Optimization Of Magnetic Field Of Halbach Array Permanent Magnet Spherical Motor Based On Support Vector Machine

With the development of modern industry,multi-degree-freedom systems have received more and more attention.Due to its compact structure and accurate control,permanent magnet spherical motor(PMSM)with a single axis has gradually become a replacement for conventional multi-degree-of-freedom transmission mechanisms.Currently,the research on PMSM has been still in the theoretical exploration stage.Especially for the optimization of the motor structure parameters,the related theoretical methods are poor.How to establish a PMSM model that is accurate and suitable for fast and massive iterative calculation is an important part in multi-degree-freedom motor research.The waveform and amplitude of the air-gap magnetic density of PMSM not only affect the vibration and noise,but also affect the torque output.Therefore,it is necessary to rationally optimize the magnetic field of PMSM.In this paper,according to the special structure of the spherical rotor of the Halbach array PMSM,the axial air-gap magnetic field is analyzed and optimized.The fundamental harmonic amplitude and waveform distortion are the important indicators to measure the performance of magnetic field.In this paper,the three-dimensional(3-D)finite element model of the Halbach array PMSM is established.The influence of the motor structural parameters on the amplitude and waveform of the axial air-gap magnetic is analyzed.The range of the optimized design variables is preliminarily determined.In order to reduce the computational cost and improve the modeling efficiency,the idea of nonparametric modeling based on support vector machine(SVM)is introduced.The sample data for modeling is obtained by orthogonal experiment,which effectively reduces the times of experiment.The grid search(GS)algorithm,genetic algorithm(GA)and particle swarm optimization(PSO)algorithm are used to optimize the parameters of SVM model.And the prediction accuracy of the models is compared.Then an improved GS algorithm with half space and variable step is proposed to improve the efficiency of model parameter optimization.Based on the model parameters obtained by the improved GS algorithm,a nonlinear regression model of the axial air-gap magnetic field is established.In order to avoid the excessive rotor mass affecting the dynamic response of the motor,the moment of inertia of Halbach array PMSM is calculated.Based on the established mathematical model,the PSO algorithm is employed to optimize the motor structure.The multi-objective optimization is converted to single-objective optimization by adding weight coefficients to three objective functions.And the optimization results under different weight coefficients are presented.In order to select the optimal solution from a series of feasible solutions,the technique for order preference by similarity to ideal solution(TOPSIS)is introduced.Finally,the performances of the motor before and after optimization are compared to verify the effectiveness and efficiency of the optimization method for the structural design of the complex PMSM.