Cycling comfort on asphalt pavement: Influence of the pavement-tyre interface on vibration

Attainment of cycling comfort on urban roads encourages travelers to use bicycles more often, which has social and environment benefits such as to reduce congestion, air pollution and carbon emissions. Cycling vibration is responsible for the cyclists’ perception of (dis)comfort. How asphalt pavement's surface characteristics relate to cycling comfort, however, remains undiscovered. In this study, the cycling vibration intensity on 46 sections of 24 urban roads was tested using a dynamic cycling comfort measure system while the cyclists’ perception of vibration was identified via questionnaires; the cycling comfort was then defined based on the cycling vibration. To record the accurate pavement-tyre interface under a stable environment, a total of 19 pavement sections were scanned using a 3D digital camera. These 3D models were then 3D printed, which are used to conduct the pressure film test using a self-developed pavement-tyre interface test system. Three ranges of pressure films were adopted to characterize the pavement-tyre interface via 9 parameters, namely contact area (A c ), unit bearing area (B u ), stress intensity (S i ), stress uniformity (S u ), kurtosis (S ku ), spacing (Sp a ), maximum peak spacing (Sp max ), radius ratio (R r ) and fractal dimension (F d ), in consideration of the area characteristics, pressure amplitude, peak spacing and shape of the interface. Finally, the significant interface parameters were identified, and the regression model between interface parameters and cycling comfort was established. Results show that the cycling vibration was described to be ‘very comfortable’ when the human exposure to vibration level (a wv ) was less than 1.78 m/s 2 ; ‘comfortable’ when the a wv was between 1.78 m/s 2 and 2.20 m/s 2 ; and ‘uncomfortable’ when the a wv was greater than 2.20 m/s 2 . The average stress on rear wheel-pavement interface is higher than that of the front wheel. B u-0.6 , Sp a-0.6 , and F d-0.6 are significant to cycling vibration. The 2LW pressure film is recommended for use to measure the bicycle pavement-tyre interface. The recommended interface characteristics are less than 7 mm 2 of the unit bearing area, 6 mm of average spacing and 2.38 of fractal dimension. Finally, dense asphalt mixture performs better in providing cycling comfort than the gap-graded asphalt mixture. Results of this study contribute to current knowledge on bike lane comfort and pavement design, the findings should be interested in cyclists, transport planners, and road authorities

The effects of roughness on the area of contact and on the elastostatic friction: FEM simulation of micro-scale rough contact and real world applications

Roughness is everywhere. Every object, every surface we touch or look at, is rough. Even when it looks smooth and flat, if analyzed at the proper length scale, it will reveal roughness. Thus, macro-scale, micro-scale, and even nano-scale roughness exist. What is even more fascinating, is that most of the rough structures, which can be observed at a given length scale, repeat themselves at smaller length scales, as in a fractal. The first implication of the rough nature of surfaces is that what we perceive as a full, solid, and smooth contact area, is in reality a collection of fragmented microscopical contact patches, composed of single contact points. Given its intrinsic complexity, the modeling of the real area of contact has been the subject of a huge amount of studies, which yielded different and contrasting results. As it is easy to imagine, the real area of contact is crucial for many real-world applications, such as the prediction of wear and fretting, charge and heat conduction, and frictional effect.Let alone think of how an acting load is normally believed to be uniformly distributed over the contact surface, and how variable and uneven it must, in reality, appear at microscopic length scales. The importance of roughness, together with our knowledge in parallel computing and fast solution methods, are the premises of the current work. In this study, we analyze rough contact between realistic surfaces, and we resolve it numerically at micro-scale, to understand its meso- and macro-scale effects. We do this by means of the Finite Element Method, in combination with an optimal multi-grid strategy and a spatial decomposition to perform the computations on highly parallel super-computers. We concentrate on the type of surfaces for which it is believed that molecular and chemical effects can be neglected.We simulate the contact between an elastic cube and diverse rigid rough surfaces, under different loading conditions, and we derive empirical laws which describe the influence of well known roughness parameters on important features such as contact evolution and static friction production. We also define bounds on the uncertainty of our measurements, to make clear the level up to which our predictions have to be considered reliable and applicable. Literature on roughness is densely populated by models, approaches, and theoretical predictions about the evolution of the real area of contact. An exhaustive comparison of our results with such corpus of works, articles, books, and theses would be infeasible. We therefore compare our results on the real area of contact to the predictions of two widely accepted theories (one by B. N. J. Persson, the other by A. W. Bush, R. D. Gibson, and T. R. Thomas), which have often proved to be interpretable as asymptotical bounds, for systems at low pressures. For large pressures, and consequent large areas of contact, we also compare our results to the newly developed and semi-empirical theory by Yastrebov, Molinari, and Anciaux. Finally, we test our method on the real world problem of tyre-asphalt interactions on wet roads, comparing the results obtained by our method to data from other studies, collected on real highways and runways, and to a theoretical model, which is close, in the assumptions, to our numerical experiments

Modelling scattering of electromagnetic waves in layered media: An up-to-date perspective

This paper addresses the subject of electromagnetic wave scattering in layered media, thus covering the recent progress achieved with different approaches. Existing theories and models are analyzed, classified, and summarized on the basis of their characteristics. Emphasis is placed on both theoretical and practical application. Finally, patterns and trends in the current literature are identified and critically discussed

Mehrskalige Modellierung von Gummi-Hysteresereibung auf rauen Oberflächen

The performance of car tires on road tracks is strongly affected by hysteretic friction. In order to optimize driving characteristics, like minimizing fuel consumption, improving skid resistance, increasing tire durability, and increasing vehicle controllability during steering and braking, the rolling friction coefficient should be predicted properly. The accurate and efficient modeling and prediction of the hysteretic friction is still a challenge. In the past decade, two different modeling frameworks have attracted significant attention. They are the viscoelastic half-space (VHS)-based contact mechanics model, based on linear kinematics and implemented with the boundary element method (BEM), and the viscoelastic contact model in the finite deformation framework implemented with the finite element method (FEM). The first one has the ability to model all involved length scales at once with a reduced computational cost under the assumption of a flat geometry of the rough surface and small deformations. The second one does not have these limitations and is able to predict the friction coefficient accurately in the finite deformation framework, but at much higher computational cost. It is not able to investigate all involved length scales at once since it needs an extremely fine mesh refinement, which leads to an impractically slow simulation. This work has two major aims. The first goal is to study the accuracy of geometrical and rheological linearity assumptions in evaluation of rolling friction coefficient. This is done by comparing the simulation results of tire tread block in contact with a sinusoidal road track surface using the linear VHS-based model and the finite deformation model in terms of rolling friction coefficient, contact area, and pressure distributions. It has been found that accurate rolling friction predictions can be obtained through the linear VHS-based model within Reynolds assumption for moderate values of root mean square slopes, whereas finite deformation computations should be adopted for large root mean square slopes. The contact area is much more sensitive to the geometrical and rheological nonlinearities than the rolling friction coefficient. The second goal of the thesis is to establish a new hybrid (nonlinear FEM/linear BEM) multiscale method which combines the advantages of both methods. The presented hybrid multiscale approach has proven to be a suitable tool to study rolling-friction coefficient within a plausible degree of accuracy for relative large contact area and low sliding velocities. It allows a more faster calculation of friction coefficient than the finite deformation model.Das Verhalten von Pkw-Reifen auf Straßenoberflächen wird stark von hysteretischer Reibung beeinflusst. Um die Fahreigenschaften zu optimieren, beispielsweise zur Reduktion des Kraftstoffverbrauchs, der Verbesserung der Griffigkeit, der Erhöhung der Reifenhaltbarkeit und der Verbesserung der Kontrolle während des Lenkens und Bremsens, sollte die hysteretische Reibung richtig vorhergesagt werden. Die genaue und effiziente Vorhersage von hysteretischer Reibung, sowohl von theoretischer wie numerischer Seite, ist eine Herausforderung. Im letzten Jahrzehnt haben zwei verschiedene Modellierungsverfahren an Aufmerksamkeit gewonnen. Sie sind: das viskoelastische Halbraummodell, das auf einer linearen Kinematik basiert und mit der Randelemente-Methode implementiert wurde, sowie das viskoelastische Kontaktmodell im Rahmen finiter Deformationen, das mit der Finite-Elemente-Methode implementiert wurde. Mit der ersten Methode können alle beteiligten Längenskalen gleichzeitig und mit reduziertem Berechnungsaufwand simuliert werden, wobei eine flache Geometrie der rauen Oberfläche und lineare Verformungen angenommen werden. Die zweite Methode hat diese Einschränkungen nicht und kann den Reibkoeffizienten genau vorhersagen, jedoch bei weitaus höherer Berechnungszeit. Hierbei können jedoch nicht alle beteiligten Längenskalen gleichzeitig untersucht werden, da ein sehr feines Netz benötigt würde, was zu inakzeptabel langen Simulationen führt. Diese Arbeit hat zwei Hauptziele. Das erste Ziel besteht darin, die Auswirkungen geometrischer und rheologischer Linearitätsannahmen bei der Berechnung des Reibkoeffizienten zu untersuchen. Dies erfolgt durch Vergleich der Simulationsergebnisse eines Reifenprofilblocks in Kontakt mit einer sinusförmigen Oberfläche, unter Verwendung des linearen viskoelastischen Halbraummodells, das mit der Randelemente-Methode implementiert wurde, und des viskoelastischen Kontaktmodells im Rahmen finiter Deformationenund der Finite-Elemente-Methode. Betrachtet wurden Reibkoeffizient, Kontaktfläche und Druckverteilung. Es wurde festgestellt, dass mit dem viskoelastischen Halbraum Modell innerhalb der Linearitätsannahmen genaue Vorhersagen der Reibung für kleine Werte der lokaler Oberflächen-Steigung erhalten werden können, wohingegen für große Steigungen finite Deformationen berücksichtigt werden sollten. Das zweite Ziel dieser Arbeit ist die Etablierung einer neuen, hybriden (nichtlinearerFiniten-Elemente / linearer Randelemente) -Multiskalenmethode, die die Vorteile beider Verfahren kombiniert. Die vorgestellte Hybrid-Multiskalen-Methode hat sich als geeignetes Werkzeug erwiesen, um den Reibkoeffizienten mit einem angemessenen Genauigkeitsgrad für niedrige Gleitgeschwindigkeiten zu untersuchen; Sie ermöglicht eine schnellere Berechnung des Reibkoeffizienten als das nichtlineare FE-Modell