A new equivalent method of permanent magnets and analytical solution of air-gap magnetic field of permanent magnet linear synchronous motors

It is difficult to obtain an analytical solution of magnetic field of permanent magnet linear synchronous motors due to longitudinal opening of its primary iron-core. This paper presents a new equivalent method of permanent magnets for analytical of magnetic field. Firstly, the physical model of the motor is proposed under a series assumptions based on features of the motor. Through analysis of characteristics of magnetic materials and the equivalent current method of permanent magnets, the paper proposes that the magnet array is treated as independent field source at the analytical region boundary, and derivates its mathematic form of equivalent boundary condition of permanent magnets. By this equivalent method, the Poisson equation of describing magnetic field is simplified into the second order homogeneous partial differential equation and can be easily solved. Finally, analytical of air-gap magnetic field is conducted and the analytical solution is conveniently obtained. By comparing with other research works, the correctness of the analytical result is confirmed. The proposed method could be further applied to explore analytical of magnetic fields for different regions of permanent magnet linear synchronous motors.