Wassim Habchi

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.

High surface area electrodes in ionic polymer transducers: Numerical and experimental investigations of the electro-chemical behavior

Ionomeric polymer transducer (IPT) is an electroactive polymer that has received considerable attention due to its ability to generate large bending strain (>5%) and moderate stress at low applied voltages (±2 V). Ionic polymer transducers consist of an ionomer, usually Nafion, sandwiched between two electrically conductive electrodes. A novel fabrication technique denoted as the direct assembly process (DAP) enabled controlled electrode architecture in ionic polymer transducers. A DAP built transducer consists of two high surface area electrodes made of electrically conducting particles uniformly distributed in an ionomer matrix sandwiching an ionomer membrane. The purpose of this paper is to investigate and simulate the effect of these high surface area particles on the electro-chemical response of an IPT. Theoretical investigations as well as experimental verifications are performed. The model used consists of a convection-diffusion equation describing the chemical field as well as a Poisson equation d...

A Film Thickness Correction Formula for Double-Newtonian Shear-Thinning in Rolling EHL Circular Contacts

Lubricants which contain a polymeric thickener will often display a second Newtonian plateau in measured flow curves. Like other manifestations of shear-dependent viscosity, this shear response will lead to an inaccurate prediction when the classical film-thickness formulas are employed. A correction formula has been developed from numerical experiments for a range of parameters of the double-Newtonian modified Carreau equation. The parameters of this shear-thinning model were selected from measurements for real lubricants obtained in Couette viscometers and a capillary viscometer. In addition, a full EHL film thickness formula has been derived from the same numerical experiments. The correction formula and the full formula were successfully validated using published film thickness data and published viscosity data for an EHL reference liquid, a polymer solution. Clearly, viscometer measurements of shear-dependent viscosity which contain the inflection leading to the second Newtonian are essential for a film-thickness calculation when a high-molecular-weight component of the lubricant is present.

Comment on “History, Origins and Prediction of Elastohydrodynamic Friction” by Spikes and Jie

Progress in the classical field of EHL has for decades been paralyzed by the assumption that shear thinning should be indistinguishable from the shear dependence of the viscosity of a liquid heated by viscous dissipation and that the parameters of this simple shear dependence can be obtained from the shape of a friction curve. In the last few years, by abandoning this assumption and employing real viscosity measured with viscometers, there has been revolutionary progress in predicting film thickness and friction. Now, Spikes and Jie conclude that the previous assumption has as much merit as the use of viscosity measured in viscometers. This suggestion may be popular among those who wish to ignore viscometer measurements in favor of extracting properties from friction curves. However, within the subject article, there are numerous misstatements of fact and misrepresentations by omission, and the recent progress using real viscosity is not acknowledged. The debate has degenerated into a friction curve fitting competition which is not helpful. The great progress of the last few years would not have been possible using the concepts and methods espoused in this article.

Biologically inspired highly efficient buoyancy engine

Undersea distributed networked sensor systems require a miniaturization of platforms and a means of both spatial and temporal persistence. One aspect of this system is the necessity to modulate sensor depth for optimal positioning and station-keeping. Current approaches involve pneumatic bladders or electrolysis; both require mechanical subsystems and consume significant power. These are not suitable for the miniaturization of sensor platforms. Presented in this study is a novel biologically inspired method that relies on ionic motion and osmotic pressures to displace a volume of water from the ocean into and out of the proposed buoyancy engine. At a constant device volume, the displaced water will alter buoyancy leading to either sinking or floating. The engine is composed of an enclosure sided on the oceans end by a Nafion ionomer and by a flexible membrane separating the water from a gas enclosure. Two electrodes are placed one inside the enclosure and the other attached to the engine on the outside. The semi-permeable membrane Nafion allows water motion in and out of the enclosure while blocking anions from being transferred. The two electrodes generate local concentration changes of ions upon the application of an electrical field; these changes lead to osmotic pressures and hence the transfer of water through the semi-permeable membrane. Some aquatic organisms such as pelagic crustacean perform this buoyancy control using an exchange of ions through their tissue to modulate its density relative to the ambient sea water. In this paper, the authors provide an experimental proof of concept of this buoyancy engine. The efficiency of changing the engines buoyancy is calculated and optimized as a function of electrode surface area. For example electrodes made of a 3mm diameter Ag/AgCl proved to transfer approximately 4mm3 of water consuming 4 Joules of electrical energy. The speed of displacement is optimized as a function of the surface area of the Nafion membrane and its thickness. The 4mm3 displaced volume obtained with the Ag/AgCl electrodes required approximately 380 seconds. The thickness of the Nafion membrane is 180μm and it has an area of 133mm3.

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.

Effect of lubricant rheology on friction in coated elastohydrodynamic lubricated contacts

This work investigates the effect of lubricant rheology on friction in coated elastohydrodynamic contacts. Two lubricants with relatively different properties are selected and two coating configurations are considered. The first coating type consists of a soft material with a low thermal inertia while the second is a hard material with a high thermal inertia. The former is known to decrease friction while the latter increases it compared to uncoated contacts. The original expectation was that the lubricant with higher P–T dependence of viscosity would exhibit higher relative friction deviation from the uncoated case. It turned out that this is only true in the linear and thermoviscous friction regimes at low and high slide-to-roll ratios, respectively.

An Exact and General Model Order Reduction Technique for the Finite Element Solution of Elastohydrodynamic Lubrication Problems

This work presents an exact and general model order reduction (MOR) technique for a fast finite element resolution of elastohydrodynamic lubrication (EHL) problems. The reduction technique is based on the static condensation principle. As such, it is exact and it preserves the generality of the solution scheme while reducing the size of its corresponding model and, consequently, the associated computational overhead. The technique is complemented with a splitting algorithm to alleviate the hurdle of solving an arising semidense matrix system. The proposed reduced model offers computational time speed-ups compared to the full model ranging between a factor of at least three and at best 15 depending on operating conditions. The results also reveal the robustness of the proposed methodology which allows the resolution of very highly loaded contacts with Hertzian pressures reaching several GPa. Such cases are known to be a numerical challenge in the EHL literature. [DOI: 10.1115/1.4035154]

Coupling Strategies for Finite Element Modeling of Thermal Elastohydrodynamic Lubrication Problems

This paper investigates coupling strategies for finite element modeling (FEM) of thermal elastohydrodynamic lubrication (TEHL) problems. The TEHL problem involves a strong coupling between several physics: solid mechanics, fluid mechanics, and heat transfer. Customarily, this problem is split into two parts (elastohydrodynamic (EHD) and thermal) and the two problems are solved separately while an iterative procedure is established between their respective solutions. This weak coupling strategy involves a loss of information, as each problem is not made intimately aware of the evolution of the other problem’s solution during the resolution procedure. This typically leads to slow convergence rates. The current work offers a full coupling strategy for the TEHL problem, i.e., both the EHD and thermal parts are solved simultaneously in a monolithic system. The system of equations is generated from a finite element discretization of the governing field variables: hydrodynamic pressure, solids elastic deformation, and temperature. The full coupling strategy prevents any loss of information during the resolution procedure leading to very fast convergence rates (solution is attained within a few iterations only). The performance of the full coupling strategy is compared to that of different weak coupling strategies. Out of simplicity, only steady-state line contacts are considered in this work. Nevertheless, the proposed methodology, results, and findings are of a general nature and may be extrapolated to circular or elliptical contacts under steady-state or transient conditions. [DOI: 10.1115/1.4034956]