Elrod-Adams cavitation model for a new nonlinear Reynolds equation in piezoviscous hydrodynamic lubrication

摘要

In previous studies, different cavitation models have been incorporated into the classical Reynolds equation in piezoviscous regimes. The advantages of the Elrod-Adams cavitation model compared with the Reynolds model have been demonstrated in this classical framework. Recently, a new nonlinear Reynolds equation was rigorously justified for lubricated line contact problems by introducing the piezoviscous Barus law into the departure Navier-Stokes equations before passing to the thin film limit. In addition, the corresponding nonlinear first order ordinary differential equation (ODE) has been proposed. In the present study, we incorporate the Elrod-Adams model for cavitation and we pose the free boundary problem associated with the nonlinear first order ODE, which involves a multivalued Heaviside operator for the relationship between the lubricant pressure and saturation. After analyzing the qualitative properties of the solution, we propose suitable numerical techniques for solving the problem as well as obtaining the lubricant pressure, saturation, and viscosity. Finally, we give some numerical results to illustrate the performance of the proposed numerical methods as well as comparisons with alternative models.