Computing hydrodynamic pressure in mixed lubrication by modified Reynolds equation

Abstract

Nowadays, even with the available computing power, complete deterministic solutions of large or dynamically loaded bearings are not possible in acceptable amounts of computing time. Therefore, in order to model mixed lubrication conditions, the Reynolds equation is modified by the introduction of flow factors that take into account the roughness effects. Patir and Cheng proposed the most known model. In their model, flow factors are obtained from the statistical parameters of the surface roughness. The flow factors can also be computed from deterministic calculation on a sample of the studied surface or by using the homogenization technique on the same surface sample. In this article, three approaches are compared. Moreover, the influence of the surface deformation due to asperity contact over the flow factors is investigated.

Keywords

Mixed lubrication flow factors homogenization asperity deformation

Get full access to this article

View all access options for this article.

References

Tzeng

Saibel

. Surface roughness effect on slider bearing lubrication. STLE Trans 1967; 10: 334–338.

Christensen

. Stochastic models for hydrodynamics lubrication of rough surfaces. Int J Mech Eng 1970; 184(55): 1013–1022.

Patir

Cheng

. An average flow model for determining effects of three-dimensional roughness on partial hydrodynamic lubrication. ASME J Lubr Technol 1978; 100: 12–17.

Patir

Cheng

. An average flow model to lubrication between rough sliding surfaces. ASME J Lubr Technol 1979; 101: 220–230.

Peklenik

. New developments in surface characterization and measurement by means of random process analysis. Proc Instn Mech Engrs 1967; 182(3K): 108–126.

Tripp

. Surface roughness effects in hydrodynamic lubrication: the flow factor method. Trans ASME 1983; 105: 458–465.

. On the effects of roughness orientation—a mapping and double scale analysis of flow factors. J Tribol Trans ASME 1992; 114: 747–756.

Harp

Salant

. Inter-asperity cavitation and global cavitation in seals: an average flow analysis. Tribol Int 2002; 35: 113–121.

Meng

Cen

. On elastic deformation, inter-asperity cavitation and lubricant thermal effects on flow factors. Tribol Int 2009; 42: 260–274.

10.

Dragomir R, Bonneau D, Ragot P, et al. Pressure and shear flow factors calculation for orthotropic rough surfaces. In: Proceedings of ASME/STLE IJTC, San Diego, CA, 22–24 October 2007.

11.

Lunde

Tonder

. Pressure and shear flow in a rough hydrodynamic bearing flow factor calculation. J Tribol Trans ASME 1997; 119: 549–555.

12.

Bayada

Chambat

. New models in the theory of the hydrodynamic lubrication of rough surfaces. Trans ASME 1988; 110: 402–407.

13.

Bayada

Chambat

. Homogenization of the Stokes system in a thin ﬁlm ﬂow with rapidly varying thickness. Math Model Numer Anal 1989; 23(2): 205–234.

14.

Almqvist

Fabricius

Spencer

. Similarities and differences between the flow factor method by Patir and Cheng and homogenization. J Tribol Trans ASME 2011; 133: 031702–1 (5 pp).

15.

Tonder

. Simulation of 3-D random rough surface by 2-D digital filter and Fourier analysis. Int J Mach Tools Manuf 1992; 32: 83–90.

16.

Venner

Lubrecht

. Multilevel methods in lubrication. Tribology series, vol. 37 , Amsterdam: Elsevier, 2000.

17.

Kim

Cho

. The flow factors considering the elastic deformation for the rough surface with a non-Gaussian height distribution. Tribol Trans 2008; 51: 213–220.

18.

Sahlin

Larsson

Almqvist

. A mixed lubrication model incorporating measured surface topography: Part I – Theory of flow factors. Proc IMechE Part J: J Engineering Tribology 2010; 224: 335–351.

19.

Fatu

Hajjam

Bonneau

. Analysis of non-Newtonian and piezoviscous effects in dynamically loaded connecting-rod bearings. Proc IMechE Part J: J Engineering Tribology 2005; 219: 209–224.

20.

Bayada

Martin

Vazquez

. Micro-roughness effects in (elasto)hydrodynamic lubrication including a mass-flow preserving cavitation model. Tribol Int 2006; 39: 1707–1718.