Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-19T03:25:17.523Z Has data issue: false hasContentIssue false
  • English
  • Français

Stress relaxation effect in elastico-viscous lubricants in gears and rollers

Published online by Cambridge University Press:  11 April 2006

A. Harnoy
A. Harnoy
Affiliation:
Department of Mechanical Engineering, University of Rhodesia, Salisbury
Get access Rights & Permissions [Opens in a new window]

Abstract

The stress relaxation effect in an incompressible elastico-viscous fluid is investigated for the case of the lubrication of line-contact rollers. Two extreme cases are considered: that of low pressures with rigid surfaces and constant viscosity and that of heavily loaded elasto-hydrodynamic lubrication. In order to solve this problem, a new invariant material time derivative is suggested. This derivative is referred to a co-ordinate system attached to the principal axes of the strain-rate tensor, while the former derivatives have been referred to the fluid particle. It is shown that, unlike the previous derivatives, the new one enables a separate parametric description of the stress relaxation process and the first normal-stress difference. The results show that a significant increase in the load capacity is obtained, owing to the relaxation time of the fluid. The investigation is for fluids with a relaxation time small compared with the transit time of the lubricant through the bearing.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 76 , Issue 3 , 11 August 1976 , pp. 501 - 517
Copyright
© 1976 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Appeldorn, J. K. 1968 Trans. A.S.M.E., J. Lub. Tech. 90, 526.
Burton, R. A. 1960 Analytical investigation of viscoelastic effect in the lubrication of rolling contact. A.S.L.E. Trans. 3, 1.Google Scholar
Cameron, A. 1953 Surface failure in gears. J. Inst. Petrol. 40, 191.Google Scholar
Cameron, A. 1966 The Principles of Lubrication, p. 203. Longmans.
Coleman, B. O. & Noll, W. 1960 An approximation theorem for functionals, with application in continuum mechanics. Arch. Rat. Mech. Anal. 6, 355.Google Scholar
Davies, M. J. & Walters, K. 1972 The behaviour of non-Newtonian lubricants in journal bearings. Proc. Conf. Rheology of Lubricants, Nottingham.
Harnoy, A. 1971 Second order effects in the flow behaviour of lubricants. Ph.D. thesis, Technion, Israel Institute of Technology, Haifa.
Harnoy, A. 1974 The effects of stress relaxation and cross stresses in lubricants with polymer additives. Proc. Int. Conf. C.N.R.S. Polymers Lubrication, Brest, France.
Harnoy, A. & Hanin, M. 1974 Second order, elastico-viscous lubricants in dynamically loaded bearings. A.S.L.E. Trans. 17, 166.Google Scholar
Horowitz, H. H. & Steidler, F. E. 1960 The calculated journal-bearing performance of polymer thickened lubricants. A.S.L.E. Trans. 3, 124.Google Scholar
Metzner, A. B., White, J. L. & Denn, M. M. 1966 Constitutive equations for viscoelastic fluids for short deformation periods and for rapidly changing flows: significance of the Deborah number. A.I.Ch.E. J. 12, 863.Google Scholar
Milne, A. A. 1957 A theory of rheodynamic lubrication for a Maxwell liquid. Proc. Conf. Lubricants Wear, Inst. Mech. Engrs, London.
Pearson, J. R. A. 1967 The lubrication approximation applied to non-Newtonian flow problems: a perturbation approach. In Non-Linear Partial Differential Equations (ed. W. F. Ames), p. 73. Academic.
Philippoff, W. 1968 Viscoelasticity and its application to lubrication. Trans. A.S.M.E., J. Lub. Tech. 90, 561.Google Scholar
Prager, W. 1961 An elementary discussion of definitions of stress rate. Quart. Appl. Math. 18, 403.Google Scholar
Reiner, M. 1964 The Deborah number. Physics To-day, 17, 62.Google Scholar
Reiner, M., Hanin, M. & Harnoy, A. 1969 An analysis of lubrication with elastico-viscous liquid. Israel J. Tech. 7, 273.Google Scholar
Rivlin, R. S. & Ericksen, J. L. 1955 Stress deformation relations for isotropic materials. J. Rat. Mech. Anal. 4, 323.Google Scholar
Walters, K. 1972 New concepts in theoretical and experimental rheology. Proc. Conf. Rheology of Lubricants, Nottingham.