Comprehensive analysis of the influence of structural and dynamic parameters on the accuracy of nano-precision positioning stages

doi:10.1007/s11465-019-0538-x

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 Author(s): 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:

https://academic.hep.com.cn/fme/EN/10.1007/s11465-019-0538-x
https://academic.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	$e x$	$e y$	$e θ z$	$e z$	$e θ x$	$e θ y$	$e m x$	$e m y$	$e m θ z$
$Δ z F x$ ↓	Sca ↑, Scw ↓, St ↑	Scw ↓	Sca ↑, Scw ↓, St ↑	Scw ↓	Scw ↓	Sca ↑, Scw ↓, St ↑	Sca ↑, Scw ↓, St ↑	Sca ↑, St ↑	Sca ↑, Scw ↓, St ↑
$\| Δ x F y \|$ ↓	PE ↓	( $Δ x F y$ ↓) St ↑	St ↓				St ↓	( $Δ x F y$ ↓) St ↑
$\| Δ z F y \|$ ↓		St ↓		St ↓	St ↓			( $Δ z F y$ ↓) 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 x bsv

and

Δ y bsv

on dynamic errors

Fig.11 Simulation results of the effects of

Δ y bsh

on dynamic errors

Fig.12 Simulation results of the effects of

Δ z bsh

on dynamic errors

Displacement of the center point	$e x$	$e y$	$e θ z$	$e z$	$e θ x$	$e θ y$	$e m x$	$e m y$	$e m θ z$
$\| Δ x bsv \|$ ↓	SB ↓			SB ↓, Scw ↓, Sca ↓ (Sca→min, when $Δ x b s v$ ≈10 mm)		SB ↓	SB ↓		SB ↓, St ↓
$\| Δ y bsv \|$ ↓		SB ↓		SB ↓, St ↓	SB ↓			SB ↓	SB ↓, Sca ↓, Scw ↓
$\| Δ y bsh \|$ ↓		PE ↓	Sca ↓, Scw ↓				( $Δ y bsh$ ↓) Sca ↑	Sca ↓
$\| Δ z bsh \|$ ↓				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	$e x$	$e y$	$e θ z$	$e z$	$e θ x$	$e θ y$	$e m x$	$e m y$	$e m θ z$
$K bsv$ ↑	AL ↓	St ↓, SB ↓	Scw ↓	St ↓	St ↓, SB ↓	Sca ↓, Scw ↓, SB ↓	Sca ↓, Scw ↓, SB ↓	St ↓, SB ↓	SS ↓, SB ↓
$K bsh$ ↑	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	$e x$	$e y$	$e θ z$	$e z$	$e θ x$	$e θ y$	$e m x$	$e m y$	$e m θ z$
$e f_bs_x y$ ↓	SS ↓	SS ↓		SS ↓	SS ↓	SS ↓	SS ↓	SS ↓	SS ↓
$e f_bm_y$ ↓	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	$Δ z F x$ /mm	$Δ x F y$ /mm	$Δ x bsv$ /mm	$Δ y bsv$ /mm	$Δ y bsh$ /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

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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