JPH10146031A - Permanent magnet rotating electric machine and electric vehicle - Google Patents

Abstract

PROBLEM TO BE SOLVED: To suppress the peak value of induced voltage to an effective value by approximating the waveform of induced voltage to sine wave. SOLUTION: As a permanent magnet 8, an object in such form that the angle θ becomes smaller than the angle ϕ when defined that the angle that the side on stator side, that is, the width of the peripheral face forms to the axis θ and that the angle that the side on anti-stator side, that is, the width of the peripheral face forms to the axis is ϕ is used. Here, the angle θ takes a value in the range of 0<θ<45, because the number of poles of the permanent magnet is eight. Then, using a permanent magnet 8 where the angle θ is 26 deg. and the angle ϕ is 36 deg. as a result of computation will bring the waveform of induced voltage close to sine wave. Hereby, design of the permanent magnet rotating electric machine which can gets maximum drive torque while suppressing the peak value of induced voltage becomes possible.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a permanent magnet rotating electric machine and an electric vehicle, and more particularly to a permanent magnet rotating electric machine constituted by arranging and fixing a plurality of permanent magnets in a circumferential direction of a rotor.

[0002]

2. Description of the Related Art Conventionally, as one type of rotating electric machine, a permanent magnet rotating electric machine using a permanent magnet as a magnetic field generating means of a rotor has been used.

As a conventional permanent magnet rotating electric machine, a permanent magnet rotating electric machine using a permanent magnet embedded type rotor is disclosed in Japanese Patent Application Laid-Open No. 5-761.
No. 46 is described.

This publication discloses a stator in which three-phase stator windings are arranged in a plurality of slots formed in an annular stator core. Further, as the rotor, a plurality of storage portions extending in the axial direction are formed on the inner peripheral portion of the substantially circular rotor core fitted and fixed to the rotation shaft, and a permanent magnet having a rectangular cross section is formed in the storage portion. A configuration is disclosed in which arbitrary adjacent permanent magnets are inserted so as to generate magnetic fluxes of opposite polarities toward the rotor surface. The rotor is rotatably disposed in the annular stator with an inner peripheral portion of the stator core and a predetermined rotation gap.

A rotating electric machine using a rectangular permanent magnet as described above has a high efficiency because the field weakening is apt to be effective at high speed rotation. Therefore, the present invention is effective for a device that requires high-speed rotation in nature, such as a drive motor for an electric vehicle.

[0006]

However, the above-described conventional permanent magnet rotating electric machine has the following problems with respect to the induced voltage waveform.

[0007] When the rotor is rotated by an external force, an induced voltage is generated in the rotating electric machine, and a current flows through the energizing circuit or the control circuit. Therefore, in order to protect the control circuit more safely, the control circuit is designed to measure the effective value of the induced voltage at a predetermined rotation speed in advance and to withstand the value or to suppress the value.

However, the actual induced voltage appears in a form in which some waveforms are superimposed on a sine wave. Since the effective value is the average value of the waveform, there always exists a peak value exceeding √2 times the effective value. Therefore, in order to more reliably protect a control circuit designed to cope with √2 times the effective value, it is necessary to make the peak value close to √2 times the effective value.

To reduce the peak value, it is conceivable to reduce the amount of magnetic flux itself generated by the permanent magnet. However, if the amount of magnetic flux is reduced, the driving torque when the rotating electric machine is operated as an electric motor is naturally reduced. I do.

In view of the above, an object of the present invention is to suppress the peak value of the induced voltage with respect to the effective value without lowering the driving torque in a permanent magnet rotating electric machine.

Another object of the present invention is to provide a safer electric vehicle by suppressing the peak value of the induced voltage generated by the permanent magnet rotating electric machine when the vehicle is braking or downhill.

[0012]

SUMMARY OF THE INVENTION An object of the present invention is to provide a permanent magnet comprising a stator having a winding and a rotor having a plurality of permanent magnets arranged and fixed in a circumferential direction in the stator with a rotating gap. This is achieved by a permanent magnet rotating electric machine characterized in that the waveform of the induced voltage approximates a sine wave.

[0013] Further, the object is to provide a stator having a winding,
A permanent magnet rotating electric machine having a rotor in which a plurality of permanent magnets are arranged and fixed in a circumferential direction, the permanent magnet being arranged so that a waveform of an induced voltage approximates a sine wave. The permanent magnet rotating electric machine is characterized in that the circumferential length of the surface on the stator side is set.

Another object of the present invention is to provide an electric vehicle using a permanent magnet rotating electric machine as a drive motor, wherein a waveform of an induced voltage generated by the permanent magnet rotating electric machine at the time of braking or downhill of the vehicle is approximated to a sine wave. This is achieved by

[0015]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS Hereinafter, a permanent magnet rotating electric machine according to an embodiment of the present invention will be described with reference to the drawings.

FIG. 1 is a circumferential sectional view of an embodiment in which the present invention is applied to a three-phase eight-pole, 48-slot inner-rotor permanent-magnet rotating electric machine. FIG. 1 shows one pole pair. FIG. 2 is a magnetic flux density distribution diagram of FIG.

The permanent magnet rotating electric machine includes a stator 1 and a rotor 6, and the rotor 6 is rotatably disposed on the stator 1 with a rotating gap 5 (gap) as shown in the figure.

The stator 1 has a substantially annular stator core 2.
U-phase stator winding U is provided in 48 slots 3 formed in
1, V-phase stator winding V1 and W-phase stator winding W
1 is inserted and arranged. Openings 4 are formed in the inner peripheral portion of the stator core corresponding to the respective slots.

On the other hand, the rotor 6 has a rotor core 7
Are fitted and fixed, and a storage part is formed in the rotor core 7 for inserting and fixing eight neodymium permanent magnets 8 (8a, 8b in the figure) in the axial direction. As shown in the figure, the permanent magnets 8 are arranged such that adjacent magnets have opposite polarities, and the rotor core 7 is formed by laminating many silicon steel plates.

At this time, in the cross section of the permanent magnet 8 in the circumferential direction, the angle formed by the side on the stator side, that is, the outer peripheral surface width with respect to the axis is θ, and the side on the opposite stator side, that is, the inner peripheral surface width is When the angle with respect to the axis is φ, a shape having a shape in which θ is smaller than φ is used.

It is to be noted that θ and φ can be similarly defined when the permanent magnet 8 has a trapezoidal shape as shown in FIG.
For example, in the case of an arch shape, θ and φ indicate the angle between the end point and the other end point of the arch on the stator side with respect to the axis, and the angle between the end point and the other end point of the arch on the anti-stator side with respect to the axis. .

In this case, when the magnitude of θ is changed, the waveform of the induced voltage generated when the rotor is rotated by an external force changes. When the magnitude of φ is changed, the magnitude of the driving torque of the rotating electric machine changes because φ defines the maximum circumferential width of the permanent magnet 8.

Here, since the number of poles of the permanent magnet is 8, θ (degree) can take a value in the range of 0 <θ <45.
When θ is close to 45 degrees, it is difficult to obtain reluctance torque because the circumferential width of the auxiliary salient pole is extremely small. Conversely, when it is close to 0, the waveform of the induced voltage depends on φ instead of θ, but there is no value of φ that simultaneously achieves both the realization of the ideal waveform described below and the maximization of the driving torque. .

Then, when θ is sampled, θ is 2
The induced voltage waveforms at the maximum rotation speed when the angle is set to 4, 26, 28 degrees and when set to 32, 34, 36 degrees are as shown in FIGS. 3 and 4, respectively.

As shown in the figure, the induced voltage waveform includes a convex waveform in which five peaks are superimposed on a sine wave, a waveform in which there are relatively few irregularities and approximates a sine wave, and a concave waveform in which five valleys are superimposed. It appears that it appears with the regularity described in.

That is, θ is 18.75 <θ <26.25
When 33 is within the range of 33.75 <θ <41.25, a concave waveform appears, and when θ is within the range of 26.25 <θ <33.75, a convex waveform appears. Θ is about 26.25
In the case of degrees and 33.75 degrees, a waveform having relatively few irregularities and approximating a sine wave appears.

More specifically, when τs is a slot pitch of the stator and n is a natural number, θ is {(2n−1) +0.5} × τs <θ <(2n + 0.5) ×
When it is within the range of τs, a convex waveform appears, and when θ is (n + 0.5) × τs, the unevenness decreases, and θ becomes (2n + 0.5) × τs <θ <{(2n + 1) +0.5} ×
It can be seen that a concave waveform appears when it is within the range of τs.

The peak values of these waveforms are the peak value of the convex portion having an electrical angle of 90 degrees in the case of the convex waveform, and the peak values of two convex portions sandwiching the concave portion having the electrical angle of 90 degrees in the case of the concave waveform. Become. Therefore, the peak value becomes the minimum when a waveform having no irregularities, that is, a waveform approximating a sine wave appears.

In this embodiment, the reason why the induced voltage waveforms are closest to the sine wave is that θ is about 26 degrees or about 3 degrees.
It can be seen from the figure that the time is 4 degrees.

Next, in order to quantitatively evaluate to what extent the actual induced voltage waveform approximates a sine wave, a waveform deviation rate is defined, and the waveform deviation rate due to θ is shown in a graph in FIG.

Here, the waveform deviation rate is

[0032]

(Equation 1)

The definition is as follows. This equation shows that if the induced voltage waveform is a sine wave, the voltage at an armature angle of 90 degrees is the effective value of √
It is based on being twice. That is, when this value is greater than 1, the waveform is convex, and when it is less than 1, the waveform is concave.

From this graph, it can be seen that θ is 26 degrees and 34 degrees.
It can be seen that the induced voltage waveform approximates a sine wave near the degree.

By the way, this angle is referred to as the slot pitch τs
27.5 = n + 0.5 times (n is a natural number) of 7.5 degrees
When compared with 5 degrees and 33.75 degrees, in FIGS. 3, 4 and 5, the values match at least within a range of error ± 1 degree.

That is, when θ (degree) is a value represented by θ ≒ (n + 0.5) × τs (n is a natural number), the waveform of the induced voltage approximates a sine wave.

FIG. 6 shows the peak value and the effective value of the induced voltage when θ is changed.

In FIG. 6, the effective value increases as θ increases. This is because the larger the θ, the larger the permanent magnet, and naturally the larger the main magnetic flux. On the other hand, it can be seen that the peak value shows a stepwise change as θ increases. That is, when θ is smaller than 26 degrees, the angle slightly decreases as θ increases, and sharply increases after 26 degrees. About 3 more
It can be seen that the temperature is gradually falling again with the peak at 2 degrees.

In general, the larger the effective value is, the larger the main magnetic flux is, so that more driving torque can be obtained. On the other hand, the peak value is preferably as close as possible to √2 times the effective value as much as possible because the control circuit and the like are designed according to the effective value specific to the permanent magnet rotating electric machine. Therefore, it is considered that θ is best around 26 degrees from the viewpoint that the peak value is close to √2 times the effective value and the effective value is large in FIG.

Next, the angle φ at which the sum of the torque due to the main magnetic flux and the reluctance torque is maximum is obtained by changing φ while fixing θ to 26 degrees and correcting the amount of magnetic flux.

The driving torque T of the rotating electric machine is represented by the magnetic flux of the permanent magnet ψ, the q-axis inductance Lq, the d-axis inductance Ld, the q-axis winding current Iq, and the d-axis winding current I
Assuming d, T = ψIq + (Lq−Ld) Iq × Id.

In this equation, the first term on the right side is the torque due to the main magnetic flux of the permanent magnet, and the second term is the reluctance torque due to the rotor member between adjacent permanent magnets, ie, the auxiliary salient pole. Since these two values depend on the circumferential angle of the rotor formed by the permanent magnet and the auxiliary salient pole, respectively, the circumferential angle of the permanent magnet that maximizes the driving torque is uniquely determined for each rotor. Is determined.

FIG. 7 shows the relationship between φ and the weighted average efficiency (including the inverter loss) (considering the frequency of use of the motor). It can be seen from the figure that φ is the largest at 36 degrees.

Therefore, in the case of the present embodiment, if a permanent magnet having θ of 26 degrees and φ of 36 degrees is used, the waveform of the induced voltage approximates a sine wave, and the peak value of the induced voltage is suppressed and the maximum value is obtained. It is possible to design a permanent magnet rotating electric machine capable of obtaining a driving torque.

Further, in order to confirm the versatility of the shape of the permanent magnet according to the angles of θ and φ described above, FIG. 8 shows a magnetic flux density distribution examined for rotating electric machines having different radii, thicknesses, and outputs, and FIG. FIG. 9 shows the relationship between φ and the weighted average efficiency (including the inverter loss) in FIG. Also in this embodiment, it can be seen from FIG. 9 that the induced voltage waveform is close to a sine wave when θ is 26 degrees, and that the driving torque becomes maximum when φ is 36 degrees from FIG.

Further, the above-mentioned θ is the angle α formed by the stator teeth commonly used and the angle β formed by the stator slot.
Are approximately equal, n + 0.5 of the slot pitch τs
In the case of α (n is a natural number), when α and β are greatly different, the induced voltage waveform is a sine wave when θ ≒ n × τs + α or θ ≒ n × τs + β, where n is a natural number. Become closer to In particular, the latter is closer to a sine wave.

Further, when the angle β forming the stator slot portion and the angle γ forming the stator opening portion are greatly different, that is, when the teeth are large, the induced voltage waveform can be obtained by setting θ ≒ n × τs + γ. It becomes closer to a sine wave.

Here, when the radial length of the projection is small,
The magnetic flux of the protrusion is saturated, and γ hardly affects θ. Therefore, the degree of the influence of γ on θ is determined by the coefficient A (0
If <A ≦ 1), then θ ≒ n × τs + γ × A.

The permanent magnet 8 may be other than a neodymium magnet. FIG. 11 shows a case where the waveform distortion rate shown in FIG. 5 is examined using a ferrite magnet.

Compared with FIG. 5 using a neodymium magnet, θ is smaller by about 2 degrees in mechanical angle. This is because the ferrite magnet has a magnet strength about one-third that of the neodymium magnet. Therefore, the protrusion of the stator slot cannot be sufficiently saturated. Therefore, when a ferrite magnet is used, θ which approximates the induced voltage waveform to a sine wave is θ ≒ n × τs + γ (n is a natural number).

In the present invention, the angle θ for approximating the induced voltage waveform to a sine wave does not depend on the magnet shape. FIG.
13 shows a magnetic flux density distribution when the magnet shape is rectangular as another embodiment, FIG. 13 shows an induced voltage waveform in the embodiment of FIG. 12, and FIG. 14 shows a magnetic flux density when the magnet shape is an arc shape as another embodiment. FIG. 15 shows the distribution of the induced voltage in FIG. 14, FIG. 16 shows the magnetic flux density distribution in the case where the magnet shape is an arc trapezoid as another embodiment, and FIG.
18, the magnetic flux density distribution when the magnet shape is V-shaped as another embodiment, FIG. 19 shows the induced voltage waveform in FIG. 18, and FIG. 20 shows the magnet shape U as another embodiment. FIG. 21 shows the magnetic flux density distribution in the case of the letter shape.
FIG. 20 shows the induced voltage waveform in FIG. In each case, it can be seen that the induced voltage waveform approximates a sine wave at θ = 26 degrees as shown in the figure.

On the other hand, when the permanent magnet is partially embedded in the rotor, the density of the magnetic flux between the permanent magnet portion and the iron portion increases, so that the case of θ ≒ n × τs + γ (n is a natural number) is induced. The voltage waveform can be approximated to a sine wave. In this case, θ is the angle formed by the portion where the permanent magnet 8 is exposed on the surface of the rotor core 7 in the circumferential direction of the rotor.

FIG. 22 shows a magnetic flux density distribution when a magnet is partially embedded in an arc shape as another embodiment of the present invention, FIG. 23 shows an induced voltage waveform in FIG.
FIG. 25 shows the magnetic flux density distribution when the magnet shape is partially embedded in an arc trapezoidal shape as another embodiment in FIG.
26 shows the induced voltage waveform in FIG. 26, FIG. 26 shows the magnetic flux density distribution in a case where the magnet shape is partially trapezoidal and partially embedded as another embodiment, and FIG. 27 shows the induced voltage waveform in FIG. In each case, it can be seen that the induced voltage waveform can be approximated to a sine wave at θ = 24 degrees as shown in the figure.

Further, while suppressing the peak value of the induced voltage,
In order to reduce cogging torque and noise, it is effective to provide magnetic gaps at both ends of the magnet as shown in FIG. Here, the magnetic gap may be a space where no object exists, or may be a space where a non-magnetic substance is inserted or filled and fixed with a varnish or an adhesive.

Further, the permanent magnet rotating electric machine according to the present invention is effective when used as a drive motor for an electric vehicle.

At the time of a braking operation of an electric vehicle using a permanent magnet rotating electric machine as a drive motor or during a downhill, the rotating electric machine operates as a generator, and an induced voltage is generated in a control circuit. Normally, the control circuit is designed in accordance with the effective value of the induced voltage of the rotating electric machine, so that the induced voltage does not greatly exceed 実 効 2 times the effective value due to the peak value of the waveform as in the present invention. An electric vehicle with higher safety can be obtained by approximating the waveform to a sine wave and suppressing the peak value.

In the present invention, the number of permanent magnets (the number of poles) may be other than eight, and the number of slots of the stator may be other than forty-eight. Further, the permanent magnet 8 may be other than the neodymium magnet, and it goes without saying that the angle constituting the permanent magnet has a width within a range of a manufacturing error. In addition, those in which waveform improvement is effective can be applied not only to rotary electric machines such as an inversion type and an external rotation type but also to a linear motor and the like.

[0058]

According to the present invention, the peak value of the induced voltage can be suppressed from the effective value because the waveform of the induced voltage approximates a sine wave.

Further, according to the present invention, the peak value of the induced voltage is suppressed by setting the circumferential length of the surface of the permanent magnet on the stator side so that the waveform of the induced voltage approximates a sine wave. However, a large driving torque can be obtained.

Further, according to the present invention, by approximating the waveform of the induced voltage to a sine wave, the peak value of the induced voltage generated by the permanent magnet rotating electric machine at the time of braking or downhill of the vehicle can be suppressed, and a more safe operation can be achieved. An electric vehicle can be obtained.

[Brief description of the drawings]

FIG. 1 shows a part of a circumferential sectional view of a permanent magnet rotating electric machine according to an embodiment of the present invention.

FIG. 2 shows a magnetic flux density distribution diagram of FIG.

FIG. 3 shows an induced voltage waveform at the maximum rotation speed when θ in FIG. 1 is 24, 26, and 28 degrees.

FIG. 4 shows an induced voltage waveform at the maximum rotation speed when θ in FIG. 1 is 32, 34, and 36 degrees.

FIG. 5 is a diagram showing the relationship between θ and the waveform deviation rate in FIG. 1;

FIG. 6 shows a relationship diagram between θ in FIG. 1 and an induced voltage peak value and an effective value.

FIG. 7 shows a relationship diagram between φ in FIG. 1 and a weighted average efficiency (including inverter loss) (considering the frequency of use of the motor).

FIG. 8 is a magnetic flux density distribution diagram when θ and φ in FIG. 1 are applied to another embodiment having different radii, thicknesses, outputs, and the like.

FIG. 9 shows an induced voltage waveform in FIG.

FIG. 10 shows a relationship diagram between φ and weighted average efficiency (including inverter loss) in FIG.

FIG. 11 is a diagram showing a relationship between θ and a waveform distortion rate of a permanent magnet rotating electric machine according to another embodiment of the present invention using a ferrite magnet.

FIG. 12 shows a magnetic flux density distribution diagram of a permanent magnet rotating electric machine according to another embodiment of the present invention.

FIG. 13 shows an induced voltage waveform of FIG.

FIG. 14 shows a magnetic flux density distribution diagram of a permanent magnet rotating electric machine according to another embodiment of the present invention.

FIG. 15 shows an induced voltage waveform of FIG.

FIG. 16 shows a magnetic flux density distribution diagram of a permanent magnet rotating electric machine according to another embodiment of the present invention.

FIG. 17 shows an induced voltage waveform of FIG.

FIG. 18 shows a magnetic flux density distribution diagram of a permanent magnet rotating electric machine according to another embodiment of the present invention.

FIG. 19 shows an induced voltage waveform of FIG.

FIG. 20 shows a magnetic flux density distribution diagram of a permanent magnet rotating electric machine according to another embodiment of the present invention.

FIG. 21 shows an induced voltage waveform of FIG.

FIG. 22 shows a magnetic flux density distribution diagram of a permanent magnet rotating electric machine according to another embodiment of the present invention.

FIG. 23 shows an induced voltage waveform of FIG.

FIG. 24 shows a magnetic flux density distribution diagram of a permanent magnet rotating electric machine according to another embodiment of the present invention.

FIG. 25 shows an induced voltage waveform of FIG.

FIG. 26 shows a magnetic flux density distribution diagram of a permanent magnet rotating electric machine according to another embodiment of the present invention.

FIG. 27 shows an induced voltage waveform of FIG. 26.

FIG. 28 is a circumferential sectional view of a permanent magnet rotating electric machine according to another embodiment of the present invention.

[Explanation of symbols]

DESCRIPTION OF SYMBOLS 1 ... Stator, 2 ... Stator core, 3 ... Slot, 4 ... Opening, 5 ... Rotation gap, 6 ... Rotor, 7 ... Rotor core, 8
a, 8b: permanent magnet, 9: rotating shaft, 10: air gap.

 ──────────────────────────────────────────────────続 き Continuing on the front page (72) Inventor Takashi Kobayashi 7-1-1, Omika-cho, Hitachi City, Ibaraki Prefecture Within Hitachi Research Laboratory, Hitachi, Ltd. (72) Inventor Shoichi Kawamata 7-1-1, Omika-cho, Hitachi City, Ibaraki Prefecture No. 1 Inside Hitachi Research Laboratory, Hitachi, Ltd. (72) Inventor Suetaro Shibukawa 2520 Oji Takaba, Hitachinaka City, Ibaraki Prefecture Inside Automotive Equipment Division, Hitachi, Ltd. (72) Inventor Osamu Koizumi Oita Takahiro, Hitachinaka City, Ibaraki Prefecture 2520 Address Hitachi Automotive Equipment Division (72) Inventor Keiji Oda 2477 Takaba, Hitachinaka-shi, Ibaraki Pref.

Claims (10)

[Claims] 1. A permanent magnet rotating electric machine comprising: a stator having a winding; and a rotor arranged with a rotating gap in the stator and having a plurality of permanent magnets arranged and fixed in a circumferential direction.
A permanent magnet rotating electric machine characterized in that a waveform of an induced voltage approximates a sine wave. 2. A permanent magnet rotating electric machine comprising: a stator having a winding; and a rotor arranged with a rotating gap in the stator and having a plurality of permanent magnets arranged and fixed in a circumferential direction.
A permanent magnet rotating electric machine characterized in that the circumferential length of the surface of the permanent magnet on the stator side is set so that the waveform of the induced voltage approximates a sine wave. 3. An angle defined by a circumferential width of a surface of the permanent magnet on a stator side with respect to an axis of the rotor, wherein a slot pitch of the stator is τs (degrees). A permanent magnet rotating electric machine wherein θ (degrees) is θ ≒ (n + 0.5) × τs (n is a natural number). 4. The method according to claim 2, wherein the permanent magnet is exposed on a surface of the rotor core, and an angle θ (degree) formed by the exposed portion with respect to an axis is θ ≒ (n + 0.5) × τs. (N is a natural number). 5. The stator according to claim 2, wherein the slot pitch of the stator is τs (degree), the angle of the teeth portion of the stator is α (degree), the angle of the slot portion is β (degree), and the angle of the slot is β (degree). When the angle is γ (degree), the angle θ (degree) formed by the circumferential width of the surface of the permanent magnet on the stator side with respect to the axis of the rotor is θ ≒ n × τs + α (n is a natural number) Or θ 磁石 n × τs + β (n is a natural number) or θ ≒ n × τs + γ (n is a natural number). 6. The rotor according to claim 2, wherein the number of slots of the stator is 48, the number of poles of the permanent magnet is 8, and the circumferential width of the surface of the permanent magnet on the stator side is equal to that of the rotor. The angle formed with respect to the axis is within a range of 26 ± 1 degrees, and the angle formed by the circumferential width of the surface of the permanent magnet on the side opposite to the stator with respect to the axis of the rotor is within a range of 36 ± 1 degrees. A permanent magnet rotating electric machine characterized by the above-mentioned. 7. The method according to claim 2, wherein the angle between the circumferential width of the surface of the permanent magnet on the stator side and the axis of the rotor is θ (degree), and A permanent magnet rotating electric machine characterized in that θ is smaller than φ when an angle between a circumferential width of the surface and an axis of the rotor is φ (degree). 8. A permanent magnet rotating electric machine according to claim 7, wherein said permanent magnet has a trapezoidal cross section in a circumferential direction. 9. The permanent magnet rotating electric machine according to claim 2, wherein magnetic gaps are provided at both ends of each permanent magnet. 10. An electric vehicle using a permanent magnet rotating electric machine as a drive motor, wherein a waveform of an induced voltage generated by the permanent magnet rotating electric machine at the time of braking or downhill of the vehicle is approximated to a sine wave. Electric vehicle.