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.
References
1.
Chen
, W.
, 1971
, “Computation of Stresses and Displacements in a Layered Elastic Medium
,” Int. J. Eng. Sci.
, 9
(9
), pp. 775
–800
.2.
Cai
, S.
, and Bhushan
, B.
, 2005
, “A Numerical Three-Dimensional Contact Model for Rough, Multilayered Elastic/Plastic Solid Surfaces
,” Wear
, 259
(7–12
), pp. 1408
–1423
.3.
Ye
, N.
, and Komvopoulos
, K.
, 2003
, “Effect of Residual Stress in Surface Layer on Contact Deformation of Elastic-Plastic Layered Media
,” ASME J. Tribol.
, 125
(4
), pp. 692
–699
.4.
Kot
, M.
, Rakowski
, W.
, Lackner
, J. M.
, and Major
, Ł.
, 2013
, “Analysis of Spherical Indentations of Coating-Substrate Systems: Experiments and Finite Element Modeling
,” Mater. Des.
, 43
, pp. 99
–111
.5.
Zhou
, K.
, Keer
, L. M.
, and Wang
, Q. J.
, 2011
, “Semi-Analytic Solution for Multiple Interacting Three-Dimensional Inhomogeneous Inclusions of Arbitrary Shape in an Infinite Space
,” Int. J. Numer. Meth. Eng.
, 87
(7
), pp. 617
–638
.6.
Zhou
, K.
, Chen
, W. W.
, Keer
, L. M.
, Ai
, X.
, Sawamiphakdi
, K.
, Glaws
, P.
, and Wang
, Q. J.
, 2011
, “Multiple 3D Inhomogeneous Inclusions in a Half Space Under Contact Loading
,” Mech. Mater.
, 43
(8
), pp. 444
–457
.7.
Zhou
, K.
, Chen
, W. W.
, Keer
, L. M.
, and Wang
, Q. J.
, 2009
, “A Fast Method for Solving Three-Dimensional Arbitrarily Shaped Inclusions in a Half Space
,” Comput. Methods Appl. Mech. Eng.
, 198
(9–12
), pp. 885
–892
.8.
Zhou
, K.
, Keer
, L. M.
, and Wang
, Q. J.
, 2011
, “Analysis of Hard Coatings on a Substrate Containing Inhomogeneities
,” J. Mech. Mater. Struct.
, 6
(1–4
), pp. 627
–639
.9.
Dong
, Q.
, Zhou
, K.
, Wei
, R.
, Luo
, J.
, and Srikanth
, N.
, 2015
, “Analysis of Fluid Pressure, Interface Stresses and Stress Intensity Factors for Layered Materials With Cracks and Inhomogeneities Under Elastohydrodynamic Lubrication Contact
,” Int. J. Mech. Sci.
, 93
, pp. 48
–58
.10.
Luo
, J.
, Liu
, Y.
, and Berger
, E.
, 2000
, “Interfacial Stress Analysis for Multi-Coating Systems Using an Advanced Boundary Element Method
,” Comput. Mech.
, 24
(6
), pp. 448
–455
.11.
Yu
, C.
, Wang
, Z.
, and Wang
, Q. J.
, 2014
, “Analytical Frequency Response Functions for Contact of Multilayered Materials
,” Mech. Mater.
, 76
, pp. 102
–120
.12.
Wang
, Z.
, Yu
, C.
, and Wang
, Q.
, 2015
, “An Efficient Method for Solving Three-Dimensional Fretting Contact Problems Involving Multilayered or Functionally Graded Materials
,” Int. J. Solids Struct.
, 66
, pp. 46
–61
.13.
Wei
, J.
, Zhang
, A.
, and Gao
, P.
, 2016
, “A Study of Spur Gear Pitting Under EHL Conditions: Theoretical Analysis and Experiments
,” Tribol. Int.
, 94
, pp. 146
–154
.14.
Rehman
, W. U.
, Jiang
, G.
, Luo
, Y.
, Wang
, Y.
, Khan
, W.
, Rehman
, S. U.
, and Iqbal
, N.
, 2018
, “Control of Active Lubrication for Hydrostatic Journal Bearing by Monitoring Bearing Clearance
,” Adv. Mech. Eng.
, 10
(4
), pp. 1–17.15.
Zhu
, D.
, and Wang
, Q. J.
, 2011
, “Elastohydrodynamic Lubrication: A Gateway to Interfacial Mechanics—Review and Prospect
,” ASME J. Tribol.
, 133
(4
), p. 041001
.16.
Zhu
, D.
, Liu
, Y.
, and Wang
, Q.
, 2014
, “On the Numerical Accuracy of Rough Surface EHL Solution
,” Tribol. Trans.
, 57
(4
), pp. 570
–580
.17.
Pu
, W.
, Wang
, J.
, and Zhu
, D.
, 2016
, “Progressive Mesh Densification Method for Numerical Solution of Mixed Elastohydrodynamic Lubrication
,” ASME J. Tribol.
, 138
(2
), p. 021502
.18.
Venner
, C. H.
, and Lubrecht
, A. A.
, 2000
, Multi-Level Methods in Lubrication
, Elsevier, Amsterdam
, The Netherlands
.19.
Zhu
, D.
, 2007
, “On Some Aspects of Numerical Solutions of Thin-Film and Mixed Elastohydrodynamic Lubrication
,” Proc. Inst. Mech. Eng., Part J
, 221
(5
), pp. 561
–579
.20.
Liu
, Y.
, Chen
, W. W.
, Zhu
, D.
, Liu
, S.
, and Wang
, Q. J.
, 2007
, “An Elastohydrodynamic Lubrication Model for Coated Surfaces in Point Contacts
,” ASME J. Tribol.
, 129
(3
), pp. 509
–516
.21.
Liu
, Y.
, Wang
, Q. J.
, and Zhu
, D.
, 2008
, “Effect of Stiff Coatings on EHL Film Thickness in Point Contacts
,” ASME J. Tribol.
, 130
(3
), p. 031501
.22.
Wang
, Z.
, Wang
, W.
, Wang
, H.
, and Hu
, Y. Z.
, 2009
, “Stress Analysis on Layered Materials in Point Elastohydrodynamic-Lubricated Contacts
,” Tribol. Lett.
, 35
(3
), pp. 229
–244
.23.
Wang
, Z.
, Yu
, C.
, and Wang
, Q.
, 2015
, “Model for Elastohydrodynamic Lubrication of Multilayered Materials
,” ASME J. Tribol.
, 137
(1
), p. 011501
.24.
Reynolds
, O.
, 1886
, “On the Theory of Lubrication and Its Application to Mr. Beauchamp Tower's Experiments, Including an Experimental Determination of the Viscosity of Olive Oil
,” Proc. R. Soc. London
, 40
(242–245
), pp. 191
–203
.25.
Hu
, Y. Z.
, Wang
, H.
, Wang
, W. Z.
, and Zhu
, D.
, 2001
, “A Computer Model of Mixed Lubrication in Point Contacts
,” Tribol. Int.
, 34
(1
), pp. 65
–73
.26.
Peiran
, Y.
, and Shizhu
, W.
, 1990
, “A Generalized Reynolds Equation for Non-Newtonian Thermal Elastohydrodynamic Lubrication
,” ASME J. Tribol.
, 112
(4
), pp. 631
–636
.27.
Wang
, W. Z.
, Hu
, Y. Z.
, Liu
, Y.
, and Zhu
, D.
, 2010
, “Solution Agreement Between Dry Contacts and Lubrication System at Ultra-Low Speed
,” Proc. Inst. Mech. Eng., Part J
, 224
(10
), pp. 1049
–1060
.28.
van Leeuwen
, H.
, 2009
, “The Determination of the Pressure—Viscosity Coefficient of a Lubricant Through an Accurate Film Thickness Formula and Accurate Film Thickness Measurements
,” Proc. Inst. Mech. Eng., Part J
, 223
(8
), pp. 1143
–1163
.29.
Liu
, Y.
, Wang
, Q. J.
, Wang
, W.
, Hu
, Y.
, and Zhu
, D.
, 2006
, “Effects of Differential Scheme and Mesh Density on EHL Film Thickness in Point Contacts
,” ASME J. Tribol.
, 128
(3
), pp. 641
–653
.30.
Wang
, F. S.
, Block
, J. M.
, Chen
, W. W.
, Martini
, A.
, Zhou
, K.
, Keer
, L. M.
, and Wang
, Q. J.
, 2009
, “A Multilevel Model for Elastic-Plastic Contact Between a Sphere and a Flat Rough Surface
,” ASME J. Tribol.
, 131
(2
), p. 021409
.31.
Glovnea
, R.
, and Spikes
, H.
, 2001
, “Elastohydrodynamic Film Collapse During Rapid Deceleration—Part I: Experimental Results
,” ASME J. Tribol.
, 123
(2
), pp. 254
–261
.32.
Zhao
, J.
, and Sadeghi
, F.
, 2003
, “Analysis of EHL Circular Contact Shut Down
,” ASME J. Tribol.
, 125
(1
), pp. 76
–90
.33.
Glovnea
, R.
, and Spikes
, H.
, 2001
, “Elastohydrodynamic Film Collapse During Rapid Deceleration—Part II: Theoretical Analysis and Comparison of Theory and Experiment
,” ASME J. Tribol.
, 123
(2
), pp. 262
–267
.34.
Lu
, X.
, Dong
, Q.
, Zhou
, K.
, Zhao
, B.
, and Zhao
, B.
, 2018
, “Numerical Analysis of Transient Elastohydrodynamic Lubrication During Startup and Shutdown Processes
,” ASME J. Tribol.
, 140
(4
), p. 041504
.35.
O'Sullivan
, T.
, and King
, R.
, 1988
, “Sliding Contact Stress Field Due to a Spherical Indenter on a Layered Elastic Half-Space
,” ASME J. Tribol.
, 110
(2
), pp. 235
–240
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