Equivalent energized coil model for magnetic field of permanent-magnet spherical actuators

• A novel equivalent energized coil modeling method is proposed.
• It can be used to analyze the magnetic field of PMs without limits of geometry.
• The method is used for modeling of a novel spherical actuator with 3D magnet array.
• A research prototype and a testing apparatus have been developed.
• The magnetic field model is validated with numerical and experimental results.

Magnetic field modeling is extremely important for electromagnetic (EM) driven spherical actuators. This paper proposes a novel mathematic modeling method based on equivalent energized coil and Biot–Savart law to formulate the complex magnetic field distribution in three-dimensional (3D) space. The energized coil model is employed as an equivalent substitution of cylindrical permanent magnet (PM) poles. The magnetic field distribution of single energized coil is then formulated analytically. The complete magnetic field model of the actuator with multiple cylindrical PM poles is thus achieved from linear superpositions. Compared with other conventional approaches, as there are no omission of high order of harmonic terms, shape approximation of magnet poles and assumption of evenly distributed flux field, it helps to improve the modeling accuracy. Furthermore, this method is more generic for other flux field applications. It is available for both PM and EM poles, and theoretically could be implemented for other magnet shapes. The computational time may increase for complex magnet shapes and distribution patterns. The proposed method is applied to the spherical actuator with novel 3D magnetic pole array that helps to improve the actuator torque output. Numerical computation is conducted to validate the derived analytical magnetic field model. It shows that the analytical model fits with the result from finite element method (FEM) closely. A research prototype and an automatic experimental platform have been developed. Experiment is thus conducted to measure the magnetic field distribution of the spherical actuator. The data comparison shows that the analytical model matches the experimental measurement result well. The developed model can be employed for subsequent study of torque formulation and control implementation.