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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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Figures

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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. 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. 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. 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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