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

Abstract

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 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 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 (cfr Fig. 12): 1. Inertial Contributions (Re > 1), i.e. thick films, high speed, low viscosity; 2. High shear stresses leading to secondary flows; 3. Large deformations of the solids leading to inaccuracies of the Boussinesq equation.

A review of advances in tribology in 2020–2021

“…Reynolds and Navier-Stokes based modelling approaches are the two main approaches to predict the pressure and fluid film thickness distribution throughout the contact. Scurria et al [852] assessed both methods for different lubrication conditions in a wide EHL conditions and quantified their differences to understand advantages and limitations of both methods. They conclude that as shown in Fig.…”

“…51, for the cases with low loads and relatively high velocity of the surfaces, loss of accuracy is exhibited due to the lack of inertial contributions in the Reynolds equation; for quasi-rigid EHL cases with high loads, high shear stresses approach the value of the singular shear stress criterion in the central area of the contact and have a mild impact with respect to accuracy; for highly loaded soft EHL cases, the Reynolds based method has the loss of accuracy due to loss of accuracy Fig. 51 Main causes of the discrepancy between the RBM and the NS approach [852]. Reproduced with permission from Ref.…”

Sensitivity of TEHL Simulations to the Use of Different Models for the Constitutive Behaviour of Lubricants

“…Hajishafiee et al [29] extended Hartinger's model to include a linear elastic structural model for the solid body as well as a robust and two-way FSI coupling model, which is more appropriate for high loads. Scurria et al [30] compared the Reynolds equation and the full Navier-Stokes equation for EHL contact under isothermal conditions for Newtonian lubricants. They observed that the inertia term influenced the accuracy of the Reynolds solution, especially at low loads and relatively high speeds of rotation.…”

A quantitative analysis of double-sided surface waviness on TEHL line contacts

“…The classic Reynolds equation is obtained by averaging over film thickness and can be considered as a reduced-order model in N-1 dimensions of the N-dimensional Navier-Stokes equations. It has undoubtedly proven its worth in terms of both accuracy and computational efficiency for isothermal EHL [45,46]. On the other hand, TEHL involves compressive and shear heating in the lubricant film, as well as convective and conductive thermal transport through the lubricant film and the solid bodies.…”

“…The differences between both methods are reported to depend on the entrainment speed, Slide-to-Roll Ratio (SRR), and load. Scurria et al [46] compared the solutions of Reynolds and Navier-Stokes for EHL contact with isothermal and Newtonian lubricants. They observed that neglecting the inertia term influenced the accuracy of the Reynolds solution at low load and relatively high speeds of rotation [49].…”