超精密大行程麦克斯韦磁阻驱动器磁场建模与推力分析

为了克服大行程麦克斯韦磁阻驱动器在大气隙下漏磁大幅增加、气隙区磁场分布不均匀且非线性强烈等现象导致的磁场和推力解析模型精度较低等问题，利用考虑综合高斯函数的加权漏磁系数的磁路建模方法，改进了磁阻驱动器的三维漏磁分布计算方式，并得到了可准确描述其推力与输入电流函数关系的解析模型，从而为该类驱动器的设计及控制提供重要依据。首先，建立了大行程麦克斯韦磁阻驱动器考虑漏磁前后的工作磁路，分析了永磁偏置磁路的作用及使用永磁偏置结构后仍具有非线性的原因，并利用安培环路定律和磁路的欧姆定律以及磁场的可叠加性，建立了该磁阻驱动器的推力解析模型。然后，为了优化解析模型，提出了基于高斯曲线的加权漏磁系数计算方法，同时利用有限元仿真软件对大行程麦克斯韦磁阻驱动器的三维磁场分布及漏磁系数进行了分析计算，得到了考虑加权漏磁系数的推力解析模型。最后，搭建了大行程麦克斯韦磁阻驱动器推力测试系统，并通过对比优化前后解析模型计算推力与仿真推力和实测推力，验证了解析模型的准确性。结果表明，优化后解析模型的均方根误差仅为优化前的11.1%，其精度得到有效提升；同时，优化后解析模型计算推力与实测推力之间的均方根误差小于0.6 N，精度较高。研究结果对高端微纳制造装备与测量仪器中新型超精密驱动部件的设计有一定意义和参考价值。

Magnetic field modeling and thrust analysis of ultra-precision large stroke Maxwell reluctance actuator

In order to overcome the problems of low accuracy of the magnetic field and analytical thrust model of large stroke Maxwell reluctance actuator caused by the large magnetic flux leakage under large air gap and the uneven distribution and strong nonlinearity of magnetic field distribution in the air gap, the calculation method of three-dimensional magnetic flux leakage distribution of the reluctance actuator was improved by using the magnetic circuit modeling method considering the weighted magnetic flux leakage coefficient of integrated Gaussian function. Thus, an analytical model which could accurately describe the functional relationship between thrust and input current was obtained, which provided an important basis for the design and control of this kind of actuator. Firstly, the working magnetic circuit of the large stroke Maxwell reluctance actuator before and after considering magnetic flux leakage was established, and the function of permanent magnet bias magnetic circuit and the reason why it still had nonlinearity after using permanent magnet bias structure were analyzed. The analytical thrust model for large stroke Maxwell reluctance actuator was established by using the Ampere’s loop law, the Ohm’s law of magnetic circuit and the superposition of magnetic field. Then, a weighted magnetic flux leakage coefficient calculation method based on Gaussian distribution curve was proposed to optimize the analytical model, and the three-dimensional magnetic field distribution and magnetic flux leakage coefficient of the large stroke Maxwell reluctance actuator were analyzed and calculated by using the finite element simulation software, so that the analytical thrust model considering the weighted magnetic flux leakage coefficient was obtained. Finally, the thrust test system for large stroke Maxwell reluctance actuator was built, and the accuracy of the analytical model was verified by comparing the calculated thrust of analytical model before and after optimization with the simulated thrust and the measured thrust. The results showed that the root mean square error of the analytical model after optimization was only 11.1% of that before optimization. At the same time, the root mean square error between the calculated thrust of analytical model after optimization and the measured thrust was less than 0.6 N, which verified the high accuracy of the optimized model. The research results have certain significance and reference value for the design of new ultraprecision driving components in high-end micro/nano-manufacturing equipment and measuring instruments.