CFD Modelling of Elastohydrodynamic Lubrication

Traditionally the problem of elastohydrodynamic lubrication (EHL) has been solved using the Reynolds equations for fluid flow. In this paper we explore the finite volume method (FVM) to model fluid behaviour in rolling-element bearing systems. The effect of cavitation is modelled with a barotropic cavitation model. We investigate two cases with a cylinder on a flat plate, one under rolling and one under sliding conditions. These solutions are compared to the Reynolds-EHL approach. Towards higher loads, stability problems are encountered and strategies for dealing with these are discussed.Copyright © 2005 by ASME

[1]  L. Houpert Closure to “Discussion of ‘New Results of Traction Force Calculations in Elastohydrodynamic Contacts’” (1985, ASME J. Tribol., 107, pp. 246–247) , 1985 .

[2]  D. Dowson,et al.  Transient elastohydrodynamic analysis of elliptical contacts. Part 1: Isothermal and Newtonian lubricant solution , 2004 .

[3]  B. Sternlicht,et al.  A Numerical Solution for the Pressure, Temperature, and Film Thickness Between Two Infinitely Long, Lubricated Rolling and Sliding Cylinders, Under Heavy Loads , 1965 .

[4]  Henry Peredur Evans,et al.  A novel method for integrating first- and second-order differential equations in elastohydrodynamic lubrication for the solution of smooth isothermal, line contact problems , 1999 .

[5]  Henry Peredur Evans,et al.  On the coupling of the elastohydrodynamic problem , 1998 .

[6]  Hrvoje Jasak,et al.  A tensorial approach to computational continuum mechanics using object-oriented techniques , 1998 .

[8]  G. M. Hamilton,et al.  Negative Pressures under a Lubricated Piston Ring , 1978 .

[9]  M. Kaneta,et al.  Effects of Compressive Heating on Traction Force and Film Thickness in Point EHL Contacts , 2005 .

[10]  C. J. Greenshields,et al.  A unified formulation for continuum mechanics applied to fluid–structure interaction in flexible tubes , 2005 .

[11]  Wen Shizhu,et al.  A Generalized Reynolds Equation for Non-Newtonian Thermal Elastohydrodynamic Lubrication , 1990 .

[12]  W. 0. Winer,et al.  Correlational Aspects of the Viscosity-Temperature-Pressure Relationship of Lubricating Oils(Dr In dissertation at Technical University of Delft, 1966) , 1966 .

[13]  W. Shyy,et al.  Dynamics of attached turbulent cavitating flows , 2001 .

[14]  J. C. Jaeger,et al.  Conduction of Heat in Solids , 1952 .

[15]  Yuji Hashimoto,et al.  Analysis of Oil-Film Pressure Distribution in Porous Journal Bearings Under Hydrodynamic Lubrication Conditions Using an Improved Boundary Condition , 1997 .

[16]  Motohiro Kaneta,et al.  Effects of Thermal Conductivity of Contacting Surfaces on Point EHL Contacts , 2003 .

[17]  Scott Bair,et al.  A More Complete Description of the Shear Rheology of High-Temperature, High-Shear Journal Bearing Lubrication , 2006 .

[18]  A. Lubrecht,et al.  Transient Analysis of Surface Features in an EHL Line Contact in the Case of Sliding , 1994 .

[19]  Joel H. Ferziger,et al.  Computational methods for fluid dynamics , 1996 .

[20]  B. Hamrock,et al.  Fundamentals of Fluid Film Lubrication , 1994 .

[21]  R. Snurr,et al.  Molecular dynamics characterization of thin film viscosity for EHL simulation , 2006 .

[22]  J. L. Tevaarwerk,et al.  Shear behaviour of elastohydrodynamic oil films , 1977, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[23]  Wei Shyy,et al.  Evaluations of Cavitation Models for Navier-Stokes Computations , 2002 .

[24]  D. Dowson,et al.  Thermal elastohydrodynamic analysis of circular contacts Part 2: Non-Newtonian model , 2001 .

[25]  G. Wallis One Dimensional Two-Phase Flow , 1969 .

[26]  Roland Larsson,et al.  The Navier-Stokes approach for thermal EHL line contact solutions , 2002 .

[27]  Roland Larsson,et al.  Lubricant thermal conductivity and heat capacity under high pressure , 2000 .

[28]  D Dowson,et al.  Transient elastohydrodynamic analysis of elliptical contacts. Part 2: Thermal and Newtonian lubricant solution , 2004 .

[29]  Andreas Almqvist,et al.  A comparison between computational fluid dynamic and Reynolds approaches for simulating transient EHL line contacts , 2004 .

[30]  J. Anderson,et al.  Fundamentals of Aerodynamics , 1984 .

[31]  A. Olver,et al.  Compression of a Single Transverse Ridge in a Circular Elastohydrodynamic Contact , 2003 .

[32]  D. Dowson A generalized Reynolds equation for fluid-film lubrication , 1962 .

[33]  Scott Bair,et al.  Reference liquids for quantitative elastohydrodynamics: selection and rheological characterization , 2006 .

[34]  Farrukh Qureshi,et al.  The Generalized Newtonian Fluid Model and Elastohydrodynamic Film Thickness , 2003 .

[35]  O. Reynolds IV. On the theory of lubrication and its application to Mr. Beauchamp tower’s experiments, including an experimental determination of the viscosity of olive oil , 1886, Philosophical Transactions of the Royal Society of London.

[36]  D Dowson,et al.  Thermal elastohydrodynamic analysis of circular contacts Part 1: Newtonian model , 2001 .

[37]  K. Kobe The properties of gases and liquids , 1959 .

[38]  Carl Barus,et al.  Isothermals, isopiestics and isometrics relative to viscosity , 1893, American Journal of Science.

[39]  O. Ubbink Numerical prediction of two fluid systems with sharp interfaces , 1997 .

[40]  Ward O. Winer,et al.  The temperature, pressure and time dependence of lubricant viscosity , 2001 .

[41]  Peter Williams,et al.  Mechanical Engineering Publications , 1989 .

[42]  H. P. Evans,et al.  Coupled solution of the elastohydrodynamic line contact problem using a differential deflection method , 2000 .

[43]  Hui Wang,et al.  A Computer Thermal Model of Mixed Lubrication in Point Contacts , 2004 .

[44]  Roland Larsson,et al.  Some Remarks on the Validity of Reynolds Equation in the Modeling of Lubricant Film Flows on the Surface Roughness Scale , 2004 .

[45]  Wei Shyy,et al.  A fixed-grid, sharp-interface method for bubble dynamics and phase change , 2001 .

[46]  D Dowson,et al.  Transient elastohydrodynamic analysis of elliptical contacts. Part 3: Non-Newtonian lubricant solution under isothermal and thermal conditions , 2007 .

[47]  Christopher J. Rutland,et al.  A FULLY COMPRESSIBLE, TWO-DIMENSIONAL MODEL OF SMALL, HIGH-SPEED, CAVITATING NOZZLES , 1999 .

[48]  Hrvoje Jasak,et al.  Error analysis and estimation for the finite volume method with applications to fluid flows , 1996 .

[49]  S. Bair,et al.  High-pressure rheology of lubricants and limitations of the Reynolds equation , 1998 .

[50]  T. F. Conry,et al.  A Reynolds-Eyring Equation for Elastohydrodynamic Lubrication in Line Contacts , 1987 .

[51]  H. Spikes The half-wetted bearing. Part 1: Extended Reynolds equation , 2003 .

[52]  Lavern Dale Wedeven Optical measurements in elastohydrodynamic rolling-contact bearings , 1970 .

[53]  Clayton T. Crowe,et al.  Multiphase Flow Handbook , 2005 .

[54]  J. Barbera,et al.  Contact mechanics , 1999 .

[55]  R. Reid,et al.  The Properties of Gases and Liquids , 1977 .

[56]  L. F. Crabtree,et al.  Fundamentals of Aerodynamics - Second edition . J.D. Anderson. McGraw-Hill Book Company, Shoppenhangers Road, Maidenhead, Berks SL6 2QL. 1991. 772 pp. Illustrated. £30.95. , 1991, The Aeronautical Journal (1968).

[57]  J. C. Jaeger Moving sources of heat and the temperature at sliding contacts , 1943, Journal and proceedings of the Royal Society of New South Wales.

[58]  H P Evans,et al.  Evaluation of deflection in semi-infinite bodies by a differential method , 2000 .

[59]  Sb Park,et al.  Sound speed criterion for two-phase critical flow , 2004 .