This paper deals with modeling the non-linear rheological behavior of lubricating greases at very low shear rates. With this aim, dynamic linear viscoelastic, non-linear stress relaxation, transient and steady-state shear flow, and transient first normal stress difference measurements have been carried out on a diurea-derivative lubricating grease. A factorable non-linear viscoelasticity model, the Wagner integral model, derived from the K-BKZ constitutive equation, was used in order to predict the non-linear rheological response of the above-mentioned lubricating grease under shear. The time-dependent part of the model was described by its linear relaxation spectrum, whilst two different damping functions (Wagner and Soskey-Winter’s damping functions) were analysed as the strain-dependent factor. The continuous linear relaxation spectrum was estimated, using regularization techniques, from the dynamic linear viscoelasticity functions. The damping function was calculated from non-linear stress relaxation tests. The constitutive model, with Soskey-Winter’s damping function, predicted the steady-state flow curve, the transient shear stress and the transient first normal stress differences of the lubricating grease studied fairly well. [S0742-4787(00)01603-9]
1.
Dawtray, S., 1975, “Lubricating Greases,” in Modern Petroleum Technology, Hobson, G. D., and Pohl, W., eds., Applied Science, Essex.
2.
Sacchettini
, M.
, Magnin
, A.
, Piau
, J. M.
, and Pierrard
, J. M.
, 1985
, “Caracte`risation d’une Graisse Lubrifiante en Ecoulements Viscosime´triques Transitoires
,” J. Theor. Appl. Mech.
, 4
, pp. 165
–199
.3.
NLGI, 1994, Lubricating Grease Guide, National Lubricating Grease Institute (ed.), Kansas.
4.
Magnin
, A.
, and Piau
, J. M.
, 1988
, “Application of Freeze-Fracture Technique for Analyzing the Structure of Lubricant Greases
,” J. Mater. Res.
, 4
, pp. 990
–995
.5.
Shuff
, P. J.
, and Clarke
, L. J.
, 1991
, “Imaging of Lubricating Oil Insolubles by Electron Microscopy
,” Tribol. Int.
, 24
, pp. 381
–387
.6.
Mas
, R.
, and Magnin
, A.
, 1994
, “Rheology of Colloidal Suspensions: Case of Lubricating Greases
,” J. Rheol.
, 38
, pp. 889
–908
.7.
Gow, G., 1988, “The Time Factor in Grease Rheology,” NLGI Spokesman, Dec., pp. 415–423.
8.
Bair
, S.
, 1994
, “The High-Pressure Rheology of a Soap-Thickened Grease
,” Tribol. Trans.
, 3
, pp. 646
–650
.9.
Astarita
, G.
, 1990
, “The Engineering Reality of Yield Stress
,” J. Rheol.
, 34
, pp. 275
–277
.10.
Barnes
, H. A.
, and Walters
, K.
, 1985
, “The Yield Stress Myth?
,” Rheol. Acta
, 24
, pp. 323
–326
.11.
Bird, R. B., Armstrong, R. C., and Hassager, O., 1987, Dynamics of Polymer Liquids, Vol. 1, Wiley, New York.
12.
Barnes, H. A., Hutton, J. F., and Walters, K., 1989, An Introduction to Rheology, Elsevier, Amsterdam.
13.
Larson, R. G., 1988, Constitutive Equations for Polymer Melts and Solutions, Butterworths, Boston.
14.
Williamson
, B. P.
, Walters
, K.
, Bates
, T. W.
, Coy
, R. C.
, and Milton
, A. L.
, 1997
, “The Viscoelastic Properties of Multigrade Oils and their Effect on Journal-Bearing Characteristics
,” J. Non-Newtonian Fluid Mech.
, 73
, pp. 115
–126
.15.
Yoo
, J.
, and Kim
, K.
, 1997
, “Numerical Analysis of Thermal Elastohydrodynamics Lubrication Problems Using the Herschel-Bulkley Model
,” Tribol. Int.
, 30
, pp. 401
–408
.16.
Kuhn
, E.
, 1998
, “Investigations into the Degradation of the Structure of Lubricating Greases
,” STLE Tribol. Trans.
, 41
, pp. 247
–250
.17.
Mas
, R.
, and Magnin
, A.
, 1996
, “Rheological and Physical Studies of Lubricating Greases Before and After Use in Bearings
,” ASME J. Tribol.
, 118
, pp. 681
–686
.18.
Kuhn
, E.
, and Balan
, C.
, 1997
, “Experimental Procedure for the Evaluation of the Friction Energy of Lubricating Greases
,” Wear
, 209
, pp. 237
–240
.19.
Kaye, A., 1962, “Non-Newtonian Flow in Incompressible Fluids,” CoA Note No. 134, College of Aeronautics, Cranford, UK.
20.
Bernstein
, B.
, Kearsley
, E. A.
, and Zapas
, L. J.
, 1964
, “Thermodynamics of Perfect Elastic Fluids
,” J. Res. Natl. Bur. Stand., Sect. B
, 68B
, pp. 103
–113
.21.
Ferry, J. D., 1980, Viscoelastic Properties of Polymers, Wiley, New York.
22.
Madiedo
, J. M.
, and Gallegos
, C.
, 1997
, “Rheological Characterization of Oil-in-Water Emulsions by Means of Relaxation and Retardation Spectra
,” Recent Res. Devel. Oil Chem.
, 1
, pp. 79
–90
.23.
Madiedo
, J. M.
, and Gallegos
, C.
, 1997
, “Use of the Tikhonov Regularization Method for the Linear Viscoelastic Characterization of Emulsifying Systems
,” CIT-Inform. Tecnol.
, 8
, pp. 333
–340
.24.
Tschoegl, N. W., 1989, The Phenomenological Theory of Linear Viscoelastic Behavior, Springer Verlag, Berlin.
25.
Honerkamp
, J.
, and Weese
, J.
, 1993
, “A Non-Linear Regularization Method for the Calculation of Relaxation Spectra
,” Rheol. Acta
, 32
, pp. 65
–73
.26.
Wagner
, M. H.
, 1976
, “Analysis of Time-Dependent Non-Linear Stress-Growth Data for Shear and Elongational Flow of a Low-Density Branched Polyethylene Melt
,” Rheol. Acta
, 5
, pp. 136
–142
.27.
Laun
, H. M.
, 1978
, “Description of the Non-Linear Shear Behavior of a Low-Density Polyethylene Melt by Means of an Experimentally Determined Strain Dependent Memory Function
,” Rheol. Acta
, 17
, pp. 1
–15
.28.
Campanella
, O. H.
, and Peleg
, M.
, 1987
, “Analysis of the Transient Flow of Mayonnaise with a Coaxial Viscometer
,” J. Rheol.
, 31
, pp. 439
–452
.29.
Liang
, R. F.
, and Mackley
, M. R.
, 1994
, “Rheological Characterization of the Time and Strain Dependence for Isobutylene Solutions
,” J. Non-Newtonian Fluid Mech.
, 52
, pp. 387
–405
.30.
Mackley
, M. R.
, Marshall
, R. T. J.
, Smeulders
, J. B.
, and Zhao
, F. D.
, 1994
, “The Rheological Characterization of Polymeric and Colloidal Fluids
,” Chem. Eng. Sci.
, 49
, pp. 2551
–2565
.31.
Wang
, C. F.
, and Kokini
, J. L.
, 1995
, “Simulation of the Non-Linear Rheological Properties of Gluten Dough Using the Wagner Constitutive Model
,” J. Rheol.
, 39
, pp. 1465
–1482
.32.
Darby, R., 1976, Viscoelastic Fluids, Marcel Dekker, New York.
33.
Hutton
, J. F.
, 1975
, “On Using the Weissenberg Rheogoniometer to Measure Normal Stresses in Lubricating Greases as Examples of Materials Which Have a Yield Stress
,” Rheol. Acta
, 14
, pp. 979
–992
.34.
Groetsch, C. W., 1984, The Theory of Tikhonov Regularization for Fredholm Equations of the First Kind, Pitman, London.
35.
Press, W. H., Teukosky, S. A., Vetterling, W. T., and Flannery, B. P., 1992, Numerical Recipes in C, Cambridge University Press, Cambridge.
36.
Madiedo, J. M., 1996, “Caracterizacio´n Reologica de Emulsiones mediante Espectros de Relajacion y Retardacio´n,” Ph.D. thesis, University of Seville, Seville.
37.
Montero
, R.
, Gallegos
, C.
, Franco
, J. M.
, Muntada
, L.
, 1997
, “Caracterizacio´n Reolo´gica de Grasas Lubricantes
,” Ing. Quim.
, 341
, pp. 137
–143
.38.
Soskey
, P. R.
, and Winter
, H. H.
, 1984
, “Large Step Shear Strain Experiments with Parallel-Disk Rotational Rheometers
,” J. Rheol.
, 28
, pp. 625
–645
.39.
Buscall
, R.
, Mc Gowan
, J. L.
, and Morton-Jones
, A. J.
, 1993
, “The Rheology of Concentrated Dispersions of Weakly Attracting Colloidal Particles with and without Wall Slip
,” J. Rheol.
, 37
, pp. 621
–641
.40.
Franco
, J. M.
, Gallegos
, C.
, and Barnes
, H. A.
, 1998
, “On Slip Effects in Steady-State Flow Measurements of Oil-in-Water Food Emulsions
,” J. Food. Eng.
, 36
, pp. 89
–102
.41.
Gallegos
, C.
, Berjano
, M.
, Guerrero
, A.
, Mun˜oz
, J.
, and Flores
, V.
, 1992
, “Transient Flow of Mayonnaise Described by a Non-Linear Viscoelasticity Model
,” J. Texture Stud.
, 23
, pp. 153
–168
.42.
Gallegos
, C.
, and Franco
, J. M.
, 1995
, “Linear and Non-Linear Viscoelasticity of Food Emulsions Containing a Mixture of Two Emulsifiers
,” Les Cahiers Rheol.
, 14
, pp. 107
–116
. Copyright © 2000
by ASME
You do not currently have access to this content.
