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Research Papers: Hydrodynamic Lubrication

A Mass-Conserving Complementarity Formulation to Study Lubricant Films in the Presence of Cavitation

[+] Author and Article Information
Matteo Giacopini, Antonio Strozzi

D.I.M.e.C—Dipartimento di Ingegneria Meccanica e Civile, Università degli Studi di Modena e Reggio Emilia, via Vignolese, 905/b, 41125 Modena, Italy

Mark T. Fowell

Department of Mechanical Engineering, Imperial College London, South Kensington Campus, Exhibition Road, London SW7 2AZ, UK

Daniele Dini1

Department of Mechanical Engineering, Imperial College London, South Kensington Campus, Exhibition Road, London SW7 2AZ, UKd.dini@imperial.ac.uk

1

Corresponding author.

J. Tribol 132(4), 041702 (Sep 23, 2010) (12 pages) doi:10.1115/1.4002215 History: Received August 14, 2009; Revised July 14, 2010; Published September 23, 2010; Online September 23, 2010

A new mass-conserving formulation of the Reynolds equation is developed using the concept of complementarity. This new method overcomes the drawbacks previously associated with the use of such complementarity formulations for the solution of cavitation problems in which reformation of the liquid film occurs. Validation against a number of analytical and semi-analytical formulations, for a variety of problems including textured bearings and squeeze film dampers, is performed. The current formulation is shown to be in very good agreement with existing analytical and numerical mass-conserving solutions.

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Copyright © 2010 by American Society of Mechanical Engineers
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Figures

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Figure 1

Schematics of (a) convergent/divergent (C-D) and (b) divergent/convergent (D-C) bearing undergoing pure sliding motion

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Figure 2

(a) Comparison between the pressure distributions for case 1 (Table 1) produced by the methods of Bonneau and Hajjam (17), Kostreva (8) and Oh (9), and the authors’ method (Giacopini ). (b) Comparison between the pressure distributions for case 2 (Table 1) produced by the method of Bonneau and Hajjam (17), Kostreva (8) and Oh (9), and the authors’ method (Giacopini ). (c) Comparison between the pressure distributions for case 3 (Table 1) produced by the method of Bonneau and Hajjam (17), Kostreva (8) and Oh (9), and the authors’ method (Giacopini ).

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Figure 3

Schematic of a parallel bearing containing a single microtexture pocket, positioned toward the inlet

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Figure 4

(a) Comparison between the pressure distributions for pocketed bearing case 1 (Table 2) produced by the methods of Olver (36) and the authors’ method (Giacopini ). (b) Comparison between the pressure distributions for pocketed bearing case 2 (Table 2) produced by the methods of Olver (36) and the authors’ method (Giacopini ).

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Figure 5

Schematic of a converging bearing containing a single microtexture pocket, positioned toward the inlet

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Figure 6

Comparison between the pressure distributions for convergent pocketed bearing (Table 3) produced by the methods of Fowell (37) and the authors’ method (Giacopini )

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Figure 7

Schematic of a squeeze film damper

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Figure 8

(a) Comparison between the lengths of the cavitated region for squeeze film bearing case 1 (Table 4) produced by the methods of Optasanu and Bonneau (38) and the authors’ method (Giacopini ). (b) Comparison between the lengths of the cavitated region for squeeze film bearing case 2 (Table 4) produced by the methods of Optasanu and Bonneau (38) and the authors’ method (Giacopini ).

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Figure 9

(a) Length of the cavitated region for squeeze film bearing case 1 (Table 4) produced by the authors’ method (Giacopini ), time and mesh dependence as detailed in Table 5. (b) Density of the mixture at the center of the two plates for squeeze film bearing case 1 (Table 4) produced by the authors’ method (Giacopini ), time and mesh dependence as detailed in Table 5.

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