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

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. For the case of pressure–viscosity dependence in the Stokes equation, a new Reynolds equation in the thin film limit has been proposed by Rajagopal and Szeri. However, these authors consider some additional simplifications. In the present work, avoiding these simplifications and starting from a Stokes equation with pressure 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.Moreover, the classical model, the one proposed by Rajagopal and Szeri and the here proposed one are simulated through the development of some numerical algorithms involving finite elements method, projected relaxation techniques, duality type numerical strategies and fixed point iteration techniques. Finally, several numerical tests are performed to carry out a comparative analysis among the different models.