Guillermo E. Morales-Espejel

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

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.

Stabilized fully-coupled finite elements for elastohydrodynamic lubrication problems

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 contacts 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.

A Numerical Study of Friction in Isothermal EHD Rolling-Sliding Sphere-Plane Contacts With Spinning

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 FEM approach. Friction was thereafter investigated using 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. 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 consequences on the friction reduction that is observed in presence of spinning. They are expected to further decrease friction in real situations due to shear heating.Copyright

A Two-Phase Flow Approach for the Outlet of Lubricated Line Contacts

In the classical Reynolds equation-based modeling of lubrication, the exit area is only considered through a pressure boundary condition which fails to predict the remaining amount of lubricant on each moving surface after the film rupture. A two-phase flow model using the Navier-Stokes equations and a diffuse interface approach is developed to analyze the lubricant behavior at the exit of rolling and sliding lubricated line contacts. After physical and numerical descriptions of the two-phase flow model, results are compared with experimental data from the literature. Good agreements are found concerning pressure profiles and meniscus exit abscissas. The model is then used to study in detail the flow behavior at the exit for different surface tensions. It is shown that when surface tension effects are important, recirculation areas occur downstream the air/oil meniscus. Sliding effects on fluid distribution are then investigated. Finally, an analytical approach is proposed, as a synthesis of the numerical results.

Numerical investigation of the use of machinery low-viscosity working fluids as lubricants in elastohydrodynamic lubricated point contacts

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.

A finite element approach of the fully coupled elastohydrodynamic problem

Up to now, most of the numerical works dealing with the modelling of the isothermal elastohydrodynamic problem were based on a weak coupling resolution of the Reynolds and elasticity equations (semi-system approach). The latter were solved separately using 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 non-linear 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 complexity is the same as for classical algorithms, but with an improved convergence rate, a reduced size of the problem and a regular sparse Jacobian matrix. This method is applied to the case of a Generalized Newtonian lubricant using a powerful shear-thinning model. The results are compared with experimental data.Copyright