Due to the complex spatial magnetic field distribution and the variable motion mode, the torque analysis of spherical motors is usually carried out by the finite element method with a large amount of calculation and time consumption. In order to improve analysis efficiency, this paper proposes a spherical motor torque calculation method based on permanent magnet surface current model and Lorentz force, aiming to replace the finite element calculation. Firstly, the equivalent surface current analytical expression of the rectangular permanent magnet magnetic field is derived. Then, this expression is used to establish the three-dimensional magnetic field analytical model of Halbach array permanent magnets in the rotor. Based on this magnetic field, Lorentz force of the energized stator coil is calculated. Then, the electromagnetic torque generated by the rotor is analyzed. Finally, the analytical results of the magnetic field and the motor torque are compared with those by the finite element method and experiments, verified that under the premise of ensuring the calculation accuracy, the proposed method effectively shortens the calculation time and has higher stability.

The finite-element model is established to simulate electromagnetic forces of a permanent-magnet (PM) spherical motor using the commercial software from Ansoft. The Taguchi method is used to optimize the magnetic field density in the radial air gap and the maximum torque of the PM spherical motor. The final optimization parameters are determined by a response surface method (RSM). The simulation results of the optimized motor are compared with those of the original motor to show that the output performances of the optimized motor have improved greatly, which verifies the effectiveness and practicability of the Taguchi method on the optimization of the PM spherical motor.

In order to determine the currents required in different attitudes and torque target conditions, this paper proposes a calculation method for drive currents of permanent magnet spherical motors based on three-dimensional magnetic field, torque analytical model and optimization algorithm. Firstly, an electromagnetic torque analytical model base on equivalent surface currents of a permanent magnet and Lorentz force is proposed. The feasibility and accuracy are verified by comparing results with those by the finite element method. Then, an inverse calculation model of the motor drive current is built by combining the torque analytical model with the Particle Swarm Optimization (PSO) algorithm. At last, using the proposed drive current calculation model, the driving current characteristics of spherical motors under different energization strategies are compared and analyzed.

This article deals with the issue of manufacturing processes leading to rotor surface losses through analytical, finite element analysis (FEA) and experimental methods. Based on experiments, it is found that the rotor surface losses make the rotor temperature of radial magnetic bearings (MBs) higher than expected, and thermal ablation appeared on the rotor surface. First, we investigate the mechanism of rotor surface loss in radial MBs using an improved analytical method. The FEA is then used to validate the analytical results and explore the correlation between the degree of short-circuit faults on the rotor surface and the surface losses. This yields a more comprehensive understanding of the loss characteristics and provides ideas for improving manufacturing methods to reduce surface losses. Finally, a simple method of rotor outer circle machining, namely finish turning with fine feed, is proposed. Comparison prototypes were manufactured using the proposed method and the conventional method. The results demonstrate that the proposed method can effectively reduce the rotor surface losses of radial MBs.

This article proposes a novel detection method for diagnosing the surface interlaminar short-circuit fault (SILSCF) on radial magnetic bearing (MB) rotors. The method is specifically designed for the particular structure of MBs and provides a simplified operation procedure compared to existing methods. Since SILSCF is primarily caused by issues in the processing of the iron core, our study begins by examining the manufacturing processes of radial MB rotors and analyzing the impact of SILSCF on bearing performance. Subsequently, a detection device that utilizes the eddy current effect on the rotor surface is proposed. By employing a custom U-shaped tooling, the insulation condition of the rotor surface can be converted into distinct inductance signals. An analytical model is developed to analyze the inductance characteristics of the proposed device. After that, four prototypes of the investigated radial MB with typical SILSCFs are manufactured. Together with the validation of the analytical calculations, the most suitable test frequencies are selected and a standardized detection procedure is proposed. The final experiments demonstrate that the various degrees of SILSCFs in radial MB rotor cores can be detected with sufficient accuracy using the proposed detection device and method.