Rotary electrical machine

Abstract

The present invention provides a rotary electrical machine exhibiting low vibration and high efficiency in a high output region.　Permanent magnets (231, 232, 233) are respectively inserted into magnet slots (241, 242, 243) formed in three layers, to form one pole. When the electrical angle of the one pole is 180°, and θS1 is defined as the smaller electrical angle and θL1 is defined as the larger electrical angle from among the electrical angle which is formed by a pair of straight lines connecting the rotation center with the points of contact between an outer diameter bridge (251) and the magnet slot of the first layer, and the electrical angle which is formed by a pair of straight lines connecting the rotation center and the points of contact between the outer diameter bridge and the permanent magnet inserted in the magnet slot of the first layer, the expression 40°≤θL1かつθS1≤80° is satisfied.

Description

rotating electrical machines

[0001] The present application relates to a rotating electric machine.

[0002] Rotating electric machines for electric vehicles, hybrid vehicles, and other electrically powered vehicles are required to be compact so that they can fit into limited on-board space, and to be able to generate high torque over a wide rotation speed range of 0 to 10,000 r / min. Furthermore, to provide driving with low environmental impact and a comfortable driving feel, rotating electric machines for electrically powered vehicles are required to be highly efficient and have low vibration over the wide rotation speed range mentioned above.

[0003] A conventional rotating electric machine that meets these requirements is one in which arc-shaped permanent magnets are arranged in multiple layers on the rotor and the dimensions of the arc shape are specified to reduce the harmonic components of the magnetic flux waveform in the magnetic gap (see, for example, Patent Document 1).

[0004] JP 2019-187199 A

[0005] However, in conventional rotating electric machines, the magnetic path design does not take into account magnetic saturation in the rotor core between the permanent magnets arranged in multiple layers. As a result, there is a problem that harmonic components in the magnetic flux waveform of the magnetic gap due to magnetic saturation in the rotor core increase in the high-power range. As a result, conventional rotating electric machines have problems of increased vibration and reduced efficiency in the high-power range.

[0006] The present application has been made to solve the above-mentioned problems, and aims to provide a rotating electric machine with low vibration and high efficiency in the high output range by reducing magnetic saturation in the rotor core between permanent magnets arranged in multiple layers.

[0007] The rotating electric machine of the present application includes a stator having a stator core with a plurality of teeth arranged at equal intervals on the inner diameter side of a cylindrical core back, and an armature winding wound around the teeth, and a cylindrical rotor arranged on the inner diameter side of the stator via a magnetic gap and rotatable around a rotation axis, wherein, in a cross section perpendicular to the rotation axis, N layers of magnet slots opening from the center of rotation toward the outer diameter side are formed in the rotor from the outer diameter side to the inner diameter side, where N is an integer of 3 or more, and an outer diameter bridge is formed between each magnet slot and the outer peripheral surface of the rotor, and a permanent magnet is inserted into each of the N layers of magnet slots to form one pole, and when the electrical angle of one pole is 180°, the smaller electrical angle between a pair of straight lines connecting a point tangent to the outer diameter bridge of the magnet slot in the first layer and the center of rotation and a pair of straight lines connecting a point tangent to the outer diameter bridge of the permanent magnet inserted in the magnet slot in the first layer and the center of rotation is defined as a pole arc angle θ Ｓ１ The larger electrical angle is the pole arc angle θ Ｌ１ When 40°≦θ Ｌ１ and θ Ｓ１ The condition of ≦80° is satisfied.

[0008] In the rotating electric machine of the present application, when the electrical angle of one pole is 180°, the smaller of the electrical angle formed by a pair of straight lines connecting the center of rotation and a point tangent to the outer diameter bridge of the magnet slot of the first layer, and the electrical angle formed by a pair of straight lines connecting the center of rotation and a point tangent to the outer diameter bridge of the permanent magnet inserted into the magnet slot of the first layer, is defined as the pole arc angle θ Ｓ１ The larger electrical angle is the pole arc angle θ Ｌ１ When this is the case, 40°≦θ Ｌ１ and θ Ｓ１ Since the angle .theta..ltoreq.80.degree. is satisfied, low vibration and high efficiency can be realized in the high output range.

[0009] 1 is a cross-sectional view of a rotary electric machine according to a first embodiment; an enlarged cross-sectional view of a rotor of the rotary electric machine according to the first embodiment; a diagram showing phase voltage waveforms in a no-load state in the rotary electric machine according to the first embodiment; a diagram showing magnetic flux waveforms in a magnetic gap in the rotary electric machine according to the first embodiment; a diagram showing a relationship between a square wave model and the pole arc angles of magnetic poles of three layers in the rotary electric machine according to the first embodiment; a diagram showing paths of magnetic flux for half a pole in the rotary electric machine according to the first embodiment; a diagram showing harmonic components of the magnetic flux waveform in a magnetic gap in the rotary electric machine according to the first embodiment; a diagram showing harmonic components of the magnetic flux waveform in a magnetic gap in the rotary electric machine according to the first embodiment; a diagram showing harmonic components of the magnetic flux waveform in a magnetic gap in the rotary electric machine according to the first embodiment; a diagram showing a relationship between a square wave model and the pole arc angles of magnetic poles of three layers in the rotary electric machine according to the first embodiment; a diagram showing harmonic components of the magnetic flux waveform in a magnetic gap in the rotary electric machine according to the first embodiment; 1 is a diagram showing harmonic components of a magnetic flux waveform of a magnetic gap in a rotary electric machine according to embodiment 1. FIG. 2 is a diagram showing harmonic components of a magnetic flux waveform of a magnetic gap in a rotary electric machine according to embodiment 1. FIG. 3 is a diagram showing harmonic components of a magnetic flux waveform of a magnetic gap in a rotary electric machine according to embodiment 1. FIG. 4 is an enlarged cross-sectional view of a rotor of a rotary electric machine according to embodiment 2. FIG. 5 is an enlarged cross-sectional view of a rotor of a rotary electric machine according to embodiment 3. FIG. 6 is an enlarged cross-sectional view of a rotor of a rotary electric machine according to embodiment 4. FIG. 7 is a cross-sectional view of a rotary electric machine according to embodiment 5. FIG. 8 is a cross-sectional view of a rotary electric machine according to embodiment 6.

[0010] Hereinafter, a rotating electric machine according to an embodiment of the present invention will be described in detail with reference to the drawings. In the drawings, the same reference numerals indicate the same or corresponding parts.

[0011] Embodiment 1. Figure 1 is a cross-sectional view of a rotating electric machine according to embodiment 1. Figure 1 is a cross-sectional view in a direction perpendicular to a shaft, which is a rotation axis described below. The rotating electric machine 1 of this embodiment includes a cylindrical stator 10 and a columnar rotor 20 rotatably provided on the inner diameter side of the stator 10 via a magnetic gap. Although not shown, the rotating electric machine 1 also includes a frame on the outside of the stator 10 and a housing that covers an opening on one side of the frame and is fixed with a plurality of bolts.

[0012] The stator 10 has a stator core 11 formed by laminating core sheets of magnetic material such as electromagnetic steel sheets, and an armature winding housed in the stator core 11. The stator core 11 has a cylindrical core back 12 and teeth 13 protruding radially inward from the core back 12. There are 48 teeth 13 arranged at equal intervals in the circumferential direction. Although not shown, the armature winding is wound around the teeth 13.

[0013] The rotor 20 includes a shaft 21, which is a rotating shaft supported at both ends by first and second bearings fastened to a housing or the like, a rotor core 22 through which the shaft 21 passes, and a plurality of permanent magnets 23 arranged circumferentially within the rotor core 22. The rotor 20 is composed of eight magnetic poles, i.e., four pairs of magnetic poles. The rotor core 22 is formed by laminating core sheets of magnetic material, such as electromagnetic steel sheets. The stator 10 and the rotor 20 are arranged coaxially with the shaft 21 as the rotation axis. The stator 10 and the rotor 20 are also arranged separated by a magnetic gap. Hereinafter, the direction parallel to the shaft 21 is referred to as the axial direction, the direction perpendicular to the shaft 21 is referred to as the radial direction, and the direction in which the shaft 21 rotates is referred to as the circumferential direction. The inner diameter side refers to the direction radially approaching the shaft 21, and the outer diameter side refers to the direction radially away from the shaft 21.

[0014] FIG. 2 is an enlarged cross-sectional view of the rotor of a rotating electric machine according to this embodiment. FIG. 2 is an enlarged cross-sectional view of one magnetic pole of the rotor 20. The rotor core 22 is formed with magnet slots 241, 242, and 243 arranged in a V-shape that opens from the center of rotation C toward the outer diameter side, forming a three-layer structure in the radial direction. The magnet slots are through-holes that penetrate the rotor core 22 in the axial direction. The magnet slots are arranged in the following order from the outer diameter side to the inner diameter side: first-layer magnet slot 241, second-layer magnet slot 242, and third-layer magnet slot 243. Each layer of magnet slots 241, 242, and 243 is composed of a pair of slots formed between a central bridge 221, 222, and 223 located in the center and an outer diameter bridge 251, 252, and 253 located between the central bridge and the outer peripheral surface of the rotor core 22. A pair of permanent magnets 231, 232, and 233 is inserted in the center of each slot. The permanent magnets 231, 232, and 233 are rectangular parallelepipeds. The portions of each slot at both ends where no permanent magnet is inserted serve as flux barriers.

[0015] The permanent magnets 231, 232, and 233 in each layer have a rectangular cross section and are magnetized in the same direction as their short sides so that the generated magnetic flux is directed toward the outer diameter side. The magnetic flux passing through the permanent magnets toward the magnetic gap is the magnetic flux φ that passes through the first layer permanent magnet 231, the second layer permanent magnet 232, and the third layer permanent magnet 233 toward the magnetic gap. １ and the magnetic flux φ passing through the second layer permanent magnet 232 and the third layer permanent magnet 233 toward the magnetic gap. ２ and the magnetic flux φ passing through the third layer permanent magnet 233 and heading toward the magnetic gap. ３ They are classified into three types:

[0016] Here, the arrangement and size of each component in one magnetic pole are defined as follows: The length of the long side of the permanent magnet 231 in the first layer is W １ , the length of the long side of the permanent magnet 232 in the second layer is W ２ , the length of the long side of the permanent magnet 233 in the third layer is W ３Since the permanent magnet is magnetized in the same direction as the short side direction, the long side direction of the permanent magnet is perpendicular to the magnetization direction. Also, the radial width of the outer diameter bridge 251 of the first layer is B １ , the radial width of the outer diameter bridge 252 of the second layer is B ２ , the radial width of the third layer outer diameter bridge 253 is B ３ Furthermore, the shortest distance between the permanent magnet 231 in the first layer and the permanent magnet 232 in the second layer is defined as Lm １ , the shortest distance between the permanent magnet 232 in the second layer and the permanent magnet 233 in the third layer is Lm ２ Let's say.

[0017] Next, the angle at one magnetic pole is defined as follows: The electrical angle of one magnetic pole of the rotor 20 is 180°. The electrical angle formed by a pair of lines connecting the point of the first layer permanent magnet 231 closest to the first layer outer diameter bridge 251 and the center of rotation C is θ. １１ The electrical angle formed by a pair of straight lines connecting the center of rotation C and the inner point of the V-shape of the side of the first layer magnet slot 241 that is in contact with the first layer outer diameter bridge 251 is defined as θ １２ The electrical angle formed by a pair of straight lines connecting the point of the second layer permanent magnet 232 closest to the second layer outer diameter bridge 252 and the center of rotation C is defined as θ ２１ The electrical angle formed by a pair of straight lines connecting the center of rotation C and the inner point of the V-shape of the side of the second layer magnet slot 242 that is in contact with the second layer outer diameter bridge 252 is defined as θ ２２ The electrical angle formed by a pair of straight lines connecting the point of the third layer permanent magnet 233 closest to the third layer outer diameter bridge 253 and the rotation center C is defined as θ ３１ The electrical angle formed by a pair of straight lines connecting the center of rotation C and the inner point of the V-shape of the side of the third layer magnet slot 243 that is in contact with the third layer outer diameter bridge 253 is defined as θ ３２ Let's say.

[0018] The rotating electrical machine of this embodiment satisfies the following conditions: θ １１ and θ １２ The smaller of these is the polar arc angle θ Ｓ１ The larger one is the polar arc angle θ Ｌ１ When this is the case, 40°≦θ Ｌ１ and θ Ｓ１ ≦80°.２１ and θ ２２ The smaller of these is the polar arc angle θ Ｓ２ The larger one is the polar arc angle θ Ｌ２ When this is the case, 102.8°≦θ Ｌ２ and θ Ｓ２ ≦144°. ３１ and θ ３２ The smaller of these is the polar arc angle θ Ｓ３ The larger one is the polar arc angle θ Ｌ３ When this is the case, 154.2°≦θ Ｌ３ and θ Ｓ３ Here, the pole arc angle is defined as the electrical angle formed by a pair of lines connecting the center of rotation C and two points on each layer that are line-symmetrical with respect to the d axis of the magnetic pole.

[0019] Also, W ２ <2 x W １ Katsu W ３ <3×W １ Satisfied. Also, Lm １ >Lm ２ Furthermore, B １ <B ２ And B １ <B ３ Satisfy.

[0020] A rotating electrical machine that satisfies these conditions can achieve low vibration and high efficiency in the high output range, the reason for which will be explained below.

[0021] 3 is a diagram showing the phase voltage waveforms when there is no load in the rotating electric machine according to this embodiment. As shown in Fig. 3, the phase voltage waveform when there is no load in this rotating electric machine has three peaks at every 90° electrical angle, symmetrical about the pole center when the rotor position is near 120° electrical angle and 300° electrical angle. This is because, as shown in Fig. 2, the magnetic flux flowing into the armature winding via the magnetic gap is divided into three magnetic fluxes φ １ , φ ２ and φ ３This is because the magnetic gap is divided into three peaks. In other words, it is estimated that the magnetic flux in the magnetic gap also has a waveform with three peaks every 90° electrical angle. The magnetic flux waveform in the magnetic gap is affected by the permeance due to the shape of the stator core facing the magnetic gap. Furthermore, the magnetic flux waveform in the magnetic gap is expressed as the time derivative of the magnetic flux in the magnetic gap according to Faraday's law of electromagnetic induction. Taking these things into consideration, the phase voltage waveform under no load is the same as the magnetic flux waveform in the magnetic gap that takes into account the permeance of the magnetic gap.

[0022] Fig. 4 is a diagram showing the magnetic flux waveform of the magnetic gap in the rotating electric machine according to this embodiment. Fig. 4 is a diagram in which the magnetic flux waveform of the magnetic gap is modeled as a rectangular wave, taking into consideration that the phase voltage waveform in the no-load state shown in Fig. 3 has three peaks every 90°. In Fig. 4, the horizontal axis represents the electrical angle. In Fig. 4, the magnetic flux waveform for one period of the electrical angle of the magnetic gap is represented by a square wave. １ And width L １２ = θ １ and a square wave of height A ２ And width L ２２ = θ ２ and a square wave of height A ３ And width L ３２ = θ ３ It is modeled as a sum of three square waves.

[0023] Width of the first rectangular wave θ １ is the magnetic flux φ shown in Figure 2 １ This corresponds to the magnetic flux that flows into the magnetic gap through the path of the permanent magnet 231 in the first layer. The magnetic flux generated by the magnetomotive force of the permanent magnet 231 in the first layer is attracted in the direction of the outer diameter bridge 251 in the first layer, which has a smaller magnetic resistance than the magnetic gap. In other words, the magnetic flux φ passing through the permanent magnet 231 in the first layer １Of these, the magnetic flux passing through a path close to the first layer outer bridge 251 is attracted to the outer bridge 251 and flows into the magnetic gap. In addition, the range from the inner point of the V-shape of the side of the first layer magnet slot 241 that contacts the first layer outer bridge 251 to the outer diameter side is the first layer outer bridge 251 and is narrow. Therefore, the first layer outer bridge 251 is prone to magnetic saturation, and the magnetic flux flowing into the magnetic gap is locally reduced in this area. From these factors, the width θ of the first stage rectangular wave in the rectangular wave model of the magnetic flux waveform １ is not a design value of the actual rotor, but is an electrical angle θ formed by a pair of straight lines connecting the center of rotation C and the inner point of the V-shape of the side of the first layer magnet slot 241 that is in contact with the first layer outer diameter bridge 251. １２ and an electrical angle θ formed by a pair of straight lines connecting the point of the first layer permanent magnet 231 closest to the first layer outer diameter bridge 251 and the rotation center C. １１ It is appropriate to set it to a value between

[0024] Furthermore, θ １１ and θ １２ The magnitude relationship between the rotor and the rotor speed varies depending on the rotor design. １１ <θ １２ This shows the case of θ １ Regarding the range of θ １１ and θ １２ The smaller of these is the polar arc angle θ Ｓ１ The larger one is the polar arc angle θ Ｌ１ As, θ １１ and θ １２ This shows the range in which the effect can be obtained regardless of the magnitude of the

[0025] As shown in FIG. 4, the electrical angle 180° (=π) corresponding to one magnetic pole of the rotor is used as a reference, and the width of the rectangular wave of each stage is set to L １１ = (π - L １２ ) / 2, L ２１ = (π - L ２２ ) / 2, L ３１ = (π - L ３２ ) / 2. In this case, the magnetic flux waveform F(t) is expressed by the following equation (1) through Fourier series expansion:

[0026]

[0027] Here, f in formula (1) １ , f ２ and f ３ are respectively expressed by the following equations (2) to (4).

[0028]

[0029]

[0030]

[0031] According to the law of sum and product of trigonometric functions, equations (1) to (4) can be rearranged into the following equation (5).

[0032]

[0033] The above-mentioned L １１ = (π - L １２ ) / 2, L ２１ = (π - L ２２ ) / 2, L ３１ = (π - L ３２ ) / 2 relationship, and L １２ = θ １ , L ２２ = θ ２ , L ３２ = θ ３ Using the above relationship, equation (5) can be expressed as the following equation (6).

[0034]

[0035] 5A and 5B are diagrams showing the relationship between a rectangular wave model and the pole arc angles of the magnetic poles of the three layers in the rotating electric machine according to this embodiment. As shown in FIG. 5A, the width θ １ The width of the second rectangular wave θ ２ As shown in FIG. 5B, the width θ of the second-stage rectangular wave ２ The width of the first rectangular wave θ １ As shown in FIG. 5(c), the width θ of the second-stage rectangular wave ２ The width of the third rectangular wave θ ３The approach of the square wave width θ ３ The width of the second rectangular wave θ ２ The approaching of corresponds to a decrease in the pole arc angle of the magnetic poles in the third layer.

[0036] Fig. 6 is a diagram showing the paths of magnetic flux for half a pole in a rotating electric machine according to this embodiment. In Fig. 6, the d-axis is the direction of magnetic flux generated by a magnetic pole, and the q-axis is a direction that is electrically and magnetically perpendicular to the d-axis. In Fig. 6, the second-layer permanent magnet 232 and the third-layer permanent magnet 233 are shown as separate magnets to clearly illustrate that the amount of magnetic flux differs depending on the magnetic flux path, but they are actually one permanent magnet. The magnetic flux φ of path 1 that passes through the first-layer permanent magnet 231, the second-layer permanent magnet 232, and the third-layer permanent magnet 233 and flows out into the magnetic gap is １ The magnetic flux φ of path 2, which passes through the second layer permanent magnet 232 and the third layer permanent magnet 233 and flows out into the magnetic gap, has the magnetomotive force of three layers of permanent magnets and has the largest amount of magnetic flux. ２ has the magnetomotive force of two layers of permanent magnets, and the magnetic flux φ of path 1 １ Furthermore, the magnetic flux φ of path 3 that passes through the permanent magnet 233 in the third layer and flows out into the magnetic gap ３ has the magnetomotive force of one layer of permanent magnet, and the magnetic flux φ of path 2 ２ The magnetic flux amount of path 1 is smaller than that of path 2. １ The width in the circumferential direction where the magnetic flux flows into the magnetic gap is D. １ , magnetic flux φ of path 2 ２ The width in the circumferential direction where the magnetic flux flows into the magnetic gap is D. ２ , the magnetic flux φ of path 3 ３ The width in the circumferential direction where the magnetic flux flows into the magnetic gap is D. ３ Let's say.

[0037] It is assumed that the magnetic resistance per unit volume in the path from the magnetic pole to the magnetic gap is the same for paths 1 to 3. In order to make the magnetic saturation of the rotor core uniform in paths 1 to 3 and make the magnetic flux waveform in the magnetic gap a waveform close to a sine wave, the pole arc angle is adjusted to １ :D ２:D ３ It is desirable to set the ratio to 3:2:1.

[0038] In the rotating electric machine of this embodiment, it is desirable to set the pole arc angle of the magnetic poles in the first layer to 90°, the pole arc angle of the magnetic poles in the second layer to 150°, and the pole arc angle of the magnetic poles in the third layer to 180°. However, in reality, due to the thickness of the permanent magnets, it is not possible to set the pole arc angle of the magnetic poles in the third layer, which are the permanent magnets furthest from the magnetic pole center, to 180°. Therefore, the pole arc angle of the magnetic poles in the first layer is first determined, corresponding to the magnetic flux of path 1, which is the path closest to the magnetic pole center and has the greatest magnetic flux amount. Next, the pole arc angle of the magnetic poles in the second layer is determined within a range equal to or greater than the pole arc angle of the magnetic poles in the first layer and equal to or less than 5 / 3 of the pole arc angle of the magnetic poles in the first layer. Finally, the pole arc angle of the magnetic poles in the third layer is determined within a range equal to or greater than the pole arc angle of the magnetic poles in the second layer and equal to or less than 6 / 3 (two times) the pole arc angle of the magnetic poles in the second layer. By determining the pole arc angles of the magnetic poles in each layer in this manner, the magnetic flux waveform in the magnetic gap can be made to resemble a sine wave.

[0039] The relationship between the pole arc angles can be set in a similar manner for a rotating electric machine having four or more layers of magnetic poles. In a rotating electric machine having an N-layer magnetic pole structure, where N is an integer of 3 or more, k is an integer of 2 or more and N or less, and θ is the angle formed by a pair of lines connecting the center of rotation and the point of the permanent magnet inserted into the k-th layer magnet slot that is closest to the outer diameter bridge of the k-th layer. １ｋ The angle formed by a pair of straight lines connecting the center of rotation and the inner point of the V-shape of the side of the k-th magnet slot that is in contact with the outer diameter bridge of the k-th layer is θ ２ｋ Then, θ １ｋ and θ ２ｋ The smaller of these is the polar arc angle θ Ｓｋ The larger one is the polar arc angle θ Ｌｋ Furthermore, the maximum possible angle of the pole arc angle of the first layer, which will be described later, is set to θ １ｍａｘ The maximum angle that the pole arc angle of the kth layer can take is θ ｋｍａｘ In this case, θ Ｓｋ and θ Ｌｋ It is sufficient that the following expressions (7) and (8) are satisfied.

[0040]

[0041]

[0042] Also, θ ｋｍａｘ may be set so as to satisfy the following equation (9).

[0043]

[0044] Note that when a rotating electric machine is actually manufactured, there is an angle tolerance of about 1° in mechanical angle. Taking this into consideration, the range for specifying the pole arc angle in the 8-pole rotating electric machine of this embodiment should be set to a range with a margin of about 1×8 / 2=4° in electrical angle. It is also effective to set a similar range with a margin for rotating electric machines with 12 poles or less, which are currently widely used in motors for electric vehicles. If the number of poles of the rotating electric machine is p poles, a structure with a margin of (p / 2)° in electrical angle, including an 8-pole rotating electric machine, can achieve the same effect as this embodiment. In order to achieve a structure with a margin of (p / 2)° in electrical angle, θ Ｌｋ It is sufficient to satisfy the equation obtained by subtracting p / 2 from the left side of the above equation (7), and θ Ｓｋ It is sufficient to satisfy the equation obtained by adding p / 2 to the right side of the above equation (8).

[0045] As shown in FIG. 6 , in a rotor having three layers of magnetic poles, the magnetic flux path is divided into paths 1 to 3. Therefore, the magnetic flux of each of paths 1 to 3 flows into the stator through the magnetic gap, thereby increasing the amount of effective magnetic flux and improving the output of the rotating electric machine. In the case of a three-layer structure like the rotating electric machine of this embodiment, it is preferable to allocate three teeth per half pole. That is, in the case of eight poles (four pole pairs) like the rotating electric machine of this embodiment, a structure having 3 (= number of teeth per half pole) × 2 (= one magnetic pole) × 8 (= number of poles) = 48 teeth is sufficient. If the number of teeth is M × 3, where M is an integer greater than or equal to 2, the magnetic flux of paths 1 to 3 faces each individual tooth through the magnetic gap, thereby improving the output of the rotating electric machine.

[0046] Furthermore, as mentioned above, from the viewpoint of improving output, it is desirable to increase the magnetic flux of path 1, which is the path closest to the magnetic pole center and has the largest amount of magnetic flux. Therefore, it is conceivable to increase the width of the permanent magnet in the first layer so that all the magnetic flux generated by the magnetomotive force passes through path 1. On the other hand, as shown in Figure 6, it is also possible to strictly limit the circumferential width of the magnetic flux flowing into the magnetic gap to D. １ :D ２ :D ３ If the ratio is 3:2:1, increasing the width of the permanent magnets in the first layer to increase output will likely result in the widths of the permanent magnets in the second and third layers becoming too large, making it difficult to fit the permanent magnets inside the rotor core. Also, increasing the width of the permanent magnets will likely increase the leakage flux from the ends of the permanent magnets, resulting in an increase in magnetic flux that does not contribute to output.

[0047] Therefore, the width of the permanent magnet in the first layer is W １ The width of the permanent magnet in the kth layer is W ｋ When W ｋ <k × W １ To satisfy ｋ By setting the width W of the permanent magnet, it is possible to increase the amount of effective magnetic flux, thereby improving the output of the rotating electric machine. Here, the width of the permanent magnet is the length along the shape of the permanent magnet in a direction perpendicular to the direction of magnetization of the permanent magnet. If the permanent magnet in each layer is divided into multiple pieces, the width of the permanent magnet is the sum of the lengths along the shape of the permanent magnet in a direction perpendicular to the direction of magnetization of the multiple permanent magnets. In the rotating electric machine of this embodiment, the width W of the permanent magnet in the second layer is ２ is the width W of the first layer permanent magnet １ and the width W of the third layer permanent magnet is smaller than twice the ３ is the width W of the first layer permanent magnet １ By setting the width of the permanent magnets in this manner, it is possible to increase the width of the permanent magnets in the first layer, which contributes greatly to output, while still allowing the widths of the permanent magnets in the second and third layers to be set in consideration of the influence of magnetic saturation near the magnetic gap. As a result, the output of the rotating electric machine can be increased.

[0048] Next, in the magnetic flux paths shown in Fig. 6, attention will be focused on paths other than path 1, which supplies the main magnetic flux. Since the magnetic flux of path 3 is less than the magnetic flux of path 2, by setting the length of the magnetic path through which each magnetic flux passes according to the amount of magnetic flux, it is possible to reduce the leakage magnetic flux paths and further improve the output of the rotating electric machine. Specifically, in the rotating electric machine of this embodiment, the minimum distance Lm between the permanent magnet 231 of the first layer and the permanent magnet 232 of the second layer is １ Therefore, the minimum distance Lm between the permanent magnet 232 in the second layer and the permanent magnet 233 in the third layer ２ can be made smaller.

[0049] This configuration can also be applied to a rotating electric machine having four or more magnetic pole layers. In a rotating electric machine having an N-layer magnetic pole structure, where N is an integer of 3 or greater, and m is an integer between 2 and (N-1), the shortest distance between the permanent magnet in the (m-1)th layer and the permanent magnet in the mth layer should be greater than the shortest distance between the permanent magnet in the mth layer and the permanent magnet in the (m+1)th layer.

[0050] In the magnetic flux paths shown in Figure 6, the amount of magnetic flux in path 1 contributes most to the output, so in order to reduce the leakage flux path of the magnetic flux in path 1, it is advisable to reduce the radial width of the outer bridge of the first layer. Also, considering the centrifugal force of the permanent magnets in each layer during rotation, the centrifugal force acting on the outer bridge of the first layer is smaller than the centrifugal force acting on the outer bridge of the other layers. For this reason, the radial width B of the outer bridge of the first layer １ By making the width of the outer diameter bridges in the other layers smaller than the radial width of the outer diameter bridges in the other layers, the output of the rotating electric machine can be further improved.

[0051] Furthermore, the centrifugal force acting on the outer bridge of the second layer is greater than the centrifugal force acting on the outer bridge of the first layer, and the centrifugal force acting on the outer bridge of the third layer is greater than the centrifugal force acting on the outer bridge of the second layer. Therefore, by making the radial width of the outer bridge of the (k-1)th layer greater than the radial width of the outer bridge of the kth layer, the strength of the rotor can be improved. However, this does not apply to the relationship of the radial widths of the outer bridges of layers other than the first layer when reducing the harmonic components of the magnetic gap. For example, in the rotating electric machine shown in FIG. 2, the radial width B of the outer bridge of the first layer is１ is the radial width B of the outer diameter bridge of the second layer ２ and the radial width B of the third layer outer diameter bridge ３ Although it is smaller than B ３ is B ２ The reason for this is that the magnetic flux passing through the outer bridges in the second and subsequent layers is smaller than the magnetic flux passing through the outer bridges in the first layer, and so contributes less to the output of the rotating electric machine. The relationship between the radial width of the outer bridges is similar in multi-layer structures with four or more layers.

[0052] 7 is a diagram showing harmonic components of the magnetic flux waveform of the magnetic gap in the rotating electric machine according to this embodiment. FIG. 7 shows the result of simulating the magnetic flux waveform of the magnetic gap using a square wave model, and the width θ of the first square wave １ and the 1st to 9th harmonic components. Fig. 7(a) shows only the first terms in brackets for i=1 to 5 in equation (6), i.e., the 1st, 3rd, 5th, 7th, and 9th harmonic components. The first terms in brackets in equation (6) are the θ １ , which is a term corresponding to a change in the amplitude of the fundamental component. The values ​​on the vertical axis in FIG. 7( a) are normalized using the amplitude value of the first-order component. FIG. 7( b) shows the values ​​obtained by extracting and adding together the values ​​of the terms i=1 to 5 in equation (6), i.e., the first to ninth harmonic components. Specifically, in FIG. 7( b), parameter (1) shown by the solid line represents the value obtained by extracting and adding together the absolute values ​​of the terms i=3 to 4, i.e., the fifth and seventh harmonic components; parameter (2) shown by the dotted line represents the value obtained by extracting and adding together the absolute values ​​of the terms i=2 to 5, i.e., the third, fifth, seventh, and ninth harmonic components; and parameter (3) shown by the dashed line represents the value obtained by extracting and adding together the absolute values ​​of the terms i=1 to 5, i.e., the fundamental component and the third, fifth, seventh, and ninth harmonic components.

[0053] According to the theory of rotating electrical machines, parameter (1) is the absolute sum of the fifth- and seventh-order harmonic components, and is a value correlated with the sixth-order torque ripple, which is the main cause of vibration and noise in rotating electrical machines. Furthermore, parameters (2) and (3) are both values ​​obtained by adding together lower-order harmonic components, and are values ​​correlated with iron loss. However, with regard to iron loss, the contribution of the fundamental component is significant, and the fundamental component is correlated with output, so there is a trade-off between iron loss and output on a global scale. For these reasons, FIG. 7(b) shows both parameter (2) excluding the fundamental and parameter (3) including the fundamental.

[0054] In FIG. 7(a), first, based on the above consideration, the width θ of the first rectangular wave １ Focusing on the range of 0° to 90° assumed as the angle, the zero crossing point (2π / 5) of the fifth-order component and the zero crossing point (2π / 7) of the seventh-order component are located between the zero crossing points (2π / 9) = 40° and (4π / 9) = 80° of the ninth-order component. In FIG. 7(a), the zero crossing points of the fifth-order component and the seventh-order component are indicated by triangles. To minimize the sixth-order torque ripple and iron loss, it is sufficient to reduce parameters (1), (2), and (3). As described above, the zero crossing points are concentrated in the range 40°≦θ. １ It is expected that the minimum value will be in the range of ≦80°.

[0055] 7B, it can be seen that the minimum values ​​of the parameters (1), (2), and (3) are all within the range of 40° to 80°. If this is reflected in the rotor structure and the allowance due to the angle tolerance is taken into consideration, as in the consideration of equations (7) to (9), the eight-pole rotating electric machine of this embodiment includes a tolerance of ±4° in electrical angle, so 36°≦θ Ｌ１ and θ Ｓ１ It is preferable that the angle θ calculated from the above consideration is ≦84°. １ The maximum value 80° in the range of θ １ｍａｘ= 80° and substitute this into the above-mentioned equations (7) to (9), the pole arc angles of the magnetic poles in the second and third layers can be determined. As a result, a rotating electric machine can be obtained that can reduce sixth-order torque ripple and iron loss while achieving high output by taking into account the effects of magnetic saturation. Note that the pole arc angles of the magnetic poles in each layer can also be determined using similar considerations in rotating electric machines with four or more layers.

[0056] The pole arc angles of the magnetic poles in the second and third layers of the rotating electric machine of this embodiment can be determined by calculating, using the method described above, an appropriate range for the pole arc angle of the magnetic poles in the first layer, which contributes most to the characteristics of the rotating electric machine. In order to further enhance the effects of low vibration and high efficiency in this rotating electric machine, a structure is next described in which the pole arc angles of the magnetic poles in the second and third layers are adjusted to minimize harmonic components.

[0057] 8 is a diagram showing harmonic components of the magnetic flux waveform of the magnetic gap in the rotating electric machine according to this embodiment. FIG. 8 shows the result of simulating the magnetic flux waveform of the magnetic gap using a square wave model, and the width θ of the second square wave ２ This figure shows the relationship between the terms i=1 to 5 in equation (6), i.e., the first terms in brackets for the first, third, fifth, seventh, and ninth harmonic components. The values ​​on the vertical axis in FIG. 8(a) are normalized using the amplitude value of the first-order component. FIG. 8(b) shows the sum of the values ​​extracted from the terms i=1 to 5 in equation (6), i.e., the first to ninth harmonic components. Specifically, in FIG. 8(b), parameter (1) shown by a solid line is the value obtained by extracting terms for i=3 to 4, i.e., the fifth and seventh harmonic components, and adding up their absolute values; parameter (2) shown by a dotted line is the value obtained by extracting terms for i=2 to 5, i.e., the third, fifth, seventh, and ninth harmonic components, and adding up their absolute values; and parameter (3) shown by a dashed line is the value obtained by extracting terms for i=1 to 5, i.e., the fundamental wave component and the third, fifth, seventh, and ninth harmonic components, and adding up their absolute values.

[0058] In FIG. 8(a), first, based on the above consideration, the width θ of the second rectangular wave ２Focusing on the range of 90° to 150° assumed as the angle, the zero crossing point (2π / 3) = 120° of the third and ninth order components is located between the zero crossing point (4π / 7) = 102.8° of the seventh order component and the zero crossing point (4π / 5) = 144° of the fifth order component. In FIG. 8(a), the zero crossing points of the third and ninth order components are indicated by triangles. To minimize the sixth order torque ripple and iron loss, it is sufficient to reduce parameters (1), (2), and (3). As described above, the zero crossing points are concentrated in the range 102.8°≦θ. ２ It is expected that the minimum value will be in the range of ≦144°.

[0059] 8B, it can be seen that the minimum values ​​of the parameters (1), (2), and (3) are all within the range of 102.8° to 144°. When this is reflected in the rotor structure and the allowance due to the angle tolerance is taken into consideration, as in the consideration of equations (7) to (9), the eight-pole rotating electric machine of this embodiment includes a tolerance of ±4° in electrical angle, so 98.8°≦θ Ｌ２ and θ Ｓ２ It is preferable that the angle ≦148° is satisfied.

[0060] 9 is a diagram showing harmonic components of the magnetic flux waveform of the magnetic gap in the rotating electric machine according to this embodiment. FIG. 9 shows the result of simulating the magnetic flux waveform of the magnetic gap using a square wave model, and the width θ of the square wave in the third stage ３and the 1st to 9th harmonic components. Figure 9(a) shows only the first terms in brackets for the terms i=1 to 5 in equation (6), i.e., the 1st, 3rd, 5th, 7th, and 9th harmonic components. The values ​​on the vertical axis in Figure 9(a) are normalized using the amplitude value of the 1st-order component. Figure 9(b) shows the sum of the values ​​extracted for the terms i=1 to 5 in equation (6), i.e., the 1st to 9th harmonic components. Specifically, in FIG. 9(b), parameter (1) shown by a solid line is the value obtained by extracting terms for i=3 to 4, i.e., the fifth and seventh harmonic components, and adding up their absolute values; parameter (2) shown by a dotted line is the value obtained by extracting terms for i=2 to 5, i.e., the third, fifth, seventh, and ninth harmonic components, and adding up their absolute values; and parameter (3) shown by a dashed line is the value obtained by extracting terms for i=1 to 5, i.e., the fundamental wave component and the third, fifth, seventh, and ninth harmonic components, and adding up their absolute values.

[0061] In FIG. 9(a), first, based on the above consideration, the width θ of the third rectangular wave ３ Focusing on the range of 150° to 180°, which is assumed as the angle, the zero cross point of the 7th order component is (6π / 7) = 154.2° and the zero cross point of the 9th order component is (8π / 9) = 160°. To minimize the 6th order torque ripple and iron loss, it is sufficient to reduce parameters (1), (2), and (3). As mentioned above, the zero cross points are concentrated in the range 154.2°≦θ ３ It is expected that the minimum value will be in the range of ≦160°.

[0062] 9B, it can be seen that the minimum values ​​of the parameters (1), (2), and (3) are all within the range of 154.2° to 160°. When this is reflected in the rotor structure and the allowance due to the angle tolerance is taken into consideration, as in the consideration of equations (7) to (9), the eight-pole rotating electric machine of this embodiment includes a tolerance of ±4° in electrical angle, so 150.2°≦θ Ｌ３ and θ Ｓ３ It is preferable that the angle .ltoreq.164.degree. is satisfied.

[0063] Next, it will be explained that the pole arc angle setting based on the rectangular wave model described above is valid even when the influence of magnetic saturation that occurs in an actual rotor core is taken into consideration.

[0064] 10A and 10B are diagrams showing the relationship between the square wave model and the pole arc angles of the magnetic poles of the three layers in the rotating electric machine according to this embodiment. As shown in FIG. 10A, as the pole arc angle of the magnetic poles of the first layer increases, the distance X from the magnetic gap near the pole center to the permanent magnet of the first layer decreases. １ As the distance X near the magnetic gap between the first layer permanent magnet and the second layer permanent magnet decreases, ２ As a result, the magnetic flux from the first layer permanent magnet to the magnetic gap and the magnetic flux from the second layer magnetic pole to the magnetic gap are more likely to cause magnetic saturation in the rotor core, and the amount of magnetic flux is expected to decrease. When this phenomenon is reflected in the square wave model, the width θ of the first square wave １ As the amplitude of the square wave increases, the height of the first and second steps of the square wave decrease.

[0065] Furthermore, as shown in FIG. 10(b), when the pole arc angle of the magnetic poles in the second layer decreases, the distance X ２ As the distance X near the magnetic gap between the second and third layer permanent magnets decreases, ３ As a result, the magnetic flux from the second layer permanent magnet to the magnetic gap is more likely to cause magnetic saturation in the rotor core, and the amount of magnetic flux is expected to decrease. On the other hand, the magnetic flux from the third layer permanent magnet to the magnetic gap is more likely to cause magnetic saturation in the rotor core, and the amount of magnetic flux is expected to increase. When this phenomenon is reflected in the square wave model, the width θ of the second square wave ２ As the value of the square wave decreases, the height of the second square wave decreases and the height of the third square wave increases.

[0066] Furthermore, as shown in FIG. 10(c), when the pole arc angle of the magnetic poles in the second layer increases, the distance X ２ As the distance X near the magnetic gap between the second and third layer permanent magnets increases,３ becomes smaller. As a result, it is expected that the magnetic flux from the second layer permanent magnet to the magnetic gap will reduce magnetic saturation in the rotor core, and the amount of magnetic flux will increase. On the other hand, the magnetic flux from the third layer permanent magnet to the magnetic gap will be more likely to cause magnetic saturation in the rotor core, and the amount of magnetic flux will decrease. When this phenomenon is reflected in the square wave model, the width θ of the second square wave ２ As the value of the square wave increases, the height of the second square wave increases and the height of the third square wave decreases.

[0067] Furthermore, as shown in FIG. 10(d), when the pole arc angle of the magnetic poles in the third layer decreases, the distance X ３ As a result, the magnetic flux from the third layer permanent magnet to the magnetic gap is more likely to cause magnetic saturation in the rotor core, and the amount of magnetic flux is expected to decrease. When this phenomenon is reflected in the square wave model, the width θ of the third square wave ３ As the magnetic flux flowing into the magnetic poles of the first and second layers increases, the height of the square waves of the first and second layers also increases.

[0068] Hereinafter, when simulating the magnetic flux waveform of the magnetic gap with a rectangular wave model, a model that takes into account only the width of the rectangular wave as the pole arc angle changes as shown in Figure 5 will be referred to as a model that does not take magnetic saturation into account, and a model that takes into account the width and height of the rectangular wave as the pole arc angle changes as shown in Figure 10 will be referred to as a model that takes magnetic saturation into account. Note that here, a model that does not take magnetic saturation into account means a model that assumes that no magnetic saturation occurs in the rotor core, and a model that takes magnetic saturation into account means a model that assumes that magnetic saturation occurs in the rotor core.

[0069] 11 is a diagram showing harmonic components of the magnetic flux waveform of the magnetic gap in the rotating electric machine according to this embodiment. FIG. 11 shows the result of simulating the magnetic flux waveform of the magnetic gap using a square wave model, and the width θ of the first square wave １and the harmonic components that contribute to the sixth-order torque ripple. The values ​​on the vertical axis in FIG. 11 are obtained by extracting the terms for i=3 to 4 in Equation (6), i.e., the fifth-order and seventh-order harmonic components, and adding up their absolute values. As described above, this is a parameter that is correlated with the sixth-order torque ripple. Note that the model that takes magnetic saturation into account shown in FIG. 10 does not hold true in cases where, for example, the height of the second-order rectangular wave exceeds the height of the first-order rectangular wave or is smaller than the height of the third-order rectangular wave. Therefore, the shape of the rectangular wave of the reference model is the same as that of the model that does not take magnetic saturation into account shown in FIG. 5.

[0070] In Fig. 11, the solid line represents the simulation result using a model that does not consider magnetic saturation, and the dotted line represents the simulation result using a model that does consider magnetic saturation. As shown in Fig. 11, the harmonic components of the model that does not consider magnetic saturation are at a minimum point P1 (θ １ On the other hand, the harmonic components of the model that takes magnetic saturation into account have θ １ The harmonic components of the model that does not consider magnetic saturation and the harmonic components of the model that does consider magnetic saturation intersect at the point C1 (θ １ = 67°).

[0071] In an actual rotating electrical machine, the pole arc angle of the magnetic poles in the first layer is equal to the width θ of the rectangular wave of the reference model. １ It is thought that as the pole arc angle moves away from 67°, the distance between the permanent magnets and the distance between the permanent magnets and the magnetic gap decreases, making it more susceptible to the effects of magnetic saturation. In other words, when the pole arc angle of the magnetic poles in the first layer is near 67°, the fluctuations are similar to those of a model that does not consider magnetic saturation, and as the pole arc angle moves away from 67°, the fluctuations are closer to those of a model that does consider magnetic saturation. Therefore, given that the model that considers magnetic saturation shows a monotonous decrease, while the model that does not consider magnetic saturation reaches a minimum at 60°, it is thought that the sixth-order torque ripple will reach a minimum value in a range greater than 60°.

[0072] 12 is a diagram showing harmonic components of the magnetic flux waveform of the magnetic gap in the rotating electric machine according to this embodiment. FIG. 12 shows the result of simulating the magnetic flux waveform of the magnetic gap using a square wave model, and the width θ of the second square wave ２and the harmonic component that contributes to the sixth-order torque ripple. In Fig. 12, the solid line represents a simulation result using a model that does not consider magnetic saturation, and the dotted line represents a simulation result using a model that considers magnetic saturation.

[0073] As shown in FIG. 12, the harmonic components of the model that does not consider magnetic saturation are at a minimum point P2 (θ ２ = 106°). The harmonic components of the model that takes magnetic saturation into account have a minimum point P1 (θ ２ The harmonic components of the model that does not consider magnetic saturation and the harmonic components of the model that does consider magnetic saturation have an intersection C1 (θ ２ = 94°) and intersection point C2 (θ ２ = 112°).

[0074] In an actual rotating electric machine, the pole arc angle of the second layer magnetic pole is the width θ of the rectangular wave of the reference model. ２ = 112°, the distance between the permanent magnets and the distance between the permanent magnets and the magnetic gap decreases, which is thought to increase the susceptibility to the effects of magnetic saturation. In other words, when the pole arc angle of the magnetic poles in the second layer is near 112°, the fluctuations are closer to a model that does not consider magnetic saturation, and as the pole arc angle moves away from 112°, the fluctuations are closer to a model that does consider magnetic saturation. Therefore, it is thought that the sixth-order torque ripple reaches a minimum value when the pole arc angle of the magnetic poles in the second layer is in the range of approximately 94° to 112°.

[0075] 13 is a diagram showing harmonic components of the magnetic flux waveform of the magnetic gap in the rotating electric machine according to this embodiment. FIG. 13 shows the result of simulating the magnetic flux waveform of the magnetic gap using a square wave model, and the width θ of the square wave in the third stage ３ and the harmonic component that contributes to the sixth-order torque ripple. In Fig. 13, the solid line represents a simulation result using a model that does not consider magnetic saturation, and the dotted line represents a simulation result using a model that considers magnetic saturation.

[0076] As shown in FIG. 13, the harmonic components of the model that does not consider magnetic saturation are at a minimum point P1 (θ ３ The harmonic components of the model that takes magnetic saturation into account have a minimum point P2 (θ ３The harmonic components of the model that does not consider magnetic saturation and the harmonic components of the model that considers magnetic saturation have an intersection C1 (θ ３ = 152°) and intersection point C2 (θ ３ = 159°).

[0077] In an actual rotating electric machine, the pole arc angle of the third layer magnetic pole is the width θ of the rectangular wave of the reference model. ３ = 152°, the distance between the permanent magnets and the distance between the permanent magnets and the magnetic gap decreases, which is thought to make the effect of magnetic saturation more pronounced. That is, when the pole arc angle of the magnetic poles in the third layer is near 152°, the fluctuations are closer to a model that does not consider magnetic saturation, and as the pole arc angle moves away from 152°, the fluctuations are closer to a model that does consider magnetic saturation. Therefore, it is thought that the sixth-order torque ripple reaches a minimum value when the pole arc angle of the magnetic poles in the second layer is in the range of approximately 152° to 159°.

[0078] 14 is a diagram showing harmonic components of the magnetic flux waveform of the magnetic gap in the rotating electric machine according to this embodiment. FIG. 14 shows the result of simulating the magnetic flux waveform of the magnetic gap using a square wave model, and the width θ of the first square wave １ and the harmonic components that contribute to iron loss. The values ​​on the vertical axis in Figure 14 are calculated by extracting terms for i = 1 to 5 in Equation (6), i.e., the fundamental wave component and the third to ninth harmonic components, and adding up their absolute values. As mentioned above, these are parameters that correlate with iron loss. Note that the model that takes magnetic saturation into account shown in Figure 10 does not hold true in cases where, for example, the height of the second rectangular wave exceeds the height of the first rectangular wave or is smaller than the height of the third rectangular wave. Therefore, the shape of the rectangular wave of the reference model is the same as that of the model that does not take magnetic saturation into account shown in Figure 5.

[0079] In Fig. 14, the solid line represents the simulation result using a model that does not consider magnetic saturation, and the dotted line represents the simulation result using a model that does consider magnetic saturation. As shown in Fig. 14, the harmonic components of the model that does not consider magnetic saturation are at a minimum point P1 (θ １ On the other hand, the harmonic components of the model that takes magnetic saturation into account are １The harmonic components of the model that does not consider magnetic saturation and the harmonic components of the model that does consider magnetic saturation intersect at the point C1 (θ １ = 67°).

[0080] In an actual rotating electric machine, the pole arc angle of the first layer magnetic pole is the width θ of the rectangular wave of the reference model. １ As the pole arc angle of the magnetic poles in the first layer moves away from 57°, the distance between the permanent magnets and the distance between the permanent magnets and the magnetic gap decreases, which is thought to make the magnetic poles more susceptible to the effects of magnetic saturation. In other words, when the pole arc angle of the magnetic poles in the first layer is around 67°, the fluctuations are closer to a model that does not consider magnetic saturation, and as the pole arc angle moves away from 67°, the fluctuations are closer to a model that does consider magnetic saturation. Therefore, it is thought that iron loss reaches a minimum value when the pole arc angle of the magnetic poles in the first layer is roughly in the range of 67° or more.

[0081] 15 is a diagram showing harmonic components of the magnetic flux waveform of the magnetic gap in the rotating electric machine according to this embodiment. FIG. 15 shows the result of simulating the magnetic flux waveform of the magnetic gap using a square wave model, and the width θ of the second square wave ２ and the harmonic components that contribute to iron loss. The values ​​on the vertical axis in Fig. 15 are calculated by extracting terms for i=1 to 5 in equation (6), i.e., the fundamental wave component and the third to ninth harmonic components, and adding up their absolute values. As mentioned above, these are parameters that correlate with iron loss. In Fig. 15, the solid line represents a simulation using a model that does not consider magnetic saturation, and the dotted line represents a simulation using a model that does consider magnetic saturation.

[0082] As shown in FIG. 15, the harmonic components of the model that does not consider magnetic saturation are at a minimum point P1 (θ ２ = 110°). The harmonic components of the model that takes magnetic saturation into account have a minimum point P2 (θ ２ The harmonic components of the model that does not consider magnetic saturation and the harmonic components of the model that considers magnetic saturation have an intersection C1 (θ ２ = 113°) and intersection C2 (θ ２ = 117°).

[0083] In an actual rotating electric machine, the pole arc angle of the second layer magnetic pole is the width θ of the rectangular wave of the reference model. ２It is believed that as the pole arc angle of the second layer magnetic poles moves away from 113°, the distance between the permanent magnets and the distance between the permanent magnets and the magnetic gap decreases, making the magnetic poles more susceptible to the effects of magnetic saturation. In other words, when the pole arc angle of the second layer magnetic poles is near 113°, the fluctuations are closer to a model that does not consider magnetic saturation, and as the pole arc angle moves away from 113°, the fluctuations are closer to a model that does consider magnetic saturation. Therefore, it is believed that iron loss reaches a minimum when the pole arc angle of the second layer magnetic poles is in the range of approximately 110° to 117°.

[0084] 16 is a diagram showing harmonic components of the magnetic flux waveform of the magnetic gap in the rotating electric machine according to this embodiment. FIG. 16 shows the result of simulating the magnetic flux waveform of the magnetic gap using a square wave model, and the width θ of the square wave in the third stage ３ and the harmonic components that contribute to iron loss. The values ​​on the vertical axis in Fig. 16 are calculated by extracting terms for i=1 to 5 in equation (6), i.e., the fundamental wave component and the third to ninth harmonic components, and adding up their absolute values. As mentioned above, these are parameters that correlate with iron loss. In Fig. 16, the solid line represents a simulation using a model that does not consider magnetic saturation, and the dotted line represents a simulation using a model that does consider magnetic saturation.

[0085] As shown in FIG. 16, the harmonic components of the model that does not consider magnetic saturation are at a minimum point P2 (θ ３ The harmonic components of the model that takes magnetic saturation into account have a minimum point P1 (θ ３ The harmonic components of the model that does not consider magnetic saturation and the harmonic components of the model that considers magnetic saturation have an intersection C1 (θ ３ = 152°) and intersection point C2 (θ ３ = 157°).

[0086] In an actual rotating electric machine, the pole arc angle of the third layer magnetic pole is the width θ of the rectangular wave of the reference model. ３As the pole arc angle of the magnetic poles in the third layer moves away from 152°, the distance between the permanent magnets and the distance between the permanent magnets and the magnetic gap decreases, which is thought to make the magnetic poles more susceptible to the effects of magnetic saturation. In other words, when the pole arc angle of the magnetic poles in the third layer is near 152°, the fluctuations are closer to a model that does not consider magnetic saturation, and as the pole arc angle moves away from 152°, the fluctuations are closer to a model that does consider magnetic saturation. Therefore, it is thought that iron loss reaches a minimum when the pole arc angle of the magnetic poles in the third layer is in the range of approximately 152° to 158°.

[0087] As described above, even in a square wave model that takes into account the effects of magnetic saturation that occurs in the rotor core, parameters correlated with sixth-order torque ripple and iron loss are minimized by setting the width of the first square wave to between 36° and 84°, the width of the second square wave to between 98.8° and 148°, and the width of the third square wave to between 150.2° and 164°. As a result, a rotating electric machine designed using a square wave model that takes into account the effects of magnetic saturation can achieve low vibration and high efficiency in the high output range.

[0088] Embodiment 2. Fig. 17 is an enlarged cross-sectional view of a rotor of a rotating electric machine according to Embodiment 2. Fig. 17 is an enlarged cross-sectional view of one magnetic pole portion of rotor 20. The rotating electric machine of this embodiment has eight poles, just like the rotating electric machine of Embodiment 1, and the number of teeth of the rotor core is 48.

[0089] As shown in FIG. 17 , the rotor core 22 is formed with magnet slots 241, 242, and 243 arranged in a V-shape that opens from the center of rotation toward the outer diameter side, forming a three-layer structure in the radial direction. The magnet slots are through-holes that penetrate the rotor core 22 in the axial direction. These magnet slots are arranged in the following order from the outer diameter side to the inner diameter side: first layer magnet slot 241, second layer magnet slot 242, and third layer magnet slot 243. Each layer of magnet slots 241, 242, and 243 is composed of a pair of slots formed between a central bridge 221, 222, and 223 located in the center and an outer diameter bridge 251, 252, and 253 located between the central bridge and the outer peripheral surface of the rotor core 22. A pair of permanent magnets 231, 232, and 233 is inserted in the center of each slot. The portions at both ends of each slot where no permanent magnets are inserted serve as flux barriers.

[0090] In the rotating electric machine of this embodiment, the arrangement and size of the magnet slots and permanent magnets are the same as in the rotating electric machine of embodiment 1. Therefore, in the rotating electric machine of this embodiment, low vibration and high efficiency can be achieved in the high output range, just like in embodiment 1.

[0091] In the rotating electric machine of this embodiment, the permanent magnet 232 in the second layer is divided into two, and the permanent magnet 233 in the third layer is divided into three. The divided permanent magnets in each layer are arranged symmetrically with respect to the magnetic pole center. In other words, the divided permanent magnets in each layer are arranged adjacent to each other on the right and left sides of the V-shape to form a single permanent magnet assembly. Generally, dividing a permanent magnet reduces the eddy currents generated inside each permanent magnet, thereby reducing the eddy current loss of the entire permanent magnet. Therefore, the rotating electric machine of this embodiment can further enhance the effect of high efficiency. Furthermore, high positional accuracy is required to insert a large permanent magnet into a magnet slot. In the rotating electric machine of this embodiment, the permanent magnet is divided into multiple narrow permanent magnets, which reduces assembly tolerances. As a result, the rotating electric machine of this embodiment has a structure that facilitates rotor assembly, and the manufacturing cost of the rotating electric machine can be reduced.

[0092] In the rotating electric machine of this embodiment, the permanent magnet 232 in the second layer is divided into two and the permanent magnet 233 in the third layer is divided into three, but the permanent magnets in the second layer and above may be divided into two or more. The permanent magnet 231 in the first layer may also be divided into two or more.

[0093] Embodiment 3. Fig. 18 is an enlarged cross-sectional view of a rotor of a rotating electric machine according to Embodiment 3. Fig. 18 is an enlarged cross-sectional view of one magnetic pole portion of rotor 20. The rotating electric machine of this embodiment has eight poles, just like the rotating electric machine of Embodiment 1, and the number of teeth of the rotor core is 48.

[0094] 18 , rotor core 22 is formed with magnet slots 241, 242, and 243 arranged in a V-shape that opens from the center of rotation toward the outer diameter side, forming a three-layer structure in the radial direction. The magnet slots are through-holes that pass through rotor core 22 in the axial direction. These magnet slots are arranged in the order of first layer magnet slot 241, second layer magnet slot 242, and third layer magnet slot 243 from the outer diameter side to the inner diameter side.

[0095] In the rotating electric machine of this embodiment, the second-layer magnet slot 242 and the third-layer magnet slot 243 are bent halfway to close the V-shape. Also, in the rotating electric machine of this embodiment, the second-layer permanent magnet 232 is divided into two pieces, and the third-layer permanent magnet 233 is divided into three pieces. The two second-layer permanent magnets 232 are inserted on the inner diameter side and the outer diameter side of the bent second-layer magnet slot 242. Also, the third-layer permanent magnet 233 is divided into three pieces, with two of the permanent magnets 233 inserted on the inner diameter side of the bent third-layer magnet slot 243 and one permanent magnet 233 inserted on the outer diameter side.

[0096] In the rotating electric machine of this embodiment, as in the rotating electric machine of embodiment 1, the angle of one magnetic pole is defined as follows: The electrical angle of one pole of the rotor 20 is 180°. The electrical angle formed by a pair of lines connecting the point of the first layer permanent magnet 231 closest to the first layer outer diameter bridge 251 and the center of rotation is θ. １１ The electrical angle formed by a pair of straight lines connecting the center of rotation and the inner point of the V-shape of the side of the first layer magnet slot 241 that is in contact with the first layer outer diameter bridge 251 is defined as θ １２ The electrical angle formed by a pair of lines connecting the point of the second layer permanent magnet 232 closest to the second layer outer diameter bridge 252 and the center of rotation is defined as θ ２１ The electrical angle formed by a pair of straight lines connecting the center of rotation and the inner point of the V-shape of the side of the second layer magnet slot 242 that is in contact with the second layer outer diameter bridge 252 is defined as θ ２２ The electrical angle formed by a pair of lines connecting the point of the third layer permanent magnet 233 closest to the third layer outer diameter bridge 253 and the center of rotation is defined as θ ３１ The electrical angle formed by a pair of straight lines connecting the center of rotation and the inner point of the V-shape of the side of the third layer magnet slot 243 that is in contact with the third layer outer diameter bridge 253 is defined as θ ３２ Let's say.

[0097] The rotating electric machine of this embodiment satisfies the following conditions, similar to the rotating electric machine of the first embodiment: １１ and θ １２ The smaller of these is the polar arc angle θ Ｓ１The larger one is the polar arc angle θ Ｌ１ When this is done, θ Ｓ１ ≦84° and 36°≦θ Ｌ１ Also, θ ２１ and θ ２２ The smaller of these is the polar arc angle θ Ｓ２ The larger one is the polar arc angle θ Ｌ２ When this is done, θ Ｓ２ ≦148° and 98.8°≦θ Ｌ２ Furthermore, θ ３１ and θ ３２ The smaller of these is the polar arc angle θ Ｓ３ The larger one is the polar arc angle θ Ｌ３ When this is done, θ Ｓ３ ≦164° and 150.2°≦θ Ｌ３ Therefore, in the rotating electric machine of this embodiment, low vibration and high efficiency can be achieved in the high output range, similarly to the first embodiment.

[0098] As shown in FIG. 18, in the rotating electric machine of this embodiment, the width of the permanent magnet 231 in the first layer in the direction perpendicular to the magnetization direction is W １ The width of the permanent magnet 232 inserted on the outer diameter side of the second layer magnet slot 242 of the second layer permanent magnet 232 divided into two is W ２１ and the width of the permanent magnet 232 inserted on the inner diameter side is W ２２ Furthermore, the width of the permanent magnet 233 inserted on the outer diameter side of the third layer magnet slot 243 of the third layer permanent magnet 233 divided into three is defined as W ３１ The widths of the two permanent magnets 232 inserted on the inner diameter side are W ３２ , W ３３ In the rotating electric machine of this embodiment, W ２１ +W ２２ <2 x W １ Katsu W ３１ +W ３２ +W ３３ <3×W １ I am satisfied with the above.

[0099] In a rotating electric machine configured in this manner, the widths of the permanent magnets in the second and third layers can be set taking into account the effects of magnetic saturation near the magnetic gap. As a result, the output of the rotating electric machine can be increased. Furthermore, in a rotating electric machine configured in this manner, the rotor can be easily assembled, reducing the manufacturing cost of the rotating electric machine.

[0100] In the rotating electric machine of this embodiment, the second-layer magnet slot 242 and the third-layer magnet slot 243 are bent at one point midway so that the V shape closes. These magnet slots may be bent at two or more points, as long as the aforementioned pole arc angle conditions are met. Furthermore, the permanent magnets may be divided into three or more pieces, as long as the aforementioned relationship between the widths of the permanent magnets is met.

[0101] Embodiment 4 Fig. 19 is an enlarged cross-sectional view of a rotor of a rotating electric machine according to Embodiment 4. Fig. 19 is an enlarged cross-sectional view of one magnetic pole portion of rotor 20. The rotating electric machine of this embodiment has eight poles, just like the rotating electric machine of Embodiment 1, and the number of teeth of the rotor core is 48.

[0102] 19 , rotor core 22 is formed with magnet slots 241, 242, and 243 arranged in a V-shape that opens from the center of rotation toward the outer diameter side, forming a three-layer structure in the radial direction. The magnet slots are through-holes that pass through rotor core 22 in the axial direction. These magnet slots are arranged in the order of first layer magnet slot 241, second layer magnet slot 242, and third layer magnet slot 243 from the outer diameter side to the inner diameter side.

[0103] The rotating electric machine of this embodiment satisfies the pole arc angle conditions, as in embodiment 1. Therefore, this rotating electric machine can also achieve low vibration and high efficiency in the high output range, as in embodiment 1.

[0104] Furthermore, in the rotating electric machine of this embodiment, the flux barrier areas, which are the portions at both ends of the magnet slots 241, 242, and 243 in each layer where no permanent magnets are inserted, are larger than in the rotating electric machine of embodiment 1.

[0105] In a rotating electric machine configured in this way, the concentration of magnetic flux near the q-axis between the magnetic poles can be alleviated, which makes it possible to increase the amount of effective magnetic flux and improve output, particularly in rotating electric machines with eight or more poles and a small circumferential area per pole, or in rotating electric machines with a small radial area of ​​the rotor core due to the placement of structures on the inner diameter side of the rotor.

[0106] Let us consider a case where a rotating electric machine with N layers of magnet slots has a large flux barrier area, where no permanent magnets are inserted at both ends of each magnet slot, where N is an integer equal to or greater than 3 and k is an integer equal to or greater than 1 and N. In this rotating electric machine, the electrical angle formed by a pair of lines connecting the center of rotation and the point of the permanent magnet in the kth layer closest to the outer diameter bridge of the kth layer is defined as θ. ｋ１ The electrical angle formed by a pair of straight lines connecting the center of rotation and the inner point of the V-shape of the side of the kth layer magnet slot that is in contact with the kth layer outer diameter bridge is θ ｋ２ In this case, θ ｋ１ >θ ｋ２ If the above relationship is satisfied, the concentration of magnetic flux near the q-axis between the poles can be alleviated.

[0107] Embodiment 5. Figure 20 is a cross-sectional view of a rotating electric machine according to embodiment 5. Figure 20 is a cross-sectional view in a direction perpendicular to the shaft, which is the axis of rotation. The rotating electric machine 1 of this embodiment includes a cylindrical stator 10 and a columnar rotor 20 rotatably provided on the inner diameter side of the stator 10 via a magnetic gap.

[0108] The stator 10 has a stator core 11 formed by laminating core sheets of magnetic material such as electromagnetic steel sheets, and an armature winding housed in the stator core 11. The stator core 11 has a cylindrical core back 12 and teeth 13 protruding radially inward from the core back 12. Ninety-six teeth 13 are arranged at equal intervals in the circumferential direction.

[0109] The rotor 20 has a shaft 21 which is a rotation axis, a rotor core 22 through which the shaft 21 passes, and permanent magnets 23 which are arranged circumferentially inside the rotor core 22. The rotor 20 is composed of eight magnetic poles, i.e., four pairs of magnetic poles.

[0110] The rotating electric machine of this embodiment has an 8-pole, 96-slot configuration. The configuration of rotor 20 is the same as that of the rotor of the rotating electric machine of embodiment 1. In this rotating electric machine, the number of teeth per pole is 12. In contrast, the number of teeth per pole in the 8-pole, 48-slot rotating electric machine shown in embodiment 1 is 6.

[0111] In the rotating electric machine of this embodiment, the magnetic flux of paths 1 to 3 shown in FIG. 6 of embodiment 1 faces two teeth each via a magnetic gap. In contrast, in an 8-pole, 48-slot rotating electric machine, the magnetic flux of paths 1 to 3 faces one tooth each. In the rotating electric machine of this embodiment, the number of teeth facing the magnetic flux of paths 1 to 3 increases, making it easier for the magnetic flux of paths 1 to 3 to flow into the opposing teeth without interfering with each other. As a result, in the rotating electric machine of this embodiment, leakage magnetic flux is reduced and output can be improved.

[0112] Sixth Embodiment Fig. 21 is a cross-sectional view of a rotating electric machine according to a sixth embodiment. Fig. 21 is a cross-sectional view in a direction perpendicular to the shaft, which is the axis of rotation. The rotating electric machine 1 of this embodiment includes a cylindrical stator 10 and a columnar rotor 20 rotatably provided on the inner diameter side of the stator 10 via a magnetic gap.

[0113] The stator 10 has a stator core 11 formed by laminating core sheets of magnetic material such as electromagnetic steel sheets, and an armature winding housed in the stator core 11. The stator core 11 has a cylindrical core back 12 and teeth 13 protruding radially inward from the core back 12. There are 48 teeth 13 arranged at equal intervals in the circumferential direction.

[0114] The rotor 20 has a shaft 21 which is a rotation axis, a rotor core 22 through which the shaft 21 passes, and permanent magnets 23 which are arranged circumferentially inside the rotor core 22. The rotor 20 is composed of eight magnetic poles, i.e., four pairs of magnetic poles.

[0115] In the rotating electric machine of this embodiment, each magnetic pole of the rotor 20 is composed of four layers of permanent magnets. Although details are omitted, the rotating electric machine of this embodiment satisfies equations (7), (8), and (9) in the first embodiment when k=4. Therefore, this rotating electric machine can also achieve low vibration and high efficiency in the high output range, just like the first embodiment.

[0116] Furthermore, since the rotating electric machine of this embodiment has one magnetic pole made up of four layers of permanent magnets, the magnetic flux waveform of the magnetic gap can be made closer to a sine wave than a rotating electric machine having one magnetic pole made up of three layers of permanent magnets.

[0117] In the rotating electric machines of the first to sixth embodiments, the rotor has been described as having eight poles. However, the rotor may have any other number of poles as long as one pole is formed by a multi-layer permanent magnet. The armature winding of the stator may be either distributed winding or concentrated winding.

[0118] Furthermore, in the rotating electric machines of Embodiments 1 to 6, a central bridge is provided at the magnetic pole center of the magnet slots in each layer to increase the strength of the rotor core against centrifugal force, and the magnet slots in each layer are configured as a pair of slots symmetrical with respect to the d axis. The magnet slot in each layer may also be configured as a single slot without a central bridge. Furthermore, even in the case of magnet slots with a central bridge, the central bridge does not necessarily have to be located at the magnetic pole center.

[0119] Furthermore, the rotating electric machines of the first to sixth embodiments use permanent magnets with a rectangular parallelepiped shape. The shape of the permanent magnet is not limited to a rectangular parallelepiped shape. For example, in the cross-sectional view of the rotor shown in FIG. 2, the cross-sectional shape of the permanent magnet may be curved. Even if the cross-sectional shape of the permanent magnet is curved, the same effects as those of the first embodiment can be obtained by satisfying the conditions described in the first embodiment.

[0120] Although various exemplary embodiments are described in this application, the various features, aspects, and functions described in one or more embodiments are not limited to the application of a particular embodiment, but may be applied to the embodiments alone or in various combinations. Therefore, countless modifications not illustrated are contemplated within the scope of the technology disclosed in this application. For example, this includes cases where at least one component is modified, added, or omitted, or where at least one component is extracted and combined with components of another embodiment.

[0121] 1 Rotating electric machine, 10 Stator, 11 Stator core, 12 Core back, 13 Teeth, 20 Rotor, 21 Shaft, 22 Rotor core, 23, 231, 232, 233 Permanent magnet, 221, 222, 223 Central bridge, 241, 242, 243 Magnet slot, 251, 252, 253 Outer diameter bridge.

Claims

1. A rotating electric machine comprising: a stator having a stator core with a plurality of teeth arranged at equal intervals on the inner diameter side of a cylindrical core back and an armature winding wound around the teeth; and a cylindrical rotor arranged on the inner diameter side of the stator via a magnetic gap and rotatably arranged around a rotation axis, When N is an integer of 3 or more, in a cross section perpendicular to the rotation axis, N layers of magnet slots that open from the center of rotation toward the outer diameter side are formed in the rotor from the outer diameter side to the inner diameter side, and there are outer diameter bridges between the magnet slots and the outer peripheral surface of the rotor, and a permanent magnet is inserted into each of the N layers of magnet slots to form one pole, When the electrical angle of one pole is 180°, the smaller of the electrical angle formed by a pair of straight lines connecting the point of contact with the outer diameter bridge of the magnet slot of the first layer and the center of rotation, and the electrical angle formed by a pair of straight lines connecting the point of contact with the outer diameter bridge of the permanent magnet inserted into the magnet slot of the first layer and the center of rotation, is defined as a pole arc angle θ Ｓ１ The larger electrical angle is the pole arc angle θ Ｌ１ When 40°≦θ Ｌ１ and θ Ｓ１ ≦80°。

2. When k is an integer of 2 or more and N or less, the smaller of the electrical angle formed by a pair of straight lines connecting the rotation center and a point of contact with the outer diameter bridge of the magnet slot of the kth layer and the electrical angle formed by a pair of straight lines connecting the rotation center and a point of contact with the outer diameter bridge of the permanent magnet inserted into the magnet slot of the kth layer is defined as a pole arc angle θ Ｓｋ The larger electrical angle is the pole arc angle θ Ｌｋ The maximum electrical angle of the pole arc angle of the first layer is θ １ｍａｘ = 80°, and the maximum electrical angle of the pole arc angle of the kth layer is θ ｋｍａｘ When this is done, θ Ｌｋ satisfies the following equation (1), and θ Ｓｋ satisfies the following equation (2), and θ ｋｍａｘ 2. The rotating electric machine according to claim 1, wherein the following formula (3) is satisfied: [Equation 1] [Equation 2] [Equation 3]

3. The pole arc angle θ is defined as the smaller of the electrical angle formed by a pair of straight lines connecting the center of rotation and a point of contact with the outer diameter bridge of the magnet slot of the second layer, and the electrical angle formed by a pair of straight lines connecting the center of rotation and a point of contact with the outer diameter bridge of the permanent magnet inserted into the magnet slot of the second layer. Ｓ２ The larger electrical angle is the pole arc angle θ Ｌ２ When this is the case, 102.8°≦θ Ｌ２ and θ Ｓ２ 2. The rotating electric machine according to claim 1, wherein the angle satisfies the condition ≦144°.

4. The pole arc angle θ is defined as the smaller of the electrical angle formed by a pair of straight lines connecting the center of rotation and a point of contact with the outer diameter bridge of the magnet slot of the third layer, and the electrical angle formed by a pair of straight lines connecting the center of rotation and a point of contact with the outer diameter bridge of the permanent magnet inserted into the magnet slot of the third layer. Ｓ３ The larger electrical angle is the pole arc angle θ Ｌ３ When this is the case, 154.2°≦θ Ｌ３ and θ Ｓ３ 2. The rotating electric machine according to claim 1, wherein the angle satisfies the condition ≦160°.

5. A rotating electric machine comprising: a stator having a stator core with a plurality of teeth arranged at equal intervals on the inner diameter side of a cylindrical core back and an armature winding wound around the teeth; and a cylindrical rotor arranged on the inner diameter side of the stator via a magnetic gap and rotatably arranged around a rotation axis, When N is an integer of 3 or more, in a cross section perpendicular to the rotation axis, N layers of magnet slots that open from the center of rotation toward the outer diameter side are formed in the rotor from the outer diameter side to the inner diameter side, and there are outer diameter bridges between the magnet slots and the outer peripheral surface of the rotor, and a permanent magnet is inserted into each of the N layers of magnet slots to form one pole, When the electrical angle of one pole is 180°, the smaller of the electrical angle formed by a pair of straight lines connecting the point of contact with the outer diameter bridge of the magnet slot of the first layer and the center of rotation, and the electrical angle formed by a pair of straight lines connecting the point of contact with the outer diameter bridge of the permanent magnet inserted into the magnet slot of the first layer and the center of rotation, is defined as a pole arc angle θ Ｓ１ The larger electrical angle is the pole arc angle θ Ｌ１ When the number of poles of the rotor is p, p is an integer between 2 and 12, and (40-p / 2)°≦θ Ｌ１ and θ Ｓ１ ≦(80+p / 2)°.

6. When k is an integer of 2 or more and N or less, the smaller of the electrical angle formed by a pair of straight lines connecting the rotation center and a point of contact with the outer diameter bridge of the magnet slot of the kth layer and the electrical angle formed by a pair of straight lines connecting the rotation center and a point of contact with the outer diameter bridge of the permanent magnet inserted into the magnet slot of the kth layer is defined as a pole arc angle θ Ｓｋ The larger electrical angle is the pole arc angle θ Ｌｋ The maximum electrical angle of the pole arc angle of the first layer is θ １ｍａｘ = 80°, and the maximum electrical angle of the pole arc angle of the kth layer is θ ｋｍａｘ When this is done, θ Ｌｋ satisfies the following equation (4), and θ Ｓｋ satisfies the following equation (5), and θ ｋｍａｘ 6. The rotating electric machine according to claim 5, wherein the following formula (6) is satisfied: [Equation 4] [Equation 5] [Equation 6]

7. The pole arc angle θ is defined as the smaller of the electrical angle formed by a pair of straight lines connecting the center of rotation and a point of contact with the outer diameter bridge of the magnet slot of the second layer, and the electrical angle formed by a pair of straight lines connecting the center of rotation and a point of contact with the outer diameter bridge of the permanent magnet inserted into the magnet slot of the second layer. Ｓ２ The larger electrical angle is the pole arc angle θ Ｌ２ When this is the case, (102.8-p / 2)°≦θ Ｌ２ and θ Ｓ２ 6. The rotating electric machine according to claim 5, wherein the angle satisfies the following condition: ≦(144+p / 2)°.

8. The pole arc angle θ is defined as the smaller of the electrical angle formed by a pair of straight lines connecting the center of rotation and a point of contact with the outer diameter bridge of the magnet slot of the third layer, and the electrical angle formed by a pair of straight lines connecting the center of rotation and a point of contact with the outer diameter bridge of the permanent magnet inserted into the magnet slot of the third layer. Ｓ３ The larger electrical angle is the pole arc angle θ Ｌ３ When this is the case, (154.2-p / 2)°≦θ Ｌ３ and θ Ｓ３ 6. The rotating electric machine according to claim 5, wherein the angle satisfies the condition ≦(160+p / 2)°.

9. 9. The rotating electric machine according to claim 1, wherein when N=3 and M is an integer equal to or greater than 2, the number of teeth of the stator is the product of the number of poles of the rotor and 3 times M.

10. In the cross section perpendicular to the rotation axis, k is an integer between 2 and N, and the length of the permanent magnet in the direction perpendicular to the magnetization direction of the permanent magnet in the first layer is W １ and the length of the permanent magnet in the direction perpendicular to the magnetization direction of the permanent magnet in the kth layer is W ｋ When W ｋ <k × W １ 9. The rotating electric machine according to claim 1, wherein:

11. 11. The rotating electric machine according to claim 10, wherein, in a cross section perpendicular to the rotation axis, when m is an integer greater than or equal to 2 and less than or equal to (N-1), the shortest distance between the permanent magnet in the (m-1)th layer and the permanent magnet in the mth layer is greater than the shortest distance between the permanent magnet in the mth layer and the permanent magnet in the (m+1)th layer.

12. 12. The rotating electric machine according to claim 11, wherein the permanent magnets in the second or subsequent layers are divided in a direction perpendicular to the magnetization direction of the permanent magnets.

13. 13. The rotating electric machine according to claim 12, wherein the divided permanent magnets in the second or subsequent layers are arranged symmetrically with respect to the pole center.

14. 11. The rotating electric machine according to claim 10, wherein the radial width of the outer bridge in the first layer is smaller than the radial width of the outer bridge in the other layers.

15. 15. The rotating electric machine according to claim 14, wherein, when k is an integer greater than or equal to 2 and less than or equal to N, the radial width of the outer diameter bridge in the (k-1)th layer is smaller than the radial width of the outer diameter bridge in the kth layer.

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