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 (FEM) with a large amount of calculation and time consumption. In order to improve analysis efficiency, this article proposes a spherical motor torque calculation method based on the permanent-magnet surface current model and Lorentz force, aiming to replace the finite-element calculation. First, the equivalent surface current analytical expression of the rectangular permanent-magnet magnetic field is derived. Then, this expression is used to establish the 3-D magnetic field analytical model of Halbach array permanent magnets in the rotor. Based on this magnetic field, the 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 FEM and experiments, verified that, under the premise of ensuring the calculation accuracy, the proposed method effectively shortens the calculation time and has higher stability.

中文翻译：

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基于永磁体表面电流和洛伦兹力的永磁调心电机转矩计算

由于空间磁场分布复杂，运动方式多变，球形电机的转矩分析通常采用有限元法（FEM）进行，计算量大，耗时长。为了提高分析效率，本文提出了一种基于永磁体表面电流模型和洛伦兹力的球形电机转矩计算方法，旨在替代有限元计算。首先，推导出矩形永磁磁场的等效表面电流解析表达式。然后，该表达式用于建立转子中 Halbach 阵列永磁体的 3-D 磁场解析模型。根据该磁场，计算通电定子线圈的洛伦兹力。然后，分析转子产生的电磁转矩。最后，将磁场和电机转矩的分析结果与有限元法和实验进行了比较，验证了该方法在保证计算精度的前提下，有效缩短了计算时间，具有更高的稳定性。