阅读说明：本技术 非均匀齿永磁游标电机设计方法 (Design method of non-uniform tooth permanent magnet vernier motor ) 是由 赵飞 陶恩成 潘学伟 于 2019-09-20 设计创作，主要内容包括：本发明提供了一种非均匀齿永磁游标电机设计方法,通过将呈环形并间隔排布于电机定子上的Z<Sub>s</Sub>个定子齿划分为Z<Sub>f</Sub>个齿单元组,在任意相邻两个齿单元组中心面之间的夹角相等并保证各齿单元组中心面位置不变的条件下,调整各齿单元组内n<Sub>g</Sub>个定子齿的位置,使各齿单元组内相邻两个定子齿之间的间距与相邻两个齿单元组之间的间距不相等,并使各齿单元组内n<Sub>g</Sub>个定子齿关于该齿单元组中心面对称,通过电机定子上的非均匀分布齿结构引入与未被空载气隙磁密谐波利用的绕组磁动势谐波对应频率的目标磁导谐波,再通过非均匀分布齿结构与永磁体调制出与目标磁导谐波对应的空载气隙磁密谐波,充分利用电枢绕组磁动势谐波,增加永磁游标电机输出转矩和转矩密度。(The invention provides a design method of a non-uniform tooth permanent magnet vernier motor, which is characterized in that Z which is annular and arranged on a motor stator at intervals s Each stator tooth is divided into Z f The tooth unit groups adjust n in each tooth unit group under the conditions that the included angle between the central planes of any two adjacent tooth unit groups is equal and the position of the central plane of each tooth unit group is not changed g The positions of the stator teeth enable the space between two adjacent stator teeth in each tooth unit group to be unequal to the space between two adjacent tooth unit groups, and n in each tooth unit group g The stator teeth are symmetrical about the central plane of the tooth unit group, target magnetic conduction harmonic with frequency corresponding to winding magnetomotive force harmonic which is not utilized by no-load air gap flux density harmonic is introduced through a non-uniform distribution tooth structure on a motor stator, no-load air gap flux density harmonic corresponding to the target magnetic conduction harmonic is modulated through the non-uniform distribution tooth structure and the permanent magnet, armature winding magnetomotive force harmonic is fully utilized, and output torque and torque density of the permanent magnet vernier motor are increased.)

1. The design method of the non-uniform tooth permanent magnet vernier motor is applied to the permanent magnet vernier motor and is characterized in that the permanent magnet vernier motor comprises a rotor, a rotor and a rotor, wherein the rotor is provided with a Z-shaped structure_sThe motor stator of each stator tooth, the motor rotor matched with the motor stator, and the Z arranged on the motor rotor_rThe permanent magnets and the armature windings are respectively wound on the stator teeth; the design method of the non-uniform tooth permanent magnet vernier motor comprises the following steps:

step S1: will Z_sThe stator teeth are annularly arranged on the motor stator at intervals, and n is sequentially selected along the clockwise or anticlockwise direction_gThe stator teeth which are continuously arranged are a tooth unit group to form Z_sEach stator tooth is divided into Z_fEach tooth unit group;

step S2: under the condition that the included angle between the central planes of any two adjacent tooth unit groups is equal and the position of the central plane of each tooth unit group is not changed, adjusting n magnetomotive force harmonics in each tooth unit group according to winding magnetomotive force harmonics which are not utilized by no-load air gap flux density harmonics_gThe positions of the stator teeth are not equal to the distance between two adjacent stator teeth in each tooth unit group until the distance between two adjacent tooth unit groups is not equal to the distance between two adjacent tooth unit groups, so that Z_sThe stator teeth form a non-uniform distribution tooth structure on the motor stator;

step S3: n in each tooth unit group_gThe stator teeth are arranged to be symmetrical about the central plane of the tooth unit group, target magnetic conductance harmonics with the frequency corresponding to the winding magnetomotive force harmonics which are not utilized by the no-load air gap flux density harmonics are introduced, and the no-load air gap flux density harmonics are modulated by the non-uniform distribution tooth structure and the permanent magnets to enable the no-load air gap flux density harmonics to correspond to the target magnetic conductance harmonics.

2. The method of claim 1 wherein n is adjusted in each set of tooth units_gIn the step of positioning the stator teeth, the distance between any two adjacent tooth unit groups is equal, and Z is_fAnd the armature windings of the tooth unit groups are symmetrical.

3. The method of claim 1, further comprising adjusting n of each set of teeth in each set of teeth units_gA winding magnetomotive force harmonic selection step before the stator tooth position step, wherein the winding magnetomotive force harmonic selection stepThe method comprises the following steps: set at Z_sAnd calculating and analyzing the winding magnetomotive force harmonic component of the armature winding under the condition that the stator teeth are annularly arranged and evenly distributed at equal intervals, and selecting the winding magnetomotive force harmonic not utilized by the no-load air gap flux density harmonic.

4. A method of designing a non-uniform tooth permanent magnet vernier motor according to claim 3, wherein in the winding magnetomotive force harmonic selection step, the lowest secondary winding magnetomotive force harmonic not utilized by no-load air gap flux density harmonics is selected from the winding magnetomotive force harmonic components.

5. A method for designing a non-uniform tooth permanent magnet vernier motor as claimed in claim 3 wherein the selected number of winding magnetomotive force harmonics not utilized by no-load air gap flux density harmonics is recorded as Z_cAnd recording the permeance times of the target permeance harmonic as Z_fnThen Z is_fn＝Z_r-Z_cAnd the number of tooth unit groups Z_fSatisfy the relation Z_f＝GCD(Z_fn,Z_s) Or Z_f＝Z_s-Z_fn(ii) a Wherein GCD is the greatest common divisor.

6. The method of claim 1, wherein the no-load air gap flux density harmonic component modulated by the target flux guide harmonic and the permanent magnet satisfies the following relation:

wherein B is magnetic density, P is magnetic conductance, F is the magnetomotive force of the permanent magnet,is | nZ_r±mZ_fI order magnetic density harmonic amplitude, theta_mIs the rotor mechanical position angle; z_rThe number of pole pairs of the permanent magnet is; z_fAs a set of tooth unitsThe number of the cells; 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.

7. The method of claim 1, further comprising applying cogging torque phasors separately to Z prior to said step of introducing said target flux guide harmonics_fAnd analyzing the cogging torque harmonics of the stator teeth at the same sequence position in each tooth unit group, and modifying the tooth width and the position of the stator teeth at the same sequence position in each tooth unit group to eliminate specific sub-cogging torque harmonics.

8. The method of claim 7 wherein Z is the step of modifying the width and position of said stator teeth at the same sequential position within each of said groups of teeth units_sThe stator teeth are arranged in an equal width mode.

9. The method of claim 7 wherein said applying cogging torque phasors separately for Z_fAnd after analyzing the cogging torque harmonic waves of the stator teeth at the same sequence position in the tooth unit group, calculating the content of the target magnetic conductance harmonic wave and each effective sub-zero-load air gap flux density harmonic wave modulated by the permanent magnet, and determining a design point with the highest output torque under the condition of meeting the minimum cogging torque.

10. The method for designing a non-uniform tooth permanent magnet vernier motor as claimed in claim 9, wherein the electromagnetic torque calculated according to the analysis of the content of the target flux guide harmonic and each effective sub-no-load air gap flux density harmonic modulated by the permanent magnet satisfies the relation:

wherein k is_TIn order to be the torque coefficient of the motor,

Technical Field

The invention belongs to the technical field of permanent magnet motors and permanent magnet motor design, and particularly relates to a design method of a non-uniform tooth permanent magnet vernier motor.

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 motor stator, a motor 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 motor 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 motor rotor are modulated into a minority of pole pair magnetic fields matched with the motor 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 seriously limited.

Disclosure of Invention

The invention aims to provide a design method of a non-uniform tooth permanent magnet vernier motor, and aims to solve 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 method for designing a non-uniform tooth permanent magnet vernier motor of a non-uniform tooth permanent magnet vernier motor, the method for designing the non-uniform tooth permanent magnet vernier motor is applied to the permanent magnet vernier motor, and the permanent magnet vernier motor comprises a rotor and a rotor, wherein the rotor is provided with a Z_sThe motor stator of each stator tooth, the motor rotor matched with the motor stator, and the Z arranged on the motor rotor_rThe permanent magnets and the armature windings are respectively wound on the stator teeth; the design method of the non-uniform tooth permanent magnet vernier motor comprises the following steps:

step S1: will Z_sThe stator teeth are annularly arranged on the motor stator at intervals, and n is sequentially selected along the clockwise or anticlockwise direction_gThe stator teeth which are continuously arranged are a tooth unit group to form Z_sEach stator tooth is divided into Z_fEach tooth unit group;

step S2: at randomAdjusting n magnetic motive force harmonics in each tooth unit group according to winding magnetic motive force harmonics which are not utilized by no-load air gap flux density harmonics under the conditions that the included angles between the central planes of two adjacent tooth unit groups are equal and the position of the central plane of each tooth unit group is not changed_gThe positions of the stator teeth are not equal to the distance between two adjacent stator teeth in each tooth unit group until the distance between two adjacent tooth unit groups is not equal to the distance between two adjacent tooth unit groups, so that Z_sThe stator teeth form a non-uniform distribution tooth structure on the motor stator;

step S3: n in each tooth unit group_gThe stator teeth are arranged to be symmetrical about the central plane of the tooth unit group, target magnetic conductance harmonics with the frequency corresponding to the winding magnetomotive force harmonics which are not utilized by the no-load air gap flux density harmonics are introduced, and the no-load air gap flux density harmonics are modulated by the non-uniform distribution tooth structure and the permanent magnets to enable the no-load air gap flux density harmonics to correspond to the target magnetic conductance harmonics.

Further, n is adjusted in each of the tooth unit groups_gIn the step of positioning the stator teeth, the distance between any two adjacent tooth unit groups is equal, and Z is_fAnd the armature windings of the tooth unit groups are symmetrical.

Furthermore, the design method of the non-uniform tooth permanent magnet vernier motor further comprises the step of adjusting n in each tooth unit group_gA winding magnetomotive force harmonic selection step prior to the stator tooth position step, the winding magnetomotive force harmonic selection step comprising: set at Z_sAnd calculating and analyzing the winding magnetomotive force harmonic component of the armature winding under the condition that the stator teeth are annularly arranged and evenly distributed at equal intervals, and selecting the winding magnetomotive force harmonic not utilized by the no-load air gap flux density harmonic.

Further, in the winding magnetomotive force harmonic selection step, the lowest winding magnetomotive force harmonic which is not utilized by the no-load air gap flux density harmonic in the winding magnetomotive force harmonic component is selected.

Further, the selected number of times of the winding magnetomotive force harmonic wave which is not utilized by the no-load air gap flux density harmonic wave is recorded as Z_cAnd recording the permeance times of the target permeance harmonic as Z_fnThen Z is_fn＝Z_r-Z_cAnd the number of tooth unit groups Z_fSatisfy the relation Z_f＝GCD(Z_fn,Z_s) Or Z_f＝Z_s-Z_fn(ii) a Wherein GCD is the greatest common divisor.

Further, the no-load air gap flux density harmonic component modulated by the target magnetic conductance harmonic and the permanent magnet satisfies the following relational expression:

wherein B is magnetic density, P is magnetic conductance, F is the magnetomotive force of the permanent magnet,

is | nZ_r±mZ_fI order magnetic density harmonic amplitude, theta_mIs the rotor mechanical position angle; z_rThe number of pole pairs of the permanent magnet is; z_fThe number of the tooth unit groups is; 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.

Further, the design method of the non-uniform tooth permanent magnet vernier motor further comprises the step of applying cogging torque phasor to Z respectively before the step of introducing the target magnetic conductance harmonic wave_fAnd analyzing the cogging torque harmonics of the stator teeth at the same sequence position in each tooth unit group, and modifying the tooth width and the position of the stator teeth at the same sequence position in each tooth unit group to eliminate specific sub-cogging torque harmonics.

Further, in the step of modifying the tooth width and position of the stator teeth at the same ordinal position in each of the tooth unit groups, Z is_sThe stator teeth are arranged in an equal width mode.

Further, applying cogging torque phasor to Z respectively_fAnalyzing the cogging torque harmonics of the stator teeth at the same sequence position in the tooth unit group, and then modulating the target magnetic conductance harmonic and each modulated permanent magnetAnd calculating the content of the effective sub-zero-load air gap flux density harmonic wave, and determining the 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 is_TIn order to be the torque coefficient of the motor,

is | Z corresponding to the magnetomotive force of the winding_r±mZ_fI order magnetic density harmonic amplitude, T_eAs electromagnetic torque, B_effectEffective flux density of air gap, Z_rNumber of permanent magnet pole pairs, Z_fThe number of tooth unit groups is shown, and m is a natural number.

The design method of the non-uniform tooth permanent magnet vernier motor has the beneficial effects that: compared with the prior art, the Z-shaped stator is arranged on the stator of the motor in an annular and spaced mode_sEach stator tooth is divided into Z_fThe tooth unit groups adjust n in each tooth unit group under the conditions that the included angle between the central planes of any two adjacent tooth unit groups is equal and the position of the central plane of each tooth unit group is not changed_gThe positions of the stator teeth enable the space between two adjacent stator teeth in each tooth unit group to be unequal to the space between two adjacent tooth unit groups, a non-uniform distribution tooth structure is formed on the motor stator, and n teeth in each tooth unit group_gThe stator teeth are arranged to be symmetrical about the central plane of the tooth unit group, so that the stator windings are symmetrical in phase to phase. The non-uniform distribution tooth structure on the motor stator can be utilized to introduce the target magnetic conductance harmonic with the frequency corresponding to the winding magnetomotive force harmonic which is not utilized by the no-load air gap flux density harmonic, the no-load air gap flux density harmonic is modulated by the non-uniform distribution tooth structure and the permanent magnet, the no-load air gap flux density harmonic corresponds to the target magnetic conductance harmonic, and therefore the non-uniform distribution tooth structure and the permanent magnet correspond to each otherThe body modulates the no-load air gap flux density harmonic corresponding to the target magnetic conductance harmonic, and makes full use of 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.

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 permanent magnet vernier motor designed by the method for designing a non-uniform tooth permanent magnet vernier motor according to an embodiment of the present invention;

fig. 2 is a schematic perspective view of a motor stator with stator windings wound thereon according to the design method for a non-uniform-tooth permanent magnet vernier motor according to the embodiment of the present invention;

fig. 3 is a schematic perspective view of a motor stator designed by the method for designing a non-uniform-tooth permanent magnet vernier motor according to the embodiment of the present invention;

fig. 4 is a schematic top view of a motor stator with stator windings wound thereon according to the design method of the non-uniform-tooth permanent magnet vernier motor according to the embodiment of the present invention;

fig. 5 is a schematic structural diagram of a stator tooth dividing tooth unit group according to the method for designing a non-uniform tooth permanent magnet vernier motor according to an embodiment of the present invention;

fig. 6 is a schematic structural diagram of a cogging torque grouping of the non-uniform tooth permanent magnet vernier motor design method according to an embodiment of the present invention;

FIG. 7 is a schematic diagram illustrating a grouping of cogging torques according to the method for designing a non-uniform-tooth permanent magnet vernier motor according to an embodiment of the present invention;

fig. 8 is a schematic structural diagram of a stator winding short-distance distributed winding of the method for designing a non-uniform tooth permanent magnet vernier motor according to the embodiment of the present invention;

fig. 9 is a phasor diagram of each set of cogging torque of the non-uniform tooth permanent magnet vernier motor design method according to the embodiment of the present invention;

FIG. 10 shows a design method of a non-uniform tooth permanent magnet vernier motor according to an embodiment of the present invention, in which n is_g4-hour cogging torque subharmonic phasor diagram.

Wherein, in the drawings, the reference numerals are mainly as follows:

1-a motor stator; 11-stator teeth; 2-a motor rotor; 3-a permanent magnet; 4-an armature winding;

5-a tooth unit group; 51-central plane.

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, a method for designing a non-uniform tooth permanent magnet vernier motor of a non-uniform tooth structure according to the present invention will now be described. The invention provides a design method of a non-uniform tooth permanent magnet vernier motor of a non-uniform tooth structure, which is applied to the permanent magnet vernier motor, wherein the permanent magnet vernier motor comprises a rotor and a rotor, wherein the rotor is provided with a Z-shaped structure_sA motor stator 1 of each stator tooth, a motor rotor 2 matched with the motor stator 1, and a Z arranged on the motor rotor 2_rA permanent magnet 3 and an armature winding 4 respectively wound on each stator tooth; the design method of the non-uniform tooth permanent magnet vernier motor comprises the following steps:

step S1: will Z_sThe stator teeth are annularly arranged on the motor stator 1 at intervals, and n is selected in turn along the clockwise or anticlockwise direction_gA stator tooth arranged continuously is a tooth unit group 5 to connect Z_sEach stator tooth is divided into Z_fThe set of tooth units 5.

In this step, please refer to FIG. 2, FIG. 3 and FIG. 5, for Z_s Individual stator teeth 11 are grouped by grouping n_gThe stator teeth 11 arranged in series are divided into a set of teeth 5, such that Z_f Tooth element groups 5 and Z_sEach stator tooth 11 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 11, it is necessary to ensure n number of stator teeth 11 of each tooth group 5_gGreater than 1. Wherein Z is_s、Z_f、n_gAre all integers greater than 1.

Step S2: under the condition that the included angles between the central planes 51 of any two adjacent tooth unit groups 5 are equal and the position of the central plane 51 of each tooth unit group 5 is not changed, n magnetic motive force harmonics in each tooth unit group 5 are adjusted according to winding magnetic motive force harmonics which are not utilized by no-load air gap magnetic density harmonics_gThe position of each stator tooth is not equal to the distance between two adjacent stator teeth in each tooth unit group 5 and the distance between two adjacent tooth unit groups 5, so that Z is_sThe individual stator teeth form a non-uniform distribution tooth structure on the motor stator 1.

Specifically, in step S2, according to the operating principle of the pm machine, the pm machine torque is derived from the interaction of the permanent magnet flux density 3 and the winding magnetomotive force for the corresponding number of times, which can be expressed by the mathematical expression:

T＝k_T∑k_wnF_cnB_PMn(1-1)

wherein, in the formula B_PMnIs the no-load air gap flux density n-th harmonic amplitude; k is a radical of_TIs constant and is related to the permanent magnet motor structure; k is a radical of_wnIs the nth harmonic winding factor; f_cnIs 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.

In this step, the analysis of the magnetomotive force harmonic components of the three-phase armature winding is taken as an example for explanation: the open slot vernier motor forms a winding scheme of distributed concentrated windings due to the special pole number proportion and the large difference between the armature winding pole pair number and the stator teeth 11 number, and the armature winding pole pair number p of the vernier motor is often low (p is less than or equal to 3), as shown in fig. 8, as shown in the short-distance distributed winding example of the three-phase 18 stator teeth 11 open slot vernier motor, the pole pair proportion is selected to be 2-16-18(p-Zr-Zs), the A-phase winding is divided into p groups, each phase group comprises Zs/3/p stator teeth 11, the same direction winding is adopted on the Zs/3/p stator teeth 11, and the winding is symmetrically distributed on the motor stator 1 circle at intervals of 360/p angles, so that the p-pole effect is generated. 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 (1-2).

In this embodiment, the three-phase armature winding 4 is a three-phase symmetric centralized armature winding, and when a symmetric three-phase current i ═ Isin (ω t- α) is applied to the three-phase symmetric centralized distributed armature winding, the magnetomotive force harmonic component of the three-phase centralized double-layer armature winding satisfies the following relation:

wherein p is the pole pair number of the winding, omega is the angular speed of three-phase current input by the winding, alpha is the initial phase angle of the current, k_wFor each harmonic winding factor, F_c1For Fourier decomposition of fundamental content, θ_mIs the rotor mechanical position angle; n is a natural number sequentially valued from small to large, and m is a natural number.

In this step, referring to fig. 4, n in each tooth unit group 5 is adjusted under the condition that the included angle between the central planes 51 of any two adjacent tooth unit groups 5 is equal and the position of the central plane 51 of each tooth unit group 5 is guaranteed to be unchanged_gThe position of each stator tooth 11 is not equal to the distance between two adjacent stator teeth 11 in each tooth unit group 5 and the distance between two adjacent tooth unit groups 5, so that Z is_sThe individual stator teeth 11 form a non-uniform distribution tooth structure on the motor stator 1 to introduce a target magnetic conductance harmonic of a frequency corresponding to the winding magnetomotive force harmonic not utilized by the no-load air gap flux density harmonic. I.e. in adjusting n in each set of tooth elements 5_gAt the same time of the position of each stator tooth 11, under the condition that the included angle between the central planes 51 of any two adjacent tooth unit groups 5 is equal and the position of the central plane 51 of each tooth unit group 5 is not changed, n in each tooth unit group 5_gThe individual stator teeth 11 are arranged symmetrically with respect to the center plane 51 of the set of teeth 5, see in particular fig. 4. Each tooth unit group 5 corresponds to an arc section on the stator, and the central symmetry plane of the arc section is the central plane 51 of the tooth unit group 5.

Step S3: referring to fig. 4, n in each tooth unit set 5_gThe stator teeth are arranged symmetrically with respect to the central plane 51 of the tooth unit 5, and target magnetic conductance harmonics of frequencies corresponding to winding magnetomotive force harmonics not utilized by no-load air gap flux density harmonics are introduced through the non-uniform distribution tooth structureAnd modulating no-load air gap flux density harmonic waves with the permanent magnet 3 to enable the no-load air gap flux density harmonic waves to correspond to target magnetic conductance harmonic waves.

In step S3, n in each tooth unit group 5_gThe stator teeth 11 are arranged symmetrically with respect to the central plane 51 of the tooth unit group 5, and Z is_fThe tooth unit groups 5 are arranged to have the same distribution of stator teeth 11 so as to be wound around Z_sThe armature windings 4 on the stator teeth 11 meet the armature winding symmetry condition, so that a non-uniform distribution tooth structure on the motor stator 1 is utilized, a target magnetic permeability harmonic with a frequency corresponding to a winding magnetomotive force harmonic not utilized by a no-load air gap magnetic density harmonic is introduced, the no-load air gap magnetic density harmonic corresponding to the target magnetic permeability harmonic is modulated by the non-uniform distribution tooth structure and the permanent magnet 3, and the output torque and the torque density of the permanent magnet vernier motor are increased.

Specifically, after the stator teeth 11 on the motor stator 1 are changed according to the design rule of the non-uniform distribution tooth structure, the frequency of the air gap magnetic conductance fundamental wave is changed from Z_sIs changed into Z_fWhen only the number of times is considered to be lower than Z_sWhen the secondary winding magnetomotive force harmonic wave, the magnetic conductance harmonic wave is increased (n)_g-1,…,1)Z_fThe 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 11 in the unit.

For example, tradition 1-17-18 (p-Z)_r-Z_s) 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 3 of the permanent magnet synchronous motor is only the pole pair number Z of the permanent magnet_rA sub-harmonic. The vernier motor introduces Z in addition to the permanent magnet synchronous motor through the magnetic field modulation effect_s-Z_pThe subharmonic, however, is mainly 1 st order and 17 th order relative to the content of the winding magnetomotive force harmonic, and the low-order winding magnetomotive force harmonics such as 5, 7, 11, 13, etc., which are abundant relative to the content, are not effectively utilized. In the step, the low-density harmonic wave which is not utilized by the no-load air gap flux density harmonic wave can be selected according to the winding magnetic harmonic component relation in the formula (1-2)The secondary winding magnetomotive force harmonic wave makes use of the action of the low secondary winding magnetomotive force harmonic wave with higher amplitude and the modulated corresponding secondary air gap flux density harmonic wave to make the motor rotor 2 generate higher output torque additionally.

Compared with the prior art, the design method of the non-uniform tooth permanent magnet vernier motor provided by the invention has the advantages that the Z teeth are annularly and alternately arranged on the motor stator 1_sEach stator tooth is divided into Z_fThe tooth unit groups 5 adjust n in each tooth unit group 5 under the condition that the included angle between the central planes 51 of any two adjacent tooth unit groups 5 is equal and the position of the central plane 51 of each tooth unit group 5 is ensured to be unchanged_gThe positions of the stator teeth enable the distance between two adjacent stator teeth in each tooth unit group 5 to be unequal to the distance between two adjacent tooth unit groups 5, and enable n teeth in each tooth unit group 5_gThe individual stator teeth are arranged symmetrically with respect to the center plane 51 of the tooth unit group 5, forming a non-uniformly distributed tooth structure on the motor stator 1. The stator windings are ensured to be in interphase symmetry, namely, a non-uniform distribution tooth structure on the motor stator 1 is utilized, a target magnetic conduction harmonic with a frequency corresponding to winding magnetomotive force harmonic which is not utilized by no-load air gap flux density harmonic is introduced, no-load air gap flux density harmonic is modulated by the non-uniform distribution tooth structure and the permanent magnet 3, the no-load air gap flux density harmonic corresponds to the target magnetic conduction harmonic, the no-load air gap flux density harmonic corresponding to the target magnetic conduction harmonic is modulated by the non-uniform distribution tooth structure and the permanent magnet 3, the magnetomotive force harmonic generated by the armature winding 4 is fully utilized, and the motor additionally generates net output torque, so that the output torque and the torque density of the permanent magnet vernier motor are increased. In addition, the output torque and the torque density of the permanent magnet vernier motor can be further increased by adjusting the distance between adjacent stator teeth 11 to introduce the content of additional magnetic conduction harmonic waves with the frequency corresponding to the low-order winding magnetomotive force harmonic waves which are not utilized by the no-load air gap flux density harmonic waves.

Preferably, as a specific implementation manner of the non-uniform tooth permanent magnet vernier motor design method provided by the present invention, the non-uniform tooth permanent magnet vernier motor design method further includes adjusting n in each tooth unit group 5_gA winding magnetomotive force harmonic selection step before the position step of each stator tooth, wherein the winding magnetomotive force harmonic selection step is performedThe potential harmonic wave selecting step comprises the following steps: set at Z_sAnd calculating and analyzing the winding magnetomotive force harmonic component of the armature winding 4 under the condition that the stator teeth are annularly arranged and evenly distributed at equal intervals, and selecting the winding magnetomotive force harmonic which is not utilized by the no-load air gap flux density harmonic.

In this step, set at Z_sUnder the condition that the stator teeth 11 are annularly arranged and evenly distributed at equal intervals, the winding magnetomotive force harmonic component of the centralized armature winding 4 is calculated and analyzed through the formula (1-2) 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 mode of the design method of the non-uniform tooth permanent magnet vernier motor provided by the invention, in the winding magnetomotive force harmonic selection step, the lowest secondary winding magnetomotive force harmonic 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 secondary magnetomotive force harmonic with the highest amplitude or the magnetomotive force harmonic with higher amplitude is utilized to act on the introduced corresponding secondary air gap flux density harmonic, the motor rotor 2 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 mode of the design method of the non-uniform tooth permanent magnet vernier motor provided by the invention, the number of the selected winding magnetomotive force harmonic which is not utilized by the no-load air gap flux density harmonic is recorded as Z_cLet the number of permeations of the target permeance harmonic be Z_fnThen Z is_fn＝Z_r-Z_cAnd the number of tooth unit groups is 5Z_fSatisfy the relation Z_f＝GCD(Z_fn,Z_s) Or Z_f＝Z_s-Z_fn(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 is_sIs a multiple of 3p, so Z_s3p is likewise a multiple of 3p, the number Z of sets of tooth elements being determined by the greatest common divisor_fThe symmetry condition of the armature winding is necessarily satisfied.

Specifically, the no-load air gap flux density harmonic component modulated by the target magnetic conductance harmonic and the permanent magnet 3 satisfies the following relation:

wherein B is magnetic density, P is magnetic conductance, F is permanent magnet magnetomotive force,

is | nZ_r±mZ_fI order magnetic density harmonic amplitude, theta_mIs the rotor mechanical position angle; z_rThe number of pole pairs of the permanent magnet is; z_fThe number of the tooth unit groups is; 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, according to the formula (1-3), for example, in the tooth structure with uniformly distributed stator teeth 11, the no-load air gap flux density generated by the permanent magnet 3 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 (1-2), such as 4(2p), 8(4p), are not utilized. The design method of the non-uniform tooth permanent magnet vernier motor selects the lowest harmonic which is not utilized, namely 4(2p) times in the example. The number of permeations Z required when trying to produce 4(2p) times magnetic density_fnCan be determined by the formula (1-3), Z_fn＝Z_r(16) 2p (4) ═ 12, i.e. the additional introduction of 12 (Z)_fn) A sub-magnetic conductance harmonic. Wherein Z is_fnPermanent magnet pole pair-the number of magnetic flux densities desired.

Preferably, as a specific implementation manner of the method for designing the non-uniform-tooth permanent magnet vernier motor provided by the invention, the method for designing the non-uniform-tooth permanent magnet vernier motor further comprises the step of applying cogging torque phasor to Z respectively before the step of introducing the target magnetic conductance harmonic wave_fThe cogging torque harmonics of the stator teeth in the same order position in the tooth unit groups 5 are analyzed, and the tooth widths and positions of the stator teeth in the same order position in each tooth unit group 5 are modified to eliminate specific sub-cogging torque harmonics.

Specifically, referring to fig. 6 and 7, respectively, Z is_fInternal phases of the set of gear teeth 5Z in the same position (stator teeth 11 of the same stripe in fig. 6)_fThe individual stator teeth 11 are divided into a set of cogging torque groups 6, Z is then divided_sEach stator tooth 11 is divided into n_gGroup cogging torque group 6, see FIG. 7, and apply cogging torque phasor vs. Z_fThe cogging torque harmonics of the stator teeth 11 at the same position in the tooth unit groups 5 are analyzed, and the phase and amplitude of each sub-cogging torque harmonic of each tooth unit group 6 are changed by changing the tooth width and position of the stator teeth 11 at the same position in each tooth unit group 5, so that the specific sub-cogging torque harmonic is eliminated.

Preferably, as a specific embodiment of the design method of the non-uniform tooth permanent magnet vernier motor provided by the present invention, in the step of modifying the tooth width and position of the stator teeth in the same sequence position in each tooth unit group 5, Z is performed_sEach stator tooth is arranged in equal width to control n_gThe phase angle distribution of the harmonic phasor of the 6 tooth space torque of the tooth space torque group leads the harmonic phasor of the 6 tooth space torque of each tooth space torque group to be distributed at equal intervals so as to eliminate Z_sThe individual stator teeth 11 are unevenly distributed for the particular sub-cogging torque harmonic 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 eliminated_sThe teeth together produce a specific sub-harmonic of the cogging torque.

Preferably, as a specific embodiment of the design method of the non-uniform tooth permanent magnet vernier motor provided by the invention, Z is used_sAfter the stator teeth 11 are arranged in the step of equal width, according to the specific subharmonic phase of the cogging torque of each cogging torque group, calculating a mechanical offset angle of each stator tooth 11 in each tooth group 5 relative to a central plane 51 of the tooth group 5, and selecting a target mechanical angle from the calculated mechanical angles to determine an offset position of each stator tooth 11 in each tooth group 5.

Preferably, as a specific implementation mode of the design method of the non-uniform tooth permanent magnet vernier motor provided by the invention, the Z-direction torque phasor is respectively applied to the Z-direction torque phasors_fCogging torque harmonic generation of stator teeth at the same sequential position in the tooth unit group 5After the analysis step, the content of each effective sub-zero-load air gap flux density harmonic modulated by the target magnetic conductance harmonic and the permanent magnet 3 is calculated, and the design point with the highest output torque is determined under the condition that the cogging torque is minimum.

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 target magnetic conductance harmonic and the permanent magnet 3 satisfies the relation:

wherein k is_TIn order to be the torque coefficient of the motor,

is | Z corresponding to the magnetomotive force of the winding_r±mZ_fI order magnetic density harmonic amplitude, T_eAs electromagnetic torque, B_effectEffective flux density of air gap, Z_rNumber of permanent magnet pole pairs, Z_fThe number of tooth unit groups is shown, and m is a natural number.

Preferably, as a specific implementation manner of the design method of the non-uniform tooth permanent magnet vernier motor provided by the present invention, in the step of adjusting the tooth width and the position of the stator teeth at the same position inside each tooth unit group, n is_gAnd the cogging torque generated by the joint action of the cogging torque groups meets the following relational expression:

wherein, T_cogIs the cogging torque, k is the kth set of teeth, i is the i-th harmonic of the cogging torque, T_kiNcogMagnitude of i-th harmonic component of cogging torque, N, generated for the kth set of teeth_cogNumber Z of tooth unit groups_fAnd permanent magnet pole number 2Z_rSmallest common multiple of, theta_mFor rotor mechanical position angle, α_kAnd m is a natural number, and is the offset angle of the kth group of teeth relative to a stator reference point.

In this step, as shown in FIGS. 7 and 9, according to Z_sA non-The tooth unit group of the stator teeth distributed uniformly is divided into Z_sEach stator tooth is divided into n_gA set of cogging torque groups, each set of cogging torque groups comprising Z_fThe tooth method analyzes the cogging torque to solve the problem that the cogging torque is increased when the stator teeth are non-uniformly distributed. As shown in fig. 9, although n is inside each tooth unit group_gThe stator teeth are non-uniformly distributed, but because of Z_fN inside the set of gear teeth_gThe distribution of the teeth of each stator is the same, and the intervals of the central planes of the tooth unit groups are the same, at the moment, Z_fZ at the same position in the set of gear units_fThe stator teeth are spaced at equal distances, namely, the stator teeth are uniformly distributed.

Preferably, as a specific implementation mode of the design method of the non-uniform tooth permanent magnet vernier motor provided by the invention, Z is used_sAfter 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 alpha_ngAngle to minimize overall cogging torque. Wherein, the alpha is_ngSatisfy the relation:

wherein n is_gThe 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 α_ngAfter the angle step, the cogging torque subharmonic phasors of each set of the cogging torque groups satisfy the following relational expression:

wherein, T_cogkFor the kth set of cogging torques, i being the i-th harmonic of the cogging torque, T_kiNcogMagnitude of i-th harmonic component of cogging torque, N, generated for the kth set of teeth_cogNumber Z of tooth unit groups_fAnd permanent magnet pole number 2Z_rSmallest common multiple of, theta_mFor rotor mechanical position angle, α_kIs opposite to the k-th group of teethThe offset angle of the stator reference point, m being a natural number.

When considering cogging torque multiple harmonics, the frequency of cogging torque fundamental is determined by LCM (Z) after introducing non-uniform tooth structure_s，2Z_r) Decrease to LCM (Z)_f，2Z_r) And LCM is the least common multiple, and multiple harmonics are newly introduced in a more uniform tooth structure. By using the method, the newly introduced harmonic content can be eliminated simultaneously, and the number of the stator teeth in each tooth unit group is 4, namely n_gThe case where the group cogging torque group is 4 groups is explained: as shown in fig. 10, at this time, α_ngAt 90 deg., the phasors are of the same magnitude. The first 4 cases are given in the figure, with subsequent harmonics cycling in sequence. When alpha is_ngAt 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 4_ngThe 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 method_cogMultiple cogging torque ripple. At this time, ngN_cogThe multiple fluctuation amplitude is the superposition of the phasor amplitudes of all groups of teeth. Wherein N is_cogThe number of times of the fundamental wave of the cogging torque in the case of non-uniform teeth.

Preferably, as a specific implementation of the design method of the non-uniform tooth permanent magnet vernier motor provided by the present invention, in the non-uniform distribution tooth structure, the relative position angle of each cogging torque group can be sufficiently adjusted, so as to minimize the cogging torque result acted by the stator teeth of each cogging torque group. And in said application of cogging torque phasor pairs n_gIn the step of analyzing the cogging torque harmonics of the cogging torque groups, the phasors of the cogging torque groups 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, T_kiNcogMagnitude of i-th harmonic component of cogging torque, N, generated for the kth set of teeth_cogNumber Z of tooth unit groups_fAnd permanent magnet pole number 2Z_rSmallest common multiple of, theta_mFor rotor mechanical position angle, α_kAnd m is a natural number, and is the offset angle of the kth group of teeth relative to a stator reference point.

Preferably, as a specific implementation mode of the design method of the non-uniform tooth permanent magnet vernier motor provided by the invention, n in each tooth unit group 5 is adjusted_gIn the step of positioning each stator tooth, the distance between any two adjacent tooth unit groups 5 is equal, and Z is_fThe set of teeth 5 armature windings 4 are symmetrical.

Specifically, around Z_sThe plurality of centralized armature windings on the stator teeth 11 are in interphase 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, therefore, in the running process of the permanent magnet vernier motor, the rotor can not generate strong unilateral magnetic pull force, and the noise of the three-phase motor in high-speed running 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.