Magnetic Field Modeling and Analysis of Spherical Actuator With Two-Dimensional Longitudinal Camber Halbach Array

Magnet arrangement is important for the design of electromagnetic actuators. One novel spherical actuator with a two-dimensional (2-D) longitudinal camber Halbach array and an iron stator is proposed in this paper to improve the tilting output performance. The employment of the 2-D longitudinal camber Halbach array complicates the magnetic field distribution in actuator space and raises the challenge of analytical modeling. One superposition modeling method is thus proposed to formulate the magnetic field distribution mathematically. The magnet array is divided into radial and tangential directions, the mathematical models are obtained individually, and the superposition principle is utilized to achieve an analytical model of the actuator magnetic field eventually. This generic method helps improve the modeling precision and could be utilized for magnetic field analysis of an electromagnetic actuator with various magnet patterns. One research prototype and one experimental apparatus have been developed. It is verified that the proposed analytical model fits with experimental results and numerical computation well, which will contribute to subsequent study of motion control algorithms. This paper also shows that the proposed structure can increase the radial component of flux density and torque output compared with the conventional magnet pattern.