Research Papers: Hydrodynamic Lubrication

A Mass-Conserving Algorithm for Dynamical Lubrication Problems With Cavitation

[+] Author and Article Information
Roberto F. Ausas

 Centro Atómico Bariloche and Instituto Balseiro, 8400 Bariloche, Argentinarfausas@gmail.com

Mohammed Jai

Mathématiques, INSA de Lyon, CNRS-UMR 5208, Batiment Leonard de Vinci, F-69621 Villeurbanne, Francemohammed.jai@insa-lyon.fr

Gustavo C. Buscaglia

ICMC, Universidade de São Paulo, 13560-970 São Carlos, São Paulo, Brazilgustavo.buscaglia@icmc.usp.br

J. Tribol 131(3), 031702 (Jun 02, 2009) (7 pages) doi:10.1115/1.3142903 History: Received September 03, 2008; Revised April 27, 2009; Published June 02, 2009

A numerical algorithm for fully dynamical lubrication problems based on the Elrod–Adams formulation of the Reynolds equation with mass-conserving boundary conditions is described. A simple but effective relaxation scheme is used to update the solution maintaining the complementarity conditions on the variables that represent the pressure and fluid fraction. The equations of motion are discretized in time using Newmark’s scheme, and the dynamical variables are updated within the same relaxation process just mentioned. The good behavior of the proposed algorithm is illustrated in two examples: an oscillatory squeeze flow (for which the exact solution is available) and a dynamically loaded journal bearing. This article is accompanied by the ready-to-compile source code with the implementation of the proposed algorithm.

Copyright © 2009 by American Society of Mechanical Engineers
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Figure 1

One dimensional system considered for the squeeze-flow example

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Figure 2

(a) Film thickness H(t) used in the oscillatory squeeze flow example, (b) right cavitation boundary Σ(t) for the mass-conserving Elrod–Adams model, comparing the numerical result to the exact solution, and (c) same as Fig. 2 for the nonmass-conserving Reynolds model. Notice the detail in Figs.  22 showing the staircased shape of the numerical cavitation boundary.

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Figure 3

Schematic representation of the journal bearing and the computational domain considered

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Figure 4

Evolution with time of the journal’s center, applied loads WXa, WYa and load capacity WX and WY (changing its sign to ease the comparison with WXa and WYa)

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Figure 5

Detail of the evolution with time of the applied loads WXa, WYa and load capacity WX and WY (changing its sign to ease the comparison with WXa and WYa

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Figure 6

Convergence study: evolution with time of the maximum value of the pressure

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Figure 7

Convergence study: evolution with time of the eccentricity



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