Torque multi-objective optimization method for outer rotor permanent magnet motor

Abstract

The application discloses a torque optimization method for an outer rotor permanent magnet synchronous motor, and comprises the following steps: 1) design parameter selection: selecting key characteristics of a motor stator slot as design parameters, including slot shoulder height H s1 , tooth length H s2 , chord length B s0 and slot shoulder width B s1 ; 2) finite element model construction: establishing a multi-objective finite element model with tooth slot torque, torque ripple and average torque as targets; 3) analytical model establishment: establishing an analytical model of motor torque by using an energy method and a repeating unit method, and comparing with the finite element model to verify the accuracy of the analytical model; 4) response surface model construction: based on simulation data of the finite element model, performing finite element analysis by using a central composite design (CCD), constructing a response surface model, and performing sensitivity analysis on design variables to determine the influence of each variable on optimization targets; and 5) optimization efficiency improvement: determining an optimal configuration in a design space by using an adaptive genetic aggregation algorithm (AGA), so as to achieve a multi-objective optimization effect.

Description

Technical Field

[0001] This invention relates to the field of motor torque control, and specifically to a multi-objective torque optimization method for an external rotor permanent magnet motor. Background Technology

[0002] Electric vehicles equipped with external rotor permanent magnet synchronous motors (ERPMSMs) offer significant advantages in system efficiency, vehicle body control, and platform development, making them a research hotspot and important development direction in the next generation of electric vehicles. With the increasing demand for high-precision drive control of PMSMs, torque performance, as a crucial performance indicator of the motor, directly impacts its stable operation. Therefore, when optimizing the design of ERPMSMs, particular attention must be paid to the control of torque parameters to ensure stable motor operation.

[0003] In permanent magnet synchronous motors (PMSMs), torque parameters include torque ripple, cogging torque, and average torque. Torque ripple refers to the fluctuations in the motor's output torque during operation. PMSM torque ripple is typically caused by multiple factors, including non-uniformity of the magnetic field distribution, control strategy, and current control quality. Like other brushless DC motors, PMSMs generate cogging torque due to the interaction between the permanent magnets and the slotted armature core, leading to vibration and noise, and affecting the system's control accuracy. Average torque typically refers to the average output torque over a single motor operating cycle. During this cycle, the torque varies with the rotor position; therefore, the average torque is the average value of the torque variation within that cycle. In practical applications, the magnitude of the average torque is crucial to motor performance, affecting output power, efficiency, and stability. To reduce torque ripple and cogging torque, optimization of control algorithms and structural parameters are primarily employed. The former utilizes high-performance control algorithms, such as Field-Oriented Control (FOC) or Direct Torque Control (DTC), which can effectively reduce torque ripple. Zhou et al. proposed an improved PTC algorithm based on an extended control set (ECSPTC). In this algorithm, more candidate voltage vectors are extended to the control set, forming an ECS, thereby improving torque control accuracy and reducing torque ripple. X. Wang et al. proposed a composite torque regulator to optimize the torque tracking performance of a direct torque control permanent magnet synchronous motor driver. In the composite torque regulator, two new variable hysteresis bands are designed and combined with two constant hysteresis bands. By introducing the proposed composite torque regulator, the effects of torque deviation and time delay on torque ripple can be eliminated. W. Zhang et al. proposed a novel PMSM, namely a full harmonic torque PMSM, which utilizes all harmonics of magnetic dynamics to improve electromagnetic torque. Xia Kun et al. designed a new circuit topology and control method to suppress commutation torque ripple in a permanent magnet brushless DC motor. They adopted a power conversion circuit with a quasi-Z-source network as the main body added to the front stage of the three-phase bridge arm. During commutation, the DC bus voltage is adjusted by the quasi-Z-source network, thereby suppressing commutation torque ripple. Lu et al. proposed a maximum torque optimization control scheme for a DTP-PMSM driver for low-frequency and static operation. Both isolated neutral point and open winding structures were considered. A constrained nonlinear optimization problem was established, and the limit of the current amplitude was calculated as the limit of the inequality constraint to avoid local overheating. Then, the theoretically highest torque output capability was obtained using the interior point method.

[0004] Regarding the optimization of structural parameters, R. Islam et al. studied the torque ripple and cogging torque variation of tilted rotor permanent magnet synchronous motors. They investigated the influence of slot / pole combination and magnet shape on the magnitude and harmonic content of torque waveforms in PMSM drivers. Z. Shi et al. studied the cogging torque and dynamic performance of PMSMs at different tilt angles. Furthermore, they investigated the different effects of slot tilt angle on positive and negative rotational performance. Then, by comprehensive consideration, they studied the optimal tilt angle for PMSMs. K. Abbaszadeh used the slot opening tilt method to reduce sawtooth torque. A three-layer stator model of a six-pole PM-BLDC motor (18 slots, six poles, 5cm length) was considered, and a 2D dual model of this 3D slot opening tilt model was extracted. The angular offset of the slot opening positions of the first and third layers compared to the middle layer was used as optimization parameters. Optimization was performed using different optimization algorithms. F. Rezaee Alam et al. constructed a response surface method (RSM) model using polynomial regression. The experiment employed RSM as the statistical design method to study the influence of parameters on response changes. In this study, the optimal shift angle was determined to minimize cogging torque. Li Zheng et al. used the rotation torque and yaw torque of a permanent magnet rotor yaw three-degree-of-freedom motor as optimization objectives, applied the Taguchi algorithm to screen out the structural parameters that have a significant impact on the motor torque, constructed the response surface numerical model equation through finite element experiments, and analyzed the influence of the interaction between various factors in the response surface model on the response value.

[0005] In summary, torque optimization of the ERPMSM can be achieved by changing the motor's structural parameters and algorithmic control. However, while the aforementioned studies reduced torque ripple and cogging torque, they neglected the impact on average torque and output performance. Therefore, this paper conducts supplementary research in this area. This paper uses a finite element model and center composite experimental design (CCD) to establish a response surface model, and employs AGAA to optimize the stator slot tooth profile parameters, obtaining the optimal solution globally. The optimization results show that the motor's cogging torque is reduced (45.64%), torque ripple is decreased (8.5%), while the average torque increases (49.46%), and the motor's output torque efficiency is improved by 5.90%. This ensures that the output torque of the external rotor PMSM remains essentially unchanged, improving working efficiency and ultimately making the motor's operating performance more stable.

[0006] External rotor permanent magnet motors are widely used in electric vehicles and industrial drives due to their high efficiency and high power density. However, due to their complex electromagnetic structure and multi-objective design requirements, traditional optimization methods struggle to simultaneously improve multiple key performance indicators of the motor. This invention proposes a multi-objective optimization method combining Response Surface Methodology (RSM) and Adaptive Genetic Aggregation Algorithm (AGA), aiming to significantly improve the motor's cogging torque, torque ripple, average torque, and output efficiency. Summary of the Invention

[0007] To address the problems existing in the prior art, this invention provides a multi-objective torque optimization method for an external rotor permanent magnet motor.

[0008] The technical solution of the present invention is as follows:

[0009] A multi-objective torque optimization method for an external rotor permanent magnet motor is proposed, and the implementation steps are as follows:

[0010] 1) Design parameter selection:

[0011] The key characteristics of the motor stator slots are determined as design parameters, including the slot shoulder height (H). s1 ), tooth length (H) s2 ), chord length (B) s0 )

[0012] and shoulder width (B) s1 ).

[0013] 2) Optimize model construction:

[0014] Establish a multi-objective optimization model with cogging torque, torque ripple, average torque, and output efficiency as objectives.

[0015] 3) Establishment of analytical model:

[0016] An analytical model of the motor torque is established using the energy method and the repetitive element method for preliminary calculation and analysis.

[0017] 3) Finite element model verification:

[0018] An electromagnetic finite element model was constructed, and its torque simulation results were rigorously compared with those of the analytical model to ensure the accuracy of the analytical model.

[0019] 4) Response surface model construction and sensitivity analysis:

[0020] A response surface model is constructed based on simulation data from the finite element model.

[0021] Sensitivity analysis was performed on the identified design variables to determine the impact of each variable on the optimization objective.

[0022] 5) Optimize efficiency and improve performance:

[0023] A central composite design method is used for finite element analysis to improve optimization efficiency and the fitting accuracy of the response surface model.

[0024] 6) Optimization of the adaptive genetic aggregation algorithm:

[0025] The adaptive genetic aggregation algorithm (AGAA) is used to explore the design space based on the response surface model, determine the optimal configuration, and achieve the effect of multi-objective optimization.

[0026] 7) Optimization result verification:

[0027] The optimization results were verified through comprehensive torque efficiency experiments, ensuring that the smoothness and performance of the optimized external rotor motor were significantly improved in actual operation.

[0028] Furthermore, step 3) is as follows:

[0029] 3.1) Analytical Model of Cogging Torque

[0030] 3.1.1) Derivation of cogging torque using the energy method

[0031] Cogging torque is caused by the change in magnetic permeability between the stator slot and the permanent magnet. Neglecting the current, we only consider the magnetic field energy of the permanent magnet:

[0032]

[0033] Among them W m The energy of the magnetic field generated by the permanent magnet;

[0034] 3.1.2) Decomposition using the repeating element method

[0035] The magnetic field energy W of each slot-pole unit m,u Approximately:

[0036]

[0037] The total cogging torque is the sum of the contributions from each unit:

[0038]

[0039] 3.1.3) Analytical Formula

[0040] The air gap permeability Λ(θ) and permanent magnet magnetomotive force F are decomposed using Fourier transform. pm (θ), the cogging torque expression is:

[0041]

[0042] in:

[0043] G k: The amplitude of the kth harmonic of the air gap permeability; F k : The amplitude of the kth harmonic of the permanent magnet magnetomotive force;

[0044] 3.2) The repeated element method is used to calculate torque ripple and average torque:

[0045] 3.2.1) Total torque decomposition:

[0046] The total torque of the motor consists of two parts: the total average torque and the total torque pulsation.

[0047] T = T all_avg +T all_rip (1)

[0048] The torque ripple component is represented as:

[0049] Where: N ps T is the number of pole pairs of the permanent magnet, α is the electrical angle, and T is the number of pole pairs of the permanent magnet prn Let p be the amplitude of the nth torque pulsation, and p be the number of repeating units;

[0050] 3.2.2) Repeated element method modeling:

[0051] Periodic structural constraints introduce constraints into the repeating element method:

[0052] b·q=p (3)

[0053] In the formula: b is the number of slots in each repeating unit, and q is the winding distribution coefficient;

[0054] Total torque ripple expression: Considering the periodic displacement θ=2π / (Npsq), the total torque ripple is expressed as:

[0055]

[0056] In the formula, Tprjn is the nth torque pulsation component of the j-th repeating unit;

[0057] 3.2.3) Derivation of average torque:

[0058] Substituting equation (4) into equation (1) using the decomposition formula, we can expand the expression for the average torque:

[0059]

[0060] Non-ideal factor correction: Considering the symmetry disruption caused by magnet displacement, a correction term is introduced:

[0061]

[0062] In the formula: T pav For the ideal average torque, ΔT jLet ΔT be the j-th order non-ideal average torque deviation. rj The deviation of the j-th order pulsation component;

[0063] Substituting equation (6) into equation (5) and rearranging, we get:

[0064] T avg =pT pav +T r +ΔT (7)

[0065] The average torque consists of an ideal component, a periodic pulsating component, and a non-ideal correction component, wherein:

[0066] Ideal average torque: Tpavg;

[0067] Periodic pulsating torque:

[0068] Non-ideal corrected torque:

[0069] 3.2.4) Torque ripple analysis:

[0070] Trigonometric function composition, using identities:

[0071]

[0072] Given the periodic displacement condition and the equation p = 2π / q, the torque pulsation exhibits a frequency doubling characteristic, with its amplitude modulated by the number of repeating elements p and the displacement angle θ. Simplifying, we get:

[0073]

[0074] 3.2.5) Key Conclusions

[0075] The average torque consists of an ideal component, a periodic pulsating component, and a non-ideal correction component;

[0076] The torque pulsation exhibits frequency doubling characteristics, and its amplitude is modulated by the number of repeating units p and the displacement angle θ.

[0077] Higher-order pulsation components introduced by non-ideal factors can be linearly corrected using the superposition principle.

[0078] This derivation strictly follows electromagnetic field theory and Fourier series expansion. By introducing the periodic displacement condition of repeating elements, a torque analytical model considering magnet asymmetry is systematically established. Results show that magnet displacement can effectively suppress torque ripples of a specific order, providing a theoretical basis for motor optimization design.

[0079] Furthermore, step 4) is as follows:

[0080] Finite element analysis was performed using a central composite design CCD to construct a response surface model:

[0081] With H s0 H s2 B s0 B s1 Let x be the independent variable and y be the response value of the motor torque parameter. A mathematical model is established, and its expression is:

[0082]

[0083] In the formula, a0 is an undetermined coefficient; x1, x2, x3, and x4 represent H respectively. s0 H s1 B s0 B s1 β0 represents the fitting error;

[0084] Expressing the above equation as a linear matrix, and using the least squares method to obtain the estimated value a of a0, as shown below, the fitted regression mathematical model is:

[0085] Y = Xa + β

[0086] A = (X T X) -1 X T Y

[0087]

[0088] Sensitivity analysis of the design variables is conducted to determine the degree of influence of each variable on the optimization objective.

[0089]

[0090] In the formula, X i For the i-th optimization parameter, Y j For the j-th optimization objective; A(Y) j / X i ) is when X i When Y is a constant j The mean, V[A(Y) j / X i )] is A(Y j / X i The variance of V(Y) j ) is Y j The variance;

[0091] The three optimization objectives are cogging torque, torque ripple, and average torque. Each optimization parameter has a different sensitivity to the optimization objective. The multi-objective sensitivity analysis is transformed into a comprehensive sensitivity analysis with weighted coefficients, and its index is expressed as:

[0092]

[0093] In the formula, Q j Weighting coefficients for different optimization objectives;

[0094] Statistical analysis was performed on the simulation results, and the experimental results were fitted using a multivariate two-dimensional model. After removing irrelevant variables, the model was corrected.

[0095] Furthermore, step 5) is as follows:

[0096] 5.1) Population initialization:

[0097] Randomly generate N initial individuals that need to uniformly cover the design space. Each individual represents a combination of design variables and is encoded as binary or real number.

[0098] That is: shoulder height H s1 Tooth length H s2 chord length B s0 and shoulder width B s1 Encode it as a real number vector X∈R, and apply boundary constraints:

[0099]

[0100] Penalty function methods or repair strategies are used to handle out-of-bounds individuals to ensure the feasibility of the solution, that is, to ensure that the input data used by the response surface model in the optimization process is valid;

[0101] Initialize genetic algorithm parameters: crossover probability P c Probability of mutation P m Maximum number of iterations T max .

[0102] The target value T is calculated using finite element analysis or a surrogate model. avg T rip T cog ;

[0103] 5.2) Construct a fitness function F(X), and quantify and aggregate the optimization objectives of cogging torque, torque ripple, and average torque through weights to form a fitness function:

[0104]

[0105] The weighting coefficients w1-w4 are dynamically adjusted according to project requirements;

[0106] 5.3) Fitness assessment and ranking: perform non-dominated ranking of individuals, calculate crowding degree, and ensure that the solution set is evenly distributed in the target space;

[0107] 5.4) Parameter settings for genetic operations:

[0108] Selection: Tournament selection will be used;

[0109] Cross: Perform simulated binary cross (SBX) or arithmetic cross on the selected parent:

[0110] X child =λX parent1 +(1-λ)X parent2 ,λ~U(0,1)

[0111] Mutation: Applying non-uniform perturbation to the mutation site:

[0112] x i ′=x i +N(0,σ i ),σ i ∝xi′

[0113] Where t is the number of iterations, gradually narrowing the search range.

[0114] 5.5) Population Update and Convergence Judgment:

[0115] The parent and offspring populations are merged, and the new generation of N individuals is selected based on non-dominant sorting and crowding. Pareto solution set analysis is used, and the process terminates when the Pareto front improvement rate (ΔPF<∈) or the maximum number of iterations is reached.

[0116] 5.6) Output all non-dominated solutions to form a set of trade-off solutions.

[0117] The beneficial effects of this invention are as follows:

[0118] The multi-objective optimization method proposed in this invention, by combining response surface methodology and adaptive genetic aggregation algorithm, effectively improves the cogging torque, torque ripple, average torque, and output efficiency of a 26-pole, 48-slot external rotor permanent magnet motor. Experimental results show that the optimized motor exhibits significant improvements in smoothness and performance, demonstrating the great potential of this optimization framework in advancing the design and operation of external rotor permanent magnet motors. Attached image description:

[0119] Figure 1 dq coordinate system diagram;

[0120] Figure 2 ERPMSM electromagnetic model;

[0121] Figure 3 Original stator tooth profile;

[0122] Figure 4 ERPMSM (a) stator; (b) rotor;

[0123] Figure 5 Optimize the flowchart;

[0124] Figure 6 Sensitivity analysis;

[0125] Figure 7 CCD layout diagram;

[0126] Figure 8 Structural parameter H s2 B s0 B s1 Cogging torque response surface under structural parameters;

[0127] Figure 9 Structural parameter H s2 B s0 B s1 Lower torque ripple response surface;

[0128] Figure 10 Structural parameter H s2 B s0 B s1 Lower average torque response surface;

[0129] Figure 11 Structural parameter H s2 B s0 B s1 Lower output efficiency response surface;

[0130] Figure 12 Torque and efficiency experiment setup;

[0131] Figure 13 Original and optimized stator models;

[0132] Figure 14 AGA convergence curve;

[0133] Figure 15 Comparison of cogging torque, torque ripple, and average torque between the original model and the optimized model;

[0134] Figure 16 Torque-speed efficiency diagrams before and after optimization: (a) original design; (b) optimized design. Detailed implementation method:

[0135] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0136] like Figure 1-16As shown, a multi-objective optimization method for a 26-pole 48-slot external rotor permanent magnet motor based on response surface methodology and adaptive genetic aggregation algorithm is presented. This method combines response surface methodology (RSM) and adaptive genetic aggregation algorithm (AGA) for multi-objective optimization of a 26-pole 48-slot external rotor permanent magnet motor.

[0137] External rotor permanent magnet motors are widely used in electric vehicles, industrial drives, and other fields due to their compact structure and high efficiency. Motor performance indicators such as cogging torque, torque ripple, average torque, and output efficiency have a significant impact on the overall performance of the motor. Therefore, optimizing motor design parameters to improve these performance indicators is of great importance.

[0138] The purpose of this invention is to propose a multi-objective optimization method for a complex 26-pole, 48-slot external rotor permanent magnet motor, aiming to improve the motor's key performance indicators. By combining response surface methodology and adaptive genetic aggregation algorithm, the key characteristics of the motor stator slots are optimized, including the slot shoulder height (H). s1 ), tooth length (H) s2 ), chord length (B) s0 ) and shoulder width (B s1 ).

[0139] Example:

[0140] An analytical model of the motor torque was established using the energy method and the repeating element method. This model provides a theoretical basis for the subsequent optimization process.

[0141] Table 1 Motor structural parameters

[0142]

[0143] Table 2 Initial Stator Dimensions and Design Space

[0144]

[0145] Table 3 Stator Fixing Parameters and Condition Parameters

[0146]

[0147]

[0148] R in Table 3 s Stator slot radius, σ s The material is LY12Z aluminum alloy, and Gap is the air gap length between the stator and the permanent magnet. These parameters are used as boundary conditions for this optimization model.

[0149] An electromagnetic finite element model was established based on Table 1. The motor torque was simulated using electromagnetic finite element analysis (FEA). The simulation results were compared with the analytical model to verify the accuracy of the analytical model.

[0150] Response surface model construction: Using Tables 2 and 3 as boundary conditions, a response surface model is constructed based on the validated analytical model and finite element simulation results. Sensitivity analysis is performed on the identified design variables to determine their impact on motor performance indicators.

[0151] Central Composite Design (CCD) Finite Element Analysis: The Central Composite Design (CCD) method is used for finite element analysis to improve the accuracy and optimization efficiency of the response surface model.

[0152] With ERPMSM's H s0 H s2 B s0 B s1 Let x be the independent variable and y be the response value of the motor torque parameter. A mathematical model is established, and its expression is:

[0153]

[0154] In the formula, a0 is an undetermined coefficient; x1, x2, x3, and x4 represent H respectively. s0 H s1 B s0 B s1 β0 represents the fitting error.

[0155] Expressing the above equation as a linear matrix, and using the least squares method to obtain the estimated value of a0, as shown below, the fitted regression mathematical model is:

[0156] Y = Xa + β

[0157] A = (X T X) -1 X T Y

[0158]

[0159] To reduce errors when fitting the quadratic response surface, a CCD was used to construct sampling points. To ensure model reliability, β was set to 1.5792. Simulations were performed using finite element software according to the experimental groups in Table 3. Because the finite element software ANSYS Maxwell 2D uses adaptive mesh generation, continuously refining the mesh based on the ongoing calculation results, slight differences exist in the mesh generation and calculation results of the PMSM model even under the same parameters. Therefore, the results of experimental groups 9 to 12 may differ slightly (data in Table 8). Statistical analysis of the simulation results was performed using Design-Expert software. A multivariate two-dimensional model was used to fit the experimental results, and the model was corrected after removing insignificant variables. For these three optimization parameters, the cogging torque T was established. cog Electromagnetic average torque T avg and electromagnetic torque pulsation T rip The optimization model.

[0160] Analysis of the results data using Design-Expert yielded the following second-order fitting models for cogging torque, torque ripple, and average torque:

[0161]

[0162] Table 4T cog Analysis of variance of the fitted model

[0163]

[0164] Table 5T rip Analysis of variance of the fitted model

[0165]

[0166] Table 6T avg Inverse analysis of the fitted model

[0167]

[0168] Table 7Q out Inverse analysis of the fitted model

[0169]

[0170]

[0171] Tables 4-7 show that for the tooth-coiling torque T cog Torque pulsation T rip Average torque T avg and output efficiency Q outThe p-values ​​of all fitted models were less than 0.05, indicating good model fit and statistical significance. The p-values ​​of all three models' misfits were greater than 0.05, indicating small and insignificant errors in the fit. The corrected coefficient of determination of the regression equation can evaluate the model's quality while considering the influence of the number of independent variables, and determine whether the relationship between the experimental factor and the response is significant. The Design-Expert statistical analysis results show that T... cog T rip T avg and Q out The corrected coefficients of determination were 0.9735, 0.9963, and 0.9952, respectively, all greater than 0.9, indicating a significant relationship between the experimental factors and the response. The model fully represents the relationship between the experimental factors and the response. It can be seen that there is a significant linear relationship between the response value and the optimization variable, demonstrating high fitting accuracy.

[0172] Table 8. CCD Experiment Arrangement and Finite Element Analysis Results

[0173]

[0174]

[0175] Applying the adaptive genetic aggregation algorithm:

[0176] An adaptive genetic aggregation algorithm is used to optimize the constructed response surface model, explore the design space, and determine the optimal configuration. The adaptive genetic algorithm is a parallel, stochastic, and efficient heuristic optimization method that simulates natural genetic mechanisms and biological evolution, primarily optimizing the selection of individual fitness. During the optimization process, gene recombination and mutation directly affect the convergence speed and quality of the optimization results.

[0177] Table 9 Parameters of the Adaptive Genetic Aggregation Algorithm

[0178]

[0179] As shown in the figure, the AGAA optimization algorithm has good convergence speed and smoothness, and tends to stabilize after 20 iterations. Based on the adaptive genetic algorithm and related optimization parameters set in this paper, the optimization results are compared with the initial optimization values ​​as shown in Table 10 (H). s1 If the parameters remain unchanged before and after optimization, and the relationship between this experimental factor and the response is not significant, it can also be deleted from Table 10.

[0180] Table 10 Comparison of optimization results and initial optimization values

[0181]

[0182] Experimental verification:

[0183] The optimization results were verified through comprehensive torque efficiency experiments, ensuring that the optimized external rotor motor has significantly improved in terms of smoothness and performance.

[0184] This paper proposes a multi-objective optimization method for a 20-pole, 18-slot in-wheel motor, integrating response surface methodology and adaptive genetic aggregation algorithm. The method is based on the tooth profile parameters of the motor stator slots: slot shoulder height H... s1 Tooth length H s2 Tooth width B s0 Shoulder width B s1 Using the motor's torque ripple, average torque, and cogging torque as design variables, a multi-objective optimization model was constructed with these as design objectives. First, sensitivity factors were introduced based on the importance of each sub-objective, establishing a unified global optimization objective function. Second, to improve optimization efficiency, a central composite design was established to obtain a finite element analysis test scheme, and the least squares method was used to fit the high-precision response surface equations of each sub-objective. Finally, an adaptive genetic aggregation algorithm was used to obtain the optimal solution in the design space based on the response surface model. The multi-objective optimization results show that the motor's cogging torque was reduced by 45.64%, torque ripple decreased by 8.50%, while the average torque increased by 49.46%, and the motor's torque output efficiency improved by 5.90%, ultimately resulting in more stable motor operation and improved working efficiency.

[0185] The optimization method proposed in this invention has the following advantages:

[0186] Multi-objective optimization: comprehensively considers cogging torque, torque ripple, average torque and output efficiency to improve the overall performance of the motor.

[0187] Accuracy: The accuracy of the model is ensured through rigorous comparison between the analytical model and the finite element simulation results. Efficiency: The combination of response surface methodology and adaptive genetic aggregation algorithm improves optimization efficiency and the reliability of the results.

[0188] Experimental results:

[0189] Experimental results demonstrate that the optimized external rotor permanent magnet motor significantly improves smoothness and performance, proving the effectiveness of the proposed optimization framework and showcasing its potential for advancing the design and operation of external rotor permanent magnet motors.

Claims

1. A torque optimization method for an external rotor permanent magnet synchronous motor, characterized in that, The method comprises the following steps: 1) design parameter selection: Key characteristics of motor stator slots, selected as design parameters, include slot shoulder height H s1 , tooth length H s2 , chord length B s0 , and slot shoulder width B s1 ; 2) finite element model construction: A multi-objective finite element model is established with the cogging torque, torque ripple and average torque as the targets; 3) analytical model establishment: An analytical model of the motor torque is established by using the energy method and the repeating unit method, and is compared with the finite element model to verify the accuracy of the analytical model; 4) response surface model construction: Based on the simulation data of the finite element model, finite element analysis is performed by using the central composite design (CCD), a response surface model is constructed, and sensitivity analysis is performed on the design variables to determine the influence of each variable on the optimization target; 5) optimization efficiency improvement: An adaptive genetic aggregation algorithm (AGA) is used to determine the optimal configuration in the design space to achieve the effect of multi-objective optimization; The step 5) is specifically as follows: 5.1) population initialization: Randomly generated N Initial individuals, need to cover the design space evenly, each individual represents a combination of design variables, encoded as binary or real numbers; i.e. shoulder height H s1 , tooth length H s2 , chord length B s0 and slot shoulder width B s1 are encoded as real vectors X ∈ R, and boundary constraints are imposed: ； The penalty function method or the repair strategy is used to process the out-of-bound individuals to ensure the feasibility of the solution, that is, to ensure that the input data used by the response surface model in the optimization process is effective; Initialize genetic algorithm parameters: crossover probability P c , mutation probability P m , maximum number of iterations T max ; Calculating the target value by finite element analysis or a proxy model T avg , T rip , T cog ; 5.2) constructing a fitness function F(X), and quantitatively aggregating the optimization targets of the cogging torque, torque ripple and average torque by using weights to aggregate them into a fitness function: ； Weighting factor , dynamically adjusted according to engineering requirements; 5.3) fitness evaluation and sorting, non-dominated sorting is performed on the individuals, the crowding degree is calculated, and it is ensured that the solution set is uniformly distributed in the target space; 5.4) parameter setting of genetic operation: Selection: tournament selection is adopted; Crossover: performing simulated binary crossover (SBX) or arithmetic crossover on the selected parents: ； Mutation: non-uniform perturbation is applied to the mutation site: ； wherein t is the number of iterations, gradually narrowing the search range; 5.5) population update and convergence judgment: Merge parent and offspring populations, select new generation by non-dominated sorting and crowding distance N of individuals; terminate when the rate of improvement of the Pareto front is less than a predetermined value or the maximum number of iterations is reached of individuals; terminate when the rate of improvement of the Pareto front is less than a predetermined value or the maximum number of iterations is reached 5.6) output all non-dominated solutions to form a trade-off scheme set.

2. The torque optimization method of an outer rotor permanent magnet synchronous motor according to claim 1, characterized in that, The step 3) is specifically as follows: 3.1) cogging torque analytical model 3.1.1) cogging torque derived by energy method The cogging torque is caused by the change of the magnetic conductance between the stator slot and the permanent magnet. The current is ignored, and only the permanent magnet magnetic field energy is considered: ； wherein W m the magnetic field energy generated by the permanent magnets; 3.1.2) decomposition by repeating unit method Magnetic field energy of each slot-pole unit W m,u Approximately: ； The total cogging torque is the superposition of the contributions of each unit: ； 3.1.3) analytical formula By Fourier decomposition of the air gap permeance Λ Wherein: ) and permanent magnet flux F pm ( 3.2) calculating torque ripple and average torque by using repeating unit method: ), the cogging torque expression is: ； 3.2.1) total torque decomposition: G k : The first air gap permeability k Second harmonic amplitude; F k The first permanent magnet magnetomotive force k Second harmonic amplitude; The total torque of the motor is composed of the total average torque and the total torque ripple: 3.2.2) repeating unit method modeling: The constraint condition of the repeating unit method is introduced under the constraint of the periodic structure: ； where the torque ripple component is expressed as: ; In the formula: N ps is the number of pairs of permanent magnet poles, a is the electrical angle, T prn is the first n torque ripple amplitude, p is the number of repeating units; 3.2.3) average torque derivation: Substitute the decomposition formula into formula (1) to expand the average torque expression: ； wherein: b is the number of slots per repeat unit, q is the winding distribution factor; Total torque ripple expression: considering periodic displacement Non-ideal factor correction: considering the symmetry destruction caused by the displacement of the magnet, a correction term is introduced: = 2π / ( N ps q ), the total torque ripple is expressed as: ； In the formula T prjn is the first j is the first n torque pulsation component of the i-th repeating unit. Combine the correction term to substitute formula (6) into formula (5) to get: The average torque is composed of the ideal component, the periodic ripple component and the non-ideal correction component, wherein: ； 3.2.4) torque ripple analysis: ； where: T pav is the ideal average torque, Δ T j is the first j order non-ideal average torque deviation, Δ T rj is the first j order fluctuation component deviation; Synthesis of trigonometric functions, use of identity: ； p, θ Ideal average torque: T pavg ; Periodic pulsing torque: ; Non-ideal correction torque: ; θ The step 4) is specifically as follows: ； Periodic displacement conditions, in combination The central composite design (CCD) is used for finite element analysis to construct a response surface model: = 2π / q， Torque ripple exhibits a frequency multiplication characteristic, with the amplitude being dependent on the number of repeating units p and the displacement angle Sensitivity analysis is performed on the design variables to determine the degree of influence of each variable on the optimization target; Modulation, simplifying to: 。 3. The torque optimization method of an external rotor permanent magnet synchronous motor according to claim 1, characterized in that, ​ ​ With H s1 , H s2 , B s0 , B s1 as the independent variable x , the motor torque parameter as the response value y , a mathematical model is established, and its expression is: ； wherein are to be determined coefficients; x 1 , x 2 , x 3 、x 4 represent respectively H s1 , H s2 , B s0 , B s1 ; β 0 is the fitting error; The above equation is expressed as a linear matrix, and the estimated value of is obtained using the least square method The fitted regression mathematical model is as follows: ； ​ ； wherein X i is the i th optimization parameter, Y j is the j th optimization objective; A Y j / X i is the mean of X i when Y j is constant, V [ A j Y i ] is the variance of / X j A i Y j / X i V j Y j Y j ​​​​ The sensitivities of three optimization objectives, i. e., the cogging torque, the torque ripple and the average torque, to the optimization parameters are different. The multi-objective sensitivity analysis is converted into a comprehensive sensitivity analysis with weight coefficients, and the index is expressed as: ； In the formula, Q j weight coefficients for different optimization objectives; The simulation results are statistically analyzed, and the experimental results are fitted by using a multi-element two-dimensional model. After eliminating irrelevant variables, the model is corrected.

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