This paper presents a general formulation of the Reynolds equation for gas and liquid lubricants, including cavitation. A finite element solution of this equation is also given. The model is compared to those obtained in the previous literature on liquid and gas lubrication. One of the advantages of the model is the continuous description of cavitation in liquid lubrication. It is possible to deal with all lubricants by adjusting the amount of gas in the fluid.
Issue Section:
Hydrodynamic Lubrication
References
1.
Reynolds
, O.
, 1886
, “On the Theory of Lubrication and Its Application to Mr. Beauchamp Tower's Experiments, Including an Experimental Determination of the Viscosity of Olive Oil
,” Philos. Trans. R. Soc. London
, 177
, pp. 157
–234
.2.
Braun
, M.
, and Hannon
, W.
, 2010
, “Cavitation Formation and Modelling for Fluid Film Bearings: A Review
,” Proc. Inst. Mech. Eng., Part J
, 224
(9
), pp. 839
–863
.3.
Qui
, Y.
, and Khonsari
, M.
, 2009
, “On the Prediction of Cavitation in Dimples Using a Mass-Conservative Algorithm
,” ASME J. Tribol.
, 131
(4
), p. 041702
.4.
Elrod
, H.
, and Adams
, M.
, 1974
, “A Computer Program for Cavitation and Starvation Problems
,” First Leeds-Lyon Symposium on Tribology—Cavitation and Related Phenomena in Lubrication
, Leeds, UK, Sept., pp. 37
–41
.5.
Elrod
, H.
, 1981
, “A Cavitation Algorithm
,” ASME J. Lubr. Technol.
, 103
(3
), pp. 350
–354
.6.
Payvar
, P.
, and Salant
, R.
, 1992
, “A Computational Method for Cavitation in a Wavy Mechanical Seal
,” ASME J. Tribol.
, 114
(1
), pp. 199
–204
.7.
Bonneau
, D.
, and Hajjam
, D.
, 2001
, “Modelisation de la Rupture et de la Reformation des Film Lubrifiants Dans les Contacts Elastohydrodynamiques
,” Rev. Eur. Elem. Finis,
10
(6–7
), pp. 679
–704
.8.
Ausas
, R.
, Jai
, M.
, and Buscaglia
, G.
, 2009
, “A Mass-Conserving Algorithm for Dynamical Lubrication Problems With Cavitation
,” ASME J. Tribol.
, 131
(3
), p. 031702
.9.
Shen
, C.
, and Khonsari
, M. M.
, 2013
, “On the Magnitude of Cavitation Pressure of Steady-State Lubrication
,” Tribol. Lett.
, 51
(1
), pp. 153
–160
.10.
Singhal
, A.
, Athavale
, M.
, Li
, H.
, and Jiang
, Y.
, 2002
, “Mathamtical Basis and Validation of the Full Cavitation Model
,” ASME J. Fluids Eng.
, 124
(3
), pp. 617
–624
.11.
Gehannin
, J.
, Arghir
, M.
, and Bonneau
, O.
, 2009
, “Evaluation of Rayleigh-Plesset Equation Based Cavitation Models for Squeeze Film Dampers
,” ASME J. Tribol.
, 131
(2
), p. 024501
.12.
Geike
, T.
, and Popov
, V.
, 2009
, “A Bubble Dynamics Based Approach to the Simulation of Cavitation in Lubricated Contacts
,” ASME J. Tribol.
, 131
(1
), p. 011704
.13.
Song
, Y.
, Gu
, C.
, and Ren
, X.
, 2015
, “Development and Validation of a Gaseous Cavitation Model for Hydrodynamic Lubrication
,” Proc. Inst. Mech. Eng. Part J
, 229
(10
), pp. 1227
–1238
.14.
Gehannin
, J.
, Arghir
, M.
, and Bonneau
, O.
, 2016
, “A Volume of Fluid Method for Air Ingestion in Squeeze Film Dampers
,” Tribol. Trans.
, 59
(2
), pp. 208
–218
.15.
Brunetiere
, N.
, 2016
, “Modelling of Reverse Flows in a Mechanical Seal
,” Tribol. Online
, 11
(2
), pp. 94
–101
.16.
Bayada
, G.
, and Chupin
, L.
, 2013
, “Compressible Fluid Model for Hydrodynamic Lubrication Cavitation
,” ASME J. Tribol.
, 135
(4
), pp. 041702
–041713
.17.
Cross
, A. T.
, Sadeghi
, F.
, Cao
, L.
, Rateick
, R. G.
, Jr., and Rowan
, S.
, 2012
, “Flow Visualization in a Pocketed Thrust Washer
,” Tribol. Trans.
, 55
(5
), pp. 571
–581
.18.
Zhang
, J.
, and Meng
, Y.
, 2012
, “Direct Observation of Cavitation Phenomenon and Hydrodynamic Lubrication Analysis of Textured Surfaces
,” Tribol. Lett.
, 46
(2
), pp. 147
–158
.19.
Gross
, W.
, 1959
, “A Gas Film Lubrication Study––Part I: Some Theoretical Analyse of Slider Bearings
,” IBM J. Res. Dev.
, 3
(3
), pp. 237
–255
.20.
Muijderman
, E.
, 1965
, “Spiral Groove Bearings
,” Ind. Lubr. Tribol.
, 17
(1
), pp. 12
–17
.21.
Bonneau
, D.
, Huitric
, J.
, and Tournerie
, B.
, 1993
, “Finite Element Analysis of Grooved Gas Thrust Bearings and Grooved Gas Face Seals
,” ASME J. Tribol.
, 115
(3
), pp. 348
–354
.22.
Hernandez
, P.
, and Boudet
, J.
, 1995
, “Modelling of the Behaviour of Dynamical Gas Seals: Calculation With a Finite Element Method Implicitly Assuring the Continuity of Flow
,” Proc. Inst. Mech. Eng. Part J
, 209
(3
), pp. 195
–201
.23.
Faria
, M.
, 2001
, “An Efficient Finite Element Procedure for Analysis of High-Speed Spiral Groove Gas Face Seals
,” ASME J. Tribol.
, 123
(1
), pp. 205
–210
.24.
Brunetiere
, N.
, and Wang
, Q.
, 2011
, “A Simplified Mass-Conservating and Continuous Cavitation Model
,” STLE Annual Meeting
, Atlanta, GA, May 15–19.25.
Wallis
, G.
, 1969
, One-Dimensional Two-Phase Flow
, McGraw-Hill
, New York.26.
Migout
, F.
, Brunetiere
, N.
, and Tournerie
, B.
, 2015
, “Study of the Fluid Film Vaporization in the Interface of a Mechanical Face Seal
,” Tribol. Int.
, 92
, pp. 84
–95
.27.
Saadat
, N.
, and Flint
, W.
, 1996
, “Expressions for the Viscosity of Liquid/Vapour Mixtures: Predicted and Measured Pressure Distributions in a Hydrostatic Bearing
,” Proc. Inst. Mech. Eng. Part J
, 210
(1
), pp. 75
–79
.28.
Heinrich
, J.
, Huyakorn
, P.
, Zienkiewicz
, O.
, and Mitchell
, A.
, 1977
, “An Upwind Finite Element Scheme for Two Dimensional Convective Transport Equation
,” Int. J. Numer. Methods Eng.
, 11
(1
), pp. 131
–143
.29.
Qiu
, Y.
, and Khonsari
, M.
, 2011
, “Investigation of Tribological Behaviors of Annular Rings With Spiral Groove
,” Tribol. Int.
, 44
(12
), pp. 1610
–1619
.30.
Zienkiewicz
, O.
, and Taylor
, R.
, 2000
, The Finite Element Method
(The Basis), 5th ed., Vol. 1
, Butterworth-Heineman
, Oxford, UK
.31.
Zienkiewicz
, O.
, and Taylor
, R.
, 2000
, The Finite Element Method
(Fluid Dynamics), 5th ed., Vol. 3
, Butterworth Heinemann
, Oxford, UK
.32.
Brunetiere
, N.
, and Tournerie
, B.
, 2005
, “Finite Element Solution of the Energy Equation in Lubricated Contacts: Application to Mechanical Face Seals
,” Eur. J. Comput. Mech.
, 14
(2–3
), pp. 213
–235
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