Analytical Modeling of Steel Shielding Cylinder in Surface-Mounted Permanent Magnet Machines

2-D analytical modeling of permanent magnet machines with shielding cylinder is a challenging task due to the saturation effect of the cylinder. This article presents a 2-D hybrid analytical solution to model surface-mounted permanent magnet machines with a shielding cylinder attached to the exterior of the rotor body. The presented model provides an accurate representation of the motor response by accounting for the saturation effect of the shielding cylinder, as well as the stator slotting effect. For this purpose, the steel shielding cylinder is modeled by a vacuum cylinder (with the exact same size/dimension) and two inner and outer virtual surface currents. The values of the surface currents are determined by using the respective magnetic circuit model. Meanwhile, the slotting effect on the tangential flux component is modeled by injecting a virtual surface current onto a slotless stator surface. Next, the radial and tangential flux densities are obtained by solving Poisson's equation via separation of variables theorem and applying relevant boundary conditions. The accuracy of the proposed model is verified by the finite element and experimental tests on the machine prototype.