This paper presents a thermal elastohydrodynamic lubrication (EHL) model for analyzing crowned roller lubrication performances under the influence of frictional heating. In this thermal EHL model, the Reynolds equation is solved to obtain the film thickness and pressure results while the energy equation and temperature integration equation are evaluated for the temperature rise in the lubricant and at the surfaces. The discrete convolution fast Fourier transform (DC-FFT) method is utilized to calculate the influence coefficients for both the elastic deformation and the temperature integration equations. The influences of the slide-to-roll ratio (SRR), load, crowning radius, and roller length on the roller lubrication and temperature rise are investigated. The results indicate that the thermal effect becomes significant for the cases with high SRRs or heavy loads. The proposed thermal EHL model is used to study the thermal-tribology behavior of an apex seal–housing interface in a rotary engine, and to assist the design of the apex seal crown geometry. A simplified crown design equation is obtained from the analysis results, validated through comparison with the optimal results calculated using the current crowned-roller thermo-EHL (TEHL) model.
Issue Section:
Elastohydrodynamic Lubrication
References
References
1.
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
(3
), pp. 695
–704
.2.
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
, pp. 119
–134
.3.
Yang
, P. R.
, and Wen
, S. H.
, 1992
, “The Behavior of Non-Newtonian Thermal EHL Film in Line Contacts at Dynamic Loads
,” ASME J. Tribol.
, 114
(1
), pp. 81
–85
.4.
Hsiao
, H. S.
, and Hamrock
, B. J.
, 1994
, “Non-Newtonian and Thermal Effects on Film Generation and Traction Reduction in EHL Line Contact Conjunctions
,” ASME J. Tribol.
, 116
(3
), pp. 559
–568
.5.
Hsiao
, H. S.
, and Hamrock
, B. J.
, 1994
, “Temperature Distribution and Thermal-Degradation of the Lubricant in EHL Line Contact Conjunctions
,” ASME J. Tribol.
, 116
(4
), pp. 794
–803
.6.
Yang
, P.
, Wang
, J.
, and Kaneta
, M.
, 2006
, “Thermal and Non-Newtonian Numerical Analyses for Starved EHL Line Contacts
,” ASME J. Tribol.
, 128
(2
), pp. 282
–290
.7.
Almqvist
, T.
, and Larsson
, R.
, 2002
, “The Navier-Stokes Approach for Thermal EHL Line Contact Solutions
,” Tribol. Int.
, 35
(3
), pp. 163
–170
.8.
Almqvist
, T.
, and Larsson
, R.
, 2008
, “Thermal Transient Rough EHL Line Contact Simulations by Aid of Computational Fluid Dynamics
,” Tribol. Int.
, 41
(8
), pp. 683
–693
.9.
Kumar
, P.
, and Khonsari
, M. M.
, 2008
, “Traction in EHL Line Contacts Using Free-Volume Pressure-Viscosity Relationship With Thermal and Shear-Thinning Effects
,” ASME J. Tribol.
, 131
(1
), p. 011503
.10.
Zhang
, B. B.
, Wang
, J.
, Omasta
, M.
, and Kaneta
, M.
, 2015
, “Effect of Fluid Rheology on the Thermal EHL Under ZEV in Line Contact
,” Tribol. Int.
, 87
, pp. 40
–49
.11.
Ochoa
, E. D.
, Otero
, J. E.
, Lopez
, A. S.
, Tanarro
, E. C.
, and Lopez
, B. D.
, 2018
, “Film Thickness Formula for Thermal EHL Line Contact Considering a New Reynolds-Carreau Equation
,” Tribol. Lett.
, 31
, p. 66
.12.
Bruggemann
, H.
, and Kollmann
, F. G.
, 1982
, “A Numerical Solution of the Thermal Elastohydrodynamic Lubrication in an Elliptical Contact
,” ASME J. Lubr. Technol.
, 104
(3), pp. 392
–400
.13.
Zhu
, D.
, and Wen
, S. Z.
, 1984
, “A Full Numerical-Solution for the Thermoelastohydrodynamic Problem in Elliptical Contacts
,” ASME J. Tribol.
, 106
(2
), pp. 246
–254
.14.
Ma
, M. T.
, 1997
, “An Expedient Approach to the Non-Newtonian Thermal EHL in Heavily Loaded Point Contacts
,” Wear
, 206
(1–2
), pp. 100
–112
.15.
Liu
, X. L.
, and Yang
, P. R.
, 2009
, “Effects of Solid Body Temperature on the Non-Newtonian Thermal EHL Behavior in Point Contacts
,” Advanced Tribology
, Springer, Berlin, pp. 169
–170
.16.
Liu
, X. L.
, Jiang
, M.
, Yang
, P. R.
, and Kaneta
, M.
, 2005
, “Non-Newtonian Thermal Analyses of Point EHL Contacts Using the Eyring Model
,” ASME J. Tribol.
, 127
(1
), pp. 70
–81
.17.
Kaneta
, M.
, and Yang
, P. R.
, 2003
, “Effects of Thermal Conductivity of Contacting Surfaces on Point EHL Contacts
,” ASME J. Tribol.
, 125
(4
), pp. 731
–738
.18.
Zhang
, J. J.
, Yang
, P. R.
, Wang
, J.
, and Guo
, F.
, 2015
, “The Effect of an Oscillatory Entrainment Velocity on the Film Thickness in Thermal EHL Point Contact
,” Tribol. Int.
, 90
, pp. 519
–532
.19.
Kaneta
, M.
, Cui
, J. L.
, Yang
, P. R.
, Krupka
, I.
, and Hartl
, M.
, 2016
, “Influence of Thermal Conductivity of Contact Bodies on Perturbed Film Caused by a Ridge and Groove in Point EHL Contacts
,” Tribol. Int.
, 100
, pp. 84
–98
.20.
Kaneta
, M.
, and Yang
, P. R.
, 2003
, “Formation Mechanism of Steady Multi-Dimples in Thermal EHL Point Contacts
,” ASME J. Tribol.
, 125
(2
), pp. 241
–251
.21.
Yang
, P. R.
, Cui
, J. L.
, Jin
, Z. M.
, and Dowson
, D.
, 2008
, “Influence of Two-Sided Surface Waviness on the EHL Behavior of Rolling/Sliding Point Contacts Under Thermal and Non-Newtonian Conditions
,” ASME J. Tribol.
, 130
(4
), p. 041502
.22.
Zhang
, B. B.
, Wang
, J.
, Omasta
, M.
, and Kaneta
, M.
, 2016
, “Variation of Surface Dimple in Point Contact Thermal EHL Under ZEV Condition
,” Tribol. Int.
, 94
, pp. 383
–394
.23.
Kuroda
, S.
, and Arai
, K.
, 1985
, “Elastohydrodynamic Lubrication Between Two Rollers
,” JSME
, 28
(241
), pp. 1367
–1372
.24.
Mostofi
, A.
, and Gohar
, R.
, 1983
, “Elastohydrodynamic Lubrication of Finite Line Contacts
,” ASME J. Lubr. Technol.
, 105
(4
), pp. 598
–604
.25.
Park
, T. J.
, and Kim
, K. W.
, 1998
, “Elastohydrodynamic Lubrication of a Finite Line Contact
,” Wear
, 223
(1–2
), pp. 102
–109
.26.
Zhu
, D.
, Wang
, J. X.
, Ren
, N.
, and Wang
, Q. J.
, 2012
, “Mixed Elastohydrodynamic Lubrication in Finite Roller Contacts Involving Realistic Geometry and Surface Roughness
,” ASME J. Tribol.
, 134
(1
), p. 011504
.27.
He
, T.
, Wang
, J. X.
, Wang
, Z. J.
, and Zhu
, D.
, 2015
, “Simulation of Plasto-Elastohydrodynamic Lubrication in Line Contacts of Infinite and Finite Length
,” ASME J. Tribol.
, 137
(4
), p. 041505
.28.
Park
, T. J.
, and Kim
, K. W.
, 1998
, “A Numerical Analysis of the Elastohydrodynamic Lubrication of Elliptical Contacts
,” Wear
, 136
, pp. 299
–312
.29.
Najjari
, M.
, and Guilbault
, R.
, 2014
, “Edge Contact Effect on Thermal Elastohydrodynamic Lubrication of Finite Contact Lines
,” Tribol. Int.
, 71
, pp. 50
–61
.30.
Wang
, X. P.
, Liu
, Y. C.
, and Zhu
, D.
, 2017
, “Numerical Solution of Mixed Thermal Elastohydrodynamic Lubrication in Point Contacts With Three-Dimensional Surface Roughness
,” ASME J. Tribol.
, 139
(1
), p. 011501
.31.
Kim
, H. J.
, Ehret
, P.
, Dowson
, D.
, and Taylor
, C. M.
, 2001
, “Thermal Elastohydrodynamic Analysis of Circular Contacts—Part 1: Newtonian Model
,” Proc. Inst. Mech. Eng.
, 215
(3
), pp. 339
–352
.32.
He
, T.
, Zhu
, D.
, Wang
, J. X.
, and Wang
, Q. J.
, 2017
, “Experimental and Numerical Investigations of the Stribeck Curves for Lubricated Counterformal Contacts
,” ASME J. Tribol.
, 139
(2
), p. 021505
.33.
Nikas
, G. K.
, 2017
, “Miscalculation of Film Thickness, Friction and Contact Efficiency by Ignoring Tangential Tractions in Elastohydrodynamic Contacts
,” Tribol. Int.
, 110
(6
), pp. 252
–263
.34.
Chen
, W. W.
, and Wang
, Q. J.
, 2008
, “A Numerical Model for the Point Contact of Dissimilar Materials Considering Tangential Tractions
,” Mech. Mater.
, 40
(11
), pp. 936
–948
.35.
Liu
, X. L.
, Ma
, M.
, Yang
, P.
, and Guo
, F.
, 2018
, “A New Method for Eyring Shear-Thinning Models in Elliptical Contacts Thermal Elastohydrodynamic Lubrication
,” ASME J. Tribol.
, 140
(5
), p. 051503
.36.
Liu
, S. B.
, Wang
, Q.
, and Liu
, G.
, 2000
, “A Versatile Method of Discrete Convolution and FFT (DC-FFT) for Contact Analyses
,” Wear
, 243
(1–2
), pp. 101
–111
.37.
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
(1
), pp. 36
–45
.38.
Roelands
, C. J. A.
, Vlutger
, J. C.
, and Watermann
, H. I.
, 1963
, “The Viscosity Temperature Pressure Relationship of Lubricating Oils and Its Correlation With Chemical Constitution
,” ASME J. Basic Eng.
, 85
(4
), pp. 601
–607
.39.
Yang
, P. R.
, and Wen
, S. Z.
, 1990
, “A Generalized Reynolds Equation for Non-Newtonian Thermal Elastohydrodynamio Lubrication
,” ASME J. Tribol.
, 112
, pp. 631
–636
.40.
Liu
, Y. C.
, Wang
, H.
, Wang
, W. Z.
, Hu
, Y. Z.
, and Zhu
, D.
, 2002
, “Methods Comparison in Computation of Temperature Rise on Frictional Interfaces
,” Tribol. Int.
, 35
(8
), pp. 549
–560
.41.
Liu
, Y. C.
, Wang
, Q. J.
, Zhu
, D.
, and Shi
, F.
, 2008
, “A Generalized Thermal EHL Model for Point Contact Problems
,” ASME
Paper No. IJTC2008-71120. 42.
Bos
, J.
, and Moes
, H.
, 1995
, “Frictional Heating of Tribological Contacts
,” ASME J. Tribol.
, 117
(1
), pp. 171
–177
.43.
Chen
, W. W.
, and Wang
, Q. J.
, 2008
, “Thermomechanical Analysis of Elastoplastic Bodies in a Sliding Spherical Contact and the Effects of Sliding Speed, Heat Partition, and Thermal Softening
,” ASME J. Tribol.
, 130
(4
), p. 041402
.44.
Ai
, X. L.
, 1993
, “Numerical Analyses of Elastohydrodynamically Lubricated Line and Point Contacts With Rough Surfaces by Using Semi-System and Multigrid Methods
,” Northwestern University, Evanston, IL.45.
Zhu
, D.
, and Hu
, Y. Z.
, 1999
, “The Study of Transition From Full Film Elastohydrodynamic to Mixed and Boundary Lubrication
,” STLE/ASME HS Cheng Tribology Surveillance
, pp. 150
–156
.46.
Hamrock
, B. J.
, and Dowson
, D.
, 1976
, “Isothermal Elastohydrodynamic Lubrication of Point Contacts—Part I: Theoretical Formulation
,” ASME J. Lubr. Technol.
, 98
(2), pp. 223
–228
.47.
Brewe
, D. E.
, and Hamrock
, B. J.
, 1977
, “Simplified Solution for Elliptical-Contact Deformation Between Two Elastic Solids
,” ASME J. Lubr. Technol.
, 99
(4
), pp. 485
–487
.Copyright © 2019 by ASME
You do not currently have access to this content.
