Liu Peng, Ouyang Yuwen, Quan Wenwen
College of Automotive and Mechanical Engineering, Changsha University of Science & Technology, Changsha 410114, China.
Micromachines (Basel). 2023 Dec 27;15(1):58. doi: 10.3390/mi15010058.
In this study, the performance of a long-stroke moving-iron proportional solenoid actuator (MPSA) was improved by combining numerical simulations and experiments. A finite element model of the MPSA was developed; its maximum and mean relative absolute errors of electromagnetic force were 4.3% and 2.3%, respectively, under typical work conditions. Seven design parameters including the cone angle, cone length, depth of the inner hole of the coil skeleton, cone width of the armature, inner cone diameter, and initial position of the moving-iron core were selected for developing the model, and the coefficient of the variation in electromagnetic force, nominal acceleration, 95% of the maximum stable output electromagnetic force, and corresponding response time were used as the performance indicators. The constraint relation between each performance indicator and the influence of each design parameter on the performance indicators were revealed using the uniform Latin hypercube experiment design, correlation analysis, and the main effect analysis method. A multi-objective optimization mathematical model of the MPSA was developed by combining traditional surrogate and machine learning models. The Pareto solution set was obtained using the nondominated sorting genetic algorithm II (NSGA-II), and three decision schemes with different attitudes were determined using the Hurwicz multi-criteria decision-making method. The results showed that a strong contradiction exists among the 95% of the maximum stable output electromagnetic force and its corresponding response time and the coefficient of the variation in electromagnetic force. The cone angle considerably influenced the performance indicators. Compared with the initial design, the coefficient of the variation in electromagnetic force was reduced by 54.08% for the positive decision, the corresponding response time was shortened by 15.65% for the critical decision, and the corresponding acceleration was enhanced by 10.32% for the passive decision. Thus, the overall performance of the long-stroke MPSA effectively improved.
在本研究中，通过数值模拟与实验相结合的方式，提高了长行程动铁式比例电磁铁执行器（MPSA）的性能。建立了MPSA的有限元模型；在典型工况下，其电磁力的最大相对绝对误差和平均相对绝对误差分别为4.3%和2.3%。选择了包括锥角、锥长、线圈骨架内孔深度、电枢锥宽、内锥直径和动铁芯初始位置在内的七个设计参数来建立模型，并将电磁力变化系数、标称加速度、最大稳定输出电磁力的95%以及相应的响应时间作为性能指标。采用均匀拉丁超立方实验设计、相关分析和主效应分析方法揭示了各性能指标之间的约束关系以及各设计参数对性能指标的影响。结合传统代理模型和机器学习模型，建立了MPSA的多目标优化数学模型。使用非支配排序遗传算法II（NSGA-II）获得帕累托解集，并采用赫维茨多准则决策方法确定了三种不同态度的决策方案。结果表明，最大稳定输出电磁力的95%及其相应响应时间与电磁力变化系数之间存在强烈矛盾。锥角对性能指标影响较大。与初始设计相比，积极决策下电磁力变化系数降低了54.08%，临界决策下相应响应时间缩短了15.65%，消极决策下相应加速度提高了10.32%。从而有效提高了长行程MPSA的整体性能。
