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JEET, Vol. 13, No. 6, November 2018 
Calculation of Magnetic Field for Cylindrical Stator Coils in Permanent Magnet Spherical Motor
Bin Li 
Area 
A  Electric Power Engineering 
Abstract 
This paper analyzed the magnetic field produced by the cylindrical stator coils of
permanent magnet spherical motor (PMSM). The elliptic equations about the vector magnetic potential
were given. Given that the eddy current effects are neglected, the magnet field of the PMSM is
regarded as irrotational field, which can be calculated by scalar magnetic potential. The current density
of cylindrical stator coil was proposed based on the definition of current density. The expression of
current density of stator coil was obtained according to the double Fourier series decomposition and
spherical harmonic functions. Then the magnetic flux density for scalar magnetic potential was
derived. Further, the influence of different parameters on radial flux density was also analyzed. Finally,
the results by the analytical method in this paper were validated by finite element analysis (FEA). 
Keyword 
Current density,Double Fourier series decomposition,PMSM,Scalar magnetic potential,Spherical harmonic functions,Vector magnetic potential.

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