Elastohydrodynamic Lubrication (EHL) is commonly known as a mode of fluid-film lubrication in which the mechanism of hydrodynamic film formation is enhanced by surface elastic deformation and lubricant viscosity increase due to high pressure. It has been an active and challenging field of research since the 1950s. Significant breakthroughs achieved in the last 10–15 years are largely in the area of mixed EHL, in which surface asperity contact and hydrodynamic lubricant film coexist. Mixed EHL is of the utmost importance not only because most power-transmitting components operate in this regime, but also due to its theoretical universality that dry contact and full-film lubrication are in fact its special cases under extreme conditions. In principle, mixed EHL has included the basic physical elements for modeling contact, or hydrodynamic lubrication, or both together. The unified mixed lubrication models that have recently been developed are now capable of simulating the entire transition of interfacial status from full-film and mixed lubrication down to dry contact with an integrated mathematic formulation and numerical approach. This has indeed bridged the two branches of engineering science, contact mechanics, and hydrodynamic lubrication theory, which have been traditionally separate since the 1880s mainly due to the lack of powerful analytical and numerical tools. The recent advancement in mixed EHL begins to bring contact and lubrication together, and thus an evolving concept of “Interfacial Mechanics” can be proposed in order to describe interfacial phenomena more precisely and collaborate with research in other related fields, such as interfacial physics and chemistry, more closely. This review paper briefly presents snapshots of the history of EHL research, and also expresses the authors’ opinions about its further development as a gateway to interfacial mechanics.
Issue Section:
Research Papers
References
1.
Hertz
, H.
, 1881, “On the Contact of Elastic Solids
,” J. Reine Angew. Math.
, 92
, pp. 156
–171
.2.
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
,” Philos. Trans. R. Soc. London
, 177
, pp. 157
–234
.3.
Martin
, H. M.
, 1916, “Lubrication of Gear Teeth
,” Engineering (London)
, 102
, pp. 119
–121
.4.
Peppler
, W.
, 1936, “Untersuchungen uber die Druckubertragung bei Belasteten und Geschmierten Umlaufenden Achsparallelen Zylindern
,” Maschinenelemente—Tagung Aachen 1935
, V.D.I.
, Berlin
, Vol. 42
.5.
Meldahl
, A.
, 1941, “Contribution to the Theory of the Lubrication of Gears and of the Stressing of the Lubricated Flanks of Gear Teeth
,” Brown Boveri Rev.
, 28
, pp. 374
382.6.
Gatcombe
, E. K.
, 1945, “Lubrication Characteristics of Involute Spur Gears—A Theoretical Investigation
,” Trans. ASME
, 67
, pp. 177
–185
.7.
Blok
, H.
, 1950, “Fundamental Mechanical Aspects of Thin Film Lubrication
,” Ann. N.Y. Acad. Sci.
, 53
, p. 779
804.8.
Grubin
, A. N.
, 1949, Fundamentals of the Hydrodynamic Theory of Lubrication of Heavily Loaded Cylindrical Surfaces
, Book No. 30, Central Scientific Research Institute for Technology and Mechanical Engineering
, Moscow
(DSIR Translation), pp. 115
–166
.9.
Ertel
, A. M.
, 1939, “Hydrodynamic Lubrication Based on New Principles
,”Akad. Nauk. SSSR, Prikladnaya Matematika i Mekhanika
, 3
(2
), pp. 41
–52
(in Russian).10.
Petrusevich
, A. I.
, 1951, “Fundamental Conclusions from the Contact-Hydrodynamic Theory of Lubrication
,” Izv. Akad. Nauk SSR. Otd. Tekh. Nauk
, 2
, pp. 209
–233
.11.
Dowson
, D.
, and Higginson
, G. R.
, 1959, “A Numerical Solution to the Elastohydrodynamic Problem
,” J. Eng. Sci.
, 1
, pp. 6
–15
.12.
Dowson
, D.
, and Higginson
, G. R.
, 1961, “New Roller Bearing Lubrication Formula
,” Engineering
, 192
, pp. 158
–159
.13.
Dowson
, D.
, and Higginson
, G. R.
, 1966, Elastohydrodynamic Lubrication
, Pergamon
, Oxford
.14.
Dowson
, D.
, and Toyoda
, S.
, 1979, “A Central Film Thickness Formula for Elastohydrodynamic Line Contacts
,” Proceedings of the Fifth Leeds-Lyon Symposium on Tribology
, Mechanical Engineering Publications
, Bury St. Edmunds, UK
, pp. 60
–65
.15.
Crook
, A. W.
, 1961, “The Lubrication of Rollers—II. Film Thickness with Relation to Viscosity and Speed
,” Philos. Trans. R. Soc. London, Ser. A
, 254
, pp. 223
–236
.16.
Crook
, A. W.
, 1963, “The Lubrication of Rollers—IV. Measurements of Friction and Effective Viscosity
,” Philos. Trans. R. Soc. London, Ser. A
, 255
, pp. 281
–312
.17.
Dyson
, A.
, Naylor
, H.
, and Wilson
, A. R.
, 1966, “The Measurement of Film Thickness in Elastohydrodynamic Contacts
,” Proc. Inst. Mech. Eng.
, 180
(3B
), pp. 119
–134
.18.
Sibley
, L. B.
, and Orcutt
, F. K.
, 1961, “Elastohydrodynamic Lubrication of Rolling Contact Surfaces
,” ASLE Trans.
, 4
, pp. 234
–249
.19.
Kannel
, J. W.
, 1966, “The Measurement of Pressure in Rolling Contacts
,” Proc. Inst. Mech. Eng.
, 180
(3B
), pp. 135
–142
.20.
Hamilton
, G. M.
, and Moore
, S. L.
, 1971, “Deformation and Pressure in an EHD Contact
,” Proc. R. Soc. London, Ser. A
, 322
, pp. 313
–330
.21.
Archard
, J. F.
, and Kirk
, M.T.
, 1961, “Lubrication at Point Contacts
,” Proc. R. Soc. London, Ser. A
, 261
, pp. 532
–550
.22.
Gohar
, R.
, and Cameron
, A.
, 1963, “Optical Measurement of Oil Film Thickness Under Elastohydrodynamic Lubrication
,” Nature (London)
, 200
, pp. 458
–459
.23.
Gohar
, R.
, and Cameron
, A.
, 1966, “The Mapping of Elastohydrodynamic Contacts
,” ASLE Trans.
, 10
, pp. 215
–225
.24.
Foord
, C. A.
, Wedeven
, L. D.
, Westlake
, F. J.
, and Cameron
, A.
, 1969-1970, “Optical Elastohydrodynamics
,” Proc. Inst. Mech. Eng., Part I
, 184
, pp. 487
–503
.25.
Archard
, J. F.
, and Cowking
, E.W.
, 1966, “Elastohydrodynamic Lubrication at Point Contacts
,” Proc. Inst. Mech. Eng.
, 180
(3B
), pp. 47
–56
.26.
Cheng
, H. S.
, 1970, “A Numerical Solution of the Elastohydrodynamic Film Thickness in an Elliptical Contact
,” ASME J. Lubr. Technol.
, 92
, pp. 155
–162
.27.
Ranger
, A. P.
, Ettles
, C. M. M.
, and Cameron
, A.
, 1975, “The Solution of the Point Contact Elastohydrodynamic Problem
,” Proc. R. Soc. London, Ser. A
, 346
, pp. 227
–244
.28.
Hamrock
, B. J.
, and Dowson
, D.
, 1976, “Isothermal Elastohydrodynamic Lubrication of Point Contacts, Part 1—Theoretical Formulation
,” ASME J. Lubr. Technol.
, 98
, pp. 223
–229
.29.
Hamrock
, B. J.
, and Dowson
, D.
, 1976, “Isothermal Elastohydrodynamic Lubrication of Point Contacts, Part 2—Ellipticity Parameter Results
,” ASME J. Lubr. Technol.
, 98
, pp. 375
–383
.30.
Hamrock
, B. J.
, and Dowson
, D.
, 1977, “Isothermal Elastohydrodynamic Lubrication of Point Contacts, Part 3—Fully Flooded Results
,” ASME J. Lubr. Technol.
, 99
, pp. 264
–276
.31.
Hamrock
, B. J.
, and Dowson
, D.
, 1977, “Isothermal Elastohydrodynamic Lubrication of Point Contacts, Part 4—Starvation Results
,” ASME J. Lubr. Technol.
, 99
, pp. 15
–23
.32.
Koye
, K. A.
, and Winer
, W. O.
, 1981, “An Experimental Evaluation of the Hamrock and Dowson Minimum Film Thickness Equation for Fully Flooded EHD Point Contacts
,” ASME J. Lubr. Technol.
, 103
, pp. 284
–294
.33.
Kumar
, P.
, Khonsari
, M. M.
, and Bair
, S.
, 2009, “Full EHL Simulations Using the Actual Ree-Eyring Model for Shear Thinning Lubricants
,” ASME J. Tribol.
, 131
, pp. 011802
.34.
Dowson
, D.
, and Ehret
, P.
, 1999, “Past, Present and Future Studies in Elastohydrodynamics
,” Proc. Inst. Mech. Eng, Part J: J. Eng. Tribol.
, 213
, pp. 317
–333
.35.
Gohar
, R.
, 2001, Elastohydrodynamics
, 2nd ed., Imperial College Press
, London
.36.
37.
Wedeven
, L. D.
, Evans
, D.
, and Cameron
, A.
, 1971, “Optical Analysis of Ball Bearing Starvation
,” ASME J. Lubr. Technol.
, 93
, pp. 349
–363
.38.
Chiu
, Y. P.
, 1974, “An Analysis and Prediction of Lubricant Film Starvation in Rolling Contact Systems
,” ASLE Trans.
, 17
, pp. 22
–35
.39.
Wolveridge
, P. E.
, Baglin
, K. P.
, and Archard
, J. F.
, 1971, “The Starved Lubrication of Cylinders in Line Contacts
,” Proc. Inst. Mech. Eng.
, 181
, pp. 1159
–1169
.40.
Chevalier
, F.
, Lubrecht
, A. A.
, Cann
, P. M. E.
, Colin
, F.
, and Dalmaz
, G.
, 1998, “Film Thickness in Starved EHL Point Contacts
,” ASME J. Tribol.
, 120
, pp. 126
–133
.41.
Cheng
, H. S.
, and Sternlicht
, B.
, 1964, “A Numerical Solution for the Pressure, Temperature, and Film Thickness Between Two Infinitely Long, Lubricated Rolling and Sliding Cylinders, Under Heavy Loads
,” ASME J. Basic Eng.
, 87
, pp. 695
–707
.42.
Dowson
, D.
, and Whitaker
, A. V.
, 1966, “A Numerical Procedure for the Solution of the Elastohydrodynamic Problem of Rolling and Sliding Contacts Lubricated by a Newtonian Fluid
,” Proc. Inst. Mech. Eng.
, 180
(3B
), pp. 119
–134
.43.
Zhu
, D.
, and Wen
, S. Z.
, 1984, “A Full Numerical Solution for the Thermoelasto-hydrodynamic Problem in Elliptical Contacts
,” ASME J. Tribol.
, 106
, pp. 246
–254
.44.
Cheng
, H. S.
, 1967, “Calculation of Elastohydrodynamic Film Thickness in High Speed Rolling and Sliding Contacts
,” MTI Technical Report No. MIT-67TR24.45.
Murch
, L. E.
, and Wilson
, W. R. D.
, 1975, “A Thermal Elastohydrodynamic Inlet Zone Analysis
,” ASME J. Lubr. Technol.
, 97
, pp. 212
–216
.46.
Gupta
, P. K.
, Cheng
, H. S.
, Zhu
, D.
, Forster
, N. H.
, and Schrand
, J. B.
, 1992, “Viscoelastic Effects in MIL-L-7808-Type Lubricant, Part I: Analytical Formulation
,” Tribol. Trans.
, 35
, pp. 269
–274
.47.
Kumar
, P.
, Anuradha
, P.
, and Khonsari
, M. M.
, 2010, “Some Important Aspects of Thermal Elastohydrodynamic Lubrication
,” Proc. Inst. Mech. Eng., Part C: J. Mech. Eng. Sci.
, 224
, pp. 2588
–2598
.48.
Orcutt
, F. K.
, 1965, “Experimental Study of Elastohydrodynamic Lubrication
,” ASLE Trans.
, 8
, pp. 381
–396
.49.
Kannel
, J. W.
, and Bell
, J. C.
, 1972, “A Method for Estimating of Temperatures in Lubricated Rolling-Sliding Gear or Bearing EHD Contacts
,” Proceedings of the Elastohydrodynamic Lubrication 1972 Symposium
, Institution of Mechanical Engineers
, Paper No. C24/72, pp. 118
–130
.50.
Turchina
, V.
, Sanborn
, D. M.
, and Winer
, W. O.
, 1974, “Temperature Measurement in Sliding Elastohydrodynamic Point Contacts
,” ASME J. Lubr. Technol.
, 96
, pp. 464
–471
.51.
Plint
, M. A.
, 1967-1968, “Traction in Elastohydrodynamic Contacts
,” Proc. Inst. Mech. Eng.
, 182
, pp. 300
–306
.52.
Johnson
, K. L.
, and Cameron
, R.
, 1967-1968, “Shear Behavior of Elastohydrodynamic Oil Films at High Rolling Contact Pressures
,” Proc. Inst. Mech. Eng.
, 182
, pp. 307
–319
.53.
Johnson
, K. L.
, and Tevaarwerk
, J. L.
, 1977, “Shear Behavior of EHD Oil Films
,” Proc. R. Soc. London, Ser. A
356
, pp. 215
–236
.54.
Bair
, S.
, and Winer
, W. O.
, 1979, “Rheological Response of Lubricants in EHD Contacts
,” Proceedings of the Fifth Leeds-Lyon Symposium on Tribology
, Mechanical Engineering Publications
, Bury St. Edmunds, UK
, pp. 162
–169
.55.
Bair
, S.
, and Khonsari
, M.
, 1996, “An EHD Inlet Zone Analysis Incorporating the Second Newtonian
,” ASME J. Tribol.
, 118
, pp. 341
–343
.56.
Bair
, S.
, 2007, High Pressure Rheology for Quantitative Elastohydrodynamics
, Elsevier Press
, Amsterdam, The Netherlands
.57.
Tanner
, R. I.
, 1985, Engineering Rheology
, Clarendon
, Oxford
.58.
Barus
, C.
, 1893, “Isothermals, Isopiestics, and Isometrics Relative to Viscosity
,” Am. J. Sci., Third Series, XLV
, 266
, pp. 87
–96
.59.
Thomas
, B. W.
, Ham
, W. R.
, and Dow
, R. B.
, 1937, “Viscosity-Pressure Characteristics of Lubricating Oils
,” Indust. Eng. Chem.
, 31
, pp. 1267
–1270
.60.
ASME Research Committee on Lubrication, 1953, “
Viscosity and Density of Over 40 Lubricating Fluids of Known Composition at Pressure to 150,000 PSI and Temperature to 425F
,” ASME. New York.61.
Cameron
, A.
, 1966, The Principles of Lubrication
, Wiley
, New York
.62.
Hirst
, W.
, and Moore
, A. J.
, 1976, “Non-Newtonian Behavior in the Elastihydrodynamic Lubrication of Rollers
,” Symposium on Lubricant Properties in Thin Lubricating Films, American Chemical Society, Division of Petroleum Chemistry, Preprints
, Vol. 21
(1
), pp. 27
–46
.63.
Roelands
, C. J. A.
, 1966, “Correlational Aspects of the Viscosity-Temperature-Pressure Relationship of Lubricating Oils
,” Ph.D. thesis, Technische Hogeschool Delft, The Netherlands.64.
Doolittle
, A. D.
, 1951, “Studies in Newtonian Flow II—The Dependence of the Viscosity of Liquids on Free-Space
,” J. Appl. Phys.
, 22
, pp. 1471
–1475
.65.
Cook
, R. L.
, Herbst
, C. A.
, and King
, H. E.
, Jr., 1993, “High-Pressure Viscosity of Glass-Forming Liquids Measured by the Centrifugal Force Diamond Anvil Cell Viscometer
,” J. Phys. Chem.
, 97
, pp. 2355
–2361
.66.
Liu
, Y. C.
, Wang
, Q. J.
, Wang
, W. Z.
, Hu
, Y. Z.
, Zhu
, D.
, Krupka
, I.
, and Hartl.
M.
, 2006, “EHL Simulation Using the Free-Volume Viscosity Model
,” Tribol. Lett.
, 23
, pp. 27
–37
.67.
Patir
, N.
, and Cheng
, H. S.
, 1979, “Effect of Surface Roughness Orientation on the Central Film Thickness in EHD Contacts
,” Proceedings of the Fifth Leeds-Lyon Symposium on Tribology
, by Mechanical Engineering Publications
, Bury St. Edmunds, UK
, pp. 15
–21
.68.
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
, pp. 12
–17
.69.
Greenwood
, J. A.
, and Tripp
, J. H.
, 1970-1971, “The Contact of Two Nominally Flat Rough Surfaces
,” Proc. Inst. Mech. Eng.
, 185
, pp. 625
–633
.70.
Zhu
, D.
, Cheng
, H. S.
, and Hamrock
, B. J.
, 1990, “Effect of Surface Roughness on Pressure Spike and Film Constriction in Elastohydrodynamically Lubricated Line Contacts
,” Tribol. Trans.
, 33
, pp. 267
–273
.71.
Zhu
, D.
, and Cheng
, H. S.
, 1988, “Effect of Surface Roughness on the Point Contact EHL
,” ASME J. Tribol.
, 110
, pp. 32
–37
.72.
Goglia
, P. R.
, Cusano
, C.
, and Conry
, T. F.
, 1984, “The Effects of Surface Irregularities on the Elastohydrodynamic Lubrication of Sliding Line Contacts, Part I—Single Irregularities, Part II—Wavy Surfaces
,” ASME J. Tribol.
, 106
, pp. 104
–119
.73.
Lubrecht
, A. A.
, 1987, “The Numerical Solution of Elastohydrodynamic Lubricated Line and Point Contact Problems using Multigrid Techniques
,” Ph.D. thesis, University of Twente, The Netherlands.74.
Kweh
, C. C.
, Evans
, H. P.
, and Sindle
, R. W.
, 1989, “Micro-Elastohydrodynamic Lubrication of an Elliptical Contact with Transverse and 3-Dimensional Roughness
,” ASME J. Tribol.
, 111
, pp. 577
–584
.75.
Chang
, L.
, Cusano
, C.
, and Conry
, T. F.
, 1989, “Effects of Lubricant Rheology and Kinematic Conditions on Micro-Elastohydrodynamic Lubrication
,” ASME J. Tribol.
, 111
, pp. 344
–351
.76.
Venner
, C. H.
, 1991, “Multilevel Solution of EHL Line and Point Contact Problems
,” Ph.D thesis, University of Twente, The Netherlands.77.
Kweh
, C. C.
, Patching
, M. J.
, Evans
, H. P.
, and Sindle
, R. W.
, 1992, “Simulation of Elastohydrodynamic Contacts Between Rough Surfaces
,” ASME J. Tribol.
, 114
, pp. 412
–419
.78.
Xu
, G.
, and Sadeghi
, F.
, 1996, “Thermal EHL Analysis of Circular Contacts With Measured Surface Roughness
,” ASME J. Tribol.
, 118
, pp. 473
–483
.79.
Zhu
, D.
, and Ai
, X.
, 1997, “Point Contact EHL Based on Optically Measured Three-Dimensional Rough Surfaces
,” ASME J. Tribol.
, 119
, pp. 375
–384
.80.
Ren
, N.
, Zhu
, D.
, Chen
, W. W.
, Liu
, Y.
, and Wang
, Q. J.
, 2009, “A Three-Dimensional Deterministic Model for Rough Surface Line Contact EHL Problems
,” ASME J. Tribol.
, 131
, 011501
.81.
Dawson
, P. H.
, 1962, “Effect of Metallic Contact on the Pitting of Lubricated Rolling Surfaces
,” J. Mech. Eng. Sci.
, 4
(16
), pp. 16
–21
.82.
Tallian
, T. E.
, 1972, “Theory of Partial Elastohydrodynamic Contacts
,” Wear
, 21
, pp. 49
–101
.83.
Johnston
, G. J.
, Wayte
, R.
, and Spikes
, H. A.
, 1991, “The Measurement and Study of Very Thin Lubricant Films in Concentrated Contacts
,” Tribol. Trans.
, 34
, pp. 187
–194
.84.
Cann
, P. M.
, Hutchinson
, J.
, and Spikes
, H. A.
, 1996, “The Development of a Spacer Layer Imaging Method (SLIM) for Mapping Elastohydrodynamic Contacts
,” Tribol. Trans.
, 39
, pp. 915
–921
.85.
Luo
, J. B.
, Wen
, S. Z.
, and Huang
, P.
, 1996, “Thin Film Lubrication. 1. Study on the Transition Between EHL and Thin Film Lubrication Using a Relative Optical Interference Intensity Technique
,” Wear
, 194
, pp. 107
–115
.86.
Hartl
, M.
, Krupka
, I.
, Poliscuk
, R.
, and Liska
, M.
, 1999, “An Automatic System for Real-Time Evaluation of EHD Film Thickness and Shape Based on the Colorimetric Interferometry
,” Tribol. Trans.
, 42
, pp. 303
–311
.87.
Guantang
, G.
, Cann
, P. M.
, Olver
, A.
, and Spikes
, H. A.
, 2000, “Lubricant Film Thickness in Rough Surface Mixed Elastohydrodynamic Contact
,” ASME J. Tribol.
, 122
, pp. 65
–76
.88.
Evans
, H. P.
, and Snidle
, R. W.
, 1981, “Inverse Solution of Reynolds Equation of Lubrication under Point Contact Elastohydrodynamic Conditions
,” ASME J. Lubr. Technol.
, 103
, pp. 539
–546
.89.
Hou
, K. P.
, Zhu
, D.
, and Wen
, S. Z.
, 1987, “An Inverse Solution to the Point Contact EHL Problem Under Heavy Loads
,” ASME J. Tribol.
, 109
, pp. 432
–436
.90.
Rohde
, S. M.
, and Oh
, K. P.
, 1975, “A Unified Treatment of Thick and Thin Film Elastohydrodynamic Problems by Using Higher Order Element Methods
,” Proc. R. Soc. London, Ser. A
343
, pp. 315
–331
.91.
Oh
, K. P.
, and Rohde
, S. M.
, 1977, “Numerical Solution of the Point Contact Problem Using the Finite Element Method
,” Int. J. Numer. Methods Eng.
, 11
, pp. 1507
–1518
.92.
Houpert
, L. G.
, and Hamrock
, B. J.
, 1986, “Fast Approach for Calculating Film Thicknesses and Pressures in Elastohydrodynamically Lubricated Contacts at Heavy Loads
,” ASME J. Tribol.
, 108
, pp. 411
–420
.93.
Okamura
, H.
, 1982, “A Contribution to the Numerical Analysis of Isothermal Elastohydrodynamic Lubrication
,” Proceedings of the Ninth Leeds-Lyon Symposium on Tribology
, pp. 313
–320
.94.
Hughes
, T. G.
, Elcoate
, C. D.
, and Evans
, H. P.
, 2000, “Coupled Solution of the Elastohydrodynamic Line Contact Problem Using a Differential Deflection Method
,” J. Mech. Eng. Sci.
, 214
, pp. 585
–598
.95.
Holmes
, M. J. A.
, Evans
, H. P.
, Hughes
, T. G.
, and Snidle
, R.W.
, 2003, “Transient Elastohydrodynamic Point Contact Analysis Using a New Coupled Differential Deflection Method, Part 1: Theory and Validation
,” Proc. Inst. Mech. Eng., Part J: J. Eng. Tribol.
, 217
, pp. 289
–303
.96.
Ai
, X.
, 1993, “Numerical Analyses of Elastohydrodynamically Lubricated Line and Point Contacts with Rough Surfaces by Using Semi-System and Multigrid Methods
,” Ph. D. thesis, Northwestern University, Evanston, IL.97.
Zhu
, D.
, and Hu
, Y. Z.
, 1999, “The Study of Transition from Full Film Elastohydrodynamic to Mixed and Boundary Lubrication
,” The Advancing Frontier of Engineering Tribology, Proceedings of the 1999 STLE/ASME H.S. Cheng Tribology Surveillance
, pp. 150
–156
.98.
Hu
, Y. Z.
, and Zhu
, D.
, 2000, “A Full Numerical Solution to the Mixed Lubrication in Point Contacts
,” ASME J. Tribol.
, 122
, pp. 1
–9
.99.
Morales-Espejel
, G. E.
, Dumont
, M. L.
, Lugt
, P. M.
, and Olver
, A. V.
, 2005, “A Limiting Solution for the Dependence of Film Thickness on Velocity in EHL Contacts with Very Thin Films
,” Tribol. Trans.
, 48
, pp. 317
–324
.100.
Liu
, Y. C.
, Wang
, Q.
, Wang
, W. Z.
, Hu
, Y. Z.
, and Zhu
, D.
, 2006, “Effects of Differential Scheme and Mesh Density on EHL Film Thickness in Point Contacts
,” ASME J. Tribol.
, 128
, pp. 641
–653
.101.
Zhu
, D.
, 2007, “On Some Aspects in Numerical Solution of Thin-Film and Mixed EHL
,” Proc. Inst. Mech. Eng., Part J: J. Eng. Tribol.
, 221
, pp. 561
–579
.102.
Lubrecht
, A. A.
, and Ioannides
, E. A.
, 1991, “Fast Solution of the Dry Contact Problem and Associated Surface Stress Field, Using Multilevel Techniques
,” ASME J. Tribol.
, 113
, pp. 128
–133
.103.
Evans
, H. P.
, and Hughes
, T. G.
, 2000, “Evaluation of Deflection in Semi-Infinite Bodies by a Differential Method
,” Proc. Inst. Mech. Eng.
, C214
, pp. 563
–584
.104.
Liu
, S. B.
, Wang
, Q.
, and Liu
, G.
, 2000, “A Versatile Method of Discrete Convolution and FFT (DC-FFT) for Contact Analyses
,” Wear
, 243
, pp. 101
–111
.105.
Liu
, S. B.
, and Wang
, Q.
, 2002, “Studying Contact Stress Fields Caused by Surface Tractions With a Discrete Convolution and Fast Fourier Transform Algorithm
,” ASME J. Tribol.
, 124
, pp. 36
–45
.106.
Wang
, W. Z.
, Wang
, H.
, Liu
, Y. C.
, Hu
, Y. Z.
, and Zhu
, D.
, 2003, “A Comparative Study of the Methods for Calculation of Surface Elastic Deformation
,” Proc. Inst. Mech. Eng., Part J: J. Eng. Tribol.
, 217
, pp. 145
–152
.107.
Guantang
, G.
, and Spikes
, H. A.
, 1995, “Behavior of Lubricants in the Mixed Elastohydrodynamic Regime
,” Proceedings of the 21st Leeds-Lyon Symposium on Tribology
, Institute of Tribology, University of Leeds
, U.K
. (Tribology Series), pp. 479
–485
.108.
Guangteng
, G.
, and Spikes
, H. A.
, 1997, “The Control of Friction by Molecular Fractionation of Base Fluid Mixtures at Metal Surfaces
,” Tribol. Trans.
, 40
, pp. 461
–469
.109.
Kaneta
, M.
, and Nishikawa
, H.
, 1999, “Experimental Study on Microelastohydro-dynamic Lubrication
,” Proc. Inst. Mech. Eng., Part J: J. Eng. Tribol.
, 213
, pp. 371
–381
.110.
Luo
, J. B.
, and Liu
, S.
, 2006, “The Investigation of Contact Ratio in Mixed Lubrication
,” Tribol. Int.
, 39
, pp. 409
–416
.111.
Krupka
, I.
, and Hartl
, M.
, 2007, “The Effect of Surface Texturing on Thin EHD Lubrication Films
,” Tribol. Int.
, 40
, pp. 1100
–1110
.112.
Krupka
, I.
, and Hartl
, M.
, 2007, “The Influence of Thin Boundary Films on Real Surface Roughness in Thin Film, Mixed EHD Contact
,” Tribol. Int.
, 40
, pp. 1553
–1560
.113.
Chang
, L.
, 1995, “A Deterministic Model for Line Contact Partial Elastohydrodynamic Lubrication
,” Tribol. Int.
, 28
, pp. 75
–84
.114.
Jiang
, X.
, Hua
, D. Y.
, Cheng
, H. S.
, Ai
, X.
, and Lee
, S. C.
, 1999, “A Mixed Elastohydrodynamic Lubrication Model with Asperity Contact
,” ASME J. Tribol.
, 121
, pp. 481
–491
.115.
Holmes
, M. J. A.
, Evans
, H. P.
, and Snidle
, R. W.
, 2005, “Analysis of Mixed Lubrication Effects in Simulated Gear Tooth Contacts
,” ASME J. Tribol.
, 127
, pp. 61
–69
.116.
Li
, S.
, and Kahraman
, A.
, 2009, “A Mixed EHL Model with Asymmetric Integrated Control Volume Discretization
,” Tribol. Int.
, 42
, pp. 1163
–1172
.117.
Zhao
, J. X.
, Sadeghi
, F.
, and Hoeprich
, M. H.
, 2001, “Analysis of EHL Circular Contact Start Up: Part I—Mixed Contact Model with Pressure and Film Thickness Results
,” ASME J. Tribol.
, 123
, pp. 67
–74
.118.
Holmes
, M. J. A.
, Evans
, H. P.
, and Snidle
, R. W.
, 2002, “Comparison of Transient EHL Calculations with a Start-Up Experiment
,” Proceedings of the the 29th Leeds-Lyon Symposium
, Elsevier
, Amsterdam
, pp. 79
–89
.119.
Zhao
, J. X.
, and Sadeghi
, F.
, 2003, “Analysis of EHL Circular Contact Shut Down
,” ASME J. Tribol.
, 125
, pp. 76
–90
.120.
Popovici
, G.
, Venner
, C. H.
, and Lugt
, P. M.
, 2004, “Effects of Load System Dynamics on the Film Thickness in EHL Contacts During Start Up
,” ASME J. Tribol.
, 126
, pp. 258
–266
.121.
Wang
, Q.
, and Zhu
, D.
, 2005, “Virtual Texturing: Modeling the Performance of Lubricated Contacts of Engineered Surfaces
,” ASME J. Tribol.
, 127
, pp. 722
–728
.122.
Felix-Quinonez
, A.
, Ehret
, P.
, and Summers
, J. L.
, 2005, “On Three-Dimensional Flat-Top Defects Passing Through an EHL Point Contact: A Comparison of Modeling with Experiments
,” ASME J. Tribol.
, 127
, pp. 51
–60
.123.
Liu
, Y. C.
, Wang
, Q.
, Zhu
, D.
, Wang
, W. Z.
, and Hu
, Y. Z.
, 2009, “Effect of Differential Scheme and Viscosity Model on Rough Surface Point Contact Isothermal EHL
,” ASME J. Tribol.
, 131
, 044501
.124.
Wang
, W. Z.
, Hu
, Y. Z.
, Liu
, Y. C.
, and Zhu
, D.
, 2010, “Solution Agreement Between Dry Contacts and Lubrication System at Ultra-Low Speed
,” Proc. Inst. Mech. Eng., Part J: J. Eng. Tribol.
, 224
, pp. 1049
–1060
.125.
Bair
, S.
, and Qureshi
, F.
, 2003, “The Generalized Newtonian Fluid Model and Elastohydrodynamic Film Thickness
,” ASME J. Tribol.
, 125
, pp. 70
–75
.126.
Bair
, S.
, 2004, “Actual Eyring Models for Thixotropy and Shear-Thinning: Experimental Validation and Application to EHD
,” ASME J. Tribol.
, 126
, pp. 728
–732
.127.
Jang
, J. Y.
, Khonsari
, M. M.
, and Bair
, S.
, 2007, “On the Elastohydrodynamic Analysis of Shear-Thinning Fluids
,” Proc. R. Soc. London
, 463
, pp. 3271
–3290
.128.
Liu
, Y. C.
, Wang
, Q. J.
, Bair
, S.
, and Vergne
, P.
, 2007, “A Quantitative Solution for the Full Shear-Thinning EHL Point Contact Problem Including Traction
,” Tribol. Lett.
, 28
, pp. 171
–181
.129.
Johnson
, K. L.
, 1985, Contact Mechanics
, Cambridge University Press
, Cambridge
.130.
Pinkus
, O.
, and Sternlicht
, B.
, 1961, Theory of Hydrodynamic Lubrication
, McGraw-Hill
, New York
.131.
Hamrock
, B. J.
, 1994, Fundamentals of Fluid Film Lubrication
, McGraw Hill
, New York
.132.
Liu
, Y. C.
, 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
, pp. 509
–516
.133.
Liu
, Y. C.
, Zhu
, D.
, and Wang
, Q.
, 2008, “Effect of Stiff Coatings on EHL Film Thickness in Point Contacts
,” ASME J. Tribol.
, 130
, 031501
.134.
Kang
, Y. S.
, Sadeghi
, F.
, and Ai
, X. L.
, 2000, “Debris Effects on EHL Contact
,” ASME J. Tribol.
, 122
, pp. 711
–720
.135.
Slack
, T. S.
, Raje
, N.
, Sadeghi
, F.
, Doll
, G.
, and Hoeprich
, M. R.
, 2007, “EHL Modeling for Non-Homogenous Materials—The Effect of Material Inclusions
,” ASME J. Tribiol.
, 129
, pp. 256
–273
.136.
Xu
, G.
, Nickel
, D. A.
, Sadeghi
, F.
, and Ai
, X. L.
, 1996, “Elastoplastohydrodynamic Lubrication with Dent Effects
,” Proc. Inst. Mech. Eng., Part J: J. Eng. Tribol.
, 210
, pp. 233
–245
.137.
Ren
, N.
, Zhu
, D.
, Chen
, W. W.
, and Wang
, Q. J.
, 2010, “Plasto-Elastohydrodynamic Lubrication (PEHL) in Point Contacts
,” ASME J. Tribol.
, 132
, 031501
.138.
Ren
, N.
, Zhu
, D.
, and Wang
, Q. J.
, 2011, “Three-Dimensional Plasto-Elastohydrodynamic Lubrication (PEHL) for Surfaces with Irregularities
,” ASME J. Tribol.
(to be published).139.
Spikes
, H. A.
, 2000, “The Borderline of Elastohydrodynamic and Boundary Lubrication
,” J. Mech. Eng. Sci.
, 214
, pp. 23
–37
.140.
Luan
, B.
, and Robbins
, M.
, 2005, “The Breakdown of Continuum Models for Mechanical Contacts
,” Nature (London)
, 435
, pp. 929
–932
.141.
Martini
, A.
, Liu
, Y.
, Snurr
, R.
, and Wang
, Q.
, 2006, “Molecular Dynamics Characterization of Thin Film Viscosity for EHL Simulation
,” Tribol. Lett.
, 21
, pp. 217
–225
.142.
Zhu
, P.
, Hu
, Y.
, Ma
, T.
, and Wang
, H.
, 2010, “Molecular Dynamics Study on Friction due to Ploughing and Adhesion in Nanometric Scratching Process
,” Tribol. Lett.
, 41
, pp. 41
–46
.Copyright © 2011
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