Analytical model for Magnetic Field Evaluation in Induction Spherical Actuators

This contribution presents an analytical formulation to derive the magnetic field spatial distribution in spherical induction actuators. The system is modeled as an ironless spherical structure, with a spherical conductive rotor and excitation coils fed with sinusoidal currents placed on a constant-radius surface. By introducing the second-order vector potential, the Helmholtz equation is solved to derive the spatial distribution of the magnetic flux density produced by a three-phase winding, considering the relative motion between the rotor and the stator magnetic field. Moreover, the algorithm estimates the developed torque directly from the spatial harmonics amplitude, avoiding the creation of a mesh grid to discretize the domain and thereby reducing computational time compared with FE simulations. The model is used to analyze an actuator with a rotor radius of about 36 mm and a stator radius of about 40 mm. Comparison with full-3D FE simulations highlighted the approach’s accuracy and computational efficiency.