阅读说明：本技术 非均匀齿永磁游标电机设计的齿槽转矩优化方法 (Tooth space torque optimization method for non-uniform tooth permanent magnet vernier motor design ) 是由 赵飞 陶恩成 李立毅 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的齿槽转矩优化方法,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,在满足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,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,充分利用电枢绕组产生的磁动势谐波,实现电机额外产生净输出转矩,从而使永磁游标电机增加输出转矩和转矩密度。并且,运用齿槽转矩相量对齿槽转矩谐波进行分析,解决非均匀分布齿结构引起齿槽转矩波动变大的问题。(The invention provides a tooth space torque optimization method for designing a non-uniform tooth permanent magnet vernier motor s Each stator tooth is divided into Z f The tooth unit groups adjust n in each tooth unit group 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 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, no-load air gap flux density harmonic corresponding to target magnetic conductance harmonic is modulated through the non-uniform distribution tooth structure and the permanent magnet, magnetomotive force harmonic generated by the armature winding is fully utilized, and the motor additionally generates net output torque, so that the permanent magnet vernier motor is increasedOutput torque and torque density. And moreover, the cogging torque harmonic is analyzed by using the cogging torque phasor, so that the problem that cogging torque fluctuation is increased due to a non-uniform distribution tooth structure is solved.)

1. The method is characterized in that the permanent magnet vernier motor comprises a rotor, a rotor shaft and a rotor shaft, wherein the rotor shaft is provided with a Z-shaped rotor, and the rotor shaft is provided with a Z-shaped rotor shaft_sThe motor stator of each stator tooth and the motor rotor matched with the motor stator are arranged in the motor rotor, and Z is arranged in the motor rotor_rFor the permanent magnet, armature windings for generating winding magnetomotive force harmonic waves are respectively arranged on the stator teeth; the cogging torque optimization method for the non-uniform tooth permanent magnet vernier motor design comprises the following steps:

step S1: will Z_sEach stator tooth is annular and arranged at intervalsThe motor stator is distributed on the motor stator; z_sEach stator tooth is divided into Z_fA set of tooth units, each set of tooth units comprising n arranged sequentially in a clockwise or counterclockwise direction_gEach of the stator teeth;

step S2: 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, n in each tooth unit group_gThe stator teeth are symmetrical about the central plane of the tooth unit group;

step S3: adjusting n in each tooth unit group according to winding magnetomotive force harmonic not utilized by no-load air gap flux density harmonic_gThe positions of the stator teeth enable the distance between two adjacent stator teeth in each tooth unit group to be unequal to the distance between two adjacent tooth unit groups, so that Z is_sThe stator teeth form a non-uniform distribution tooth structure on the motor stator;

step S4: respectively combine Z with_fZ of same order position in the tooth unit group_fDividing said stator teeth into a set of cogging torque groups to divide Z_sEach stator tooth is divided into n_gForming a cogging torque group and applying a cogging torque phasor pair n_gAnd analyzing the cogging torque harmonic waves of the cogging torque groups, and adjusting the tooth width and the tooth position of the stator teeth at the same sequence position in each tooth unit group so as to change the phase and the amplitude of the cogging torque harmonic waves of each group of the cogging torque groups and eliminate specific sub-cogging torque harmonic waves.

2. The method of claim 1, wherein in said step of adjusting the width and position of said stator teeth in the same sequential position within each of said groups of teeth units, Z is the step of optimizing cogging torque for a non-uniform tooth pm vernier motor design_sThe stator teeth are arranged in an equal width mode.

3. The method of claim 2, wherein the cogging torque optimization of the non-uniform tooth permanent magnet vernier motor design is based on Z_sEach stator tooth isAfter the step of setting the equal width, calculating to obtain mechanical offset angles of the stator teeth in each tooth unit group relative to the central plane of the tooth unit group according to the specific subharmonic phase of the cogging torque of each cogging torque group, and selecting a target mechanical angle from the calculated multiple mechanical angles to determine the offset position of each stator tooth in each tooth unit group.

4. The method of claim 3, wherein after said step of determining the offset position of each stator tooth in each said set of tooth units, and under the condition that the cogging torque of each said set of cogging torque is minimal, the modulated effective sub-no-load air gap flux density harmonic content is calculated to determine the design point with the highest output torque.

5. The cogging torque optimization method for non-uniform tooth permanent magnet vernier motor design according to claim 4, 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 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.

6. The method of claim 2, wherein said adjusting is performed within each of said groups of tooth unitsIn the step of the width and position of the stator teeth in the same order, n_gAnd the cogging torque generated by the combined action of the cogging torque groups meets the relation:

wherein, T_co_gIs the cogging torque, k is the kth set of teeth, i is the i-th harmonic of the cogging torque, T_kiNco_gMagnitude of i-th harmonic component of cogging torque, N, generated for the kth set of teeth_co_gNumber 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.

7. The method for optimizing cogging torque of a non-uniform-tooth permanent-magnet vernier motor design as claimed in claim 6, wherein after the step of arranging Zs stator teeth with equal width, the cogging torque fundamental phasor of each group of the cogging torque groups is shifted by α in sequence_ngAngle of said α_ngSatisfy the relation:

wherein n is_gThe number of sets of cogging torque sets.

8. The cogging torque optimization method for non-uniform tooth permanent magnet vernier motor design according to claim 7, wherein the cogging torque fundamental phasor of each set of the cogging torque sets is shifted by α in sequence_ngAfter the angle step, the cogging torque sub-harmonic phasors of each set of the cogging torque set satisfy the relation:

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_kAnd m is a natural number, and is the offset angle of the kth group of teeth relative to a stator reference point.

9. The method of claim 1, wherein the cogging torque optimization is performed on the applied 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.

10. The method for cogging torque optimization of a non-uniform tooth permanent magnet vernier motor design of claim 1 wherein said armature winding is a concentrated armature winding.

Technical Field

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

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, although the non-uniform distribution tooth structure of the currently designed permanent magnet vernier motor makes full use of a large number of winding magnetomotive force harmonics of the armature winding, the non-uniform distribution tooth structure inevitably causes large cogging torque fluctuation, which can cause the permanent magnet vernier motor to generate vibration and noise, and the rotation speed fluctuation occurs, so that the permanent magnet vernier motor cannot run stably, and generate vibration and noise, thereby affecting the performance of the permanent magnet vernier motor.

Disclosure of Invention

The invention aims to provide a cogging torque optimization method for designing a non-uniform tooth permanent magnet vernier motor, which aims to solve the problem that cogging torque fluctuation is increased due to the non-uniform tooth distribution structure of the permanent magnet vernier motor in the prior art.

In order to achieve the purpose, the technical scheme adopted by the invention is to provide a cogging torque optimization method for designing a non-uniform-tooth permanent magnet vernier motor, the cogging torque optimization method for designing the non-uniform-tooth permanent magnet vernier motor is applied to a permanent magnet vernier motor, and the permanent magnet vernier motor comprises a rotor with a Z-shaped structure_sA motor stator with individual stator teeth and a motor rotor matched with the motor stator, wherein the motor rotorIn the son is provided with Z_rFor the permanent magnet, armature windings for generating winding magnetomotive force harmonic waves are respectively arranged on the stator teeth; the cogging torque optimization method for the non-uniform tooth permanent magnet vernier motor design comprises the following steps:

step S1: will Z_sThe stator teeth are annularly arranged on the motor stator at intervals; z_sEach stator tooth is divided into Z_fA set of tooth units, each set of tooth units comprising n arranged sequentially in a clockwise or counterclockwise direction_gEach of the stator teeth;

step S2: 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, n in each tooth unit group_gThe stator teeth are symmetrical about the central plane of the tooth unit group;

step S3: adjusting n in each tooth unit group according to winding magnetomotive force harmonic not utilized by no-load air gap flux density harmonic_gThe positions of the stator teeth enable the distance between two adjacent stator teeth in each tooth unit group to be unequal to the distance between two adjacent tooth unit groups, so that Z is_sThe stator teeth form a non-uniform distribution tooth structure on the motor stator;

step S4: respectively combine Z with_fZ of same order position in the tooth unit group_fDividing said stator teeth into a set of cogging torque groups to divide Z_sEach stator tooth is divided into n_gForming a cogging torque group and applying a cogging torque phasor pair n_gAnd analyzing the cogging torque harmonic waves of the cogging torque groups, and adjusting the tooth width and the tooth position of the stator teeth at the same sequence position in each tooth unit group so as to change the phase and the amplitude of the cogging torque harmonic waves of each group of the cogging torque groups and eliminate specific sub-cogging torque harmonic waves.

Further, in the step of adjusting the width and position of the stator teeth at the same sequential position inside each tooth unit group, Z is_sThe stator teeth are arranged in an equal width mode.

Further, after the Zs stator teeth are arranged in an equal width manner, according to the specific subharmonic phase of the cogging torque of each cogging torque group, calculating a mechanical offset angle of each stator tooth in each tooth group relative to a central plane of the tooth group, and selecting a target mechanical angle from the calculated mechanical angles to determine an offset position of each stator tooth in each tooth group.

Further, after the step of determining the offset position of each stator tooth in each tooth unit group, and under the condition that the cogging torque of each cogging torque group is minimum, calculating each effective secondary no-load air gap flux density harmonic content of the modulation to determine a design point with the highest output 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.

Further, in the step of adjusting the tooth width and the position of the stator teeth at the same sequence position in each tooth unit group, n is_gAnd the cogging torque generated by the combined action of the cogging torque groups meets the relation:

wherein, T_cogIs the cogging torque, k is the kth set of teeth, i is i of the cogging torqueSub-harmonic, 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.

Further, after the Zs stator teeth are arranged in the equal width mode, the cogging torque fundamental wave phasors of all the cogging torque groups are sequentially shifted by alpha_ngAngle of said α_ngSatisfy the relation:

wherein n is_gThe number of sets of cogging torque sets.

Further, the fundamental wave phasor of the cogging torque of each set is shifted by alpha in sequence_ngAfter the angle step, the cogging torque sub-harmonic phasors of each set of the cogging torque set satisfy the relation:

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_kAnd m is a natural number, and is the offset angle of the kth group of teeth relative to a stator reference point.

10. Further, applying a cogging torque phasor pair 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.

Further, the armature winding is a concentrated armature winding.

The cogging torque optimization method for the design of the non-uniform tooth permanent magnet vernier motor has the beneficial effects that: compared with the prior art, the tooth space torque optimization method for the design of the non-uniform tooth permanent magnet vernier motor provided by the invention is characterized in that the Z-shaped permanent magnet vernier motor is annularly and alternately arranged on the stator of the motor_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, the magnetomotive force harmonic generated by the armature winding is fully utilized, the motor can additionally generate net output torque, and therefore the output torque and the torque density of the permanent magnet vernier motor are increased. And, applying cogging torque phasor pairs n_gCogging torque harmonics of a set cogging torque setAnd analyzing, and adjusting the tooth width and the position of the stator teeth at the same sequence position in each tooth unit group to change the phase and the amplitude of the cogging torque harmonic of each group of tooth torque groups, eliminate specific secondary cogging torque harmonic, optimize the cogging torque of the non-uniform tooth permanent magnet vernier motor and solve the problem of increased cogging torque fluctuation caused by a non-uniform distribution tooth structure.

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

fig. 2 is a schematic view of a three-dimensional structure in which a stator winding is wound on a motor stator designed by a cogging torque optimization method for designing a non-uniform-tooth permanent magnet vernier motor according to an embodiment of the present invention;

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

fig. 4 is a schematic top view of a motor stator designed by the cogging torque optimization method for designing a non-uniform-tooth permanent magnet vernier motor according to an embodiment of the present invention, and a stator winding is wound on the motor stator;

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

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

fig. 7 is a schematic structural diagram of a cogging torque grouping measured by a cogging torque optimization 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 cogging torque optimization method for the non-uniform-tooth permanent magnet vernier motor design according to the embodiment of the present invention;

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

FIG. 10 shows a cogging torque optimization method for designing a non-uniform-tooth permanent magnet vernier motor according to an embodiment of the present invention_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 cogging torque optimization method for a non-uniform tooth permanent magnet vernier motor design according to the present invention will now be described. The invention provides a tooth space torque optimization method for designing a non-uniform tooth permanent magnet vernier motor, which is applied to a permanent magnet vernier motor_sThe motor comprises a motor stator 1 of each stator tooth 11 and a motor rotor 2 matched with the motor stator 1, wherein Z is arranged in the motor rotor 2_rFor the permanent magnet 3, each stator tooth 11 is respectively provided with an armature winding 4 for generating winding magnetomotive force harmonic waves; the cogging torque optimization method for the non-uniform tooth permanent magnet vernier motor design comprises the following steps:

step S1: will Z_sThe stator teeth 11 are annularly arranged on the motor stator 1 at intervals; z_sEach of the stator teeth 11 is divided into Z_fA set of gear units 5, each set of gear units 5 comprising n arranged in sequence in a clockwise or counterclockwise direction_gThe stator teeth 11;

step S2: under the conditions 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 in each tooth unit group 5_gThe stator teeth 11 are symmetrical with respect to a center plane 51 of the tooth unit group 5.

In this step, the included angle between the central planes 51 of any two adjacent tooth unit groups 5 is equal and each tooth unit group 5 is ensuredN in each tooth unit group 5 under the condition that the position of the central surface 51 is not changed_gThe stator teeth 11 are arranged symmetrically with respect to the centre plane 51 of the set of teeth 5, and the sets of teeth 5 are displaced n within each set of teeth 5 symmetrically with respect to the centre plane 51 of each set of teeth 5_gAnd the stator teeth 11 are positioned to introduce a specific number of no-load air gap flux density harmonics according to the winding magnetomotive force harmonics not utilized by the no-load air gap flux density harmonics. 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: adjusting n in each tooth unit group 5 according to winding magnetomotive force harmonic not utilized by no-load air gap flux density harmonic_gThe positions of the stator teeth 11 are such that the distance between two adjacent stator teeth 11 in each tooth unit group 5 is not equal to the distance between two adjacent tooth unit groups 5, so as to make Z be equal to_sThe stator teeth 11 form a non-uniform distribution tooth structure on the motor stator 1.

In this step, specifically, in step S2, according to the operating principle of the permanent magnet motor, the torque of the permanent magnet motor is derived from the interaction between the flux density of the permanent magnet 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 number of pole pairs of the armature winding and the number of the stator teeth 11, the number of pole pairs p of the armature winding of the vernier motor is often low (p is less than or equal to 3), as shown in fig. 8, the pole pair proportion is selected to be 2-16-18(p is p-18) in the short-distance distributed winding example of the open slot vernier motor with 18 three phases of the stator teeth 11-Z_r-Z_s) Under the condition, the A-phase winding is divided into p groups, each group of the A-phase winding comprises Zs/3/p stator teeth 11, the Zs/3/p stator teeth 11 are wound in the same direction and are symmetrically distributed on the periphery of the motor stator 1 at intervals of 360/p angles, and therefore the p-pair pole effect is achieved. 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 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_mAnd n is a natural number which is sequentially valued from small to large in terms of the mechanical position of the rotor.

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_gWhile the positions of the stator teeth 11 are equal, 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 in each tooth unit group 5_gThe individual stator teeth 11 are arranged symmetrically with respect to the center plane 51 of the tooth unit group 5, as shown in the figure4, respectively. 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.

Preferably, referring to fig. 4, as a specific embodiment of the cogging torque optimization method for the non-uniform tooth permanent magnet vernier motor design provided in the present invention, n in each tooth unit group 5 is adjusted_gIn the position step of each stator tooth 11, the distance between any two adjacent tooth unit groups 5 is equal, and Z is_fSets of tooth units 5 and Z_sThe stator teeth 11 respectively satisfy the armature winding symmetry condition. According to the total number Z of 11 stator teeth_sWhen determining the symmetry of the three-phase armature winding, Z_sThe conditions which need to be met when the stator teeth 11 are non-uniformly distributed are that the armature windings in the ABC three-phase winding mode are ensured to have a phase difference of 120 degrees in each phase, the A-phase sub-winding and the B-phase sub-winding have a phase difference of 120 degrees, and the B-phase sub-winding and the C-phase sub-winding have a phase difference of 120 degrees, so that in the process of running of the permanent magnet vernier motor, a rotor can not generate strong unilateral magnetic pull force, and the noise of the three-phase motor in high-speed running is reduced. 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.

Step S4: respectively combine Z with_fZ of the same order position in each of the tooth unit groups 5_fEach of the stator teeth 11 is divided into a set of cogging torque groups to divide Z_sEach stator tooth 11 is divided into n_gForming a cogging torque group and applying a cogging torque phasor pair n_gAnd analyzing the cogging torque harmonics of the cogging torque groups, and adjusting the tooth widths and the positions of the stator teeth 11 in the same sequence position in each tooth unit group 5 to change the phase and the amplitude of the cogging torque harmonics of each group of the cogging torque groups and eliminate specific sub-cogging torque harmonics.

Specifically, please refer to fig. 6 and 7 for Z_fZ of the same sequential position (stator teeth 11 of the same stripe in fig. 6) inside the tooth unit group 5_fThe individual stator teeth 11 are divided into a set of cogging torque groups, then Z is divided_sEach stator tooth 11 is divided into n_gGroup cogging torque group, see FIG. 7, and apply cogging torque phasor vs. Z_fThe cogging torque harmonics of the stator teeth 11 in the same sequence 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 are changed by changing the tooth width and position of the stator teeth 11 in the same sequence position in each tooth unit group 5, so that the specific sub-cogging torque harmonic is eliminated.

Compared with the prior art, the tooth space torque optimization method for the design of the non-uniform tooth permanent magnet vernier motor provided by the invention has the advantages that the Z-shaped permanent magnet vernier motor is annularly and alternately arranged on the motor stator_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, the magnetomotive force harmonic generated by the armature winding is fully utilized, the motor can additionally generate net output torque, and therefore the output torque and the torque density of the permanent magnet vernier motor are increased. And, applying cogging torque phasor pairs n_gThe cogging torque harmonics of the cogging torque groups are analyzed, the tooth width and the position of the stator teeth at the same sequence position in each tooth unit group are adjusted, so that the phase and the amplitude of the cogging torque harmonics of each group of cogging torque groups are changed, specific secondary cogging torque harmonics are eliminated, the cogging torque of the non-uniform tooth permanent magnet vernier motor is optimized, and the problem that cogging torque fluctuation is increased due to a non-uniform distribution tooth structure is solved.

Preferably, please refer to fig. 3 and 4, which are the non-uniform tooth permanent magnet vernier motor designs provided by the present inventionIn the step of adjusting the width and position of the stator teeth 11 at the same sequential position within each tooth unit group 5, Z is an embodiment of the cogging torque optimization method_sThe stator teeth 11 are arranged in equal width to eliminate Z_sThe teeth together produce a specific sub-harmonic of the cogging torque.

In this step, Z is_sEach stator tooth 11 is set to be equal in width, and n is controlled_gThe 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 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 implementation mode of the cogging torque optimization method for the design 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 of the cogging torque optimization method for designing the non-uniform tooth permanent magnet vernier motor provided in the present invention, after the step of determining the offset position of each stator tooth 11 in each tooth unit group 5, and under the condition that the cogging torque of each cogging torque group is minimum, the modulated effective sub-no-load air gap flux density harmonic content is calculated to determine the design point with the highest output torque.

Specifically, the modulated effective sub-no-load air gap flux density harmonic content satisfies the following relational expression:

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 embodiment of the cogging torque optimization method for the non-uniform tooth permanent magnet vernier motor design provided by the present invention, in the step of adjusting the tooth width and position of the stator teeth 11 in the same sequence position in each tooth unit group 5, n is_gThe cogging torque generated by the group cogging torque group together satisfies the following relation:

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_kIs the offset angle of the kth set of teeth relative to the stator reference point.

In this step, as shown in FIGS. 5 and 6, according to Z_sDividing the tooth unit group 5 of the stator teeth 11 which are not uniformly distributed into Z_sEach stator tooth 11 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 becomes large when the stator teeth 11 are non-uniformly distributed. As shown in fig. 6, although n is inside each tooth unit group 5_gThe stator teeth 11 are non-uniformly distributed, but because of Z_fN inside the set of gear teeth 5_gThe stator teeth 11 are distributed in the same way, and the central planes 51 of the tooth unit groups 5 are spaced at the same intervalAt this time, Z_fZ of the same sequential position in the set of gear units 5_fThe stator teeth 11 are spaced apart by the same distance, which is an even distribution.

Preferably, as a specific implementation of the cogging torque optimization method for the non-uniform tooth permanent magnet vernier motor design provided by the invention, Z is used_sAfter the step of setting the width of each stator tooth 11 to be equal, the fundamental wave phasor of the cogging torque of each group of cogging torque groups is shifted by alpha in sequence_ngAngle, minimizing overall cogging torque, α_ngThe angle can be expressed as:

wherein n is_gThe number of sets of cogging torque sets.

At this time, the cogging torque fundamental wave phasors of each set of cogging torque sets are sequentially shifted by α_ngAfter the angle step, the cogging torque subharmonic phasors of each group of 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 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 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 11 in each tooth unit group 5 is 4, namely n_gThe case that the group cogging torque is 4 groupsDescription is carried out: as shown in fig. 8, 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 cogging torque optimization method for the non-uniform tooth permanent magnet vernier motor design provided in the present invention, in the non-uniform tooth distribution structure, the relative position angle of each cogging torque group can be adjusted sufficiently to minimize the cogging torque result of the stator teeth 11 of each cogging torque group acting together. And in the application of cogging torque phasor pair n_gIn the step of analyzing the cogging torque harmonic waves of the set of cogging torque sets, the phasors of each set of cogging torque sets 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_kIs the offset angle of the kth set of teeth relative to the stator reference point.

Preference is given toIn the specific implementation mode of the cogging torque optimization method for the non-uniform tooth permanent magnet vernier motor design provided by the invention, Z is used_fThe tooth unit groups 5 are wound around Z in the step of arranging the same distribution structure of the stator teeth 11_sThe plurality of centralized armature windings 4 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.

In step S3, since each pair of poles p is wound with the same polarity as the corresponding tooth, the size of p can be sufficiently adjusted within the range of the number of teeth, and the number Z of tooth unit groups should be secured in the case of three-phase concentrated double-layer armature windings, which is referred to as an example_fNumber n of stator teeth 11 of each tooth unit group 5_gThe following relation is satisfied:

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.