Effects of non-Newtonian couple stresses on the squeeze film characteristics between two different spheres

Abstract

Based upon the Stokes micro-continuum theory, a study of the effects of non-Newtonian couple stresses upon the squeeze film characteristics considering different sphere-to-sphere geometries has been presented. The non-Newtonian squeeze-film Reynolds-type equation between two spheres with different ratios is derived to take account of the non-Newtonian effects of couple stresses arising from the lubricant blended with various additives. A closed-form solution for the film pressure, the load-carrying capacity, and the response time is then obtained. Compared with the corresponding Newtonian-lubricant case, the influence of non-Newtonian couple stresses provides an increase in the load capacity, and therefore lengthens the response time to prevent sphere-to-sphere contact. In all, the effects of non-Newtonian couple stresses on the squeeze film characteristics are more emphasized under lower squeeze-film heights with larger couple-stress parameters and radius ratios. When the value of the radius ratio approaches infinity, the present results provide a close agreement with the sphere—plane systems of Conway and Lee (Conway, D. and Lee, H. C. Impact of a lubricated surface by a sphere. ASME J. Lubr. Technol., 1975, vol. 97, pp. 613–615) and of Lin (Lin, J. R. Squeeze film characteristics between a sphere and a flat plate: couple stress fluid model. Comput. Struct., 2000, vol. 75, pp. 73–80), respectively.

Keywords

squeeze films sphere-to-sphere mechanisms micro-continuum theory non-Newtonian fluids couple stresses

Get full access to this article

View all access options for this article.

References

Pinkus

Sternlicht

Theory of hydrodynamic lubrication, 1961 (McGraw-Hill, New York).

Williams

J. A.

Engineering tribology, 1994 (Oxford University, New York).

Archibald

F. R.

Load capacity and time relations for squeeze films. Trans. ASME, 1965, 78, A231–A245.

Hays

D. F.

Squeeze films for rectangular plates. ASME J. Basic Eng., 1963, 85, 243–246.

Jones

A. F.

Wilson

S. D. R.

On the failure of lubrication theory in squeezing flow. ASME J. Lubr. Technol., 1975, 97, 101–104.

Fuller

D. D.

Theory and practice of lubrication for engineers, 1956 (John Wiley & Sons, Inc., New York).

Moore

D. F.

A review of squeeze films. Wear, 1965, 8, 245–263.

Murti

P. R. K.

Squeeze films in curved circular plates. ASME J. Lubr. Technol., 1975, 97, 650–652.

Gupta

J. L.

Vora

K. H.

Analysis of squeeze films between curved annular plates. ASME J. Lubr. Technol., 1980, 102, 48–50.

10.

Dowson

Modes of lubrication in human joints. In Proceedings of the Society of Mechanical Engineers, London, 1966, vol. 101, pp. 45–54.

11.

Hamrock

B. J.

Fundamentals of fluid film lubrication, 1994 (McGraw-Hill, New York).

12.

Conway

Lee

H. C.

Impact of a lubricated surface by a sphere. ASME J. Lubr. Technol., 1975, 97, 613–615.

13.

Stokes

V. K.

Couple stresses in fluids. Phys. Fluids, 1966, 9, 1709–1715.

14.

Ariman

Sylvester

N. D.

Microcontinuum fluid mechanics — a review. Int. J. Eng. Sci., 1973, 11, 905–930.

15.

Ariman

Sylvester

N. D.

Applications of micro-continuum fluid mechanics. J. Eng. Sci., 1974, 12, 273–293.

16.

Naduvinamani

N. B.

Hiremath

P. S.

Gurubasavaraj

Static and dynamic behaviour of squeeze-film lubrication of narrow porous journal bearings with coupled stress fluid. Proc. Instn Mech. Engrs Part J: J. Engineering Tribology, 2001, 215, 45–62.

17.

Lin

J. R.

Yang

C. B.

R. F.

Effects of couple stresses in the cyclic squeeze films of finite partial journal bearings. Tribol. Int., 2001, 34, 119–125.

18.

Bujurke

N. M.

Jayaraman

The influence of couple stresses in squeeze films, Int. J. Mech. Sci., 1982, 24, 369–376.

19.

Ramanaiah

Sarkar

Squeeze films and thrust bearings lubricated by fluids with couple stresses. Wear, 1978, 48, 309–316.

20.

Ramanaiah

Squeeze films between finite plates lubricated by fluids with couple stress. Wear, 1979, 54, 315–320.

21.

Bujurke

N. M.

Patil

H. P.

An analysis of squeeze film action in porous layer bearings. Wear, 1991, 145, 385–397.

22.

Lin

J. R.

Hung

C. R.

Combined effects of non-Newtonian couple stresses and fluid inertia on the squeeze film characteristics between a long cylinder and an infinite plate. Fluid Dyn. Res., 2007, 39, 616–631.

23.

Lin

J. R.

Squeeze film characteristics between a sphere and a flat plate: Couple stress fluid model, Comput. Struct., 2000, 75, 73–80.

24.

Lin

J. R.

Couple-stress effects on the squeeze film characteristics of hemispherical bearings with reference to synovial joints. Int. J. Appl. Mech. Eng., 1996, 1, 317–332.