CN105449967B - Composite poles formula built-in radial V-type permagnetic synchronous motor - Google Patents

Composite poles formula built-in radial V-type permagnetic synchronous motor Download PDF

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Publication number
CN105449967B
CN105449967B CN201510968846.9A CN201510968846A CN105449967B CN 105449967 B CN105449967 B CN 105449967B CN 201510968846 A CN201510968846 A CN 201510968846A CN 105449967 B CN105449967 B CN 105449967B
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mrow
mfrac
msub
magnetic pole
permanent magnet
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CN105449967A (en
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郑萍
程路明
于斌
周承豫
陈敬东
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Harbin Institute Of Technology Shenyang Intelligent Industrial Technology Co ltd
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Harbin Institute of Technology
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    • HELECTRICITY
    • H02GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02KDYNAMO-ELECTRIC MACHINES
    • H02K21/00Synchronous motors having permanent magnets; Synchronous generators having permanent magnets
    • H02K21/12Synchronous motors having permanent magnets; Synchronous generators having permanent magnets with stationary armatures and rotating magnets
    • H02K21/14Synchronous motors having permanent magnets; Synchronous generators having permanent magnets with stationary armatures and rotating magnets with magnets rotating within the armatures
    • H02K21/145Synchronous motors having permanent magnets; Synchronous generators having permanent magnets with stationary armatures and rotating magnets with magnets rotating within the armatures having an annular armature coil
    • HELECTRICITY
    • H02GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02KDYNAMO-ELECTRIC MACHINES
    • H02K1/00Details of the magnetic circuit
    • H02K1/06Details of the magnetic circuit characterised by the shape, form or construction
    • H02K1/22Rotating parts of the magnetic circuit
    • H02K1/27Rotor cores with permanent magnets
    • H02K1/2706Inner rotors
    • H02K1/272Inner rotors the magnetisation axis of the magnets being perpendicular to the rotor axis
    • H02K1/2726Inner rotors the magnetisation axis of the magnets being perpendicular to the rotor axis the rotor consisting of a single magnet or two or more axially juxtaposed single magnets
    • H02K1/2733Annular magnets

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  • Engineering & Computer Science (AREA)
  • Power Engineering (AREA)
  • Permanent Field Magnets Of Synchronous Machinery (AREA)

Abstract

Composite poles formula built-in radial V-type permagnetic synchronous motor, belongs to magneto field, and the present invention is that the rare earth permanent-magnet synchronization motor air-gap field for solving the problems, such as sine wave drive has harmonic wave and local irreversible demagnetization easily occurs.The present invention includes rotor and stator, and rotor magnetic pole is one or more layers embedded V-type magnet structure;Rotor magnetic pole includes two rare earth permanent magnet magnetic poles and two ferrite permanent-magnet magnetic poles, two rare earth permanent magnet magnetic poles and two ferrite permanent-magnet magnetic poles are that 1 rare earth permanent magnet magnetic pole and 1 ferrite permanent-magnet magnetic pole are embedded in strip, V-type permanent magnet every ramped aisle of mounting groove;Two magnetic poles in same ramped aisle are the parallel magnetization with the ramped aisle vertical direction, and magnetizing direction is identical;Magnetizing direction is simultaneously to inside V-shape or simultaneously to outside V-shape.The permagnetic synchronous motor of the structure causes the reduction of Gas-gap Magnetic Field Resonance Wave content, improves electric efficiency, while ferrite permanent-magnet materials are cheap, reduces cost.

Description

Composite poles formula built-in radial V-type permagnetic synchronous motor
Technical field
The present invention relates to a kind of rotor structure of composite poles formula, belong to magneto field.
Background technology
As increasingly serious the problems such as environment and energy crisis, energy-efficient electrical equipment turns into development trend, by This has greatly facilitated high power density, the development of efficient rare earth permanent-magnet synchronization motor.But the price of rare earth permanent-magnetic material Remain high always, and rare-earth permanent-magnet electric machine is influenceed larger by rare earth permanent-magnetic material price fluctuation, therefore rare-earth permanent-magnet electric machine Cost is also affected therewith, and higher cost has greatly reduced the development space of rare earth permanent-magnet synchronization motor.And rare earth material Material belongs to rare earth material consumption excessive in non-renewable resources, electric system can also damage to environment.Therefore, ensureing On the premise of motor performance, the energy-saving efficient motor system of the few rare earth material of research, is even more the need for being not only energy strategy In the consideration of environmental protection.
For the rare earth permanent-magnet synchronization motor of sine wave drive, the air-gap field distribution that permanent-magnet material is produced is always containing humorous Wave component, these harmonic fields can cause extra iron loss and torque ripple;And rare earth permanent-magnetic material easily occurs in use Local irreversible demagnetization, especially in the case of a high temperature, permanent-magnet material irreversible demagnetization will cause the decline of motor performance.
The content of the invention
The invention aims to solve the rare earth permanent-magnet synchronization motor air-gap field of sine wave drive to there is harmonic wave and easy There is local irreversible demagnetization problem, especially in the case of a high temperature, permanent-magnet material irreversible demagnetization will cause motor performance The problem of decline, there is provided a kind of composite poles formula built-in radial V-type permagnetic synchronous motor.Before motor output performance is not influenceed Put, both reduced rare-earth permanent-magnet electric machine cost, rare-earth permanent-magnet electric machine air-gap field sine degree, solution high temperature demagnetization can be improved again and is asked Topic is with regard to great realistic meaning.
The present invention includes two technical schemes:
First technical scheme is individual layer field structure:The composite poles formula built-in radial V-type permagnetic synchronous motor, bag Rotor and stator are included, rotor is arranged on the inside of stator, radial air gap is left between rotor and stator, stator includes stator core And stator winding, stator winding is set in the internal stator groove of stator core;Rotor includes multiple rotor magnetic poles and rotor core, Rotor core along the circumferential direction uniform one layer of V-type permanent magnet mounting groove, V-type permanent magnet mounting groove is axially extended, and V-type opening Towards stator, a rotor magnetic pole is set in each V-type permanent magnet mounting groove;
Rotor magnetic pole includes two rare earth permanent magnet magnetic poles and two ferrite permanent-magnet magnetic poles, two rare earth permanent magnet magnetic poles and two Individual ferrite permanent-magnet magnetic pole is that 1 rare earth permanent magnet magnetic pole is embedded in strip, V-type permanent magnet every ramped aisle of mounting groove With 1 ferrite permanent-magnet magnetic pole;
Rare earth permanent magnet magnetic pole and ferrite permanent-magnet magnetic pole in same ramped aisle are and the ramped aisle vertical direction Parallel magnetization, and magnetizing direction is identical;Two rare earth permanent magnet magnetic poles in two ramped aisles of V-type permanent magnet mounting groove fill Magnetic direction is simultaneously to inside V-shape or simultaneously to outside V-shape.
Second technical scheme is multilayer magnetic pole structure:The composite poles formula built-in radial V-type permagnetic synchronous motor, bag Rotor and stator are included, rotor is arranged on the inside of stator, radial air gap is left between rotor and stator, stator includes stator core And stator winding, stator winding is set in the internal stator groove of stator core;Rotor includes multiple rotor magnetic poles and rotor core, Rotor core along the circumferential direction uniform n-layer V-type permanent magnet mounting groove, V-type permanent magnet mounting groove is axially extended, and each V-type is forever The V-type opening of magnet mounting groove is towards stator, and the n V-type permanent magnet mounting groove on same Radius is parallel to each other, each V One rotor magnetic pole is set in type permanent magnet mounting groove;N is the natural number more than or equal to 2;
Rotor magnetic pole includes two rare earth permanent magnet magnetic poles and two ferrite permanent-magnet magnetic poles, two rare earth permanent magnet magnetic poles and two Individual ferrite permanent-magnet magnetic pole is that 1 rare earth permanent magnet magnetic pole is embedded in strip, V-type permanent magnet every ramped aisle of mounting groove With 1 ferrite permanent-magnet magnetic pole;
Rare earth permanent magnet magnetic pole and ferrite permanent-magnet magnetic pole in same ramped aisle are and the ramped aisle vertical direction Parallel magnetization, and magnetizing direction is identical;Two rare earth permanent magnet magnetic poles in two ramped aisles of V-type permanent magnet mounting groove fill Magnetic direction is simultaneously to inside V-shape or simultaneously to outside V-shape;
Magnetizing direction with n rotor magnetic pole on Radius is consistent.
Advantages of the present invention:On the basis of conventional internal radial direction V-type rare earth permanent-magnet synchronization motor, ferrite permanent-magnet material is used Material replaces a part of rare earth permanent-magnetic material, and Ferrite Material is positioned over into rare earth permanent-magnetic material both sides.Because Ferrite Material is surplus Magnetic is less than rare earth permanent-magnetic material remanent magnetism, by combination air gap magnetic density waveform can be made to be more nearly sine wave, reduces air-gap field Harmonic content, so as to reduce stator iron loss and torque ripple caused by magnetic field harmonics.In addition, ferrite permanent-magnet materials Anti- demagnetization capability is better than rare earth permanent-magnetic material, and the anti-demagnetization capability of ferrite permanent-magnet materials is raised and strengthened with temperature, by iron oxygen Body, which is positioned over rare earth material both sides, can substantially reduce the local demagnetization risk of script rare earth permanent-magnetic material, improve motor operation reliable Property.The composite poles formula magneto replaces a part of rare earth permanent-magnetic material, drop using ferrite permanent-magnet materials with low cost Low cost, while making efficiency and operational reliability increase.
Brief description of the drawings
Fig. 1 is a kind of conventional internal radial direction V-type rare earth permanent-magnet synchronization motor structural representation, individual layer field structure;
Fig. 2 is a kind of conventional internal radial direction V-type rare earth permanent-magnet synchronization motor structural representation, double-deck field structure;
Fig. 3 is the structural representation of composite poles formula built-in radial V-type permagnetic synchronous motor described in embodiment one, individual layer Field structure;
Fig. 4 is the structural representation of composite poles formula built-in radial V-type permagnetic synchronous motor described in embodiment two, double-deck Field structure;
Fig. 5 is the concrete structure schematic diagram of the knockdown rotor magnetic pole of motor of the present invention;
Fig. 6 is the composite poles formula built-in radial V-type permagnetic synchronous motor and traditional built-in radial V-type rare earth of the present invention The air gap magnetic density waveform comparison diagram of permagnetic synchronous motor.
Embodiment
Embodiment one:Illustrate present embodiment, combination described in present embodiment with reference to Fig. 3, Fig. 5 and Fig. 6 Magnetic pole type built-in radial V-type permagnetic synchronous motor, including rotor and stator, rotor are arranged on the inside of stator, rotor and stator Between leave radial air gap, stator includes setting stator in stator core 1 and stator winding 2, the internal stator groove of stator core 1 Winding 2;Rotor includes multiple rotor magnetic poles 3 and rotor core 4, and along the circumferential direction uniform one layer of V-type permanent magnet is pacified for rotor core 4 Tankage 3-3, V-type permanent magnet mounting groove 3-3 is axially extended, and V-type opening is towards stator, each V-type permanent magnet mounting groove 3-3 One rotor magnetic pole 3 of interior setting;
Rotor magnetic pole 3 includes two rare earth permanent magnet magnetic pole 3-1 and two ferrite permanent-magnet magnetic pole 3-2, two rare earth permanent magnets Magnetic pole 3-1 and two ferrite permanent-magnet magnetic pole 3-2 are embedding in strip, V-type permanent magnet mounting groove every ramped aisle of 3-3 Enter 1 rare earth permanent magnet magnetic pole 3-1 and 1 ferrite permanent-magnet magnetic pole 3-2;
Rare earth permanent magnet magnetic pole 3-1 and ferrite permanent-magnet magnetic pole 3-2 in same ramped aisle are to be hung down with the ramped aisle Nogata to parallel magnetization, and magnetizing direction is identical;Two rare earths in V-type permanent magnet mounting groove two ramped aisles of 3-3 are forever Magnetic magnetic pole 3-1 magnetizing direction is simultaneously to inside V-shape or simultaneously to outside V-shape.
In one ramped aisle, length of the rare earth permanent magnet magnetic pole 3-1 along slope direction is a/2, ferrite permanent-magnet magnetic pole 3-2 edges The length in slope direction is b/2, and the two meets following condition:
In formula:C is the pole span of rotor magnetic pole 3;
D is V-type permanent magnet mounting groove 3-3 two ramped aisle angles;
Br2For rare earth permanent magnet magnetic pole 3-1 residual flux densities at the working temperature;Br1It is that ferrite permanent-magnet magnetic pole 3-2 is working At a temperature of residual flux density;And meet Br2>Br1
Rational proportion is carried out to rare earth permanent magnet magnetic pole 3-1 and ferrite permanent-magnet magnetic pole 3-2 size by above-mentioned formula, makes it The best air-gap field waveform of sine degree is produced, so as to advantageously reduce iron loss and torque ripple.
The anti-demagnetization capabilities of ferrite permanent-magnet magnetic pole 3-2 for being positioned over rare earth permanent magnet magnetic pole 3-1 both sides are stronger, and its coercivity With positive temperature coefficient, anti-demagnetization capability can further be strengthened during high temperature, and rare earth permanent-magnetic material is high when can improve practical application Warm easily demagnetization problem.
The overall width and thickness of pole parts 3 described in present embodiment are identical with the rare earth permanent magnet magnetic pole in Fig. 1;By such as Fig. 6 understands that composite poles formula built-in radial V-type PMSM Air Gap Flux irregularity of wave form proposed by the present invention substantially becomes It is small, but the close amplitude of its magnetic also because introduce the less Ferrite Material of remanent magnetism and diminish therewith, for ensure motor fan-out capability with Built-in radial V-type rare earth permanent-magnet synchronization motor shown in Fig. 1 is consistent, and adds the axial length of composite poles motor, but Composite poles formula motor cost is still lower than pure rare earth magneto.It will be appreciated from fig. 6 that built in composite poles formula proposed by the present invention The air gap magnetic density waveform of radial direction V-type permagnetic synchronous motor is more sinusoidal than conventional internal V-type permagnetic synchronous motor, so as to reduce Stator iron loss and torque ripple.The risk in addition, the strong anti-demagnetization capability of Ferrite Material demagnetizes when reducing motor operation, is improved The reliability of motor.
Embodiment two:Illustrate present embodiment, composite poles described in present embodiment with reference to Fig. 4 to Fig. 6 Formula built-in radial V-type permagnetic synchronous motor, including rotor and stator, rotor is arranged on the inside of stator, between rotor and stator Radial air gap is left, stator includes setting stator winding in stator core 1 and stator winding 2, the internal stator groove of stator core 1 2;Rotor includes multiple rotor magnetic poles 3 and rotor core 4, the along the circumferential direction uniform n-layer V-type permanent magnet mounting groove of rotor core 4 3-3, V-type permanent magnet mounting groove 3-3 is axially extended, and each V-type permanent magnet mounting groove 3-3 V-type opening is in towards stator It is parallel to each other with n V-type permanent magnet mounting groove 3-3 on Radius, sets one to turn in each V-type permanent magnet mounting groove 3-3 Sub- magnetic pole 3;N is the natural number more than or equal to 2;
Rotor magnetic pole 3 includes two rare earth permanent magnet magnetic pole 3-1 and two ferrite permanent-magnet magnetic pole 3-2, two rare earth permanent magnets Magnetic pole 3-1 and two ferrite permanent-magnet magnetic pole 3-2 are embedding in strip, V-type permanent magnet mounting groove every ramped aisle of 3-3 Enter 1 rare earth permanent magnet magnetic pole 3-1 and 1 ferrite permanent-magnet magnetic pole 3-2;
Rare earth permanent magnet magnetic pole 3-1 and ferrite permanent-magnet magnetic pole 3-2 in same ramped aisle are to be hung down with the ramped aisle Nogata to parallel magnetization, and magnetizing direction is identical;Two rare earths in V-type permanent magnet mounting groove two ramped aisles of 3-3 are forever Magnetic magnetic pole 3-1 magnetizing direction is simultaneously to inside V-shape or simultaneously to outside V-shape;
Magnetizing direction with the n rotor magnetic pole 3 on Radius is consistent.
In any one layer of a ramped aisle, length of the rare earth permanent magnet magnetic pole (3-1) along slope direction is ai/ 2, i=1, 2,....,n;, length of the ferrite permanent-magnet magnetic pole (3-2) along slope direction is bi/ 2, the two meets following condition:
In formula:C is the pole span of rotor magnetic pole (3);
D is two ramped aisle angles of V-type permanent magnet mounting groove (3-3);
Br2For rare earth permanent magnet magnetic pole (3-1) residual flux density at the working temperature;Br1Exist for ferrite permanent-magnet magnetic pole (3-2) Residual flux density under operating temperature;And meet Br2>Br1
In each Rotating fields, rare earth permanent magnet magnetic pole 3-1 is identical with ferrite permanent-magnet magnetic pole 3-2 size proportioning.
Rational proportion is carried out to rare earth permanent magnet magnetic pole 3-1 and ferrite permanent-magnet magnetic pole 3-2 size by above-mentioned formula, makes it The best air-gap field waveform of sine degree is produced, so as to advantageously reduce iron loss and torque ripple.
The anti-demagnetization capabilities of ferrite permanent-magnet magnetic pole 3-2 for being positioned over rare earth permanent magnet magnetic pole 3-1 both sides are stronger, and its coercivity With positive temperature coefficient, anti-demagnetization capability can further be strengthened during high temperature, and rare earth permanent-magnetic material is high when can improve practical application Warm easily demagnetization problem.
The overall width and thickness of pole parts 3 described in present embodiment are identical with the rare earth permanent magnet magnetic pole in Fig. 2;By such as Fig. 6 understands that composite poles formula built-in radial V-type PMSM Air Gap Flux irregularity of wave form proposed by the present invention substantially becomes It is small, but the close amplitude of its magnetic also because introduce the less Ferrite Material of remanent magnetism and diminish therewith, for ensure motor fan-out capability with Built-in radial V-type rare earth permanent-magnet synchronization motor shown in Fig. 2 is consistent, and adds the axial length of composite poles motor, but Composite poles formula motor cost is still lower than pure rare earth magneto.It will be appreciated from fig. 6 that built in composite poles formula proposed by the present invention The air gap magnetic density waveform of radial direction V-type permagnetic synchronous motor is more sinusoidal than conventional internal V-type permagnetic synchronous motor, so as to reduce Stator iron loss and torque ripple.The risk in addition, the strong anti-demagnetization capability of Ferrite Material demagnetizes when reducing motor operation, is improved The reliability of motor.

Claims (2)

1. composite poles formula built-in radial V-type permagnetic synchronous motor, including rotor and stator, rotor are arranged on the inside of stator, Radial air gap is left between rotor and stator, stator includes stator core (1) and stator winding (2), the inside of stator core (1) Stator winding (2) is set in stator slot;Rotor includes multiple rotor magnetic poles (3) and rotor core (4), and rotor core (4) is along circle The uniform one layer of V-type permanent magnet mounting groove (3-3) of circumferential direction, V-type permanent magnet mounting groove (3-3) is axially extended, and V-type opening surface To stator, a rotor magnetic pole (3) is set in each V-type permanent magnet mounting groove (3-3);
Characterized in that, rotor magnetic pole (3) includes two rare earth permanent magnet magnetic poles (3-1) and two ferrite permanent-magnet magnetic poles (3-2), Two rare earth permanent magnet magnetic poles (3-1) and two ferrite permanent-magnet magnetic poles (3-2) are strip, V-type permanent magnet mounting groove (3-3) 1 rare earth permanent magnet magnetic pole (3-1) and 1 ferrite permanent-magnet magnetic pole (3-2) are embedded in every ramped aisle;
Rare earth permanent magnet magnetic pole (3-1) and ferrite permanent-magnet magnetic pole (3-2) in same ramped aisle are to be hung down with the ramped aisle Nogata to parallel magnetization, and magnetizing direction is identical;Two rare earths in two ramped aisles of V-type permanent magnet mounting groove (3-3) The magnetizing direction of permanent magnetism magnetic pole (3-1) is simultaneously to inside V-shape or simultaneously to outside V-shape;
In one ramped aisle, length of the rare earth permanent magnet magnetic pole (3-1) along slope direction is a/2, ferrite permanent-magnet magnetic pole (3-2) edge The length in slope direction is b/2, and the two meets following condition:
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In formula:C is the pole span of rotor magnetic pole (3);
D is two ramped aisle angles of V-type permanent magnet mounting groove (3-3);
Br2For rare earth permanent magnet magnetic pole (3-1) residual flux density at the working temperature;Br1It is that ferrite permanent-magnet magnetic pole (3-2) is working At a temperature of residual flux density;And meet Br2>Br1
2. composite poles formula built-in radial V-type permagnetic synchronous motor, including rotor and stator, rotor are arranged on the inside of stator, Radial air gap is left between rotor and stator, stator includes stator core (1) and stator winding (2), the inside of stator core (1) Stator winding (2) is set in stator slot;Rotor includes multiple rotor magnetic poles (3) and rotor core (4), and rotor core (4) is along circle The uniform n-layer V-type permanent magnet mounting groove (3-3) of circumferential direction, V-type permanent magnet mounting groove (3-3) is axially extended, each V-type permanent magnetism The V-type opening of body mounting groove (3-3) is towards stator, and the n V-type permanent magnet mounting groove (3-3) on same Radius is mutually flat OK, a rotor magnetic pole (3) is set in each V-type permanent magnet mounting groove (3-3);N is the natural number more than or equal to 2;
Characterized in that, rotor magnetic pole (3) includes two rare earth permanent magnet magnetic poles (3-1) and two ferrite permanent-magnet magnetic poles (3-2), Two rare earth permanent magnet magnetic poles (3-1) and two ferrite permanent-magnet magnetic poles (3-2) are strip, V-type permanent magnet mounting groove (3-3) 1 rare earth permanent magnet magnetic pole (3-1) and 1 ferrite permanent-magnet magnetic pole (3-2) are embedded in every ramped aisle;
Rare earth permanent magnet magnetic pole (3-1) and ferrite permanent-magnet magnetic pole (3-2) in same ramped aisle are to be hung down with the ramped aisle Nogata to parallel magnetization, and magnetizing direction is identical;Two rare earths in two ramped aisles of V-type permanent magnet mounting groove (3-3) The magnetizing direction of permanent magnetism magnetic pole (3-1) is simultaneously to inside V-shape or simultaneously to outside V-shape;
Magnetizing direction with the n rotor magnetic pole (3) on Radius is consistent;
In any one layer of a ramped aisle, length of the rare earth permanent magnet magnetic pole (3-1) along slope direction is ai/ 2, i=1, 2,....,n;, length of the ferrite permanent-magnet magnetic pole (3-2) along slope direction is bi/ 2, the two meets following condition:
<mrow> <mfrac> <mrow> <msqrt> <mrow> <mfrac> <mrow> <msub> <mi>a</mi> <mi>i</mi> </msub> <msup> <mrow> <mo>(</mo> <msub> <mi>Br</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msub> <mi>b</mi> <mi>i</mi> </msub> <msup> <mrow> <mo>(</mo> <msub> <mi>Br</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> <mi>c</mi> </mfrac> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mrow> <mo>(</mo> <mfrac> <mi>d</mi> <mn>2</mn> </mfrac> <mo>)</mo> </mrow> </mrow> </msqrt> <mo>-</mo> <mfrac> <mn>2</mn> <mi>&amp;pi;</mi> </mfrac> <mo>{</mo> <mn>2</mn> <mrow> <mo>(</mo> <msub> <mi>Br</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mrow> <mo>(</mo> <mfrac> <mrow> <msub> <mi>a</mi> <mi>i</mi> </msub> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mrow> <mo>(</mo> <mfrac> <mi>d</mi> <mn>2</mn> </mfrac> <mo>)</mo> </mrow> </mrow> <mrow> <mn>2</mn> <mi>c</mi> </mrow> </mfrac> <mi>&amp;pi;</mi> <mo>)</mo> </mrow> <mo>+</mo> <mn>2</mn> <mrow> <mo>(</mo> <msub> <mi>Br</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> <mo>&amp;lsqb;</mo> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mrow> <mo>(</mo> <mfrac> <mrow> <mo>(</mo> <msub> <mi>a</mi> <mi>i</mi> </msub> <mo>+</mo> <msub> <mi>b</mi> <mi>i</mi> </msub> <mo>)</mo> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mo>(</mo> <mfrac> <mi>d</mi> <mn>2</mn> </mfrac> <mo>)</mo> </mrow> <mrow> <mn>2</mn> <mi>c</mi> </mrow> </mfrac> <mi>&amp;pi;</mi> <mo>)</mo> </mrow> <mo>-</mo> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mrow> <mo>(</mo> <mfrac> <mrow> <msub> <mi>a</mi> <mi>i</mi> </msub> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mrow> <mo>(</mo> <mfrac> <mi>d</mi> <mn>2</mn> </mfrac> <mo>)</mo> </mrow> </mrow> <mrow> <mn>2</mn> <mi>c</mi> </mrow> </mfrac> <mi>&amp;pi;</mi> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> <mo>}</mo> </mrow> <mrow> <mfrac> <mn>2</mn> <mi>&amp;pi;</mi> </mfrac> <mo>{</mo> <mn>2</mn> <mrow> <mo>(</mo> <msub> <mi>Br</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mrow> <mo>(</mo> <mfrac> <mrow> <msub> <mi>a</mi> <mi>i</mi> </msub> <mi>sin</mi> <mrow> <mo>(</mo> <mfrac> <mi>d</mi> <mn>2</mn> </mfrac> <mo>)</mo> </mrow> </mrow> <mrow> <mn>2</mn> <mi>c</mi> </mrow> </mfrac> <mi>&amp;pi;</mi> <mo>)</mo> </mrow> <mo>+</mo> <mn>2</mn> <mrow> <mo>(</mo> <msub> <mi>Br</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> <mo>&amp;lsqb;</mo> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mrow> <mo>(</mo> <mfrac> <mrow> <mo>(</mo> <msub> <mi>a</mi> <mi>i</mi> </msub> <mo>+</mo> <msub> <mi>b</mi> <mi>i</mi> </msub> <mo>)</mo> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mo>(</mo> <mfrac> <mi>d</mi> <mn>2</mn> </mfrac> <mo>)</mo> </mrow> <mrow> <mn>2</mn> <mi>c</mi> </mrow> </mfrac> <mi>&amp;pi;</mi> <mo>)</mo> </mrow> <mo>-</mo> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mrow> <mo>(</mo> <mfrac> <mrow> <msub> <mi>a</mi> <mi>i</mi> </msub> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mrow> <mo>(</mo> <mfrac> <mi>d</mi> <mn>2</mn> </mfrac> <mo>)</mo> </mrow> </mrow> <mrow> <mn>2</mn> <mi>c</mi> </mrow> </mfrac> <mi>&amp;pi;</mi> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> <mo>}</mo> </mrow> </mfrac> <mo>&amp;le;</mo> <mn>2</mn> <mi>%</mi> </mrow>
In formula:C is the pole span of rotor magnetic pole (3);
D is two ramped aisle angles of V-type permanent magnet mounting groove (3-3);
Br2For rare earth permanent magnet magnetic pole (3-1) residual flux density at the working temperature;Br1It is that ferrite permanent-magnet magnetic pole (3-2) is working At a temperature of residual flux density;And meet Br2>Br1
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