Abstract
The elastohydrodynamic lubrication line contact problem between a functionally graded material (FGM) coated half-plane and a rigid cylindrical punch is investigated. The inhomogeneous elastic properties of the FGM coating are expressed by the exponential model. The lubricant between two solids is supposed to be the Newtonian fluid. The fluid viscosity and density are considered to be dependent on the fluid pressure. To determine the unknown film thickness and fluid pressure at the lubricant contact region, a numerical iterative method is employed to simultaneously solve the flow rheology equation, Reynolds equation, load balance equation, and film thickness equation. Influences of the stiffness ratio of the FGM coating, the resultant normal load, the punch radius, and the entraining velocity on the lubricant film thickness and fluid pressure are analyzed.
Issue Section:
Elastohydrodynamic Lubrication
References
1.
Wei
, J.
, Zhang
, A. Q.
, and Gao
, P.
, 2016
, “A Study of Spur Gear Pitting Under EHL Conditions: Theoretical Analysis and Experiments
,” Tribol. Int.
, 94
, pp. 146
–154
. 10.1016/j.triboint.2015.08.0372.
Ogura
, T.
, Okuda
, A.
, Imanishi
, M.
, Miyano
, A.
, Amano
, M.
, Nishioka
, N.
, Kamiyama
, R.
, and Higuchi
, K.
, 2019
, “Electrohydraulic Lithotripsy for Pancreatic Duct Stones Under Digital Single-Operator Pancreatoscopy (With Video)
,” Digest Dis. Sci.
, 64
(5
), pp. 1377
–1382
. 10.1007/s10620-018-5374-z3.
Hamrock
, B. J.
, and Dowson
, D.
, 1976
, “Isothermal Elastohydrodynamic Lubrication of Point Contacts Part 1—Theoretical Formulation
,” ASME J. Lubr. Tech.
, 98
(2
), pp. 223
–228
. 10.1115/1.34528014.
Grubin
, A. N.
, 1949
, Fundamentals of the Hydrodynamic Theory of Lubrication of Heavily Loaded Cylindrical Surfaces
, Central Scientific Research Institute for Technology and Mechanical Engineering
, Moscow
, Book No. 30, DSIR Trans No. 337
, pp. 115
–166
.5.
Dowson
, D.
, and Higginson
, G. R.
, 1959
, “A Numerical Solution to the Elastohydrodynamic Problem
,” J. Mech. Eng. Sci.
, 1
(1
), pp. 6
–15
. 10.1243/JMES_JOUR_1959_001_004_026.
Archard
, J. F.
, and Cowking
, E. W.
, 1965
, “Elastohydrodynamic Lubrication of Point Contacts
,” Proc. Inst. Mech. Eng. E.
, 180
(2
), pp. 47
–56
.7.
Cheng
, H. S.
, 1965
, “A Refined Solution to the Thermal-Elastohydrodynamic Lubrication of Rolling and Sliding Cylinders
,” ASLE Trans.
, 8
(4
), pp. 397
–410
. 10.1080/056981965089721108.
Yang
, P. R.
, and Wen
, S. Z.
, 1990
, “A Forward Iterative Numerical Method for Steady-State Elastohydrodynamically Lubricated Line Contacts
,” Tribol. Int.
, 23
(1
), pp. 17
–22
. 10.1016/0301-679X(90)90067-Y9.
Liu
, J.
, Chen
, Y.
, He
, Z.
, and Yang
, S.
, 2014
, “A Fast Compound Direct Iterative Algorithm for Solving Transient Line Contact Elastohydrodynamic Lubrication Problems
,” Front Mech. Eng.
, 9
(2
), pp. 156
–167
. 10.1007/s11465-014-0297-710.
Chu
, L. M.
, Hsu
, H. C.
, Lin
, J. R.
, and Chang
, Y. P.
, 2012
, “Inverse Approach for the Pressure, Temperature, and Pressure-Viscosity Index Determination in TEHL of Line Contacts
,” Ind. Lubr. Tribol.
, 64
(5
), pp. 294
–302
. 10.1108/0036879121124968311.
Cui
, J.
, Yang
, P.
, Kaneta
, M.
, and Krupka
, I.
, 2017
, “Numerical Study on the Interaction of Transversely Oriented Ridges in Thermal Elastohydrodynamic Lubrication Point Contacts Using the Eyring Shear-Thinning Model
,” Proc. Inst. Mech. Eng. Part J: J. Eng. Trib.
, 231
(1
), pp. 93
–106
. 10.1177/135065011664694312.
Quinonez
, A. F.
, 2018
, “Numerical Analysis of Transverse Reciprocating Velocity Effects in EHL Point Contacts
,” Tribol. Int.
, 126
, pp. 1
–8
. 10.1016/j.triboint.2018.05.00313.
Kudish
, I. I.
, Volkov
, S. S.
, Vasiliev
, A. S.
, and Aizikovich
, S. M.
, 2018
, “Lubricated Point Heavily Loaded Contacts of Functionally Graded Materials. Part 1. Dry Contacts
,” Math. Mech. Solids
, 23
(7
), pp. 1061
–1080
. 10.1177/108128651770468914.
Kudish
, I. I.
, Volkov
, S. S.
, Vasiliev
, A. S.
, and Aizikovich
, S. M.
, 2018
, “Lubricated Point Heavily Loaded Contacts of Functionally Graded Materials. Part 2. Lubricated Contacts
,” Math. Mech. Solids
, 23
(7
), pp. 1081
–1103
. 10.1177/108128651770469015.
Maier
, D.
, Hager
, C.
, Hetzler
, H.
, Fillot
, N.
, Vergne
, P.
, Dureisseix
, D.
, and Seemann
, W.
, 2016
, “Fast Solution of Transient Elastohydrodynamic Line Contact Problems Using the Trajectory Piecewise Linear Approach
,” ASME J. Tribol.
, 138
(1
), p. 011502
. 10.1115/1.403106416.
Peng
, Y. J.
, Zhao
, N.
, Zhang
, M. Q.
, Li
, W.
, and Zhou
, R. C.
, 2018
, “Non-Newtonian Thermal Elastohydrodynamic Simulation of Helical Gears Considering Modification and Misalignment
,” Tribol. Int.
, 124
, pp. 46
–60
. 10.1016/j.triboint.2018.03.02517.
Xiao
, H. F.
, Sun
, Y. Y.
, and Xu
, J. W.
, 2018
, “Investigation Into the Normal Contact Stiffness of Rough Surface in Line Contact Mixed Elastohydrodynamic Lubrication
,” Tribol. Trans.
, 61
(4
), pp. 742
–753
. 10.1080/10402004.2017.140417718.
Kumar
, R.
, Azam
, M. S.
, and Ghosh
, S. K.
, 2019
, “Influence of Stochastic Roughness on Performance of a Rayleigh Step Bearing Operating Under Thermo-Elastohydrodynamic Lubrication Considering Shear Flow Factor
,” Tribol. Int.
, 134
, pp. 264
–280
. 10.1016/j.triboint.2019.01.02519.
Morales-Espejel
, G. E.
, and Quiñonez
, A. F.
, 2019
, “On the Complementary Function Amplitude for Film Thickness in Micro-EHL
,” Tribol. Int.
, 131
, pp. 631
–636
. 10.1016/j.triboint.2018.11.02420.
Habchi
, W.
, 2019
, “A Schur-Complement Model-Order-Reduction Technique for the Finite Element Solution of Transient Elastohydrodynamic Lubrication Problems
,” Adv. Eng. Softw.
, 127
, pp. 28
–37
. 10.1016/j.advengsoft.2018.10.00721.
Mary
, C.
, Philippon
, D.
, Devaux
, N.
, Fillot
, N.
, Laurent
, D.
, Bair
, S.
, and Vergne
, P.
, 2016
, “Bridging High Pressure Rheology and Film-Forming Capacity of Polymer-Base Oil Solutions in EHL
,” Tribol. Int.
, 93
, pp. 502
–510
. 10.1016/j.triboint.2014.08.00622.
Suresh
, S.
, Giannakopoulos
, A. E.
, and Alcala
, J.
, 1997
, “Spherical Indentation of Compositionally Graded Materials: Theory and Experiments
,” Acta Mater.
, 45
(4
), pp. 1307
–1321
. 10.1016/S1359-6454(96)00291-123.
Suresh
, S.
, 2001
, “Graded Materials for Resistance to Contact Deformation and Damage
,” Science
, 292
(5526
), pp. 2447
–2451
. 10.1126/science.105971624.
Çömez
, İ
, El-Borgi
, S.
, Kahya
, V.
, and Erdol
, R.
, 2016
, “Receding Contact Problem for Two-Layer Functionally Graded Media Indented by a Rigid Punch
,” Acta Mech.
, 227
(9
), pp. 2493
–2504
. 10.1007/s00707-016-1648-825.
Rhimi
, M.
, El-Borgi
, S.
, Said
, W. B.
, and Jemaa
, F. B.
, 2009
, “A Receding Contact Axisymmetric Problem Between a Functionally Graded Layer and a Homogeneous Substrate
,” Int. J. Solids Struct.
, 46
(20
), pp. 3633
–3642
. 10.1016/j.ijsolstr.2009.06.00826.
Pender
, D. C.
, Padture
, N. P.
, Giannakopoulos
, A. E.
, and Suresh
, S.
, 2001
, “Gradients in Elastic Modulus for Improved Contact-Damage Resistance. Part I: The Silicon Nitride-Oxynitride Glass System
,” Acta Mater.
, 49
(16
), pp. 3255
–3262
. 10.1016/S1359-6454(01)00200-227.
Çömez
, İ
, 2013
, “Contact Problem of a Functionally Graded Layer Resting on a Winkler Foundation
,” Acta Mech.
, 224
(11
), pp. 2833
–2843
. 10.1007/s00707-013-0903-528.
Chen
, S. H.
, Yan
, C.
, and Soh
, A.
, 2009
, “Adhesive Behavior of Two-Dimensional Power-Law Graded Materials
,” Int. J. Solids Struct.
, 46
(18–19
), pp. 3398
–3404
. 10.1016/j.ijsolstr.2009.05.00629.
Jin
, F.
, Guo
, X.
, and Zhang
, W.
, 2013
, “A Unified Treatment of Axisymmetric Adhesive Contact on a Power-Law Graded Elastic Half-Space
,” ASME J. Appl. Mech.
, 80
(6
), pp. 1
–9
. 10.1115/1.402398030.
Liu
, T. J.
, and Li
, P. X.
, 2019
, “Two-Dimensional Adhesion Mechanics of a Graded Coated Substrate Under a Rigid Cylindrical Punch Based on a PWEML Model
,” Appl. Math. Model.
, 69
, pp. 1
–14
. 10.1016/j.apm.2018.12.00231.
Chen
, P. J.
, and Chen
, S. H.
, 2013
, “Thermo-Mechanical Contact Behavior of a Finite Graded Layer Under a Sliding Punch With Heat Generation
,” Int. J. Solids Struct.
, 50
(7–8
), pp. 1108
–1119
. 10.1016/j.ijsolstr.2012.12.00732.
Chen
, P. J.
, Chen
, S. H.
, and Peng
, J.
, 2015
, “Sliding Contact Between a Cylindrical Punch and a Graded Half-Plane With an Arbitrary Gradient Direction
,” ASME J. Appl. Mech.
, 82
(4
), pp. 1
–9
. 10.1115/1.402978133.
Zhou
, Y. T.
, Zhang
, C. Z.
, Zhong
, Z.
, and Wang
, L. H.
, 2019
, “Transient Thermo-Electro-Elastic Contact Analysis of a Sliding Punch Acting on a Functionally Graded Piezoelectric Strip Under Non-Fourier Heat Conduction
,” Eur. J. Mech. A/Solids
, 73
, pp. 90
–100
. 10.1016/j.euromechsol.2018.07.00634.
Aizikovich
, S. M.
, and Vasiliev
, A. S.
, 2013
, “A Bilateral Asymptotic Method of Solving the Integral Equation of the Contact Problem of the Torsion of an Elastic Half-Space Inhomogeneous in Depth
,” J. Appl. Math. Mech.
, 77
(1
), pp. 91
–97
. 10.1016/j.jappmathmech.2013.04.01135.
Chen
, P. J.
, and Chen
, S. H.
, 2013
, “Partial Slip Contact Between a Rigid Punch With an Arbitrary Tip-Shape and an Elastic Graded Solid With a Finite Thickness
,” Mech. Mater.
, 59
, pp. 24
–35
. 10.1016/j.mechmat.2012.12.00336.
Kudish
, I. I.
, Volkov
, S. S.
, Vasiliev
, A. S.
, and Aizikovich
, S. M.
, 2016
, “Some Criteria for Coating Effectiveness in Heavily Loaded Line Elastohydrodynamically Lubricated Contacts—Part II: Lubricated Contacts
,” ASME J. Tribol.
, 138
(2
), p. 021505
. 10.1115/1.403095837.
Kudish
, I. I.
, Volkov
, S. S.
, Vasiliev
, A. S.
, and Aizikovich
, S. M.
, 2017
, “Effectiveness of Coatings With Constant, Linearly, and Exponentially Varying Elastic Parameters in Heavily Loaded Line Elastohydrodynamically Lubricated Contacts
,” ASME J. Tribol.
, 139
(2
), p. 021502
. 10.1115/1.403336038.
Liu
, Y. C.
, Chen
, W. W.
, Zhu
, D.
, Liu
, S. B.
, and Wang
, Q. J.
, 2007
, “An Elastohydrodynamic Lubrication Model for Coated Surfaces in Point Contacts
,” ASME J. Tribol.
, 129
(3
), pp. 509
–516
. 10.1115/1.273643339.
Elsharkawy
, A. A.
, Holmes
, M. J. A.
, Evans
, H. P.
, and Snidle
, R. W.
, 2006
, “Micro-Elastohydrodynamic Lubrication of Coated Cylinders Using Coupled Differential Deflection Method
,” Proc. Inst. Mech. Eng. Part J: J. Eng. Trib.
, 220
(1
), pp. 29
–41
. 10.1243/13506501J1000540.
Habchi
, W.
, 2015
, “Influence of Thermo-Mechanical Properties of Coatings on Friction in Elastohydrodynamic Lubricated Contacts
,” Tribol. Int.
, 90
, pp. 113
–122
. 10.1016/j.triboint.2015.04.02041.
Yu
, C. Y.
, Meng
, X. H.
, and Xie
, Y. B.
, 2017
, “Numerical Simulation of the Effects of Coating on Thermal Elastohydrodynamic Lubrication in Cam/Tappet Contact
,” Proc. Inst. Mech. Eng. Part J: J. Eng. Trib.
, 231
(2
), pp. 221
–239
. 10.1177/135065011665204642.
Hamrock
, B. J.
, Schmid
, S. R.
, and Jacobson
, B. O.
, 2004
, Fundamentals of Fluid Film Lubrication
, 2nd ed., Marcel Dekker
, New York
. (Taylor & Francis, London, distributor).43.
Roelands
, C.
, 1966
, Correlation Aspects of the Viscosity–Temperature–Pressure Relationship of Lubrication Oils
, Technische Hogeschool Delf
, The Netherlands
.44.
Houpert
, L.
, 1985
, “New Results of Traction Force Calculation in Elastohydrodynamic Contacts
,” ASME J. Tribol.
, 107
(2
), pp. 241
–248
. 10.1115/1.326103345.
Dowson
, D.
, and Higginson
, G. R.
, 1966
, Elasto-Hydrodynamic Lubrication, the Fundamentals of Roller and Gear Lubrication
, Pergamon Press
, Oxford, UK
.46.
Guler
, M.
, and Erdogan
, F.
, 2004
, “Contact Mechanics of Graded Coatings
,” Int. J. Solids Struct.
, 41
(14
), pp. 3865
–3889
. 10.1016/j.ijsolstr.2004.02.02547.
Gradshteyn
, I. S.
, and Ryzhik
, I. M.
, 2000
, Table of Integrals. Series, and Products
, Academic
, New York
.48.
Johnson
, K. L.
, 1985
, Contact Mechanics
, Cambridge University Press
, Cambridge
.49.
Hills
, D. A.
, Nowell
, D.
, and Sackfield
, A.
, 1993
, Mechanics of Elastic Contacts
, Butterworth Heinemann
, Oxford
.50.
Erdogan
, F.
, and Gupta
, G. D.
, 1972
, “On the Numerical Solution of Singular Integral Equations
,” Q. Appl. Math.
, 29
(4
), pp. 525
–534
. 10.1090/qam/40827751.
Ke
, L. L.
, and Wang
, Y. S.
, 2007
, “Two-Dimensional Sliding Frictional Contact of Functionally Graded Materials
,” Eur. J. Mech. A/Solids
, 26
(1
), pp. 171
–188
. 10.1016/j.euromechsol.2006.05.007Copyright © 2020 by ASME
You do not currently have access to this content.
