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Influence of relative difference between paired guide rails on motion accuracy in closed hydrostatic guideways

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Abstract

There have been many researches concerning the motion errors of hydrostatic guideways because they directly affect the accuracy of machined parts. Actually, each paired guide rail has its own profile feature, and the position error also cannot be zero, so the relative difference between guide rails should not be neglected. In this paper, a typical closed hydrostatic guideway with four pads is taken as the sample, and the quasi-static analysis model is directly developed by incorporating the concept of pose, which is then employed to study the effect of relative difference on motion accuracy in the field of hydrostatic guideways. The numerical results demonstrate that, the greater the amplitude deviation, the larger the motion errors, while the influence of the wavelength deviation on motion accuracy exhibits regularity only within some intervals, the phase deviation mainly affects the angular but not the linear motion error, the influence from the parallelism error is not significant. Moreover, it is figured out that the fluctuation of the difference between the average film thicknesses of two adjacent pads does result in the variation of the motion errors, the greater the fluctuation, the larger the motion errors. The revealed mechanisms are expected to be valuable for designers.

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Abbreviations

L :

Length of hydrostatic table

H :

Width of hydrostatic table

B :

Height of hydrostatic table

l :

Center spacing between two adjacent pads

M :

Length of pad

W :

Width of pad

E 1 :

Guide rail 1 ’s profile error amplitude

λ 1 :

Guide rail 1 ’s profile error wavelength

φ 1 :

Guide rail 1 ’s profile error phase

E 2 :

Guide rail 2’s profile error amplitude

λ 2 :

Guide rail 2’s profile error wavelength

φ 2 :

Guide rail 2’s profile error phase

{A} :

Reference coordinate system

B :

Hydrostatic table coordinate system

C :

Neutral plane coordinate systems of rail 1

D :

Neutral plane coordinate systems of rail 2

h 0 :

Sum of oil film clearance h01 and h02

A p :

Description of point p on the curved profile in {A}

D p :

Description of point p on the curved profile in {D}

A q :

Description of point q on the hydrostatic table in {A}

B q :

Description of point q on the hydrostatic table in {B}

A B R :

Rotation matrix (representing the orientation of {D} relative to {A})

A B R :

Rotation matrix (representing the orientation of {B} relative to {A})

A p Do :

Translation vector of {D} relative to {A}

A q Bo :

Translation vector of {B} relative to {A}

F 0 :

External force acting on the hydrostatic table

F1 ~ F4 :

The four oil film reaction forces

e :

Arm of F0

z A :

Linear motion error

θ :

Angular motion error

i :

Number of pad

j :

Number of point in one pad plane

A q ij :

Coordinates of the jth point in the ith pad plane in {A}

B q ij :

Coordinates of the jth point in the ith pad plane in {B}

P r :

Hydrostatic pressure in the recess

A e :

Effective bearing area of the rectangle pad

Q :

Flow rate corresponding to Pr

Q 0 :

Flow rate for Pr = 0

K r :

Flow ratio of PM controller

P s :

Supply pressure

R :

Flow resistance of the land

h :

Nominal oil film thickness

h a :

Average oil film thickness

A land :

Projected area of land in the plane OAXAYA

DEV(E):

Amplitude deviation

DEV(λ):

Wavelength deviation

δ(φ):

Phase deviation

α :

Parallelism error between paired guide rails

η :

Hydrostatic oil dynamic viscosity

l λ :

The ratio of l to λ

A Z 1 :

Explicit mathematical functions of rail 1

A Z 2 :

Explicit mathematical functions of rail 2

ρ :

The difference between ha of two adjacent pads

HGS:

Hydrostatic guide shoe

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Acknowledgments

This work was financially supported by the National Science and Technology Major Project of the Ministry of Science and Technology of China (2017ZX04022001-207). We appreciate the invaluable expert comments and advice on the paper from all anonymous reviewers.

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Authors and Affiliations

  1. Department of Mechanical and Electrical Engineering, Xiamen University, Xiamen, 361005, China

    Chenchun Shi, Zhenzhong Wang & Yunfeng Peng

Authors
  1. Chenchun Shi
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  2. Zhenzhong Wang
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  3. Yunfeng Peng
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Corresponding author

Correspondence to Zhenzhong Wang.

Additional information

Recommended by Editor No-cheol Park

Chenchun Shi received his master degree from Ningbo University, Zhejiang, China. He is currently a postgraduate student pursuing the Ph.D. in Xiamen University (XMU), China. His research interest is mainly focused on precision engineering and manufacturing.

Zhenzhong Wang received his B.S and Ph.D. in mechanical engineering from Department of Mechanical and Electrical Engineering, Xiamen University in 2003 and 2009. He is currently an Associate Professor of mechanical engineering at Xiamen University. His current research interests include advanced optical manufacturing.

Yunfeng Peng received his Ph.D. in mechanical engineering from Harbin Institute of Technology in 2006. He is currently a Professor of mechanical engineering at Xiamen University. His current research interests include Intelligent Manufacturing, precision and ultraprecision machine tools, tribology, etc.

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Shi, C., Wang, Z. & Peng, Y. Influence of relative difference between paired guide rails on motion accuracy in closed hydrostatic guideways. J Mech Sci Technol 34, 631–648 (2020). https://doi.org/10.1007/s12206-020-0109-4

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  • DOI: https://doi.org/10.1007/s12206-020-0109-4

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