Voltage-Induced Friction with Application to Electrovibration

Due to the growing interest in robotic and haptic applications, voltage-induced friction has rapidly gained in importance in recent years. However, despite extensive experimental investigations, the underlying principles are still not sufficiently understood, which complicates reliable modeling. We present a macroscopic model for solving electroadhesive frictional contacts which exploits the close analogy to classical adhesion theories, like Johnson-Kendall-Roberts (JKR) and Maugis, valid for electrically neutral bodies. For this purpose, we recalculate the adhesion force per unit area and the relative surface energy from electrostatics. Under the assumption of Coulomb friction in the contact interface, a closed form equation for the friction force is derived. As an application, we consider the frictional contact between the fingertip and touchscreen under electrovibration in more detail. The results obtained with the new model agree well with available experimental data of the recent literature. The strengths and limitations of the model are clearly discussed.TU Berlin, Open-Access-Mittel – 201

A Solution Set-Based Entropy Principle for Constitutive Modeling in Mechanics

Entropy principles based on thermodynamic consistency requirements are widely used for constitutive modeling in continuum mechanics, providing physical constraints on a priori unknown constitutive functions. The well-known M\"uller-Liu procedure is based on Liu's lemma for linear systems. While the M\"uller-Liu algorithm works well for basic models with simple constitutive dependencies, it cannot take into account nonlinear relationships that exist between higher derivatives of the fields in the cases of more complex constitutive dependencies. The current contribution presents a general solution set-based procedure, which, for a model system of differential equations, respects the geometry of the solution manifold, and yields a set of constraint equations on the unknown constitutive functions, which are necessary and sufficient conditions for the entropy production to stay nonnegative for any solution. Similarly to the M\"uller-Liu procedure, the solution set approach is algorithmic, its output being a set of constraint equations and a residual entropy inequality. The solution set method is applicable to virtually any physical model, allows for arbitrary initially postulated forms of the constitutive dependencies, and does not use artificial constructs like Lagrange multipliers. A Maple implementation makes the solution set method computationally straightforward and useful for the constitutive modeling of complex systems. Several computational examples are considered, in particular, models of gas, anisotropic fluid, and granular flow dynamics. The resulting constitutive function forms are analyzed, and comparisons are provided. It is shown how the solution set entropy principle can yield classification problems, leading to several complementary sets of admissible constitutive functions; such problems have not previously appeared in the constitutive modeling literature

Ergebnis experimenteller Untersuchungen für Druckkammlager im Mischreibungsgebiet

Bereitgestellt werden tabellarisch aufbereitete Versuchsergebnisse sowie der zugehörige Versuchsplan für innerhalb des Forschungsprojektes „Einsatz von Druckkämmen zur Effizienzsteigerung von schrägverzahnten Getrieben“ (als Teil des Schwerpunktprogrammes 1551: „Ressourceneffiziente Konstruktionselemente“ durch die Deutsche Forschungsgemeinschaft DFG gefördert) durchgeführte Versuche zur Standfestigkeit von Druckkammlagern unter Mischreibungsbedingungen. Mittels eines vollfaktoriellen, zweistufigen Versuchsplanes wurden die Gestaltungsparameter Laufflächenneigungswinkel, Laufbahnbreite, Streckgrenze des Grundwerkstoffs, Oberflächenhärte der Laufbahnen und Schlupfverhältnis hinsichtlich der kurzzeitig unter Mischreibungsbedingungen ertragbaren Zielgrößen Axiallast und daraus abgeleiteten Vergleichspressung untersucht. Der tabellarische Versuchsplan mit den erreichten Zielgrößen findet sich in der tabulatorgetrennten ASCII-Datei: Erg_Tab_DK_MR.txt; weitere Erläuterungen werden in dem beigefügten PDF-Dokument bereitgestellt

Cosmological Structure Formation with Augmented Lagrangian Perturbation Theory

We present a new fast and efficient approach to model structure formation with Augmented Lagrangian Perturbation Theory (ALPT). Our method is based on splitting the displacement field into a long and a short-range component. The long-range component is computed by second order LPT (2LPT). This approximation contains a tidal nonlocal and nonlinear term. Unfortunately, 2LPT fails on small scales due to severe shell crossing and a crude quadratic behaviour in the low density regime. The spherical collapse (SC) approximation has been recently reported to correct for both effects by adding an ideal collapse truncation. However, this approach fails to reproduce the structures on large scales where it is significantly less correlated with the N-body result than 2LPT or linear LPT (the Zeldovich approximation). We propose to combine both approximations using for the short-range displacement field the SC solution. A Gaussian filter with a smoothing radius r_S is used to separate between both regimes. We use the result of 25 dark matter only N-body simulations to benchmark at z=0 the different approximations: 1st, 2nd, 3rd order LPT, SC and our novel combined ALPT model. This comparison demonstrates that our method improves previous approximations at all scales showing ~25% and ~75% higher correlation than 2LPT with the N-body solution at k = 1 and 2 h Mpc^-1, respectively. We conduct a parameter study to determine the optimal range of smoothing radii and find that the maximum correlation is achieved with r_S = 4 - 5 h^-1 Mpc. This structure formation approach could be used for various purposes, such as setting-up initial conditions for N-body simulations, generating mock galaxy catalogues, cosmic web analysis or for reconstructions of the primordial density fluctuations.Comment: 6 pages and 4 figure