A stator skew effect evaluation design method and system based on a genetic algorithm

Abstract

The application provides a stator skew effect evaluation design method and system based on a genetic algorithm, relates to the technical field of interior permanent magnet synchronous motors, and comprises the following steps: a finite element simulation model of the permanent magnet synchronous motor is constructed, motor parameters are preset, and a grid is set; under a non-excitation condition, tooth slot torque data are obtained by scanning in a preset skew angle range; after three-phase current excitation is added, a no-load back electromotive force waveform diagram is generated, and a total harmonic distortion rate of the back electromotive force is analyzed; an output torque waveform diagram is generated based on the scanning data to calculate torque pulsation; and the tooth slot torque, the distortion rate, and the torque pulsation are taken as evaluation indexes to input a genetic algorithm to calculate an optimal skew angle. According to the method, multiple parameters are optimized in cooperation, the tooth slot torque, the distortion rate, and the torque pulsation are taken as joint evaluation indexes, the comprehensive performance is optimal through genetic algorithm weight distribution, torque pulsation and harmonic distortion are significantly reduced, motor operation stability and efficiency are improved, and the problem of skew effect quantitative evaluation design is solved.

Description

Technical Field

[0001] The present application relates to the technical field of built-in permanent magnet synchronous motors, and in particular to a stator skew effect evaluation and design method and system based on a genetic algorithm. Background Art

[0002] In motor manufacturing, stator slot skew is a key technology for suppressing motor vibration and noise. By modulating the air gap magnetic field through axial skew, vibration and noise can be reduced, improving overall motor performance. However, current evaluation and design methods for stator slot skew effects are incomplete, making it difficult to quantify the comprehensive impact of the slot angle on torque stability. High-speed permanent magnet synchronous motors require simultaneous optimization of both cogging torque (a direct effect) and no-load back EMF harmonics (an indirect effect), but the industry lacks corresponding evaluation and design methods and systems. Summary of the Invention

[0003] To solve the above technical problems, the present application provides a stator skew effect evaluation and design method based on genetic algorithm. By comprehensively considering multiple factors such as slot torque, no-load back electromotive force, and torque pulsation, the stator skew effect is accurately evaluated, and the design of the optimal skew angle is determined, thereby optimizing the motor performance.

[0004] The technical solutions provided in this application are as follows:

[0005] A stator skew effect evaluation and design method based on a genetic algorithm comprises the following steps:

[0006] Import the prepared motor model diagram into the finite element software, build a finite element simulation model of the permanent magnet synchronous motor, preset the simulation model parameters of the motor, and set the grids for the stator, rotor, and air gap;

[0007] Taking the zero-degree stator straight slot as the reference, under no excitation conditions, with the preset slot angle θj as the step size, multiple sets of sampling data are scanned within the preset stator slot angle range to generate a cogging torque waveform and obtain the cogging torque data;

[0008] Add three-phase current excitation in the simulation software, generate the no-load back electromotive force periodic function waveform based on the multiple sets of sampled data obtained by scanning, extract the fundamental and harmonic components through Fourier transform processing, and calculate the total harmonic distortion rate of the back electromotive force. Alternatively, based on the fundamental and harmonic components obtained in the case of straight stator slots, introduce the skew coefficient K i The total harmonic distortion rate of back electromotive force is calculated;

[0009] Generate output torque waveform based on multiple sets of sampled data acquired through scanning, and calculate output torque pulsation;

[0010] The cogging torque, total harmonic distortion rate of back electromotive force, and torque ripple are used as evaluation indicators, and weights are set respectively. The three sets of data corresponding to the skew angle are input, and the optimal stator skew angle is calculated through genetic algorithm.

[0011] Furthermore, the simulation model parameters of the preset motor include: pole arc coefficient, stator core and rotor core materials, and permanent magnet materials;

[0012] The stator / rotor mesh was set to 4 mm and the air gap to 0.1 mm.

[0013] Furthermore, the preset stator slot angle range is 0-30 degrees; the θj angle step value range is 0-1 degree.

[0014] Furthermore, the cogging torque data is analyzed by the following formula:

[0015] ;

[0016] Where: z is the number of stator slots; L a is the axial length of the stator core; R1 is the inner radius of the stator; R2 is the outer radius of the armature; G n is the Fourier decomposition coefficient of the square of the relative air gap permeability; n is the number of cogging torques; m 0 is the vacuum permeability; is the relative position angle between the stator and rotor; B ran and B rbn is the Fourier decomposition coefficient of the quadratic air gap magnetic flux;

[0017] Furthermore, the relationship between the stator skew slot and the air gap flux density is expressed as follows:

[0018] ;

[0019] ;

[0020] Where: B ran and B rbn is the Fourier decomposition coefficient of the air gap flux squared; z is the number of stator slots; n is the number of cogging torques; i j is the stator slot offset angle; p is the number of rotor pole pairs; α p is the pole arc coefficient of the permanent magnet pole.

[0021] Furthermore, a three-phase current excitation is added in the simulation software, and the three-phase current excitation is set according to the following formula:

[0022] ;

[0023] The calculation formula of the total harmonic distortion rate of back electromotive force is:

[0024] ;

[0025] Among them, THD is the total harmonic distortion rate of back electromotive force; U1 is the effective value of fundamental voltage; U3, U 5、 U 7... U n etc. are the effective values ​​of each harmonic voltage;

[0026] The introduction of the skew coefficient K i The total harmonic distortion rate of the back electromotive force is calculated to satisfy the expression:

[0027] Harmonic amplitude after skew slot = straight slot amplitude × K i .

[0028] Furthermore, the relationship between the slant distance coefficient β and the skew angle satisfies the expression:

[0029] ;

[0030] Where: τ P is the pole distance; L a is the axial length of the stator core; i j is the stator slot offset angle;

[0031] Chute coefficient K i formula:

[0032] ;

[0033] Where: oh is the harmonic order; β is the slant distance coefficient.

[0034] Furthermore, the output torque waveform is generated based on the multiple sets of sampled data obtained by scanning, and the output torque pulsation is calculated; specifically, the output torque T of the multiple sets of sampled data is generated by simulation. out , set the highest peak and the lowest peak in the waveform as T omax With T omin , subtract the two components and divide by the average output torque Ton to obtain the output torque ripple Tr; the specific calculation formula is:

[0035] .

[0036] This application also provides a stator skew effect evaluation and design system based on a genetic algorithm, comprising:

[0037] The motor model construction module is used to import the prepared motor model diagram into the finite element software, build the finite element simulation model of the permanent magnet synchronous motor, preset the simulation model parameters of the motor, and set the grids of the stator, rotor, and air gap;

[0038] The cogging torque simulation module is used to obtain multiple sets of sampling data by scanning the preset stator skew angle range with a preset slot angle θj as a step size, taking the zero-degree stator straight slot as the reference under no excitation conditions, and generating a cogging torque waveform to obtain the cogging torque data.

[0039] Excitation condition setting module, used to add three-phase current excitation in simulation software;

[0040] The no-load back-electromotive force analysis module is used to generate a no-load back-electromotive force periodic function waveform based on multiple sets of sampled data acquired through scanning, extract the fundamental and harmonic components through Fourier transform processing, and calculate the total harmonic distortion rate of the back-electromotive force, or, based on the fundamental and harmonic components acquired in the case of straight stator slots, introduce the skew coefficient K i The total harmonic distortion rate of back electromotive force is calculated;

[0041] A torque pulsation calculation module is used to generate an output torque waveform diagram based on multiple sets of sampled data obtained through scanning, and calculate the output torque pulsation;

[0042] The genetic algorithm evaluation module is used to use the cogging torque, back electromotive force total harmonic distortion rate, and torque ripple as evaluation indicators, set weights for each, input the three sets of data corresponding to the skew angle, and calculate the optimal stator skew angle through the genetic algorithm.

[0043] Furthermore, the three-phase current is set to excite according to the formula:

[0044] ;

[0045] The calculation formula of the total harmonic distortion rate of back electromotive force is:

[0046] ;

[0047] Among them, THD is the total harmonic distortion rate of back electromotive force; U1 is the effective value of fundamental voltage; U3, U 5、 U 7... U n etc. are the effective values ​​of each harmonic voltage;

[0048] Chute coefficient Ki The formula is:

[0049] ;

[0050] Where: oh is the harmonic order, β is the slant distance coefficient;

[0051] Introducing the skew coefficient K i The total harmonic distortion rate of the back electromotive force is calculated to meet the expression:

[0052] Harmonic amplitude after skew slot = straight slot amplitude × K i .

[0053] This application uses a genetic algorithm to evaluate the stator skew effect by comprehensively considering multiple factors such as slot torque, no-load back electromotive force, and torque pulsation. The slot torque, back electromotive force total harmonic distortion rate, and torque pulsation are used as joint evaluation indicators. The optimal comprehensive performance is achieved through genetic algorithm weight allocation, which can accurately determine the optimal slot angle and effectively improve the motor performance.

[0054] Beneficial effects:

[0055] Optimizing no-load back EMF: Introducing the skew coefficient K i The total harmonic distortion rate of the back-EMF was analyzed. The calculation is simple and can quantify the attenuation effect of high-order harmonics. The results show that the total harmonic distortion rate of the back-EMF dropped from 8.7% to 1.2%, and the waveform approached the ideal sine wave. This not only improves the output torque stability, but also indirectly improves the motor efficiency and reduces energy loss during motor operation.

[0056] The method of the present application can find the skew slot angle that maximizes the reduction in cogging torque, and by calculating the output torque pulsation and combining it with genetic algorithm for optimization, it can effectively reduce the torque pulsation during motor operation, making the motor output torque more stable and improving the motor's operating quality and reliability.

[0057] This application provides a systematic design evaluation method and system that comprehensively considers the impact of multiple factors on motor performance, avoiding the limitations of traditional methods that rely on single-factor optimization. Through the global optimization capabilities of genetic algorithms, the optimal skew angle can be quickly and accurately found, providing a scientific basis for motor design, shortening the design cycle and reducing R&D costs.

[0058] The method of this application is not limited by the specific parameters of the motor and has wide applicability. By adjusting the preset parameters and weights, the design of the same type of built-in permanent magnet synchronous motor can be optimized to meet the needs of different application scenarios.

[0059] This application effectively solves the problems of inaccurate evaluation and difficult optimization of the stator skew effect in the existing technology through an innovative evaluation design method and system, provides strong technical support for improving the performance of built-in permanent magnet synchronous motors, and has important practical application value and broad application prospects. BRIEF DESCRIPTION OF THE DRAWINGS

[0060] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments recorded in this application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0061] Figure 1 This is a flowchart of a stator skew effect evaluation and design method based on genetic algorithm for this application;

[0062] Figure 2 Schematic diagram of the cross-sectional structure of the stator in an interior permanent magnet synchronous motor (2a is a stator straight slot structure, 2b is a stator skew slot structure);

[0063] Figure 3 Schematic diagram of an axial cross-section structure of a built-in permanent magnet synchronous motor;

[0064] Figure 4 : is a cogging torque waveform diagram in this embodiment;

[0065] Figure 5 1 is a diagram of a no-load back electromotive force waveform in this embodiment;

[0066] Figure 6 for Figure 5 Fourier decomposition diagram of the no-load back EMF waveform;

[0067] Figure 7 FIG1 is a waveform diagram of an air gap magnetic flux density in this embodiment;

[0068] Figure 8 for Figure 7 Fourier decomposition diagram of the air gap magnetic flux waveform;

[0069] Figure 9 FIG1 is a diagram of an output torque waveform in this embodiment; DETAILED DESCRIPTION

[0070] In order to help those skilled in the art better understand the technical solutions in this application, the technical solutions in the embodiments of this application will be clearly and completely described below. Obviously, the embodiments described are only part of the embodiments of this application, not all of the embodiments. Based on the embodiments in this application, all other embodiments obtained by those skilled in the art without making any creative efforts shall fall within the scope of protection of this application.

[0071] It should be noted that when an element is referred to as being “fixed on” or “set on” another element, it can be directly on the other element or indirectly set 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 indirectly connected to the other element.

[0072] It should be understood that the terms "length", "width", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside", "outside", etc., indicating the orientation or positional relationship, are based on the orientation or positional relationship shown in the accompanying drawings, and are only for the convenience of describing the present application and simplifying the description, and do not indicate or imply that the genetic algorithm-based stator skew effect evaluation design method or element must have a specific orientation, be constructed and operated in a specific orientation, and therefore should not be understood as limiting the present application.

[0073] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be understood to indicate or imply relative importance or implicitly specify the number of technical features indicated. Thus, a feature specified as "first" or "second" may explicitly or implicitly include one or more of such features. Throughout the description of this application, "plurality" or "several" means two or more, unless otherwise specifically defined.

[0074] It should be noted that the structures, proportions, sizes, etc. illustrated in the drawings of this specification are only used to match the contents disclosed in the specification for people familiar with this technology to understand and read, and are not used to limit the conditions under which this application can be implemented. Therefore, they have no substantive technical significance. Any structural modification, change in proportional relationship or adjustment of size should still fall within the scope of the technical content disclosed in this application without affecting the efficacy and purpose that can be achieved by this application.

[0075] The embodiments of the present application are written in a progressive manner.

[0076] See also Figure 1 to Figure 9 As shown, a stator skew effect evaluation and design method based on genetic algorithm includes the following steps:

[0077] Import the prepared motor model diagram into the finite element software, build a finite element simulation model of the permanent magnet synchronous motor, preset the simulation model parameters of the motor, and set the grids for the stator, rotor, and air gap;

[0078] Taking the zero-degree stator straight slot as the reference, under no excitation conditions, with the preset slot angle θj as the step size, multiple sets of sampling data are scanned within the preset stator slot angle range to generate a cogging torque waveform and obtain the cogging torque data;

[0079] Add three-phase current excitation in the simulation software, generate the no-load back electromotive force periodic function waveform based on the multiple sets of sampled data obtained by scanning, extract the fundamental and harmonic components through Fourier transform processing, and calculate the total harmonic distortion rate of the back electromotive force. Alternatively, based on the fundamental and harmonic components obtained in the case of straight stator slots, introduce the skew coefficient K i The total harmonic distortion rate of back electromotive force is calculated;

[0080] Generate output torque waveform based on multiple sets of sampled data acquired through scanning, and calculate output torque pulsation;

[0081] The cogging torque, total harmonic distortion rate of back electromotive force, and torque ripple are used as evaluation indicators, and weights are set respectively. The three sets of data corresponding to the skew angle are input, and the optimal stator skew angle is calculated through genetic algorithm.

[0082] The simulation model parameters of the preset motor include: pole arc coefficient, stator core and rotor core materials, and permanent magnet materials. As a feasible approach, the simulation model parameters of the motor are set with reference to Table 1:

[0083] Table 1

[0084]

[0085] The motor model can be drawn by CAD software. The motor designed in this method is a 4-pole 24-slot internal permanent magnet synchronous motor. p（ The cogging torque cycle is 1, the pole arc coefficient is 0.775, and both the stator and rotor cores are made of 20WTG-1500 material. The permanent magnet steel is Sm2Co17-32H (2:17 samarium-cobalt alloy), a rare earth metal with excellent magnetic properties. The simulation model was then created in the finite element simulation software Maxwell. The stator, rotor, and air gap were meshed. The stator and rotor mesh size was 4 mm, and the air gap was 0.1 mm.

[0086] Furthermore, in the preset stator skew angle range of 0-30 degrees and the θj angle step size of 0-1 degree, in this embodiment, the preset stator skew angle range is preferably 0-22.5 degrees and the θj angle step size is 0.75 degrees. Specifically, without any excitation, with a 0° straight slot as the comparison object, the internal permanent magnet motor rotates at a constant value of 1° / s, with a skew angle θj of 0.75° as the step size, 30 sets of data are scanned from 0 to 22.5° in the simulation finite element software, and a cogging torque waveform is generated to obtain the cogging torque data. The cogging torque data is analyzed by the following formula:

[0087] ;

[0088] The analytical formula of the cogging torque is referred to as Equation 1), where: z is the number of stator slots; L a is the axial length of the stator core; R1 is the inner radius of the stator; R2 is the outer radius of the armature; G n is the Fourier decomposition coefficient of the square of the relative air gap permeability; n is the number of cogging torques; m 0 is the vacuum permeability; is the relative position angle between the stator and rotor; B ran and B rbn is the Fourier decomposition coefficient of the quadratic air gap magnetic flux;

[0089] Furthermore, the cogging torque in a permanent magnet motor is caused by the interaction between the permanent magnets and the motor core slot structure. When the armature winding is not energized, it is the negative derivative of the magnetic field energy with respect to the position angle. That is, the above formula 1) is calculated according to the following formula:

[0090] 2);

[0091] In formula 2): W is the energy stored in the motor magnetic field, is the relative position angle between the stator and rotor, T cog is the permanent magnet motor cogging torque;

[0092] 3);

[0093] Where: m 0 is the relative magnetic permeability, B r ( (i) is the remanence of the permanent magnet, h m ( (i) is the distribution of the permanent magnet's magnetizing length along the circumferential direction, d ( i , α) is the effective air gap length, V is the integral area of ​​the permanent magnet and the air gap;

[0094] To [h m ( i ) / h m ( i )+ δ( i , α)] 2 and B r 2 ( (i) Expand the expression after Fourier transform:

[0095] 4);

[0096] 5);

[0097] Where: G0 is a constant; B r0 =α P (B r ) 2 ; B ran and B rbn is the Fourier decomposition coefficient of the air gap magnetic flux squared; B r is the remanent magnetism of the permanent magnet at 0 degrees; α p is the pole arc coefficient of the permanent magnet pole;

[0098] It should be noted that ; Among them, B( i , α) is the distribution function of the air gap flux density; θ represents the angle of change along the motor rotation direction;

[0099] Substituting Equations 4) and 5) into Equation 3) and then combining Equation 2) yields the analytical formula for the cogging torque in Equation 1).

[0100] Furthermore, the relationship between the stator skew slot and the air gap flux density is expressed as follows:

[0101] 6);

[0102] 7);

[0103] Where: B ran and B rbn is the Fourier decomposition coefficient of the air gap flux squared; z is the number of stator slots; n is the number of cogging torques; i j is the stator slot offset angle; pis the number of rotor pole pairs; α p is the pole arc coefficient of the permanent magnet pole.

[0104] The stator slot is skewed by changing the air gap flux density B ran With B rbn The angle affects the motor output torque fluctuation.

[0105] Furthermore, a three-phase current excitation is added in the simulation software, and the three-phase current excitation is set according to the following formula:

[0106] 8);

[0107] The calculation formula of the total harmonic distortion rate of back electromotive force is:

[0108] 9);

[0109] Among them, THD is the total harmonic distortion rate of back electromotive force; U1 is the effective value of fundamental voltage; U3, U 5、 U 7... U n etc. are the effective values ​​of each harmonic voltage;

[0110] The introduction of the skew coefficient K i The total harmonic distortion rate of the back electromotive force is calculated to satisfy the expression:

[0111] Harmonic amplitude after skew slot = straight slot amplitude × K i .

[0112] Furthermore, the relationship between the slant distance coefficient β and the skew angle satisfies the expression:

[0113] 10);

[0114] Where: τ P is the pole distance; L a is the axial length of the stator core; i j is the stator slot offset angle;

[0115] Chute coefficient K i formula:

[0116] 11);

[0117] Where: oh is the harmonic order; β is the slant distance coefficient.

[0118] As a feasible method, the present application uses the no-load back electromotive force periodic function waveform generated by scanning 30 sets of sampling data as a time domain signal to obtain a series of numerical points, and then performs FFT (Fourier) processing to map the obtained periodic function to the frequency domain to obtain the fundamental wave and higher harmonics.

[0119] 12);

[0120] Where: Z represents the harmonic amplitude, the real part a and the imaginary part b represent the coefficients of the cosine and sine components respectively;

[0121] It should be noted that those skilled in the art know that the effective value of the harmonic voltage can be calculated using the formula of the harmonic amplitude.

[0122] The fundamental wave has the smallest frequency, so the phase difference is the smallest, and the skew slot will not cause much loss to the fundamental wave; the harmonics have higher frequencies and larger phase differences, and can cancel each other out when superimposed. Therefore, after the stator skew slots are installed, the fundamental wave and each harmonic must be multiplied by a skew coefficient less than 1 on the basis of the straight slots. K i In this application method, by introducing the skew coefficient K i , the total harmonic distortion of the motor's back EMF is obtained. This calculation is simple and can also quantify the effect of high-order harmonic attenuation. The stator skew slots, through axial offset and superposition, form a gradient magnetic field coupling, which can selectively suppress high-order spatial harmonics through phase modulation. Specifically, when the motor skews one stator tooth pitch, a skew coefficient is introduced into the fundamental wave and each order harmonic. The skew coefficient is used to correct the amplitude of the fundamental wave and each order harmonic, thereby obtaining the amplitude of the fundamental wave and each order harmonic during skew. The voltage waveform of the generator during skew is calculated through synthetic superposition.

[0123] After actual testing and verification, the quantitative analysis data of harmonic suppression is shown in Table 2:

[0124] Table 2

[0125]

[0126] For high-order harmonic elimination, the amplitudes of the 5th, 7th and 11th harmonics are attenuated by 32.31%, 84.53% and 87.81% respectively, effectively suppressing the electromagnetic noise and vibration caused by the slot effect and magnetic field distortion. At the same time, the total harmonic distortion rate of the back electromotive force is reduced from 8.7% in the straight slot case to 1.2% in the optimal skew slot, and the waveform approaches the ideal sine wave; effectively improving the output torque stability.

[0127] Furthermore, the output torque waveform is generated based on the multiple sets of sampled data obtained by scanning, and the output torque pulsation is calculated; specifically, the output torque T of the multiple sets of sampled data is generated by simulation. out, set the highest peak and the lowest peak in the waveform as T omax With T omin , subtract the two components and divide by the average output torque Ton to obtain the output torque ripple Tr; the specific calculation formula is:

[0128] .

[0129] In this embodiment, the lower and upper limits of the chute angle are preferably set to 0°~22.5°; a value of 0° represents a straight chute state. The population size of each generation is set in the genetic algorithm. The population size determines the number of individuals (candidate solutions for the chute angle) in each generation. The population size is set to 50, and the maximum number of iterations is 100, that is, the algorithm runs for a maximum of 100 generations until the stopping condition is met. Each generation represents an "evolution", that is, new candidate solutions are generated through selection, crossover and mutation.

[0130] It can be understood that a value of 0° represents a straight slot state. In this embodiment, the preferred angle step is 0.75, and the number of angle points numDataPoints = 31; (22.5 - 0) / 0.75 + 1 = 31. The sampled data of the skew slot angle, cogging torque, back electromotive force total harmonic distortion rate, and torque ripple read by the MATLAB software are shown in Table 3:

[0131] Table 3

[0132]

[0133] As a specific application of the algorithm:

[0134] clc;

[0135] clear all;

[0136] % Import data from the obtained table file

[0137] filename = 'jyl.xlsx';

[0138] data = readtable(filename); % Read table data

[0139] % Assume that the column names of the data table are: 'Angle', 'ToothSlotTorque', 'TotalHarmonic Distortion', 'TorqueRipple'

[0140] angles = data.Angle; % Get the angle column

[0141] toothSlotTorque = data.ToothSlotTorque; % Get the tooth slot torque column

[0142] Total Harmonic Distortion = data.Total Harmonic Distortion; % Get the total harmonic distortion (THD) column of back EMF

[0143] torqueRipple = data.TorqueRipple; % Get the torque ripple column

[0144] % Weight

[0145] weight1 = 0.3;

[0146] weight2 = 0.3;

[0147] weight3 = 0.4;

[0148] % Define genetic algorithm optimization function

[0149] fitnessFunction = @(x) weight1 * interp1(angles, toothSlotTorque, x,'linear', 'extrap') + ...

[0150] weight2 * interp1(angles, Total Harmonic Distortion, x, 'linear', 'extrap') + ...

[0151] weight3 * interp1(angles, torqueRipple, x, 'linear', 'extrap');

[0152] % Genetic algorithm parameter settings

[0153] lb = 0; % lower limit of the angle

[0154] ub = 22.5; % upper limit of angle

[0155] options = optimoptions('ga', 'Display', 'iter', 'PopulationSize', 50,'MaxGenerations', 100);

[0156] % Run the genetic algorithm

[0157] [optimalAngle, minFitness] = ga(fitnessFunction, 1, [], [], [], [],lb, ub, [], options);

[0158] % Output optimal chute angle

[0159] disp(['Optimal chute angle:', num2str(optimalAngle)]);

[0160] disp(['Corresponding comprehensive evaluation value:', num2str(minFitness)]);

[0161] In this implementation, cogging torque, back EMF total harmonic distortion (THD), and torque ripple (Tr) were weighted to 0.3, 0.3, and 0.4, respectively. Three sets of data corresponding to the skew angle were input, and a genetic algorithm was used to calculate the optimal motor performance for this motor design with a skew angle θj = 15°. The genetic algorithm used in this application uses a population size of 50 to ensure diversity while minimizing computational overhead. A maximum number of 100 iterations ensures optimal solutions within a reasonable timeframe. Weights are determined based on the impact of each evaluation metric on motor performance. Torque ripple has a significant impact on motor performance, so it receives the highest weight.

[0162] This application uses the control variable method to actually verify the result data of stator skew = 15°, and determines that when the stator skew angle is appropriate, the tooth slot torque amplitude can be reduced. It is minimum when it is tilted across one stator tooth pitch, reducing it to 0.0953mNm. The optimal reduction of the stator skew for this data is measured to be 99.93%.

[0163] This application also provides a stator skew effect evaluation and design system based on a genetic algorithm, comprising:

[0164] The motor model construction module is used to construct a finite element simulation model of the permanent magnet synchronous motor, preset the simulation model parameters of the motor, and set the grid for the stator, rotor, and air gap;

[0165] The cogging torque simulation module is used to obtain multiple sets of sampled data by scanning the preset stator skew angle range with the skew angle θj as the step size under no excitation conditions, generate a cogging torque waveform, and obtain cogging torque data;

[0166] The excitation condition setting module is used to set the three-phase current as the excitation in the simulation. The three-phase current is set as the excitation according to formula 8):

[0167] 8);

[0168] The no-load back-EMF analysis module is used to perform FFT (Fourier) processing on the no-load back-EMF periodic function waveform generated by the multiple sets of sampled data obtained by scanning, extract the fundamental and harmonic components, and calculate the total harmonic distortion rate of the back-EMF, or, based on the fundamental and harmonic components obtained in the case of straight stator slots, introduce the skew coefficient K i The total harmonic distortion rate of back electromotive force is calculated;

[0169] The calculation formula of the total harmonic distortion rate of back electromotive force is:

[0170] 9);

[0171] Among them, THD is the total harmonic distortion rate of back electromotive force; U1 is the effective value of fundamental voltage; U3, U 5、 U 7... U n etc. are the effective values ​​of each harmonic voltage;

[0172] Chute coefficient K i The formula is:

[0173] 11);

[0174] Where: oh is the harmonic order, β is the slant distance coefficient;

[0175] Introducing the skew coefficient K i The total harmonic distortion rate of the back electromotive force is calculated to meet the expression:

[0176] Harmonic amplitude after skew slot = straight slot amplitude × K i ;

[0177] The torque pulsation calculation module is used to scan multiple sets of sampled data to generate output torque waveforms and calculate the output torque pulsation;

[0178] The genetic algorithm evaluation module is used to use the cogging torque, back electromotive force total harmonic distortion rate, and torque ripple as evaluation indicators, set weights for each, input the three sets of data corresponding to the skew angle, and calculate the optimal skew angle.

[0179] This application scheme comprehensively considers multiple factors, including cogging torque, no-load back EMF, and torque ripple, and uses a genetic algorithm to evaluate the stator skew effect. Cogging torque, THD, and torque ripple are combined as evaluation indicators. The genetic algorithm weights are assigned to achieve optimal overall performance, accurately determining the optimal skew angle and effectively improving motor performance. This application scheme is not limited by specific motor parameters and has broad applicability, providing strong technical support for the performance improvement design of interior permanent magnet synchronous motors.

[0180] The above description of the disclosed embodiments is intended to enable one skilled in the art to implement or use the present application. Various modifications to these embodiments will be readily apparent to one skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present application. Therefore, the present application is not limited to the embodiments shown herein, but is intended to conform to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A stator skew effect evaluation and design method based on genetic algorithm, characterized in that: The following steps are involved: Import the prepared motor model diagram into the finite element software, build a finite element simulation model of the permanent magnet synchronous motor, preset the simulation model parameters of the motor, and set the grids for the stator, rotor, and air gap; Taking the zero-degree stator straight slot as the reference, under no excitation conditions, with the preset slot angle θj as the step size, multiple sets of sampling data are scanned within the preset stator slot angle range to generate a cogging torque waveform and obtain the cogging torque data; Add three-phase current excitation in the simulation software, generate the no-load back electromotive force periodic function waveform based on the multiple sets of sampled data obtained by scanning, extract the fundamental and harmonic components through Fourier transform processing, and calculate the total harmonic distortion rate of the back electromotive force. Alternatively, based on the fundamental and harmonic components obtained in the case of straight stator slots, introduce the skew coefficient K i The total harmonic distortion rate of back electromotive force is calculated; Among them, the three-phase current is set according to the formula: ； The calculation formula of the total harmonic distortion rate of back electromotive force is: ； Among them, THD is the total harmonic distortion rate of back electromotive force; U1 is the effective value of fundamental voltage; U3, U 5、 U 7... U n is the effective value of each harmonic voltage; Chute coefficient K i The formula is: ； Where: ω is the harmonic order, β is the slant distance coefficient; Introducing the skew coefficient K i The total harmonic distortion rate of the back electromotive force is calculated to meet the expression: Harmonic amplitude after skew slot = straight slot amplitude × K i ; Generate output torque waveform based on multiple sets of sampled data acquired through scanning, and calculate output torque pulsation; The cogging torque, total harmonic distortion rate of back electromotive force, and torque ripple are used as evaluation indicators, and weights are set respectively. The three sets of data corresponding to the skew angle are input, and the optimal stator skew angle is calculated through genetic algorithm.

2. The stator skew effect evaluation and design method based on genetic algorithm according to claim 1, characterized in that: The simulation model parameters of the preset motor include: pole arc coefficient, stator core and rotor core materials, and permanent magnet materials; The stator / rotor mesh was set to 4 mm and the air gap to 0.1 mm.

3. The stator skew effect evaluation and design method based on genetic algorithm according to claim 2, characterized in that: The preset stator slot angle range is 0-30 degrees; the θj angle step value range is 0-1 degree.

4. The stator skew effect evaluation and design method based on genetic algorithm according to claim 3, characterized in that: The cogging torque data is analyzed using the following formula: Where: z is the number of stator slots; L a is the axial length of the stator core; R1 is the inner radius of the stator; R2 is the outer radius of the armature; G n is the Fourier decomposition coefficient of the square of the relative air gap permeability; n is the number of cogging torque; μ 0 is the vacuum permeability; is the relative position angle between the stator and rotor; B ran and B rbn is the Fourier decomposition coefficient of the quadratic air gap magnetic flux.

5. The stator skew effect evaluation and design method based on genetic algorithm according to claim 4, characterized in that: The relationship between the stator skew slot and the air gap flux density is expressed as follows: 6)； 7)； Where: B ran and B rbn is the Fourier decomposition coefficient of the air gap flux squared; z is the number of stator slots; n is the number of cogging torques; θ j is the stator slot offset angle; p is the number of rotor pole pairs; α p is the pole arc coefficient of the permanent magnet pole.

6. The stator skew effect evaluation and design method based on genetic algorithm according to claim 5, characterized in that: The relationship between the slant coefficient β and the chute angle satisfies the expression: 10)； Where: τ P is the pole distance; L a is the axial length of the stator core; θ j is the stator slot offset angle; Chute coefficient K i formula: 11)； Where: ω is the harmonic order; β is the slant distance coefficient.

7. The stator skew effect evaluation and design method based on genetic algorithm according to any one of claims 1 to 6, characterized in that: The method generates an output torque waveform diagram based on multiple sets of sampled data obtained by scanning, and calculates the output torque pulsation; specifically includes: generating the output torque T of multiple sets of sampled data by simulation out , set the highest peak and the lowest peak in the waveform as T omax With T omin , subtract the two components and divide them by the average output torque Ton to obtain the output torque pulsation Tr.

8. A stator skew effect evaluation and design system based on genetic algorithm, characterized in that: include: The motor model construction module is used to import the prepared motor model diagram into the finite element software, build the finite element simulation model of the permanent magnet synchronous motor, preset the simulation model parameters of the motor, and set the grids of the stator, rotor, and air gap; The cogging torque simulation module is used to obtain multiple sets of sampling data by scanning the preset stator skew angle range with a preset slot angle θj as a step size, taking the zero-degree stator straight slot as the reference under no excitation conditions, and generating a cogging torque waveform to obtain the cogging torque data. Excitation condition setting module, used to add three-phase current excitation in simulation software; The no-load back-electromotive force analysis module is used to generate a no-load back-electromotive force periodic function waveform based on multiple sets of sampled data acquired through scanning, extract the fundamental and harmonic components through Fourier transform processing, and calculate the total harmonic distortion rate of the back-electromotive force, or, based on the fundamental and harmonic components acquired in the case of straight stator slots, introduce the skew coefficient K i The total harmonic distortion rate of back electromotive force is calculated; A torque pulsation calculation module is used to generate an output torque waveform diagram based on multiple sets of sampled data obtained through scanning, and calculate the output torque pulsation; The genetic algorithm evaluation module uses the cogging torque, back-electromotive force total harmonic distortion rate, and torque ripple as evaluation indicators, sets weights for each, inputs the three sets of data corresponding to the skew angle, and calculates the optimal stator skew angle through genetic algorithm. Among them, the three-phase current is set according to the formula: ； The calculation formula of the total harmonic distortion rate of back electromotive force is: ； Among them, THD is the total harmonic distortion rate of back electromotive force; U1 is the effective value of fundamental voltage; U3, U 5、 U 7... U n is the effective value of each harmonic voltage; Chute coefficient K i The formula is: ； Where: ω is the harmonic order, β is the slant distance coefficient; Introducing the skew coefficient K i The total harmonic distortion rate of the back electromotive force is calculated to meet the expression: Harmonic amplitude after skew slot = straight slot amplitude × K i .

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