Abstract
An analysis of non-Newtonian effects on lubrication flows is presented based on the upper-convected Maxwell constitutive equation, which is the simplest viscoelastic model having a constant viscosity and relaxation time. By employing characteristic lubricant relaxation times in all order of magnitude analysis, a perturbation method is developed to analyze the flow of a non-Newtonian lubricant between two surfaces. The effect of viscoelasticity on the lubricant velocity and pressure fields is examined, and the influence of minimum film thickness on lubrication characteristics is investigated. Numerical simulations show a significant enhancement in the pressure field when the minimum film thickness is sufficiently small. This mechanism suggests that viscoelasticity does indeed produce a beneficial effect on lubrication performance, which is consistent with experimental observations.
Similar content being viewed by others
References
H. A. Barnes, J. F. Hutton and K. Walters, An Introduction to Rheology. Amsterdam: Elsevier (1989) 212pp.
R.B. Bird, R.C. Armstrong and O. Hassager, Dynamics of Polymetric Liquids, Vol. 1, Fluid Mechanics. New York: John Wiley and Sons (1987) 672pp.
A. Cameron, Basic Lubrication Theory. London: Longman Group Limited (1971) 195pp.
R. I. Tanner, Engineering Rheology. Second Edition, Oxford: Oxford University Press (2000) 559pp.
M. J. Davies and K. Walters, The behaviour of non-newtonian lubricants in Journal bearings–a theoretical study. In: T. C. Davenport (ed.), Rheology of Lubricants. New York: Applied Science Publishers (1972) pp. 16–37.
B. P. Williamson, K. Walters, T. W. Bates, R. C. Coy and A. L. Milton, The viscoelastic properties of multigrade oils and their effect on journal-bearing characteristics. J. Non-Newtonian Fluid Mech. 73 (1997) 115–126.
T. W. Bates, B. Williamson, J. A. Spearot and C. K. Murphy, A correlation between engine oil rheology and oil film thickness in engine journal bearing. Soc. Automotive Eng. Paper No. 860376, (1986).
M. J. Crochet and K. Walters, Computational rheology: a new science. Endeavour, New Series 17 (1993) 64–77.
A. Z. Szeri, Fluid Film Lubrication Theory and Design. Cambridge: Cambridge University Press (1998) 414pp.
G. W. Roberts and K. Walters, Oil viscoelastic effects in journal bearing lubrication. Rheol Acta 31 (1992) 55–62.
A. Rastogi and R. K. Gupta, Lubricant elasticity and the performance of dynamically loaded journal bearings. J. Rheol. 34 (1990) 1337–1356.
A. Z. Szeri, Some extensions of the lubrication theory of Osborne Reynolds. ASME J. Tribology 109 (1987) 21–37.
A. R. Davies and X. K. Li, Numerical modelling of pressure and temperature effects in viscoelastic flow between eccentrically rotating cylinders. J. Non-Newtonian Fluid Mech. 54 (1994) 331–350.
D. Dowson and G. R. Higginson, Elastic-hydrodynamic Lubrication. New York: Pergamon Press (1977) 235pp.
E. R. Khayat, Transient two-dimensional coating flow of a viscoelastic fluid on a substracte of arbitrary shape. J. Non-Newtonian Fluid Mech. 95 (2000) 199–233.
J. A. Tichy, Non-Newtonian lubrication with the convected Maxwell model. Transactions of the ASME. 118 (1996) 344–348.
Y. L. Zhang, O. K. Matar and R. V. Craster, Surfactant spreading on a thin weakly viscoelastic film. J. Non-Newtonian Fluid Mech. 105 (2002) 53–78.
X. K. Li, D. Gwynllyw, A. R. Davies and T. N. Phillips, Three-dimensional effects in dynamically loaded journal bearings. Int. J. Nurner. Methods Fluids 29 (1999) 311–341.
D. Dowson and C. M. Taylor, Cavitation in bearings. Annu. Rev. Fluid Mech. 11 (1979) 35–66.
C. E. Brennen, Cavitation and Bubble Dynamics. Oxford: Oxford University Press (1995) 282 pp.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Zhang, R., Li, X.K. Non-Newtonian effects on lubricant thin film flows. J Eng Math 51, 1–13 (2005). https://doi.org/10.1007/s10665-004-1342-z
Issue Date:
DOI: https://doi.org/10.1007/s10665-004-1342-z