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)     

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.     

Stabilization of sliding motion by partial stiction

Rotating friction disks are utilized in many drivetrain components such as dry clutches and their actuator systems. Even the simplest pin-on-disk or disk-on-disk mechanical systems with Coulomb friction reveal a rich dynamical behavior with different types of motions. Examining the radial dynamics of minimal friction disk models, it is a prevalent assumption to have pure sliding frictional contacts. Governed by the systems' design parameters and initial conditions, stable large amplitude motions at higher rotation speeds are possible. Using a Coulomb friction model with sticking and sliding instead, gives similar motions with alternating phases of sticking and sliding. However, the amplitude can be decreased significantly by these intermittent phases of stick and slip. It is suggested to exploit such motions with partial stiction in order to reduce amplitudes and thus stabilize the systems. Similar effects can be observed in 3D-multibody simulations and measurements of double clutch actuator systems. However, for these systems analytical treatment is not feasible any more due to the number of involved degrees of freedom. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modeling of large deformation frictional contact in powder compaction processes

In this paper, the computational aspects of large deformation frictional contact are presented in powder forming processes. The influence of powder–tool friction on the mechanical properties of the final product is investigated in pressing metal powders. A general formulation of continuum model is developed for frictional contact and the computational algorithm is presented for analyzing the phenomena. It is particularly concerned with the numerical modeling of frictional contact between a rigid tool and a deformable material. The finite element approach adopted is characterized by the use of penalty approach in which a plasticity theory of friction is incorporated to simulate sliding resistance at the powder–tool interface. The constitutive relations for friction are derived from a Coulomb friction law. The frictional contact formulation is performed within the framework of large FE deformation in order to predict the non-uniform relative density distribution during large deformation of powder die pressing. A double-surface cap plasticity model is employed together with the nonlinear contact friction behavior in numerical simulation of powder material. Finally, the numerical schemes are examined for efficiency and accuracy in modeling of several powder compaction processes.     

Effect of sliding velocity on area of real contact and on force of friction in high-elastic materials

The velocity dependence of the force of friction and the area of real contact of SKN-18, SKN-26, and SKN-40 rubbers has been simultaneously determined on an optical instrument. In the region of small sliding velocities the area of real contact is virtually independent of the sliding velocity, while the force of friction increases in proportion to the logarithm of the sliding velocity, in accordance with the molecular-kinetic theory of friction. At high sliding velocities a deviation in the velocity dependences of both quantities is observed. The constant of friction has been determined over the entire velocity range and the resulting velocity dependence is examined in molecular terms.Mekhanika Polimerov, Vol. 3, No. 2, pp. 309–311, 1967     

Frictional contact of elastomer materials on rough rigid surfaces

The frictional behavior of elastomer materials is still unexplored, but very important for many industrial applications. Special attention is turned to rubber friction on rough road tracks. Due to the non‐rigid material characteristics of the rubber it is not sufficient to use a constant friction coefficient like Coulombs law. The frictional qualities depend on many different influences like sliding velocity, applied normal stress, surface roughness, material properties and the temperature in the contact zone. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Bifurcation analysis of a stochastic non-smooth friction model

Non-smooth friction systems such as systems with dry friction show several bifurcation phenomena. The discontinuity of these so called slip-stick vibrations makes these systems interesting and there has been a lot of research in this field, see for example Hinrichs [1]. Due to the non-smooth friction force even the deterministic system shows a rich bifurcation behavior. Measurements indicate that the friction coefficient which plays a large role in the system behavior is not deterministic but can be described as a friction characteristic with added white noise. Therefore, the stochastic characteristic is introduced into the non-smooth system and the change of the bifurcation behavior is studied. (© 2009 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.     

A qualitative analysis of the dynamics of a disc on an inclined plane with friction

The problem of the motion of a disc on an inclined plane with dry friction is investigated. It is shown that, if the friction coefficient is greater than the slope of the plane, the disk will come to rest after a certain finite time, and its sliding and rotation will cease simultaneously. The limit position of the instantaneous centre of velocities is indicated. The limit motions of the disc in the case when the ratio of the friction coefficient to the slope of the plane is equal to or less than unity: uniform sliding (in the case of a general position) and equiaccelerated sliding (always) of the disc along the line of greatest slope of the plane, respectively, are obtained. The case when the friction coefficient is equal to the slope, while the initial sliding velocity is directed upwards along the line of greatest slope, is an exception. In this case, the disc comes to rest after a finite time, and the sliding velocity and the angular velocity of the disc vanish simultaneously.     

Generation of surface waves through friction: FEM investigation

Sliding friction between two bodies can generate elastic vibration. This study uses a finite-element model comprising an elastic body sliding against a flat rigid surface with constant coefficient of friction. For the elastic body a structured topography is taken into account. The model shows traveling surface waves, which depend on the asperities of the sliding surface. It can be shown that the surface structure and its inertia are the cause for elastic waves in the contact region. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Friction induced flutter instability - on modeling and simulation of brake-squeal -

The issue of this contribution are self–excited vibrations due to sliding friction between moving elastic bodies. Starting from Hamiltons principle, the normal contact is implemented by two different approaches. Assuming discretizations in a spatial coordinate frame, the structure of the resulting equations of motions is outlined. For a simple model of a disc–brake, stability charts of the steady–state are presented, which show a considerable influence of the motion of the disc on the stability behavior. Finally, the influence of penalty approaches to the normal contact is addressed shortly. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Bifurcation analysis of a stochastic non-smooth friction model

Non-smooth systems with stochastic parameters are important models e.g. for brake and cam follower systems. They show special bifurcation phenomena, such as grazing bifurcations. This contribution studies the influence of stochastic processes on bifurcations in non-smooth systems. As an example, the classical mass on a belt system is considered, where stick-slip vibrations occur. Measurements indicate that the friction coefficient which plays a large role in the system behavior is not deterministic but can be described as a friction characteristic with added white noise. Therefore, a stochastic process is introduced into the non-smooth model and its influence on the bifurcation behavior is studied. It is shown that the stochastic process may alter the bifurcation behavior of the deterministic system. (© 2010 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)     

Simulation of friction phenomena between randomly rough elastic surfaces

Friction induced vibrations are a widely studied field in which the friction coefficient is one of the most important parameters. Measurements show that the friction coefficient underlies stochastic fluctuations. To gain more knowledge about the friction coefficient a finite element study is carried out in order to simulate the friction forces. The Bowden-Tabor model is implemented which calculates the friction force as the force which is needed to shear apart contact areas hold together by welding or adhesion. The dependency of the friction value on sliding velocity and normal pressure can be determined with this model. Different realization are studied and the stochastic properties of the friction value such as mean value, standard deviation, amplitude spectrum and correlation coefficient can be calculated depending on the roughness of the surface. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Friction and rheological properties of resin-impregnated glass tape

The dependence of the dynamic coefficient of friction of resin-impregnated glass tape on the sliding speed over the mandrel surface and the viscosity of the resin is derived. The formulas obtained are confirmed by the results of experiments which indicate a linear dependence of the coefficient of friction on the sliding speed of the tape over a metal mandrel. Graphically, this dependence is expressed by straight lines with a common origin and a slope that increases with the viscosity of the resin. The coefficient of friction of glass tape sliding over a prewound layer at low speeds also has a linear dependence. At high speeds the dependence takes the form of a damped curve.Translated from Mekhanika Polimoerov, No. 1, pp. 166–170, January–February, 1976.     

A two-parameter friction model

The new friction model proposed in this paper takes all types of friction into account: sliding, pivoting and rolling friction. The model depends on two parameters. With a zero value of one parameter it is converted into the Contensou–Zhuravlev model, and with a zero value of the other parameter it is converted into the Coulomb model.The interaction of a body with the bearing surface during translational motion of the body is described fairly adequately by the classical model of dry friction (Coulomb's law). In the case of plane-parallel translational motion of the body, the Contensou–Zhuravlev model must be used;1, 2 this model takes both sliding friction and pivoting friction into account. The friction model proposed below is suitable for describing arbitrary translational motion of the body.     

Molecular dynamics simulation of lubricated contact between textured surfaces

In this contribution, the friction at atomical scale has been investigated by using molecular dynamics (MD) simulations. This work surves as a preliminary study on the influence of surface texture on the friction at atomic scale, where simple rectangular grooves are added to the contact surface. Our results suggest definite dependence of the friction on the orientation of the grooves, which decreases as the velocity increases. For a given velocity, an optimal direction of sliding which gives the minimum averaged friction coefficient can be identified. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Adaptive sliding mode control of a high-precision ball-screw-driven stage

High-precision position control has been widely used in scientific instruments and semiconductor fabrication equipment. Traditionally, controllable displacements with sub-micron and nano-level resolution are usually achieved by piezoelectric actuators because of their high bandwidth and ease of control. However, the travel range of piezoelectric actuator is usually small. In this paper, the ball-screw-driven system is studied to provide long-range and high-precision performance for positioning and tracking control. In such a system, the friction dynamics are divided into the static and the dynamic regimes to describe the dynamic behavior of a conventional ball-screw-driven x-y stage. The same form of adaptive sliding mode controllers are designed in the static and dynamic regimes to obtain the precision performance for controlled stage. A proportional-integral switching surface is proposed to make it easy to assign the performance of the systems in the sliding mode motion and the controller is robust without knowing the bound of disturbance in advance. An illustrative example is included to demonstrate that the system achieves high precision (10 nm) and long-range (10 cm) positioning performance with repeatability and robustness by the proposed control approach.     

Verification of an anisotropic Coulomb adhesion-friction law for contact surfaces with periodic structure

Sliding friction forces and so-called adhesion forces are the main mechanical characteristics to describe contact interaction. Both together are representing 2D surface constitutive laws in analogy to e.g. elasto-plasticity for 3D continua. The classical model to generalize the Coulomb friction law into anisotropic domains is to introduce an anisotropic friction tensor. Michalowski and Mroz in [1] proposed the structure of the friction tensor considering the sliding of a rigid block on an inclined surface. Zmitrowicz in [2] developed the theoretical basis for the structure of the friction tensor on symmetry groups for the tensor. The current contribution is aimed at verification of this modeling process based on a homogenization procedure for a very fine discretization representing the exact structure of the surface. The validation issue with realistic experiments given in [4] is discussed as well. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)