Two-Degree-of-Freedom Maglev Platform for Micro Machining
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摘要:
为消除激光微细加工移动台中的机械摩擦，提出一种由三组子单元共同悬浮驱动的新型磁浮平台. 首先，介绍平台结构及其工作原理，三组子单元具有相同的结构，由永磁体和电磁线圈构成；分析线圈对永磁体的作用力，并对磁悬浮平台能够实现稳定悬浮的平面范围进行讨论；其次，建立磁悬浮平台的平面内的动力学模型以及子单元位移与平台位移的变换方程；再者，基于分散控制策略，设计子单元系统相应的模糊PD （proportional-derivative）控制器；最后，搭建实物平台，并对其进行静态悬浮实验、步进响应实验、双轴组合工作实验. 结果表明：该磁悬浮平台在 ±2 mm的平面范围内可忽略竖直方向的运动控制；在静态悬浮时，磁悬浮平台在
x 方向均方根误差仅为2.95 μm，最大跟踪误差为11 μm；同时磁悬浮平台具备4 mm的运动行程以及双轴组合工作能力.Abstract:In order to eliminate mechanical friction in the mobile laser table for micro machining, a new maglev platform jointly driven by three sets of levitated subunits was proposed in this paper. Firstly, the platform structure and working principle were introduced. The three sets of subunits had the same structure, consisting of permanent magnets and electromagnetic coils; the force of the coils applying on the permanent magnets was analyzed, and the plane range in which the maglev platform could achieve stable levitation was discussed. Secondly, the in-plane dynamics model of the maglev platform was established, and the equation of the transformation relationship between the displacement of the subunit and that of the platform was built. Subsequently, based on the decentralized control strategy, the corresponding fuzzy proportional-derivative controller of the subunit system was designed. Finally, a physical platform was built, and the static levitation experiment, step response experiment, and two-axis combined working experiment were conducted on the platform. The results show that the maglev platform can ignore the motion control in the vertical direction within the plane range of ±2 mm, and it has a root mean squared error in the
x direction of only 2.95 μm and a maximum tracking error of 11 μm during static levitation. Meanwhile, the maglev platform has a motion displacement of 4 mm and two-axis combined working ability. -
图 2 不同偏移距离下电磁力在x、y、z方向的分量
Figure 2. Components of electromagnetic force in x, y, and z directions at different offset distances
图 3 竖直方向上的电磁力与永磁斥力之和以及k值
Figure 3. Sum of electromagnetic force and permanent magnet repulsion in vertical direction and k value
图 10 磁悬浮平台在x、y方向的静态悬浮过程
Figure 10. Static levitation process of maglev platform in x and y directions
表 1 拟合后的各项系数
Table 1. Various coefficients after fitting
系数 km1/（N·m−1） ke1/（N·m−1） kI1/（N·A−1） 数值 42.030 0.039 −0.617 
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表 2 模糊控制器参数
Table 2. Parameters of fuzzy controller
项目 $ E$ $ {E}_{{\rm{c}}} $ $ \Delta {K}_{{\rm{p}}} $ $ \Delta {K}_{{\rm{d}}} $ 基本论域 [−2，2] [−1，1] [−0.01，0.01] [−0.1，0.1] 模糊论域 [−6，6] [−6，6] [−6.00，6.00] [−6.0，6.0] 模糊子集 {NB,NM,NS,ZO,PS,PM,PB} 量化因子 1/3 1/6 1/600 1/60
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表 3 $ {\Delta K}_{{\rm{p}}} $的模糊规则
Table 3. Fuzzy rule of $ {\Delta K}_{{\rm{p}}} $
$ {E}_{{\rm{c}}} $ $ E $ NB NM NS ZO PS PM PB NB NB NB NM ZO ZO ZO PS NM NB NM NM ZO ZO PS PS NS NM NM NS ZO PS PM PM ZO NM NM NS NS PS PM PM PS NM NS NS NS NM PB PB PM NS NS ZO PM PM PB PB PB ZO ZO ZO PM PB PB PB
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表 4 $ {\Delta K}_{{\rm{d}}} $的模糊规则
Table 4. Fuzzy rule of $ {\Delta K}_{{\rm{d}}} $
$ {E}_{{\rm{c}}} $ E NB NM NS ZO PS PM PB NB PS ZO ZO ZO ZO PB PB NM NS NS NS NS ZO PS PS NS NB NM NS ZO PS PS PS ZO NB NM NM NS PS PS PM PS NB NB NM NS ZO PS PM PM NM NS NS NS ZO PS PM PB PS PS ZO ZO ZO PB PB
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