Modeling And Analysis Of Unilateral/bilateral Excitation Permanent-Magnet Vernier Machine Based On Equivalent Magnetic Network Method

Permanent magnet vernier(PMV)motor has the advantages of compact structure,high power density,and the characteristic of offering high torque at low speed,is suitable for the direct drive applications of wind power generation,electric vehicles and urban railway system.However,the PMV motors have complex multi-pole and multi-tooth structure,which leads to severe magnetic leakage and local magnetic saturation.Besides,flux modulation will further increases the complexity of air gap magnetic field distribution,which brings great difficulty in electromagnetic field analysis.Finite element method was commonly used in the design and analysis of PMV motors.Although it has high accuracy,huge computational cost and time cost are required in parametric analysis,and it cannot meets the requirement of high efficiency.Therefore,the equivalent magnetic network method(EMNM)is proposed to be applied in the rapid analysis of PMV motor.EMNM can be divided into two categories.The first one predetermines the flux path according to magnetic lines,called magnetic circuit based EMNM,which is suitable for the modeling of regular magnetic field.The second one uses the grids to simulate magnetic circuit,without setting the flux path,called grid based EMNM,which is suitable for complex magnetic field.In this paper,the two EMNMs are researched for the electromagnetic performance analysis of a bilateral excitation PMV motor(coils and permanent magnets are respectively placed in stator and rotor)and a unilateral excitation PMV motor(coils and permanent magnets are all placed in stator),respectively.The region division method of complex magnetic field,the permeance calculation method and the equivalent method of air-gap permeance are putted forward,as well as two kinds of new modular mesh generation schemes.Specific ideas and research results are as follows:For the bilateral excitation PMV motor,the characteristics of magnetic field distribution and its influencing factors are analyzed firstly.It is shown that the magnetic field distributions are complex in air gap area,but simple and regular in the other areas.Besides,the air gap magnetic field will be greatly affected by the armature current,and its flux distributions is quite different in no-load and on-load condition.Hence,both the no-load model and on-load model are established.For the no-load model,the modeling scheme of air gap magnetic field is mainly introduced,including the determination of permeance shape,the calculation of permeance and the establishment of the connections of permeances.Moreover,the model solving process is introduced in detail.For the on-load model,a simplified equivalent scheme of air gap permeance is proposed on the basis of no-load model,and the tangential component of end permeance of the modulation tooth is neglected,which make the on-load model more inductive than the no-load one.In addition,iterative divergence occurs due to the over saturation in armature teeth that caused by the winding magnetomotive force,then a magnetic circuit conversion method is proposed in this paper to solve the problem.For the unilateral excitation PMV motor,own to the particularity of its structure,the air gap magnetic field is extremely complex,and it is difficult to set the magnetic paths.Hence,the mesh based EMNM is used for modeling.Two new mesh generation methods are proposed,including square segmentation method and regular hexagon segmentation method.The mesh cells generated by the new segmentation methods have the characteristics of symmetry,modularization and flexibility,can improve the model accuracy and modeling efficiency.The permeance calculation formula,the arrangement of cells and the numbering law of nodes are discussed in detail.According to the characteristics of the magnetic field distribution,the grid based EMNM is applied to the modeling of air gap region,and the nonlinear magnetic circuit method is applied to the modeling of other regions.Magnetic flux leakage,magnetic saturation and end effect are taken into account in the model.In addition,an improved nonlinear algorithm is proposed,which has good convergence accuracy when the core is seriously saturated.Finally,the simulation results of the models are compared with the experimental results and the finite element simulation results.The comparison results have verified the accuracy and effectiveness of the established magnetic network models.