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RESEARCH PAPERS

The Validity of the Reynolds Equation in Modeling Hydrostatic Effects in Gas Lubricated Textured Parallel Surfaces

[+] Author and Article Information
Y. Feldman, I. Etsion, S. Haber

Department of Mechanical Engineering, Technion-Israel Institute of Technology, Faculty of Mechanical Engineering, Technion City, Haifa, 32000, Israel

Y. Kligerman1

Department of Mechanical Engineering, Technion-Israel Institute of Technology, Faculty of Mechanical Engineering, Technion City, Haifa, 32000, Israelmermdyk@tx.technion.ac.il

1

Corresponding author.

J. Tribol 128(2), 345-350 (Nov 03, 2005) (6 pages) doi:10.1115/1.2148419 History: Received April 10, 2005; Revised November 03, 2005

Microdimples generated by laser surface texturing (LST) can be used to enhance performance in hydrostatic gas-lubricated tribological components with parallel surfaces. The pressure distribution and load carrying capacity for a single three-dimensional dimple, representing the LST, were obtained via two different methods of analysis: a numerical solution of the exact full Navier-Stokes equations, and an approximate solution of the much simpler Reynolds equation. Comparison between the two solution methods illustrates that, despite potential large differences in local pressures, the differences in load carrying capacity, for realistic geometrical and physical parameters, are small. Even at large clearances of 5% of the dimple diameter and pressure ratios of 2.5 the error in the load carrying capacity is only about 15%. Thus, for a wide range of practical clearances and pressures, the simpler, approximate Reynolds equation can safely be applied to yield reasonable predictions for the load carrying capacity of dimpled surfaces.

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Copyright © 2006 by American Society of Mechanical Engineers
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Figures

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Figure 2

Streamlines of the gas flow at the mid cross section of a dimple: (a) without flow recirculation, c=3μm, hp=15μm; (b) with flow recirculation at the top of the dimple, c=5μm, hp=20μm

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Figure 3

Transition from recirculation (above) and no circulation (below) and the recirculation inception line as function of the aspect ratio ε and dimensionless clearance δ

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Figure 4

Isobars (in MPa) of the gas pressure distribution at the mid cross section of a dimple obtained from the NS equations: (a) without flow recirculation, c=3μm, hp=15μm; (b) with flow recirculation at the top of the dimple, c=5μm, hp=20μm

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Figure 5

A comparison of the pressure distributions obtained from the NS and Reynolds equations: (a) maximum relative difference between the NS and the Reynolds equations versus dimple aspect ratio ε at various dimensionless clearance values δ; (b) the dimensionless pressure distribution at the mid cross section of the dimple for δ=0.05 and ε=0.15

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Figure 6

Comparison of load carrying capacities, W, obtained from the NS (solid lines) and the Reynolds (dashed line) equations versus dimple aspect ratio ε at various dimensionless clearance values δ

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Figure 7

A load capacity relative error map indicating that for a wide range of clearances, δ and pressure ratios, po∕pa, the Reynolds equation is valid.

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Figure 1

The geometrical model: (a) a segment of infinitely long strip of dimples; (b) a cross section at the middle of one imaginary cell

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