Decoupling Design and Experimental Research of XY Workbenchs Driven by MMCA

doi:10.3969/j.issn.1004-132X.2026.08.008

Abstract

Abstract:

In order to meet the demands of high-end equipment manufacturing for high-performance XY worktables， a design scheme was proposed for the XY workbench driven by macro-micro composite with long stroke and high precision characteristics. Firstly， a novel series-parallel hybrid decoupling guidance mechanism was designed， and the dynamics model of the workbenchs was established based on bond graph theory. Secondly， the finite element method and response surface methodology were combined to optimize the output forces and macro-motion error compensation of the MMCA. Then， through static and modal analysis， the effective load capacity and vibration characteristics of the worktable were obtained. Finally， a prototype of the worktable was fabricated， and an experimental test platform was set up for testing. The results show that the optimized MMCA achieves an output forces of 135 N and a macro-motion error compensation of 34 μm at a current of 4 A， representing increases of 32.61% and 12.1%， respectively， compared to the pre-optimization values. The worktable’s working range is 49.94 mm×50.04 mm， with cross-coupling rates of 0.0511% and 0.0549% in the X and Y directions， respectively. During macro-motion positioning tests with strokes of 1 mm， 20 mm， and 49 mm without micro-motion compensation， the steady-state displacement errors in both directions are less than 20 μm. When micro-motion compensation is applied for 49 mm stroke positioning， the maximum errors in the X and Y directions are 0.25 μm and 0.21 μm， respectively. In the resolution experiments， the resolutions in the X and Y directions reachs 59 nm and 56 nm， respectively. The results demonstrate that the proposed XY workbench driven by MMCA offers advantages such as large stroke， low cross-coupling rate， and high resolution， providing a theoretical and technical foundation for high-performance XY workbenches in high-end equipment manufacturing.

Key words: macro-micro composite actuator（MMCA）, XY workbench, hybrid decoupling, bonding diagram, responsive surface optimization, precision positioning

摘要：

为满足高端装备制造领域对高性能XY工作台的需求，提出了一种具有大行程和高精度特性的宏微复合驱动XY工作台设计方案。首先设计了一种新型的串并联混合解耦导向机构，并基于键合图理论建立了工作台的动力学模型；然后将有限元法与响应面法相结合，优化了宏微复合驱动器（MMCA）的输出力和宏动误差补偿量；进而通过静力学和模态分析获得了工作台的有效负载能力和振动特性；最后加工了工作台样机，搭建实验测试平台进行测试。结果显示：优化后的MMCA在电流为4 A时，输出力为135 N，宏动误差补偿量为34 μm，较优化前分别增大了32.61 %和12.1 %；工作台的工作范围为49.94 mm×50.04 mm，X方向和Y方向的交叉耦合率分别为0.0511 %和0.0549 %；在未采用微动补偿情况下进行1、20、49 mm宏动大行程定位测试，两方向的稳态位移误差均小于20 μm；当采用微动补偿进行49 mm大行程定位时，X方向与Y方向的最大误差分别为0.25 μm和0.21 μm；在分辨力实验中，X方向与Y方向的分辨力分别达到59 nm和56 nm。研究结果表明，所提宏微复合驱动XY工作台具有大行程、低交叉耦合率和高分辨力等优点，该成果为高端装备制造领域提供高性能XY工作台奠定了理论与技术基础。

关键词: 宏微复合驱动器, XY工作台, 混合解耦, 键合图, 响应面法, 精密定位

CLC Number:

TH703

YU Caofeng, YANG Kun, SHEN Gang, XIAO Zhihao, WANG Ning. Decoupling Design and Experimental Research of XY Workbenchs Driven by MMCA[J]. China Mechanical Engineering, 2026, 37(8): 1889-1899.

喻曹丰, 杨坤, 沈刚, 肖志豪, 王宁. 宏微复合驱动XY工作台解耦设计与实验研究[J]. 中国机械工程, 2026, 37(8): 1889-1899.

Figures/Tables 26

Fig.1 Schematic diagram of XY worktable driven by macro-micro composite

Fig.2 Schematic diagram of the series-parallel hybrid decoupling guidance mechanism structure

Fig.3 Dynamic model of the workbench in the X-direction

Fig.4 Global bond graph model of the workbench in the X-direction

Tab.1 Relationship between effort variables and flow variables for each section

结	势变量	流变量
1	e₁=e₂+e₃+e₄	f₁=f₂=f₃=f₄
GY	e₄=K_bf₅， e₅=K_bf₄	⋮
1	e₅=e₆+e₇	f₅=f₆=f₇
0	e₇=e₈=e₁₁	f₇=f₈+f₁₁
1	e₈=e₉+e₁₀	f₈=f₉=f₁₀
1	e₁₁=e₁₂+e₁₃+e₁₄	f₁₁=f₁₂=f₁₃=f₁₄

Fig.5 Dynamic characteristics of the workbench in the X-direction

Tab.2 Parameters related to the X-direction of the workbench

部件	参数	值
MMCA	运动部件质量M_d/kg	2
	电感L_i/H	0.017
	电阻R_i/Ω	6.7
	力常数K_b/（N·A $- 1$ ）	35.16
X方向载物台	质量M_X /kg	1.5
X方向载物台	黏性摩擦因数μ	120

Tab.2 Parameters related to the X-direction of the workbench

部件	参数	值
MMCA	运动部件质量M_d/kg	2
	电感L_i/H	0.017
	电阻R_i/Ω	6.7
	力常数K_b/（N·A $- 1$ ）	35.16
X方向载物台	质量M_X /kg	1.5
X方向载物台	黏性摩擦因数μ	120

Fig6 Schematic diagram of the MMCA structure

Tab.3 Initial values of related parameters

A	B	C	D
10	4	5	4

Fig.7 Response surface analysis plot

Tab.4 Optimal solution derived from Box-Behnken design

	A	B	C	D	E	F	合意性
值	9.96	5.0	5.99	5.0	143.922	33.003	0.984
取整	10.0	5.0	6.0	5.0
单位	mm	mm	mm	mm	N	μm

Fig.8 Comparison of MMCA performance before and after optimization

Fig.9 Deformation of the XY workbench under a 50 N load at different displacements

Tab.5 Deformation of the worktable under different loads during displacement

负载	0 mm位移		25 mm位移		50 mm位移
负载	X/mm	Y/mm	X/mm	Y/mm	X/mm	Y/mm
50 N	5.48×10⁶	3.91×10⁶	8.63×10⁶	8.38×10⁶	1.26×10⁵	1.11×10⁵
100 N	1.09×10⁵	7.81×10⁶	1.72×10⁵	1.68×10⁵	2.52×10⁵	2.21×10⁵
150 N	1.65×10⁵	1.17×10⁵	2.59×10⁵	2.51×10⁵	3.78×10⁵	3.32×10⁵
200 N	2.19×10⁵	1.56×10⁵	3.45×10⁵	3.35×10⁵	5.04×10⁵	4.42×10⁵
250 N	2.74×10⁵	1.95×10⁵	4.31×10⁵	4.19×10⁵	6.29×10⁵	5.23×10⁵

Fig.10 Four modal vibration modes of XY workbench driven by macro-micro composite

Fig.11 MMCA output force testing platform

Fig.12 Prototype and experimental setup

Fig.13 Optimization result testing of the MMCA

Fig.14 Displacement coupling test

Fig.15 Displacement curves when driving simultaneously in the X and Y directions

Fig.16 Square trajectory test

Fig.17 Test results of macro-motion positioning errors

Fig.18 Control strategy block diagram

Fig.19 Positioning errors at maximum travel

Fig.20 Positioning resolution test

Tab.6 Performance comparison of the XY workbench

参数	工作范围	分辨力	交叉耦合率/%	负载能力/N
本文	49.94 mm×50.04 mm	56 nm	0.05	250
文献［7］	30.76 μm×29.79 μm	29.3 nm	2.02	10
文献［13］	11.3 μm×10.6 μm	20 nm	0.07	1.2
文献［17］	20.4 mm×20.6 mm	100 nm	无	196
文献［18］	11.75 mm×11.66 mm	200 nm	1.3	196
文献［23］	15 mm×15 mm	0.4 μm	11.06	196

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