A Full-System Approach of the Elastohydrodynamic Line/Point Contact Problem

Abstract

The solution of the elastohydrodynamic lubrication (EHL) problem involves the simultaneous resolution of the hydrodynamic (Reynolds equation) and elastic problems (elastic deformation of the contacting surfaces). Up to now, most of the numerical works dealing with the modeling of the isothermal EHL problem were based on a weak coupling resolution of the Reynolds and elasticity equations (semi-system approach). The latter were solved separately using iterative schemes and a finite difference discretization. Very few authors attempted to solve the problem in a fully coupled way, thus solving both equations simultaneously (full-system approach). These attempts suffered from a major drawback which is the almost full Jacobian matrix of the nonlinear system of equations. This work presents a new approach for solving the fully coupled isothermal elastohydrodynamic problem using a finite element discretization of the corresponding equations. The use of the finite element method allows the use of variable unstructured meshing and different types of elements within the same model which leads to a reduced size of the problem. The nonlinear system of equations is solved using a Newton procedure which provides faster convergence rates. Suitable stabilization techniques are used to extend the solution to the case of highly loaded contacts. The complexity is the same as for classical algorithms, but an improved convergence rate, a reduced size of the problem and a sparse Jacobian matrix are obtained. Thus, the computational effort, time and memory usage are considerably reduced.

An adaptive finite element procedure for fully-coupled point contact elastohydrodynamic lubrication problems

“…Note that the equivalent elastic surface contains the total elastic properties of the original contact surfaces, and hence the solution will define the total elastic deformation of both contacting surfaces [2,21].…”

“…where H 0 is a central offset film thickness and D is the elastic deformation [1,21] (see Section 2.2).…”

“…In [21] it is demonstrated that a geometry of size 60 × 60 × 60 is sufficiently large to provide accurate solutions for this non-dimensional model.…”

“…Habchi et al [20][21][22] also used a fully-coupled approach to solve the EHL problems. This technique is different however since it replaced the half-space solution method with the direct finite element approximation of the linear elasticity equation on a finite contact domain.…”

The Effect of DLC Coating Thickness on Elstohydrodynamic Friction

“…The temperature increase in the lubricant film would reduce the viscosity and thereby reduce the coefficient of friction. In a more recent study [6], the present authors used a more advanced and thoroughly validated [5,[20][21][22] 3D numerical model to predict the effect of thin insulating layers on full film elastohydrodynamic (EHD) friction to be compared with experimental measurements. The presented simulations, validated by experiments, showed that applying a thin diamond-like carbon coating to metal surfaces creates an insulating effect that, due to the increased liquid lubricant film temperature at the center of the contact, locally reduces lubricant viscosity and thus friction.…”