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This paper proposes a monolayer Halbach array based permanent magnet spherical motor (PMSpM) using cubic permanent magnets (PM). The research aims to provide a fast computing model to calculate the magnetic field for this PMSpM, which helps for future PMSpM optimization and control study. Three thickness equivalence principles are provided and compared for cubic PMs. The magnetic scalar potential is introduced, and the spherical harmonics expansion is implemented for rotor magnetic field analysis. Engineering revision is used to reduce the Legendre function deviation in polar angle direction. Torques and forces are deduced using the Lorentz force law, and relatively simple models of this PMSpM for both magnetic fields and torques are acquired. In addition, a prototype motor has been developed, and the analytic results of air-gap flux density and torque are compared with their finite element simulation and experimental results, which are proved consistent. It is concluded that the fundamental component of the spherical harmonics can be used to present the magnetic field model, which uses fewer integrals than the Biot-Savart law based solution, and the modeling results of the magnetic field flux density, forces and torques are in line with the expectations. The analytic models are proved correct.

In this paper, a sensorless rotor posture detection method based on the mutual inductance voltage of the stator coil is proposed to simplify the position detection element of a reluctance spherical motor. Firstly, the numerical relationship between the stator/rotor pole misalignment angle and the mutual inductance voltage of the stator coil is analyzed, which is used as the basis for judging the spatial position of the rotor. Secondly, an experimental platform is designed to verify the consistency between the calculated value and the experimental value of the mutual inductance voltage and to determine the appropriate excitation signal. Thirdly, based on the real-time voltages generated by the stator coil mutual inductance, an intelligent algorithm is used to invert the 3-DoF (degree-of-freedom) position angle of the spherical rotor combined with the motor structure constraints. The experimental results show that the detection method has a good on-line detection effect, and the population standard deviation is within 1.8° Therefore, the developed technique can be used for replacing the position detection method with sensors.

A spherical motor has multiple degrees of freedom. Its motion control requires an accurate attitude detection system. This study proposes a low-cost microelectromechanical system (MEMS) inertial measurement sensor to detect the attitude of the spherical motor. The proposed sensor combines a three-axis gyroscope and a three-axis accelerometer to obtain raw position data of spherical motors to estimate rotor's attitude. To improve the accuracy of the estimated attitude from the raw position data, the authors reduce the inclination angle error between the motor's rotor and MEMS sensor's coordinate systems by compensating axial angle error. A high-speed camera that generally provides high accuracy of the attitude is used as a calibration device for comparison and validation. Experimental results show that the MEMS inertial measurement sensor can achieve accurate attitude estimation that is suitable for motion control of a spherical motor.