Analytical Solution Of Magnetic Field In Embedded Permanent Magnet Machines

Embedded permanent magnet motors have been widely used in industrial and household appliances.In particular,electric vehicles require high efficiency,high power density and a constant power speed range.Compared with other types of permanent magnet motor,the embedded permanent magnet synchronous motor has more concentrated permanent magnet flux and stronger mechanical structure,thus providing better performance.Therefore,embedded permanent magnet synchronous motor(PMSM)has become a very powerful competitor in industrial applications,and its design and optimization are very important.In this paper,the accurate subdomain model of the embedded permanent magnet synchronous motor is established,and the different analytical solutions of the subdomain under different magnetization modes of the permanent magnet and different stator winding arrangement modes are considered.Taking a 6-pole 36-slot permanent magnet synchronous motor as an example,the analytical solution is compared with the finite element and experiment to verify the accuracy of the model.Firstly,in the two-dimensional polar coordinate plane,an accurate subdomain model of radial and parallel magnetization of arc-shaped permanent magnets and different arrangements of stator slot windings(single winding,double winding left and right arrangement and double winding up and down arrangement)is established,The general solution of the magnetic potential equation of the corresponding subdomain was obtained by Fourier decomposition and mirror image method.Then,an accurate subdomain model of a permanent magnet synchronous motor with rectangular permanent magnets is established in the two-dimensional polar coordinate plane,and the influence of saturation is considered.Based on the same principle of constant magnetic energy product and constant polar arc coefficient,rectangular magnets are equivalent to two sector regions.The entire motor is divided into seven simple sub-domains,including inner sector permanent magnets,outer sector permanent magnets,permanent magnets,and air gaps.Between the part,the air gap,the stator slot and the two saturation regions.Before the equivalent of the permanent magnets,that is,the rectangular permanent magnets,the shorter the leakage flux path,the more severe the saturation,and the range of the saturation region was determined.Finally,the corresponding Poisson's and Laplace's equations are written in each sub-domain column,and the magnetic potential equations and corresponding coefficients of each sub-domain are determined according to the separation variable method and the interface conditions of each sub-domain.Under no-load conditions,the analytical calculation solutions of air-gap magnetic field and no-load backelectromotive force are compared with finite element.The analytical calculation solutions of air-gap magnetic field under load are compared with finite element.The analytical calculation solution of moment is compared with finite element and experiment.Verifying the accuracy of the analysis model.