A theoretical and computational framework for the analysis of fully transient, thermomechanically coupled, frictional rolling contact based on an arbitrary Lagrangian–Eulerian (ALE) kinematical description is presented. In particular, a computationally efficient methodology for mixed control between the ALE referential velocities and their corresponding driving forces is developed and discussed in depth. Numerical examples involving two-dimensional (2D) cylinder–plate rolling contact are presented, covering a range of transient, thermomechanically coupled rolling contact phenomena, taking place on a broad range of time scales. Here, particular points of emphasis include dynamical effects in the vicinity of the contact region and the time scales on which mechanical and thermal mechanisms operate.
Issue Section:
Elastohydrodynamic Lubrication
References
1.
Hertz
, H.
, 1882
, “Über die berührung fester elastischer körper (On the Contact of Elastic Solids)
,” J. Reine Angew. Math.
, 92
, pp. 156
–171
.2.
Carter
, F. W.
, 1926
, “On the Action of a Locomotive Driving Wheel
,” Proc. R. Soc. London, Ser. A
, 112
(760
), pp. 151
–157
.3.
Johnson
, K. L.
, 1987
, Contact Mechanics
, Cambridge University Press
, Cambridge, UK
.4.
Bhargava
, V.
, Hahn
, G. T.
, and Rubin
, C. A.
, 1985
, “An Elastic–Plastic Finite Element Model of Rolling Contact, Part 1: Analysis of Single Contacts
,” ASME J. Appl. Mech.
, 52
(1
), pp. 67
–74
.5.
Xu
, B.
, and Jiang
, Y.
, 2001
, “Elastic–Plastic Finite Element Analysis of Partial Slip Rolling Contact
,” ASME J. Tribol.
, 124
(1
), pp. 20
–26
.6.
Gao
, C. H.
, Huang
, J. M.
, Lin
, X. Z.
, and Tang
, X. S.
, 2006
, “Stress Analysis of Thermal Fatigue Fracture of Brake Disks Based on Thermomechanical Coupling
,” ASME J. Tribol.
, 129
(3
), pp. 536
–543
.7.
Wang
, Z.
, Jin
, X.
, Keer
, L. M.
, and Wang
, Q.
, 2012
, “A Numerical Approach for Analyzing Three-Dimensional Steady-State Rolling Contact Including Creep Using a Fast Semi-Analytical Method
,” Tribol. Trans.
, 55
(4
), pp. 446
–457
.8.
Kalker
, J. J.
, 1990
, Three-Dimensional Elastic Bodies in Rolling Contact
(Solid Mechanics and Its Applications), Kluwer Academic Publishers
, Dordrecht, The Netherlands.9.
Vollebregt
, E. A. H.
, 2012
, “User Guide for CONTACT, Vollebregt & Kalker's Rolling and Sliding Contact Model
,” Version 13.1, VORTech, Delft, The Netherlands, Technical Report No. TR09-03.10.
Vollebregt
, E. A. H.
, Iwnicki
, S. D.
, Xie
, G.
, and Shackleton
, P.
, 2012
, “Assessing the Accuracy of Different Simplified Frictional Rolling Contact Algorithms
,” Veh. Syst. Dyn.
, 50
(1
), pp. 1
–17
.11.
Nackenhorst
, U.
, 2004
, “The ALE-Formulation of Bodies in Rolling Contact: Theoretical Foundations and Finite Element Approach
,” Comput. Methods Appl. Mech. Eng.
, 193
, pp. 4299
–4322
.12.
Donéa
, J.
, and Huerta
, A.
, 2003
, Finite Element Methods for Flow Problems
, Wiley
, Hoboken, NJ.13.
Zeid
, I.
, and Padovan
, J.
, 1981
, “Finite Element Modeling of Rolling Contact
,” Comput. Struct.
, 14
(1–2
), pp. 163
–170
.14.
Oden
, J. T.
, and Lin
, T. L.
, 1986
, “On the General Rolling Contact Problem for Finite Deformations of a Viscoelastic Cylinder
,” Comput. Methods Appl. Mech. Eng.
, 57
(3
), pp. 297
–367
.15.
Padovan
, J.
, 1987
, “Finite Element Analysis of Steady and Transiently Moving/Rolling Nonlinear Viscoelastic Structure—I. Theory
,” Comput. Struct.
, 27
(2
), pp. 249
–257
.16.
Nackenhorst
, U.
, 1993
, “On the Finite Element Analysis of Steady State Rolling Contact
,” Contact Mechanics—Computational Techniques
, Computational Mechanics Publication
, Southampton, UK
, pp. 53
–60
.17.
Ziefle
, M.
, and Nackenhorst
, U.
, 2008
, “Numerical Techniques for Rolling Rubber Wheels: Treatment of Inelastic Material Properties and Frictional Contact
,” Comput. Mech.
, 42
(3
), pp. 337
–356
.18.
Suwannachit
, A.
, and Nackenhorst
, U.
, 2013
, “A Novel Approach for Thermomechanical Analysis of Stationary Rolling Tires Within an ALE-Kinematic Framework
,” Tire Sci. Technol.
, 41
(3
), pp. 174
–195
.19.
Draganis
, A.
, Larsson
, F.
, and Ekberg
, A.
, 2014
, “Finite Element Analysis of Transient Thermomechanical Rolling Contact Using an Efficient Arbitrary Lagrangian–Eulerian Description
,” Comput. Mech.
, 54
(2
), pp. 389
–405
.20.
Draganis
, A.
, Larsson
, F.
, and Ekberg
, A.
, 2015
, “Finite Element Modelling of Frictional Thermomechanical Rolling/Sliding Contact Using an Arbitrary Lagrangian–Eulerian Formulation
,” Proc. Inst. Mech. Eng., Part J
, 229
(7
), pp. 870
–880
.21.
Kalker
, J. J.
, 1991
, “Wheel–Rail Rolling Contact Theory
,” Wear
, 144
, pp. 243
–261
.22.
Schweizer
, B.
, and Wauer
, J.
, 2001
, “Atomistic Explanation of the Gough–Joule-Effect
,” Eur. Phys. J. B
, 23
(3
), pp. 383
–390
.23.
Ottosen
, N. S.
, and Ristinmaa
, M.
, 2005
, The Mechanics of Constitutive Modeling
, Elsevier
, Amsterdam, The Netherlands.24.
Wriggers
, P.
, 2006
, Computational Contact Mechanics
, Springer
, Heidelberg, Germany.25.
Thompson
, D. J.
, 1991
, “Theoretical Modelling of Wheel–Rail Noise Generation
,” Proc. Inst. Mech. Eng., Part F
, 205
(2
), pp. 137
–149
.26.
Draganis
, A.
, Larsson
, F.
, and Ekberg
, A.
, 2012
, “Numerical Evaluation of the Transient Response due to Non-Smooth Rolling Contact Using an Arbitrary Lagrangian–Eulerian Formulation
,” Proc. Inst. Mech. Eng., Part J
, 226
(1
), pp. 36
–45
.27.
Codina
, R.
, Onate
, E.
, and Cervera
, M.
, 1992
, “The Intrinsic Time for the Streamline Upwind/Petrov–Galerkin Formulation Using Quadratic Elements
,” Comput. Methods Appl. Mech. Eng.
, 94
(2
), pp. 239
–262
.28.
Brezzi
, F.
, Bristeau
, M.-O.
, Franca
, L. P.
, Mallet
, M.
, and Rogé
, G.
, 1992
, “A Relationship Between Stabilized Finite Element Methods and the Galerkin Method With Bubble Functions
,” Comput. Methods Appl. Mech. Eng.
, 96
(1
), pp. 117
–129
.29.
Baiocchi
, C.
, Brezzi
, F.
, and Franca
, L. P.
, 1993
, “Virtual Bubbles and Galerkin-Least-Squares Type Methods (Ga.L.S.)
,” Comput. Methods Appl. Mech. Eng.
, 105
(1
), pp. 125
–141
.30.
Brezzi
, F.
, Marini
, D.
, and Russo
, A.
, 1998
, “Applications of the Pseudo Residual-Free Bubbles to the Stabilization of Convection-Diffusion Problems
,” Comput. Methods Appl. Mech. Eng.
, 166
(1–2
), pp. 51
–63
.31.
Craig
, R. R.
, and Kurdila
, A. J.
, 2006
, Fundamentals of Structural Dynamics
, Wiley
, Hoboken, NJ.Copyright © 2017 by ASME
You do not currently have access to this content.
