Image Method With Distributed Multipole Models for Analyzing Permanent-Magnet-Based Electromagnetic Actuators

Many high-torque electromagnetic problems involve solving three dimensional (3D) magnetic fields of the permanent magnets (PMs) and/or electromagnet magnets (EMs) in the presence of magnetically conducting surfaces. This paper extends the distributed multi-pole (DMP) method, which offers a means to present the three-dimensional magnetic field solution in closed form, to account for the effects of the magnetic conducting boundary using an image method. We validate the DMP/image method by comparing the torques calculated using the Lorentz force equation and Maxwell stress tensor against numerical results computed using a finite element method (FEM). While two methods agree to within 5% in maximum torque, the DMP/image method takes less than 1% of the FEM computation time. With the numerically validated torque computation, we demonstrate how the DMP/image method can be used to analyze designs of a spherical wheel motor as illustrative practical applications.