Journal of Jilin University(Engineering and Technology Edition) ›› 2024, Vol. 54 ›› Issue (2): 385-393.doi: 10.13229/j.cnki.jdxbgxb.20220323

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Mechanical model of rigid⁃flexible coupling positioning stage based on floating coordinate method

Zhi-jun YANG(),Chi ZHANG,Guan-xin HUANG()   

  1. State Key Laboratory of Precision Electronic Manufacturing Technology and Equipment，Guangdong University of Technology，Guangzhou 510006，China
  • Received:2022-03-29 Online:2024-02-01 Published:2024-03-29
  • Contact: Guan-xin HUANG E-mail:yangzj@gdut.edu.cn;guanxinhuang@gdut.edu.cn

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Abstract:

The precision of traditional precision positioning stages are limited due to mechanical friction， so it is difficult to meet the motion requirements of large stroke and high precision. In this paper， a single drive rigid-flexible coupling positioning stage combined with macro- micro composite structure was proposed. Compared with the other macro-micro composite stage， it greatly simplified the design of mechanical structure and motion control system. Based on the floating coordinate method and finite element method， the static and dynamic model of the single drive rigid-flexible coupling positioning stage was established. The analysis results of these models were compared with the static analysis results of ABAQUS finite element software and the analytical solution of the simplified dynamic model， the maximum relative errors were 1.6% and 3.72% respectively. It is proved that this theoretical model has high prediction accuracy， which can provide parameters for the optimal design and precision motion control of the single drive rigid-flexible coupling stage.

Key words: mechanical engineering, rigid-flexible coupling dynamics, finite element analysis, flexure hinge, positioning stage

CLC Number: 

  • TH113.1

Fig.1

Single drive rigid-flexible coupling stage"

Fig.2

Geometric model of single drive rigid-flexible coupling stage"

Fig.3

Distribution diagram of flexure hinges"

Fig.4

Schematic diagram of flexure hinge dimensions"

Fig.5

Schematic diagram of stage coordinates"

Table 1

Quality parameters of stages"

平台类型质量/kg
柔性平台2.2625
刚性平台c10.0974
刚性平台c20.0974
刚性平台c30.0974
刚性平台c40.0974

Table 2

Material parameters of flexure hinges"

柔性铰链类型杨氏模量E/Gpa剪切模量G/Gpa

泊松比

υ

长度

l/mm

厚度

t/mm

宽度

w/mm

直角7226.90.330121.020
簧片21181.90.28830.436

Fig.6

Detail diagram of flexure hinges deformation"

Table 3

Stiffness error（traslation）"

工作方向平动/mkPA/（N·m-1）kPA/（N·m-1）误差/%
X2.25E-94.44E94.39E91.19
Y6.79E-81.47E81.47E80.33
Z1.16E-98.60E98.59E90.13

Table 4

Stiffiness error（rotation）"

工作 方向转动/ radkZA/ （N?m·rad-1）kZM/ （N?m·rad-1）误差/%
θX1.19E-78.43E78.43E70.05
θY1.44E-76.93E76.91E70.14
θZ2.92E-73.43E73.38E71.60

Fig.7

Simplified model of the single drive rigid-flexible coupling stage"

Table 5

Parameters of simplified model"

参数物理意义
mf刚性平台的质量
ms柔性平台的质量
Js柔性平台的转动惯量
Kr刚柔耦合平台绕X轴方向转动刚度
Kt刚柔耦合平台沿Y轴方向平动刚度
ds柔性平台相对于惯性坐标系沿Y轴方向的平动位移
Δdf刚性平台相对于浮动坐标系沿Y轴方向的平动位移
θs柔性平台绕惯性坐标系X轴方向的转动位移
Ff刚性平台受到Y轴方向的集中力
Fs柔性平台受到Y轴方向的集中力
Ms柔性平台受到X轴方向的集中力矩

Fig.8

Dynamic error of the flexible stage deformation along Y-axis"

Fig.9

Dynamic error of the flexible stage deformation around X-axis"

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