CN106529085A - Mathematical Model of Motor and Optimization Method of Permanent Magnet Synchronous Linear Motor - Google Patents

Abstract

The invention relates to a mathematical model of a motor and an optimization method of a permanent magnet synchronous linear motor, wherein the optimization method comprises the following steps: performing cross operation optimization on the width of the magnetic pole of the motor by combining a PSO algorithm and a genetic algorithm; the optimization algorithm and the optimization method overcome the defects that the motor in the prior art has a complex structure, a large volume and high cost, the motor generates large oscillation during operation, and the motor has low operation rotating speed, poor reliability and the like, are favorable for enabling the no-load counter electromotive force waveform of the motor to be close to sine, reducing the thrust fluctuation of the linear motor and optimizing the performance of the motor.

Description

Mathematical Model of Motor and Optimization Method of Permanent Magnet Synchronous Linear Motor

technical field

The invention relates to an optimization method of a linear motor based on a particle swarm optimization (hereinafter referred to as PSO) combined with a genetic algorithm crossover operation. The algorithm is used to optimize the performance of a linear motor so that the no-load back EMF of the motor is close to a sinusoidal waveform. In this way, the thrust fluctuation of the motor can be reduced.

Background technique

In recent years, linear motors have developed rapidly and are widely used in various occasions. In some high-speed processing fields, linear motors gradually replace ordinary servo drive systems. The linear motor directly generates electromagnetic thrust through electric energy, which has the advantages of simple structure, small size, large thrust, low loss, and fast dynamic response speed. However, the large fluctuation of thrust affects the performance of the linear motor to a large extent, making the motor running process Excessive vibration will be generated in it, which will deteriorate its servo operation performance. In order to improve its driving performance, reducing the thrust fluctuation of the linear motor is an urgent improvement of the linear motor.

There are many factors affecting the thrust fluctuation of the linear motor, including the cogging effect, the end effect and the no-load back EMF waveform of the motor. The present invention focuses on the influence of the no-load back EMF waveform of the linear motor on its thrust fluctuation.

The PSO algorithm is derived from the study of bird predation behavior and is a general heuristic search technology. Find the optimal solution particle in the population by iteratively updating the velocity and position of the particles in the population.

Contents of the invention

The purpose of the present invention is to provide a mathematical model of the motor so as to optimize the structure of the motor.

In order to solve the above-mentioned technical problem, the present invention provides a kind of mathematical model of electric machine, said mathematical model is expressed by the equivalent magnetization intensity spatial distribution function M (x) of electric machine, namely

in,

In the formula: B _r is the residual magnetization of the permanent magnet, μ ₀ is the air permeability, τ _m is the width of the permanent magnet, τ is the pole pitch of the permanent magnet, m _n is the intermediate variable, and n is the number of magnetic poles of the motor.

In yet another aspect, the present invention also provides an optimization algorithm, comprising:

The cross operation optimization of particles is carried out by PSO algorithm combined with genetic algorithm.

Further, the method of combining the PSO algorithm with the genetic algorithm to optimize the cross operation of the particles includes:

The particle velocity is updated as follows:

v=w×v+c ₁ ×rand()×(pBest-present)+c ₂ ×rand()×(gBest-present);

The particle position is updated as follows: present=present+v;

The expression for the inertia weight:

In the formula: v is the current velocity of the particle; present is the current position of the particle;

rand() is a random constant between 0 and 1;

pBest and gBest are the individual extremum and global extremum of a particle respectively;

c ₁ and c ₂ are the acceleration weights corresponding to the individual extremum and the global extremum of a certain particle;

w is the inertia weight; present is the current position of the particle;

w _max and w _min represent the maximum value and minimum value of the inertia weight respectively;

K' _max is the maximum number of iteration steps; K' is the current number of iteration steps;

After multiple optimizations, the global extremum is found in the population.

In the third aspect, the present invention also provides an optimization method for a permanent magnet synchronous linear motor, so as to overcome the defect of motor oscillation caused by thrust fluctuation in the prior art.

The optimization method of the permanent magnet synchronous linear motor includes: performing cross calculation optimization on the magnetic pole width of the motor through the PSO algorithm combined with the genetic algorithm.

Further, the method for optimizing the cross operation of the magnetic pole width of the motor through the PSO algorithm combined with the genetic algorithm includes the following steps:

Step S1, initializing settings;

Step S2, establishing an expression for the change of the air gap flux density with the position angle θ;

Step S3, optimizing the width of the magnetic poles by cross calculation.

Further, the method for initializing settings in step S1 includes:

The permanent magnet synchronous linear motor is suitable for adopting an asymmetric magnetic pole structure, the magnetic pole width is θ ₁ , and its adjacent magnetic pole widths are θ ₂ , θ ₃ , ..., θ _n , n is the number of magnetic poles of the motor, and the selection θ ₁ and θ ₂ are reference variables, let It is the ratio of the magnetic pole width of the motor to its adjacent magnetic pole width, and k is a positive number.

Further, in the step S2, the method for establishing the expression of the air gap magnetic density changing with the position angle θ includes:

Fourier decomposition is performed on the air-gap magnetic density waveform, and the expression of the air-gap magnetic density changing with the position angle θ is as follows:

In formula (11), a _n is the amplitude of the nth harmonic, and its expression is as follows:

In formula (12), B ₁ and B ₂ are the air-gap magnetic density amplitudes under different magnetic poles respectively, and n is a positive integer

The relationship between θ ₁ and θ ₂ is as described in formula (10), that is, θ ₁ =kθ ₂ (13).

Further, in the step S3, the magnetic pole width is optimized by cross operation, namely

Take the pole width of the motor as the optimization goal;

Taking the k value as the velocity variable in the particle swarm algorithm, and the magnetic pole shoe as the dependent variable, each independent variable particle finds its own individual extremum pBest through its own learning, and cross-comparisons with other particles in the particle swarm to obtain The global extremum gBest is obtained, and the global extremum gBest is the optimal value of the pole shoe; choose the appropriate k value as the best ratio between the magnetic pole width of the motor and the adjacent magnetic pole width, so that the magnetic pole shoe can obtain the best performance. That is, the magnetic properties are optimal.

The beneficial effects of the present invention are that the optimization algorithm and optimization method of the present invention overcome the complex structure, large volume, high cost, and large vibration caused by the operation of the motor in the existing known technology, and the motor has low operating speed and reliable It also helps to make the no-load back EMF waveform of the motor close to sinusoidal, reduce the thrust fluctuation of the linear motor, and optimize the performance of the motor.

Description of drawings

The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

Fig. 1 is the flowchart of PSO algorithm among the present invention;

Fig. 2 is a flow chart of the optimization method of the permanent magnet synchronous linear motor of the present invention.

detailed description

The present invention is described in further detail now in conjunction with accompanying drawing. These drawings are all simplified schematic diagrams, which only illustrate the basic structure of the present invention in a schematic manner, so they only show the configurations related to the present invention.

The mathematical model of permanent magnet synchronous linear motor is a high-order, nonlinear, strongly coupled multivariable system. The excitation effect of permanent magnets is analyzed by the equivalent magnetization method, and its equivalent magnetization spatial distribution function M(x) can be expressed by Fourier series:

in,

In the formula: B _r is the residual magnetization of the permanent magnet; μ ₀ is the air permeability; τ _m is the width of the permanent magnet; τ is the pole pitch of the permanent magnet, and m _n is the intermediate variable.

According to Maxwell (Maxwell) equations, establish the Poisson equations in the air gap region and the permanent magnet region:

In the formula, A ₁ and A ₂ are the vector magnetic potentials in the air gap region and the permanent magnet region, respectively.

The air gap region and the permanent magnet region satisfy the following boundary conditions:

Substituting formula (4) into formula (3), the air gap magnetic flux density is obtained:

in,

In the formula: A _n1 , B _n1 , T _n are intermediate variables; h _m is the thickness of the permanent magnet; g is the length of the air gap.

The PSO algorithm is an intelligent optimization algorithm for simulating bird foraging. By iterating the optimization variable into the objective function to judge whether it is the optimal solution, this optimization algorithm based on the iterative mode has more obvious advantages in finding the optimal solution for continuous variables. Therefore, each optimization variable has its own variation range set, and in each iteration process, the particles in the particle swarm determine the next movement direction through their own learning and learning from the optimal particle in the swarm, that is, the particles pass through Track two extreme values to update itself, one is the optimal solution that the particle itself can find, which is the individual extreme value pBest, and the other is the optimal solution in the particle population, that is, the global extreme value gBest. The specific steps of the algorithm are shown in Figure 1.

Assuming that there are n particles in the m-dimensional space, the coordinates of each particle are _{Xi = (x i1 ,} x _i2 ,..., x _im ), and have fitness related to the optimization objective function f(x) (usually directly The objective function is regarded as the fitness of particles), and each particle has its own velocity V _i =(v _i1 , v _i2 , . . . , v _im ). For the i-th particle, the historical best position experienced by it is recorded as P _i =(p _i1 ,p _i2 ,…,p _im ), and the best position of all particles is recorded as P _g =(p _g1 ,p _g2 ,...,p _gm ).

The following describes the PSO algorithm combined with the crossover operation in the genetic algorithm. Let pBest and gBest be the historical best of a particle and the current global best respectively, let the elements at a random corresponding position in the two vectors intersect to strengthen the historical best of the particle to the global best After learning, the historical best after crossover and the current global best become pBest and gBest respectively. pBest and bBest determine the speed update of particles at the same time. For each particle, its historical optimum has not changed. For the entire particle swarm, the current global optimum has not changed. This crossover process only affects the particle speed. update.

Particle speed update:

v=w×v+c ₁ ×rand()×(pBest-present)+c ₂ ×rand()×(gBest-present) (7)

Particle position update: present=present+v (8)

In formulas (7) and (8): v is the velocity of the particle, present is the current position of the particle, rand() is a random constant between 0 and 1, c ₁ and c ₂ are the individual extremum and global extremum of a certain particle The corresponding acceleration weights are normal numbers and usually take 2; w is the inertia weight. The introduction of the inertia weight makes the global search ability and local search ability of the PSO algorithm significantly improved, so as not to fall into the local optimal solution. present is the current position of the particle .

The expression for the inertia weight:

In formula (9): w _max and w _min represent the maximum value and minimum value of inertia weight respectively, K' _max is the maximum number of iteration steps; K' is the number of current iteration steps.

As shown in FIG. 2 , the above embodiment also provides an optimization method for a permanent magnet synchronous linear motor, so as to overcome the defect of motor oscillation caused by thrust fluctuation in the prior art.

The optimization method of the permanent magnet synchronous linear motor includes: performing cross calculation optimization on the magnetic pole width of the motor through the PSO algorithm combined with the genetic algorithm, and the steps include the following:

Step S1, initializing settings;

The present invention adopts an asymmetric magnetic pole structure, the magnetic pole width is θ ₁ , and its adjacent magnetic pole widths are θ ₂ , θ ₃ , ..., θ _n (n is the number of magnetic poles of the motor), and θ ₁ and θ ₂ are selected as reference variable, let (k is a positive number) (10);

Step S2, establish the expression of the air gap magnetic density changing with the position angle θ, that is

Fourier decomposition is performed on the air-gap magnetic density waveform, and the expression of the air-gap magnetic density changing with the position angle θ is as follows:

In formula (11), a _n is the amplitude of the nth harmonic, and its expression is as follows:

In formula (12), B ₁ and B ₂ are the air-gap magnetic density amplitudes under different magnetic poles, and n is a positive integer

The relationship between θ ₁ and θ ₂ is described in formula (10): θ ₁ = kθ ₂ (13)

In formula (13), k is a positive number, and the variable of magnetic pole width is closely related to the value of k.

Step S3, optimize the width of the magnetic pole by cross operation, that is,

Taking the k value as the velocity variable in the particle swarm algorithm, and the magnetic pole shoe as the dependent variable, each independent variable particle finds its own individual extremum pBest through its own learning, and cross-comparisons with other particles in the particle swarm to obtain The global extremum gBest is obtained, so this extremum gBest is the optimal value of the magnetic pole shoe.

Selecting an appropriate value of k means obtaining the optimum ratio of the magnetic pole width of the motor to the adjacent magnetic pole width, which determines the best performance of the magnetic pole piece and makes the magnetism optimal.

The k value determines the magnetic pole width of the linear motor, optimizes the structure of the motor, reduces the thrust fluctuation of the motor, and enhances the stability of the motor during operation.

Inspired by the above-mentioned ideal embodiment according to the present invention, through the above-mentioned description content, relevant workers can make various changes and modifications within the scope of not departing from the technical idea of the present invention. The technical scope of the present invention is not limited to the content in the specification, but must be determined according to the scope of the claims.

Claims (8)

1. A mathematical model of a motor, characterized in that, represents the mathematical model by the equivalent magnetization spatial distribution function M (x) of the motor, i.e. $\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; \&infin;</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}\frac{\mathrm{<span\; class="notranslate">\; 4</span>}{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}}{{\mathrm{<span\; class="notranslate">\; \&mu;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}{\mathrm{<span\; class="notranslate">\; \&tau;m</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}}\mathrm{<span\; class="notranslate">\; the\; s</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; no</span>}\frac{{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}\mathrm{<span\; class="notranslate">\; \&tau;</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; the\; s</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; no</span>}\frac{{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; sinm</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ;</span>$ in, In the formula: B _r is the residual magnetization of the permanent magnet, μ ₀ is the air permeability, τ _m is the width of the permanent magnet, τ is the pole pitch of the permanent magnet, m _n is the intermediate variable, and n is the number of magnetic poles of the motor. 2. An optimization algorithm, characterized in that, comprising: The cross operation optimization of particles is carried out by PSO algorithm combined with genetic algorithm. 3. optimization algorithm according to claim 2, is characterized in that, The method that the PSO algorithm is combined with the genetic algorithm to carry out the cross operation optimization of the particles includes: The particle velocity is updated as follows: v=w×v+c ₁ ×rand()×(pBest-present)+c ₂ ×rand()×(gBest-present); The particle position is updated as follows: present=present+v; The expression for the inertia weight: In the formula: v is the current velocity of the particle; present is the current position of the particle; rand() is a random constant between 0 and 1; pBest and gBest are the individual extremum and global extremum of a particle respectively; c ₁ and c ₂ are the acceleration weights corresponding to the individual extremum and the global extremum of a certain particle; w is the inertia weight; present is the current position of the particle; w _max and w _min represent the maximum value and minimum value of the inertia weight respectively; K' _max is the maximum number of iteration steps; K' is the current number of iteration steps; After multiple optimizations, the global extremum is found in the population. 4. An optimization method for a permanent magnet synchronous linear motor, characterized in that, The cross operation optimization of the magnetic pole width of the motor is carried out through the PSO algorithm combined with the genetic algorithm. 5. The optimization method according to claim 4, characterized in that, The method for optimizing the cross operation of the magnetic pole width of the motor through the PSO algorithm combined with the genetic algorithm comprises the following steps: Step S1, initializing settings; Step S2, establishing an expression for the change of the air gap flux density with the position angle θ; Step S3, optimizing the width of the magnetic poles by cross calculation. 6. The optimization method according to claim 5, characterized in that, The method for initializing settings in the step S1 includes: The permanent magnet synchronous linear motor is suitable for adopting an asymmetric magnetic pole structure, the magnetic pole width is θ ₁ , and its adjacent magnetic pole widths are θ ₂ , θ ₃ , ..., θ _n , n is the number of magnetic poles of the motor, and the selection θ ₁ and θ ₂ are reference variables, let It is the ratio of the magnetic pole width of the motor to its adjacent magnetic pole width, and k is a positive number. 7. The optimization method according to claim 6, characterized in that, In the step S2, the method for establishing the expression of the air gap magnetic density changing with the position angle θ includes: Fourier decomposition is performed on the air-gap magnetic density waveform, and the expression of the air-gap magnetic density changing with the position angle θ is as follows: $\mathrm{<span\; class="notranslate">\; B</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; +</span>\underset{\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; \&infin;</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; o</span>}\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 11</span>}<span\; class="notranslate">\; )</span>$ In formula (11), a _n is the amplitude of the nth harmonic, and its expression is as follows: ${\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 2</span>}{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}{\mathrm{<span\; class="notranslate">\; no</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}}\mathrm{<span\; class="notranslate">\; the\; s</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; no</span>}\frac{{\mathrm{<span\; class="notranslate">\; n\&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; 2</span>}{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; no</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}}\mathrm{<span\; class="notranslate">\; the\; s</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; \&lsqb;</span>\frac{\mathrm{<span\; class="notranslate">\; no</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; 8</span>}}<span\; class="notranslate">\; \&rsqb;</span><span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 2</span>}{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; no</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}}\mathrm{<span\; class="notranslate">\; the\; s</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; \&lsqb;</span>\frac{\mathrm{<span\; class="notranslate">\; no</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}{\mathrm{<span\; class="notranslate">\; 8</span>}}<span\; class="notranslate">\; \&rsqb;</span><span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 2</span>}{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}{\mathrm{<span\; class="notranslate">\; no</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}}\mathrm{<span\; class="notranslate">\; the\; s</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; n\&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 12</span>}<span\; class="notranslate">\; )</span>$ In formula (12), B ₁ and B ₂ are the air-gap magnetic density amplitudes under different magnetic poles; The relationship between θ ₁ and θ ₂ is as described in formula (10), that is, θ ₁ =kθ ₂ (13). 8. The optimization method according to claim 7, characterized in that, In the step S3, the magnetic pole width is optimized by cross operation, namely Take the pole width of the motor as the optimization goal; Taking the k value as the speed variable in the particle swarm algorithm, and the magnetic pole shoe as the dependent variable, each independent variable particle finds its own individual extremum pBest through its own learning, and cross-comparisons with other particles in the particle swarm to obtain The global extremum gBest is obtained, and the global extremum gBest is the optimal value of the magnetic pole shoe; Selecting an appropriate k value is the optimal ratio of the magnetic pole width of the motor to the adjacent magnetic pole width, so that the magnetic pole piece can obtain the best performance, that is, the magnetic field is optimal.