Patent Publication Number: US-10320254-B2

Title: Permanent magnet motor and electric power steering apparatus

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     This application is a National Stage of International Application No. PCT/JP2013/069737 filed Jul. 22, 2013, the contents of all of which are incorporated herein by reference in their entirety. 
     TECHNICAL FIELD 
     The present invention relates to a permanent magnet motor what is called a multi-phase multi-structured permanent magnet motor including multi-phase stator windings made of a plurality of windings in multiple structures, and to an electric power steering apparatus including the permanent magnet motor for a wheeled vehicle. 
     BACKGROUND ART 
     A permanent magnet motor including multi-phase multi-structured stator windings is well known and has features in which torque pulsation or ripple(s) is reduced by driving the multi-phase multi-structured stator windings each at different phases, and also, a fail-safe function is enhanced due to multi-structuring the multi-phase windings. Therefore, such a permanent magnet motor is used as a motor in an electric power steering apparatus for a wheeled vehicle such as an automotive vehicle, for example. 
     A conventional multi-phase multi-structured permanent magnet motor disclosed in Patent Document 1 includes multi-phase stator windings made of a plurality of windings in multiple structures, and has a configuration in which each of the windings does not commonly use magnetic paths in a gap between the rotor and the stator. 
     RELATED ART DOCUMENT 
     [Patent Document 1] Japanese Laid-Open Patent Publication No. H07-264822 
     SUMMARY OF THE INVENTION 
     Problems to be Solved by the Invention 
     Because the conventional multi-phase multi-structured permanent magnet motor disclosed in Patent Document 1 has a structure of concentrated winding in which armature windings are concentratedly wound on teeth, so that there arises a problem in that a winding factor is small according to the short-pitch winding, and, as a result, the quantity of permanent magnet use increases, resulting in increase in costs. 
     Meanwhile, in a case of a multi-phase multi-structured permanent magnet motor in which a structure is of distributed winding being multi-phase and multi-structured, and also magnetic paths are commonly used between multi-structured windings each other, there arises a problem in that the magnetic coupling of armature windings each other becomes stronger, so that the controllability is lowered. Particularly, in a configuration in which portions of a rotor core exist on the side nearer to a stator than the middle diameter between the maximum outer diameter and the minimum outer diameter of permanent magnets, there significantly arises a problem in that, because inductance becomes larger, an effect of a field-weakening control can be efficiently exerted, while on the contrary, the magnetic coupling of armature windings each other becomes stronger. 
     The present invention has been directed at solving these problems in a conventional multi-phase multi-structured permanent magnet motor described above, and an object of the invention is to provide a permanent magnet motor which can weaken the magnetic coupling of different groups of armature windings each other, and to enhance the controllability. 
     In addition, an object of the present invention is to provide an electric power steering apparatus including a permanent magnet motor which can weaken, in the multi-phase multi-structured stator windings, the magnetic coupling of different groups of armature windings each other, and to enhance the controllability. 
     Means for Solving the Problems 
     A permanent magnet motor according to the present invention comprises: 
     a rotor including a rotor core fixed on a motor shaft, and permanent magnets fixed on the rotor core; and 
     a stator including a stator core, whose inner circumferential face opposes to an outer circumferential face of the rotor by means of a magnetic air gap, having a plurality of slots for accommodating armature windings, and a plurality of teeth, the permanent magnet motor is characterized in that: 
     the armature windings are constituted of a plurality of groups of multi-phase windings; 
     the plurality of groups of multi-phase windings is supplied with electric power from individual inverters in every one of respective groups; 
     portions of the rotor core exist on a side nearer to the stator than a middle diameter between a maximum outer diameter and a minimum outer diameter of the permanent magnets; 
     the plurality of teeth each include respective flanges; 
     the flanges each have a lateral side portion thereof opposing to a lateral side portion of a flange being provided in the teeth adjacent to each other and protruding in a circumferential direction of the stator core; 
     when a height in the lateral side portion of the flanges in a radial direction of the stator core is defined as h, and a length of the magnetic air gap is defined as g, relationship
 
1≤ h/g≤ 2
 
is held; and also,
 
     when a circumferential distance between opposing faces of the flanges ( 56 ) being adjacent to each other is defined as a, relationship
 
 a/g≥ 0.2
 
is satisfied.
 
     In addition, an electric power steering apparatus according to the present invention on which the permanent magnet motor is mounted, and torque is produced by the permanent magnet motor so as to assist steering of a driver, is characterized in that the permanent magnet motor is placed in such a direction that the motor shaft is in parallel with an extending direction of a rack shaft for driving a steering wheel of a wheeled vehicle. 
     Effects of the Invention 
     According to the permanent magnet motor of the present invention, such an effect can be achieved that the magnetic coupling of different groups of armature windings each other can be weakened, so that the controllability is enhanced, and at the same time, an effect of a field-weakening control can be efficiently exerted. 
     In addition, according to the electric power steering apparatus of the present invention, such an effect is achieved that a large quantity of torque-ripple reduction is made possible, and also the magnetic coupling can be weakened, so that the apparatus can also be applied to a large-size wheeled vehicle, and fuel consumption of the wheeled vehicle can be lowered. There exists an effect that the controllability is enhanced, and at the same time, the apparatus can be reduced in its size. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         FIG. 1  is an illustrative diagram for explaining an electric drive device in an electric power steering apparatus according to Embodiment 1 of the present invention; 
         FIG. 2  is an illustrative diagram for explaining circuits of a permanent magnet motor and an ECU according to Embodiment 1 of the present invention; 
         FIG. 3  is a cross section diagram illustrating a permanent magnet motor according to Embodiment 1 of the present invention; 
         FIG. 4  is an illustrative diagram for explaining an equivalent circuit of an armature winding of a permanent magnet motor according to Embodiment 1 of the present invention; 
         FIG. 5  is an illustrative diagram for a q-axis circuit configuration of a permanent magnet motor according to Embodiment 1 of the present invention; 
         FIG. 6  is a cross section diagram illustrating an enlarged view of a stator core of a permanent magnet motor according to Embodiment 1 of the present invention; 
         FIGS. 7A and 7B  are illustrative diagrams for explaining the magnetic coupling between a first armature winding and a second armature winding of a permanent magnet motor according to Embodiment 1 of the present invention; 
         FIG. 8  is an illustrative diagram for explaining NT (speed-torque) characteristics of a permanent magnet motor according to Embodiment 1 of the present invention; 
         FIG. 9  is a cross section diagram illustrating an enlarged view of a stator core in Modification Example 1 of a permanent magnet motor according to Embodiment 1 of the present invention; 
         FIG. 10  is a cross section diagram illustrating an enlarged view of a stator core in Modification Example 2 of a permanent magnet motor according to Embodiment 1 of the present invention; 
         FIG. 11  is a cross section diagram illustrating a permanent magnet motor according to Embodiment 2 of the present invention; 
         FIG. 12  is a cross section diagram illustrating a permanent magnet motor according to Embodiment 3 of the present invention; 
         FIG. 13  is a cross section diagram illustrating a permanent magnet motor according to Embodiment 4 of the present invention; and 
         FIG. 14  is an illustrative diagram for explaining the electric power steering apparatus including the permanent magnet motor according to Embodiment 1 of the present invention. 
     
    
    
     EMBODIMENTS FOR CARRYING OUT THE INVENTION 
     Embodiment 1 
       FIG. 14  is an illustrative diagram for explaining an electric power steering apparatus including a permanent magnet motor according to Embodiment 1 of the present invention. In  FIG. 14 , a driver of a wheeled vehicle such as an automotive vehicle steers a steering wheel (not shown in the figure), and its steering torque by the driver is transmitted to a steering shaft  1  by means of a steering-wheel shaft (not shown in the figure). At this time, steering torque detected by a torque sensor  2  is converted into an electric signal, and transferred to an ECU (Electronic Control Unit)  4  by way of a cable (not shown in the figure) and through a first connector  3 . The ECU  4  includes a control board, and inverter circuits (not shown in the figure) for driving the permanent magnet motor  5  according to Embodiment 1 of the present invention as will be described later. Note that, in the following explanation, the permanent magnet motor  5  may simply be referred to also as the motor. 
     Meanwhile, information of the wheeled vehicle such as a wheel speed(s) thereof is converted into an electric signal, and is transferred to the ECU  4  by way of a second connector  6 . In the ECU  4 , required assist torque is calculated from the information of the wheeled vehicle such as steering torque and a wheel speed(s) thereof described above, and electric currents are supplied to the motor  5  by way of inverters. The motor  5  is placed in an orientation parallel with a moving direction of a rack shaft as a motor&#39;s shaft direction is shown by the double arrows “A.” In addition, electric source-power into the ECU  4  is supplied form a battery and/or an alternator by way of a power-source connector  7 . 
     Torque produced by the motor  5  undergoes deceleration by a gear box  8  in which a belt (not shown in the figure) and a ball screw (not shown in the figure) are built, and thrust force is produced to move the rack shaft (not shown in the figure) existing inside of a housing  9  in a direction shown by the double arrows “A,” so that steering force of the driver is assisted. According to the arrangement that the rack shaft moves in the direction shown by the double arrows “A,” right and left tie-rods  10  and  11  of the wheeled vehicle move, and tire-wheels undergo turn-directions, so that the wheeled vehicle can be cornered. The driver can corner the wheeled vehicle with lesser steering force assisted by the torque of the motor  5 . Note that, right and left rack boots  12  and  13  of the wheeled vehicle are provided to prevent the ingress of a foreign object into the electric power steering apparatus. Note also that, the motor  5  and ECU  4  are integrally fixed, and constitute an electric drive device  100 . 
     Next, the explanation will be made for the electric drive device  100  described above.  FIG. 1  is an illustrative diagram for explaining the electric drive device in the electric power steering apparatus according to Embodiment 1 of the present invention. The electric drive device  100  illustrated in  FIG. 1  has a structure in which the motor  5  and ECU  4  according to Embodiment 1 of the present invention are integrally fixed. In  FIG. 1 , the explanation will be made first for the permanent magnet motor  5 . The motor  5  has a stator core  14  formed by laminating electrical steel sheets, armature windings  15  accommodated in slots of the stator core  14  as will be described later, and a frame  16  for fixing the stator core  14 . One end-portion of the frame  16  in an axial direction is fixed to a motor housing  17  by bolts  18  and  19 . 
     On the motor housing  17 , a first bearing  20  is fixed. In addition, in an inner circumferential portion of a wall portion  21  formed on the other end-portion of the frame  16  in the axial direction, a second bearing  22  is fixed. Although the wall portion  21  is integrally formed with the frame  16 , the wall portion may be separately formed therefrom. On a motor shaft  23 , a rotor core  24  formed by laminating electrical steel sheets is fixed by press-fit. The motor shaft  23  is supported by means of the first bearing  20  and the second bearing  22  rotationally movable with respect to the motor housing  17  and the frame  16 . 
     On one end-portion of the motor shaft  23  in the axial direction, namely, on the side of the output shaft, a pulley  27  is inserted by press-fit. The pulley  27  works to transmit driving force of the motor  5  to a belt (not shown in the figure) of the electric power steering apparatus. On the other end-portion of the motor shaft  23  in the axial direction, a sensor permanent-magnet  25  is fixed. On the rotor core  24  described above, permanent magnets  26  are fixed. Note that, in  FIG. 1 , an example is shown in which the permanent magnets  26  are fixed on a surface of the rotor core  24 ; however, a structure may be adopted in which they are embedded in the rotor core  24 . The description for these structures will be made later in detail. 
     Next, the explanation will be made for the ECU  4 . The ECU  4  is provided with the first connector  3  for receiving a signal from the torque sensor  2  described above, the second connector  6  for acquiring the information of the wheeled vehicle such as a wheel speed(s) thereof, and the power-source connector  7  for supplying electric source-power. In addition, for the ECU  4 , a first inverter circuit and a second inverter circuit are provided in order to drive the motor as will be described later. The first inverter circuit has a first switching device group  281  made of six MOS-FETs or the like. The second inverter circuit has a second switching device group  282  made of six MOS-FETs or the like. 
     As for each of the switching devices in the first and second switching device group  281  and  282 , a case is conceivable as exemplary configurations in which flip chips or microchips are mounted on a DBC (Direct Bonded Copper) board, microchips are molded by a resin to form a module, and the like. Each of the switching devices generates heat, because electric currents for driving the motor flow. For dealing therewith, each of the switching devices is so structured that the device contacts with a heat sink  29  by means of adhesive, an insulating sheet and the like to dissipate the heat therethrough. 
     In the first and second inverter circuits, smoothing capacitors, coils for noise removal, power relays, busbars for electrically connecting these parts, and so on are provided other than the switching devices described above; however, they are omitted in  FIG. 1 . The busbars are integrally formed with a resin, and form an intermediate member  30 . In addition, adjacent to the intermediate member  30 , a control board  31  is provided. This control board  31  transmits control signals to the first and second switching device group  281  and  282  so as to suitably drive the motor  5 , based on the information received from the first and second connectors  3  and  6 . 
     The control signals are transferred by connection members (not shown in the figure) which electrically connect between the control board  31 , and each of the switching devices of the first and second switching device group  281  and  282 . These connection members are fixed on semiconductor devices and the control board  31  by wire bonding, press-fit, soldering, and so on. The first and second inverter circuits constituted of these semiconductor devices, and the control board  31  are covered by an ECU casing  32 . The ECU casing  32  may be formed of a resin or may be formed of a metal of aluminum or the like, or may be in a configuration forming a combination of a resin and a metal of aluminum or the like. As for a placement of the control board  31 , the control board is placed along a surface perpendicular to an axial direction of the motor shaft  23  of the motor  5 . 
     On a side face of the heat sink  29  opposing to the motor  5 , a sensor unit  33  is placed. The sensor unit  33  has a magnetic sensor  34 , a sensor board  35 , a sensor connection member  36 , and a sensor supporting member  37 ; the sensor board  35  on which the magnetic sensor  34  is mounted is fixed on the heat sink  29  by a screw(s) (not shown in the figure). 
     The magnetic sensor  34  is placed on the same axis as the axial center of the motor shaft  23 , and is also placed at a position mutually corresponding to the sensor permanent-magnet  25 ; by detecting a magnetic field in which the sensor permanent-magnet  25  generates and detecting the orientation of the magnetic field, the magnetic sensor detects a rotor&#39;s rotation angle of the motor  5 . The sensor connection member  36  is held by the sensor supporting member  37 , and the member electrically connects the sensor board  35  of the sensor unit  33 , and the control board  31  to each other. These connections may also be made by press-fit, or by soldering. Note that, because the sensor connection member  36  is required to pass through the heat sink  29  and the intermediate member  30 , a through hole (not shown in the figure) is provided for the heat sink  29  and the intermediate member  30  so that the sensor connection member  36  passes through them. Note also that, though not shown in the figure, the intermediate member  30  is configured to provide a guide therein for positioning the sensor connection member  36 . 
     In  FIG. 1 , a recessed portion  38  is provided in the heat sink  29 , so that the distance is increased between the magnetic sensor  34  mounted on the sensor board  35  of the sensor unit  33 , and the top face of the heat sink  29 , namely, the bottom face of the recessed portion  38 . The heat sink  29  is fixed on the frame  16  of the motor  5  by means of a screw(s), a shrink fit, and the like. According to the above, by fixing the heat sink  29  on the frame  16  of the motor  5 , the heat of the heat sink  29  can be transferred to the frame  16 . 
     The ECU  4  supplies suitable drive currents to the armature windings  15  of the motor  5  in accordance with a rotor&#39;s rotation angle of the motor  5  being detected by the sensor unit  33 . 
     Note that, in  FIG. 1 , an example is shown in which the magnetic sensor  34  is mounted on the sensor board  35 , other than the control board  31 ; however, as a configuration in which the magnetic sensor is mounted on the control board  31 , a structure may also be adopted in such a manner that magnetic flux leaking from the sensor permanent-magnet  25  through the heat sink  29  is detected. In addition, the configuration may also be taken so that the positional relationship between the intermediate member  30  and the control board  31  is reversed for their placement of  FIG. 1 . Moreover, in  FIG. 1 , a configuration of applying the magnetic sensor  34  is shown as the configuration of the sensor unit for detecting a position of the rotor; however, it is needless to say that a resolver may be applied to the configuration. 
     Next, the explanation will be made for a circuit configuration of the portions of inverters in the ECU  4 .  FIG. 2  is an illustrative diagram for explaining circuits of the motor and the ECU according to Embodiment 1 of the present invention. Note that, for the sake of simplicity in  FIG. 2 , the armature windings are only shown for the motor  5 . The armature windings  15  of the motor  5  are constituted of a first armature winding  39  made of a first phase-U winding U 1 , a first phase-V winding V 1  and a first phase-W winding W 1 , and a second armature winding  40  made of a second phase-U winding U 2 , a second phase-V winding V 2  and a second phase-W winding W 2 . In  FIG. 2 , the first and second armature windings  39  and  40  are shown as Y connections; however, they may also be in Δ connections. 
     In the ECU  4  shown in  FIG. 2 , the portions of electric power circuits of the inverters are only shown for the sake of simplicity. Into the ECU  4 , a DC voltage is supplied from an electric power source  43  such as a battery by way of a coil  44  for noise removal. The ECU  4  includes two groups of inverter circuits: a first inverter circuit  41  and a second inverter circuit  42 . Into the first inverter circuit  41 , the DC voltage is supplied from the electric power source  43  by way of the coil and a first power relay  45 , and the first inverter circuit supplies three-phase currents to the first armature winding  39 . Into the second inverter circuit  42 , the DC voltage is supplied from the electric power source  43  by way of the coil  44  and a second power relay  46 , and the second inverter circuit supplies three-phase currents to the second armature winding  40 . Note that in  FIG. 2 , the electric power source  43  is shown as if it exist inside of the ECU  4 ; however, as for the electric power source  43  under actual circumstances, electric power is supplied from a power source, being external to the ECU  4 , such as an onboard battery by way of connectors. 
     The first and second power relays  45  and  46  each are constituted of two MOS-FETs, and operate so that, by turning off the MOS-FETs at the time of a malfunction or the like, an excessively large current does not flow through each of the inverter circuits  41  and  42 . Note that, in  FIG. 2 , the electric power source  43 , the coil  44 , the first power relay  45  and the second power relay  46  are connected in this order; however, it is needless to say that the first power relay  45  and the second power relay  46  may be connected at a position nearer to the electric power source  43  than the coil  44 . 
     A first smoothing capacitor  47  is connected across input terminals of the first inverter circuit  41 , and a second smoothing capacitor  48 , connected across input terminals of the second inverter circuit  42 . Note that, in  FIG. 2 , the first and second smoothing capacitors  47  and  48  each constitute one capacitor; however, it is needless to say that a plurality of capacitors may be constituted so that the capacitors are connected in parallel with one another. 
     The first and second inverter circuits  41  and  42  each constitute a three-phase bridge circuit using six MOS-FETs. The first inverter circuit  41  includes a first arm in which a MOS-FET  11  and a MOS-FET  12  are connected in series, a second arm in which a MOS-FET  13  and a MOS-FET  14  are connected in series, and a third arm in which a MOS-FET  15  and a MOS-FET  16  are connected in series; these first through third arms are connected in parallel with one another. On a GND (ground potential) side of the MOS-FET  12 , the MOS-FET  14  and the MOS-FET  16  each positioned at lower levels of those first through third arms, shunt resistors  49 ,  50  and  51  are connected one by one, respectively. 
     Similarly, the second inverter circuit  42  includes a first arm in which a MOS-FET  21  and a MOS-FET  22  are connected in series, a second arm in which a MOS-FET  23  and a MOS-FET  24  are connected in series, and a third arm in which a MOS-FET  25  and a MOS-FET  26  are connected in series; these first through third arms are connected in parallel with one another. On a GND (ground potential) side of the MOS-FET  22 , the MOS-FET  24  and the MOS-FET  26  each positioned at lower levels of those first through third arms, shunt resistors  52 ,  53  and  54  are connected one by one, respectively. 
     Each of the shunt resistors  49  through  54  described above is used for detecting an electric current value. Note that, an example is shown in which the shunt resistors are provided in the number of three for every one of the first and second inverter circuits  41  and  42 ; however, it may be adopted that two shunt resistors are provided for every one of the first and second inverter circuits  41  and  42 , and it is needless to say that, because an electric current detection is possible even with one shunt resistor, such configuration may also be adopted. 
     In supplying electric currents from the first inverter circuit  41  into the motor  5 , as illustrated in  FIG. 2 , a current is supplied from the series connected portion between the MOS-FET  11  and the MOS-FET  12  to a phase-U 1  of the first armature winding  39  of the motor  5  by way of busbars or the like; a current is supplied from the series connected portion between the MOS-FET  13  and the MOS-FET  14  to a phase-V 1  of the first armature winding  39  of the motor  5  by way of busbars or the like; and a current is supplied from the series connected portion between the MOS-FET  15  and the MOS-FET  16  to a phase-W 1  of the first armature winding  39  of the motor  5  by way of busbars or the like. 
     In supplying electric currents from the second inverter circuit  42  into the motor  5 , as illustrated in  FIG. 2 , a current is supplied from the series connected portion between the MOS-FET  21  and the MOS-FET  22  to a phase-U 2  of the second armature winding  40  of the motor  5  by way of busbars or the like; a current is supplied from the series connected portion between the MOS-FET  23  and the MOS-FET  24  to a phase-V 2  of the second armature winding  40  of the motor  5  by way of busbars or the like; and a current is supplied from the series connected portion between the MOS-FET  25  and the MOS-FET  26  to a phase-W 2  of the second armature winding  40  of the motor  5  by way of busbars or the like. 
     In  FIG. 2 , motor relays are not shown which electrically break between the motor  5  and the first and second inverter circuits  41  and  42  when some kind of malfunction occurs in the ECU  4 ; however, in order to provide the motor relays, a case is conceivable in which they are provided at the neutral points N 1  an N 2  of the first and second armature windings  39  and  40 , and a case, in which they are provided between the motor  5  and the first and second inverter circuits  41  and  42 . 
     The first and second inverter circuits  41  and  42  performs switching each of the MOS-FETs by transmitting to them signals from control circuits (not shown in the figure) in accordance with a rotor&#39;s rotation angle of the motor  5  detected by means of a rotation angle sensor  55  included in the motor  5 , so that desired three phase currents are supplied into the first and second armature windings  39  and  40 . Note that, as for the rotation angle sensor  55 , the magnetic sensor is used, for example. To be specific, used are a configuration which combines a permanent magnet, and a GMR (Giant Magneto Resistive effect) sensor or an AMR (Anisotropic Magneto Resistance) sensor, a resolver, etc. 
     Next, the explanation will be made in more detail for the permanent magnet motor according to Embodiment 1 of the present invention.  FIG. 3  is a cross section diagram illustrating the permanent magnet motor according to Embodiment 1 of the present invention. In  FIG. 1  through  FIG. 3 , a stator  501  is provided which has an inner circumferential face opposing, through a gap, to an outer circumferential face of a rotor  502 . The stator  501  has the armature windings  15  made of the aforementioned the first armature winding  39  and the second armature winding  40 , and the stator core  14 . The stator core  14  is constituted of an annular core back  140  formed by a magnetic material of electrical steel sheets or the like, and teeth  141  extending from the core back  140  toward the inner radial side. 
     The armature windings  15  are accommodated in slots  142  provided between the adjacent teeth  141 . Although not shown in the figures, insulating paper or the like is inserted between the armature windings  15  and the stator core  14 , so that the electrical insulation is secured therebetween. The teeth  141  are provided in the number of 48 in total, and therefore, the slots  142  are also in the number of 48. In one of the slots  142 , coils of the armature windings  15  are accommodated. 
     As described above, the first armature winding  39  is constituted of three phases of the phase-U 1 , the phase-V 1  and the phase-W 1 , and the second armature winding  40 , constituted of three phases of the phase-U 2 , the phase-V 2  and the phase-W 2 . As for the placements of windings, they are placed from a first slot ( 1 ) in the order of U 1 , U 2 , W 1 , W 2 , V 1  and V 2  as shown in  FIG. 3 ; the windings are thereafter placed from a seventh slot ( 7 ) also in the order of U 1 , U 2 , W 1 , W 2 , V 1  and V 2 , and are placed up to a 48th slot ( 48 ) in a similar order. Namely, the first armature winding  39  and the second armature winding  40  are placed in the adjacent slots  142 . 
     However, the armature windings are placed so that, in the phase-U 1  of the first slot ( 1 ) and the phase-U 1  of the seventh slot ( 7 ), the orientations of their electric currents are mutually reversed. Namely, the configuration of distributed winding is taken in which the armature windings are wound from the first slot ( 1 ) to the seventh slot ( 7 ). Therefore, it can be said that the armature windings each are placed to bridge the six teeth in total. This corresponds to the electrical angle of 180 degrees, so that a short-pitch factor becomes “1”; and thus, magnetic flux in which the permanent magnets  26  generate can be effectively utilized, so that such an effect can be achieved as obtaining a motor of a small size and high torque, and as reducing the costs in comparison with a motor having a small winding factor, because the quantity of the permanent magnets  26  can be reduced. 
     In an inside space portion of the stator  501 , the rotor  502  is provided that includes the permanent magnets  26  on a surface of the rotor core  24 . The permanent magnets  26  are placed side by side in an equal interspace therebetween, in the number of eight, in a circumferential direction of the rotor  502 , and take the configuration of eight magnetic poles. Magnetic polarities of the adjacent permanent magnets  26  are reversed to each other. In addition, in the rotor core  24 , eight protrusion portions  241  are provided; non-magnetic gaps for reducing leakage flux are provided between the protrusion portions  241  and the permanent magnets  26 . These protrusion portions  241  have an effect to reduce an air gap between the stator  501  of the motor  5  and the rotor  502  thereof, resulting in increase in the inductance. As a result, the field-weakening control facilitates exerting its effect, so that such an effect can be achieved as enhancing the torque at the time of fast rotation. 
     The rotor core  24  is formed by laminating electrical steel sheets or the like, and the electrical steel sheets are mutually joined to one another by swaging portions  243 . At the central portion of the rotor core  24 , the motor shaft  23  passes through. Moreover, in the rotor core  24 , eight holes  242  are provided. By providing these holes  242 , an effect can be achieved as obtaining weight reduction and inertia reduction of the rotor core  24 . 
     Next, in the permanent magnet motor according to Embodiment 1 of the present invention, the explanation will be made for the reasons why torque ripples are reduced. As illustrated in  FIG. 3 , the number of the slots  142  in the stator core  14  of the motor  5  is “48,” and the number of poles is “8,” thereby revealing that the slot pitch is “360 degrees/48×4=30 degrees” in electrical angles. In addition, because the first armature winding  39  and the second armature winding  40  are accommodated in the adjacent slots, the phase-U 1  and the phase-U 2  have mutually a shifted phase by an electrical angle 30 degrees. The phase-V 1  and the phase-V 2 , and the phase-W 1  and the phase-W 2  also have mutually the shifted phase by an electrical angle 30 degrees. 
     Accordingly, when, in the first armature winding  39  and the second armature winding  40 , three-phase alternating currents are energized in which their phases are shifted mutually by an electrical angle of 30 degrees, the phases are reversed in a torque ripple in the sixth at an electrical angle produced by the magnetomotive force of the first armature winding  39 , and a torque ripple in the sixth at an electrical angle produced by the magnetomotive force of the second armature winding  40 , so that the torque ripples in the sixth at electrical angles are cancelled out. In order to flow electric currents with the different phases into the first armature winding  39  and the second armature winding  40 , it is possible to implement the arrangement by providing two inverter circuits of the aforementioned first and second inverter circuits  41  and  42  illustrated in  FIG. 2 , and by performing individual controls, respectively. Note that, if a phase difference in the electric currents of the first armature winding  39  and the second armature winding  40  is in vicinity to 20 degrees through 40 degrees, similar effects can be obtained. 
     In  FIG. 3 , the rotor  502  includes the protrusion portions  241  formed in the rotor core  24 , and the height of the protrusion portions  241  each is set so that, on the side nearer to the stator  501  than the middle diameter between the maximum outer diameter and the minimum outer diameter of the permanent magnets  26 , an outer circumferential face of the rotor core  24 , namely, an outer circumferential face of the protrusion portions  241  is positioned. In the configuration described above, reluctance torque can be obtained by utilizing changes in magneto-resistance of the rotor core  24 . In a motor which produces reluctance torque, the field-weakening control effectively operates because the d-axis inductance is increased, so that the torque at the time of fast rotation is enhanced. 
     However, in the motor where the first armature winding  39  and the second armature winding  40  are accommodated in the mutually adjacent slots as illustrated in  FIG. 3 , the magnetic coupling between the first armature winding  39  and the second armature winding  40  becomes significant, in a case in which the rotor core  24  is provided on the side nearer to the stator  501  than the middle diameter between the maximum outer diameter and the minimum outer diameter of the permanent magnets  26 , in comparison with a case other than this. This is because the rotor core  24  being nearer to the stator  501  has a working-effect to lower the magneto-resistance between the first armature winding  39  and the second armature winding  40 . 
       FIG. 4  is an illustrative diagram for explaining an equivalent circuit of the armature winding of the permanent magnet motor according to Embodiment 1 of the present invention. In  FIG. 4 , Vu designates each terminal voltage of the armature winding; iu, armature current; R, resistance; ve, induced voltage; lm, leakage inductance; and M, mutual inductance. The suffix “1” indicates the primary side; and the suffix “2,” the secondary side. In addition, symbol “n” corresponds to a turn ratio in a transformer. Note that, in these values, the symbols lm and M indicate in particular, differ from those values used in a usual motor control, quantities of inductance between two phase in multiple structures placed in parallel with each other. Moreover, because the numbers of windings of those windings connected in parallel with one another are generally the same in a multi-structured multi-phase winding alternating-current motor, “n=1.” Because equivalent circuits of the phase-V 1  and the phase-V 2 , the phase-W 1  and the phase-W 2 , the phase-U 1  and the phase-V 2 , the phase-U 1  and the phase-W 2 , the phase-V 1  and the phase-U 2 , the phase-V 1  and the phase-W 2 , the phase-W 1  and the phase-U 2 , and the phase-W 1  and the phase-V 2  are also the same as that in  FIG. 4 , an equivalent circuit in the d-q axes is the same as the equivalent circuit shown in  FIG. 4 , even when coordinates conversion is performed from the three phases including the phase-U, the phase-V and the phase-W, in the case of three-phase balance, to the d-q axes of the rotor. 
       FIG. 5  is an illustrative diagram for a q-axis circuit configuration of the permanent magnet motor according to Embodiment 1 of the present invention, and illustrates a q-axis equivalent circuit in a block diagram form when the coordinates conversion is performed to the rotor&#39;s d-q axes. In  FIG. 5 , vq 1  and vq 2  designate q-axis voltages of the first armature winding and the second armature winding, respectively; iq 1  and iq 2 , q-axis currents of the first armature winding and the second armature winding, respectively; Lq 1  and Lq 2 , q-axis components of self inductance of the first armature winding and the second armature winding, respectively; Ra 1  and Ra 2 , resistance components of the first armature winding and the second armature winding, respectively; and Mq 12  and Mq 21 , q-axis components of mutual inductance between the first armature winding and the second armature winding, respectively. Symbol “s” designates a differential operator of the Laplace transform. Symbols vq 12  and vq 21  designate disturbance voltages superimposed on the first armature winding and the second armature winding due to mutual inductance between the first armature winding and the second armature winding, respectively. Note that,  FIG. 5  is a diagram showing the equivalent circuit on the rotor&#39;s q-axis; however, an equivalent circuit on the rotor&#39;s d-axis is in a similar configuration. 
     Because the disturbance voltages are proportional to the differential values that are control response frequencies of electric currents, the disturbance voltages become larger as fast as the electric currents are controlled by the motor control, so that the motor control becomes difficult to cancel out the torque ripples in high response frequencies. 
     Next, consideration will be given to an influence of the disturbance voltages in Embodiment 1 of the present invention. Here, as is clear from  FIG. 5 , in a multi-structured multi-phase winding alternating-current motor having the multi-structured armature windings as described above, the disturbance voltages mutually act, and act on a current control system as disturbance values iq 1 ′ and iq 2 ′. The disturbance values iq 1 ′ and iq 2 ′ are given from the block diagram of the q-axis equivalent circuit in  FIG. 5 , as Equation (1) and Equation (2) described below, respectively. 
     
       
         
           
             
               
                 
                   
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                   Equation 
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     Here, iq 1 , iq 2  designate q-axis currents of the first armature winding and the second armature winding, respectively; Ra 1 , Ra 2 , resistance values of the first armature winding and the second armature winding, respectively; Lq 1 , Lq 2 , q-axis components of self inductance of the first armature winding and the second armature winding, respectively; and Mq 12 , Mq 21 , q-axis components of mutual inductance which indicates the interference between the first armature winding and the second armature winding. 
     When the frequencies for the electric current control become high, a Laplace transform&#39;s differential operator “s” becomes larger, and in addition, it is clear from Equation (1) and Equation (2) that the disturbance values each approximately depend on magnetic coupling Mq 12 /Lq 1  or magnetic coupling Mq 21 /Lq 2 . When the magnetic coupling becomes stronger, the disturbance value is increased, so that, in accordance with the increased disturbance in a current control system, it is not possible to heighten the response in the current control system, resulting in decreasing the motor&#39;s controllability. Note that, it may be regarded as “Mq 12 /Lq 1 ≅Mq 21 /Lq 2 ,” because the armature in the case of Embodiment 1 has a structure in which the first armature winding and the second armature winding are symmetrical with each other. Therefore, the explanation will be hereinafter made for the magnetic coupling as Mq 12 /Lq 1 . 
     In the motor where the first armature winding  39  and the second armature winding  40  are accommodated in the mutually adjacent slots  142  as illustrated in  FIG. 3 , there arises a problem in that the magnetic coupling Mq 12 /Lq 1  between the first armature winding  39  and the second armature winding  40  becomes stronger, in a case in which the circumferential face of the rotor core  24  is positioned on the side nearer to the stator  501  than the middle diameter between the maximum outer diameter and the minimum outer diameter of the permanent magnets  26 , in comparison with a case other than this, so that the motor&#39;s controllability is lowered. 
       FIG. 6  is across section diagram illustrating an enlarged view of the stator core of the permanent magnet motor according to Embodiment 1 of the present invention. In  FIG. 6 , the stator  501  is provided with the stator core  14  having the core back  140 , the teeth  141  and the slots  142 , and the armature windings  15  accommodated inside the slots  142 . Although insulating paper or the like is provided between the armature windings  15  and the stator core  14  for securing the electrical insulation, such insulating paper is omitted in  FIG. 6 . At the front ends of the teeth  141 , flanges  56  are provided. In  FIG. 6 , the width of the narrowest portions of the teeth  141  is indicated as “w”; the distance of the adjacent flanges  56 , as “a”; and a radial height between opposing faces of the adjacent flanges  56  of the stator core  14 , as “h.” Curved face portions R 1  are provided on the inner radial sides of faces where the adjacent flanges  56  are opposing to each other. The height “h” is defined as the height of regions excluding the curved face portions R 1 . According to the motor for EPS usage, the curved face portions R 1  each are set in the degree of 0.2 [mm] through 0.4 [mm]. 
     The rotor  502  takes a configuration of the rotor core  24  and the permanent magnets  26  which are placed on the surface of the rotor core, and the protrusion portions  241  are formed on both sides of the permanent magnets  26 . The protrusion portions  241  protrude toward the side of the inner circumferential face of the stator  501 ; the height of the protrusion portions each is set so that they protrude on the side nearer to the stator  501  than the middle diameter between the maximum outer diameter Rout and the minimum outer diameter Rin of the permanent magnets  26 . In order to prevent scattering the permanent magnets  26 , there also arises a case in which the outer circumferential face of the rotor  502  is covered overall by a pipe made of a non-magnetic metal such as SUS or aluminum; however, the pipe is omitted in  FIG. 6 . The length of a magnetic air gap between the outer circumferential face of the rotor  502  and the inner circumferential face of the stator  501  is “g.” When the outer circumferential face of the rotor  502  is covered by a pipe made of a metal, the thickness of the pipe made of a metal is included in the length of the magnetic air gap. 
     In  FIG. 6 , the configuration is taken so that the relationship “1≤h/g≤2” is held between the radial height “h” of the faces where the adjacent flanges  56  of the stator core  14  are opposing to each other, and the length “g” of the magnetic air gap. In addition, the configuration is taken so that the relationship “a/g≥0.2” is satisfied between a circumferential distance “a” between the faces where the adjacent flanges  56  of the stator core are opposing to each other, and the length “g” of the magnetic air gap. 
     By taking the configuration described above, the leakage flux increases between the adjacent flanges  56 , so that the inductance Lq 1  increases. Meanwhile, in order to interlink magnetic flux through different groups of the armature windings  15 , the magnetic flux must pass twice through the faces where the adjacent flanges  56  are opposing to each other; however, the interlinkage flux can be reduced, because “a/g≥0.2” being defined. Accordingly, an effect can be achieved as obtaining a value of Mq 12  which becomes smaller. As a result, a value of Mq 12 /Lq 1  can be made smaller, so that the motor&#39;s controllability can be enhanced. For this reason, it can be namely said that ensuring both an effect of the field-weakening control due to the increase in the inductance, and the reduction in the magnetic coupling has hitherto been difficult, but both of them can be ensured. 
       FIGS. 7A and 7B  are illustrative diagrams for explaining the magnetic coupling between the first armature winding and the second armature winding of the permanent magnet motor according to Embodiment 1 of the present invention.  FIG. 7A  shows the relationships among: a radial height “h” of the faces where the adjacent flanges  56  are opposing to each other, and the length “g” of the magnetic air gap; motor&#39;s torque; and magnetic coupling. The horizontal axis indicates h/g, and the vertical axes indicate the torque and the magnetic coupling. As for the torque, the percent values are indicated by setting the torque at 100 [%] when “h/g=0.83,”, and, as for the magnetic coupling, Mq 12 /Lq 1  [%] is indicated. By taking “h/g≤2,” the leakage flux into the adjacent teeth  141  can be reduced, so that the reduction of torque becomes slightly 0.5 [%] or less. On the other hand, by taking “1≤h/g,” the magnetic coupling Mq 12 /Lq 1  becomes a value of 69 [%] or less, so that there exists an effect that a frequency response of the control can be heightened, and a frequency response required for the motor control of the electric power steering apparatus (EPS) can be obtained. 
     Meanwhile,  FIG. 7B  is the diagram showing the relationship between: a circumferential distance “a” between opposing faces of the adjacent flanges  56  in the teeth  141  of the stator core  14 , and the length “g” of a magnetic air gap between the rotor  502  and the stator  501 ; and the magnetic coupling. The horizontal axis indicates a/g, and the vertical axis indicates the magnetic coupling Mq 12 /Lq 1 . By taking “a/g≥0.2,” the magnetic coupling Mq 12 /Lq 1  becomes a value of 69 [%] or less, so that such an effect can be achieved that a frequency response of the control can be heightened, and a frequency response required for the motor control of electric power steering can be obtained. 
       FIG. 8  is an illustrative diagram for explaining NT (speed-torque) characteristics of the permanent magnet motor according to Embodiment 1 of the present invention, and the relationships between a motor&#39;s rotational speed N and torque T are shown; the horizontal axis indicates the motor&#39;s rotational speed N [r/min], and the vertical axis indicates the torque T [Nm]. The comparison is made and shown for two kinds of motor ( 1 ) and motor ( 2 ) having the same rated torque. It can be known that the rated torque T 1 =T 2 . The suffix “1” indicates the motor ( 1 ), and the suffix “2,” the motor ( 2 ). 
     In  FIG. 8 , the curve C 1  indicates the characteristic of the motor ( 1 ), exemplifying a motor of a surface permanent magnet type in which the rotor core  24  is not provided on the side nearer to the stator  501  than the middle diameter between the maximum outer diameter and the minimum outer diameter of the permanent magnets  26 . The curve C 2  indicates the characteristic of the motor ( 2 ), exemplifying a case in which the rotor core  24  is provided on the side nearer to the stator  501  than the middle diameter between the maximum outer diameter and the minimum outer diameter of the permanent magnets  26 , namely, the case of the permanent magnet motor according to Embodiment 1 of the present invention. 
     When the rotor core  24  is provided on the side nearer to the stator  501  than the middle diameter between the maximum outer diameter and the minimum outer diameter of the permanent magnets  26  as the case of the motor ( 2 ), the torque at the time of fast rotation is enhanced (curve C 2 ), because the inductance is increased, and the field-weakening control exerts its effect. When the comparison is made in the numbers of no-load revolutions, it can be known that N 01 &lt;N 02 . Meanwhile, the numbers of rated revolutions N 1  and N 2  are approximately in coincidence with each other. Therefore, it can be understood that the rated output of the motor ( 2 ) is approximately equivalent in comparison with that of the motor ( 1 ), and the torque in the high revolution range is enhanced to a large extent. When the rotor core  24  is provided on the side nearer to the stator  501  than the middle diameter between the maximum outer diameter and the minimum outer diameter of the permanent magnets  26  as the conventional technology, the magnetic coupling of different groups of armature windings each other is strong, so that the controllability is lowered; however, according to the configuration in Embodiment 1 of the present invention, the reduction in the magnetic coupling can be achieved. 
     Modification Example 1 of Embodiment 1 
       FIG. 9  is a cross section diagram illustrating an enlarged view of a stator core in Modification Example 1 of the permanent magnet motor according to Embodiment 1 of the present invention. In the permanent magnet motor illustrated in  FIG. 9 , the configuration is taken in which the relationship “1≤h/g≤2” is held between a radial height “h” of the faces where the adjacent flanges  56  are opposing to each other in the teeth  141  of the stator core  14 , and the length “g” of the magnetic air gap. 
     In addition, the configuration is taken in which the relationship “a/g≥0.2” is satisfied between a circumferential distance “a” between opposing faces of the adjacent flanges  56  in the teeth  141  of the stator core  14 , and the length “g” of a magnetic air gap. Moreover, the curved face portions R 1  are provided on the inner radial sides of faces where the adjacent flanges  56  are opposing to each other, and also curved face portions R 2  are provided on the outer radial sides. The height “h” is defined as the height of regions excluding the curved face portions R 1  and R 2 . 
     According to the motor for EPS usage, the curved face portions R 1  and R 2  each are set in the degree of 0.2 [mm] through 0.4 [mm]. It is needless to say that the effect described in the explanation of  FIG. 6  can be obtained by taking the configuration described above; in addition, by providing the curved face portions R 1  and R 2 , there exists an effect that the magneto-resistance increases between the curved face portions R 1  and R 2  of the adjacent flanges  56 , and the magnetic coupling can be weakened. Moreover, by providing the curved face portions R 1  and R 2  on both the inner radial side and outer radial side, there also exists an effect that stamping of electrical steel sheets by die-cutting becomes easier, and the life of dies is prolonged. 
     Even when the curved face portions each are provided on either one of the inner radial side and outer radial side, such an effect can be achieved that the magneto-resistance increases between the curved face portions of the adjacent flanges, so that the magnetic coupling can be weakened. 
     Modification Example 2 of Embodiment 1 
       FIG. 10  is a cross section diagram illustrating an enlarged view of a stator core in Modification Example 2 of the permanent magnet motor according to Embodiment 1 of the present invention. In Modification Example 2 illustrated in  FIG. 10 , when the width of the teeth  141 , on the outer radial side than the flanges  56 , in the portions where the teeth  141  become the narrowest is defined as “w”; the maximum outer diameter of the rotor core  24 , as Rout; and the number of slots, as Ns, the configuration takes to hold the following Equation (3).
 
0.4×2π( R out+ g+h )/ Ns≤w≤ 0.5×2π( R out+ g+h )/ Ns   Equation (3)
 
     For example, when magnetic flux density in a motor&#39;s gap of the motor using a rare-earth magnet of neodymium-iron-boron system for the permanent magnets  26  is 0.8 T, and in a case in which magnetic flux entirely passes through the teeth  141  under the condition where Equation (3) is held, the maximum value of magnetic flux density becomes approximately in the degree of 1.6 T through 2.0 T in the portions where the teeth  141  become the narrowest. According to this arrangement, because magnetic saturation can be mitigated in the portions where the teeth  141  become the narrowest, the rated torque is enhanced. In addition, because the self inductance becomes larger due to the mitigation of magnetic saturation, such an effect can be achieved as reducing the magnetic coupling Mq 12 /Lq 1 , so that the controllability is enhanced. 
     In addition, when a circumferential width of the slots  142  in the portions where the teeth  141  become the narrowest is defined as S 1 , the relationship w≤S 1  is given. This is because the slot&#39;s width is equal to or larger than the width of the teeth, large cross-sectional areas of the slots can be secured. As a result, large cross-sectional areas of the armature windings can additionally be secured, there also exists an effect that the reduction of copper losses and output enhancement of the motor can be achieved. 
     From the relationships between Equation (3) described above, and “S 1 +w=2π(Rout+g+h)/Ns,” for S 1 
 
0.5×2π( R out+ g+h )/ Ns≤S 1≤0.6×2π( R out+ g+h )/ Ns   Equation (4)
 
can be expressed. According to this configuration, the maximum value of magnetic flux density becomes approximately in the degree of 1.6 T through 2.0 T in the portions where the teeth  141  become the narrowest as described above. According to this arrangement, because the magnetic saturation can be mitigated in the portions where the teeth  141  become the narrowest, the rated torque is enhanced.
 
     Moreover, because the self inductance becomes larger due to the mitigation of magnetic saturation, such an effect can be achieved as reducing the magnetic coupling Mq 12 /Lq 1 , so that the controllability is enhanced. In addition, as illustrated in  FIG. 10 , the configuration is so adopted that a slot&#39;s circumferential width becomes larger in accordance with a position toward an outer radial side, and that the width of the slots becomes the maximum value of S 2  in the vicinity of the core back. By taking the configuration described above, there exists an effect that the leakage flux leaking between the adjacent teeth  141  can be reduced, and the motor&#39;s torque can be enhanced, so that the quantity of permanent magnet use can be reduced. In addition, because large cross-sectional areas of the slots can be secured in comparison with a configuration in which the width of the slots  142  is constant, there also exists an effect that large cross-sectional areas of the armature windings  15  can additionally be secured, and copper losses can be reduced, so that the motor&#39;s output can be enhanced. 
     Up to this time, the examples are described in which two armature windings in total of the first armature winding  39  and the second armature winding  40 ; however, similar effects can be obtained even in multi-structured windings having three or more armature windings. 
     By mounting the permanent magnet motor of Embodiment 1 described above on an electric power steering apparatus, a large quantity of torque-ripple reduction in the sixth is made possible. Although there arises a problem in that the magnetic coupling becomes stronger at the same time of increased output of the motor, and that the motor&#39;s controllability is lowered, the magnetic coupling can be reduced, so that such an effect can be additionally achieved as applying the electric power steering apparatus also to a large-size wheeled vehicle, and lowering fuel consumption. In particular, because the motor described above is low in vibration and low in noise even when its output is high, the motor is suitable for an electric power steering apparatus in which the motor is placed in an orientation parallel with a moving direction of a rack shaft used for an application of the high output. 
     Embodiment 2 
     In Embodiment 1, the explanation has been made for the structure where the permanent magnets are placed on a surface of the rotor core; however, in Embodiment 2, a structure is adopted in which the permanent magnets are embedded in the rotor core to make a permanent magnet motor (IPM).  FIG. 11  is a cross section diagram illustrating the permanent magnet motor according to Embodiment 2 of the present invention. In  FIG. 11 , the stator  501  takes the same structure as that in the case of  FIG. 3  in Embodiment 1. 
     In the rotor  502 , which differs from the case in  FIG. 3 , the permanent magnets  26  each in a planar shape are placed being embedded in permanent magnet hole-portions  57  formed in the rotor core  24 . The permanent magnet hole-portions  57  are formed in an equal interspace therebetween, in the number of eight, in proximity at around an outer circumferential face of the rotor core  24  in a circumferential direction thereof, and the permanent magnets  26  are embedded one by one for each of the permanent magnet hole-portions  57 . The permanent magnets  26  circumferentially neighboring to each other are placed so that their magnetic polarities are set in the reversed directions. 
     Moreover, on the side nearer to the stator  501  than the permanent magnets  26 , slits  58  are provided in the rotor core  24 . In  FIG. 11 , five slits are placed for each of the magnetic poles. In the slits  58 , a non-magnetic material such as air or a resin is filled. The slits  58  each are slantingly placed so that magnetic flux is directed toward the center of magnetic pole. According to this arrangement, the motor&#39;s torque is increased, and a motor of a small size and high output can be obtained. In the rotor core  24 , the holes  242  are provided. By providing the holes  242 , weight reduction and inertia reduction can be achieved. The rotor core  24  is formed by laminating electrical steel sheets or the like, and the electrical steel sheets are mutually joined to one another by the swaging portions  243 . In the center of the rotor core  24 , the motor shaft  23  passes through. 
     As described above, in a case of the interior permanent magnet type, the rotor core  24  exists nearer to the stator core  14 , so that the magneto-resistance between the stator core  14  and the rotor core  24  becomes smaller; as a result, such tendency can be observed that the magnetic coupling between the first armature winding  39  and the second armature winding  40  becomes stronger; however, by taking the structure as described in Embodiment 2, such an effect can be achieved as weakening the magnetic coupling, and enhancing the controllability. In addition, because reluctance torque can be used, the quantity of use of the permanent magnets  26  can be reduced. Moreover, because the inductance is increased, and the field-weakening control can exert its effect, so that such an effect can also be achieved that the torque at the time of fast rotation is enhanced. 
     Embodiment 3 
       FIG. 12  is a cross section diagram illustrating a permanent magnet motor according to Embodiment 3 of the present invention; the motor is referred to as a spoke (Spoke) type IPM. In  FIG. 12 , the stator  501  takes the same structure as that in the case of  FIG. 3  in Embodiment 1. The rotor  502  has a structure different from that in the cases in  FIG. 3  and  FIG. 11  described above. In the rotor  502 , the motor shaft  23  being the rotational shaft, and the rotor core  24  are provided in the outer side of the motor shaft  23 . 
     The permanent magnets  26  each take shapes in such a manner that their radial length is longer in comparison with their circumferential length, and these permanent magnets  26  are circumferentially placed side by side in an equal interspace therebetween, in the number of eight. As for the directions of magnetization of the permanent magnets  26 , they are magnetized in such directions that the permanent magnets&#39; N pole and S pole correspond to “N” and “S” shown in  FIG. 12 , respectively. Namely, the opposing faces of the adjacent permanent magnets  26  to each other are magnetized to mutually form the same magnetic pole. By taking the directions of magnetization described above, the magnetic flux is concentrated in the rotor core  24 , so that there exists an effect that the magnetic flux density is heightened. In addition, the rotor core  24  interposes between the adjacent permanent magnets  26 . Faces of the rotor core  24  opposing to the inner circumferential face of the stator  501 , namely, the outer circumferential faces are formed in the shape of curved planes. And then, the shape of these curved planes each takes a protrusion-shape curved plane  61  so that the length of a gap to the stator  501  becomes smaller at the midpoint between the adjacent permanent magnets  26 . 
     By taking the shape described above, an waveform of magnetic flux density produced in the air gap between the inner circumferential face of the stator  501  and the outer circumferential faces of the rotor  502  can be made smooth, so that cogging torque and the torque ripples can be reduced. Moreover, non-magnetic portions  59  are provided so that they contact with end faces toward radially inner sides of the permanent magnets  26 . These non-magnetic portions  59  may be made of air, or may be adopted to be filled with a resin, or may be adopted in which a non-magnetic metal such as stainless or aluminum is inserted in them. By providing the non-magnetic portions  59  as described above, the leakage flux of the permanent magnets  26  can be reduced. 
     Interconnecting portions  60  are provided between portions of the rotor core  24  interposed by the adjacent permanent magnets  26 , and portions of the rotor core  24  provided to surround the outer circumference of the motor shaft  23 . These interconnecting portions  60  have workings to mechanically join between the rotor core  24  and the motor shaft  23 . In the rotor core  24  between the adjacent permanent magnets  26 , the holes  242  are provided. By making the holes  242  of air, an effect can be achieved as obtaining weight reduction and inertia reduction of the rotor  502 . 
     In a case of the interior permanent magnet type, the rotor core  24  exists nearer to the stator core  14 , so that the magneto-resistance between the stator core  14  and the rotor core  24  becomes smaller; as a result, such tendency can be observed that the magnetic coupling between the first armature winding  39  and the second armature winding  40  becomes stronger; however, by taking the configuration of Embodiment 3, such an effect can be achieved as weakening the magnetic coupling between the first armature winding  39  and the second armature winding  40 , and enhancing the controllability. In addition, because reluctance torque can be used, the quantity of use of the permanent magnets  26  can be reduced. Moreover, because the inductance is increased, and the field-weakening control can exert its effect, so that such an effect can also be achieved that the torque at the time of fast rotation is enhanced. 
     Embodiment 4 
       FIG. 13  is a cross section diagram illustrating a permanent magnet motor according to Embodiment 4 of the present invention; the motor is referred to as a so-called permanent magnet motor of consequent-pole (consequent pole) type. In  FIG. 13 , the stator  501  takes the same structure as that in the case of  FIG. 3  in Embodiment 1. The rotor  502  has a structure different from that in  FIG. 3 ,  FIG. 11  and  FIG. 12 . In the rotor  502 , the motor shaft  23  being the rotational shaft, and the rotor core  24  are provided in the outer side of the motor shaft  23 . On the surface of the rotor core  24 , the permanent magnets  26  are placed, being circumferentially placed in an equal interspace therebetween, in the number of four. 
     As for the orientations of magnetization of the permanent magnets  26 , they are magnetized in such a manner that the N poles are toward radially outer sides, and the S poles are toward radially inner sides, so that salient pole portions  62  of the rotor core  24  between the adjacent permanent magnets  26  presumably function as the S poles. Namely, the motor operates as a motor equivalent to the one with eight magnetic poles. This type of motor is generally referred to as a motor of consequent-pole type. The holes  242  of the rotor core  24  and the swaging portions  243  thereof are as described in  FIG. 3  and  FIG. 11 . 
     In the motor of consequent-pole type as described above, the rotor core  24  exists nearer to the stator core  14 , so that the magneto-resistance between the stator core  14  and the rotor core becomes smaller; as a result, such tendency can be observed that the magnetic coupling between the first armature winding  39  and the second armature winding  40  becomes stronger; however, by taking the structure as described in Embodiment 4, such an effect can be achieved as weakening the magnetic coupling, and enhancing the controllability. In addition, due to the reduction in the number of components of the permanent magnets  26 , such an effect can be obtained as reducing the costs. Because the inductance is increased, and the field-weakening control can exert its effect, so that such an effect can also be achieved that the torque at the time of fast rotation is enhanced. Moreover, in  FIG. 13 , an example is shown in which the permanent magnets  26  are placed on a surface of the rotor core  24 ; however, it is needless to say that similar effects can be achieved even in a motor of the consequent-pole type having a structure in which the permanent magnets  26  are embedded in the rotor core  24  as illustrated in  FIG. 11 . 
     Note that, in the present invention, each of the embodiments can be freely combined, and each of the embodiments can be appropriately modified and/or eliminated without departing from the scope of the invention. 
     The permanent magnet motor according to each of the embodiments of the present invention described above gives a concrete form to any one of the inventions described below. 
     (1) A permanent magnet motor comprises: 
     a rotor including a rotor core fixed on a motor shaft, and permanent magnets fixed on the rotor core; and 
     a stator including a stator core, whose inner circumferential face opposes to an outer circumferential face of the rotor by means of a magnetic air gap, having a plurality of slots for accommodating armature windings, and a plurality of teeth, the permanent magnet motor is characterized in that: 
     the armature windings are constituted of a plurality of groups of multi-phase windings; 
     the plurality of groups of multi-phase windings is supplied with electric power from individual inverters in every one of respective groups; 
     portions of the rotor core exist on a side nearer to the stator than a middle diameter between a maximum outer diameter and a minimum outer diameter of the permanent magnets; 
     the plurality of teeth each include respective flanges; 
     the flanges each have a lateral side portion thereof opposing to a lateral side portion of a flange being provided in the teeth adjacent to each other and protruding in a circumferential direction of the stator core; 
     when a height in the lateral side portion of the flanges in a radial direction of the stator core is defined as h, and a length of the magnetic air gap is defined as g, relationship
 
1≤ h/g≤ 2
 
is held; and also,
 
     when a circumferential distance between opposing faces of the flanges ( 56 ) being adjacent to each other is defined as a, relationship
 
 a/g≥ 0.2
 
is satisfied.
 
     According to the permanent magnet motor as set forth in item (1) described above, such an effect can be achieved as weakening the magnetic coupling of different groups of armature windings each other, and enhancing the controllability. At the same time, an effect of the field-weakening control can be efficiently exerted. 
     (2) The permanent magnet motor as set forth in item (1) described above is characterized in that: 
     the armature windings are constituted of two groups of three-phase armature windings made of a first armature winding and a second armature winding; 
     the first armature winding is supplied with an electric current from a first inverter circuit; 
     the second armature winding is supplied with an electric current from a second inverter circuit; 
     the first armature winding includes a phase-U 1  winding, a phase-V 1  winding and a phase-W 1  winding; 
     the second armature winding includes a phase-U 2  winding, a phase-V 2  winding and a phase-W 2  winding; 
     the phase-U 1  winding and the phase-U 2  winding are side by side accommodated in the slots adjacent to each other; 
     the phase-V 1  winding and the phase-V 2  winding are side by side accommodated in the slots adjacent to each other; 
     the phase-W 1  winding and the phase-W 2  winding are side by side accommodated in the slots adjacent to each other; and 
     electric currents each flowing through the first armature winding and the second armature winding mutually have a phase difference of an electrical angle of twenty degrees or more, and an electrical angle of forty degrees or less. 
     According to the permanent magnet motor as set forth in item (2) described above, there exists an effect that both a large quantity of torque-ripple reduction in the sixth at an electrical angle, and the reduction in the magnetic coupling can be ensure. 
     (3) The permanent magnet motor as set forth in item (1) or item (2) described above is characterized in that the lateral side portion of the flanges includes a curved face portion on either one of a portion positioned on an inner radial side of the stator, and a portion positioned on an outer radial side thereof. 
     According to the permanent magnet motor as set forth in item (3) described above, such an effect can be achieved as increasing the magneto-resistance between the “R” portions of the adjacent flanges by providing the curved face portions, and weakening the magnetic coupling. 
     (4) The permanent magnet motor as set forth in item (1) or item (2) described above is characterized in that the lateral side portion of the flanges includes curved face portions on both a portion positioned on an inner radial side of the stator, and a portion positioned on an outer radial side thereof. 
     According to the permanent magnet motor as set forth in item (4) described above, such an effect can be achieved as increasing the magneto-resistance between the curved face portions of the adjacent flanges by providing the curved face portions, and weakening the magnetic coupling. In addition, there also exists an effect that, by providing the curved face portions on both the inner radial side and the outer radial side, stamping by die-cutting becomes easier, and the life of dies is prolonged. 
     (5) The permanent magnet motor as set forth in item (4) described above is characterized in that the lateral side portion of the flanges each provided on adjacent teeth and opposing to each other is formed to be side by side in parallel with the other lateral side portion. 
     According to the permanent magnet motor as set forth in item (5) described above, such an effect can be achieved as increasing the magneto-resistance between the curved face portions of the adjacent flanges by providing the curved face portions, and weakening the magnetic coupling. In addition, there also exists an effect that, by providing the curved face portions on both the inner radial side and the outer radial side, stamping by die-cutting becomes easier, and the life of dies is prolonged. Moreover, because the faces where the flanges oppose to each other are side by side in parallel with another face, the magneto-resistance becomes uniform in those portions. Because through these faces, magnetic flux leaks into the neighboring teeth, such an effect can be achieved as reducing in the magnetic coupling Mq 12 /Lq 1 , and, as a result, enhancing the motor&#39;s controllability. 
     (6) The permanent magnet motor as set forth in any one of items (1) through (5) described above is characterized in that, 
     when a width of portions of the teeth, existing from the flanges on an outer radial side of the stator, where a circumferential width of the stator becomes a smallest is defined as w, a maximum outer diameter of the rotor core is defined as Rout, and the number of slots is defined as Ns, the width w of the portions of the teeth satisfies a relationship
 
0.4×2π( R out+ g+h )/ Ns≤w≤ 0.5×2π( R out+ g+h )/ Ns.  
 
     According to the permanent magnet motor as set forth in item (6) described above, because the magnetic saturation can be mitigated in the portions where the teeth become the narrowest, the self inductance is increased, so that such an effect can be achieved as reducing in the magnetic coupling Mq 12 /Lq 1 , and enhancing the controllability. 
     (7) The permanent magnet motor as set forth in any one of items (1) through (5) described above is characterized in that, 
     when a circumferential width of the slots corresponding to a portion of the teeth, existing from the flanges on an outer radial side of the stator, where the circumferential width of the stator becomes a smallest is defined as S 1 , a maximum outer diameter of the rotor core is defined as Rout, and the number of slots is defined as Ns, the width S 1  of the slots satisfies a relationship
 
0.5×2π( R out+ g+h )/ Ns≤S 1≤0.6×2π( R out+ g+h )/ Ns , and also
 
     the circumferential width of the slots gradually increases in accordance with a position on an outer radial side of the stator, and is maximized on a back-portion of the slots ( 142 ) or a back-portion&#39;s vicinity thereof. 
     According to the permanent magnet motor as set forth in item (7) described above, large cross-sectional areas of the slots can be secured, and thus, there also exists an effect that large cross-sectional areas of the armature windings can additionally be secured, so that copper losses can be reduced, and the motor&#39;s output can be enhanced. In addition, because a slot&#39;s circumferential width is large in the vicinity of the core back, there exists an effect that the magneto-resistance between the slots is increased so that the leakage flux is lowered, and there exists an effect that the motor&#39;s torque can be enhanced, and the quantity of permanent magnet use can be reduced. 
     (8) The permanent magnet motor as set forth in any one of items (1) through (7) described above is characterized in that: 
     the permanent magnets are placed on a surface of the rotor core opposing to the stator core; 
     the rotor core includes protrusion portions provided in portions where the permanent magnets are not placed; and 
     a gap is provided between the protrusion portions and the permanent magnets. 
     According to the permanent magnet motor as set forth in item (8) described above, the protrusion portions have an effect to shorten the motor&#39;s air gap, so that the inductance is increased. According to this configuration, the field-weakening control facilitates exerting its effect, so that there exists an effect that the torque at the time of fast rotation can be enhanced. Meanwhile, there arises a problem in that, because of the existence in the protrusion portions of the rotor core, magnetic coupling of different groups of armature windings each other becomes stronger; however, there exists an effect that the magnetic coupling can be weakened according to the configuration of the present invention. 
     (9) The permanent magnet motor as set forth in any one of items (1) through (7) described above is characterized in that the permanent magnets are placed in hole-portions formed in the rotor core. 
     According to the permanent magnet motor as set forth in item (9) described above, the field-weakening control can be efficiently used because the inductance is increased, so that such an effect can be achieved that the torque at the time of fast rotation is enhanced. Because a protective pipe to prevent scattering the permanent magnets  26  becomes unnecessary, there exists an effect that the costs can be lowered. Meanwhile, there arises a problem in that, because the magnetic gap between the rotor core and the stator core is small, magnetic coupling of different groups of armature windings each other becomes stronger; however, there exists an effect that the magnetic coupling can be weakened according to the configuration of the present invention. 
     (10) The permanent magnet motor as set forth in any one of items (1) through (7) described above is characterized in that: 
     the permanent magnets are formed such that a length thereof in a radial direction of the rotor is larger in comparison with a length in a circumferential direction thereof; 
     directions of magnetization of the permanent magnets are in such orientations that faces of the adjacent permanent magnets opposing to each other mutually form an identical magnetic pole; 
     the rotor core interposes between the adjacent permanent magnets; 
     the rotor core has curved-plane portions on faces opposing to the stator core, and also includes non-magnetic portions provided at positions contacting with end faces toward radially inner sides of the permanent magnets; and 
     the curved-plane portions each are formed in a protrusion shape so that, in a middle portion between the adjacent permanent magnets, a length of the magnetic air gap is smaller than that of another portion. 
     According to the permanent magnet motor as set forth in item (10) described above, there exists an effect that, by concentrating magnetic flux of the permanent magnets so that the magnetic flux density is heightened, the torque can be enhanced, and the motor, be small-sized. By forming a curved plane in a protrusion shape, the reduction of the torque ripples and cogging torque can be achieved. By providing the non-magnetic portions on the radially inner sides of the permanent magnets, the leakage flux is lowered, so that such an effect can be achieved as enhancing the torque and obtaining a motor being small-sized. Meanwhile, there arises a problem in that, because the magnetic gap between the rotor core and the stator core is small, magnetic coupling of different groups of armature windings each other becomes stronger; however, there exists an effect that the magnetic coupling can be weakened according to the configuration of the present invention. 
     (11) An electric power steering apparatus on which a permanent magnet motor as set forth in any one of items (1) through (10) described above is mounted, and torque is produced by the permanent magnet motor so as to assist steering of a driver, is characterized in that the permanent magnet motor is placed in such a direction that the motor shaft is in parallel with an extending direction of a rack shaft for driving a steering wheel of a wheeled vehicle. 
     According to the electric power steering apparatus as set forth in item (11) described above, a large quantity of torque-ripple reduction in the sixth is made possible. In addition, there arises a problem in that the magnetic coupling becomes stronger at the same time of increased output of the motor, so that the controllability is lowered; however, the magnetic coupling can be weakened, so that such an effect can be achieved as applying the electric power steering apparatus also to a large-size wheeled vehicle, and lowering fuel consumption. 
     INDUSTRIAL APPLICABILITY 
     The present invention can be utilized in a field of a motor including a permanent magnet (s) and in that of an electric power steering apparatus using the motor, and particularly in the field of a wheeled vehicle such as an automotive vehicle. 
     [Explanation of Numerals and Symbols]