Georg Vorlaufer

Meeting the Contact-Mechanics Challenge

This paper summarizes the submissions to a recently announced contact-mechanics modeling challenge. The task was to solve a typical, albeit mathematically fully defined problem on the adhesion between nominally flat surfaces. The surface topography of the rough, rigid substrate, the elastic properties of the indenter, as well as the short-range adhesion between indenter and substrate, were specified so that diverse quantities of interest, e.g., the distribution of interfacial stresses at a given load or the mean gap as a function of load, could be computed and compared to a reference solution. Many different solution strategies were pursued, ranging from traditional asperity-based models via Persson theory and brute-force computational approaches, to real-laboratory experiments and all-atom molecular dynamics simulations of a model, in which the original assignment was scaled down to the atomistic scale. While each submission contained satisfying answers for at least a subset of the posed questions, efficiency, versatility, and accuracy differed between methods, the more precise methods being, in general, computationally more complex. The aim of this paper is to provide both theorists and experimentalists with benchmarks to decide which method is the most appropriate for a particular application and to gauge the errors associated with each one.

Molecular dynamics simulations of mixed lubrication with smooth particle post-processing

A post-processing method for molecular dynamics (MD) simulations of friction based on the smooth particle approach is proposed, allowing--among other features--the introduction and evaluation of a solid-solid contact area arising due to direct asperity interaction. In order to illustrate the feasibility of this scheme, a large number of MD calculations of lubricated nanotribological systems with various asperity geometries and carefully selected numbers of lubricant molecules were carried out and analysed. In this manner, it is shown that the friction force as a function of load agrees very well with a three-parameter friction law which, in addition to the adhesion- and the load-controlled terms, contains a load-independent offset.

Combined finite element-boundary element method modelling of elastic multi-asperity contacts

Abstract A novel formulation of elastic multi-asperity contacts based on the boundary element method (BEM) is presented for the first time, in which the influence coefficients are numerically calculated using a finite element method (FEM). The main advantage of computing the influence coefficients in this manner is that it makes it also possible to consider an arbitrary load direction and multilayer systems of different mechanical properties in each layer. Furthermore, any form of anisotropy can be modelled too, where Greens functions either become very complicated or are not available at all. The rest of the contact analysis is then performed applying a custom-developed boundary element algorithm. The scheme was tested by considering the frictionless contact between a flat surface and a sphere. The obtained results are in good agreement with the analytical solution known for a Hertzian contact. Applied to either a frictionless or a frictional contact between real surfaces of different samples, our FEM-BEM method has shown that the composite roughness of surfaces in contact uniquely determines the contact pressure distribution.

On the three-term kinetic friction law in nanotribological systems

A post-processing method, which maps the punctiform atoms in molecular dynamics (MD) simulations of boundary lubrication onto smoothed particles, is used to estimate the asperity contact area defined by the minimum cross-section of the formed solid bridges. It is then shown that this asperity contact area excellently agrees with the projected area resulting from a Voronoi tessellation of the corresponding contact zone, and that it can be applied to compute the constitutive system parameters of a three-term friction law, which is found to hold for any boundary-lubricated nanotribological system. Finally, an attempt is made to relate the load-independent friction offset observed in boundary-lubricated nanotribological systems without solid-solid contact to the structural order as measured by the entropy, which is estimated within the single macromolecule approach based on covariance (super)matrices of the carbon backbone atoms in the lubricant.

Numerical estimation of wear in reciprocating tribological experiments

In order to numerically simulate the contact pressure distribution and area during sliding when wear occurs, the combined finite element method and boundary element method (FEM–BEM) developed by the authors is extended based on a linear wear law merged with the space- and time-resolved cumulative dissipated frictional energy. In each computed time step, the dissipated frictional energy and the wear rate are determined. Simultaneously, the topography of surfaces in contact are updated after every sliding cycle, providing for each sliding cycle a new input for BEM which is consequently used to redetermine the contact pressure distribution. The numerical results obtained with the proposed FEM–BEM algorithm are found to match qualitatively well with the amount of wear observed in high-frequency reciprocating rig experiments. This demonstrates the suitability of the FEM–BEM contact scheme for wear applications.

Finite and boundary element method contact mechanics on rough, artificial hip joints

An extremely small roughness of constant height magnitude is considered on the femoral head of an artificial hip joint in order to determine the consequences of various regular shapes and clearances on the mechanical performance of this hip prosthesis via a properly coupled finite and boundary element method. In addition, different material combinations typical for widely used hard-on-hard and hard-on-soft hip joint replacements are also taken into account. By analysing the calculated pressure distribution and contact area between the femoral head and the acetabular cup in frictionless dry contact irrespective of material pairings in hip joints, it is shown that both the wavelength of roughness and the clearance significantly affect these mechanical quantities and accordingly too loose or too tight hip implants have to be avoided. Finally, in terms of all numerical findings a suitable optimal design of hip implants is also discussed.

Comparison of parametric and profilometric surface analysis methods on machined surfaces

Abstract In this work, a comparison of three different methods for analysing topographies and roughness on machined metal surfaces is presented. To obtain comparable results, the measurements were done on one and the same set of samples. For this purpose, an atomic force microscope (AFM), a confocal white light microscope, and a scattering light system were used to analyse the topography of samples of the same material, but with the topographies occurring step by step from the grinding process to the polishing process. Based on the results of the investigations with the parametric system (scattering light sensor) and the profilometric systems (AFM, confocal white light microscope), we established a correlation between the roughness parameters and the scattering light parameter. It is shown that the different methods lead to different roughness parameters of the same surface.

Online monitoring of a belt grinding process by using a light scattering method

Industrially ground surfaces often have a characteristic surface topography known as chatter marks. The surface finishing is mainly monitored by optical measurement techniques. In this work, the monitoring of an industrial belt grinding process with a light scattering sensor is presented. Although this technique is primarily applied for parametric surface roughness analysis, here it is shown that it enables also the measurement of the surface topography, i.e., the chatter marks occurring during the belt grinding process. In particular, it is proven that the light scattering method is appropriate to measure online the topography of chatter marks. Furthermore, the frequency analysis of the data reveals that the wavelength of chatter marks strongly depends on process parameters, such as the grinding speed.

Experimental Validation of the Simulated Steady-State Behavior of Porous Journal Bearings

This study deals with a comparison between new experiments on the frictional behavior of porous journal bearings and its prediction by previous numerical simulations. The tests were carried out on bearings lubricated with polyalphaolefin-based oils of distinct viscosities. The theoretical model underlying the simulations includes the effects of cavitation by vaporization and accounts for the sinter flow by virtue of Darcys law. The effective eccentricity ratio corresponding to the experimentally imposed load is estimated by an accurate numerical interpolation scheme. The comparison focuses on the hydrodynamic branches of the Stribeck curve by dimensional analysis, where the variations of the lubricant viscosity with temperature are of main interest. The numerically calculated values of the coefficient of friction are found to reproduce the experimentally obtained ones satisfactorily well in terms of overall trends, yet the former lie predominantly below the measured ones, which results in a low-positive correlation between the two.

Multiresolution analysis of angle-resolved light scattering measurements on ground surfaces

Grinding processes causes the formation of a characteristic surface structure, known as chatter marks. In this work, an angle-resolved light scattering technique is used to characterise them. In order to identify the chatter marks in a measured profile, the fast Fourier transform (FFT) is usually applied to the measured data. The FFT, however only for strictly periodic data yields unambiguous results. To overcome this, the multiresolution analysis (MRA) is also applied by means of the lifting scheme. In this manner, it is shown that chatter marks, for example, can be uniquely identified by applying the multiresolution analysis to the angle-resolved light scattering data, even when FFT fails to do this. Thus MRA alone or alternatively in combination with FFT, opens new opportunities for optical online control in case of industrial surface finishing processes.