中文摘要：

在简述永磁转子偏转式三自由度电机的工作原理和优越性能的基础上，针对该新型永磁多自由度电机的结构提出了气隙磁场的计算方案，建立了球坐标下标量磁位和气隙磁通密度的计算公式。同时基于三维有限元软件，建立起转子磁场模型并进行仿真计算，给出了不同充磁模式下的磁通密度分布情况，与解析计算结果进行了对比验证。理论分析和计算结果表明了所设计结构的有效性，转子易于实现三自由度偏转运动，其结果可为进一步的研究和实验设计提供借鉴和参考。

英文摘要：

Based on the brief introduction of the operation pri ,cipl and superior performance of PM deflection type three-de grees-of freedom motors in this paper, the new PM motor air-gap magnetic field calculation schemes have been presented and the scalar magnetic flux density calculation formula in the spherical coordinate are established. The rotor magnetic field model is built in 3D finite element software and computed with simulation to derive the flux density distribution under different magneti zation modes. The results by these two methods are compared and validated. The theoretical analysis and computation results demonstrate the effectiveness of the designed structure; the rotor is easy to achieve three-degrees-of-freedom deflection motion, which can provide references for further research and experimental design.