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Research Papers: Hydrodynamic Lubrication

A New Approach for Studying Cavitation in Lubrication

[+] Author and Article Information
Andreas Almqvist

Associate Professor
Machine Elements,
Luleå University of Technology,
Luleå 97187, Sweden
e-mail: andreas.almqvist@ltu.se

John Fabricius

Assistant Professor
Mathematics,
Luleå University of Technology,
Luleå 97187, Sweden
e-mail: john.fabricius@ltu.se

Roland Larsson

Professor
Machine Elements,
Luleå University of Technology,
Luleå 97187, Sweden
e-mail: roland.larsson@ltu.se

Peter Wall

Professor
Mathematics,
Luleå University of Technology,
Luleå 97187, Sweden
e-mail: peter.wall@ltu.se

Contributed by the Tribology Division of ASME for publication in the JOURNAL OF TRIBOLOGY. Manuscript received June 17, 2013; final manuscript received October 24, 2013; published online November 20, 2013. Assoc. Editor: Daniel Nélias.

J. Tribol 136(1), 011706 (Nov 20, 2013) (6 pages) Paper No: TRIB-13-1121; doi: 10.1115/1.4025875 History: Received June 17, 2013; Revised October 24, 2013

The underlying theory, in this paper, is based on clear physical arguments related to conservation of mass flow and considers both incompressible and compressible fluids. The result of the mathematical modeling is a system of equations with two unknowns, which are related to the hydrodynamic pressure and the degree of saturation of the fluid. Discretization of the system leads to a linear complementarity problem (LCP), which easily can be solved numerically with readily available standard methods and an implementation of a model problem in matlab code is made available for the reader of the paper. The model and the associated numerical solution method have significant advantages over today's most frequently used cavitation algorithms, which are based on Elrod–Adams pioneering work.

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References

Giacopini, M., Fowell, M. T., Dini, D., and Strozzi, A., 2010, “A Mass-Conserving Complementarity Formulation to Study Lubricant Films in the Presence of Cavitation,” J. Tribol., 132(4), p. 041702. [CrossRef]
Bayada, G., Martin, S., and Vazquez, C., 2005, “Two-Scale Homogenization of a Hydrodynamic Elrod-Adams Model,” Asymptotic Anal., 44(1), pp. 75–110.
Bayada, G., Martin, S., and Vázquez, C., 2005, “An Average Flow Model of the Reynolds Roughness Including a Mass-Flow Preserving Cavitation Model,” J. Tribol., 127(4), pp. 793–802. [CrossRef]
Elrod, H. G., 1981, “A Cavitation Algorithm,” J. Tribol., 103, pp. 350–354.
Bayada, G., Talibi, M. E. A., and Hadi, K. A., 2007, “Existence and Uniqueness for a Non-Coercive Lubrication Problem,” J. Math. Anal. Appl., 327, pp. 585–610. [CrossRef]
Cottle, R. W., Pang, J. S., and Stone, R. E., 2009, “The Linear Complementarity Problem,” Report No. 60, SIAM, Philadelphia, PA.
Elrod, H. G., and Adams, M. L., 1975, “A Computer Program for Cavitation and Starvation Problems,” Cavitation and Related Phenomena in Lubrication, D.Dowson, M.Godet, and C. M.Taylor, eds., Mechanical Engineering Publications, ITC, Sugar Grove, IL, pp. 37–43.
Vijayaraghavan, D., and Keith, T. G., Jr., 1989, “Development and Evaluation of a Cavitation Algorithm,” STLE Tribol. Trans., 32(2), pp. 225–233. [CrossRef]
Bertocchi, L., Dini, D., Giacopini, M., Fowell, M. T., and Baldini, A., 2013, “Fluid Film Lubrication in the Presence of Cavitation: A Mass-Conserving Two-Dimensional Formulation for Compressible, Piezoviscous and Non-Newtonian Fluids,” Tribol. Int., 67, pp. 61–71. [CrossRef]
Sahlin, F., Almqvist, A., Larsson, R., and Glavatskih, S., 2007, “A Cavitation Algorithm for Arbitrary Lubricant Compressibility,” Tribol. Int., 40(8), pp. 1294–1300. [CrossRef]
Almqvist, A., Spencer, A., and Wall, P., 2013, “Matlab Routines Solving a Linear Complementarity Problem Appearing in Lubrication With Cavitation,” http://www.mathworks.com/matlabcentral/fileexchange/41484
Olver, A. V., Fowell, M. T., Spikes, H. A., and Pegg, I. G., 2006, “‘Inlet Suction’, a Load Support Mechanism in Non-Convergent, Pocketed, Hydrodynamic Bearings,” Proc. Inst. Mech. Eng., Part J: J. Eng. Tribol., 220(2), pp. 105–108. [CrossRef]
Fowell, M., Olver, A. V., Gosman, A. D., Spikes, H. A., and Pegg, I., 2007, “Entrainment and Inlet Suction: Two Mechanisms of Hydrodynamic Lubrication in Textured Bearings,” J. Tribol., 129(2), pp. 336–347. [CrossRef]
Evans, L. C., 2010, Partial Differential Equations, 2nd ed., Vol. 19 of Graduate Studies in Mathematics, American Mathematical Society, Providence, RI.

Figures

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Fig. 1

Schematic illustration of the modeled pocket bearing

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Fig. 2

The analytical and the numerical pressure solutions, for the pocket bearing with input parameters given Table 1, β=5·108 and N = 512

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Fig. 3

Influence of the bulk modulus on fluid film pressure

Grahic Jump Location
Fig. 4

Double parabolic slider. Geometry (left), pressure distributions (right). pε are numerical solutions of Eq. (36) and p0 is the numerical solution of (28). All solutions are obtained with N = 128.

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