Journal of Engineering Mathematics

, Volume 83, Issue 1, pp 57–79 | Cite as

A new cavitation model in lubrication: the case of two-zone cavitation

  • Gustavo C. Buscaglia
  • Ionel Ciuperca
  • Eric Dalissier
  • Mohammed Jai
Article
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Abstract

A generalization of the Elrod–Adams model of cavitation in lubricated devices is proposed, such that the translation velocity \(V\) for the saturation field \(\theta \) can be given any value between \(S/2\) and \(S\), with \(S\) being the relative speed of the surfaces. The lack of uniqueness of the classical model when \(V\ne S/2\) is explained and a suitable supplementary condition is proposed to fix this issue. The new model is rigorously analyzed, though in the simplified mathematical setting of a one-dimensional problem with a single pressurized region. The main result states the existence of a unique solution globally in time, unless of course the cavitation boundary leaves the domain or disappears. A few preliminary numerical examples are included to illustrate the model.

Keywords

Cavitation Hydrodynamic lubrication Piston ring  Reynolds equation Tribology 
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Notes

Acknowledgments

The authors acknowledge partial support from FAPESP (Brazil), CNPq (Brazil), and Renault (France).

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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  • Gustavo C. Buscaglia
    • 1
  • Ionel Ciuperca
    • 2
  • Eric Dalissier
    • 3
  • Mohammed Jai
    • 3
  1. 1.ICMCUniversidade de São PauloSao CarlosBrazil
  2. 2.Mathématiques, CNRS-UMR 5208Université Lyon 1, Institut Camille JordanVilleurbanne-CedexFrance
  3. 3.MathématiquesVilleurbanneFrance

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