Computing the External Magnetic Scalar Potential due to an Unbalanced Six-Pole Permanent Magnet Motor

The accurate computation of the external magnetic field from a permanent magnet motor is accomplished by first computing its magnetic scalar potential. In order to find a solution which is valid for any arbitrary point external to the motor, a number of proven methods have been employed. Firstly, A finite element model is developed which helps generate magnetic scalar potential values valid for points close to and outside the motor. Secondly, charge simulation is employed which generates an equivalent magnetic charge matrix. Finally, an equivalent multipole expansion is developed through the application of a toroidal harmonic expansion. This expansion yields the harmonic components of the external magnetic scalar potential which can be used to compute the magnetic field at any point outside the motor. INTRODUCTION In order to accurately compute the external magnetic field from a permanent-magnet motor valid for both the near-field and the far-field, a technique which employs toroidal harmonics is developed. This method is most useful for validating magnetic field measurements close to the hull of a cylindrical motor and for accurately predicting the far-field solution when other methods, such as a finite element analysis, are not very accurate. The well-known method of charge simulation, nicely explained in Schwab (1988), is employed so that the permanent magnet motor may be replaced by its equivalent charge distribution on an external circular cylinder. This technique was first employed by Kwon et al. (2004) for studying the external field from a permanent magnet motor. Kwon implemented this method for a spherical system. However, in order to more accurately map the geometry of a motor, a circular cylindrical geometry is more useful.