Abstract
This study allows contact models based on semi-analytical methods including the impacts of thermoelastic deformations in contacts of finite dimension bodies. The proposed method controls heat flows crossing free boundaries. A comparison with finite element analysis (FEA) reveals that the proposed method can reduce the calculation times by more than 98%. The paper introduces the thermoelasticity effects into thermal-elastohydrodynamic lubrication (TEHL) modeling of line contact problems. The analysis reveals that including thermoelastic deformations changes the pressure profile and tends to localize the pressure close to the distribution center. Compared to TEHL simulations, the examined configurations caused an overall increase in the maximum pressure by about 9%, an overall film thickness reduction of about 7%, and an overall temperature increase of about 2 K.
References
1.
Wang
, K. L.
, and Cheng
, H. S.
, 1980
, “Thermal Elastohydrodynamic Lubrication of Spur Gears
,” NASA Tech Briefs NASA CR 3241.2.
Liu
, M.
, Zhang
, J.
, Xu
, P.
, Cai
, H.
, Ku
, H.
, and Wu
, C.
, 2019
, “Thermal Elastohydrodynamic Lubrication Analysis of Helical Gear Pair Under Starved Lubrication Condition
,” Lubr. Sci.
, 31
(7
), pp. 321
–334
. 3.
Meng
, X.
, Yu
, C.
, Xie
, Y.
, and Mei
, B.
, 2018
, “Thermal Insulation Effect on EHL of Coated Cam/Tappet Contact During Start Up
,” Ind. Lubr. Tribol.
, 70
(6
), pp. 917
–926
. 4.
Liu
, Z.
, Pickens
, D.
, He
, T.
, Zhang
, X.
, Liu
, Y.
, Nishino
, T.
, and Jane Wang
, Q.
, 2019
, “A Thermal Elastohydrodynamic Lubrication Model for Crowned Rollers and Its Application on Apex Seal-Housing Interfaces
,” ASME J. Tribol.
, 141
(4
), p. 041501
. 5.
Williamson
, M.
, and Majumdar
, A.
, 1992
, “Effect of Surface Deformations on Contact Conductance
,” ASME J. Heat Transfer-Trans. ASME
, 114
(4
), pp. 802
–810
. 6.
Chin-Tu
, L.
, and Bryant
, M. D.
, 1994
, “Thermoelastic Evolution of Contact Area and Mound Temperatures in Carbon Graphite Electrical Brushes
,” Wear
, 174
(1–2
), pp. 137
–146
. 7.
Albers
, A.
, Martin
, P.
, and Lorentz
, B.
, 2011
, “Modeling and Design of Contacts in Electrical Connectors
,” Proceedings of the 18th Int. Conf. Eng. Des. (ICED 11)
, Lyngby/Copenhagen, Denmark
, Aug. 15–19
, Impacting Soc. Through Eng. Des., 4
, pp. 268
–277
.8.
Hertz
, H.
, 1896
, Miscellaneous Papers.9.
Hartnett
, M. J.
, 1980
, “A General Numerical Solution for Elastic Body Contact Problems
,” Solid Contact Lubr.
, 39
, pp. 51
–66
.10.
de Mul
, J. M.
, Kalker
, J. J.
, and Fredriksson
, B.
, 1986
, “The Contact Between Arbitrarily Curved Bodies of Finite Dimensions
,” ASME J. Tribol.
, 108
(1
), pp. 140
–148
. 11.
Liu
, S.
, and Hua
, D. Y.
, 2009
, “Three-Dimensional Semiperiodic Line Contact–Periodic in Contact Length Direction
,” ASME J. Tribol.
, 131
(2
), p. 021408
. 12.
Johnson
, K. L.
, 1985
, Contact Mechanics
, Cambridge University Press
.13.
Poon
, C. Y.
, and Sayles
, R. S.
, 1994
, “Numerical Contact Model of A Smooth Ball on an Anisotropic Rough Surface
,” ASME J. Tribol.
, 116
(4
), pp. 194
–201
. 14.
Tian
, X.
, and Bhushan
, B.
, 1996
, “A Numerical Three-Dimensional Model for the Contact of Rough Surfaces by Variational Principle
,” ASME J. Tribol.
, 118
(1
), pp. 33
–42
. 15.
Willner
, K.
, 2008
, “Fully Coupled Frictional Contact Using Elastic Halfspace Theory
,” ASME J. Tribol.
, 130
(3
), p. 031405
. 16.
Chen
, W. W.
, and Wang
, Q. J.
, 2009
, “A Numerical Static Friction Model for Spherical Contacts of Rough Surfaces, Influence of Load, Material, and Roughness
,” ASME J. Tribol.
, 131
(2
), p. 021402
. 17.
Hetényi
, M.
, 1970
, “A General Solution for the Elastic Quarter Space
,” ASME J. Appl. Mech.
, 37
(1
), pp. 70
–76
. 18.
Hetényi
, M.
, 1960
, “A Method of Solution For The Elastic Quarter-Plane
,” ASME J. Appl. Mech.
, 27
(2
), pp. 289
–296
. 19.
Keer
, L. M.
, Lee
, J. C.
, and Mura
, T.
, 1983
, “Hetényi’s Elastic Quarter Space Problem Revisited
,” Int. J. Solids Struct.
, 19
(6
), pp. 497
–508
. 20.
Hanson
, M. T.
, and Keer
, L. M.
, 1995
, “Mechanics of Edge Effects on Frictionless Contacts
,” Int. J. Solids Struct.
, 32
(3–4
), pp. 391
–405
. 21.
Guilbault
, R.
, 2011
, “A Fast Correction for Elastic Quarter-Space Applied to 3D Modeling of Edge Contact Problems
,” ASME J. Tribol.
, 133
(3
), p. 031402
. 22.
Yalpanian
, A.
, and Guilbault
, R.
, 2020
, “A Fast Correction for Half-Space Theory Applied to Contact Modeling of Bodies with Curved Free Surfaces
,” Tribol. Int.
, 147
, p. 13
. 23.
Yang
, J.
, and Komvopoulos
, K.
, 2005
, “Impact of a Rigid Sphere on an Elastic Homogeneous Half-Space
,” ASME J. Tribol.
, 127
(2
), p. 325
–330
. 24.
Bachtar
, F.
, Chen
, X.
, and Hisada
, T.
, 2006
, “Finite Element Contact Analysis of the Hip Joint
,” Med. Biol. Eng. Comput.
, 44
(8
), pp. 643
–651
. 25.
Chatterjee
, B.
, and Sahoo
, P.
, 2014
, “Finite Element Based Contact Analysis of Fractal Surfaces—Effect of Varying Elastic Modulus
,” Procedia Eng.
, 90
, pp. 116
–122
. 26.
Sahoo
, P.
, and Ghosh
, N.
, 2007
, “Finite Element Contact Analysis of Fractal Surfaces
,” J. Appl. Phys.
, 40
(14
), pp. 4245
–4252
. 27.
Reddy
, A. R. A. C.
, 2015
, “Finite Element Analysis of Friction Welding Process for UNS C23000 Brass and AISI 1021 Steel
,” Int. J. Sci. Res.
, 4
(5
), pp. 1691
–1696
.28.
Lindemann
, Z.
, Skalski
, K.
, Wlosinski
, W.
, and Zimmerman
, J.
, 2006
, “Thermo-Mechanical Phenomena in the Process of Friction Welding of Corundum Ceramics and Aluminium
,” Bull. Polish Acad. Sci.
, 54
(1
), pp. 1
–8
. 29.
Gropper
, D.
, Wang
, L.
, and Harvey
, T. J.
, 2016
, “Hydrodynamic Lubrication of Textured Surfaces: A Review of Modeling Techniques and Key Findings
,” Tribol. Int.
, 94
, pp. 509
–529
. 30.
Li
, J.
, and Berger
, E. J.
, 2003
, “A Semi-Analytical Approach to Three-Dimensional Normal Contact Problems with Friction
,” Comput. Mech.
, 30
(4
), pp. 310
–322
. 31.
Li
, J.
, and Berger
, E. J.
, 2001
, “A Boussinesq-Cerruti Solution Set for Constant and Linear Distribution of Normal and Tangential Load Over a Triangular Area
,” J. Elast.
, 63
(2
), pp. 137
–151
. 32.
Hamilton
, D. B.
, Walowit
, J. A.
, and Allen
, C. M.
, 1966
, “A Theory of Lubrication by Micro-Irregularities
,” ASME J. Basic Eng.
, 88
(1
) pp. 177
–185
. 33.
Etsion
, I.
, Kligerman
, Y.
, and Halperin
, G.
, 1999
, “Analytical and Experimental Investigation of Laser-Textured Mechanical Seal Faces
,” Tribol. Trans.
, 42
(3
), pp. 511
–516
. 34.
Wakuda
, M.
, Yamauchi
, Y.
, Kanzaki
, S.
, and Yasuda
, Y.
, 2003
, “Effect of Surface Texturing on Friction Reduction Between Ceramic and Steel Materials Under Lubricated Sliding Contact
,” Wear
, 254
(3–4
), pp. 356
–363
. 35.
Kuroki
, H.
, Nezaki
, K.
, Wakabayashi
, T.
, and Nakamura
, K.
, 2014
, “Application of Linear Friction Welding Technique to Aircraft Engine Parts
,” IHI Eng. Rev.
, 47
(1
), pp. 40
–43
.36.
Jl
, J.
, Renee
, B.
, and Jacoby
, B. R.
, 1991
, “Fundamental Mechanisms Affecting Friction Welding Under Vacuum
,” Doctoral dissertation
, Massachusetts Institute of Technology
.37.
Effertz
, P. S.
, Fuchs
, F.
, and Enzinger
, N.
, 2017
, “Modelling the Flash Formation of Linear Friction Welded 30CrNiMo8 High Strength Steel Chains
,” Int. J. Adv. Manuf. Technol.
, 92
(5–8
), pp. 2479
–2486
. 38.
Jedrasiak
, P.
, Shercliff
, H. R.
, McAndrew
, A. R.
, and Colegrove
, P. A.
, 2018
, “Thermal Modelling of Linear Friction Welding
,” Mater. Des.
, 156
, pp. 362
–369
. 39.
Sukumaran
, J.
, Baets
, P. D.
, and Fauconnier
, D.
, 2018
, “Frictional Heating in Dry and Lubricated Contacts,” ASM Handbook:volume 18: Friction, Lubrication, and Wear Technology
, ASM International, pp. 67
–80
. 940.
Balci
, M. N.
, Yildirim
, B.
, and Dag
, S.
, 2015
, “Analysis of Frictional Contacts with Heat Generation Considering Temperature Dependent Properties
,” Int. J. Mech. Sci.
, 101–102
, pp. 59
–69
. 41.
Cooper
, M. G.
, Mikic
, B. B.
, and Y
, M. M.
, 1969
, “Thermal Contact Conductance
,” Int. J. Heat Mass Transf.
, 12
(3
), pp. 279
–300
. 42.
Mikic
, B. B.
, 1974
, “Thermal Contact Conductance; Theoretical Considerations
,” Int. J. Heat Mass Transf.
, 17
(2
), pp. 205
–214
. 43.
Bahrami
, M.
, Yovanovich
, M. M.
, and Culham
, J. R.
, 2005
, “Thermal Contact Resistance at Low Contact Pressure: Effect of Elastic Deformation
,” Int. J. Heat Mass Transf.
, 48
(16
), pp. 3284
–3293
. 44.
Sternberg
, E.
, and Mcdowell
, E. L.
, 1957
, “On the Steady-State Thermoelastic Problem for the Half-Space
,” Q. Appl. Math.
, 14
(4
), pp. 381
–398
. 45.
Barber
, J. R.
, 1971
, “The Solution of Heated Punch Problems by Point Source Methods
,” Int. J. Eng. Sci.
, 9
(12
), pp. 1165
–1170
. 46.
Barber
, J. R.
, and Martin-Moran
, C. J.
, 1982
, “Green’s Functions for Transient Thermoelastic Contact Problems for the Half-Space
,” Wear
, 79
(1
), pp. 11
–19
. 47.
Akbari
, M.
, Sinton
, D.
, and Bahrami
, M.
, 2009
, “Moving Heat Sources in a Half-Space: Effect of Source Geometry
,” ASME 2009 Heat Transf. Summer Conf. Proc. Pap.
, pp. 685
–694
.48.
Kachanov
, M. L.
, Shafiro
, B.
, and Tsukrov
, I.
, 2003
, Handbook of Elasticity Solutions
, Kluwer Academic Publishers
.49.
Incropera
, F. P.
, and De Witt
, D. P.
, 1981
, “Fundamentals of Heat Transfer.”50.
Johnson
, K. L.
, 1987
, Contact Mechanics
, University Press, Cambridge
.51.
Najjari
, M.
, and Guilbault
, R.
, 2014
, “Edge Contact Effect on Thermal Elastohydrodynamic Lubrication of Finite Contact Lines
,” Tribol. Int.
, 71
, pp. 50
–61
. 52.
Wymer
, D. G.
, and Cameron
, A.
, 1974
, “Elastohydrodynamic Lubrication of a Line Contact
,” Proc. Inst. Mech. Eng.
, 188
(1
), pp. 221
–238
. Copyright © 2022 by ASME
You do not currently have access to this content.
