An Efficient 3D Model of Heterogeneous Materials for Elastic Contact Applications Using Multigrid Methods

International audienceAbstract: A 3D graded coating/substrate model based on multigrid techniques within a finite difference frame work is presented. Localized refinement is implemented to optimize memory requirement and computing time. Validation of the solver is performed through a comparison with analytical results for (i) a homogeneous material and (ii) a graded material. The algorithm performance is analyzed through a parametric study describing the influence of layer thickness (0.01 < t/a < 10) and mechanical properties (0.005 < E-c/E-s < 10) of the coating on the contact parameters (P-h, a). Three-dimensional examples are then presented to illustrate the efficiency and the large range of possibilities of the model. The influence of different gradations of Young's modulus, constant, linear and sinusoidal, through the coating thickness on the maximum tensile stress is analyzed, showing that the sinusoidal gradation best accommodates the property mismatch of two successive layers. A final case is designed to show that full 3D spatial property variations can be accounted for. Two spherical inclusions of different size made from elastic solids with Young's modulus and Poisson's ratio are embedded within an elastically mismatched finite domain and the stress field is computed

Influence des rugosités de surface sur la fatigue de contact en roulement

La fatigue de contact est essentiellement initiée en surface. Un modèle analytique a été développé afin de déterminer les surpressions dues aux rugosités en condition de contact sec élastique. Une analyse du champ de contrainte a été conduite ensuite afin d'identifier le cisaillement maximum. Enfin, un abaque de risque en fonction des paramètres de rugosité et des conditions de contact est proposé

Superlubricity of glycerol by self-sustained chemical polishing

International audienceAn impressive superlow coefficient of friction (CoF) as low as 0.004 (nearly equivalent to the rolling coefficient) was obtained by sliding a steel ball against a tetrahedral amorphous diamond-like carbon (ta-C) coating in glycerol under a boundary lubrication regime. X-ray photoelectron spectroscopy (XPS) and atomic force microscopy (AFM) revealed substantial changes in the surface chemistry and topography in the friction track. As shown by XPS analysis, a transfer of iron atoms from the steel ball to the ta-C layer occurred, forming iron oxy-hydroxide (FeOOH) termination on both surfaces. Between them, theoretical calculations show that a nanometre-thick fluid film consisting of glycerol and its degradation products prevents direct contact between the solid surfaces by nm-thick film EHL lubrication and results in the superlow friction, in agreement with the experiment. Furthermore, molecular dynamics (MD) simulations reveal that hydrogen atoms act as "low-friction brushes" between sliding layers of crystalline FeOOH, resulting also in low friction. A new model of sustainable green superlubricity is proposed. The tribo-formation of FeOOH with glycerol leads to a unique polishing process, which in turn leads to a self-sustained Elasto-Hydrodynamic Lubrication (EHL) regime until the very thin fluid film is no more than a few nanometres thick. At lower thicknesses, the hydroxide layer takes over. Wear of the ta-C coating is negligible, while wear on the steel ball is very moderate and acceptable for many practical applications, such as bio-tribology and the food industry, in which green lubrication is especially needed

Calcul 3D massif revêtu -Techniques multi-grilles avec raffinement local (MGL)

Un outil de simulation 3D élastique linéaire pour l'analyse du comportement de matériaux revêtus est proposé. Les équations de Lamé généralisées sont discrétisées par différences finies et résolues à l'aide des techniques MGL. Des systèmes de plus de 400 millions d'inconnues sont résolus pour des temps de calcul acceptables. Ainsi le problème de contact entre massifs revêtus est abordé avec la finesse nécessaire pour traiter des variations de propriétés sur des épaisseurs faibles (0,01<e/a<2). Une étude paramétrique montre l'influence de l'amplitude et de la forme des variations de propriétés

Influence of Surface Waviness on the Thermal Elastohydrodynamic Lubrication of an Eccentric-Tappet Pair

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Multi-Level Methods in Lubrication

Efficient numerical solution of realistic and, therefore, complex equation systems occupies many researchers in many disciplines. For various reasons, but mainly in order to approximate reality, a very large number of unknowns are needed. Using classical techniques, the solution of such a system of equations would take too long, and so sometimes MultiLevel techniques are used to accelerate convergence. Over the last one and a half decades, the authors have studied the problem of Elastohydrodynamic Lubrication, governed by a complex integro-differential equation. Their work has resulted in a very efficient and stable solver. In this book they describe the different intermediate problems analyzed and solved, and how those ingredients finally come together in the EHL solver. A number of these intermediate problems, such as Hydrodynamic Lubrication and Dry Contact, are useful in their own right. In the Appendix the full codes of the Poisson problem, the Hydrodynamic Lubrication problem, the dry contact solver and the EHL solver are given. These codes are all written in 'C' language, based on the 'ANSI-C' version

Lubricated Impact Dynamics and Pressure Spike Generation: Expanding on Contributions of Dr. R. Gohar

The current paper focuses on the research of Dr. R. Gohar and in particular on his impacting ball and pressure spike measurement work. Its scope then expands to discuss contributions from other researchers concerning these two fields. The authors combined the two themes in a numerical study of an impacting contact. This study shows the detailed position of the pressure spike as a function of time. Then, the pressure spike position velocity is derived, and it is demonstrated that this velocity varies with time. As such, the paper concludes that the pressure spike shape itself must vary with time

Central film thickness prediction for line contacts under pure impact

International audienceThe lubricant film thickness in lubricated rolling contacts can be predicted quantitatively thanks to the work of Dowson, Higginson, Hamrock and others. However, most industrial applications are governed by time dependent operating conditions. For the most extreme time dependent case (impact), no film thickness predictions exist. The current work derives a dimensionless Reynolds line contact equation based on the Johnson dry contact impact analysis. It is shown that similar to the film thickness under rolling conditions, the Piezoviscous Elastic impact problem is governed by only 2 parameters. The numerical results are curve fitted to obtain a central film thickness predictive equation

Film thickness prediction in elastohydrodynamically lubricated elliptical contacts

International audienceThis paper analyses the minimum and central film thickness evolution of elastohydrodynamically lubricated contacts, from circular to wide elliptical contacts. It is shown that already for moderate ellipticity, the minimum film thickness is found on the centre-line of the contact, rather than in the side lobes as for the circular contact. In such cases, the film thickness can be accurately predicted from an equivalent line contact, defined as the line contact with the same Hertzian pressure, radius of curvature, and speed and oil parameters. In this paper, a formula is presented to predict the central film thickness in elliptical contacts using prediction formulas for the line and circular contacts as limiting cases, and the results of numerical calculations to fit the film thickness variation with ellipticity. The formula gives an accurate prediction of the central film thickness over the entire ellipticity regime