Quantitative Analysis of Reynolds and Navier–Stokes Based Modeling Approaches for Isothermal Newtonian Elastohydrodynamic Lubrication

When simulating elastohydrodynamic lubrication, two main approaches are usually followed to predict the pressure and fluid film thickness distribution throughout the contact. The conventional approach relies on the Reynolds equation to describe the thin lubricant film, which is coupled to a Boussinesq description of the linear elastic deformation of the solids. A more accurate, yet a time-consuming method is the use of computational fluid dynamics in which the Navier–Stokes equations describe the flow of the thin lubricant film, coupled to a finite element solver for the description of the local contact deformation. This investigation aims at assessing both methods for different lubrication conditions in different elastohydrodynamic lubrication (EHL) regimes and quantify their differences to understand advantages and limitations of both methods. This investigation shows how the results from both approaches deviate for three scenarios: (1) inertial contributions (Re > 1), i.e., thick films, high speed, and low viscosity; (2) high shear stresses leading to secondary flows; and (3) large deformations of the solids leading to inaccuracies of the Boussinesq equation.