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Technical Briefs

Coupled Nonlinear Effects of Random Surface Roughness and Rarefaction on Slip Flow in Ultra-Thin Film Gas Bearing Lubrication

[+] Author and Article Information
Wen-Ming Zhang

State Key Laboratory of Mechanical System and Vibration,School of Mechanical Engineering,  Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai 200240, Chinawenmingz@sjtu.edu.cn

Guang Meng, Zhi-Ke Peng

State Key Laboratory of Mechanical System and Vibration,School of Mechanical Engineering,  Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai 200240, China

Di Chen

National Key Laboratory of Micro/Nano Fabrication Technology,  Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai 200240, China

J. Tribol 134(2), 024502 (Apr 12, 2012) (8 pages) doi:10.1115/1.4006443 History: Received June 16, 2010; Revised December 08, 2010; Published April 11, 2012; Online April 12, 2012

A mathematical model of gaseous slip flow in ultra-thin film gas bearings is numerically analyzed incorporating effects of surface roughness, which is characterized by fractal geometry. The Weierstrass-Mandelbrot (W-M) function is presented to represent the multiscale self-affine roughness of the surface. A modified Reynolds equation incorporating velocity slip boundary condition is applied for the arbitrary range of Knudsen numbers in the slip and transition regimes. The effects of bearing number, Knudsen number, geometry parameters of the bearing and roughness parameters on the complex flow behaviors of the gas bearing are investigated and discussed. Numerical solutions are obtained for various bearing configurations under the coupled effects of rarefaction and roughness. The results indicate that roughness has a more significant effect on higher Knudsen number (rarefaction effect) flows with higher relative roughness. Surface with larger fractal dimensions yield more frequency variations in the surface profile, which result in an obviously larger incremental pressure loss. The Poiseuille number increases not only with increasing of rarefaction effect but also with increasing the surface roughness. It can also be observed that the current study is in good agreement with solutions obtained from the linearized Boltzmann equation.

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Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 1

Schematic diagram of the microbearing with random roughness surface

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Figure 2

Nondimensional pressure distribution of the slider bearing with smooth and rough surfaces for different thicknesses of the gas film

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Figure 3

Nondimensional load carrying capacity as a function of the bearing number for models 3 and 7

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Figure 4

Nondimensional load carrying capacity as a function of the relative roughness height σ/Dh with different breadth parameter ε at Λ=22.52

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Figure 5

Variation of streamwise location of the load carrying capacity with the inverse Knudsen number for different relative roughness heights σ/Dh

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Figure 6

Variation of nondimensional velocity distribution through gas bearing of models 1, 3, 4 with smooth surface and models 5(a), 7(a), 8(a) with random rough surface

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Figure 7

Variation of nondimensional velocity distribution in the gas bearing for models 3 and 7 at the streamwise location Xc=0.5

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Figure 8

Effect of fractal dimension on the relative Poiseuille number for rarefied flow in the gas bearing

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Figure 9

Variation of the nondimensional slip length through the gas bearing for the models 5–7(a) with different thicknesses of the gas film

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Figure 10

Nondimensional slip length as a function of the Knudsen number with comparisons of smooth and rough surfaces

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