A new more consistent Reynolds model for piezoviscous hydrodynamic lubrication problem in line contact devices

Guy Bayada (1) , Begonia Cid (2) , Guillermo Garcia (2) , Carlos Vazquez (3)

1 ICJ - Institut Camille Jordan
2 matematica aplicada
3 departemento matematicas

Hydrodynamic lubrication problems in piezoviscous regime are usually modeled by the classical Reynolds equation combined with a suitable law for the pressure dependence of viscosity. By taking into account the pressure-viscosity depen- dence in the Stokes equation and to derive the Reynolds equation in the thin film limit, a new model has been proposed by Rajagopal & Szeri. However, these authors consider some additional simplifications. In the present work, avoiding these simplifications and starting from a Stokes equation with pres- sure dependence of viscosity through Barus law, a new Reynolds model for line contact lubrication problems is deduced, in which the cavitation phenomenon is also taken into account. Thus, the new complete model consists of a nonlinear free boundary problem associated to the proposed new Reynolds equation.

Domaines: Modélisation et simulation; Equations aux dérivées partielles [math.AP]; Analyse numérique [math.NA]

Guy Bayada, Begonia Cid, Guillermo Garcia, Carlos Vazquez. A new more consistent Reynolds model for piezoviscous hydrodynamic lubrication problem in line contact devices. Applied Mathematical Modelling, 2013, 10.1016/j.apm.2013.03.072. ⟨10.1016/j.apm.2013.03.072⟩. ⟨hal-00822675⟩