Fluid film lubrication in the presence of cavitation: a mass-conserving two-dimensional formulation for compressible, piezoviscous and non-Newtonian fluids

A mass-conserving formulation of the Reynolds equation has been recently proposed by some of the authors to deal with cavitation in lubricated contacts [1]. This formulation, based on the mathematical derivation of a linear complementarity problem (LCP), 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. In the present paper, the methodology favoured in [1], already successfully applied to solve textured bearing and squeeze problems in the presence of cavitation in a one dimensional domain for incompressible fluids, has been extended to include the effects of fluid compressibility, piezoviscosity and the non-Newtonian fluid behaviour and it has been also applied to the analysis of two dimensional problems. The evolution of the cavitated region and the contact pressure distribution are studied for a number of different configurations which can be considered as relevant benchmarks. In particular, some of the results obtained with the proposed scheme are critically analysed and compared with the predictions obtained using alternative formulations, including full CFD calculations. The stability of the proposed algorithm and its flexibility in terms of implementation of different models for compressibility, piezoviscosity and non-Newtonian behaviour are highlighted.