A torque optimization method for outer rotor brushless DC motor

Abstract

The present invention relates to the field of brushless DC motor torque optimization, and discloses a method for optimizing the torque of an outer rotor brushless DC motor, including establishing a parameterized finite element model of an outer rotor brushless DC motor to solve the performance; constructing a Pearson correlation coefficient matrix framework under the motor model structural parameters and output response; obtaining key structural dimension parameter variables for different response targets; establishing an optimal prediction meta-model that can replace the finite element calculation model; optimizing the meta-model for multiple torque targets to obtain the Pareto optimal frontier; using the CRITIC‑TOPSIS evaluation model to evaluate and sort the relative merits of the Pareto solution set to obtain the optimal structural dimension parameters. Compared with the prior art, the present invention can realize the rapid optimization of the multi-torque performance of the motor, abandon the disadvantage of slow iterative calculation of the finite element model, and the selected evaluation model comprehensively considers the differences and correlations between various torque performance indicators, and its evaluation results are objective and comprehensive.

Description

Technical Field

[0001] The invention relates to the field of brushless DC motor torque optimization, and in particular to a method for optimizing the torque of an outer rotor brushless DC motor. Background Art

[0002] The topology of the motor plays a vital role in weakening the cogging torque and torque pulsation. Cogging torque is the reluctance torque generated by the interaction between the teeth of the motor stator core and the permanent magnets of the rotor. Due to the existence of the stator teeth of the brushless DC motor, when the magnetic pole position of the permanent magnet on the rotor changes, the magnetic permeance of the main magnetic circuit will change accordingly, causing the air gap magnetic field to produce a sawtooth fluctuation in the spatial distribution, thereby causing the back electromotive force waveform of the motor to be distorted, and generating an additional periodic torque pulsation. Although the cogging torque has little effect on the average output torque of the motor, it will cause vibration and noise in the motor during operation, especially when the motor is working under light load or low speed conditions, the cogging torque pulsation is particularly prominent, reducing the reliability of the motor drive system. During the motor speed regulation process, if the frequency of the cogging torque is close to the mechanical natural frequency of the motor drive system, resonance and severe noise will occur.

[0003] In the current field of motor torque optimization design, there are still a series of key issues that need to be solved. Traditional optimization design methods are often limited to single parameter optimization. Although parameters can be optimized locally, it is difficult to achieve the goal of global optimization. Although multi-objective optimization can provide a Pareto optimal solution set, how to choose the best solution still depends largely on the subjective judgment of decision makers. In addition, the use of finite element models for optimization design faces the challenges of high computational complexity and long time consumption, which greatly limits the efficiency and practicality of optimization design. Summary of the invention

[0004] Purpose of the invention: In view of the problems pointed out in the background technology, the present invention discloses a method for optimizing the torque of an outer rotor brushless DC motor, which adopts the optimal prediction meta-model as an alternative model for optimization design, and combines the evaluation model to screen the best solution from the Pareto optimal solution set, effectively reducing the calculation complexity of the machine torque optimization, shortening the optimization cycle, and improving the optimality and reliability of the solution.

[0005] Technical solution: The present invention discloses a method for optimizing the torque of an outer rotor brushless DC motor, comprising:

[0006] Step (1) establishing a parameterized finite element model of an outer rotor brushless DC motor to solve the performance;

[0007] Step (2) constructing a Pearson correlation coefficient matrix framework between the motor model structural parameters and the output response;

[0008] Step (3) obtaining key structural dimension parameter variables for different response targets and determining the number and range of variables;

[0009] Step (4) The approximate function fitting between the target response and the structural independent variable is realized by using the moving least squares-polynomial regression-kriging MLS-Polynomial-Kriging mixed model, and the optimal prediction meta-model MOP is established based on the mixed model;

[0010] Step (5) performing multi-torque target optimization on the optimal prediction meta-model MOP to obtain the Pareto optimal frontier;

[0011] Step (6) Use the CRITIC-TOPSIS evaluation model to evaluate and rank the relative merits of the Pareto solution set to obtain the optimal structural size parameters.

[0012] Furthermore, step (1) includes: performing parametric modeling on the outer rotor brushless DC motor through the pre-processing software Ansys Maxwell, the parameterized structural variables include air gap length, pole arc coefficient, permanent magnet thickness, slot width, upper slot shoulder width, lower slot shoulder width and slot depth, and solving the output response as average electromagnetic torque, torque pulsation and cogging torque peak-to-peak value.

[0013] Furthermore, in step (2), experimental DOE sample sampling is performed on the motor model under finite element solution to obtain sufficient sample data for correlation analysis.

[0014] Furthermore, in step (2), the Pearson correlation coefficient between the structural parameter and the output response is calculated and defined as follows:

[0015]

[0016] Where, X i There are seven decision variables, Y i are three optimization objectives, E(X) is the average value of the decision variables, and n is the total number of DOE sampling points.

[0017] Furthermore, in step (4), the determination coefficient R is introduced 2 To characterize the fitting degree and prediction accuracy of the optimal prediction meta-model MOP, it can be expressed as:

[0018]

[0019]

[0020] In the formula, SS T is the sum of squares of the differences between the true data and its mean, SS R is the sum of squares of the mean differences between the predicted data and the true data, SS Eis the sum of the squares of the differences between the actual data and the predicted data; i is the real data of the sample target variable, is the MOP prediction data; R 2 The closer it is to 1, the better the prediction effect of the optimal meta-model MOP is.

[0021] Furthermore, the evolutionary algorithm EA is used to optimize the multi-torque objectives of the optimal prediction meta-model MOP.

[0022] Furthermore, the weights of the average electromagnetic torque, torque ripple and cogging torque peak-to-peak value are calculated using the CRITIC model; the Pareto front solution set is scored and ranked using the TOPSIS model;

[0023] 1) Constructing the CRITIC model:

[0024] Calculate the contrast strength θ of the jth indicator j :

[0025]

[0026] Calculate the contradiction and correlation coefficient between different indicators:

[0027]

[0028] In the formula, r ij represents the correlation coefficient between two indicators, f j Indicates the degree of contradiction between indicator j and other indicators;

[0029] Calculate the information carrying capacity and weight of indicators:

[0030]

[0031] In the formula, C j represents the amount of information contained in the jth evaluation index, W j represents the weight assigned to the jth evaluation index;

[0032] 2) The TOPSIS model is constructed as follows:

[0033] The weighted data sample is y ij =W j h ij , the weighted decision matrix is ​​Y = [y ij ] m×n ;

[0034] The ideal solution is:

[0035] The negative ideal solution is:

[0036] Compute the positive ideal solution distance:

[0037] Compute the negative ideal solution distance:

[0038] Compute the relative closeness of each solution to the positive and negative ideal solutions:

[0039] Among them, the higher the relative closeness, the higher the score, that is, the plan i with the highest score is the optimal plan.

[0040] Beneficial effects:

[0041] The present invention combines the metamodel with the CRITIC-TOPSIS model, aiming to accurately identify the key factors affecting the multi-torque system. In this process, the present invention uses Pearson correlation analysis to effectively screen out factors that have a significant impact on torque performance by quantifying the linear relationship between variables. The introduction of the metamodel significantly reduces the complexity and dimension of the finite element calculation, thereby greatly reducing the time cost of the optimization design and effectively shortening the optimization cycle. In addition, the application of the evaluation model CRITIC-TOPSIS further improves the optimality of the solution and the reliability of the results, ensuring the accuracy and effectiveness of the optimization design. This method can improve the efficiency of torque performance optimization and also provide technical guidance for torque research and practice. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 It is a flowchart of the outer rotor brushless DC motor torque optimization method provided in an embodiment of the present application;

[0043] Figure 2 It is a two-dimensional radial section view of the motor structure before (left) and after (right) optimization in the embodiment of the present application;

[0044] Figure 3 is a Pearson correlation analysis heat map of the motor structural parameters and output response in the embodiment of the present application;

[0045] Figure 4 is a second-order response surface diagram of torque pulsation and two highly critical structural parameters corresponding to the meta-model in the embodiment of the present application;

[0046] Figure 5 is a comparison diagram of electromagnetic torque and torque ripple before and after optimization in the embodiment of the present application;

[0047] Figure 6 It is a comparison diagram before and after the optimization of the cogging torque in the embodiment of the present application. DETAILED DESCRIPTION

[0048] The present invention will be further described below in conjunction with the accompanying drawings.

[0049] like Figure 1 As shown, the present invention discloses a method for optimizing the torque of an outer rotor brushless DC motor, which is implemented based on a meta-model and a CRITIC-TOPSIS method and specifically includes the following steps:

[0050] (1) Establish a parametric finite element model of the outer rotor brushless DC motor and solve its performance.

[0051] In the embodiment of the present application, a 10-pole 12-slot outer rotor brushless DC motor is selected, and the parameterized structural variables include air gap length, pole arc coefficient, permanent magnet thickness, slot width, upper slot shoulder width, lower slot shoulder width and slot depth. The output response solved is the average electromagnetic torque, torque pulsation and cogging torque peak-to-peak value.

[0052] (2) Construct the Pearson correlation coefficient matrix framework between the motor model structural parameters and output response.

[0053] Import the motor calculation model solved in step (1) into the OptiSLang software, perform design experiment DOE sampling, set 500 groups of sampling and select the ALHS method based on AMOP to sample the motor model data, perform Pearson correlation analysis on the 500 groups of sampling parameters to quantify the correlation between the parameter variables and the response target, thereby intuitively revealing the degree of influence of each parameter on the target response and their mutual relationship. The Pearson correlation heat map results are shown in the figure below. Figure 3 As shown, the Pearson correlation coefficient is defined to measure the correlation between the decision variables and the optimization objectives, which can be expressed as:

[0054]

[0055] In the formula, X i There are seven decision variables, Y i are three optimization objectives, E(X) is the average value of the decision variable, and n is the total number of sampling points.

[0056] (3) Obtain the key structural dimension parameter variables for different response targets and determine the number and range of variables. Specifically, reduce the optimization variable range of low-correlation parameters and increase the optimization variable range of high-correlation parameters.

[0057] (4) Establish the optimal prediction meta-model MOP that can replace the finite element calculation model.

[0058] In this embodiment, the approximate function fitting between the target response and the structural independent variable is realized by using the moving least squares-polynomial regression-kriging MLS-Polynomial-Kriging mixed model to establish the optimal prediction meta-model MOP, and the determination coefficient R is used to calculate the optimal prediction meta-model MOP. 2To characterize the fitting degree and prediction accuracy of MOP, it can be expressed as:

[0059]

[0060]

[0061] In the formula, SS T is the sum of squares of the differences between the true data and its mean, SS R is the sum of squares of the mean differences between the predicted data and the true data, SS E is the sum of the squares of the differences between the actual data and the predicted data; i is the real data of the sample target variable, is the MOP prediction data; R 2 The closer it is to 1, the better the prediction effect of the meta-model MOP is.

[0062] (5) Perform multi-torque target optimization on the optimal prediction meta-model MOP to obtain the Pareto optimal frontier.

[0063] This optimization process involves a method for optimizing MOP using an evolutionary algorithm (EA) integrated into the OptiSLang platform. The software platform has built-in multiple algorithm modules, allowing users to conveniently and efficiently use various algorithms to optimize the computational model.

[0064] The peak-to-peak value of the motor cogging torque and the average electromagnetic torque are obtained by finite element solution in step (1). The torque ripple can be expressed as:

[0065]

[0066] Where, T ripple , T max , T min and T avg They are torque ripple, maximum average electromagnetic torque, minimum average electromagnetic torque and average electromagnetic torque respectively.

[0067] The motor multi-torque target optimization model and constraints are shown in the following formula:

[0068] minF(x)=[-T avg ,T ripple ,T cog ]

[0069]

[0070] Where, T avg0 , T ripple0 With T cog0They are the average electromagnetic torque, torque pulsation and cogging torque peak-to-peak value under the initial design of the motor; ag is the air gap length, emb is the pole arc coefficient, mth is the permanent magnet thickness, bs0 is the slot width, bs1 is the upper slot shoulder width, bs2 is the lower slot shoulder width, and hs2 is the slot depth.

[0071] (6) The Pareto solution set obtained in the above steps is matrixed and normalized. Regarding the number of m objects to be evaluated, i.e., the number of Pareto solutions, the m×n decision matrix of n evaluation indicators is defined as:

[0072] D=[d ij ] m×n ,(i=1,2,…,m; j=1,2,…,n)

[0073] Where, d ij Represents the initial sample data of the i-th object to be evaluated corresponding to the j-th evaluation indicator.

[0074] Normalize the positive and negative correlation indicators under multiple indicators:

[0075]

[0076] In the formula, di'j represents the normalized sample data of the i-th object to be evaluated corresponding to the j-th evaluation index; max(d j ) and min(d j ) represents the maximum and minimum sample data of the jth evaluation index in the initial decision matrix.

[0077] According to the above processing, the new decision matrix after normalization is:

[0078] D′=[d i ' j ] m×n ,(i=1,2,…,m; j=1,2,…,n)

[0079] The Z-score method is used to standardize the normalized decision matrix:

[0080]

[0081] In the formula, h ij is the standardized sample data of the i-th object to be evaluated of the j-th evaluation indicator; represents the average value of the jth evaluation index in the normalized decision matrix; std(d j ) represents the standard deviation of the jth evaluation index in the normalized decision matrix.

[0082] (7) Constructing the CRITIC model:

[0083] Calculate the contrast strength θ of the jth indicator j :

[0084]

[0085] Calculate the contradiction and correlation coefficient between different indicators:

[0086]

[0087] In the formula, r ij represents the correlation coefficient between two indicators, f j Indicates the degree of contradiction between indicator j and other indicators.

[0088] Calculate the information carrying capacity and weight of indicators:

[0089]

[0090] In the formula, C j represents the amount of information contained in the jth evaluation index, W j Represents the weight assigned to the jth evaluation indicator.

[0091] (8) The TOPSIS model is constructed as follows:

[0092] The weighted data sample is y ij =W j h ij , the weighted decision matrix is ​​Y = [y ij ] m×n ;

[0093] The ideal solution is:

[0094] The negative ideal solution is:

[0095] Compute the positive ideal solution distance:

[0096] Compute the negative ideal solution distance:

[0097] Compute the relative closeness of each solution to the positive and negative ideal solutions:

[0098] Among them, the higher the relative closeness, the higher the score, that is, the plan i with the highest score is the optimal plan.

[0099] Through the above calculation process, the CRITIC model assigns weights to the target evaluation in the Pareto optimal solution set. The calculation of each indicator and weight is shown in Table 1. The calculation results of TOPSIS are shown in Table 2. The initial values ​​and optimal values ​​of the motor structure parameters are shown in Table 3.

[0100] Table 1

[0101]

[0102] Table 2

[0103]

[0104] Table 3

[0105]

[0106] Figure 3 The correlation between different structural parameters and torque is shown in detail. When examining the relationship between electromagnetic torque and multiple structural parameters, except for slot width and air gap length, the influence of other parameters on electromagnetic torque is relatively balanced. However, when focusing on torque pulsation and cogging torque, the influence of pole arc coefficient and slot width on these two is particularly significant. Figure 4 The relationship between two key factors, pole arc coefficient and notch width corresponding to a response target torque ripple, is described.

[0107] Figure 5 The changes in electromagnetic torque before and after the optimization of the motor structure were compared in detail. After optimization, the average electromagnetic torque of the motor increased from 3.3748N·m to 3.9986N·m, an increase of 18.5%. At the same time, the change in torque pulsation was also significantly reduced, from 17.5% to 3%, a decrease of 14.5%. This change shows that under the same input power, the optimized motor can generate greater torque, thereby meeting the same power requirements, while reducing the consumption of electrical energy, thereby reducing operating costs. In addition, the cogging torque was also significantly improved during the optimization process of electromagnetic torque and torque pulsation. The results are shown in the figure below. Figure 6 As shown in the figure, the optimized cogging torque is reduced from 0.5576N·m to 0.1230N·m, a decrease of 77.9%. This significant reduction not only effectively reduces the vibration and noise of the motor, but also improves the stability and smoothness of the motor, providing a strong guarantee for the long-term stable operation of the motor.

[0108] The present invention integrates finite element analysis, correlation analysis, metamodel technology, multi-objective optimization strategy and hybrid evaluation model to form a set of efficient and accurate torque performance optimization methods. In this process, the present invention cleverly uses Pearson correlation analysis to accurately screen out key factors that have a significant impact on torque performance by deeply quantifying the linear relationship between variables, thereby achieving targeted optimization. At the same time, the moving least squares-polynomial regression-Kriging MLS-Polynomial-Kriging hybrid model is used to construct the optimal prediction metamodel, which significantly reduces the complexity and calculation dimension of finite element analysis, greatly shortens the time cost of optimization design, and effectively improves the optimization efficiency. In addition, the hybrid evaluation model CRITIC-TOPSIS adopted by the present invention further improves the optimality of the solution and the reliability of the results by comprehensively evaluating various indicators, ensuring the accuracy and effectiveness of the optimization design. The implementation of the present invention not only improves the efficiency of torque performance optimization, but also provides certain technical guidance and support for research in the field of torque.

[0109] The above embodiments are only for illustrating the technical concept and features of the present invention, and their purpose is to enable people familiar with the technology to understand the content of the present invention and implement it accordingly, and they cannot be used to limit the protection scope of the present invention. Any equivalent transformation or modification made according to the spirit of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for optimizing the torque of an outer rotor brushless DC motor, characterized in that: include: Step (1) establishing a parameterized finite element model of an outer rotor brushless DC motor to solve the performance; The outer rotor brushless DC motor was parametrically modeled using the pre-processing software Ansys Maxwell. The parametric structural variables included air gap length, pole arc coefficient, permanent magnet thickness, slot width, upper slot shoulder width, lower slot shoulder width, and slot depth. The output response was solved to obtain the average electromagnetic torque, torque ripple, and cogging torque peak-to-peak value. Step (2) constructing a Pearson correlation coefficient matrix framework between the motor model structural parameters and the output response; Step (3) obtaining key structural dimension parameter variables for different response targets and determining the number and range of variables; Step (4) The approximate function fitting between the target response and the structural independent variable is realized by using the moving least squares-polynomial regression-kriging MLS-Polynomial-Kriging mixed model, and the optimal prediction meta-model MOP is established based on the mixed model; Introducing the coefficient of determination R 2 To characterize the fitting degree and prediction accuracy of the optimal prediction meta-model MOP, it can be expressed as: In the formula, SS T is the sum of squares of the differences between the true data and its mean, SS R is the sum of squares of the mean differences between the predicted data and the true data, SS E is the sum of the squares of the differences between the actual data and the predicted data; i is the real data of the sample target variable, is the MOP prediction data; R 2 The closer it is to 1, the better the prediction effect of the optimal metamodel MOP is; Step (5) performing multi-torque target optimization on the optimal prediction meta-model MOP to obtain the Pareto optimal frontier; Step (6) Use the CRITIC-TOPSIS evaluation model to evaluate and rank the relative merits of the Pareto solution set to obtain the optimal structural size parameters.

2. The outer rotor brushless DC motor torque optimization method according to claim 1, characterized in that: In step (2), experimental DOE sample sampling is performed on the motor model under finite element solution to obtain sufficient sample data for correlation analysis.

3. The outer rotor brushless DC motor torque optimization method according to claim 2, characterized in that: In step (2), the Pearson correlation coefficient between the structural parameters and the output response is calculated and defined as follows: In the formula, X i There are seven decision variables, Y i are three optimization objectives, E(X) is the average value of the decision variables, and n is the total number of DOE sampling points.

4. The outer rotor brushless DC motor torque optimization method according to claim 1, characterized in that: In step (5), the evolutionary algorithm EA is used to perform multi-torque target optimization on the optimal prediction meta-model MOP.

5. The outer rotor brushless DC motor torque optimization method according to claim 1, characterized in that: In step (6), the weights of the average electromagnetic torque, torque ripple and cogging torque peak-to-peak value are calculated using the CRITIC model; and the Pareto front solution set is scored and ranked using the TOPSIS model; 1) Constructing the CRITIC model: Calculate the contrast strength θ of the jth indicator j : Calculate the contradiction and correlation coefficient between different indicators: In the formula, r ij represents the correlation coefficient between two indicators, f j Indicates the degree of contradiction between indicator j and other indicators; Calculate the information carrying capacity and weight of indicators: In the formula, C j represents the amount of information contained in the jth evaluation index, W j represents the weight assigned to the jth evaluation index; 2) The TOPSIS model is constructed as follows: The weighted data sample is y ij =W j h ij , the weighted decision matrix is ​​Y = [y ij ] m×n ; The ideal solution is: The negative ideal solution is: Compute the positive ideal solution distance: Compute the negative ideal solution distance: Compute the relative closeness of each solution to the positive and negative ideal solutions: Among them, the higher the relative closeness, the higher the score, that is, the plan i with the highest score is the optimal plan.

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