Figure 7 - uploaded by Erik Hansen

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# Contact pressure as a function of the gap coordinate. The value of h 0 = 0 corresponds to the roughness meltdown plane for the specific roughness shown in Figure 3.

Source publication

A considerable number of surface texture investigations is based on pin-on-disc tribometers. This work shows that a crucial role in the reproducibility of the results, e.g. Stribeck curves, is played by the geometry of the pin surface. The investigation is based on an elastohydrodynamic model of a pin-on-disc tribometer which is validated with expe...

## Contexts in source publication

**Context 1**

... an exact prediction about the extension of this plastically deformed subsurface volume cannot easily be made and subsurface plastic deformation is therefore omitted for the sake of a simple contact model. The precalculated contact pressure in dependence of the gap coordinate is visualized in Figure 7. Bowden and Tabor [26] also give an expression for the shear stress τ c in the contact surface of two metals without a normal load. ...

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## Citations

... Attention is paid to double the size of the kernel in each direction and to zero pad the hydrodynamic pressure field such that a linear instead of a circular convolution is obtained. After the convolution, the deformation and pressure fields are resized to their original size [23,32,33]. After computing ⃗ G and ⃗ F , the Newton-Raphson method is used to determine the updates of non-dimensional relative pressure ⃗ p * and cavity fraction ⃗ [10]: ...

Many engineering applications rely on lubricated gaps where the hydrodynamic pressure distribution is influenced by cavitation phenomena and elastic deformations. To obtain details about the conditions within the lubricated gap, solvers are required that can model cavitation and elastic deformation effects efficiently when a large amount of discretization cells is employed. The presented unsteady EHL-FBNS solver can compute the solution of such large problems that require the consideration of both mass-conserving cavitation and elastic deformation. The execution time of the presented algorithm scales almost with Nlog(N)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$N\log (N)$$\end{document} where N is the number of computational grid points. A detailed description of the algorithm and the discretized equations is presented. The MATLAB©\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{\copyright }$$\end{document} code is provided in the supplements along with a maintained version on GitHub to encourage its usage and further development. The output of the solver is compared to and validated with analytical, simulated, and experimental results from the literature to provide a detailed comparison of different discretization schemes of the Couette term in presence of gap height discontinuities. As a final result, the most favorable scheme is identified for the unsteady study of surface textures in ball-on-disc tribometers under EHL conditions.

... Attention is paid to double the size of the kernel in each direction and to zero pad the hydrodynamic pressure field such that a linear instead of a circular convolution is obtained. After the convolution, the deformation and pressure fields are resized to their original size [23,31,32]. ...

Many engineering applications rely on lubricated gaps where the hydrodynamic pressure distribution is influenced by cavitation phenomena and elastic deformations. To obtain details about the conditions within the lubricated gap, solvers are required that can model cavitation and elastic deformation effects efficiently when a large amount of discretization cells is employed. The presented unsteady EHL-FBNS solver can compute the solution of such large problems that require the consideration of both mass-conserving cavitation and elastic deformation. The execution time of the presented algorithm scales almost with N log( N ) where N is the number of computational grid points. A detailed description of the algorithm and the discretized equations is presented. The MATLAB © code is provided in the supplements along with a maintained version on GitHub to encourage its usage and further development. The output of the solver is compared to and validated with simulated and experimental results from the literature to provide a detailed comparison of different discretization schemes of the Couette term in presence of gap height discontinuities. As a final result, the most favourable scheme is identified for the unsteady study of surface textures in ball-on-disc tribometers under severe EHL conditions.

... Empirically, it has been found that, in the hydrodynamic regime, the friction coefficient μ (the ratio of friction force and normal force) scales with the "conventional" Hersey number, defined as Hr ≡ ðηU 0 =F N Þ, where η, U 0 , and F N are the viscosity, sliding velocity, and normal force, respectively. The scaling has been suggested to be linear [5,11], although more recent work uses a power-law relation [12][13][14][15]. ...

Most frictional contacts are lubricated in some way, but is has proven difficult to measure and predict lubrication layer thicknesses and assess how they influence friction at the same time. Here we study the problem of rigid-isoviscous lubrication between a plate and a sphere, both experimentally and theoretically. The liquid layer thickness is measured by a novel method using inductive sensing, while the friction is measured simultaneously. The measured values of the layer thickness and friction on the disk are well described by the hydrodynamic description of liquid flowing through a contact area. This allows us to propose a modified version of the Hersey number that compares viscous to normal forces and allows us to rescale data for different geometries and systems. The modification overcomes the shortcomings of the commonly used Hersey number, adds the effects of the geometry of the configuration on the friction, and successfully predicts the lubrication layer thickness.