CN115130237A - A method for determining the structural dimension parameters of a magnetic levitation workbench - Google Patents

Abstract

The invention provides a method for determining a structural size parameter of a magnetic suspension workbench. Determining variables to be optimized, wherein the optimization variables comprise: structural parameters to be optimized of the magnetic suspension workbench and optimization constraint conditions of the magnetic suspension workbench; constructing a magnetic force numerical model of the magnetic suspension workbench based on the magnetic field model; and normalizing a plurality of optimization targets such as mass reduction, power consumption, efficiency improvement, rigidity reduction and the like, and then combining the normalized optimization targets to form a composite optimization target function, wherein a related magnetic force calculation part in the composite optimization target function is solved based on the established integral magnetic force numerical model of the magnetic suspension workbench. The method has the advantages that the multi-objective intelligent optimization method is combined with the parallelizable numerical electromagnetic model of the magnetic suspension workbench, so that the method for selecting the structure size of the magnetic suspension workbench with good universality is obtained, and the optimization efficiency of the structure parameters of the magnetic suspension workbench and the accuracy of the optimization result are improved.

Description

A method for determining the structural dimension parameters of a magnetic levitation workbench

technical field

The invention belongs to the field of magnetic suspension workbenches, and in particular relates to a method for determining the structural dimension parameters of a magnetic suspension workbench.

Background technique

As a new type of driving element, the magnetic levitation workbench has been extensively researched and developed in the past few decades. The magnetic suspension table does not need the support of mechanical guide rails, and can directly realize two-dimensional plane drive with large stroke, which greatly simplifies the mechanical movement structure, and is small in size and light in weight, and can achieve high-speed movement. In addition, since no mechanical or air bearing support is required, precision motion can be achieved under vacuum conditions. These advantages make it have broad application prospects in semiconductor lithography systems and other high-precision industrial fields.

High-precision manufacturing fields such as semiconductor lithography have strict requirements on power consumption and heat dissipation. Selecting appropriate electromagnetic structure parameters can effectively reduce power consumption and improve motor efficiency. In addition, in the process of processing, especially in contact operation, in order to ensure the stability of the workbench, the magnetic suspension system should have high structural static stiffness characteristics. Sufficient magnetic force to compensate for changes in load. The change of the structural parameters of the actuator will affect the static stiffness of the structure and the upper limit of the output magnetic force within the motion range of the system. Selecting the appropriate structural parameters is the basic condition for obtaining high performance, and at the same time, it can also reduce the burden of the control system and reduce the manufacturing cost of the magnetic levitation workbench. Therefore, how to optimize the structural parameters of the magnetic levitation workbench to obtain the magnetic levitation workbench with the best motion performance and cost, and improve the product competitiveness is an imminent task in the research of magnetic levitation motors.

However, due to the particularity of the structure of the maglev workbench, the optimization method for traditional motors is not suitable for the maglev workbench. At present, the domestic magnetic levitation motor structure optimization methods still remain in the optimization of a single optimization objective, or for multiple optimization objectives, separate each optimization objective, and optimize separately. The optimization method mostly adopts the finite element optimization method with long time and rough optimization results. There is no effective and generalized method for optimizing the structural parameters of the magnetic levitation motor, which makes the research and development cycle of the magnetic levitation workbench long and the cost is high.

SUMMARY OF THE INVENTION

In view of the above situation, it is necessary to provide a general and efficient method for optimizing the structural parameters of the magnetic levitation workbench in order to solve the problems of lack of generalization, high efficiency and unsatisfactory optimization results in the structural parameter optimization process of the magnetic levitation workbench in the prior art.

A method for optimizing structural parameters of a general magnetic suspension workbench, comprising:

Step 1: Determine the variables to be optimized, and the optimized variables include: structural parameters to be optimized of the magnetic suspension workbench, and optimization constraints of the magnetic suspension workbench;

The step 1 is specifically:

According to the preset structural parameters to be optimized and the remaining fixed structural parameter values of the motor, the magnetic field generated by each permanent magnet in the magnetic suspension motor is numerically modeled, and the numerical modeling results of all the magnets are superimposed to obtain the overall magnetic field of the magnetic suspension workbench. Model;

Step 2: Build a numerical model of the magnetic force of the magnetic levitation workbench based on the magnetic field model;

The step 2 is specifically:

The magnetic force model of the magnetic levitation motor is the superposition result of the magnetic force on each coil of the magnetic levitation motor. Calculate the Lorentz force on each coil in the magnetic levitation workbench, establish a magnetic force numerical model for each coil, and superimpose the magnetic force models of all coils. Obtain the overall magnetic numerical model of the magnetic levitation workbench;

Step 3: Multiple optimization objectives, such as reducing mass, power consumption, improving efficiency, reducing stiffness, etc., are normalized and merged to form a composite optimization objective function. The relevant magnetic force calculation part in the composite optimization objective function is based on The established numerical model of the overall magnetic force of the magnetic levitation workbench is solved;

Step 4: Parallelize the overall magnetic numerical model of the magnetic levitation workbench in the composite optimization objective function according to its superposition form to form a parallelized structure, and then combine the composite optimization objective function with the intelligent optimization algorithm. Search and obtain the optimal structural parameters of the magnetic levitation table within the optimization constraints such as suspension force and structure range.

According to the determined motor structure parameters to be optimized, the invention establishes the magnetic field model and the magnetic force model of the multi-free magnetic suspension workbench based on the magnetic charge node method and the Gauss quadrature method, and has universality for different types of magnetic suspension motors. Then, according to the normalized and merged multi-objective optimization function, combined with the intelligent optimization algorithm particle swarm method and the established numerical model of the magnetic suspension plane motor, the motor is optimized, so as to achieve the purpose of optimizing the structural parameters of the magnetic suspension workbench.

The advantage of the invention is that the multi-objective intelligent optimization method is combined with the parallelizable numerical electromagnetic model of the magnetic suspension workbench, so as to obtain a method for selecting the structure size of the magnetic suspension workbench with good versatility, and the optimization efficiency of the structural parameters of the magnetic suspension workbench is improved. and the accuracy of the optimization results.

Description of drawings

FIG. 1 is a flowchart of a multi-objective optimization method for a magnetic levitation workbench in an embodiment of the present invention.

Fig. 2 is a flow chart of the magnetic field modeling of the magnetic levitation workbench in the optimization method of the present invention.

FIG. 3 is an optimization process based on an intelligent optimization algorithm PSO in an embodiment of the present invention.

Detailed ways

Hereinafter, the technical solutions in the embodiments of the present invention will be described clearly and completely with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. . Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

Please refer to FIG. 1 , which is the overall process of optimizing the structural parameters of the magnetic levitation workbench in the present invention, including steps S1-S4.

Step S1, determine the structural parameters of the magnetic levitation table to be optimized (such as the thickness of the coil, the length and thickness of the permanent magnet), and the constraints in the optimization process (such as the minimum levitation force, the range of the parameters to be optimized, etc.).

One or more of the structural parameters to be optimized in the above steps can be selected according to requirements, and the constraint optimization conditions can also be set according to actual equality constraints and inequality constraints.

In step S2, a magnetic field numerical model and a magnetic force numerical model of the magnetic levitation workbench are established according to the parameters to be optimized and the remaining fixed parameters.

Among them, the magnetic field model is constructed using the magnetic charge node method, and the overall magnetic field effect of the permanent magnet is equivalent to the superposition of the effects of the magnetic fields generated by several fixed points, and the magnetic field of each magnet in the magnetic suspension table is constructed separately. The superposition of the magnetic field effects constitutes the magnetic field model of the magnetic levitation workbench. Please refer to Figure 2 for the specific steps. Since the permanent magnets do not affect each other, the magnetic field models of all permanent magnets are constructed simultaneously in a multi-channel parallel manner, and it is judged whether the model construction of each permanent magnet is completed. Wait for the construction of the magnetic field models of all permanent magnets. Once complete, the build results are superimposed to obtain the overall magnetic field strength of the maglev table.

For the construction of the magnetic force model in step S2, the Gauss quadrature method is used for each coil of the magnetic levitation motor to convert the volume fraction of the coils in the magnetic force model into the form of a weighted sum, so as to obtain a numerical model, and superimpose the magnetic force models of all coils Obtain the numerical magnetic model of the magnetic levitation table.

Step S3, the present invention has a general type for multi-objective optimization problems and single-objective optimization problems. When facing multiple optimization objectives, it is necessary to normalize the optimization objectives, so that the evaluation function can truly reflect the intelligent optimization algorithm. actual optimization. Step S3 is for multi-objective optimization, based on the maximum or minimum value of each objective, and the multi-objective multiplication and division method is adopted to combine and convert into single-objective optimization.

Step S4, based on the composite optimization objective function obtained in step S3, an intelligent optimization algorithm is introduced to search for the global optimal parameters, and the evaluation function in the intelligent optimization algorithm is parallelized by using the summation form of the magnetic numerical model of the magnetic levitation table constructed in S2. It can improve the global search speed of the intelligent optimization algorithm, so as to quickly obtain the optimal structural size parameters of the magnetic levitation workbench.

Please refer to Fig. 2 for the specific process of constructing the magnetic field model of the magnetic levitation table in step S2.

According to the principle of the magnetic charge method, the magnetic field generated by the permanent magnet can be equivalent to the superposition of the actions of multiple independent source points D _k , and the magnetic flux density B at point G can be regarded as the sum effect of all the magnetic charge nodes on the magnet, Its calculation expression is:

where T corresponds to the number of endpoints of the permanent magnet geometry.

According to this expression, for the size of the magnetic field at a certain point in space, we can first calculate the magnitude of the electromagnetic force generated by the permanent magnet i of each magnetic levitation table at that position, and then superimpose the magnetic field generated by each permanent magnet, and judge whether there is The calculation of the magnetic field of all the permanent magnets of the entire magnetic suspension workbench at this point is not completed. If all the magnetic fields are completed, the magnetic fields obtained by the calculation will be superimposed to obtain the numerical model of the magnetic field.

Due to the superposition property of the numerical model, it is convenient to parallelize the evaluation function in the subsequent optimization, and the numerical model has higher magnetic calculation accuracy. Therefore, based on the obtained magnetic field model, a numerical model of the magnetic force of the magnetic levitation table is constructed through the Lorentz force integral.

Since the Lorentz force integral is continuous, the volume integral for the coil can be reduced to the form of the summation of triple numerical integrals by Gaussian quadrature:

为作用在线圈i上的高斯节点，w_gi为高斯求积的权重，线圈的整体区域分为8个部分，相对应的将整个线圈积分转换为八个分段积分，因此，高斯节点

实际上可以对应到不同线圈分段上的实际高斯节点

通过这种方式，就不存区域无法积分的问题，因为内外积分间每次求导都是相互独立的。考虑到线圈坐标系与永磁体坐标系的不同，因此需要通过转换矩阵R和平移矢量t构建起磁通密度与电流密度以及电磁力矢量的关联机制，实现在坐标系间的任意转换。单个线圈与磁铁间的作用力可以表示为：In the formula,

For the Gaussian node acting on the coil i, w _gi is the weight of the Gaussian product, and the overall area of the coil is divided into 8 parts, correspondingly, the entire coil integral is converted into eight segment integrals. Therefore, the Gaussian node

Can actually correspond to actual Gaussian nodes on different coil segments

In this way, there is no problem that the area cannot be integrated, because each derivation between the inner and outer integrals is independent of each other. Considering the difference between the coil coordinate system and the permanent magnet coordinate system, it is necessary to construct the correlation mechanism between the magnetic flux density, the current density and the electromagnetic force vector through the transformation matrix R and the translation vector t, so as to realize any conversion between the coordinate systems. The force between a single coil and a magnet can be expressed as:

可以根据线圈和永磁体阵列的设计参数进行计算。从表达式结果可以看出，这种数值积分方式将各层的求解独立化，在后续的评价函数计算可进行并行化处理，从而提升优化效率。where q _c is the index number of the coil segment, and

Calculations can be made based on the design parameters of the coil and permanent magnet array. It can be seen from the expression results that this numerical integration method makes the solution of each layer independent, and the subsequent evaluation function calculation can be parallelized, thereby improving the optimization efficiency.

Please refer to FIG. 3 , which is an embodiment of the present invention based on a particle swarm optimization (Particle SwarmOptimization, PSO) in an intelligent optimization algorithm. The particle swarm optimization algorithm belongs to a global search random algorithm, and its design principle originates from the social behavior of natural creatures. In each iteration of particle swarm optimization, the velocity and position of particles are updated according to two elements: one is the best position of the individual (particle); the other is the best position of the swarm. Therefore, the proposed optimization method can realize the optimization of the structure size of the magnetic levitation workbench based on the particle swarm intelligent optimization algorithm.

In the whole optimization process, when optimizing the k _d dimensions first, the number N _g and size N _p of the population should be determined. The parameters that need to be optimized mainly include the permanent magnet thickness h _c , the coil thickness h _m and the width R _out of the magnetic levitation table. The parameter range can also be set according to the actual needs, and the three degrees of freedom of each particle in the particle swarm optimization algorithm are only three degrees of freedom. Corresponding to optimization variables h _c , h _m and R _out respectively:

x ₁ →h _c ,x ₂ →h _m ,x ₃ →R _out (4)

Therefore, each particle is a three-dimensional vector, and the jth particle in the lth particle swarm can be expressed as:

The velocity of each particle can also be represented by a three-dimensional vector:

为其当前位：First, the initial positions and velocities of all particles are randomly generated in the entire searchable space of h _c , h _m and R _out or within a specific range. Then, the fitness of each particle is calculated based on the numerical magnetic model and the objective function, the individual historical optimal position of the lth particle of the jth group

for its current bit:

的适应度f_obj结果，从中选择最优组位置

by comparing each

The fitness f _obj result of , from which to choose the optimal group position

的历史迭代最优结果，那么

表示的空间位置会替换为前位粒子的位置。相应的，

也是通过类似的比较替换的方式进行更新。每次进行迭代更新时，粒子的移动速度的更新量由种群组的最优位置

和个体的最优历史位置

决定。第s次和第s+1次迭代之间，粒子速度的更新方法为：If the position of the particle is within the feasible region, the evaluation function result f _obj can be calculated. if the f _obj is better than

The optimal result of historical iteration, then

The represented spatial position is replaced with the position of the preceding particle. corresponding,

It is also updated in a similar way of comparing and replacing. Each time the iterative update is performed, the update amount of the particle's moving speed is determined by the optimal position of the population group.

and the optimal historical position of the individual

Decide. Between the sth and s+1th iterations, the update method of particle velocity is:

和

对每个粒子的相对吸引力的加速度系数，它们为粒子的认知系数和社会度参数。r₁和r₂均为随机数，处于区间[0，1]内。对于第s+1次迭代，粒子的位置应为：where w is the coefficient of inertia and _C1 and _C2 are

and

The acceleration coefficients of the relative attraction to each particle, which are the particle's cognitive coefficient and social degree parameters. Both r ₁ and r ₂ are random numbers, which are in the interval [0, 1]. For iteration s+1, the particle's position should be:

where χ represents the time step, which is actually used as a shrinkage factor. If the new particle position obtained by the update of formula (3.28) is outside the feasible region given by the constraint formula, it is necessary to select a boundary position that is closest to the current position through some algorithms. Another way is to convert the constrained problem into an unconstrained problem for optimization by adding a penalty function term. The algorithm will continue to repeat the above iterative update process until the global optimal solution is finally obtained.

In each iterative search process, the calculation accuracy of the fitness f _obj corresponding to each particle will directly affect the effectiveness of the final optimization result, and the fitness calculation also determines the overall multi-objective optimization efficiency.

Therefore, as can be seen from Figure 3, by introducing the numerical electromagnetic force model into the multi-objective optimization, the summation expression of the numerical model is combined with parallel computing, so that the electromagnetic force in the fitness function of each particle is The solution is transformed into the superposition form of the force acting on each permanent magnet in the Halbach permanent magnet array. Whenever the fitness calculation is performed, the electromagnetic force solution part of the fitness function of each particle is calculated by the corresponding permanent magnet calculation module. When it is judged that the calculation of the electromagnetic force corresponding to all the permanent magnets is completed, the calculation results of each module are added to quickly obtain the corresponding total magnetic force and bring it into the calculation of the fitness function.

On the other hand, the combination of the numerical electromagnetic model of the magnetic levitation workbench and the multi-objective optimization can also rely on the higher calculation accuracy of the numerical model to further ensure the validity of the optimization results.

It should be understood that the parts not described in detail in this specification belong to the prior art.

It should be understood that the above description of the preferred embodiments is relatively detailed, and therefore should not be considered as a limitation on the protection scope of the patent of the present invention. In the case of the protection scope, substitutions or deformations can also be made, which all fall within the protection scope of the present invention, and the claimed protection scope of the present invention shall be subject to the appended claims.

Claims (1)

1. The method for determining the structural size parameters of the magnetic suspension workbench is characterized by comprising the following steps:

step 1: determining variables to be optimized, wherein the optimization variables comprise: structural parameters to be optimized of the magnetic suspension workbench and optimization constraint conditions of the magnetic suspension workbench;

the step 1 specifically comprises the following steps:

according to the structural parameters to be optimized and the residual fixed structural parameter values preset by the motor, performing numerical modeling on the magnetic field generated by each permanent magnet in the magnetic suspension motor, and superposing the numerical modeling results of all the magnets to obtain an integral magnetic field model of the magnetic suspension workbench;

and 2, step: constructing a magnetic force numerical model of the magnetic suspension workbench based on the magnetic field model;

the step 2 specifically comprises the following steps:

calculating Lorenz force borne by each coil in the magnetic suspension workbench, establishing a magnetic force numerical model for each coil, and superposing the magnetic force models of all the coils to obtain an integral magnetic force numerical model of the magnetic suspension workbench;

and 3, step 3: normalizing a plurality of optimization targets such as mass reduction, power consumption, efficiency improvement, rigidity reduction and the like, and then combining the normalized optimization targets to form a composite optimization target function, wherein a related magnetic force calculation part in the composite optimization target function is solved based on the established integral magnetic force numerical model of the magnetic suspension workbench;

and 4, step 4: and performing parallelization processing on the whole magnetic force numerical model of the magnetic suspension workbench in the composite optimization objective function according to the superposition form of the magnetic suspension workbench to form a parallelization structure, then combining the composite optimization objective function with an intelligent optimization algorithm, and searching and obtaining the optimal magnetic suspension workbench structure parameters in the optimization constraint conditions of the preset minimum suspension force, the structure range and the like.

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