Abstract:
A brushless motor capable of increasing energy density by effective utilization of reluctance torque. The brushless motor comprises a stator ( 5 ) and a rotor ( 1 ) having a lateral surface opposed to the stator ( 5 ). The stator ( 5 ) comprises a plurality of radially extending iron cores ( 10 ) and a plurality of windings ( 11 ) for generating a magnetic field in each iron core ( 10 ). The rotor ( 1 ) comprises a plurality of permanent magnets ( 2 ) and a magnetic field line inducing body disposed between each permanent magnet ( 2 ) and the lateral surface.

Description:
BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to a brushless motor. More particularly, the present invention relates to a brushless motor used as a driving source of an industry robot, a machine tool, an electric car or an electric train. 
     2. Description of the Related Art 
     In order to miniaturize a motor and to increase output power and torque thereof, it is important that an energy density Edc is high, which implies a ratio of the volume of the motor to the output power. Moreover, in order to simplify the structure of the motor, it is important to minimize the number of slots for winding arrangement and make a working efficiency of a winding operation higher. 
     Such a brushless motor is disclosed in Japanese Laid Open Patent Application (JP-A-Heisei, 11-98791). As shown in  FIG. 1 , the known brushless motor is a surface magnet type brushless DC motor including 14 poles and 12 slots. The brushless motor is provided with: a group of permanent magnets  102  placed on a cylindrical surface of a rotor  101  in which 14 poles are arranged in series; and a stator  104  in which 12 slots  103 - 1  to  103 - 12  are radially placed on the same circumference at a same angular interval. One set of windings  105 -U 1 ,  105 -V 1  and  105 -W 1  and another set of windings  105 -U 2 ,  105 -V 2  and  105 -W 2 , which respectively positionally correspond to each other, are placed at positions in which phases are mutually shifted counter-clockwise by an electric angle of 120 degrees, in six pairs of slots, each of which is composed of two slots adjacent to each other, among 12 slots  103 - 1  to  103 - 12 . Moreover, six windings  105 -U 1 ′,  105 -V 1 ′,  105 -W 1 ′,  105 -U 2 ′,  105 -V 2 ′ and  105 -W 2 ′ are respectively placed such that they are shifted by a rotational angle of 30 degrees with respect to the six windings  105 -U 1 ,  105 -V 1 ,  105 -W 1 ,  105 -U 2 ,  105 -V 2  and  105 -W 2 . A U-phase voltage having a phase of 0 is provided for the winding  105 -U 1  and the windings  105 -U 2 ,  105 -U 1 ′ and  105 -U 2 ′. A V-phase voltage having a phase delayed by about 120 degrees from that of the U-phase voltage is provided for the windings  105 -V 1 ,  105 -V 2 ,  105 -V 1 ′ and  105 -V 2 ′. A W-phase voltage having a phase delayed by about 120 degrees from that of the V-phase voltage is provided for the windings  105 -W 1 ,  105 -W 2 ,  105 -W 1 ′ and  105 -W 2 ′. 
     An output torque T of the known brushless motor is given by the following equation:
 
 T=p{φ·I   a ·cos (β)+( L   q   −L   d ) I   a   2 ·sin(2β)/2}.  (1)
 
Here,
         p: Number of Pole Pairs (Number of Poles/2)   φ: Maximum armature flux linkage of the permanent magnet   I a : Armature current   β: Phase of armature current   L d : Direct-axis inductance (Inductance in the d-axis direction)   L q : Quadrature-axis inductance (Inductance in the q-axis Direction)
 
The phase of the armature current is defined under the assumption that the phase of the U-phase voltage is 0. The first term on the right side of the equation (1) represents a magnet torque, and the second term on the right side represents a reluctance torque.
       

     In the above-mentioned surface magnet type brushless motor, in which the permanent magnet is placed on the surface of an iron core  101 , the following equation:
 
 L   q   ≈L   d ,  (2)
 
can be established from the property of that structure. Here, the symbol “≈” indicates that the L q  is approximately (substantially or nearly) equal to the L d .
 
     Thus, the output torque of the surface magnet type brushless motor is substantially given by the following equation:
 
 T=p{φ·I   a ·cos(β)}.
 
Accordingly, the output component represented by the second term on the right side of the previous equation is 0. That component is not outputted. The surface magnet type brushless motor can effectively use only the magnet torque indicated by the first term on the right side of the equation (1). Hence, the increase in the energy density is suppressed.
 
     It is desirable to increase the energy density by effectively using the reluctance torque indicated by the second term on the right side of the equation (1). 
     SUMMARY OF THE INVENTION 
     Therefore, an object of the present invention is to provide a brushless motor in which the energy density is increased by effectively using the reluctance torque. 
     Another object of the present invention is to suppress a torque ripple of the brushless motor. 
     Still another object of the present invention is to reduce an armature current of the brushless motor. 
     Still another object of the present invention is to decrease a supply voltage to be provided for the brushless motor. 
     Still another object of the present invention is to miniaturize the brushless motor. 
     In order to attain the objects of the present invention, the brushless motor includes a stator and a rotor having a lateral surface opposed to the stator. The stator has a plurality of radially extending iron cores and a plurality of windings for generating magnet fields in the respective iron cores. The rotor includes a plurality of permanent magnets and magnet force line inducing bodies located between the permanent magnets and the lateral surface. 
     Here, it is desirable that an output torque T is given by the following equation:
 
 T=p{φ·I   a ·cos(β)+( L   q   −L   d ) I   a   2 ·sin(2β)/2},
 
where
         p: Number of Pole Pairs (Number of Poles/2)   φ: Maximum armature flux linkage of the permanent magnet   I a : Armature current   β: Phase of armature current   L d : Direct-axis inductance (Inductance in the d-axis direction)   L q : Quadrature-axis inductance (Inductance in the q-axis Direction)
 
while the following equation:
 
L q ≈L d ,
 
does not hold.
       

     Also, it is preferable that the rotor has holes into which the permanent magnets are inserted in the axis direction of the rotor. 
     Preferably, three-phase direct current is provided for the windings. 
     Preferably, the windings include a first set of windings and a second set of windings, and the first set of three-phase windings and the second set of three-phase windings are arranged to be symmetrical with respect to a line. 
     Also, it is preferable that the windings include a first group of three-phase windings and a second group of three-phase windings, windings having the same phase of the first and second groups of three-phase windings are adjacent to each other in the same rotation direction, the first group of three-phase windings include a first set of three-phase windings and a second set of three-phase windings, the first set of three-phase windings and the second set of three-phase windings are arranged to be approximately geometrically symmetrical with respect to a line, the second group of three-phase windings include another first set of three-phase windings and another second set three-phase windings, and the other first set three-phase windings and the other second set of three-phase windings are arranged to be approximately geometrically symmetrical with respect to a line. 
     It is preferable that the number of the windings is N, the number of the permanent magnets is P, and that P is greater than the N. 
     In this case, it is preferable that one of prime factors of the P is greater than any of prime factors of the N. 
     It is also preferable that the prime factor of N is 2 and 3, and the prime factor of P is 2 and 7. 
     Also, P preferably satisfies the following equation:
 
12≦P≦30,
 
     Preferably, N is 12, and P is 14. 
     Preferably, a section of the permanent magnet in a flat plane vertical to a central axis of the rotor is rectangular, the rectangle has short sides and long sides longer than the short sides, and the long sides are opposed to the lateral surface. 
     Preferably, the permanent magnet has a shape of a substantially rectangular parallelepiped, and a distance d between a center of the rotor and a magnetic pole surface opposed to the lateral surface among surfaces of the permanent magnets satisfies the following equation:
 
 d≧r−D /10,
 
Here,
 
 D =2 πr/P, 
         r: Radius of the rotor, and   P: Number of the permanent magnets.       

     Also, the following equation
 
0≦( L   q   −L   d )/ L   d ≦0.3,
 
preferably holds, where
         L q : Quadrature-axis inductance of the rotor, and   L d : Direct-axis inductance of the rotor.       

     Moreover, it is preferable that the magnetic force line inducting bodies include a direct axis magnetic force line inducting body for inducing magnetic fluxes in the direct axis direction of the rotor, the magnetic force line inducting bodies having a gap extending in the quadrature axis direction of the rotor. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  shows a brushless motor in a first embodiment according to the present invention; 
         FIG. 2  shows a configuration of the brushless motor in the first embodiment according to the present invention; 
         FIG. 3  is a graph showing a performance comparison of a brushless motor; 
         FIG. 4  is another graph showing a performance comparison of a brushless motor; 
         FIG. 5  shows a configuration of a brushless motor in a second embodiment according to the present invention; 
         FIG. 6  shows a configuration of a rotor  31 ; 
         FIG. 7  is an expanded view showing a part of the rotor  31 ; 
         FIG. 8A  is a view explaining an effective magnet area rate Mgc; 
         FIG. 8B  is a view explaining an effective magnet area rate Mgc; 
         FIG. 9  shows a dependency of an effective magnet area rate Mgc and a magnetic flux density B e  on a pole number P; 
         FIG. 10  shows a dependency of a q-axis inductance on a pole number P; 
         FIG. 11  shows a dependency of an armature current I a  on an embedded amount x; 
         FIG. 12  shows a relation between an embedded amount x and (L q −L d )/L d ; 
         FIG. 13  shows a configuration of a brushless motor in a third embodiment; 
         FIG. 14  is an expanded view showing a configuration of a rotor  31 ′; 
         FIG. 15  shows an electric car including a brushless motor; and 
         FIG. 16  shows an electric train including a brushless motor. 
     
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     First Embodiment 
     A brushless motor in the first embodiment is a brushless DC motor driven by a three-phase pulse direct current. The brushless motor has a rotor  1  shown in FIG.  2 . The rotor  1  is constituted by a magnetic force line inducing material for inducing a magnetic force line, such as silicon steel or electro-magnetic steel. A 14-pole permanent magnet  2  is embedded in the rotor  1 . The 14-pole permanent magnet  2  corresponds to 14 permanent magnets. The 14 permanent magnets  2  are inserted and placed in 14 pillar holes  4  opened through the rotor  1  in an axis direction. The pillar holes  4  are trapezoidal on a section orthogonal to the axis. One rectangular bar magnet is pressed to be place in each of the pillar holes  4 . A magnetic force line, which is oriented from a South pole to a North pole in each of the permanent magnets  2 , is oriented in the axis direction. The directions of the magnetic force lines generated by the two magnets adjacent to each other are opposite to each other. The 14 permanent magnets  2  are arrayed at the same angle interval (=360°/14) on the same circumference. The magnetic force lines, generated by the 14 magnets arrayed in the circumference direction as mentioned above, are generated by the synthesis of the magnetic force line oriented in the circumference direction and the magnetic force line oriented in the axis direction. 
     The rotor  1  has a stator  5  having the structure of a bearing. The stator  5  includes a cylindrical ring iron core  8 , iron cores  10   1 - 10   12  extending in a radius direction from the ring iron core  8 , and windings  11   1 - 11   12 . Hereafter, the iron cores  10   1 - 10   12  may be collectively referred to as iron cores  10 , and the windings  11   1 - 11   12  may be collectively referred to as windings  11 . The ring iron core  8  and the iron cores  10  are integrally formed into one unit. There is micro clearance between a cylindrical surface, which is an outer circumference surface of the rotor  1  and an inner surface of the iron core  10  in the radius direction. The iron cores  10  are placed on the same circumference at a same interval (=360°/12). A center of the ring iron core  8  is coincident with a center of the rotor  1 . Twelve slots  9   1 - 9   12  are respectively formed between the two iron cores adjacent to each other among the iron cores  10 . 
     The windings  11   1 - 11   12  are respectively wounded around the iron cores  10   1 - 10   12 . The three windings  11   1 ,  11   5 , and  11   99  of the 12 windings  11  constitute a first set of windings. The three windings, constituting the first set of windings, are placed on the same circumference at the same interval (=120°=°360°/3). Other three windings  11   7 ,  11   11 , and  11   3  of the twelve windings  11  are placed respectively positionally corresponding to the first set windings  11   1 ,  11   5 , and  11   99  with respect to a line, and they constitute a second set of windings. Here, a center of the line symmetry corresponds to a rotational axis centerline of the rotor  1 . 
     The first set winding and the second set winding constitute a first group of windings. The six windings constituting a second group winding are placed respectively adjacently in the same rotation direction in the six windings of the first group winding. 
     Phases of armature currents provided for the windings  11   1 - 11   12  are denoted by symbols U, V, W, U′, V′ and W′ shown in  FIG. 2. A  U-phase armature current is provided for the windings  11   1 ,  11   6 ,  11   7 , and  11   12 , a V-phase armature current provided for the windings  11   4 ,  11   5 ,  11   10 , and  11   11 , and a W-phase armature current is provided for the windings  11   2 ,  11   3 ,  11   8 , and  11   9 . The U-phase armature current, the V-phase armature current and the W-phase armature current are pulse direct currents whose phases are shifted by about 120° from each other. The temporal intervals of the U-phase, V-phase and W-phase armature currents are controlled, namely, the magnetic field rotation speed is controlled so that the rotor  1  is rotated at any rotationally angular speed. 
     Also, the directions in which the currents flow through the windings  11   1 - 11   12  are denoted by symbols U, V, W, U′, V′ and W′ in FIG.  2 . The directions of the currents denoted by the symbols U, V and W are opposite to the directions of the currents denoted by the symbols U′, V′ and W′, respectively. The currents in the directions opposite to each other when they are viewed from on the same circumference direction line flow through the two windings located symmetrically with respect to the line. For example, the currents in the directions opposite to each other flow through the winding  11   1  and the winding  11   7 . The polarities of the two permanent magnets  2  placed positionally corresponding to a certain rotation angle position, in the two windings having the above-mentioned configuration are opposite to each other. For example, although a South pole of a permanent magnet  2   1  is oriented in the rotor  1 , a North pole of the permanent magnet  2   8  is oriented in the rotor  1 . The armature currents in the directions opposite to each other simultaneously flow through the respective windings of the first group winding and the respective windings of the second group winding which have the same phase and are adjacent to the above-mentioned respective windings. For example, the armature currents in the directions opposite to each other flow through the winding  11   1  and the winding  11   12 . 
     In the brushless motor according to the present invention, the fact that an output torque is larger than that of the known brushless motor is introduced from the equation (1). The equation (1) is as follows:
 
 T=p ( T   M   +T   R )
 
 T   M   =φ·I   a ·cos(β),
 
 T   R =( L   q   −L   d ) I   a   2 ·sin(2β)/2
 
where T M  is the magnet torque, and T R  is the reluctance torque.
 
     The 14 permanent magnets  2   1 - 2   14  are embedded in the rotor  1  and thus the density of magnetic force lines closed by a magnetic route in the rotor  1  is higher than that of the known motor in FIG.  1 . Such a difference causes the values of and to be further targetless, which results in the positive establishment of the following equation:
 
L q &gt;L d ,  (4)
 
     Let us compare the known brushless motor with the brushless motor according to the present invention. When the output torque of the known brushless motor is represented by T′ and the output torque of the brushless motor according to the present invention is represented by T, the following equation:
 
T′&lt;T,  (5)
 
is established from the condition (4).
 
       FIGS. 3 ,  4  show the performances comparison between the known brushless motor and the brushless motor according to the present invention.  FIG. 3  shows the performance comparison with regard to the relation between the rotation speed and the output torque, and  FIG. 4  shows the performance comparison with regard to the relation between the rotation speed and the output. In the brushless motor according to the present invention, both the output torque (its unit is Nm) and the output (its unit is J in terms of kW) are greater than those of the known brushless motor. 
     Moreover, the brushless motor according to the present invention succeeds to the following merits of the known brushless motor in their original states.
     (1) The brushless motor has a high winding coefficient and a high energy density.   (2) The number of slots is reduced, and the productivity efficiency is high.   (3) A cogging torque generation index, namely, the least common multiple of the pole number  14  and the slot number  12  is large, and a torque ripple frequency is increased.   

     The high torque ripple frequency is effective since it minimizes the influence on a mechanical system, which is usually controlled at a low frequency band. 
     Moreover, the inner installation of the permanent magnet stimulates the structure of the protruded pole in the magnetic force system so that the L q  is not equal to the L d . Thus, the reluctance torque is effectively used, which leads to the higher energy density, namely, the higher output. Conversely, the miniaturization is possible. 
     Second Embodiment 
     A brushless motor in the second embodiment is a brushless DC motor having the structure similar to that of the brushless motor in the first embodiment. The brushless motor in the second embodiment differs from the brushless motor in the first embodiment in the structure of the rotor. The brushless motor in the second embodiment includes a stator  5  and a rotor  31  as shown in FIG.  5 . The structure of the stator  5  is equal to that explained in the first embodiment. 
     The rotor  31  is opposed to the stator  5  on a rotor side surface  31   a . The rotor  31  is rotatably connected to a shaft  32 . The rotor  31  is rotated on the shaft  32 . 
     The rotor  31  includes a rotor iron core  33  and  14  permanent magnets  34   1 - 34   14  as shown in FIG.  2 . The permanent magnets  34   1 - 34   14  are collectively referred to as permanent magnets  34 . 
     The rotor iron core  33  is formed of laminated silicon steel plates. The respective silicon steel plates are electrically insulated from each other. This reduces the loss by eddy currents. Each of the silicon steel plates is blanked out and provided with holes into which permanent magnets  34  are embedded. The permanent magnets  34  are inserted into the holes. That is, the permanent magnets  34  are embedded in the rotor iron core  33 . By the way, the rotor iron core  33  may be made of another material such as electromagnetic steel plates. 
       FIG. 6  shows the structure in the axis direction of the rotor  31 .  FIG. 6  shows the structure of the permanent magnet  34   2  among the permanent magnets  34 . The other permanent magnets  34  have the same structure as the permanent magnet  34   2 . Each of the permanent magnets  34  is composed of a plurality of magnets  35  connected in the axis direction of the rotor  31 , as shown in FIG.  6 . The magnets  35  are electrically insulated from each other. Thus, the loss caused by the eddy currents is suppressed. 
     The permanent magnets  34  substantially have the shape of a rectangular parallelepiped. The permanent magnets  34  having the shape of the rectangular parallelepiped are advantageous in that the permanent magnets  34  are easily produced. In the known brushless motor shown in  FIG. 1 , permanent magnets having curved surfaces are placed on a side of the rotor  101 . The fabrication of permanent magnets having the curved surfaces increases the cost. In the brushless motor in this embodiment, on the other hand, the permanent magnets  34  have the shape of the rectangular parallelepiped, and thus the cost is reduced. 
     The North poles of the permanent magnets  34   1 ,  34   3 ,  34   5 ,  34   7 ,  34   9 ,  34   11 , and  34   13  among the permanent magnets  34  are located on the outer side of the rotor  31  in the radius direction, and their South poles are located on the inner side of the rotor  31 . On the other hand, the South poles of the permanent magnets  34   2 ,  34   4 ,  34   6 ,  34   8 ,  34   10 ,  34   12 , and  34   13  among the permanent magnets  34  are located on the outer side in the radius direction of the rotor  31 , and their North poles are located on the inner side in the radius direction of the rotor  31 . That is, the two permanent magnets adjacent to each other among the permanent magnets  34  generate the magnetic force lines in the directions opposite to each other. 
       FIG. 7  is an expanded view showing a part of the rotor  31 . The permanent magnet  34  has an opposing surface  34   a  opposed to a rotor side surface  31   a  of the rotor  31  and an opposing surface  34   b  opposed to a center  11   b  of the rotor  31 . The two magnetic poles of the permanent magnets  34  are located on the opposing surfaces  34   a , and  34   b . The opposing surfaces  34   a  and  34   b  forms the long sides of a rectangle formed on a section of the permanent magnet  34  located in a direction vertical to a central axis of the rotor  31 . 
     The permanent magnets  34  are placed in the vicinity of the rotor side surface  31   a . The rotor side surface  31   a  and the permanent magnets  34  are located the closest to each other at end portions  34   c . That is, when an embedded amount of the permanent magnet  34  is assumed to be x and a distance between the rotor side surface  31   a  and the end portions  34   c  is assumed to be L, the following equation:
 
x&gt;L,
 
holds. Here, the embedded amount x is defined as the difference between a radius r of the rotor  31  and a distance d to the center  11   b  of the rotor  31  from the opposing surface  34   a , which is the plane opposed to the rotor side surface  31   a  among the surfaces of the permanent magnets  34 . Then, the embedded amount x is given by:
 
 x=r−d.   (6)
 
     Since the rotor  31  has the above-mentioned structure, the magnetic flux generated by the permanent magnets  34  is more effectively used for the generation of the magnet torque. The rotor side surface  31   a  and the permanent magnets  34  are located the closest to each other at the end portions  34   c , and this reduces the magnetic force lines passing between the rotor side surface  31   a  and the end  34   c  among the magnetic force lines generated by the permanent magnets  34 . Thus, the stronger magnet torque is generated. In this way, the brushless motor in this embodiment can obtain the strong magnet torque in the same way as the known brushless motor. 
     From the viewpoint of the generation of the magnet torque, the distance L between the rotor side surface  31   a  and the end portion  34   c  is desired to be narrow. The narrower the distance between the rotor side surface  31   a  and the end portion  34   c , the smaller the number of the magnetic force lines passing between the rotor side surface  31   a  and the end portion  34   c  among the magnetic force lines generated by the permanent magnets  34 . The distance between the rotor side surface  31   a  and the end portion  34   c  is desired to be selected such that substantially all of the magnetic force lines generated by the permanent magnets  34  pass through the rotor side surface  31   a.    
     On the other hand, a narrow distance between the rotor side surface  31   a  and the end portions  34   c  weakens the mechanical strength for the rotor iron core  33  to retain the permanent magnet  34 . If the mechanical strength is excessively weak, the rotor iron core  33  is damaged to thereby detach the permanent magnet  34  from the rotor  31  while the rotor  31  is rotated. The distance between the rotor side surface  31   a  and the end portions  34   c  is desirable to be selected as the minimum distance while keeping the mechanical strength at which the permanent magnet  34  is not detached while the rotor  31  is rotated. According to the experiment of the inventor, it is validated that the distance between the rotor side surface  31   a  and the end portion  34   c  can be selected so as to pass at least 95% of the magnetic force lines generated by the magnetic pole on the opposing surface  34   a  through the rotor side surface  31   a  while keeping the necessary mechanical strength. 
     The permanent magnets  34  does not face on the rotor side surface  31   a , while the permanent magnets  34  are placed in the vicinity of the rotor side surface  31   a . The permanent magnet  34  is embedded in the rotor iron core  33 . That is, the rotor iron core  33  contains a magnetic force line inducing body  33   a  located between the permanent magnets  34  and the rotor side surface  31   a.    
     The existence of the magnetic force line inducing body  33   a  contributes to a drop in an input voltage V of the brushless motor in this embodiment. The input voltage V is given by:
 
 V =√6·{( RI   d   +ωL   q   I   q ) 2 +( RI   q   −ωL   d   I   d   +V   c ) 2 } 1/2 ,  (7)
 
where
         R: Resistance of the armature   ω: Angular frequency of the rotor rotation   I d : d-axis component of the armature current I a  (I d =I a  sin(β).)   I q : q-axis component of the armature current I a  (I q =I a  cos(β).)   V c : Induced voltage in the armature coil by the rotation of the rotor.
 
The existence of the magnetic force line inducing body  33   a  causes a field weakening on the rotor  31 . Moreover, the existence of the magnetic force line inducing body  33   a  leads to the increase in an inductance L d  in a direct axis direction. Accordingly, (−ωL d I d +V c ) approaches 0. As is understood from the equation (7), as the (−ωL d I d +V c ) is close to 0, the input voltage V becomes lower. In this way, the existence of the magnetic force line inducing body  33   a  results in the drop in the input voltage V of the brushless motor.
       

     The existence of the magnetic force line inducing body  33   a  simultaneously contributes to the generation of the reluctance torque. That is, the brushless motor uses the magnet torque similar to that of the known brushless motor, and further uses the reluctance torque. The brushless motor in this embodiment can obtain the high torque, since the magnet torque is used at the high efficiency, and additionally the reluctance torque is used. 
     However, differently from the known brushless motor, the ratio occupied by the reluctance torque is low in the torque generated by the brushless motor in this embodiment. This is because the permanent magnets  34  are placed in the vicinity of the rotor side surface  31   a  and the volume of the magnetic force line inducing body  33   a  is small. The main torque generated by the brushless motor in this embodiment is the magnet torque. Since the generated torque is mainly the magnet torque, the torque ripple is low in the brushless motor in this embodiment. 
     In the brushless motor in this embodiment, the number of the permanent magnets  34 , namely, the pole number P has a large influence on the property of the brushless motor in this embodiment. In the brushless motor in this embodiment, the number of the permanent magnets  34  is determined as described below so that the property is improved. The number of the permanent magnets  34  may be referred to as the pole number P. 
     First, the number of the permanent magnets  34  is determined to be greater than the number of the slots  9 . In other words, the number of the permanent magnets  34  is determined to be greater than the number of the iron cores  10  and the number of the windings  11  since the number of the slots  9  is equal to the number of the iron cores  10  and the number of the windings  11 . Thus, the magnetic circuit is uniformed to thereby suppress the torque ripple. 
     Moreover, the number of the permanent magnets  34  is selected from the range between 12 and 30. The validity of selecting the number of the permanent magnets  34  from the range between 12 and 30 is discussed in the following. 
     At first, let us suppose that a thickness of the permanent magnets  34  is virtually 0 as shown in FIG.  8 A. Here, the reason why the thickness of the permanent magnets  34  is virtually 0 is to consider the ideal case in which the permanent magnets  34  can be placed in the densest condition. The opposing surface  34   a  opposed to the rotor side surface  31   a  among the surfaces of the permanent magnets  34  constitutes an inscribed polygon of the rotor  31  on the section of the rotor  31 . 
     Let us define the effective magnet area rate Mgc as a ratio of a sum of areas of opposing surfaces  34   a  of the permanent magnets  34  to an area of the rotor side surface  31   a . Then, the effective magnet area rate Mgc is represented by:
 
 Mgc=δ/D *100(%).
 
Here,
 
 D =2 πr/P, 
         r: the radius of rotor  31 , and   P: Pole Number (Number of Permanent Magnets).
 
Also, δ implies a width of the opposing surface  34   a  of the permanent magnets  34  in a circumference direction of the rotor  31 . The fact that the effective magnet area rate Mgc is close to 100(%) implies that a larger number of magnetic force lines generated by the permanent magnets  34  come in inter-linkage with the windings  11   1 - 11   12 .
       

     A curved line  41  of  FIG. 9  indicates the dependency of the effective magnet area rate Mgc on the pole number P. As shown in  FIG. 9 , the greater the pole number P, the higher the effective magnet area rate Mgc. It is substantially saturated at the pole number P of 12. From this fact, it can be understood that a magnetic flux density B of the magnetic fluxes in inter-linkage with the windings  11   1 - 11   12  can be substantially maximized by setting the pole number P to 12 or more when the thickness of the permanent magnet  34  is assumed to be virtually 0. 
     However, the infinitely thin permanent magnets  34  can not be actually considered. The thickness of the permanent magnets  34  is desired to be thin, however, the thickness of the permanent magnets  34  is limited by the mechanical strength, the coercive force of the permanent magnet  34  and other factors. Also, the permanent magnet  34  cannot be in contact with the rotor side surface  31   a . As mentioned above, the distance L between the ends of the permanent magnets  34  and the rotor side surface  31   a  is desired to be short. However, in order to keep the mechanical strength, it is necessary that the distance L is longer than a certain value. Hereafter, let us consider the case in which the permanent magnet  34  has a certain thickness β and there is a certain distance L between the ends of the permanent magnets  34  and the rotor side surface  31   a , as shown in FIG.  8 B. 
     The width δ of the opposing surface  34   a  is decreased by the existence of the thickness β of the permanent magnets  34 . The fact that the permanent magnets  34  have the thickness β implies the reduction in a magnetic force density B e  of the magnetic fluxes passing through the rotor side surface  31   a.    
     Also, the existence of the distance L to the rotor side surface  31   a  from the end portion of the permanent magnet  34  causes a magnetic circuit to be generated between the opposing surfaces  34   a  of the two permanent magnets  34  adjacent to each other. The magnetic resistance of the magnetic circuit is smaller as the distance between the two opposing surfaces  34   a  is shorter. Here, as the number of the permanent magnets  34  is greater, the distance between the two opposing surfaces  34   a  is shorter, which leads to the smaller magnetic resistance between them. This implies the increase in the magnetic fluxes that do not contribute to the torque generation since it is closed within the rotor  31 , if the number of the permanent magnets  34  is greater. 
     Due to both the effects of the effective magnet area rate Mgc and the magnetic resistance between the two opposing surfaces  34   a , the magnetic force density B e  of the magnetic fluxes passing through the rotor side surface  31   a  provides the dependency in which it becomes maximum at a certain pole number P. A curved line  42  in  FIG. 9  shows the dependency on the pole number P of the magnetic force density B e  of the magnetic fluxes passing through the rotor side surface  31   a , when the thickness β of the permanent magnet  34  and the distance L to the rotor side surface  31   a  from the end portions of the permanent magnets  34  are set to the values that the applicant considers as the minimum values which can be actually set on Nov. 8, 2000. Here, the magnetic force density B e  is standardized such that the magnetic flux density of the magnetic fluxes passing through the rotor side surface  31   a  is 100 under assumption that the magnet faces on the entire rotor side. 
     As indicated by the curved line  42  of  FIG. 9 , in the range in which the pole number P is 12 or less, the magnetic force density B e  of the magnetic fluxes passing through the rotor side surface  31   a  is sharply increased as the pole number P is greater. If the pole number P becomes greater than 12, the magnetic force density B e  is almost saturated, and it has the maximum value when the pole number P is 16. If the pole number P exceeds 16, the magnetic force density B e  becomes gradually smaller. The pole number P in which the magnetic force density B e  exceeds 85 (arb. unit) is in the range from 12 to 30. In this way, the magnetic force density B e  of the magnetic fluxes passing through the rotor side surface  31   a  can be increased by setting the range of the pole number P to be from 12 to 30. As the magnetic force density B e  is increased, the output torque of the brushless motor is stronger correspondingly to the increase. 
     Also, in view of a different standpoint, an input current required to obtain a certain output torque can be reduced by setting the range of the pole number P to be from 12 to 30. As well known, the output torque T is proportional to the armature current I a  flowing through the windings  11   1 - 11   12  and the magnetic force density B of the magnetic fluxes in inter-linkage with the windings  11   1 - 11   12 , and 
      TαI a ·B. 
     That is,
 
I a αT/B.  (8)
 
As is understood from the equation (8), if the larger number of magnetic flux lines generated by the permanent magnets  34  come in inter-linkage with the windings  11   1 - 11   12 , the armature current I a  required to obtain the certain output torque is reduced. The fact that the armature current I a  can be reduced implies that a capacity of an amplifier for supplying an electric power to the brushless motor can be dropped. Such property is preferable in that the brushless motor is used as a power source for an electric car having a limit of a space.
 
     As can be understood from the above-mentioned facts, the stronger output torque can be obtained by selecting the pole number P as being in the range from 12 to 30. Also, it is possible to reduce the armature current I a  required to obtain the certain output torque. 
     Selecting the pole number P as being 12 or more is also preferable in terms of dropping a quadrature axis inductance L q .  FIG. 10  shows the dependency on the pole number P of the quadrature axis inductance L q  under the condition in which the permanent magnets  34  are placed such that the sum of the areas of the opposing surfaces  34   a  is maximum for each pole number P. In the range in which the pole number P is 12 or less, the quadrature axis inductance L q  is sharply dropped when the pole number P is greater. In the range in which the pole number P is 12 or more, the degree of the drop becomes slow. 
     Here, as can be understood from the equation (7), the drop in the quadrature axis inductance L q  enables the drop in the input voltage V to the windings  11   1 - 11   12 . That is, the input voltage V to the windings  11   1 - 11   12  can be extremely dropped by selecting the pole number P as being 12 or more. 
     As mentioned above, from the two viewpoints of the increase in the effective magnetic force density B e  and the drop in the input voltage V, it can be understood that the pole number P of the brushless motor is desired to be in the range from 12 to 30. 
     The brushless motor in this embodiment satisfies the above-mentioned conditions, the number of the poles being 14, and the number of the slots  9  being 12. In the brushless motor in this embodiment, the number of the poles and the numbers of the slots may be any combination besides the 14 poles and the 12 slots. However, from the viewpoint of the miniaturization and the higher output, it is desired to employ the structure composed of the 14 poles and the 12 slots, as described in this embodiment. 
     Moreover, in the brushless motor, the permanent magnets  34  are placed at positions as described below so that the property is improved. 
     The positions of the permanent magnets  34  are selected such that the embedded amount x satisfies the following equation:
 
 x≦D /10,  (9)
           D =2 πr/P,      r: the radius of the rotor  31 , and   P: the pole number (the number of the permanent magnets  34 ).
 
The small embedded amount x implies that the permanent magnets  34  and the rotor side surface  31   a  are closer to each other. By the way, the condition of the equation (9) has the same meaning as the establishment of the following equation:
 
 d≧r−D /10,  (9′)
 
with respect to the distance d between the opposing surface  34   a  and the center  11   b  of the rotor  31 . The longer distance d implies that the permanent magnets  34  are further closer to the rotor side surface  31   a.  
       

       FIG. 11  shows the dependency on the embedded amount x of the armature current I a  flowing through the windings  11   1 - 11   12  required to generate a certain torque.  FIG. 11  shows a peak value of the armature current I a . As shown in  FIG. 11 , the fact that x≦D/10 results in the extreme drop in the armature current I a  flowing through the windings  11   1 - 11   12 . 
     In other words, the positions of the permanent magnets  34  are selected so as to establish the following equation:
 
( L   q   −L   d )/ L   d ≦0.3.  (10)
 
 FIG. 12  shows the correspondence between the embedded amount x and the (L q −L d )/L d . The embedded amount x and (L q −L d )/L d  correspond to each other in a one-to-one relationship. The smaller the embedded amount x, the smaller the (L q −L d )/L d . When x=D/10, (L q −L d )/L d =0.3. The equation (9) corresponds to the equation (10) in a one-to-one relationship.
 
     On the contrary, even if the structure of the rotor iron core  33  and the positions of the permanent magnets  34  are different from the above-mentioned cases, if they are selected so as to satisfy the condition of the equation (10), it is possible to obtain the effect similar to that of the case when the shape of the rotor iron core  33  and the positions of the permanent magnets  34  are equal to those of the above-mentioned case. 
     Here, the following equation:
 
 L   q   −L   d ≧0,  (11)
 
preferably holds. This is because the output torque is reduced when L q −L d &lt;0, as can be understood from the equation (1).
 
     That is, it preferably satisfies the following equation:
 
0≦( L   q   −L   d )/ L   d ≦0.3  (12)
 
     Third Embodiment 
     A brushless motor in the third embodiment is the brushless DC motor having the structure similar to that of the second embodiment. In the brushless motor in the third embodiment, the structure of a rotor differs from those of the first and second embodiments. In particular, the structure of a rotor iron core differs from those of the first and second embodiments. The other portions in the third embodiment are equal to those of the first and second embodiments. 
       FIG. 13  shows the structure of the brushless motor in the third embodiment. The brushless motor in the second embodiment is provided with a rotor  31 ′ and a stator  5 . The structure of the stator  5  is equal to that explained in the first embodiment. 
       FIG. 14  is an expanded view showing a part of the rotor  31 ′. The rotor  31 ′ includes a rotor iron core  33 ′ and the permanent magnets  34 . The permanent magnet  34  has the opposing surface  34   a  opposite to the rotor side surface  31   a  of the rotor  31  and the opposing surface  34   b  opposed to the center  11   b  of the rotor  31 . The two magnetic poles of the permanent magnet  34  are located on the opposing surfaces  34   a , and  34   b . The permanent magnets  34  generate the magnetic flux lines in the radius direction of the rotor  31 ′. 
     The North poles of the permanent magnets 34 1 ,  34   3 ,  34   5 ,  34   7 ,  34   9 ,  34   11 , and  34   13  among the permanent magnets  34  are located on the outer side in the radius direction of the rotor  31 , and their South poles are located on the inner side of the rotor  31 . On the other hand, the South poles of the permanent magnets  34   2 ,  34   4 ,  34   6 ,  34   8 ,  34   10 ,  34   12 ,  34   14  among the permanent magnets  34  are located on the outer side in the radius direction of the rotor  31 , and their North poles are located on the inner side in the radius direction of the rotor  31 . That is, the two permanent magnets adjacent to each other among the permanent magnets  34  generate the magnetic force lines in the directions opposite to each other. 
     The permanent magnet  34  is placed in the vicinity of a rotor side surface  31   a ′. Although the permanent magnet  34  is placed in the vicinity of the rotor side surface  31   a ′, it does not face on the rotor side surface  31   a . The permanent magnet  34  is embedded in the rotor iron core  33 ′. The permanent magnet  34  is substantially the rectangular parallelepiped. The rotor side surface  31   a  and the permanent magnet  34  are located the closest to each other at the end portion  34   c.    
     The rotor  31 ′ having the above-mentioned structure increases the number of the magnetic flux lines in inter-linkage with the stator  5  after passing through the rotor side surface  31   a , among the magnetic flux lines generated by the permanent magnets  34 . 
     Here, slits  33   a ′ are formed in the rotor iron core  33 ′. The slits  33   a ′ extend from the end portions  34   c  of the permanent magnets  34  towards a rotor side  11 ′. However, the slits  33   a ′ do not reach the rotor side  11 ′. 
     The slits  33   a ′ further reduce the number of the magnetic flux lines closed within the rotor  31 ′, among the magnetic flux lines generated by the permanent magnets  34 . Thus, the brushless motor in the third embodiment can obtain the strong magnet torque, similarly to the second embodiment. 
     Also, the rotor iron core  33 ′ has a direct axis magnetic flux line induction body  33   b ′ located between the permanent magnets  34  and the rotor side surface  31   a . The direct axis magnetic flux line induction body  33   b ′ extends from the rotor side surface  31   a ′ to a direct axis (d-axis) direction of the rotor  31 ′, and reaches the surface of the permanent magnets  34 . The magnetic flux lines in the direct axis direction generated by the permanent magnets  34  pass through the direct axis magnetic flux line induction body  33   b ′, and reach the rotor side surface  31   a ′, and further come in inter-linkage with the stator  5 . The direct axis magnetic flux line induction body  33   b ′ determines the direct axis inductance L d  of the rotor  31 ′. The direct axis inductance L d  is especially determined by a width in a circumference direction of the direct axis magnetic flux line induction body  33   b′.    
     The width of the circumference direction of the direct axis magnetic flux line induction body  33   b ′ is selected such that (−ωL d +V c ) is substantially 0. Here, ω is the angular frequency of the rotation of the rotor  31 ′, V c  is the induced voltage in the windings  11   1 - 11   12  by the rotation of the rotor. As can be understood from the equation (5), since (−ωL d +V c ) is selected as being substantially 0, it is possible to drop the input voltage V of the brushless motor. 
     Moreover, a gap  33   c ′ is formed in the rotor iron core  33 ′. The gap  33   c ′ is located between the permanent magnets  34  and the rotor side surface  31   a . The gap  33   c ′ extends in a quadrature axis (q-axis) direction. This results in the decrease in a quadrature axis inductance L q  of the rotor  31 ′. As can be understood from the equation (5), the decrease in the quadrature axis inductance L q  leads to the decrease in the input voltage V of the brushless motor. 
     In this way, in the brushless motor in the third embodiment, it is possible to further decrease the input voltage V of the brushless motor. 
     Even in the case of the third embodiment, similarly to the second embodiment, the positions of the permanent magnets  34  and the shape of the rotor iron core  33 ′ are desired to be selected so as to establish the following equation:
 
0≦( L   q   −L   d )/ L   d ≦0.3.  (13)
 
     Preferably, the brushless motor based on the first, second or third embodiment is used to drive the electric car.  FIG. 15  shows the electric car including the brushless motor in the first or second embodiment. A battery  51  is installed in the electric car. The battery  51  is connected to a high voltage relay  52 . The high voltage relay  52  sends a voltage to respective units of the electric car. An amplifier  53  sends a voltage to a brushless motor  50  on the basis of a movement of an accelerator pedal  54 . The brushless motor based on any of the first, second and third embodiments is placed as the brushless motor  50 . The brushless motor  50  drives drive wheels  57  through a transmission  55  and drive shafts  56 . In the electric car including the brushless motor  50 , the feature of the brushless motor  50  enables a capacity of the amplifier  53  to be reduced. 
     Moreover, preferably, the brushless motor based on the first, second or third embodiment is placed in the electric train.  FIG. 16  shows the configuration of the electric train including the brushless motor in the embodiment. A pantograph  61  is installed in the electric train. The pantograph  61  comes in contact with a wiring  62  to which a power supply voltage is sent. Then, it sends the power supply voltage to an amplifier  63 . The amplifier  63  is connected to a controller  64 . A throttle lever  64   a  is installed in the controller  64 . The amplifier  63  sends an input voltage to a brushless motor  60 , on the basis of a movement of the throttle lever  64   a . The brushless motor based on any of the first, second and third embodiments is placed as the brushless motor  60 . The brushless motor  60  drives drive wheels  67  through a transmission  65  and drive shafts  66 . In the electric train including the brushless motor  60 , the feature of the brushless motor  60  enables a capacity of the amplifier  63  to be reduced. 
     As mentioned above, according to the present invention, it is possible to increase the output torque of the brushless motor. 
     According to the present invention, it is possible to suppress the torque ripple of the brushless motor. 
     According to the present invention, it is possible to reduce the armature current of the brushless motor. 
     Also, according to the present invention, it is possible to drop the input voltage of the brushless motor. 
     Moreover, according to the present invention, it is possible to miniaturize the brushless motor. 
     Industrial Applicability 
     
         
         Brushless Motor