed according to an embodiment of the present invention is shown. The axial field electric machine includes a housing  10  (the center section of which is shown removed), multiple stator assemblies  12  (e.g., each including a conductor element similar to the one shown in  FIG. 14 ) connected to one another and disposed within housing  10 , and magnetic elements  14  (e.g., similar to the one shown in  FIG. 4 ) connected to a shaft  16  that extends axially through housing  10 . In this example, the conductor elements make up the stator of the electric machine and the magnetic elements make up the rotor. One skilled in the art will appreciate that in an alternative embodiment, conductor elements can serve as the rotor and the magnetic elements can serve as the stator in the electric machine.  
      Housing  10  includes two endpieces  18  and  20 , each having multiple housing ventilation openings  22 . Housing  10  may also include at least one removable midsection piece between endpieces  18  and  20  that is indicated as a phantom line in  FIGS. 1-3  but not shown for purposes of clarity. Endpieces  18  and  20  and the removable midsection pieces can be made of a light-weight plastic or metal (e.g., aluminum). Bolts  24  extend from endpiece  18  axially through housing  10  through each stator assembly  12  and are secured by nuts  26  at endpiece  20 . At one end of housing  20 , ball bearings  28  retained between a first bearing race  30  connected to shaft  16  and a second bearing race  32 ′ connected to endpiece  18  facilitate rotation of shaft  16  with respect to housing  10 . A similar bearing arrangement having ball bearings  34  retained between a first bearing race  36  connected to shaft  16  and a second bearing race  38  connected to endpiece  20  facilitate rotation of shaft  16  at the other end of housing  10 .  
      In this embodiment, magnetic elements  14  are interleaved with stator assemblies  12  in the axial field electric machine. As shown in  FIG. 14 , conductor element  121  may include sockets  42  allowing any number of the stator assemblies  12  to be assembled into the electric machine. Conversely, the stator assemblies can be removed from the electric machine as desired. Removable pins  40  plug into sockets  42  to electrically connect each stator assembly  12  to an axially adjacent stator assembly  12 . Accordingly, depending on the desired application (e.g., power output requirements), a selected number of stator assemblies  12  and magnetic elements  14  can be added to or subtracted from the electric machine as necessary.  
      An example of a stator assembly is shown in  FIG. 11 . In this embodiment, conductor element  121  is embedded, molded or similarly encased in a substantially annular stator casing  104  made of a suitable dielectric or insulative material. Stator assembly  12  has bores  106  through which bolts  24  may be extended to physically interconnect them, as described above with respect to  FIGS. 1 and 2 . As similarly described above, stator assembly  12  has sockets  42  that may be electrically interconnected by removable pins  40 . Stator casing  104  has a central opening  108  through which shaft  16  extends when the electric machine is assembled, as illustrated in  FIG. 2 . The diameter of shaft  16  is less than that of central opening  108  to facilitate airflow through the axial field electric machine.  
      The modular construction of the electric machine facilitates selection of an operating voltage. Operating voltage is proportional to the total conductor length for each phase. Thus, an operating voltage may be selected by adjusting the total conductor length for each phase. Each stator assembly  12  has conductors  110 ,  112 ,  114  and  116 , each defining one of the four phases. (See, e.g.,  FIG. 13 .) By connecting, for example, conductor  110  in each stator assembly  12  in parallel with conductor  110  in all other stator assemblies  12 , the total conductor length for phase-1 is minimized. Conversely, by connecting, for example, conductor  110  in each stator assembly  12  in series with conductor  110  in all other stator assemblies  12 , the total conductor length for phase-1 is maximized. The modular construction facilitates selectively connecting the conductors of adjacent stator assemblies in either series or parallel.  
      One skilled in the art will appreciate that the magnetic element in the electric machine described herein can be replaced with an suitably constructed aluminum disk to operate the electric machine as an induction machine.  
      As illustrated in  FIG. 1 , each stator assembly  12  has indicia  158 ,  160  and  162 , such as adhesive labels, each indicating one of the voltages that may be selected. An operating voltage can be selected by connecting each stator assembly  12  in an angular orientation in which the indicia indicating a certain voltage are aligned. Indicia  158  are labeled “120” to indicate 120 volts; indicia  160  are labeled “480” to indicate 480 volts; and indicia  162  are labeled “960” to indicate 960 volts. In the exemplary embodiment and the relative angular orientation of stator assemblies  12  shown in  FIG. 1 , indicia  158  are aligned to select an operating voltage of 120 volts. To change the operating voltage, one need only uncouple one or more stator assemblies  12  and rotate them to realign indicia  158  such that they align to indicate a different operating voltage.  
      As illustrated schematically in  FIG. 23 , stator assemblies  12  are interconnected to select a first operating voltage, such as 120 volts. Broken lines indicate an electrical connection. With respect to phase-1, each end of conductor  110  in each stator assembly  12  is connected by a removable pin  40  to the corresponding end of conductor  110  in another stator assembly  12 . Thus, all conductors  110  are connected in parallel. Similarly, with respect to phase-2, each end of conductor  112  in each stator assembly  12  is connected by a removable pin  40  to the corresponding end of conductor  112  in another stator assembly  12 . Thus, all conductors  112  are connected in parallel. All conductors  114  and  116  are similarly connected in parallel. Pins  40  at one of the endmost stator assemblies  12  may be connected to electrical power leads  44  ( FIG. 1 ). It should be noted that all indicia  158  are aligned, but indicia  160  and indicia  162  are not aligned.  
      As illustrated schematically in  FIG. 24 , stator assemblies  12  are interconnected to select a second operating voltage, such as 960 volts. As in  FIG. 24 , broken lines indicate an electrical connection. With respect to phase-1, with the exception of the two endmost stator assemblies  12 , a first end of conductor  110  in each stator assembly  12  is connected by a removable pin  40  to a second end of conductor  110  in another stator assembly  12 . Thus, all conductors  110  are connected in series. Similarly, with respect to phase-2, with the exception of the two endmost stator assemblies  12 , a first end of conductor  112  in each stator assembly  12  is connected by a removable pin  40  to a second end of conductor  112  in another stator assembly  12 . Thus, all conductors  112  are connected in series. All conductors  114  and  116  are similarly connected in series. Pins  40  at the endmost stator assemblies  12  may be connected to electrical power leads  44  ( FIG. 1 ). It should be noted that all indicia  162  are aligned, but indicia  158  and indicia  160  are not aligned.  
      As illustrated schematically in  FIG. 25 , stator assemblies  12  are interconnected to select a third operating voltage, such as 480 volts. In the same manner as in  FIGS. 23 and 24 , broken lines indicate an electrical connection. With respect to phase-1, with the exception of the two endmost stator assemblies  12 , the corresponding first and second ends of conductors  110  in two adjacent stator assemblies  12  are connected to each other by a removable pin  40 ; a first end of conductor  110  in one of those stator assemblies  12  is connected by a removable pin  40  to a second end of conductor  110  in a third stator assembly  12 ; and the corresponding first and second ends of conductors  110  in the third stator assembly  12  and an adjacent fourth stator assembly  12  are connected to each other by a removable pin  40 . Thus, two conductors  110  are connected in parallel form a group, and then these groups are connected in series. Similarly, with respect to phase-2, with the exception of the two endmost stator assemblies  12 , the corresponding first and second ends of conductors  112  in two adjacent stator assemblies  12  are connected to each other by a removable pin  40 ; a first end of conductor  112  in one of those stator assemblies  12  is connected by a removable pin  40  to a second end of conductor  112  in a third stator assembly  12 ; and the corresponding first and second ends of conductors  112  in the third stator assembly  12  and an adjacent fourth stator assembly  12  are connected to each other by a removable pin  40 . Thus, groups of two conductors  112  are connected in parallel, and then these groups are connected in series. All conductors  114  and  116  are similarly connected in parallel groups of two that are connected in series. Pins  40  at the endmost stator assemblies  12  may be connected to electrical power leads  44  ( FIG. 1 ). It should be noted that all indicia  160  are aligned, but indicia  158  and indicia  162  are not aligned.  
      Those skilled in the art will appreciate that the conductors may be interconnected in various combinations of series and parallel groups to provide more than three selectable voltages. Moreover, the illustrated set of voltages is exemplary only; in view of the teachings herein, persons of skill in the art will readily be capable of constructing a electric machine operable at other voltages.  
      Electrical power leads  44  extend into housing  10  and have plugs  46  that connect to sockets  42  in one of the two endmost stator assemblies  12 . Although  FIG. 3  illustrates a power lead  44  connected to the endmost stator assembly  12  adjacent endpiece  20 , it could alternatively be connected to the endmost stator assembly  12  adjacent endpiece  18  or an intermediate stator assembly  12 . As illustrated in  FIGS. 1 and 3 , openings or ports  48  and  50  in endpieces  18  and  20 , respectively, admit plugs  46  into housing- 10 . A sensor  52 , such as a Hall-effect sensor, is mounted to endpiece  20 . Sensor  52  is adjacent the endmost magnetic element  14  for sensing pole transitions, as described below with respect to the operation of the electric machine. One skilled in the art will appreciate that other devices can be used to sense pole transitions in a magnetic element  14 . For example, an optical grating may be placed around the periphery of an magnetic element and an opticoupler can be used to sense reflected light from the grating using a stationary light source to indicate the position of the magnetic poles relative to the stator assemblies.  
     Second Embodiment  
      A second embodiment of the electric machine of the present invention is shown in FIGS.  12 ,  27 - 29  using the conductor element of  FIGS. 16-20 . Referring to  FIG. 12 , a cross section of this axial field electric machine is shown. The axial field electric machine  200  is similar in construction to the electric machine of  FIGS. 1 and 3 . Electric machine  200  includes a plurality of magnetic elements  201 , such as rotor disks, attached to a shaft  205 . In this example, shaft  205  has a configuration similar to that which is shown in  FIG. 9 . Hubs of axially adjacent magnetic elements are separated by a ring separator  209 . Electric machine  200  includes a plurality of conductor elements  202  and connector support elements  203 , the construction of which is described in further detail below. As with the electric machine design of  FIGS. 1 and 3 , electric machine  200  has a modular design in that any number of conductor elements  202  (and connector support elements  203 ) and magnetic elements  201  may be added to or subtracted from the electric machine as desired.  
      In this embodiment, each conductor element includes a frame, such as frame  210  shown in  FIG. 27 . In the front view of  FIG. 27 , frame  210  includes mounting holes  212 , for insertion of a bolt or the like to secure one frame to one or more such frames in the electric machine. Frame  210  also includes apertures  211  to allow air flow into and out of the electric machine.  
      Referring to  FIG. 28 , a front view of the connector support element  203  is shown. The connector support element  203  also includes mounting holes  212  (as in  FIG. 27 ) for mounting to an adjacent frame  210 . Connector pin assemblies  217  are provided to electrically connect selected conductor phases of one conductor element to selected conductor phases of an axially adjacent connector assembly. In this embodiment, the connector pin assembly includes a number of pins  220  coupled to a number of sockets  221 . Accordingly, pins  220  of one connector support element  203  mate with sockets  221  of an axially adjacent connector support element  203 . A Hall sensor  216  can be provided for sensing pole transitions in a magnetic element rotating within an opening of the connector support element. Also, high voltage switches  218  can be provided to switch power on and off to the conductor phases of the conductor element (see  FIG. 29 ).  
      Referring to  FIG. 29 , a partially completed axial field electric machine is shown with a conductor element of  FIGS. 16-20 , the connector support element  203  of  FIG. 28 , and the magnet of  FIG. 3 . The high voltage switches  218  and connector pin assemblies  217  are selectively coupled to conductor phases of the conductor element. In this example, the conductor element is shown in  FIG. 16  and includes mounting holes for mounting it to adjacent conductor elements.  
      Controller  
      As illustrated in  FIG. 21 , the electric machine may be configured as a motor by connecting a brushless motor controller  130  of an essentially conventional design. In this example, brushless motor controller  130  receives a pole sense signal  132  from sensor  52  ( FIG. 3 ) and generates signals  134  (φ 1 −),  136  (φ 1 +),  138  (φ 2 −),  140  (φ 2 +),  142  (φ 3 −),  144  (φ 3 +),  146  (φ 4 −) and  148  (φ 4 +) for the conductor phases in conductor element  121  in.  FIG. 14 . Signals  134 ,  136 ,  138 ,  140 ,  142 ,  144 ,  146  and  148  are coupled to electrical leads  44 , as described above with respect to  FIG. 2 .  
      As shown in the timing diagram of  FIG. 22 , brushless motor controller  130  attempts to drive current in each phase while that phase is subjected to flux from a pole sector in magnet  54 . As described in further detail herein, it is preferable if the width of the radial portion of the conductor phases that pass through the flux of the magnet  54  have a width that does not exceed the transition width d between adjacent poles as shown in  FIG. 6 . Accordingly, as a phase conductor travels across one magnet pole face, current is being driven into each phase conductor 75% of the time.  
      In the timing diagram of  FIG. 22 , the voltage amplitude signals for each of the phases are shown. In this example, the voltage amplitude for each phase fluctuates between +350V, 0V, and −350V D.C. The brushless motor controller  130  includes a chopping or pulse-width modulating (PWM) circuit, as is known in the art, which converts the D.C. voltage signal into a square wave signal having a duty cycle between 0 and 100%. In this example, the frequency of the pulse-width modulation is 20 KHz. Looking at the voltage signal for φ 1 , the signal is at 0V when the φ 1  phase conductor is completely within a transition width between magnet poles. In  FIG. 22 , the pole sense signal is generated when a transition width is passing the pole sensor. As the phase conductor passes from the transition width to the next pole sector, the voltage amplitude jumps to ±350V (depending on direction of rotation) and the duty cycle is set to a low value (e.g., 5%). The duty cycle can be raised as the phase conductor moves into the pole sector, and the duty cycle is at a maximum when the phase conductor is completely within a pole sector. The selection of a maximum duty cycle depends on the desired current in each conductor phase (e.g., based on torque, speed, and/or power requirements). The duty cycle is again lowered when the phase conductor once again begins to move within the next transition width. The duty cycle is lowered to zero when the phase conductor is completely within the transition width. As the phase conductor moves into the next pole, the duty cycle is increased, but the voltage level is inverted (i.e., from positive to negative or negative to positive). In  FIG. 22 , one pole sense signal is generated which is related to the presence of the φ 1  conductors in the transition width. Pole sense signals relative to the phase conductors φ 2 -φ 4  can be generated based on the pole sense signal for φ 1 . Alternatively, pole sense signals can be generated for all poles (e.g., using an optical grating pattern around the periphery of a magnet).  
      The motor controller can be easily modified to provide the same voltage signals for any number of phases, such as the eight phases shown in  FIG. 16  and the twelve phases shown in  FIG. 20 . In the case of eight phases, current will be conducted in each phase 87.5% of the time. In the case of twelve phases, current WIll be conducted in each phase 91.67% of the time.  
      As shown in these embodiments, only the phase conductor within the transition width d closest to the midpoint (e.g.,  70  in  FIG. 6 ) between magnet poles is nonconducting at any rotor position. Therefore at any given rotor position a motor having N phase windings will have 100(N−1)/N percent of its phase conductors conducting current and producing torque. As a result, the electric machine maximizes its conductor utilization, which maximizes efficiency, motor constant, and power density.  
      Design Considerations  
      With the structure of the axial field electric machine given above for the first embodiment, the specific design of the conductor elements  121  and the magnetic elements  14  to achieve high efficiency, high motor constant, and high power density is given below. With this design algorithm, the axial field electric machine of this embodiment minimizes the I 2 R loss denoted P r  earlier, minimizes the core loss P c , minimizes eddy current losses, and maximizes the production of torque. As a result, the electric machine will achieve and maintain high efficiency over a wide range of speeds, will exhibit a high motor constant, and achieve high power density because torque production is optimized.  
      Referring to  FIG. 31 , a graph is shown of the efficiency of an electric machine constructed according to the present invention. In comparison to  FIG. 30 , the electric machine obtains a higher efficiency over a broader range of operating points. Accordingly, in a traction application requiring operation of the electric machine at several operating points, the average efficiency will be far in excess of a typical electric machine.  
      A first design objective is to select an axial spacing between adjacent magnetic elements in the axial field electric machine. As discussed above, the stator assemblies  12  are disposed between adjacent magnetic elements. The permanent magnet flux, as described by its flux density B, that passes from one magnetic element axially through a stator assembly, then through the adjacent magnetic element determines the torque and back EMF (i.e., the performance) of the axial field electric machine. As such, it defines the operating point of the motor. This operating point is commonly characterized in the art as the intersection between the magnetic circuit load line and the demagnetization curve of the permanent magnet material used in the magnetic elements. Here the magnetic circuit is a mathematical characterization of the physical path taken by the magnetic field and its interaction with the materials in that path. Two example demagnetization curves of a magnet are shown in  FIG. 7 . As is known in the art, curve  71  is the demagnetization curve of a magnet that does not have a knee, whereas demagnetization curve  72  has a knee where the characteristic bends toward the horizontal axis when the curve nears the axis. The presence of a knee, the slope of the curves, and the intersection of the curves with the two axes is a function of the magnet material type as well as temperature, with higher performance and generally more expensive magnet material having higher points of intersection and no knee at room temperature.  
      Also shown in  FIG. 7  are three example magnetic circuit load lines,  81 ,  82 , and  83  each having a different slope. The absolute value of the load line slope is known in the art as the permeance coefficient, PC, which is illustrated in  FIG. 7 . In its simplest form, the permeance coefficient is approximated by 
 
 PC=L   m   /L   g   (Eq. 3) 
 
 where L m  is the magnet length in the direction of magnetization (i.e., the axial direction in this invention) and L g  is the net magnetic flux path length in air (including that through stator assemblies disposed between adjacent magnetic elements). Based on this approximation and with reference to  FIG. 7 , for a fixed magnet length L m , the electric machine operating flux density B m  is inversely proportional to L g . See for example, B m  marking flux density at the intersection of magnet demagnetization curve  71  and load line  82 . As L g  increases, the flux density operating point B m  decreases and as L g  decreases, B m  increases. 
 
      With this understanding of the inverse relationship between the electric machine flux density operating point B m  and the net magnetic flux path length in air L g , the optimum spacing between magnetic elements is based on the ideas (a) if L g  is zero, B m  is maximized giving the potential for high torque since torque is proportional to flux density. However, if L g  is zero there is no room between axially adjacent magnetic elements for stator assemblies containing conductor elements through which torque can be created. Therefore L g =0 is not feasible. (b) On the other hand, if L g  is made very large, the conductor elements can be made very thick in the axial direction, which minimizes the I 2 R losses. However, making L g  large forces the flux density operating point B m  to such a small value that little torque can be generated. Therefore making L g  large is not feasible. (c) The product of field intensity H (i.e., the horizontal axis in  FIG. 7 ) and flux density B (i.e., the vertical axis in  FIG. 7 ) is energy density. As such, it is known in the art that operating a permanent magnet where the absolute value of the product of the flux density operating point B m  and the field intensity point H m  is greatest, maximizes the usable energy available from the magnet material. In other words, operating at the maximum energy density point provides the maximum flux density for the least magnet volume or mass. For an electric machine seeking to maximize power density, this is an optimum operating point. For most commonly available permanent magnet materials, the maximum energy density point occurs at or near a permeance coefficient of one.  FIG. 7  illustrates this point at the intersection of demagnetization curve  71  and load line  82 . Using this value, a permeance coefficient of one as dictated by Eq. 3 implies that the optimum spacing between adjacent magnetic elements (“S” in  FIG. 15 ) is equal to the axial length of the magnet (L m  in  FIG. 6 ).  
      A second design objective is to determine the optimum size of the transition width (“d” in  FIG. 6 ) between adjacent poles of a magnet  54 . In the transition width area, flux emanating from one magnet pole flows in approximately a semicircular path to an adjacent pole on the same magnet  54 , rather than traversing axially to an adjacent magnet. Under the assumption that the transition between axial flow to an adjacent magnet versus semicircular flow to an adacent magnet occurs when the flux paths are equal in length, the transition width is given by 
 
 d= 2 L   g /π  (Eq. 4) 
 
 where L g  is the spacing  77  in  FIG. 15 . Therefore, once the spacing  77  is determined by the maximum energy density point of the magnet, Eq. 4 gives the transition width. 
 
      A third design objective is to determine the maximum width of each conductor phase, i.e., the section that extends radially in the conductor element through which torque producing magnetic flux flows, e.g.,  131   c  in  FIG. 16 . According to an embodiment of the present invention, the maximum width of each conductor phase is selected to be no wider than the transition width d as given be Eq. 4. This choice maximizes motor efficiency as well as motor constant and power density for two reasons. First, it minimizes losses due to eddy currents induced in each conductor phase due to motion of the magnet  54 . By limiting the width of the conductor phase to the transition width, at no time does any conductor phase simultaneously experience significant magnetic flux in both the North and South directions. As a result, there are no instants where significant eddy currents are induced in any conductor phase, which in turn increases motor efficiency and indirectly power density. Second, by limiting the width of conductor phases, more conductor phases can be placed radially around the circumference of the conductor element, thereby increasing the number of phase windings and the percentage of the conductor phases conducting current and producing torque simultaneously. As stated earlier, this maximizes torque production while minimizing losses. For example, the exemplary conductor element in  FIG. 14  has thirty-two radial sections and four phase windings or motor phases. The number of motor phases is generally given by length of the outer periphery of sector  57  divided by the transition width. The number of motor phases is in effect the number of transition widths that fit within sector  57 . If R is the outer radius of a sector  57 , N s  is the number of sectors needed to form a complete annulus, and d is the transition width, the number of motor phases N p  is given by 
 
 N   p (2 πR )/( dN   s )  (Eq. 5) 
 
 Those skilled in the art will recognize that some dimensional variations in R and d are typically required to make the number of motor phases given by Eq. 5 closely approximate an integer. 
 
 Uses 
 
      The axial field electric machine may be used to power any suitable type of device, machine or vehicle. For example, it may be used in domestic appliances such as refrigerators and washing machines. It may also be used to power vehicles such as automobiles, trains and boats. One such use as a power plant in a vehicle is illustrated in  FIG. 26 . In the embodiment illustrated in  FIG. 26 , the axial field electric machine is mounted in a casing  164  that functions as the hub for a traction device such as the rubber tire  166  of an automotive vehicle  168 . The shaft  170  is fixedly, i.e., non-rotatably, connected to the body of vehicle  168 . The rotor disks  172 , which are of substantially the same construction as described above with respect to other embodiments, are fixedly connected to casing  164  and thus rotate with tire  166 . The stator assemblies  174  are fixedly connected to shaft  170  but are otherwise constructed as described above with respect to other embodiments. In operation, the rotation of rotor disks  172  propels the vehicle while the shaft remains stationary with respect to the ground.  
      In another application shown in  FIG. 8 , the axial field electric machine of the present invention can be used to reduce operating costs for an air conditioner unit. In  FIG. 8 , an axial field electric machine  230  operating as a motor and constructed according to an embodiment of the present invention is coupled to a compressor  231  in the air conditioner unit  232 . Due to its small size (i.e., relative to other motors used in these units) and high efficiency, the axial field electric machine  230  can be sealed within the compressor  231  in the air conditioner unit  232 . Because of the high efficiency of electric machine  230 , the operating costs for the air conditioner unit  232  can be substantially reduced.  
      The axial field electric machine of the present invention can be used in a variety of other applications. While this electric machine can be used in virtually any electric machine application, its high efficiency, motor constant, and power density make it attractive for applications where these traits have significant value to the end user or product. For example, the electric machine of the present invention is attractive for many battery driven applications such as electric vehicles, including wheel chairs, scooters for elderly people, golf carts, and undersea vehicles. In these applications, the low mass and high efficiency of the present invention increases the vehicle range before battery recharging. The electric machine of the present invention is also valuable in other portable applications such as portable generators for commercial and military use. In these applications, the low mass of the present invention makes it easier to transport the end product and also saves fuel due to the increased energy conversion efficiency of the generator. Yet another area where the electric machine of the present invention will be useful is in applications requiring tight integration of the electric machine with the end product. Examples in this area include robotics, semiconductor processing equipment, embedded pumps and compressors, and a variety of other high throughput automatic tasks. As it stands, the electric machine of the present invention is superior or competitive in almost all applications. The degree to which it makes inroads in any application is dependent upon the degree with which high efficiency, motor constant, and power density impact the end product in which the electric machine appear. For example, it is unlikely that the electric machine of the present invention will become popular in hand-held consumer hair dryers, residential vacuum cleaners, and consumer appliances. Since high efficiency, motor constant, and power density are not as important as cost in these applications, the present invention will appear in these applications only if the materials and manufacturing cost of the present invention become competitive with the electric machines currently used in these applications.  
      Other embodiments and modifications of the present invention will occur readily to those of ordinary skill in the art in view of these teachings. Therefore, this invention is to be limited only by the following claims, which include all such other embodiments and modifications when viewed in conjunction with the above specification and accompanying drawings.