Friction of polymeric materials

The dry friction between a polymeric and a metallic surface is considered on the assumption that the friction power is such that heating of the surfaces can be neglected. The effect of the dimensionless specific load (ratio of nominal stress to elastic hardness of the polymer) on the friction process of elastomers and rigid polymers is analyzed and expressions are given for calculating the coefficients of friction of these materials at large values of the nominal stress.

     

Determination of a stochastic friction coefficient depending on a randomly rough surface

The goal of this contribution is to calculate the the friction coefficient for a scanned surface of a worn brake pad. The data shows that the asperities can be approximated by paraboloids which allows to calculate the contact force and area with the Hertz contact model if the deformation is elastic. The friction force is calculated with the Bowden-Tabor approach which suggests that the friction force is the force to shear apart contacting asperities. This is considered to be the dominant friction cause in dry contact. To generate many surfaces with similar peak statistics the spectral decomposition is used. The friction coefficient and it's stochastic properties is calculated for these surfaces. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modeling and simulations of the clutch dynamics using approximations of the resulting friction forces

The work presents the effectiveness of a certain class of approximate models of the resulting friction force found during simulations of a simplified model of clutch dynamics. The friction models are based on integral expressions assuming fully developed sliding and Coulomb's classical law of friction on each element of the planar contact. Special approximations of the integral model of the friction force and the moment are proposed, which are based on Padé approximants and their generalizations. The system of clutch dynamics is simplified to a friction disk on a rotating master disk. Two different configurations are investigated, including the coaxial and non-coaxial arrangement of the disks. The model based on the generalization of Padé approximants is compared with the corresponding approximants based on the Taylor series expansion and with the model using the integral expressions for the resultant friction force and torque components.     

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)     

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)     

Multiscale simulation for description of rubber friction

The interaction between tire and road generates the transferable forces, which are necessary for driving dynamics and safety. These forces are based on friction between rubber material and pavement surface and depend on the roughness of the pavement, the slip velocity, the contact pressure and the temperature. Based on the finite element method, the friction coefficient is calculated by numerical simulation. The roughness of the pavement surface is described by the height difference correlation function (HDCF), which allows partitioning into different length scales. This multiscale approach is suitable to understand and to evaluate friction phenomena. These phenomena are hysteresis friction based on dissipation inside the rubber material and adhesion friction, which describes the direct bonding between two materials. Given, that the material parameters of rubber highly depend on temperature and the frictional dissipation leads to a warming of the rubber, the provision for these effects is necessary for a realistic desciption of friction. The method allows an understanding of friction phenomena on the micro-scale like the real contact area or the microscopic contact pressure. Also, the temperature distribution inside the tire cross-section can be illustrated. The resulting coefficient of friction is validated by experimental data based on linear friction tests and compared to analytical solutions. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Nature and mechanism of friction of rubberlike polymers in different physical states

We have investigated the frictional properties of crosslinked butadiene-nitrile and butadiene-styrene copolymers and natural rubber in friction against polished steel under vacuum conditions in the temperature interval from –200 to +150° C, which embraces the glassy and high-elastic states, as well as the transition region between them. The temperature dependence of polymer friction is characterized by two maxima, a principal and a low-temperature maximum. The principal maximum, observed in the glass transition region, is not associated with the mechanical loss maximum observed in the polymers themselves. The temperature dependence of the force of friction is composed of three parts. In the high-elastic region there is an increase in the force of friction with fall in temperature, in accordance with the molecular-kinetic theory of friction of rubberlike polymers. In this region the nature of friction is associated with mechanical losses in the surface layer of polymer. The mechanical losses inside the polymer itself are unimportant. The deviation from the theoretical curve and the fall in the force of friction below a certain temperature in the transition region are chiefly associated with a decrease in the actual area of contact as the polymer passes into the glassy state. In the glassy region the friction is significantly determined by the mechanical losses in the polymer itself associated with the repeated elastic and forced-elastic deformation of the asperities in the layer of polymer in contact with the rigid surface. Therefore the low-temperature maximum is closely related to the mechanical loss maximum observed in the same temperature region in dynamic tests. Apart from this, the friction maximum is also associated with the increase in the forces of adhesion and the reduction of the actual area of contact at temperatures at which a forced-elastic mechanism of compression of the polymer asperities is not realized.Mekhanika Polimerov, Vol. 3, No. 1, pp. 123–135, 1967     

Friction properties of highly elastic materials at high contact pressures

A newly designed high-pressure tribometer has been employed to investigate the pressure dependence of the friction force of SKN-40 crosslinked butadiene-nitrile rubber in contact with a steel surface on the pressure range to 1200 kgf/cm² (20°C). Over the entire range of contact pressures the friction process is molecular-kinetic in nature and characterized by a linear dependence of the friction force on the logarithm of the sliding velocity. In the region of normal pressures up to 200 kgf/cm², where the effect of pressure on the friction force reduces to the formation of the actual contact area, the friction constant (proportionality factor relating the friction force and the actual contact area) is practically independent of the pressure. At pressures above 200–300 kgf/cm² the increase in the friction force at fixed actual contact area is attributable to the effect of pressure on the friction constant. The nature of this effect is related not with an increase in the chain-surface interaction energy (the activation energy does not increase), but with an increase in the forces of adhesion owing to the greater number of polymer chain-steel surface contacts on the actual contact area (increase in contact density).Lenin Moscow State Pedagogical Institute, Laboratory for Problems of Polymer Physics. Translated from Mekhanika Polimerov, No. 1, pp. 140–146, January–February, 1971.     

Consideration of friction between layers in determining the stress-strain state of structures with nonideal layer contact

A mathematical model for calculation of structures in a three-dimensional installation allowing for layer slippage with friction was constructed. The examples examined show that consideration of friction in problems of calculating laminated structures with nonideal layer contact can introduce an essential correction in the stress—strain state of the structure. In slabs with a freely sagging lower surface, friction is perceived for important friction coefficients and increases when the slippage surface approaches the loaded surface. In masses with a rigidly attached lower surface, even insignificant friction coefficients lead to essential redistribution of the stress—strain state.Ukraine Transportation University, Kiev, Ukraine. Translated from Mekhanika Kompozitnykh Materialov, Vol. 33, No. 2, pp. 192–199, March–April, 1997.     

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)     

On the motion of a heavy body with a circular base on a horizontal plane and riddles of curling

In this paper we discuss the dynamics of an axisymmetric rigid body whose circular area moves upon a horizontal rough surface. We investigate the interaction between the character of the law of friction and the curvature of the body’s trajectory. For the case of a curling stone it is shown that the observed effects can only be explained using the dependence of the friction coefficient on the Gümbel number. The procedure for constructing the law of friction based on experimental data is developed. It is shown that the available data can only be substantiated by means of anisotropic friction. The simplest model of such friction is constructed which provides quantitative coincidence with the experiment.     

Maximum force of friction in rubber-metal friction pairs under conditions of constant compressive deformation of the rubber

The maximum force of friction at the initial moment of slip has been investigated on rubber-metal friction pairs under conditions of constant compressive deformation of the rubber during transition from the high-elastic to the glassy state. Filled butadiene-nitrile rubber compounds were studied in the temperature range from +20 to –50°C. The temperature dependence of the maximum force of friction has a sharply expressed maximum near the glass transition temperature. As the temperature falls, the force of friction at first increases, in accordance with the molecular-kinetic theory. As the temperature continues to fall, in the transition region the maximum force of friction begins to rise more sharply owing to a sharp increase in the volume-mechanical friction component. The fall in the maximum force of friction below the glass transition point associated with a decrease in the deformed volume of rubber due to shrinkage and with the reduced mechanical loss factor.Mekhanika Polimerov, Vol. 3, No. 3, pp. 533–538, 1967     

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.     

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)     

The interaction of surface topography and friction dynamics in brake systems described by a Cellular Automaton

The friction coefficient μ , which is the quotient of the friction force R and the normal force N is in principal not a stationary material parameter, but also dependent on for instance the relative velocity, the normal load, the temperature, the climate conditions, the location and the event itself. The dynamics in the boundary layer between a brake disc and a brake pad is closely linked with the surface topography dynamics. Growing and destroying processes of hard, thin patches, carrying the friction power, determine the time-dependence of the friction coefficient. This interaction between friction and wear has already been simulated with a set of differential equations [2-4], which give an idea about the equilibrium of flow in the contact zone and which are able to describe the fading effect, for example. Based on this assumption we discretised the boundary layer with a Cellular Automaton [5], which makes it possible to have a more detailed look at the processes in the contact area. This paper will show new conclusions concerning the interdependencies of the friction behaviour and the surface topography. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Effect of normal load on the temperature and velocity dependence of the force of friction for high-elastic materials

The problem of the effect of normal load on the temperature and velocity dependence of the force of friction is examined for rubbers based on SKN-18, SKN-26, and SKN-40. In the temperature range from 18°–100°C the force of friction for these rubbers falls linearly with increase in temperature. The effect of loads up to 10⁷N/cm² on the temperature dependence of the force of friction for SKN-18, SKN-26, and SKN-40 rubbers reduces to a change in the real contact area or an increase in the temperature dependence with increase in load.The velocity dependence of the force of friction for SKN-18 rubber reveals a weak dependence of the activation energy and the average "jump distance" of the molecular chains on specific load. In the low-velocity region the force of friction depends linearly on the logarithm of velocity, at velocities above 0.44 cm/min and pressures of 30×10⁵ N/cm² the force of friction increases sharply due to an increase in uncontrolled heating of the friction surfaces.Mekhanika Polimerov, Vol. 1, No. 4, pp. 123–129, 1965     

Influence of friction in material characterization in microindentation measurement

A comprehensive computational study is undertaken to identify the influence of friction in material characterization by indentation measurement based on elasto- plastic solids. The impacts of friction on load versus indentation depth curve, and the values of calculated hardness and Young’s modulus in conical and spherical indentations are shown in this paper. The results clearly demonstrate that, for some elasto-plastic materials, the curves of load versus indentation depth obtained either by spherical or conical indenters with different friction coefficients, cannot be distinguished. However, if utilizing the parameter β (see text for details), to quantify the deformation of piling-up or sinking-in, it is easy to find that the influence of friction on piling-up or sinking-in in indentation is significant. Therefore, the material parameters which are related to the projected area will also have a large error caused by the influence of friction. The maximum differences on hardness and Young’s modulus can reach 14.59% and 6.78%, respectively, for some elastic materials shown in this paper. These results do not agree with those from researchers who stated that the instrumented indentation experiments are not significantly affected by friction.     

Self-excited oscillations of a two-mass oscillator with dry “stick-slip” friction

A system of two masses, moving along a single straight line, is considered. The first is connected by a spring to a fixed point, while the second is connected by a spring to the first and is in contact with a belt with dry friction moving with constant velocity. A piecewise-constant model of dry friction with different coefficients of friction, sliding and at rest, is used. The limit “stick-slip” type cycles are investigated analytically. It is shown numerically that in the case of equal masses there are forward and reverse limit cycles. The period of the oscillations of the forward and reverse cycles increases as the ratio of the stick and slip coefficients of friction increases, and decreases when the velocity of the belt increases. The reverse cycle exists for all values of the parameters of the problem, while the forward cycle exists up to a certain critical value of the ratio of the stick and slip coefficients of friction, and this critical value increases when the velocity of the belt increases.     

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.