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Research Papers: Mixed and Boundary Lubrication

A Model of Mixed Lubrication Based on Non-Normalized Discretization and Its Application for Multilayered Materials

[+] Author and Article Information
Qingbing Dong

School of Mechanical Engineering,
Chongqing University,
Chongqing 400030, China
e-mail: qdong002@cqu.edu.cn

Zhanjiang Wang

Department of Mechanical Engineering,
Southwest Jiaotong University,
Sichuan 610031, China

Dong Zhu

College of Power and Energy Engineering,
Harbin Engineering University,
145 Nantong Street, Nangang District,
Harbin 150001, Heilongjiang, China

Fanming Meng

School of Mechanical Engineering;State Key Laboratory of Mechanical
Transmission,
Chongqing University,
Chongqing 400030, China

Lixin Xu

School of Mechanical Engineering,
Chongqing University,
Chongqing 400030, China

Kun Zhou

School of Mechanical and Aerospace
Engineering,
Nanyang Technological University,
50 Nanyang Avenue,
Singapore 639798

1Corresponding author.

Contributed by the Tribology Division of ASME for publication in the JOURNAL OF TRIBOLOGY. Manuscript received May 16, 2018; final manuscript received November 18, 2018; published online January 16, 2019. Assoc. Editor: Wang-Long Li.

J. Tribol 141(4), 042101 (Jan 16, 2019) (10 pages) Paper No: TRIB-18-1189; doi: 10.1115/1.4042074 History: Received May 16, 2018; Revised November 18, 2018

This study presents a generalized model of mixed elastohydrodynamic lubrication, in which the dimensional Reynolds equation is discretized according to a modified differential scheme based on the full analysis of the pressure balance within the lubrication region. The model is capable of a wide range of lubrication regimes from fully hydrodynamic down to boundary lubrication, and both the steady-state and the time-dependent conditions can be considered. A simplified computational procedure is proposed for elliptical contacts without the ellipticity parameters specified. The evolution of lubrication behavior at startup and shutdown conditions is investigated and the transient effect of surface waviness is discussed. The model application is then extended to contacts of multilayered materials, and the effects of the layer stiffness and the fabrication methods on the stress fields and lubrication performance are analyzed. The conclusions may potentially provide some insightful information for the design and analysis of functional materials and their engineering structures.

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Figures

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Fig. 1

The equivalent configuration upon the coordinate rotation

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Fig. 2

Plots of pressure and film thickness at the entrainment velocities of ux=uy=0 along the (a) x and (b) y directions, respectively

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Fig. 3

Evolution of lubrication for a startup process to ux=1.0 m/s at t = (a) 6 ms, (b) 8 ms, (c) 10 ms, (d) 12 ms, and (e) the development of film thickness along the x direction

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Fig. 4

Evolution of lubrication for a shutdown process from an initial velocity of ux=1.0 m/s at t = (a) 0 ms, (b) 10 ms, (c) 20 ms, and (d) the collapse of film thickness along the x direction

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Fig. 5

Pressure and film thickness profiles along the x direction when a surface with waviness passes through the computational domain at t = (a) 0 ms, (b) 4 ms, (c) 6 ms, and (d) 8 ms

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Fig. 6

Evolution of lubrication for an elliptical contact with the radii of Rx=20 mm and Ry=40 mm at a velocity of |u|=1 m/s with an angle of θ=π/4

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Fig. 7

Plots of pressure for the single-layered substrate at ux=uy=0 along the (a) x and (b) y directions, respectively

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Fig. 8

Pressure and film thickness for a single layer with the thickness of (a) hc=0.5a0 and (b) hc=1.0a0 along the x directions at ux=1.0 m/s

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Fig. 9

Contours of von Mises stresses in the xz plane for a single layer with the thickness of hc=0.5a0 for (a) Ec=0.25Es and (b) Ec=4.0Es and hc=1.0a0 for (c) Ec=0.25Es and (d) Ec=4.0Es at ux=1.0 m/s

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Fig. 10

Normalized stress components at the layer–substrate interface for the single layer of various moduli with a thickness of (a) hc=0.5a0 and (b) hc=1.0a0

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Fig. 11

Fabrication methods of (a) case 1 and (b) case 2, and (c) the contour of surface roughness

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Fig. 12

Pressure and film thickness profiles for alternatively fabricated stiff and compliant layers at (a) ux=uy=0 and (b) ux=0.1 m/s; von Mises stresses in the xz plane for (c) case 1 and (d) case 2 at ux=0.1 m/s

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Fig. 13

Fabrication methods of layers with (a) increasing moduli and (b) decreasing moduli, (c) the contour of surface roughness, and (d) pressure and film thickness profiles

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Fig. 14

The von Mises stress contours in the xz plane for (a) case 3 and (b) case 4 at ux=0.1 m/s

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