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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**

... schematic setup of the Plint TE-92 HS tribometer from Phoenix Tribology (Kingsclere, UK) that was used for the experiments of Braun et al. [8] is depicted in Figure 1. It shows the rotating disc that is pressed with the normal force F N against the pin. ...

**Context 2**

... resulting corrected elastic deformation h el,c is also shown in Figure 8. As displayed in Figure 10, the Stribeck curves based on the uncorrected and corrected halfspace formulas only differ slightly. The reason is that the difference in both elastic displacements is mainly due to the offset implied by the correction constant a. ...

**Context 3**

... reason is a less sparse system matrix because of the off-diagonal homogenization factors in Matrix A and the additional interpolation of the homogenization factors. Based on the measured pin and roughness profiles shown in the Figures 2 and 3, the Stribeck curves are computed with both roughness methods and the obtained results are displayed Figure 11. Note that both methods use the roughness profile for the computation of the contact mechanics as described in section 3.2. ...

**Context 4**

... the transition point of the purely EHL to the mixed lubrication regime can be defined as the critical disc velocity U c at which the minimum gap coordinate above the pin min (h 0 ( x)) is equal to R p . This is visualized in Figure 12 with the results of the meltdown gap height method. ...

**Context 5**

... parabola is designed to closely fit the measured pin profile in the center while the other one is chosen (within a parameter study) such that it captures the experimentally determined transition point from EHL to mixed lubrication in the Stribeck curve. The corresponding pin profiles and computed Stribeck curves are depicted in Figures 13 and 14. ...

**Context 6**

... correspond to a relative decrease of 5%, 25% and 50% of the reference center height. The resulting Stribeck curves are displayed in Figure 15. Afterwards, the change in the friction coefficient relative to the reference profile is computed for each velocity as displayed in Figure 16. ...

**Context 7**

... resulting Stribeck curves are displayed in Figure 15. Afterwards, the change in the friction coefficient relative to the reference profile is computed for each velocity as displayed in Figure 16. It shows that a measurement deviation of 25% or 0.5µm in the characteristic length of the reference pin causes a maximum difference in the friction coefficient of more than 80%. ...

**Context 8**

... schematic setup of the Plint TE-92 HS tribometer from Phoenix Tribology (Kingsclere, UK) that was used for the experiments of Braun et al. [8] is depicted in Figure 1. It shows the rotating disc that is pressed with the normal force F N against the pin. ...

**Context 9**

... parabola is designed to closely fit the measured pin profile in the center while the other one is chosen (within a parameter study) such that it captures the experimentally determined transition point from EHL to mixed lubrication in the Stribeck curve. The corresponding pin profiles and computed Stribeck curves are depicted in Figures 10 and 11. The predicted friction coefficient is in very good agreement with the experimental data [8] in the boundary regime while there is a difference by about one order magnitude in the EHL regime. ...

**Context 10**

... correspond to a relative decrease of 5%, 25% and 50% of the reference center height. The resulting Stribeck curves are displayed in Figure 12. Afterwards, the change in the friction coefficient relative to the reference profile is computed for each velocity as displayed in Figure 13. ...

**Context 11**

... resulting Stribeck curves are displayed in Figure 12. Afterwards, the change in the friction coefficient relative to the reference profile is computed for each velocity as displayed in Figure 13. It shows that a measurement deviation of 25% or 0.5µm in the characteristic length of the reference pin causes a maximum difference in the friction coefficient of more than 80%. ...

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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.