On the Effect of Contact Compliance on Vibrational Smoothing of Dry Friction

High-frequency vibrations may be utilized in order to smooth the characteristics of dry friction at low sliding velocities and, consequently, quench undesired friction induced phenomena. Many studies have been published so far, most of them using classical Coulomb friction models and yielding compact results. Unfortunately, the agreement with related experimental results is insufficient. As the Coulomb model overestimates the smoothing effect, improved modelling seems to be necessary. Based on Dahl's friction model, the effect of longitudinal and transverse high-frequency vibrations on a 1-DoF-friction oscillator is investigated here. Accounting for contact compliance, a reduction of the smoothing effect is observed. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Bifurcation and chaos in friction-induced vibration

Friction-induced vibration is a phenomenon that has received extensive study by the dynamics community. This is because of the important industrial relevance and the ever-evolving development of new friction models. In this paper, we report the result of bifurcation study of a single-degree-of-freedom mechanical oscillator sliding over a surface. The friction model we use is that developed by Canudas de Wit et al., a model that is receiving increasing acceptance from the mechanics community. Using this model, we find a stable limit cycle at intermediate sliding speed for a single-degree-of-freedom mechanical oscillator. Moreover, the mechanical oscillator can exhibit chaotic motions. For certain parameters, numerical simulation suggests the existence of a Silnikov homoclinic orbit. This is not expected in a single-degree-of-freedom system. The occurrence of chaos becomes possible because the friction model contains one internal variable. This demonstrates a unique characteristic of the friction model. Unlike most friction models, the present model is capable of simultaneously modeling self-excitation and predicting stick–slip at very low sliding speed as well.     

Parameter study of a multi-body friction oscillator

In many technical applications sliding contacts with multiple contact points or engagements exist, like between seals and rough surfaces, between grinding wheel and workpiece, or between granular material and storage box. In a simplified way these contacts can be represented by a friction oscillator with multiple bodies. The behavior of the friction oscillator with one body is already well known. However only few studies exist on the behavior of a friction oscillator with multiple bodies. In this study especially the dynamical behavior depending on the number of bodies, the friction characteristic and the velocity of the belt has been investigated. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On nonsmooth bifurcations in a simple friction oscillator

We consider a simple friction oscillator with one degree of freedom using a non-smooth, three-parameter fricion model accounting for both, a decreasing and increasing dynamic friction force depending on the relative velocity. An analysis of global non-smooth bifurcations is performed numerically and parameter domains are computed for the existence of stick-slip oscillations. Special emphasis is placed upon the occurrence of stick-slip oscillations with negative relative velocity. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Analytical investigation of steady-state stability and Hopf-bifurcations occurring in sliding friction oscillators with application to low-frequency disc brake noise

This article presents an analytical investigation on stability and local bifurcation behavior due to exponentially decaying friction characteristics in the sliding domain of a simple friction oscillator, which is commonly referred to as “mass-on-a-belt”-oscillator. Friction is described by a friction coefficient which in the sense of Stribeck depends on the relative velocity between the two tribological partners.For such a characteristic the stability and bifurcation behavior are discussed. It is shown, that the system can undergo a subcritical Hopf-bifurcation from an unstable steady-state fixed-point to an unstable limit cycle, which separates the basins of the stable steady-state fixed-point and the self-sustained stick-slip limit cycle.Therefore, only a local examination of the eigenvalues at the steady-state, as is the classical approach when investigating conditions for the onset of friction-induced vibrations, may not give the whole picture, since the stable region around the steady-state fixed-point may be rather small.Furthermore, the results of above considerations are applied to a brake-noise problem. It is found that, in contrast to squeal, a decaying friction characteristic may be a satisfying explanation for the onset low-frequency groan. The analytical results are compared with experimental measurements.     

Modelling of dynamical systems with motion dependent discontinuities

The paper introduces two concepts for describing and solving dynamical systems with motion dependent discontinuities such as clearances, impacts, dry friction, or combination of these phenomena. The first approach assumes any dynamic system can be considered as continuous in a finite number of continuous subspaces, which together form so-called global hyperspace. Global solution is obtained by “gluing” local solutions obtained by solving the problem in the continuous subspaces. An efficient numerical algorithm is presented, and then used to solve dynamics of a piecewise oscillator, which has been also verified experimentally. The second approach considers that in reality the system parameters do not change in an abrupt manner. Therefore, a smooth contiunuous function is used to model a transition between the subspaces, in particular the sigmoid function is employed. This allows to control the degree of abruptness on the intersections of the continuous subspaces. An asymmetrical, piecewise linear oscillator has been examined to provide recommendations regarding validity of this approach.     

Bifurcation Behavior of a 1DOF Sliding Friction Oscillator

This article deals with different types of friction models and their influence on the behavior of a simple 1 degree-of-freedom (DOF) sliding friction oscillator which is in literature commonly referred to as “mass-on-a-belt”-oscillator. The examined friction characteristics are assumed to be proportional to the applied normal force and only dependend on the relative velocity between the mass and the belt. For an exponential and a generalized cubic friction characteristic, the linear stability of the steady-state and the bifurcation behavior in the sliding domain are examined. It is shown that the resulting phase plots of the observed system are strongly dependent on the chosen friction characteristic. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Experimental investigation of an oscillator with discontinuous support considering different system aspects

Non-smooth characteristics are, in general, the source of difficulties for the modeling and simulation of natural systems. These characteristics are usually related to either the friction phenomenon or the discontinuous behavior as intermittent contacts. This article develops an experimental investigation concerning non-smooth systems with discontinuous support. An experimental apparatus is developed in order to analyze the nonlinear dynamics of a single-degree of freedom system with discontinuous support. The apparatus is composed by an oscillator constructed by a car, free to move over a rail, connected to an excitation system. The discontinuous support is constructed considering mass–spring systems separated by a gap to the car position. This apparatus is instrumented to obtain all the system state variables. System dynamical behavior shows a rich response, presenting dynamical jumps, bifurcations and chaos. Different configurations of the experimental set up are treated in order to evaluate the influence of the internal impact within the car and also support characteristics in the system dynamics.     

Impulse-based control of simple oscillators within the nonsmooth mechanics approach

An impulse-based control scheme for a simple spring-mass oscillator subject to set-valued friction forces is presented. In contrast to PD or PID control laws, the proposed control law prevents non-zero steady state errors and limit cycles. Motivated by Wouw and Leine [1], it is shown that impulse-based control laws can lead to satisfactory behavior if the oscillator starts sticking. In order to realize a practical implementation, the equations of motion are extended by a mathematical model of the actuator dynamics. The analysis is undertaken in the framework of nonsmooth mechanical systems. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

An Inertial Proximal Method for Maximal Monotone Operators via Discretization of a Nonlinear Oscillator with Damping

Set-Valued and Variational Analysis - The ‘heavy ball with friction’ dynamical system x + γx + ?f(x)=0 is a nonlinear oscillator with damping (γ&;gt;0). It has been...     

Electrostatic Ash and Water Flow Mixture Modeling

Slurry flow consisting of 63% electrostatic filter ash and 37% water is subject of investigation reported in this contribution which tries to determine the most appropriate rheological model. The authors have modeled experimental data obtained from actual experimental setup, i.e. pipe viscometer and derived model parameters for Power Law as well as for Sisko model. Based on this analysis a numerical simulation of experiment has been attempted using well known Power Law model and taking the advantage of CFX 4.3 numerical code. This was mainly attempted in order to verify use of the same numerical package later for purpose of building a library of friction coefficients to be used in pipe flow analysis with lumped parameters computer code.     

An extended LuGre friction model incorporating frictional aging

In this contribution, the LuGre model is extended and the effect of frictional aging is incorporated using the state variable approach. The adapted friction model is used in combination with a single-degree-of-freedom oscillator to investigate the basic effects on the stick-slip amplitude and period. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A Spiral Tribometer for Dynamic Friction Measurements

Basically there exists a significant interest in dynamic friction models [1]. These dynamic models describe μ as a time dependent process parameter. The indentification of the belonging parameters needs a special kind of measurements. This is due to the fact that the measurements with the classical pin on disk arrangement give stationary values of μ only, the measurements of dynamic properties are even infeasible. A new advanced tribometer has been developed. This tribometer allows measurements of complex unsteady friction processes. The experimental characteristics and the realization of this novel tribometer are presented by concrete measurements. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A distributed friction model for energy dissipation in carbon nanotube-based composites

Being lighter and stiffer than traditional metallic materials, nanocomposites have great potential to be used as structural damping materials for a variety of applications. Studies of friction damping in the nanocomposites are largely experimental, and there has been a lack of understanding of the damping mechanism in nanocomposites. A new friction contact model is developed to study the energy dissipation of carbon nanotube (CNT)-based composites under dynamic loading. The model incorporates the spatially-distributed nature of the CNT in order to capture the stick/slip phenomenon at the interface and treats the total slip force in a statistical sense. The effects of several parameters on energy dissipation are investigated, including the excitation’s amplitude, the interaction between CNT’s ends and matrix, the orientation, concentration, and diameter distribution of the CNTs inside the matrix. The results are in good agreement with experimental observations in the literature.     

Effect of orientation and crystallinty on the friction and wear of polytetrafluoroethylene

A study has been made of the laws governing the changes in wear of polytetrafluoroethylene (PTFE) in relation to the degree of crystallinity and the changes in friction and wear of preoriented PTFE in relation to the working conditions of the metal-polymer friction pair. From the experimental results, conclusions may be drawn concerning the possibility of increasing the wear resistance of polymers by modifying their structural characteristics.Mekhanika Polimerov, Vol. 2, No. 1, pp. 87–92, 1966     

Modelling of lateral oscillations in the interface of brake systems

The research of the dynamics in the boundary layer of brake pads can afford revealing technical expertise concerning different phenomena occurring in brake systems (e.g. squealing, judder, Hot Spots). For manufacturers of brake systems, the phenomenon “squealing” is of particular interest due to the desired driving comfort. The mentioned phenomena have been researched by numerous scientists. Different models have been developed and approved by experimental results. The authors agree upon the fact that the main excitation mechanism of the mentioned effects in brake systems is caused by the variation of the lateral (in-plane) friction force and friction torque respectively [1]. A model describing the dynamical interaction of friction and wear in the contact zone of brake systems has been introduced in [2]. Based on this theory, the brake pad's boundary layer consists of characteristic hard and smooth structures on the mesoscopic length scale. A new concept of the initiation of the squealing mechanism is based on the synchronisation mechanism of these so-called patches emerging from the dynamical interaction of the friction partners. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the Influence of High-Frequency Excitation on Systems with Dynamic Friction

By imposing high-frequency vibrations to a system, the characteristics of dry friction for low sliding velocities can be smoothed and, consequently, undesired friction induced phenomena such as stick-slip motion can be quenched. Many studies have been published so far, most of them focussing on the reduction of friction between metal surfaces and using classical Coulomb friction models. Within this contribution the effect of high-frequency excitation on dry friction taking into account dynamic friction models will be discussed. To this end, the friction law suggested by Dahl is used and the resulting friction characteristics are compared to those obtained for the classical Coulomb friction model. Using Dahl's friction model, a reduction of the smoothing effect is observed. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

波浪、海洋土参数对海床稳定性影响

基于Yamamoto的多孔弹性介质模型,研究了波生底床的稳定性.通过给出的有限深底床下土响应分析解,针对三种土质底床,讨论了主要波参数和土参数对这些底床稳定性的影响.与其他土模型计算结果进行了比较,分析了海洋土内部Coulomb摩擦因素的影响.