Design and Simulation Analysis of Magnetic Field of a Four-stable State Digital Electromagnetic Actuator Array
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摘要: 为了消除模拟执行器中安装反馈传感器造成的空间局限性对系统紧凑性设计需求带来负面影响和多磁体环境下空间静磁力耦合计算复杂等问题,应用电磁驱动原理设计并静态模拟分析了一种新型四稳态数字电磁执行器阵列,绘制阵列结构的磁通密度空间分布图,并基于Furlani空间磁感应方程进行阵列系统空间磁场建模,提出了新型多磁体间快速静磁耦合计算方法(单重叠加法)。模拟对比结果表明,单重叠加法的模型(即Matlab模型)与系统校验模型(即Radia模型)相比,单磁体所受静磁合力最大误差仅为2.94%;与传统计算方法(多重叠加法)相比,单重叠加法计算效率提高约65.82%,有较好的准确性和高效性;执行器阵列空间磁通密度分布具有均匀性、一致性和独立性。Abstract: In order to eliminate the negative impact of space limitation caused by the installation of feedback sensors in analog actuators due to compact design requirements and the complex magnetic coupling calculation problem in a multi-magnet environment, a new four-stable state digital electromagnetic actuator array is designed by using the electromagnetic drive principle and the spatial distribution of magnetic induction intensity of the actuator array and then analyzed. Based on the Furlani space magnetic induction equation, the modeling of the actuator array is carried out, and a new fast magnetostatic coupling calculation method (single overlap addition) between multiple magnets is proposed. Compared with the check model (i.e., the Radia model) of the actuator array, the single overlap adding model (i.e., the MATLAB model) has a maximum magnetostatic force error of only 2.94%. Compared with the traditional calculation method, the accuracy and efficiency of the single overlap adding calculation method improves by about 65.82%. The actuator array's spatial flux density distribution is uniform, consistent, and independent.
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表 1 执行器单元设计参数
磁铁种类 尺寸参数 磁化强度 MPM 1.33 mm×1.33 mm×2 mm 1.33 T FPM 2.5 mm×2.5 mm×1.25 mm 0.6 T 表 2 Mathematica模拟结果的ITF
执行器 x方向力/N y方向力/N 合力/N 1 -1.08×10-5 1.08×10-5 1.53×10-5 2 1.08×10-5 -1.08×10-5 1.53×10-5 3 -1.08×10-5 1.08×10-5 1.53×10-5 4 1.08×10-5 -1.08×10-5 1.53×10-5 表 3 Mathematica模拟结果的ATF
执行器 x方向力/N y方向力/N 合力/N 1 -1.65×10-3 -1.72×10-3 2.41×10-3 2 -1.72×10-3 -1.65×10-3 2.41×10-3 3 -1.65×10-3 -1.72×10-3 2.41×10-3 4 -1.72×10-3 -1.65×10-3 2.41×10-3 表 4 Mathematica模拟结果的TOF
执行器 1 2 3 4 TOF/N 2.38×10-3 2.38×10-3 2.38×10-3 2.38×10-3 表 5 Matlab模拟结果的ITF
执行器 x方向力/N y方向力/N 合力/N 1 -1.08×10-5 1.08×10-5 1.53×10-5 2 1.08×10-5 -1.08×10-5 1.53×10-5 3 -1.08×10-5 1.08×10-5 1.53×10-5 4 1.08×10-5 -1.08×10-5 1.53×10-5 表 6 Matlab模拟结果的ATF
执行器 x方向力/N y方向力/N 合力/N 1 -1.63×10-3 -1.72×10-3 2.37×10-3 2 -1.72×10-3 -1.72×10-3 2.43×10-3 3 -1.63×10-3 -1.63×10-3 2.31×10-3 4 -1.72×10-3 -1.63×10-3 2.37×10-3 表 7 Matlab模拟结果的TOF
执行器 1 2 3 4 TOF/N 2.37×10-3 2.43×10-3 2.31×10-3 2.37×10-3 表 8 Mathematica和Matlab模拟结果中ITF误差
执行器 x方向力/N y方向力/N 合力/N 1 0 0 0 2 0 0 0 3 0 0 0 4 0 0 0 表 9 Mathematica和Matlab中模拟结果ATF误差
执行器 x方向力/N y方向力/N 合力/N 1 2×10-5 0 4×10-5 2 0 7×10-5 2×10-5 3 2×10-5 0 1×10-4 4 0 2×10-5 4×10-5 表 10 Mathematica和Matlab模拟结果中TOF误差
执行器 误差值/N 误差/% 1 1×10-5 0.42 2 5×10-5 2.52 3 7×10-5 2.94 4 1×10-5 0.42 表 11 模拟运行环境配置
类别 型号 处理器 英特尔第四代酷睿i5-4200M 内存 8 GB 主硬盘 闪迪SDSSDA120G 表 12 运行时间对比表
多重叠加法 单重叠加法 运行时间差值 7.9 s 2.7 s 5.2 s -
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