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Research Papers: Micro-Nano Tribology

Combined Effects of Surface Roughness and Rarefaction in the Region Between High Wave Number-Limited and High Bearing Number-Limited Lubricant Flows

[+] Author and Article Information
James White

6017 Glenmary Road,
Knoxville, TN 37919

Contributed by the Tribology Division of ASME for publication in the JOURNAL OF TRIBOLOGY. Manuscript received June 17, 2014; final manuscript received August 21, 2014; published online October 3, 2014. Assoc. Editor: Min Zou.

J. Tribol 137(1), 012001 (Oct 03, 2014) (10 pages) Paper No: TRIB-14-1133; doi: 10.1115/1.4028411 History: Received June 17, 2014; Revised August 21, 2014

Analytical methods and techniques are required for design and analysis of low clearance gas-bearings that account for the combined influence of surface roughness and Knudsen number. Analytical methods for the lubrication equation are currently available for bearings that are either high wave number-limited or high bearing number-limited. There are few useful analytical methods in the range between these limiting extremes that account for the combined effect of roughness and rarefaction. That is the focus of this paper as it extends the work reported by White (2013, “Surface Roughness Effects in the Region Between High Wave Number and High Bearing Number-Limited Lubricant Flows,” ASME J. Tribol., 135(4), p. 041706) to include rarefaction effects. Results of an analytical study will be reported that investigates a wedge bearing geometry using perturbation methods and multiple-scale analysis over a wide range of Knudsen numbers for roughness on moving and stationary surfaces. The solution technique developed allows nonlinear aspects of the lubrication equation to be retained in the analysis. Solutions will be presented graphically and discussed. Results indicate that most of the bearing sensitivity to Knudsen number can be accounted for by a modified form of the bearing number.

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References

Tzeng, S. T., and Saibel, E., 1967, “Surface Roughness Effect on Slider Bearing Lubrication,” ASLE Trans., 10(3), pp. 334–338. [CrossRef]
Christensen, H., and Tønder, K., 1969, “Tribology of Rough Surfaces: Stochastic Models of Hydrodynamic Lubrication,” Technical University of Norway, Trondheim, Norway, SINTEF Report No. 10/69-18.
Christensen, H., and Tønder, K., 1971, “The Hydrodynamic Lubrication of Rough Bearing Surfaces of Finite Width,” ASME J. Lubr. Technol., 93(3), pp. 324–330. [CrossRef]
Rhow, S. K., and Elrod, H. G., 1974, “The Effects on Bearing Load-Carrying Capacity of Two-Sided Striated Roughness,” ASME J. Lubr. Technol., 96(4), pp. 554–560. [CrossRef]
Elrod, H. G., 1978, “A Review of Theories for the Fluid Dynamic Effects of Roughness on Laminar Lubricating Films,” Proceedings of the Fourth Leeds–Lyon Symposium on Tribology Effects of Surface Roughness in Lubrication, Lyon, France, pp. 11–26.
Elrod, H. G., 1979, “A General Theory for Laminar Lubrication With Reynolds Roughness,” ASME J. Lubr. Technol., 101(1), pp. 8–14. [CrossRef]
White, J. W., 1980, “Surface Roughness Effects on the Load Carrying Capacity of Very Thin Compressible Lubricating Films,” ASME J. Lubr. Technol., 102(4), pp. 445–451. [CrossRef]
White, J. W., 1983, “The Effect of Two Sided Surface Rouhness on Ultra-Thin Gas Films,” ASME J. Lubr. Technol., 105(1), pp. 131–137. [CrossRef]
White, J. W., 1992, “The Influence of Longitudinal Surface Roughness on the Load Carrying Capacity of a Thin Compressible Gas Film,” Adv. Inf. Storage Syst., 4, pp. 139–153.
White, J. W., 1993, “The Effect of Two-Dimensional Surface Roughness on the Load-Carrying Capacity of a Thin Compressible Gas Film,” ASME J. Tribol., 115(2), pp. 246–252. [CrossRef]
White, J. W., 1999, “An Averaging Technique for the Analysis of Rough Surface High Bearing Number Gas Flows,” ASME J. Tribol., 121(2), pp. 333–340. [CrossRef]
Greengard, C., 1989, “Large Bearing Numbers and Stationary Reynolds Roughness,” ASME J. Tribol., 111(1), pp. 136–141. [CrossRef]
Buscaglia, G., and Jai, M., 2001, “A New Numerical Scheme for Nonuniform Homogenized Problems: Application to the Nonlinear Reynolds Compressible Equation,” Math. Probl. Eng., 7(4), pp. 355–377. [CrossRef]
Buscaglia, G., and Jai, M., 2004, “Homogenization of the Generalized Reynolds Equation for Ultra-Thin Gas Films and Its Resolution by FEM,” ASME J. Tribol., 126(3), pp. 547–552. [CrossRef]
White, J., 2010, “A Gas Lubrication Equation for High Knudsen Number Flows and Striated Rough Surfaces,” ASME J. Tribol., 132(2), p. 021701. [CrossRef]
White, J., 2011, “Numerical Solution of the Boltzmann Based Lubrication Equation for the Air-Bearing Interface Between a Skewed Slider and a Disk With Discrete Data Tracks,” ASME J. Tribol., 133(2), p. 021901. [CrossRef]
White, J., 2012, “A Lubrication Equation Incorporating Two-Dimensional Roughness Effects, With Emphasis on the Patterned Data Islands of a Recording Disk,” ASME J. Tribol., 134(1), p. 011901. [CrossRef]
White, J., 2012, “Comparison of Moving and Stationary Surface Roughness Effects on Bearing Performance, With Emphasis on High Knudsen Number Flow,” ASME J. Tribol., 134(3), p. 031705. [CrossRef]
Patir, N., and Cheng, H. S., 1978, “An Average Flow Model for Determining Effects of Three-Dimensional Roughness on Partial Hydrodynamic Lubrication,” ASME J. Lubr. Technol., 100(1), pp. 12–17. [CrossRef]
Mitsuya, Y., 1984, “A Simulation Method for Hydrodynamic Lubrication of Surfaces With Two-Dimensional Isotropic or Anisotropic Roughness Using Mixed Average Film Thickness,” Bull. JSME, 27(231), pp. 2036–2044. [CrossRef]
Li, W. L., and Weng, C. I., 1997, “Modified Average Reynolds Equation for Ultra-Thin Film Gas Lubrication Considering Roughness Orientations at Arbitrary Knudsen Numbers,” Wear, 209(1–2), pp. 292–300. [CrossRef]
White, J. W., Raad, P. E., Tabrizi, A. H., Ketkar, S. P., and Prabhu, P. P., 1986, “A Numerical Study of Surface Roughness on Ultra-Thin Gas Films,” ASME J. Tribol., 108(2), pp. 171–177. [CrossRef]
Raad, P. E., and White, J. W., 1989, “Entrance and Stationary Roughness Effects on the Load Carrying Capacity of a Wide Wedge Gas Bearing,” ASME J. Tribol., 111(1), pp. 41–48. [CrossRef]
Raad, P. E., and Kuria, I. M., 1989, “Two Side Texture Effects on Ultra-Thin Wide Wedge Gas Bearings,” ASME J. Tribol., 111(4), pp. 719–725. [CrossRef]
Crone, R. M., Jhon, M. S., Bhushan, B., and Karis, T. E., 1991, “Modeling the Flying Characteristics of a Rough Magnetic Head Over a Rough Rigid Disk Surface,” ASME J. Tribol., 113(4), pp. 739–749. [CrossRef]
White, J., 2010, “Surface Roughness Effects on Air-Bearing Performance Over a Wide Range of Knudsen and Wave Numbers,” ASME J. Tribol., 132(3), p. 031703. [CrossRef]
White, J., 2013, “Surface Roughness Effects in the Region Between High Wave Number and High Bearing Number limited Lubricant Flows,” ASME J. Tribol., 135(4), p. 041706. [CrossRef]
Fukui, S., and Kaneko, R., 1990, “A Database for Interpolation of Poiseuille Flow Rates for High Knudsen Number Lubrication Problems,” ASME J. Tribol., 112(1), pp. 78–83. [CrossRef]
Schmitt, J. A., and DiPrima, R. C., 1978, “Asymptotic Methods for a General Finite Width Gas Slider Bearing,” ASME J. Lubr. Technol., 100(2), pp. 254–260. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

Surface roughness configuration (a) stationary roughness and (b) moving roughness

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Fig. 2

Effect of modified bearing number on net force for two values of Knudsen number

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Fig. 3

Pressure profile segments for two values of Knudsen number: (a) modified bearing number  = 1 and (b) modified bearing number  = 10.

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Fig. 4

Effect of modified bearing number on net force for several values of Knudsen number and inclination

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Fig. 5

Effect of modified bearing number on net force for three values of Knudsen number and three sets of (ɛ,m) values

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Fig. 6

Effect of modified bearing number on the net force ratio, Fnet/Fnet(kref = 0), for several values of Knudsen number

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Fig. 7

Effect of modified bearing number on the net force ratio, Fnet/Fnet(kref = 1.), for several values of Knudsen number

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Fig. 8

Influence of effective bearing number, Λ3, on net force ratio for several values of Knudsen number and inclination

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Fig. 9

Effect of modified bearing number on mass flow rate function, m·x/Λ, for several values of Knudsen number and inclination

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Fig. 10

Influence of effective bearing number, Λ3, on mass flow rate function, m·x/Λ, for several values of Knudsen number and inclination

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