79,233 research outputs found

    Stability Properties of Equilibrium Sets of Controlled Linear Mechanical Systems with Dry Friction

    Get PDF
    The dynamics of mechanical systems with dry friction elements, modeled by set-valued force laws, can be described by differential inclusions. The switching and set-valued nature of the friction force law is responsible for the hybrid character of such models. An equilibrium set of such a differential inclusion corresponds to a stationary mode for which the friction elements are sticking. The attractivity properties of the equilibrium set are of major importance for the overall dynamic behavior of this type of systems. Conditions for the attractivity of the equilibrium set of linear MDOF mechanical systems with multiple friction elements are presented. These results are obtained by application of a generalization of LaSalle’s principle for differential inclusions of Filippov-type. Besides passive systems, also systems with negative viscous damping are considered. For such systems, only local attractivity of the equilibrium set can be assured under certain conditions. Moreover, an estimate for the region of attraction is given for these cases. The results are illustrated by means of a 2DOF example. Moreover, the value of the attractivity results in the context of the control of mechanical systems with friction is illuminated

    Micro Surface Texturing for Friction Control

    Get PDF
    Recently, surface texturing has gained momentum as a way to control the friction which is involved in various applications and systems, such as components of internal combustion engines, dies and punches of the metal forming processes and Micro-electrical-mechanical Systems (MEMS). This dissertation demonstrates that under dry sliding, there is a specific significant surface texturing parameter at which the coefficient of friction should be at a minimum. This dissertation met this objective through an extensive study of the relevant literature on surface texturing and friction, analysing the friction mechanisms involved in dry sliding, and highlighting the key factors that control friction as the real area of contact and material properties. An analytical proof is derived demonstrating that a minimum friction force exists if the two components of the friction force, adhesion and mechanical deformation, are differentiated with respect to the real contact area. In addition, numerical simulations and experimental work were performed to test this hypothesis. In the two and three dimensional finite element models, normal and sliding contact between a rigid indenter and elastic-plastic surfaces, which are textured by circular and hexagonal dimples of different sizes and densities, are simulated and analysed. Circular craters of different sizes and densities, are fabricated using laser ablation on hardened tool steel samples, while the hexagonal dimples are fabricated using photo-lithography. The dimples are arranged in adjacent equilateral triangles layout. Coefficients of friction were measured using a scratch tester under dry sliding conditions and constant load. In addition, adhesion forces were estimated using an Atomic Force Microscope (AFM). The adhesion force is found to be exponentially decreasing with the increase of the spatial texture density. The dimensionless quantity, spatial texture density (D/L) was identified as the most significant texturing parameter. It is equal to the ratio of the size of the crater (D) to the distance between the centres of two consecutive craters (L). A minimum coefficient of friction exits at values of spatial texture densities that lie between 0.25 and 0.5

    Theory of differential inclusions and its application in mechanics

    Full text link
    The following chapter deals with systems of differential equations with discontinuous right-hand sides. The key question is how to define the solutions of such systems. The most adequate approach is to treat discontinuous systems as systems with multivalued right-hand sides (differential inclusions). In this work three well-known definitions of solution of discontinuous system are considered. We will demonstrate the difference between these definitions and their application to different mechanical problems. Mathematical models of drilling systems with discontinuous friction torque characteristics are considered. Here, opposite to classical Coulomb symmetric friction law, the friction torque characteristic is asymmetrical. Problem of sudden load change is studied. Analytical methods of investigation of systems with such asymmetrical friction based on the use of Lyapunov functions are demonstrated. The Watt governor and Chua system are considered to show different aspects of computer modeling of discontinuous systems

    On the genesis of directional friction through bristle-like mediating elements

    Get PDF
    We propose an explanation of the genesis of directional dry friction, as emergent property of the oscillations produced in a bristle-like mediating element by the interaction with microscale fluctuations on the surface. Mathematically, we extend a convergence result by Mielke, for Prandtl-Tomlinson-like systems, considering also non-homothetic scalings of a wiggly potential. This allows us to apply the result to some simple mechanical models, that exemplify the interaction of a bristle with a surface having small fluctuations. We find that the resulting friction is the product of two factors: a geometric one, depending on the bristle angle and on the fluctuation profile, and a energetic one, proportional to the normal force exchanged between the bristle-like element and the surface. Finally, we apply our result to discuss the with the nap/against the nap asymmetry

    A predictive model of energy savings from top of rail friction control

    Get PDF
    In this paper the authors present a predictive model of train energy requirements due to the application of a top of rail friction modifier (TOR-FM) versus dry wheel / rail conditions. Using the VAMPIRE® Pro simulation package, train energy requirements are modeled for two sets of TOR-FM frictional conditions, one using full Kalker coefficients and the other by using a Kalker factor of 18%. Both scenarios use a top of rail saturated coefficient of friction of 0.35. Under both TOR-FM frictional conditions, train energy savings are shown for complete laps of the Transportation Technology Center Inc.’s (TTCI) Transit Test Track (TTT) loop, and also when isolating only the tangent section of the loop. However, the magnitude of energy savings varies greatly depending on the Kalker coefficient factor used, highlighting the need to model this relationship as accurately as possible. These simulation results are compared with data obtained from a field study, in which train energy savings of 5.3% (lap) and 7.8% (tangent) are shown due to the application of TOR-FM

    Rheological and restoring force models regarding belt tensioner dymamic behavior: prediction and experiment

    Get PDF
    The objective of this paper is to compare the Masing and modified Dahl model efficiency regarding the prediction of the hysteretic behavior of a belt tensioner used for automotive engines. A first experimental study with deflection imposed on the tensioner is carried out to identify hysteresis loop parameters for the two models. The models are then implemented in the general motion equations modeling the behavior of a belt - tensioner - mass system. The comparison beteen numerical and experimental results show that these two models perform satisfactorily and that the modified Dahl model is a little more efficient

    Non-Filippov dynamics arising from the smoothing of nonsmooth systems, and its robustness to noise

    Get PDF
    Switch-like behaviour in dynamical systems may be modelled by highly nonlinear functions, such as Hill functions or sigmoid functions, or alternatively by piecewise-smooth functions, such as step functions. Consistent modelling requires that piecewise-smooth and smooth dynamical systems have similar dynamics, but the conditions for such similarity are not well understood. Here we show that by smoothing out a piecewise-smooth system one may obtain dynamics that is inconsistent with the accepted wisdom --- so-called Filippov dynamics --- at a discontinuity, even in the piecewise-smooth limit. By subjecting the system to white noise, we show that these discrepancies can be understood in terms of potential wells that allow solutions to dwell at the discontinuity for long times. Moreover we show that spurious dynamics will revert to Filippov dynamics, with a small degree of stochasticity, when the noise magnitude is sufficiently large compared to the order of smoothing. We apply the results to a model of a dry-friction oscillator, where spurious dynamics (inconsistent with Filippov's convention or with Coulomb's model of friction) can account for different coefficients of static and kinetic friction, but under sufficient noise the system reverts to dynamics consistent with Filippov's convention (and with Coulomb-like friction).Comment: submitted to: Nonlinear Dynamic

    Non-deterministic dynamics of a mechanical system

    Get PDF
    A mechanical system is presented exhibiting a non-deterministic singularity, that is, a point in an otherwise deterministic system where forward time trajectories become non-unique. A Coulomb friction force applies linear and angular forces to a wheel mounted on a turntable. In certain configurations the friction force is not uniquely determined. When the dynamics evolves past the singularity and the mechanism slips, the future state becomes uncertain up to a set of possible values. For certain parameters the system repeatedly returns to the singularity, giving recurrent yet unpredictable behaviour that constitutes non-deterministic chaotic dynamics. The robustness of the phenomenon is such that we expect it to persist with more sophisticated friction models, manifesting as extreme sensitivity to initial conditions, and complex global dynamics attributable to a local loss of determinism in the limit of discontinuous friction.Comment: 22 pages, 8 figure
    corecore