CN105449967A - Combined magnetic pole built-in radial direction V type permanent magnet synchronous motor - Google Patents

Abstract

The combined magnetic pole type built-in radial V-shaped permanent magnet synchronous motor belongs to the field of permanent magnet motors. The invention solves the problems of harmonics and partial irreversible demagnetization in the air gap magnetic field of rare earth permanent magnet synchronous motors driven by sine waves. The present invention includes a rotor and a stator. The rotor poles have one or more layers of embedded V-shaped permanent magnet structures; the rotor poles include two rare earth permanent magnet poles and two ferrite permanent magnet poles, two rare earth permanent magnet poles and two permanent magnet poles. Each ferrite permanent magnet pole is strip-shaped, and each ramp channel of the V-shaped permanent magnet mounting groove is embedded with a rare earth permanent magnet pole and a ferrite permanent magnet pole; two magnetic poles in the same ramp channel Both are parallel magnetization perpendicular to the slope channel, and the magnetization direction is the same; the magnetization direction is simultaneously to the inside of the V-shape or to the outside of the V-shape. The permanent magnet synchronous motor with this structure reduces the harmonic content of the air gap magnetic field, improves the motor efficiency, and at the same time, the ferrite permanent magnet material is cheap, reducing the cost.

Description

Combined magnetic pole type built-in radial V-type permanent magnet synchronous motor

technical field

The invention relates to a combined magnetic pole type rotor structure, which belongs to the field of permanent magnet motors.

Background technique

With the increasingly serious problems of the environment and energy crisis, high-efficiency and energy-saving electrical equipment has become a development trend, which greatly promotes the development of high-power-density, high-efficiency rare earth permanent magnet synchronous motors. However, the price of rare earth permanent magnet materials has remained high, and rare earth permanent magnet motors are greatly affected by price fluctuations of rare earth permanent magnet materials, so the cost of rare earth permanent magnet motors is also affected. The development space of magnetic synchronous motor. Moreover, rare earth materials are non-renewable resources, and excessive use of rare earth materials in motor systems will also cause damage to the environment. Therefore, under the premise of ensuring the performance of the motor, it is not only the need of energy strategy, but also the consideration of environmental protection to study the high-efficiency and energy-saving motor system with less rare earth materials.

For rare earth permanent magnet synchronous motors driven by sine waves, the air gap magnetic field distribution generated by permanent magnet materials will always contain harmonic components, and these harmonic magnetic fields will cause additional iron loss and torque fluctuations; and rare earth permanent magnet materials in use It is prone to local irreversible demagnetization, especially at high temperature, irreversible demagnetization of permanent magnet materials will lead to a decline in motor performance.

Contents of the invention

The purpose of the present invention is to solve the problems of harmonics and partial irreversible demagnetization in the air-gap magnetic field of rare earth permanent magnet synchronous motors driven by sine waves, especially under high temperature conditions, the irreversible demagnetization of permanent magnet materials will lead to the decline of motor performance. Provided is a combined magnetic pole type built-in radial V-shaped permanent magnet synchronous motor. Under the premise of not affecting the output performance of the motor, it is of great practical significance to reduce the cost of rare earth permanent magnet motors, increase the sine degree of the air gap magnetic field of rare earth permanent magnet motors, and solve the problem of high temperature demagnetization.

The present invention comprises two technical schemes:

The first technical solution is a single-layer magnetic pole structure: the combined magnetic pole type built-in radial V-shaped permanent magnet synchronous motor includes a rotor and a stator, the rotor is arranged inside the stator, and a radial air gap is left between the rotor and the stator. The stator includes a stator core and a stator winding. The stator winding is arranged in the inner stator slot of the stator core; the rotor includes a plurality of rotor poles and a rotor core. The slots extend in the axial direction, and the V-shaped opening faces the stator, and a rotor pole is arranged in each V-shaped permanent magnet installation slot;

The rotor poles include two rare earth permanent magnet poles and two ferrite permanent magnet poles, the two rare earth permanent magnet poles and two ferrite permanent magnet poles are all long strips, and the V-shaped permanent magnet installation slots have a ramp channel Both are embedded with a rare earth permanent magnet pole and a ferrite permanent magnet pole;

The rare earth permanent magnet poles and ferrite permanent magnet poles in the same ramp channel are magnetized parallel to the vertical direction of the ramp channel, and the magnetization direction is the same; the two rare earth permanent magnet poles in the two ramp channels of the V-shaped permanent magnet installation groove The magnetization directions of the permanent magnet poles are simultaneously toward the inside of the V-shape or toward the outside of the V-shape.

The second technical solution is a multi-layer magnetic pole structure: the combined magnetic pole type built-in radial V-shaped permanent magnet synchronous motor includes a rotor and a stator, the rotor is arranged inside the stator, and a radial air gap is left between the rotor and the stator. The stator includes a stator core and a stator winding. The stator winding is arranged in the inner stator slot of the stator core; the rotor includes a plurality of rotor poles and a rotor core. The slots extend in the axial direction, the V-shaped opening of each V-shaped permanent magnet installation slot faces the stator, n V-shaped permanent magnet installation slots on the same radius are parallel to each other, and a rotor pole is set in each V-shaped permanent magnet installation slot ; n is a natural number greater than or equal to 2;

The rotor poles include two rare earth permanent magnet poles and two ferrite permanent magnet poles, the two rare earth permanent magnet poles and two ferrite permanent magnet poles are all long strips, and the V-shaped permanent magnet installation slots have a ramp channel Both are embedded with a rare earth permanent magnet pole and a ferrite permanent magnet pole;

The rare earth permanent magnet poles and ferrite permanent magnet poles in the same ramp channel are magnetized parallel to the vertical direction of the ramp channel, and the magnetization direction is the same; the two rare earth permanent magnet poles in the two ramp channels of the V-shaped permanent magnet installation groove The magnetization direction of the permanent magnet pole is to the inside of the V shape or to the outside of the V shape at the same time;

The magnetization directions of n rotor poles on the same radius are consistent.

The advantages of the present invention are: on the basis of the traditional built-in radial V-type rare earth permanent magnet synchronous motor, a part of the rare earth permanent magnet material is replaced by a ferrite permanent magnet material, and the ferrite material is placed on both sides of the rare earth permanent magnet material. Since the remanence of ferrite materials is lower than that of rare earth permanent magnet materials, the combination can make the air-gap flux density waveform closer to a sine wave and reduce the harmonic content of the air-gap magnetic field, thereby reducing the stator iron loss caused by magnetic field harmonics and torque fluctuations. In addition, the anti-demagnetization ability of ferrite permanent magnet materials is stronger than that of rare earth permanent magnet materials, and the anti-demagnetization ability of ferrite permanent magnet materials increases with the increase of temperature. Placing ferrite on both sides of rare earth materials can greatly reduce the original The local demagnetization risk of rare earth permanent magnet materials improves the reliability of motor operation. The combined magnetic pole permanent magnet motor uses low-cost ferrite permanent magnet materials to replace a part of rare earth permanent magnet materials, thereby reducing costs and increasing efficiency and operational reliability.

Description of drawings

Figure 1 is a schematic diagram of the structure of a traditional built-in radial V-type rare earth permanent magnet synchronous motor, with a single-layer magnetic pole structure;

Figure 2 is a schematic structural diagram of a traditional built-in radial V-type rare earth permanent magnet synchronous motor, with a double-layer magnetic pole structure;

Fig. 3 is a structural schematic diagram of a combined magnetic pole type built-in radial V-shaped permanent magnet synchronous motor according to Embodiment 1, with a single-layer magnetic pole structure;

Fig. 4 is a structural schematic diagram of the combined magnetic pole type built-in radial V-shaped permanent magnet synchronous motor described in the second embodiment, with a double-layer magnetic pole structure;

Fig. 5 is the specific structure schematic diagram of the combined rotor magnetic pole of the motor of the present invention;

Fig. 6 is a comparison diagram of the air-gap flux density waveforms of the combined magnetic pole built-in radial V-type permanent magnet synchronous motor of the present invention and the traditional built-in radial V-type rare earth permanent magnet synchronous motor.

detailed description

Specific Embodiment 1: The present embodiment will be described below in conjunction with Fig. 3, Fig. 5 and Fig. 6. The combined magnetic pole type built-in radial V-type permanent magnet synchronous motor described in the present embodiment includes a rotor and a stator, and the rotor is arranged inside the stator. There is a radial air gap between the rotor and the stator. The stator includes a stator core 1 and a stator winding 2. The stator winding 2 is arranged in the inner stator slot of the stator core 1; the rotor includes a plurality of rotor poles 3 and a rotor core 4. The rotor core 4 A layer of V-shaped permanent magnet installation grooves 3-3 is evenly distributed along the circumferential direction. The V-shaped permanent magnet installation grooves 3-3 extend axially, and the V-shaped opening faces the stator. Each V-shaped permanent magnet installation groove 3-3 Set a rotor pole 3;

The rotor pole 3 includes two rare earth permanent magnet poles 3-1 and two ferrite permanent magnet poles 3-2, and the two rare earth permanent magnet poles 3-1 and two ferrite permanent magnet poles 3-2 are long One rare-earth permanent magnet pole 3-1 and one ferrite permanent magnet pole 3-2 are embedded in each ramp channel of strip-shaped and V-shaped permanent magnet installation grooves 3-3;

The rare earth permanent magnet poles 3-1 and the ferrite permanent magnet poles 3-2 in the same ramp channel are magnetized parallel to the vertical direction of the ramp channel, and the magnetization direction is the same; the V-shaped permanent magnet installation groove 3-3 The magnetization direction of the two rare-earth permanent magnet poles 3-1 in the two slope channels is toward the inside of the V-shape or toward the outside of the V-shape at the same time.

In a ramp channel, the length of the rare earth permanent magnet pole 3-1 along the slope direction is a/2, and the length of the ferrite permanent magnet pole 3-2 along the slope direction is b/2, both of which meet the following conditions:

$\frac{\sqrt{\frac{\mathrm{<span\; class="notranslate">\; a</span>}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; Br</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; b</span>}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; Br</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; c</span>}}\mathrm{<span\; class="notranslate">\; the\; s</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; d</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}<span\; class="notranslate">\; \{</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; Br</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; the\; s</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; d</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; c</span>}}\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; Br</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&lsqb;</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; (</span>\frac{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; d</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; c</span>}}\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; the\; s</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; d</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; c</span>}}\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&rsqb;</span><span\; class="notranslate">\; \}</span>}{\frac{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}<span\; class="notranslate">\; \{</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; Br</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; sin</span>}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; d</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; c</span>}}\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; Br</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&lsqb;</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; (</span>\frac{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; d</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; c</span>}}\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; sin</span>}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; d</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; c</span>}}\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&rsqb;</span><span\; class="notranslate">\; \}</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \%</span>}$

In the formula: c is the pole pitch of the rotor pole 3;

d is the angle between the two ramp passages of the V-shaped permanent magnet mounting groove 3-3;

Br ₂ is the remanence density of the rare earth permanent magnet pole 3-1 at the working temperature; Br ₁ is the remanence density of the ferrite permanent magnet pole 3-2 at the working temperature; and Br ₂ >Br ₁ is satisfied.

According to the above formula, the size of the rare earth permanent magnet pole 3-1 and the ferrite permanent magnet pole 3-2 are reasonably proportioned to make it produce the best sine wave of the air gap magnetic field, which is beneficial to reduce iron loss and torque fluctuation.

The ferrite permanent magnet pole 3-2 placed on both sides of the rare earth permanent magnet pole 3-1 has a strong anti-demagnetization ability, and its coercive force has a positive temperature coefficient, and the anti-demagnetization ability will be further strengthened at high temperature, which can improve practical application When the rare earth permanent magnet material is easy to demagnetize at high temperature.

The total width and thickness of the magnetic pole part 3 described in this embodiment are the same as the rare earth permanent magnet magnetic poles in Fig. 1; as can be seen from Fig. The distortion rate of the dense waveform is significantly reduced, but the magnetic density amplitude is also reduced due to the introduction of ferrite materials with small residual magnetism. In order to ensure the output capacity of the motor and the built-in radial V-type rare earth The permanent magnet synchronous motor remains the same, increasing the axial length of the combined magnetic pole motor, but the cost of the combined magnetic pole motor is still lower than that of the pure rare earth permanent magnet motor. It can be seen from Fig. 6 that the air-gap flux density waveform of the combined magnetic pole built-in radial V-type permanent magnet synchronous motor proposed by the present invention is more sinusoidal than that of the traditional built-in V-type permanent magnet synchronous motor, thereby reducing stator iron loss and torque fluctuation. In addition, the strong anti-demagnetization ability of the ferrite material reduces the risk of demagnetization during the operation of the motor and improves the reliability of the motor.

Specific embodiment two: The present embodiment is described below in conjunction with Fig. 4 to Fig. 6, the combined magnetic pole type built-in radial V-type permanent magnet synchronous motor described in the present embodiment includes a rotor and a stator, the rotor is arranged inside the stator, and the rotor and the stator A radial air gap is left between them, the stator includes a stator core 1 and a stator winding 2, and the stator winding 2 is arranged in the inner stator slot of the stator core 1; the rotor includes a plurality of rotor poles 3 and a rotor core 4, and the rotor core 4 is along the circumferential direction Evenly distributed n layers of V-shaped permanent magnet installation grooves 3-3, the V-shaped permanent magnet installation grooves 3-3 extend in the axial direction, and the V-shaped openings of each V-shaped permanent magnet installation groove 3-3 face the stator and are on the same radius The n V-shaped permanent magnet installation grooves 3-3 are parallel to each other, and a rotor pole 3 is arranged in each V-shaped permanent magnet installation groove 3-3; n is a natural number greater than or equal to 2;

The rotor pole 3 includes two rare earth permanent magnet poles 3-1 and two ferrite permanent magnet poles 3-2, and the two rare earth permanent magnet poles 3-1 and two ferrite permanent magnet poles 3-2 are long One rare-earth permanent magnet pole 3-1 and one ferrite permanent magnet pole 3-2 are embedded in each ramp channel of strip-shaped and V-shaped permanent magnet installation grooves 3-3;

The rare earth permanent magnet poles 3-1 and the ferrite permanent magnet poles 3-2 in the same ramp channel are magnetized parallel to the vertical direction of the ramp channel, and the magnetization direction is the same; the V-shaped permanent magnet installation groove 3-3 The magnetization directions of the two rare-earth permanent magnet poles 3-1 in the two slope channels are simultaneously toward the inside of the V shape or toward the outside of the V shape;

The magnetization directions of the n rotor poles 3 on the same radius are consistent.

In a slope channel of any one layer, the length of the rare earth permanent magnet pole (3-1) along the slope direction is a _i /2, i=1, 2,..., n;, the ferrite permanent magnet pole (3-2) The length along the slope direction is b _i /2, both of which meet the following conditions:

$\frac{\sqrt{\frac{{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; Br</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; Br</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; c</span>}}\mathrm{<span\; class="notranslate">\; the\; s</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; d</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}<span\; class="notranslate">\; \{</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; Br</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}\mathrm{<span\; class="notranslate">\; the\; s</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; d</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; c</span>}}\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; Br</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&lsqb;</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; (</span>\frac{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; d</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; c</span>}}\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}\mathrm{<span\; class="notranslate">\; the\; s</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; d</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; c</span>}}\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&rsqb;</span><span\; class="notranslate">\; \}</span>}{\frac{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}<span\; class="notranslate">\; \{</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; Br</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}\mathrm{<span\; class="notranslate">\; the\; s</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; d</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; c</span>}}\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; Br</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&lsqb;</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; (</span>\frac{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; d</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; c</span>}}\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}\mathrm{<span\; class="notranslate">\; the\; s</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; d</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; c</span>}}\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&rsqb;</span><span\; class="notranslate">\; \}</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \%</span>}$

In the formula: c is the pole pitch of the rotor pole (3);

D is the included angle of the two ramp passages of the V-shaped permanent magnet mounting groove (3-3);

Br ₂ is the remanence density of the rare earth permanent magnet pole (3-1) at the working temperature; Br ₁ is the remanence density of the ferrite permanent magnet pole (3-2) at the working temperature; and Br ₂ >Br ₁ is satisfied.

In each layer structure, the size ratio of the rare earth permanent magnet pole 3-1 and the ferrite permanent magnet pole 3-2 is the same.

According to the above formula, the size of the rare earth permanent magnet pole 3-1 and the ferrite permanent magnet pole 3-2 are reasonably proportioned to make it produce the best sine wave of the air gap magnetic field, which is beneficial to reduce iron loss and torque fluctuation.

The ferrite permanent magnet pole 3-2 placed on both sides of the rare earth permanent magnet pole 3-1 has a strong anti-demagnetization ability, and its coercive force has a positive temperature coefficient, and the anti-demagnetization ability will be further strengthened at high temperature, which can improve practical application When the rare earth permanent magnet material is easy to demagnetize at high temperature.

The total width and thickness of the magnetic pole part 3 described in this embodiment are the same as the rare earth permanent magnet magnetic poles in Fig. 2; as can be seen from Fig. The distortion rate of the dense waveform is significantly reduced, but the magnetic density amplitude is also reduced due to the introduction of ferrite materials with small residual magnetism. In order to ensure the output capacity of the motor and the built-in radial V-type rare earth The permanent magnet synchronous motor remains the same, increasing the axial length of the combined magnetic pole motor, but the cost of the combined magnetic pole motor is still lower than that of the pure rare earth permanent magnet motor. It can be seen from Fig. 6 that the air-gap flux density waveform of the combined magnetic pole built-in radial V-type permanent magnet synchronous motor proposed by the present invention is more sinusoidal than that of the traditional built-in V-type permanent magnet synchronous motor, thereby reducing stator iron loss and torque fluctuation. In addition, the strong anti-demagnetization ability of the ferrite material reduces the risk of demagnetization during the operation of the motor and improves the reliability of the motor.

Claims (4)

1. Combined magnetic pole type built-in radial V-type permanent magnet synchronous motor, including rotor and stator, the rotor is arranged inside the stator, a radial air gap is left between the rotor and the stator, the stator includes the stator core (1) and the stator winding ( 2), the stator winding (2) is arranged in the inner stator slot of the stator core (1); the rotor includes a plurality of rotor poles (3) and the rotor core (4), and the rotor core (4) is evenly distributed in a layer of V-shaped along the circumferential direction The permanent magnet installation groove (3-3), the V-shaped permanent magnet installation groove (3-3) extends along the axial direction, and the V-shaped opening faces the stator, and a rotor is arranged in each V-shaped permanent magnet installation groove (3-3) pole (3); It is characterized in that the rotor poles (3) include two rare earth permanent magnet poles (3-1) and two ferrite permanent magnet poles (3-2), two rare earth permanent magnet poles (3-1) and two The ferrite permanent magnet poles (3-2) are all elongated, and each slope channel of the V-shaped permanent magnet installation groove (3-3) is embedded with a rare earth permanent magnet pole (3-1) and an iron Oxygen permanent magnet pole (3-2); The rare earth permanent magnet poles (3-1) and ferrite permanent magnet poles (3-2) in the same ramp channel are magnetized parallel to the vertical direction of the ramp channel, and the magnetization direction is the same; V-shaped permanent magnets are installed The magnetization directions of the two rare earth permanent magnet poles (3-1) in the two slope channels of the slot (3-3) are simultaneously toward the inside of the V shape or toward the outside of the V shape. 2. according to claim 1 said combined magnetic pole type built-in radial V-type permanent magnet synchronous motor, it is characterized in that, in a ramp channel, the length of the rare earth permanent magnet pole (3-1) along the slope direction is a/2, iron The length of the oxygen body permanent magnet pole (3-2) along the slope direction is b/2, and the two satisfy the following conditions: $\frac{\sqrt{\frac{\mathrm{<span\; class="notranslate">\; a</span>}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; Br</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; b</span>}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; Br</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; c</span>}}\mathrm{<span\; class="notranslate">\; the\; s</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; d</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}<span\; class="notranslate">\; \{</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; Br</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; the\; s</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; d</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; c</span>}}\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; Br</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&lsqb;</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; (</span>\frac{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; d</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; c</span>}}\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; the\; s</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; d</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; c</span>}}\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&rsqb;</span><span\; class="notranslate">\; \}</span>}{\frac{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}<span\; class="notranslate">\; \{</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; Br</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; sin</span>}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; d</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; c</span>}}\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; Br</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&lsqb;</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; (</span>\frac{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; d</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; c</span>}}\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; sin</span>}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; d</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; c</span>}}\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&rsqb;</span><span\; class="notranslate">\; \}</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \%</span>}$ In the formula: c is the pole pitch of the rotor pole (3); D is the included angle of the two ramp passages of the V-shaped permanent magnet mounting groove (3-3); Br ₂ is the remanence density of the rare earth permanent magnet pole (3-1) at the working temperature; Br ₁ is the remanence density of the ferrite permanent magnet pole (3-2) at the working temperature; and Br ₂ >Br ₁ is satisfied. 3. Combined magnetic pole type built-in radial V-type permanent magnet synchronous motor, including rotor and stator, the rotor is set inside the stator, a radial air gap is left between the rotor and the stator, the stator includes the stator core (1) and the stator winding ( 2), the stator winding (2) is arranged in the inner stator slot of the stator core (1); the rotor includes a plurality of rotor poles (3) and the rotor core (4), and the rotor core (4) is evenly distributed along the circumferential direction with n layers of V-shaped The permanent magnet installation groove (3-3), the V-shaped permanent magnet installation groove (3-3) extends along the axial direction, the V-shaped opening of each V-shaped permanent magnet installation groove (3-3) faces the stator, and is on the same radius The n V-shaped permanent magnet installation grooves (3-3) are parallel to each other, and a rotor pole (3) is arranged in each V-shaped permanent magnet installation groove (3-3); n is a natural number greater than or equal to 2; It is characterized in that the rotor poles (3) include two rare earth permanent magnet poles (3-1) and two ferrite permanent magnet poles (3-2), two rare earth permanent magnet poles (3-1) and two The ferrite permanent magnet poles (3-2) are all elongated, and each slope channel of the V-shaped permanent magnet installation groove (3-3) is embedded with a rare earth permanent magnet pole (3-1) and an iron Oxygen permanent magnet pole (3-2); The rare earth permanent magnet poles (3-1) and ferrite permanent magnet poles (3-2) in the same ramp channel are magnetized parallel to the vertical direction of the ramp channel, and the magnetization direction is the same; V-shaped permanent magnets are installed The magnetization directions of the two rare earth permanent magnet poles (3-1) in the two slope channels of the groove (3-3) are simultaneously toward the inside of the V shape or toward the outside of the V shape; The magnetization directions of n rotor poles (3) on the same radius are consistent. 4. according to claim 3 said combined magnetic pole type built-in radial V-type permanent magnet synchronous motor, it is characterized in that, in a ramp passage of any one layer, the length of the rare earth permanent magnet pole (3-1) along the slope direction is a _i /2, i=1, 2,...., n;, the length of the ferrite permanent magnet pole (3-2) along the slope direction is b _i /2, and the two satisfy the following conditions: $\frac{\sqrt{\frac{{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; Br</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; Br</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; c</span>}}\mathrm{<span\; class="notranslate">\; the\; s</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; d</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}<span\; class="notranslate">\; \{</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; Br</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}\mathrm{<span\; class="notranslate">\; the\; s</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; d</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; c</span>}}\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; Br</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&lsqb;</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; (</span>\frac{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; d</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; c</span>}}\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}\mathrm{<span\; class="notranslate">\; the\; s</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; d</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; c</span>}}\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&rsqb;</span><span\; class="notranslate">\; \}</span>}{\frac{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}<span\; class="notranslate">\; \{</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; Br</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}\mathrm{<span\; class="notranslate">\; the\; s</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; d</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; c</span>}}\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; Br</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&lsqb;</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; (</span>\frac{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; S</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; d</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; c</span>}}\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}\mathrm{<span\; class="notranslate">\; the\; s</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; d</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; c</span>}}\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&rsqb;</span><span\; class="notranslate">\; \}</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \%</span>}$ In the formula: c is the pole pitch of the rotor pole (3); D is the included angle of the two ramp passages of the V-shaped permanent magnet mounting groove (3-3); Br ₂ is the remanence density of the rare earth permanent magnet pole (3-1) at the working temperature; Br ₁ is the remanence density of the ferrite permanent magnet pole (3-2) at the working temperature; and Br ₂ >Br ₁ is satisfied.