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Lubrication of machine elements such as gears and bearings appears to be essential for the good functioning of a mechanical system. In many applications, the pressure generated within tribological interfaces is high enough to induce elastic deformations at the surface of the contacting bodies. This lubrication regime is known as ElastoHydroDynamic (EHD) Lubrication. It involves a strong coupling between fluid mechanics, solid mechanics and lubricant rheology which makes the problem highly non-linear. So far, most of the numerical studies of lubricated contacts were carried out by using finite difference1, 2 or finite volume3 methods. More recently, CFD4 approach has been proposed to solve Navier-Stokes equations. The use of finite elements was limited to the case of journal bearings operating under hydrodynamic regime5, 6. In this work, we present a new approach for the numerical study of EHD circular contact using the finite element method (FEM) to solve the Reynolds equation, Boussinesq’s theory to calculate the elastic deformation of the surfaces and various physical laws to account the lubricant rheological behavior (WLF, Doolittle, Carreau). The advantage of choosing FEM is the availability of finite elements packages which permits to reduce the time spent in implementation and adapting the method to tribological applications. We use a multiphysics FEM software to solve the EHD circular contact and to obtain numerical results under broader operating conditions than those imposed during experiments. To reduce calculation time, we introduced multigrid method for solving the Reynolds equation and multi-integration technique for the elastic problem.

So far, most of the numerical studies concerning elastohydrodynamic point contact lubrication have been realized using finite differences. This paper describes a finite element approach for the modelling of both, thick and thin film lubrication in circular contacts under isothermal elastohydrodynamic regime. Multigrid techniques are used to accelerate the convergence and reduce calculation time. The use of the finite element method (FEM) offers two advantages: first, the existence of high level ready-to-use Finite Element commercial software which reduces the time spent in implementing the method and second, the easier adaptability to different and various physical models such as lubricant rheology, starvation effects, thermal effects, non-Newtonian behaviour, etc. The numerical model is presented in detail and an example of its adaptation taking into account non-Newtonian effects is shown. Finally, a comparison is made between Newtonian and non-Newtonian solutions, exhibiting differences obtained when using both models, especially at high shear rates where the film thickness and the friction coefficients are overestimated by a Newtonian approach.

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.

This work presents a model for elastohydrodynamic (EHD) lubrication problems. A finite element full-system approach is employed. The hydrodynamic and elastic problems are solved simultaneously which leads to fast convergence rates. The free boundary problem at the contact’s exit is handled by a penalty method. For highly loaded contacts, the standard Galerkin solution of Reynolds equation exhibits an oscillatory behaviour. The use of artificial diffusion techniques is proposed to stabilize the solution. This approach is then extended to account for non-Newtonian lubricant behaviour and thermal effects. Artificial diffusion procedures are also introduced to stabilize the solution at high loads.

This paper presents a numerical investigation of the local behavior of highly loaded thermal elastohydrodynamic contacts. The study is a continuation to a previous work of the authors where it was found that neglecting the dependence of lubricants' thermal properties on pressure and temperature leads to an underestimation of friction coefficients under high sliding regime. In this work, the local phenomena behind these observations are investigated. The results suggest that a redistribution of heat from the center of the contact towards the environment is taking place, leading to globally lower temperatures inside the contact, which leads to higher friction coefficients

This study proposes a numerical investigation of the potential use of machinery working fluids as lubricants in contacts operating under an elastohydrodynamic regime. These fluids are usually of very low viscosity and pressure–viscosity dependence. This is why, unmixed with oil, they have been of little interest for the tribological community. Hence, their rheological properties are poorly known. In fact, these are restricted to a narrow range of conditions compared to the range of interest in EHL applications. This is why some measurements are carried out in order to determine both the viscosity and density of these uncommon lubricants. Besides, their viscosity being low, high-mean entrainment speeds are required for a sufficiently thick lubricant film to build up. This leads to an important thermal dissipation within the contact. Thermal effects are included in the analysis in order to make the estimation of film thicknesses and friction coefficients in these contacts as accurate as possible. Results are discussed in the light of the peculiar properties of machinery low-viscosity working fluids.

The classical ElastoHydroDynamic (EHD) theory assumes a Newtonian lubricant and an isothermal operating regime. In reality, lubricating oils do not behave as perfect Newtonian fluids. Moreover, in most operating conditions of an engineering system, especially at high speeds, thermal effects are important and temperature can no longer be considered as constant throughout the system. This is one reason why there has always been a gap between numerical results and experimental data. This paper aims to show that this gap can be reduced by taking into consideration the heat generation that takes place in the contact and using appropriate rheological models. For this, a unique thermal ElastoHydrodynamic lubrication model is developed for both Newtonian and non-Newtonian lubricants. Pressure, film thickness and traction results are then compared to their equivalent isothermal results and experimental data. The agreement between thermal calculations and experiments reveals the necessity of considering thermal effects in EHD models.

This paper presents a study of the spinning influence on film thickness and friction in EHL circular contacts under isothermal and fully flooded conditions. Pressure and film thickness profiles are computed with an original full-system finite element approach. Friction was thereafter investigated with the help of a classical Ree–Eyring model to calculate the longitudinal and transverse shear stresses. An analysis of both the velocity and shear stress distributions at every point of the contact surfaces has allowed explaining the fall of the longitudinal friction coefficient due to the occurrence of opposite shear stresses over the contact area. Moreover in the transverse direction spinning favors large shear stresses of opposite signs, decreasing the fluid viscosity by non-Newtonian effects. These effects have direct and coupled consequences on the friction reduction that is observed in the presence of spinning. They are expected to further decrease friction in real situations due to shear heating.

The aim of this paper is to study the effects of pressure and temperature dependence of a conventional lubricant's thermal properties on the behaviour of heavily loaded thermal elastohydrodynamic lubrication (TEHL) contacts. For this purpose, a typical mineral oil (Shell T9) is selected and the dependence of its transport properties on pressure and temperature is investigated. Appropriate models are then developed for these dependencies. The latter are included in a TEHL solver in order to investigate their effect on the behaviour of circular EHD contacts. The results reveal the necessity of a thermal analysis including the pressure and temperature dependence of thermal properties for a good estimation of film thicknesses and mostly traction coefficients in circular EHD contacts operating under severe conditions. Numerical results are compared with experiments, showing a very good agreement over the considered ranges. This thorough validation of a thermal EHL framework for the calculation of film thickness and friction offers a previously unavailable opportunity to investigate the effects of variations in material properties.