CN110581632B - Non-uniform tooth topological structure permanent magnet vernier motor and magnetic field modulation method thereof - Google Patents
Non-uniform tooth topological structure permanent magnet vernier motor and magnetic field modulation method thereof Download PDFInfo
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- CN110581632B CN110581632B CN201910891338.3A CN201910891338A CN110581632B CN 110581632 B CN110581632 B CN 110581632B CN 201910891338 A CN201910891338 A CN 201910891338A CN 110581632 B CN110581632 B CN 110581632B
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02K—DYNAMO-ELECTRIC MACHINES
- H02K1/00—Details of the magnetic circuit
- H02K1/06—Details of the magnetic circuit characterised by the shape, form or construction
- H02K1/12—Stationary parts of the magnetic circuit
- H02K1/14—Stator cores with salient poles
- H02K1/146—Stator cores with salient poles consisting of a generally annular yoke with salient poles
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02K—DYNAMO-ELECTRIC MACHINES
- H02K21/00—Synchronous motors having permanent magnets; Synchronous generators having permanent magnets
- H02K21/12—Synchronous motors having permanent magnets; Synchronous generators having permanent magnets with stationary armatures and rotating magnets
- H02K21/24—Synchronous motors having permanent magnets; Synchronous generators having permanent magnets with stationary armatures and rotating magnets with magnets axially facing the armatures, e.g. hub-type cycle dynamos
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02K—DYNAMO-ELECTRIC MACHINES
- H02K3/00—Details of windings
- H02K3/04—Windings characterised by the conductor shape, form or construction, e.g. with bar conductors
- H02K3/18—Windings for salient poles
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
- H02P23/00—Arrangements or methods for the control of AC motors characterised by a control method other than vector control
- H02P23/14—Estimation or adaptation of motor parameters, e.g. rotor time constant, flux, speed, current or voltage
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
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Abstract
The invention provides a non-uniform tooth topological structure permanent magnet vernier motor and a magnetic field modulation method thereof, the non-uniform tooth topological structure permanent magnet vernier motor is characterized in that a plurality of tooth units are arranged on a stator ring at intervals, the distance between two adjacent stator teeth in each tooth unit is not equal to the groove distance of a tooth unit groove formed between two adjacent tooth units, and a plurality of stator teeth in each tooth unit are symmetrical relative to the central plane of the tooth unit, so that a non-uniform distribution tooth structure is formed on the stator ring, a target magnetic permeability harmonic wave with the frequency corresponding to winding magnetomotive force harmonic not utilized by no-load air gap magnetic permeability harmonic wave is introduced, the no-load air gap magnetic permeability harmonic wave is modulated by the non-uniform distribution tooth structure and a permanent magnet, so that the no-load air gap magnetic permeability harmonic wave corresponding to the target magnetic permeability harmonic wave is modulated by the non-uniform distribution tooth structure and the permanent magnet, magnetomotive force harmonic waves generated by the armature winding are fully utilized, and the output torque and the torque density of the permanent magnet vernier motor are increased.
Description
Technical Field
The invention belongs to the technical field of permanent magnet motors and permanent magnet motor design, and particularly relates to a non-uniform tooth topological structure permanent magnet vernier motor and a magnetic field modulation method thereof.
Background
The Vernier motor (Vernier motor) is a low-speed large-torque direct drive type motor, and has wide application prospects in new energy fields such as electric vehicles, wind power generation, sea wave power generation and the like. The vernier motor is a permanent magnet motor with unequal numbers of stator and rotor poles, and mainly comprises a stator, a rotor and a magnetic field modulation part. The current open slot type permanent magnet vernier motor is generally provided with a plurality of stator slots for accommodating armature windings uniformly along the circumferential direction of a stator, a convex part between each stator slot forms a stator tooth, and the magnetic field modulation (magnetic field modulation) is carried out through a uniformly distributed stator tooth structure, so that a majority of pole pair magnetic fields of a rotor are modulated into a minority of pole pair magnetic fields matched with the stator, and stable electromagnetic torque is generated. However, the permanent magnet vernier motor with the uniformly distributed tooth structure can cause a large amount of winding magnetomotive force harmonics of the armature winding to be underutilized, and the improvement of the output torque and the torque density of the permanent magnet vernier motor is severely limited.
Disclosure of Invention
The invention aims to provide a non-uniform tooth topological structure permanent magnet vernier motor to solve the problems that the permanent magnet vernier motor in the prior art cannot fully utilize winding magnetomotive force harmonic waves and limit the improvement of the output torque and the torque density of the permanent magnet vernier motor.
In order to achieve the above object, the technical scheme adopted by the invention is to provide a non-uniform tooth topology structure permanent magnet vernier motor, which comprises a stator and a rotor, wherein the rotor comprises a rotor frame and a plurality of pairs of permanent magnets arranged on the rotor frame; the stator comprises a stator ring, a plurality of tooth units and a plurality of stator windings, wherein the tooth units and the stator windings are arranged on the stator ring at equal intervals; each tooth unit comprises a plurality of stator teeth, and each stator tooth is provided with a stator winding; the plurality of stator teeth in each tooth unit are symmetrical relative to the central plane of the tooth unit, and the distance between every two adjacent stator teeth in each tooth unit is not equal to the groove pitch of the tooth unit grooves.
Further, the stator winding is a three-phase symmetric concentrated armature winding.
Further, each of the tooth units includes ngThe stator teeth are arranged in sequence, and the number of the tooth units is ZfThe number of the stator teeth on the stator is ZsThen, then
Wherein Z iss、Zf、ngAre each an integer greater than 1.
Further, the tooth widths of the stator teeth of the plurality of tooth units are equal.
Furthermore, the included angles between the central planes of two adjacent tooth units are equal.
The invention provides a non-uniform tooth topological structure permanent magnet vernier motor which has the beneficial effects that: compared with the prior art, the non-uniform tooth topological structure permanent magnet vernier motor provided by the invention has the advantages that the plurality of tooth units are arranged on the stator ring at intervals, the distance between two adjacent stator teeth in each tooth unit is not equal to the groove distance of the tooth unit groove formed between the two adjacent tooth units, and the plurality of stator teeth in each tooth unit are symmetrical relative to the central plane of the tooth unit, so that the stator teeth on the stator form a non-uniform distribution tooth structure, the target magnetic conduction harmonic with the frequency corresponding to the winding magnetomotive force harmonic not utilized by the no-load air gap magnetic density harmonic is introduced, the no-load air gap magnetic density harmonic is modulated by the non-uniform distribution tooth structure and the permanent magnet, the no-load air gap magnetic density harmonic corresponding to the target magnetic conduction harmonic is fully utilized by the armature winding, the motor can additionally generate net output torque, so that the output torque and the torque density of the permanent magnet vernier motor are increased.
The invention also aims to provide a modulation method of the non-uniform tooth topological structure permanent magnet vernier motor, which solves the problems that the permanent magnet vernier motor in the prior art cannot fully utilize winding magnetomotive force harmonic waves, and the output torque and the torque density of the permanent magnet vernier motor are limited to be improved.
In order to achieve the purpose, the technical scheme adopted by the invention is to provide a magnetic field modulation method of a non-uniform tooth topological structure permanent magnet vernier motor, which comprises the steps of introducing a target magnetic conductance harmonic with the frequency corresponding to a winding magnetomotive force harmonic which is not utilized by a no-load air gap flux density harmonic, modulating the no-load air gap flux density harmonic by the target magnetic conductance harmonic and a permanent magnet, wherein the no-load air gap flux density harmonic corresponds to the winding magnetomotive force harmonic which is not utilized by the no-load air gap flux density harmonic.
Further, the magnetic field modulation method of the non-uniform tooth topology permanent magnet vernier motor further comprises a winding magnetomotive force harmonic selection step before the step of introducing the target magnetic conductance harmonic, wherein the winding magnetomotive force harmonic selection step comprises the following steps: and under the condition that a plurality of stator teeth are annularly arranged and uniformly distributed at equal intervals, calculating and analyzing the winding magnetomotive force harmonic component of the armature winding, and selecting the winding magnetomotive force harmonic not utilized by the no-load air gap flux density harmonic.
Further, the magnetic field modulation method of the non-uniform tooth topology permanent magnet vernier motor further comprises a cogging torque optimization step before the target flux guide harmonic introduction step, wherein the cogging torque optimization step comprises the following steps: and respectively analyzing the cogging torque harmonic of the stator teeth at the same sequence position in the plurality of tooth units by using the cogging torque phasor, and eliminating the specific sub-cogging torque harmonic by modifying the tooth width and the position of the stator teeth at the same sequence position in each tooth unit.
Further, after the cogging torque optimization step, calculating the content of each effective sub-zero-load air gap flux density harmonic modulated by the target flux guide harmonic and the permanent magnet, and determining a design point with the highest output torque under the condition of meeting the minimum cogging torque.
Further, the electromagnetic torque obtained by analyzing and calculating the content of each effective sub no-load air gap flux density harmonic modulated by the permanent magnet according to the target magnetic conductance harmonic satisfies the relation:
wherein k isTIn order to be the torque coefficient of the motor,
is | Z corresponding to the magnetomotive force of the windingr±mZfI order magnetic density harmonic amplitude, TeAs electromagnetic torque, BeffectEffective flux density of air gap, ZrNumber of permanent magnet pole pairs, ZfThe number of the tooth units, and m is a natural number.
The method for modulating the magnetic field of the non-uniform tooth topological structure permanent magnet vernier motor has the beneficial effects that: compared with the prior art, the method for modulating the magnetic field of the non-uniform tooth topological structure permanent magnet vernier motor has the advantages that the plurality of tooth units are arranged on the stator ring at intervals, the distance between two adjacent stator teeth in each tooth unit is not equal to the groove distance of the tooth unit groove formed between the two adjacent tooth units, and the plurality of stator teeth in each tooth unit are symmetrical relative to the central plane of the tooth unit, so that the stator teeth on the stator ring form a non-uniform distribution tooth structure, and the three-phase symmetry of the stator tooth windings is ensured. Then, a target magnetic permeability harmonic with a frequency corresponding to winding magnetomotive force harmonic which is not utilized by the no-load air gap flux density harmonic can be introduced through the non-uniform distribution tooth structure on the stator, the no-load air gap flux density harmonic is modulated through the non-uniform distribution tooth structure and the permanent magnet, the no-load air gap flux density harmonic corresponds to the target magnetic permeability harmonic, the no-load air gap flux density harmonic corresponding to the target magnetic permeability harmonic is modulated through the non-uniform distribution tooth structure and the permanent magnet, the magnetomotive force harmonic generated by the armature winding is fully utilized, the motor additionally generates net output torque, and the output torque and the torque density of the permanent magnet vernier motor are increased.
Drawings
In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings needed to be used in the embodiments or the prior art descriptions will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings based on these drawings without inventive exercise.
Fig. 1 is a schematic perspective view of a non-uniform tooth topology permanent magnet vernier motor according to an embodiment of the present invention;
fig. 2 is a schematic perspective view of a stator winding wound on a stator of a non-uniform tooth topology permanent magnet vernier motor according to an embodiment of the present invention;
fig. 3 is a schematic perspective view of a stator of a non-uniform tooth topology permanent magnet vernier motor according to an embodiment of the present invention;
fig. 4 is a schematic top view of a stator winding wound on a stator of a non-uniform tooth topology permanent magnet vernier motor according to an embodiment of the present invention;
fig. 5 is a schematic structural diagram of a stator tooth dividing tooth unit in the method for modulating the magnetic field of the non-uniform tooth topology permanent magnet vernier motor according to the embodiment of the present invention;
fig. 6 is a schematic structural diagram of a cogging torque grouping in a non-uniform tooth topology permanent magnet vernier motor magnetic field modulation method according to an embodiment of the present invention;
fig. 7 is a schematic diagram illustrating a cogging torque grouping condition in a non-uniform tooth topology permanent magnet vernier motor magnetic field modulation method according to an embodiment of the present invention;
fig. 8 is a schematic structural diagram of a stator winding short-distance distribution winding in the method for modulating the magnetic field of the non-uniform tooth topology permanent magnet vernier motor according to the embodiment of the present invention;
fig. 9 is a phasor diagram of each set of cogging torque in the method for modulating the magnetic field of the non-uniform tooth topology permanent magnet vernier motor according to the embodiment of the present invention;
FIG. 10 shows a method for modulating a magnetic field of a non-uniform tooth topology permanent magnet vernier motor according to an embodiment of the present inventiong4-hour cogging torque subharmonic phasor diagram;
fig. 11 is a schematic structural view of each tooth unit on the stator according to the embodiment of the present invention, wherein each tooth unit includes four stator teeth uniformly distributed;
fig. 12 is a schematic structural diagram of a stator provided in an embodiment of the present invention, in which each tooth unit includes four stator teeth that are non-uniformly distributed.
Wherein, in the drawings, the reference numerals are mainly as follows: .
1-a stator; 11-a stator ring; 12-a tooth unit; 121-stator teeth; 13-a stator winding;
2-a rotor; 21-a rotor frame; 22-a permanent magnet;
3-a central plane; 4-tooth unit groove.
Detailed Description
In order to make the technical problems, technical solutions and advantages of the present invention more apparent, the present invention is described in detail with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
It will be understood that when an element is referred to as being "secured to" or "disposed on" another element, it can be directly on the other element or be indirectly on the other element. When an element is referred to as being "connected to" another element, it can be directly connected to the other element or be indirectly connected to the other element.
Furthermore, the terms "first", "second" and "first" are used for descriptive purposes only and are not to be construed as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of the present invention, "a plurality" means two or more unless specifically defined otherwise. The meaning of "a number" is one or more unless specifically limited otherwise.
In the description of the present invention, it should be noted that, unless otherwise explicitly specified or limited, the terms "mounted," "connected," and "connected" are to be construed broadly, e.g., as meaning either a fixed connection, a removable connection, or an integral connection; can be mechanically or electrically connected; either directly or indirectly through intervening media, either internally or in any other relationship. The specific meanings of the above terms in the present invention can be understood by those skilled in the art according to specific situations.
Referring to fig. 1 to fig. 3, a non-uniform tooth topology permanent magnet vernier motor according to the present invention will now be described. The invention provides a non-uniform tooth topological structure permanent magnet vernier motor which comprises a stator 1 and a rotor 2, wherein the rotor 2 comprises a rotor frame 21 and a plurality of pairs of permanent magnets 22 arranged on the rotor frame 21; the stator 1 comprises a stator ring 11, a plurality of tooth units 12 and a plurality of stator windings 13, wherein the tooth units 12 are arranged on the stator ring 11 at equal intervals, and a tooth unit groove 4 is formed between every two adjacent tooth units 12; each tooth unit 12 comprises a plurality of stator teeth 121, and each stator tooth 121 is provided with a stator winding 13; the plurality of stator teeth 121 in each tooth unit 12 are symmetrical about the central plane 3 of the tooth unit 12, and the space between two adjacent stator teeth 121 in each tooth unit 12 is not equal to the slot pitch of the tooth unit slots 4, so that the stator teeth 121 on the stator 1 form a non-uniform tooth distribution structure. Each tooth unit 12 corresponds to an arc segment on the stator ring 11, and the central symmetry plane of the arc segment is the central plane 3 of the tooth unit 12.
Specifically, the plurality of stator teeth 121 in each tooth unit 12 are symmetrical about the central plane 3 of the tooth unit 12, i.e., two or more stator teeth 121 may be included in each tooth unit 12, and two or more stator teeth 121 in each tooth unit 12 are symmetrical about the central plane 3 of the tooth unit 12. As shown in fig. 11 and 12, when each tooth unit 12 includes four or more stator teeth 121, the plurality of stator teeth 121 in each tooth unit 12 may be uniformly distributed or non-uniformly distributed under the condition that the plurality of stator teeth 121 in each tooth unit 12 satisfy symmetry with respect to the central plane 3 of the tooth unit 12, when the plurality of stator teeth 121 in each tooth unit 12 are non-uniformly distributed, a target magnetic flux density harmonic of a frequency corresponding to a winding magnetomotive force harmonic not used by a no-load air gap magnetic density harmonic is introduced, the no-load air gap magnetic density harmonic is modulated by the non-uniform distribution tooth structure and the permanent magnet 22 to correspond to the no-load air gap magnetic density harmonic, and the no-load air gap magnetic density harmonic corresponding to the target magnetic flux harmonic is modulated by the non-uniform distribution tooth structure and the permanent magnet 22 to fully utilize a potential harmonic generated by the armature winding, the motor additionally generates net output torque, and the output torque and the torque density of the permanent magnet vernier motor are increased.
Compared with the prior art, the non-uniform tooth topological structure permanent magnet vernier motor provided by the invention has the advantages that the plurality of tooth units 12 are arranged on the stator ring 11 at intervals, the distance between two adjacent stator teeth 121 in each tooth unit 12 is not equal to the groove distance of the tooth unit groove 4 formed between two adjacent tooth units 12, and the plurality of stator teeth 121 in each tooth unit 12 are symmetrical relative to the central plane 3 of the tooth unit 12, so that the stator teeth 121 on the stator 1 form a non-uniform distribution tooth structure, a target magnetic conduction harmonic with the frequency corresponding to the winding magnetomotive force harmonic not utilized by the no-load air gap magnetic density harmonic is introduced, the no-load air gap magnetic density harmonic is modulated by the non-uniform distribution tooth structure and the permanent magnet 22, the no-load air gap magnetic density harmonic corresponds to the target magnetic conduction harmonic, and the no-load magnetic density harmonic corresponding to the target magnetic conduction harmonic is modulated by the non-load air gap magnetic density harmonic and the permanent magnet, magnetomotive force harmonic waves generated by the armature winding are fully utilized, the motor additionally generates net output torque, and the output torque and the torque density of the permanent magnet vernier motor are increased.
Preferably, as a specific implementation manner of the non-uniform tooth topology permanent magnet vernier motor provided by the present invention, the stator winding 13 is a three-phase symmetric centralized armature winding, which ensures that the three-phase winding is symmetric and the cogging torque is not increased rapidly after the stator teeth 121 are non-uniformly distributed, thereby reducing the cogging torque fluctuation and improving the running stability of the permanent magnet vernier motor.
Specifically, the following description will be given taking the analysis of the magnetomotive force harmonic component of the three-phase armature winding as an example: the open slot type vernier motor has a large difference between the number of pole pairs of the armature winding and the number of the stator teeth 121 due to the special pole number ratio, so that a winding scheme of distributed concentrated windings is formed, and the number p of the pole pairs of the armature winding of the vernier motor is usually low (p is less than or equal to 3). As shown in fig. 8, the stator winding 13 includes an a-phase sub-winding, a B-phase sub-winding, and a C-phase sub-winding, wherein the a-phase sub-winding, the B-phase sub-winding, and the C-phase sub-winding are respectively divided into p groups, each group of the phase includes Zs/3/p stator teeth 121, the Zs/3/p stator teeth 121 are wound in the same direction, and are symmetrically distributed around the stator ring 11 at an interval of 360/p angles, so as to generate a p-pole pair effect. Even harmonics of winding magnetomotive force generated by the opposite poles cannot be mutually offset, so that even harmonic components exist in the winding magnetomotive force in the following formula (1-1).
When symmetrical three-phase current I ═ I sin (ω t- α) is introduced into the three-phase symmetrical centralized armature winding, the magnetomotive force harmonic component of the three-phase centralized double-layer armature winding meets the following relational expression:
wherein p is a coilThe number of pole pairs, omega is the angular speed of three-phase current input by the winding, alpha is the initial phase angle of the current, kwFor each harmonic winding factor, Fc1For Fourier decomposition of fundamental content, θmN is a natural number sequentially valued from small to large in terms of the mechanical position of the rotor 2.
Further, referring to fig. 2 and fig. 3, as an embodiment of the non-uniform tooth topology permanent magnet vernier motor provided in the present invention, each tooth unit 12 includes ngA plurality of stator teeth 121 arranged on the stator ring 11 in sequence, and the number of the tooth units 12 is ZfThe number of the stator teeth 121 on the stator ring 11 is ZsThen, then
Wherein Z iss、Zf、ngAre each an integer greater than 1.
Specifically, please refer to fig. 2, 3 and 5, and Z issThe stator teeth 121 are annularly and alternately arranged on the stator ring 11, and n is selected in turn in the clockwise or counterclockwise directiongA plurality of stator teeth 121 arranged in series as a tooth unit 12 to form a tooth unitsEach stator tooth 121 being divided into ZfTooth unit 12, make ZfTooth units 12 and ZsEach stator tooth 121 satisfies the relation
To ensure that additional permeance harmonic content at frequencies corresponding to the low-order winding magnetomotive force harmonic not utilized by the no-load air gap flux density harmonic can be introduced by adjusting the spacing between adjacent stator teeth 121, the number n of stator teeth 121 of each tooth unit 12 must be ensuredgGreater than 1.
Further, referring to fig. 2 and 3, as an embodiment of the non-uniform tooth topology permanent magnet vernier motor according to the present invention, the plurality of tooth units 12 have the same distribution structure of the stator teeth 121, such that the stator teeth are wound around ZsThe plurality of centralized armature windings on the stator teeth 121 are in interphase symmetry, so that the three-phase windings are symmetrical and the cogging torque is not increased rapidly after the stator teeth 121 are distributed non-uniformly, therebyThe cogging torque fluctuation is reduced, and the running stability of the permanent magnet vernier motor is improved.
Further, referring to fig. 2 and 3, as an embodiment of the non-uniform tooth topology permanent magnet vernier motor provided in the present invention, the tooth widths of the stator teeth 121 of the plurality of tooth units 12 are equal to eliminate ZsThe teeth generate specific subharmonic of the cogging torque together, so that the cogging torque is not increased rapidly after the stator teeth 121 are distributed non-uniformly, the cogging torque fluctuation is reduced, and the running stability of the permanent magnet vernier motor is improved.
Further, referring to fig. 2 and fig. 3, as an embodiment of the non-uniform tooth topology permanent magnet vernier motor according to the present invention, an included angle between the central planes 3 of any two adjacent tooth units 12 is equal, that is, the distance between any two adjacent tooth units 12 is equal, and Z is equalfTooth units 12 and ZsThe stator teeth 121 respectively satisfy the armature winding symmetry condition. According to the number Z of the total stator teeth 121sWhen determining the symmetry of the three-phase armature winding, ZsThe condition to be satisfied when the stator teeth 121 are non-uniformly distributed is to ensure that the armature windings of the phase a sub-winding, the phase B sub-winding and the phase C sub-winding have a mechanical angle difference of 120 degrees respectively. The principle of analyzing the magnetomotive force harmonic components of other armature windings of each phase is the same as that of analyzing the magnetomotive force harmonic components of the armature windings of three phases under the symmetrical condition.
In this embodiment, under the condition that the included angle between the central planes 3 of any two adjacent tooth units 12 is equal and the position of the central plane 3 of each tooth unit 12 is not changed, n magnetic motive force harmonics of the windings in each tooth unit 12 are adjusted according to the magnetic density harmonics of the no-load air gapgThe position of each stator tooth 121 is not equal to the distance between two adjacent stator teeth 121 in each tooth unit 12 and the distance between two adjacent tooth units 12, so that Z issThe stator teeth 121 form a non-uniform distribution tooth structure on the stator ring 11, so that a target magnetic conductance harmonic with a frequency corresponding to a winding magnetomotive harmonic which is not utilized by a no-load air gap magnetic density harmonic under the condition of uniform distribution of the stator teeth 121 can be introduced by using the non-uniform distribution tooth structure on the stator ring 11, and the target magnetic conductance harmonic is modulated by the non-uniform distribution tooth structure and the permanent magnet 22The no-load air gap flux density harmonic corresponding to the harmonic fully utilizes the magnetomotive force harmonic generated by the armature winding to realize that the motor additionally generates net output torque, thereby increasing the output torque and the torque density of the permanent magnet vernier motor.
The invention also provides a magnetic field modulation method of the non-uniform tooth topological structure permanent magnet vernier motor, which comprises the steps of introducing target magnetic conductance harmonic waves with the frequency corresponding to winding magnetomotive force harmonic waves which are not utilized by no-load air gap flux density harmonic waves, modulating no-load air gap flux density harmonic waves through the target magnetic conductance harmonic waves and the permanent magnets 22, and enabling the no-load air gap flux density harmonic waves to correspond to the winding magnetomotive force harmonic waves which are not utilized by the no-load air gap flux density harmonic waves.
In the step, a target magnetic conductance harmonic with the frequency corresponding to the winding magnetomotive force harmonic not utilized by the no-load air gap flux density harmonic is introduced through the non-uniform distribution tooth structure, and the no-load air gap flux density harmonic corresponding to the winding magnetomotive force harmonic not utilized by the no-load air gap flux density harmonic is modulated through the target magnetic conductance harmonic and the permanent magnet 22, so that the output torque and the torque density of the permanent magnet vernier motor are increased.
Specifically, the method for modulating the magnetic field of the non-uniform tooth topological structure permanent magnet vernier motor provided by the invention comprises the following steps:
step S1: will ZsThe stator teeth 121 are annularly and alternately arranged on the stator ring 11 of the stator 1, and n is selected in turn along the clockwise or counterclockwise directiongA plurality of stator teeth 121 arranged in series as a tooth unit 12 to form a tooth unitsEach stator tooth 121 being divided into Zf A tooth unit 12.
In this step, please refer to FIG. 2, FIG. 3 and FIG. 5, for ZsThe individual stator teeth 121 are grouped by grouping ngThe stator teeth 121 arranged in series are divided into a tooth unit 12 such that ZfTooth units 12 and ZsEach stator tooth 121 satisfies the relation
To ensure that additional magnetic permeance harmonics of frequencies corresponding to the lower order winding magnetomotive force harmonics not utilized by the no-load air gap flux density harmonics can be introduced by adjusting the spacing between adjacent stator teeth 121Content, the number n of stator teeth 121 of each tooth unit 12 must be ensuredgGreater than 1.
Step S2: under the condition that the included angle between the central planes 3 of any two adjacent tooth units 12 is equal and the position of the central plane 3 of each tooth unit 12 is not changed, n in each tooth unit 12 is adjusted according to the winding magnetomotive force harmonic which is not utilized by the no-load air gap flux density harmonicgThe position of each stator tooth 121 is not equal to the distance between two adjacent stator teeth 121 in each tooth unit 12 and the distance between two adjacent tooth units 12, so that Z issThe individual stator teeth 121 form a non-uniformly distributed tooth structure on the stator ring 11.
Specifically, in step S2, the pm machine torque is derived from the interaction of the flux density of the permanent magnet 22 and the winding magnetomotive force at the corresponding number of times, which can be expressed by the mathematical expression:
T＝kT∑kwnFcnBPMn(1-2)
wherein, in the formula BPMnIs the no-load air gap flux density n-th harmonic amplitude; k is a radical ofTIs constant and is related to the permanent magnet motor structure; k is a radical ofwnIs the nth harmonic winding factor; fcnIs the winding magnetomotive force harmonic amplitude; n is the number of specific sub-winding magnetomotive force harmonics not utilized by the no-load air gap flux density harmonics.
Step S3: referring to FIG. 4, n in each tooth unit 12gThe stator teeth 121 are arranged symmetrically with respect to the center plane 3 of the tooth unit 12, and Z isfThe teeth units 12 are arranged to have the same distribution of stator teeth 121 so as to be wound around ZsThe plurality of concentrated armature windings on each stator tooth 121 are arranged symmetrically with respect to each other.
In step S3, since each pair of poles p is wound with the same polarity as the corresponding teeth, the size of p can be sufficiently modulated within the range of the number of teeth, and the number Z of tooth units of 12 should be ensured in the case of three-phase concentrated double-layer armature windings, which is referred to as an examplefThe number n of stator teeth 121 of each tooth unit 12gThe following relation is satisfied:
step S4: and introducing a target magnetic conductance harmonic with a frequency corresponding to the winding magnetomotive force harmonic not utilized by the no-load air gap flux density harmonic, and modulating the no-load air gap flux density harmonic through the non-uniform distribution tooth structure and the permanent magnet 22 to enable the no-load air gap flux density harmonic to correspond to the target magnetic conductance harmonic, so that the output torque and the torque density of the permanent magnet vernier motor are increased.
In step S4, after the stator teeth 121 on the stator 1 are changed according to the above non-uniform tooth structure design rule, the number of times of the gap permeance fundamental wave is ZsIs changed into ZfWhen only the number of times is considered to be lower than ZsWhen the secondary winding magnetomotive force harmonic wave, the magnetic conductance harmonic wave is increased (n)g-1,…,1)ZfThe subharmonic and the magnetic conductance harmonic content are obviously richer, and the additionally introduced magnetic conductance harmonic content can be modulated by changing the distribution rule of the stator teeth 121 in the unit.
For example, tradition 1-17-18 (p-Z)r-Zs) The no-load air gap magnetic field of the vernier motor with the pole number ratio is mainly fundamental wave and 17 th harmonic wave, and the net output torque is generated by the action of the no-load air gap magnetic field and the fundamental wave and the 17 th harmonic wave of the winding magnetomotive force respectively. Generally speaking, the main harmonic of the no-load magnetomotive force generated by the permanent magnet 22 of the permanent magnet synchronous motor is only the pole pair number Z of the permanent magnet 22rA sub-harmonic. The vernier motor introduces Z in addition to the permanent magnet synchronous motor through the magnetic field modulation effects-ZpThe subharmonic, however, is only 1 st order and 17 th order relative to the harmonic content of the winding magnetomotive force, and the low-order winding magnetomotive force harmonics such as 5, 7, 11, 13, etc., which are abundant relative to the harmonic content of the winding magnetomotive force, are not effectively utilized. In this step, the low-order winding magnetomotive force harmonic not utilized by the no-load air gap flux density harmonic can be selected according to the winding magnetomotive harmonic component relational expression in the expression (1-1), so that the motor rotor 22 can additionally generate higher output torque by utilizing the action of the low-order winding magnetomotive force harmonic with higher amplitude and the modulated corresponding sub-air gap flux density harmonic.
Compared with the prior art, the magnetic field modulation method of the non-uniform tooth topological structure permanent magnet vernier motor has the advantages that the plurality of tooth units 12 are arranged on the stator ring 11 at intervals, the distance between two adjacent stator teeth 121 in each tooth unit 12 is not equal to the groove distance of the tooth unit groove 4 formed between two adjacent tooth units 12, and the plurality of stator teeth 121 in each tooth unit 12 are symmetrical relative to the central plane 3 of the tooth unit 12, so that the stator teeth 121 on the stator 1 form a non-uniform distribution tooth structure, a target magnetic conduction harmonic with the frequency corresponding to the winding magnetomotive force harmonic which is not utilized by the no-load air gap magnetic density harmonic is introduced, the no-load air gap magnetic density harmonic is modulated by the non-uniform distribution tooth structure and the permanent magnet 22 to correspond to the no-load air gap magnetic density harmonic, and the no-load air gap magnetic density harmonic corresponding to the target magnetic conduction harmonic is further modulated by the non-uniform distribution tooth structure and the permanent magnet 22, magnetomotive force harmonic waves generated by the armature winding are fully utilized, the motor additionally generates net output torque, and the output torque and the torque density of the permanent magnet vernier motor are increased.
Preferably, referring to fig. 3 and fig. 4, as a specific implementation of the magnetic field modulation method for the non-uniform tooth topology permanent magnet vernier motor provided in the present invention, the magnetic field modulation method for the non-uniform tooth topology permanent magnet vernier motor further includes a winding magnetomotive force harmonic selection step before the step of introducing the target magnetic conductance harmonic, and the winding magnetomotive force harmonic selection step includes: under the condition that the plurality of stator teeth 121 are arranged in an annular shape and uniformly distributed at equal intervals, the winding magnetomotive force harmonic components of the armature winding are calculated and analyzed, and winding magnetomotive force harmonics which are not utilized by no-load air gap flux density harmonics are selected.
In this step, assume that Z issUnder the condition that the stator teeth 121 are annularly arranged and evenly distributed at equal intervals, the winding magnetomotive force harmonic component of the centralized armature winding is calculated and analyzed through the formula (1-1) according to the magnetic field modulation principle of the permanent magnet vernier motor, and the winding magnetomotive force harmonic not utilized by the no-load air gap flux density harmonic is selected.
Preferably, as a specific implementation manner of the magnetic field modulation method for the non-uniform tooth topology permanent magnet vernier motor provided by the invention, in the winding magnetomotive force harmonic selection step, the lowest-order or lower-order winding magnetomotive force harmonic with higher content, which is not utilized by the no-load air gap flux density harmonic, in the winding magnetomotive force harmonic component is selected, so that the lowest-order magnetomotive force harmonic with the highest amplitude or the magnetomotive force harmonic with higher amplitude is utilized to act on the introduced corresponding lower-order air gap flux density harmonic, the motor rotor 22 additionally generates higher output torque, and the output torque and the torque density of the permanent magnet vernier motor are further increased.
Preferably, as a specific implementation manner of the magnetic field modulation method of the non-uniform tooth topological structure permanent magnet vernier motor provided by the invention, the number of times of selecting winding magnetomotive force harmonics which are not utilized by no-load air gap flux density harmonics is recorded as ZcLet the number of permeations of the target permeance harmonic be ZfnThen Z isfn＝Zr-ZcAnd the number Z of tooth units 12fSatisfy the relation Zf＝GCD(Zfn,Zs) Or Zf＝Zs-Zfn(ii) a Wherein GCD is the greatest common divisor.
In this step, a three-phase armature winding symmetric permanent magnet vernier motor with 2p times of winding magnetomotive force harmonic is taken as an example for explanation, because Z issIs a multiple of 3p, so Zs3p is likewise a multiple of 3p, the number Z of tooth elements being 12, determined by the greatest common divisorfThe symmetry condition of the armature winding is necessarily satisfied.
Specifically, the no-load air gap flux density harmonic component modulated by the target flux guide harmonic and the permanent magnet 22 satisfies the following relation:
wherein B is magnetic density, P is magnetic conductance, F is permanent magnet magnetomotive force,
is | nZr±mZfI order magnetic density harmonic amplitude, thetamIs the rotor mechanical position angle; zrThe number of pole pairs of the permanent magnet is; zfThe number of the tooth units; theta is the angle between different positions on the rotor and a reference point; m is a natural number, and n is an odd number not less than 1.
In this step, the permanent magnets 22 are produced according to the formula (1-4), for example in a tooth structure in which the stator teeth 121 are uniformly distributedThe magnetic density of the raw no-load air gap is mainly 2(p) and 16 (Z)r) The subharmonics, corresponding to the number of armature winding magnetomotive force harmonics, are utilized, while the remaining lower harmonics in equation (1-1), such as 4(2p), 8(4p), are not utilized. The design method selects the lowest harmonic that is not utilized, i.e., 4(2p) in this example. The number of permeations Z required when trying to produce 4(2p) times magnetic densityfnCan be determined by the formula (1-4), Zfn＝Zr(16) 2p (4) ═ 12, i.e. the additional introduction of 12 (Z)fn) A sub-magnetic conductance harmonic.
Preferably, as a specific implementation manner of the magnetic field modulation method of the non-uniform tooth topology permanent magnet vernier motor provided in the present invention, the magnetic field modulation method of the non-uniform tooth topology permanent magnet vernier motor further includes a cogging torque optimization step before the step of introducing the target magnetic conductance harmonic by using the non-uniform distribution tooth structure on the stator 1, and the cogging torque optimization step includes: cogging torque harmonics of the stator teeth 121 in the same ordinal position in the plurality of tooth units 12 are analyzed respectively using cogging torque phasors, and specific sub-cogging torque harmonics are eliminated by modifying the tooth width and position of the stator teeth 121 in the same ordinal position in each tooth unit 12.
Specifically, referring to fig. 6 and 7, respectively, Z isfZ of the same sequential position (stator teeth 121 of the same stripe in fig. 6) inside the tooth unit 12fEach stator tooth 121 is divided into a set of cogging torque groups, and Z is divided intosEach stator tooth 121 is divided into ngGroup cogging torque group, see FIG. 7, and apply cogging torque phasor vs. ZfThe cogging torque harmonics of the stator teeth 121 at the same ordinal position in the tooth unit 12 are analyzed, and the phase and amplitude of each sub-cogging torque harmonic of each group of the cogging torque harmonics are changed by changing the tooth width and position of the stator teeth 121 at the same ordinal position in each tooth unit 12, so that a specific sub-cogging torque harmonic is eliminated.
Preferably, referring to fig. 3 and 4, as an embodiment of the magnetic field modulation method for the non-uniform tooth topology permanent magnet vernier motor provided in the present invention, in the step of adjusting the tooth width and the position of the stator teeth 121 at the same sequential position inside each tooth unit 12, the step is to perform a step of adjusting the tooth width and the position of the stator teeth 121 at the same sequential position inside each tooth unit 12In (1), Z issThe stator teeth 121 are arranged to have the same width to eliminate ZsThe teeth together produce a specific sub-harmonic of the cogging torque.
Specifically, Z issThe stator teeth 121 are set to be equal in width, and n is controlledgThe phase angle distribution of the torque harmonic phasors of the tooth-space torque group tooth-space makes the torque harmonic phasors of the tooth-space torque groups of the tooth-space torque distributed at equal intervals so as to eliminate ZsThe individual stator teeth 121 are non-uniformly distributed for the particular sub-cogging torque harmonics introduced. And, each group of teeth generating each group of tooth slot torque phasor is set to be a specific interval, so that the equal amplitude and equal rotation angle distribution of each group of tooth slot torque phasor are ensured, and Z is eliminatedsThe teeth together produce a specific sub-harmonic of the cogging torque.
Preferably, as a specific implementation manner of the magnetic field modulation method of the non-uniform tooth topology permanent magnet vernier motor provided by the invention, Z is setsAfter the stator teeth 121 are set to the equal width step, according to the specific subharmonic phase of the cogging torque of each cogging torque group, calculating a mechanical offset angle of each stator tooth 121 in each tooth unit 12 with respect to the central plane 3 of the tooth unit 12, and selecting a target mechanical angle from the calculated plurality of mechanical angles to determine an offset position of each stator tooth 121 in each tooth unit 12.
Preferably, as a specific implementation manner of the magnetic field modulation method of the non-uniform tooth topology permanent magnet vernier motor provided by the invention, after the cogging torque optimization step, a design point with the highest output torque is determined under the condition that the cogging torque is minimum by calculating the content of each effective sub-no-load air gap flux density harmonic modulated by the target flux guide harmonic and the permanent magnet 22.
Specifically, the electromagnetic torque obtained by analyzing and calculating the content of each effective sub no-load air gap flux density harmonic modulated by the permanent magnet 22 according to the target magnetic conductance harmonic satisfies the relation:
wherein the content of the first and second substances,kTin order to be the torque coefficient of the motor,
is | Z corresponding to the magnetomotive force of the windingr±mZfI order magnetic density harmonic amplitude, TeAs electromagnetic torque, BeffectEffective flux density of air gap, ZrNumber of permanent magnet pole pairs, ZfThe number of the tooth units, and m is a natural number.
Preferably, as a specific embodiment of the magnetic field modulation method for the non-uniform tooth topology permanent magnet vernier motor provided in the present invention, in the step of adjusting the tooth width and the position of the stator teeth 121 at the same sequence position inside each tooth unit 12, n isgAnd the cogging torque generated by the joint action of the cogging torque groups meets the following relational expression:
wherein, TcogIs the cogging torque, k is the kth set of teeth, i is the i-th harmonic of the cogging torque, TkiNcogMagnitude of i-th harmonic component of cogging torque, N, generated for the kth set of teethcogNumber of tooth units ZfAnd permanent magnet pole number 2ZrSmallest common multiple of, thetamFor rotor mechanical position angle, αkIs the offset angle of the kth set of teeth relative to the stator reference point.
In this step, as shown in FIGS. 7 and 9, according to ZsThe tooth units 12 of the stator teeth 121 which are not uniformly distributed are divided into ZsEach stator tooth 121 is divided into ngA set of cogging torque groups, each set of cogging torque groups comprising ZfThe tooth method analyzes the cogging torque to solve the problem that the cogging torque becomes large when the stator teeth 121 are non-uniformly distributed. As shown in fig. 6, although n is an inner part of each tooth unit 12gThe stator teeth 121 are non-uniformly distributed, but because of ZfN inside the tooth unit 12gThe stator teeth 121 are distributed in the same manner and the center planes 3 of the tooth units 12 are spaced at the same interval, in which case ZfZ of the same order position in the tooth unit 12fThe stator teeth 121 are spaced apart by the same distance, which is an even distribution.
Preferably, referring to fig. 10, as a specific embodiment of the magnetic field modulation method for the non-uniform tooth topology permanent magnet vernier motor provided in the present invention, Z is setsAfter the stator teeth are set to be of equal width, sequentially shifting the cogging torque fundamental phasor of each group of cogging torque groups by alphangAngle to minimize overall cogging torque. Wherein, the alpha isngSatisfy the relation:
wherein n isgThe number of sets of cogging torque sets.
In this case, the cogging torque fundamental wave phasors of each of the cogging torque groups are sequentially shifted by αngAfter the angle step, the cogging torque subharmonic phasors of each set of the cogging torque groups satisfy the following relational expression:
wherein, TcogkFor the kth set of cogging torques, i being the i-th harmonic of the cogging torque, TkiNcogMagnitude of i-th harmonic component of cogging torque, N, generated for the kth set of teethcogNumber of tooth units ZfAnd permanent magnet pole number 2ZrSmallest common multiple of, thetamFor rotor mechanical position angle, αkIs the offset angle of the kth set of teeth relative to the stator reference point.
When considering cogging torque multiple harmonics, the frequency of cogging torque fundamental is determined by LCM (Z) after introducing non-uniform tooth structures，2Zr) Decrease to LCM (Z)f，2Zr) And LCM is the least common multiple, and multiple harmonics are newly introduced in a more uniform tooth structure. By using the above method, the newly introduced harmonic content can be eliminated simultaneously, and the number of the stator teeth 121 in each tooth unit 12 is 4, that is, ngThe case where the group cogging torque group is 4 groups is explained: as shown in the figures, 10,at this time alphangAt 90 deg., the phasors are of the same magnitude. The first 4 cases, with subsequent harmonics cycling in turn, are given in fig. 10. When alpha isngAt a multiple of 90 deg., the l +1 th tooth phase can be expressed as l90 deg. with reference to a certain time in the cogging torque group. The method is based on the premise that l cannot be equal to a multiple of 4, e.g. alpha is an integer multiple of 4ngThe harmonic waves are multiples of 360 degrees, and all the harmonic waves are in a superposition relation, so that the cogging torque can be maximized. The other values of l can achieve the effect of eliminating low-order harmonic waves, and the method eliminates the harmonic waves with the harmonic frequency not being 4 times in the cogging torque. It can be seen that the number of eliminations unequal to ngN can be eliminated by this methodcogMultiple cogging torque ripple. At this time, ngNcogThe multiple fluctuation amplitude is the superposition of the phasor amplitudes of all groups of teeth. Wherein N iscogThe number of times of the fundamental wave of the cogging torque in the case of non-uniform teeth.
Preferably, as a specific implementation manner of the magnetic field modulation method of the non-uniform tooth topology permanent magnet vernier motor provided by the present invention, in the non-uniform distribution tooth structure, the relative position angle of each of the cogging torque groups can be adjusted sufficiently to minimize the cogging torque result acted by the stator teeth 121 of each of the cogging torque groups. And in said application of cogging torque phasor pairs ngIn the step of analyzing the cogging torque harmonic waves of the cogging torque groups, phasor phasors of the cogging torque groups of each group satisfy the relation:
wherein the content of the first and second substances,
in the form of phasors of the cogging torque of the kth group, i being the i-th harmonic of the cogging torque, TkiNcogMagnitude of i-th harmonic component of cogging torque, N, generated for the kth set of teethcogNumber of tooth units ZfAnd permanent magnet pole number 2ZrSmallest common multiple of, thetamFor rotor mechanical position angle, αkIs the offset angle of the kth set of teeth relative to the stator reference point.
Preferably, as a specific implementation manner of the magnetic field modulation method of the non-uniform tooth topology permanent magnet vernier motor provided by the invention, the magnetic field modulation method is wound around ZsThe centralized armature windings on the stator teeth 121 are in phase symmetry, so that the phase difference between the phase a sub-winding and the phase B sub-winding is 120 degrees, and the phase difference between the phase B sub-winding and the phase C sub-winding is 120 degrees, so that the rotor 2 does not generate strong unilateral magnetic tension in the operation process of the permanent magnet vernier motor, and the noise of the three-phase motor in high-speed operation is reduced.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents and improvements made within the spirit and principle of the present invention are intended to be included within the scope of the present invention.
Claims (10)
1. The permanent magnet vernier motor with the non-uniform tooth topological structure is characterized by comprising a stator and a rotor, wherein the rotor comprises a rotor frame and a plurality of pairs of permanent magnets arranged on the rotor frame; the stator comprises a stator ring, a plurality of tooth units and a plurality of stator windings, wherein the tooth units and the stator windings are arranged on the stator ring at equal intervals; each tooth unit comprises a plurality of stator teeth, and each stator tooth is provided with a stator winding; in the same tooth unit: at least four stator teeth are arranged at intervals along the circumferential direction of the stator, the at least four stator teeth are symmetrical about the central plane of the tooth unit, the distance between every two adjacent stator teeth is not equal to the groove pitch of the tooth unit grooves, and the at least four stator teeth are distributed at unequal intervals; each tooth unit corresponds to one arc section on the stator ring, and the central symmetry plane of the arc section is the central plane of the tooth unit.
2. The non-uniform tooth topology permanent magnet vernier motor as claimed in claim 1, wherein said stator winding is a three-phase symmetric concentrated armature winding.
3. The non-uniform tooth topology permanent magnet vernier motor of claim 1, wherein each of said tooth units comprises ngThe stator teeth are arranged in sequence, and the number of the tooth units is ZfThe number of the stator teeth on the stator is ZsThen, then
Wherein Z iss、Zf、ngAre each an integer greater than 1.
4. The non-uniform tooth topology permanent magnet vernier motor as claimed in claim 3, wherein the tooth widths of the stator teeth of a plurality of said tooth units are equal.
5. The non-uniform tooth topology permanent magnet vernier motor of claim 1, wherein the included angle between the central planes of two adjacent tooth units is equal.
6. A magnetic field modulation method of a non-uniform tooth topology permanent magnet vernier motor according to any one of claims 1 to 5, characterized by comprising the step of introducing a target permeance harmonic of a frequency corresponding to a winding magnetomotive force harmonic not utilized by a no-load air gap magnetic density harmonic through a non-uniform distribution tooth structure on the stator of the non-uniform tooth topology permanent magnet vernier motor, so that the target permeance harmonic generates an electromagnetic torque.
7. The method for modulating the magnetic field of a non-uniform tooth topology permanent magnet vernier motor according to claim 6, further comprising a winding magnetomotive force harmonic selection step prior to the step of introducing the target permeance harmonic, the winding magnetomotive force harmonic selection step comprising: and under the condition that a plurality of stator teeth are annularly arranged and uniformly distributed at equal intervals, calculating and analyzing the winding magnetomotive force harmonic component of the armature winding, and selecting the winding magnetomotive force harmonic not utilized by the no-load air gap flux density harmonic.
8. The method of claim 6, further comprising a cogging torque optimization step prior to the step of introducing the target permeance harmonic, the cogging torque optimization step comprising: and respectively analyzing the cogging torque harmonic of the stator teeth at the same sequence position in the plurality of tooth units by using the cogging torque phasor, and eliminating the specific sub-cogging torque harmonic by modifying the tooth width and the position of the stator teeth at the same sequence position in each tooth unit.
9. The method for modulating the magnetic field of the non-uniform tooth topology permanent magnet vernier motor according to claim 8, wherein after the step of cogging torque optimization, a design point with the highest output torque is determined by calculating the content of the target flux guide harmonic and each effective sub-no-load air gap flux density harmonic modulated by the permanent magnet under the condition of meeting the minimum cogging torque.
10. The magnetic field modulation method of the non-uniform tooth topology permanent magnet vernier motor according to claim 9, wherein the electromagnetic torque obtained by analyzing and calculating the content of each effective sub no-load air gap flux density harmonic modulated by the permanent magnet and the target flux guide harmonic satisfies the relation:
wherein k isTIn order to be the torque coefficient of the motor,
is | Z corresponding to the magnetomotive force of the windingr±mZfI order magnetic density harmonic amplitude, TeAs electromagnetic torque, BeffectEffective flux density of air gap, ZrNumber of permanent magnet pole pairs, ZfThe number of the tooth units, and m is a natural number.
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