Equivalent Energized Coil Model for Magnetic Field of PM Spherical Actuator

Unlike conventional two-dimensional (2D) magnet array in electromagnetic spherical actuators, a novel 3D magnetic pole array is proposed to improve the actuator torque output. This paper proposes a mathematic modeling method based on the equivalent energized coil and Biot-Savart law to formulate the complex magnetic field distribution of the spherical rotor in 3D space. The energized coil model is employed as an equivalent substitution of the cylindrical PM poles. By using Biot-Savart law, the magnetic field distribution of a single energized coil is obtained analytically. The whole model of the rotor is thus achieved from the principle of linear superposition. Compared with other conventional modeling approach, this method is more generic. It is not constrained by geometry of magnets. Numerical computation is conducted to validate the derived analytical magnetic field model. The analytical model fits with the result from finite element method (FEM) closely.