Analysis Of Rotor Magnetic Field End Effect Of The Permanent Magnet Spherical Motor

With the rapid development of the advanced technology,such as robots and satellite position detection,permanent magnet spherical motor(PMSM)which is able to realize multi-dimensional movement with single shaft becomes a hot topic for research scholars.The magnetic field distribution surrounding the rotor permanent magnets(PMs)is closely related to the spherical structure of the PMSM.Some part of magnetic field lines could not completely corss through the main magnetic circuit at the end of the motor,but through the air or the rotor yoke for closing,which produces the end leakage magnetic field and causes the end magnetic field distortion.End leakage magnetic field of the motor not only cause interference on the main magnetic field,but also affect the static and dynamic performance of the motor,and reduces the motor efficiency.Eddy current caused by end leakage magnetic field distortion leads to temperature rise at the end of the motor parts,and reduces the reliability of the equipment.So,it is necessary to analyze the end effect of the motor.In this paper,the end effect of the Halbach array PMSM and related issuese are analyzed.The rotor magnetic poles of the Halbach array PMSM are spherical cone structure,and the air-gap magnetic field of the rotor magnetic poles along the latitude direction shows distortion characteristics.The magnetic field distribution could be divided into two areas,which is sinusoidal zone and end distortion zone.In order to study the end leakage magnetic field of the Halbach array PMSM along the latitude direction,the magnetic field distribution of the Halbach array PMs in the air gap is calculated using the scalar magnetic potential.Laplace and Poisson equations of the scalar magnetic potential in the spherical coordinate system are derived.To analyze the end leakage magnetic field of the Halbach array PMSM in the latitudinal direction,concept of mechanical pseudo cycle in the motor latitudinal direction is proposed and the cycle of Fourier series is redefined.A completed three dimensional analytical expression of the Halbach array PMSM magnetic field distribution is derived by the new Fourier series and spatial integral technology,in which the end leakage magnetic field is contained.The results obtained by the proposed analytical method are compared with the numerical results,i.e.The results by the finite element method(FEM),which verifies the correctness of the analytical method.The simulation results show that the the magnetic field end effect along the latitudinal direction has a greatinfluence on motor eddy current loss,and double layer PMSM is considered to weaken the influence of end effect on motor performance.Based on the analysis of the magnetic field distribution of the Halbach array PMSM,the remanent magnetization expression of the model is derived.According to the same solution throughway to analyze the three dimensional magnetic field distribution of double layer PMSM.Analytical results and finite element results show that the eddy current loss of the Halbach array PMSM is larger than that of the double layer PMSM,and proportion of the eddy current loss caused by the end effect of the Halbach array PMSM is larger than that of the double layer PMSM.Finally,The magnetic field results obtained by the proposed analytical method are compared with the experimental results,and the leakage magnetic field results obtained by the analytical method are coincident with the experimental result,which verifies the effectiveness of the analytical method to calculate leakage magnetic field.