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Research Papers: Hydrodynamic Lubrication

A Modified Average Reynolds Equation for Rough Bearings With Anisotropic Slip

[+] Author and Article Information
Hsiang-Chin Jao

Department of Materials Science
and Engineering,
National Cheng Kung University,
No. 1 University Road,
Tainan 701, Taiwan
e-mail: q28991067@mail.ncku.edu.tw

Kuo-Ming Chang

Department of Mechanical Engineering,
National Kaohsiung University
of Applied Sciences,
No. 415 Chien Kung Road,
Kaohsiung 807, Taiwan
e-mail: koming@cc.kuas.edu.tw

Li-Ming Chu

Department of Mechanical Engineering,
Southern Taiwan University
of Science and Technology,
No. 1 Nantai Street,
Tainan 710, Taiwan
e-mail: lmchu@mail.stust.edu.tw

Wang-Long Li

Department of Materials Science
and Engineering,
National Cheng Kung University,
No. 1 University Road,
Tainan 701, Taiwan
e-mail: wlli@mail.ncku.edu.tw

1Corresponding author.

Contributed by the Tribology Division of ASME for publication in the JOURNAL OF TRIBOLOGY. Manuscript received February 14, 2015; final manuscript received June 14, 2015; published online August 6, 2015. Assoc. Editor: Min Zou.

J. Tribol 138(1), 011702 (Aug 06, 2015) (14 pages) Paper No: TRIB-15-1054; doi: 10.1115/1.4030901 History: Received February 14, 2015

A lubrication theory that includes the coupled effects of surface roughness and anisotropic slips is proposed. The anisotropic-slip phenomena originate from the microscale roughness at the atomic scale (microtexture) and surface properties of the lubricating surfaces. The lubricant flow between rough surfaces (texture) is defined as the flow in nominal film thickness multiplied by the flow factors. A modified average Reynolds equation (modified ARE) as well as the related factors (pressure and shear flow factors, and shear stress factors) is then derived. The present model can be applied to squeeze film problems for anisotropic-slip conditions and to sliding lubrication problems with restrictions to symmetric anisotropic-slip conditions (the two lubricating surfaces have the same principal slip lengths, i.e., b1x=b2x and b1y=b2y). The performance of journal bearings is discussed by solving the modified ARE numerically. Different slenderness ratios 5, 1, and 0.2 are considered to discuss the coupled effects of anisotropic slip and surface roughness. The results show that the existence of boundary slip can dilute the effects of surface roughness. The boundary slip tends to “smoothen” the bearings, i.e., the derived flow factors with slip effects deviate lesser from the values at smooth cases (pressure flow factors φxxp,φyyp=1; shear flow factors φxxs=0; and shear stress factors φf,φfp=1 and φfs=0) than no-slip one. The load ratio increases as the dimensionless slip length (B) decreases exception case is also discussed or the slenderness ratio (b/d) increases. By controlling the surface texture and properties, a bearing with desired performance can be designed.

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Figures

Grahic Jump Location
Fig. 1

Schematic diagram of roughness surface

Grahic Jump Location
Fig. 2

Effect of dimensionless slip length (B) on Poiseuille flow rate correctors (Qpx)

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Fig. 3

Effect of dimensionless slip length (B) on roughness coefficients: (a) fx and (b) gx

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Fig. 4

Effect of dimensionless slip length (B1x and B2x) on pressure flow factors (φxxp) for: (a) longitudinal type roughness, γ=9, (b) isotropic type roughness, γ=1, and (c) transversely type roughness, γ=1/9. (d) Effects of film thickness ratio (Hs) and Peklenik number (γ) on pressure flow factor (φxxp). (e) Effects of dimensionless slip length (B) and Peklenik number (γ) on pressure flow factor (φxxp) for symmetric slip (B1x=B2x=B). (f) Effects of Peklenik number (γ) and film thickness ratio (Hs) pressure flow factor (φxxp) for various combinations of (B1x, B2x).

Grahic Jump Location
Fig. 5

Effects of dimensionless slip length (B) and Peklenik number (γ) on shear flow factor (φxxs)

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Fig. 6

Effect of dimensionless slip length on shear stress factors: (a) φP and φfp and (b) φC. (c) Effects of dimensionless slip length and Peklenik number (γ) on shear stress factors (φf and φfp). (d) Effects of dimensionless slip length on shear stress factors (φfs) for stationary roughness (σ1=0 and σ2=σ), two-sided roughness (σ1=σ2), and moving roughness (σ1=σ and σ2=0).

Grahic Jump Location
Fig. 7

Effects of dimensionless slip lengths (Bx and By) on dimensionless load capacity at: (a) b/d=0.2, (b) b/d=1, and (c) b/d=5

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Fig. 8

(a) Effects of dimensionless slip length (B) and Peklenik number (γ) on load ratio by using b/d=0.2 for stationary roughness (σ1=0 and σ2=σ), two-sided roughness (σ1=σ2), and moving roughness (σ1=σ and σ2=0). (b) Effects of dimensionless slip length (B) and Peklenik number (γ) on load ratio by using b/d=1.0 for stationary roughness (σ1=0 and σ2=σ), two-sided roughness (σ1=σ2), and moving roughness (σ1=σ and σ2=0). (c) Effects of dimensionless slip length (B) and Peklenik number (γ) on load ratio by using b/d=5.0 for stationary roughness (σ1=0 and σ2=σ), two-sided roughness (σ1=σ2), and moving roughness (σ1=σ and σ2=0).

Grahic Jump Location
Fig. 9

Effect of dimensionless slip lengths (Bx and By) on dimensionless friction force (Fs) for stationary roughness (σ1=0 and σ2=σ), two-sided roughness (σ1=σ2), and moving roughness (σ1=σ and σ2=0)

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Fig. 10

COF ratios as functions of dimensionless slip lengths (Bx and By) at: (a) b/d=0.2, (b) b/d=1, and (c) b/d=5

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