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Frontiers of Mechanical Engineering

Front. Mech. Eng.    2019, Vol. 14 Issue (3) : 255-272     https://doi.org/10.1007/s11465-019-0538-x
RESEARCH ARTICLE
Comprehensive analysis of the influence of structural and dynamic parameters on the accuracy of nano-precision positioning stages
Chengyuan LIANG, Fang YUAN, Xuedong CHEN, Wei JIANG, Lizhan ZENG, Xin LUO()
State Key Laboratory of Digital Manufacturing Equipment and Technology, Huazhong University of Science and Technology, Wuhan 430074, China
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Abstract

Nano-precision positioning stages are characterized by rigid-flexible coupling systems. The complex dynamic characteristics of mechanical structure of a stage, which are determined by structural and dynamic parameters, exert a serious influence on the accuracy of its motion and measurement. Systematic evaluation of such influence is essential for the design and improvement of stages. A systematic approach to modeling the dynamic accuracy of a nano-precision positioning stage is developed in this work by integrating a multi-rigid-body dynamic model of the mechanical system and measurement system models. The influence of structural and dynamic parameters, including aerostatic bearing configurations, motion plane errors, foundation vibrations, and positions of the acting points of driving forces, on dynamic accuracy is investigated by adopting the H-type configured stage as an example. The approach is programmed and integrated into a software framework that supports the dynamic design of nano-precision positioning stages. The software framework is then applied to the design of a nano-precision positioning stage used in a packaging lithography machine.

Keywords nano-precision positioning stage      analysis and design      structural and dynamic parameters      dynamic accuracy      systematic modeling     
Corresponding Authors: Xin LUO   
Just Accepted Date: 01 April 2019   Online First Date: 05 May 2019    Issue Date: 24 July 2019
 Cite this article:   
Chengyuan LIANG,Fang YUAN,Xuedong CHEN, et al. Comprehensive analysis of the influence of structural and dynamic parameters on the accuracy of nano-precision positioning stages[J]. Front. Mech. Eng., 2019, 14(3): 255-272.
 URL:  
http://journal.hep.com.cn/fme/EN/10.1007/s11465-019-0538-x
http://journal.hep.com.cn/fme/EN/Y2019/V14/I3/255
Fig.1  Structure of the H-type nano-precision positioning stage
Fig.2  Dynamic topology of the H-type nano-precision positioning stage
Fig.3  Equivalent dynamic model of a single aerostatic bearing
Fig.4  Experimental data on aerostatic bearing capacity [35] and fitting curve based on Richards model
Fig.5  Measurement beam path of a single-axis plane mirror interferometer. (a) Ideal beam path; (b) actual beam path
Fig.6  System dynamic accuracy model
Fig.7  Movement trajectory in system simulation
Fig.8  Simulation results of dynamic errors corresponding to different positions of driving force acting points
Displacement of the driving force acting point ex ey eθ z ez eθx eθy emx emy em θz
ΔzFx Sca ↑, Scw ↓, St ↑ Scw ↓ Sca ↑, Scw ↓, St ↑ Scw ↓ Scw ↓ Sca ↑, Scw ↓, St ↑ Sca ↑, Scw ↓, St ↑ Sca ↑, St ↑ Sca ↑, Scw ↓, St ↑
|Δ xFy| PE ↓ ( ΔxFy↓) St ↑ St ↓ St ↓ ( Δ xFy↓) St ↑
|Δ zFy| St ↓ St ↓ St ↓ ( Δ zFy↓) St ↓ St ↓
Tab.1  Effects of the positions of driving force acting points on dynamic errors
Fig.9  Aerostatic bearing models with different stiffness characteristics. 1 bar=105 Pa
Fig.10  Simulation results of the effects of Δ xbsv and Δybsv on dynamic errors
Fig.11  Simulation results of the effects of Δ ybsh on dynamic errors
Fig.12  Simulation results of the effects of Δ zbsh on dynamic errors
Displacement of the center point ex ey eθz ez eθx eθy emx emy emθ z
|Δ xbsv| SB ↓ SB ↓, Scw ↓, Sca ↓ (Sca→min, when Δxbsv≈10 mm) SB ↓ SB ↓ SB ↓, St ↓
|Δ ybsv| SB ↓ SB ↓, St ↓ SB ↓ SB ↓ SB ↓, Sca ↓, Scw ↓
|Δ ybsh| PE ↓ Sca ↓, Scw ↓ ( Δ ybsh↓) Sca ↑ Sca ↓
|Δ zbsh| Sca ↓, Scw ↓ Sca ↓ Sca ↓ St ↑ Sca ↓
Tab.2  Effects of the center point positions of aerostatic bearing groups on dynamic errors
Stiffness of aerostatic bearing ex ey eθz ez eθx eθy emx emy emθ z
Kbsv AL ↓ St ↓, SB ↓ Scw ↓ St ↓ St ↓, SB ↓ Sca ↓, Scw ↓, SB ↓ Sca ↓, Scw ↓, SB ↓ St ↓, SB ↓ SS ↓, SB ↓
Kbsh AL ↓ PE ↓ SS ↓, SB ↓ Scw ↓ Scw ↓, St ↓ Scw ↓, St ↓
Tab.3  Effects of the stiffness of aerostatic bearings on dynamic errors
Fig.13  Simulation results of motion errors corresponding to constant stiffness and nonlinear stiffness models
Fig.14  Simulation results of motion errors corresponding to different preloading errors
Fig.15  Simulation results of motion errors corresponding to different initial film thickness errors
Fig.16  Simulation results of motion errors corresponding to different nonlinear stiffness models. 1 bar=105 Pa
Fig.17  Simulation results of dynamic errors corresponding to flatness errors on different planes
Flatness error of motion plane ex ey eθ z ez eθ x eθ y emx em y em θz
ef_bs_ xy SS ↓ SS ↓ SS ↓ SS ↓ SS ↓ SS ↓ SS ↓ SS ↓
ef_bm_ y St ↓, SB ↓, PE ↓ SS ↓ SS ↓ SS ↓ SS ↓
Tab.4  Effects of flatness errors of motion planes on dynamic errors
Fig.18  Simulation results of dynamic errors affected by foundation vibrations with different amplitudes
Fig.19  Design framework supporting the dynamic design of nano-precision positioning stages
Scheme ΔzFx/mm Δ xFy/mm Δ xbsv/mm Δ ybsv/mm Δ ybsh/mm Bearing in AB_bs_h
Original ?17.8 10.5 10.2 ?3.8 ?3.8 Original bearing
Optimized ?5.0 5.0 5.0 ?2.0 ?2.0 Modified bearing
Tab.5  Structural parameters in the original and optimized schemes
Fig.20  Stiffness characteristics of the original and modified bearings
Scheme Minimum/nm Maximum/nm Mean/nm Standard deviation/nm
Original ?11.0 15.9 ?1.1 5.8
Optimized ?6.4 11.4 ?0.7 3.5
Tab.6  Simulation results of positioning errors of the original and optimized schemes
Fig.21  Simulation results of positioning errors of the original and optimized schemes
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