A good and accurate prediction of the elastohydrodynamic lubrication behaviour requires consideration of the constitutive equation for the lubricant. In particular, for applications involving synthetic oils or mineral oil with polymeric additives that exhibit shear-thinning behaviour, the use of an appropriate pressure-viscosity relationship for the lubricant is required to predict the EHL behaviour more accurately [1–3]. For this reason, this paper aims to emphasize the importance of implementing piezo-viscous models with accurate treatment methods in EHL applications. Due to the high pressure in an EHL contact, in fact, the elastic deformation of the surfaces and pressure dependence of viscosity play the pivotal role and in many applications, the lubricant exhibits a shear-thinning behaviour which significantly affects the film thickness [4–6]. The effects of different pressure–viscosity relationships, including the exponential model, the Roelands’ model and specifically, the Doolittle model are investigated and a generalized formulation that can efficiently treat shear-thinning fluids with provision for compressibility in the EHL contact is presented.
In the light of above facts, models for 1D and 2D EHL contacts for simulating the behaviour of the pressure distribution and the shape of the film thickness using a generalized Reynolds equation and shear-thinning fluids is developed. In particular for EHL 2D problem a more accurate full multigrid approach has been used and both the analysis is based upon the assumptions of isothermal condition. In this work, in fact, we show that the piezo-viscous rheology of the lubricant plays an important role in determining the value of pressure peaks. Pressure profiles and film shapes are showed and variations of the minimum and central film thickness with dimensionless parameters are also presented. It is found that the real pressure–viscosity behaviour predicted by the free-volume model yields a higher viscosity at the low-pressure area which results in a larger central film thickness. Therefore, due to use of the free-volume model, the presented results are more consistent with literature experimental observations and the Doolittle model effectively predicts the film thickness that closely matches experiments and properly characterizes the behaviour of shear-thinning lubricants.