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     

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.     

The calculation of the energy losses in a sliding elastic contact with friction and wear (the plane problem)

The plane problem of the sliding contact of a punch with an elastic foundation when there is friction and wear is considered. Assuming the existence of a steady solution in a moving system of coordinates, relations are derived between the sliding velocity, the wear, the contact stresses and the displacements for an arbitrary dependence of the wear rate on the contact pressure. Taking into account the presence of a deformation component of the friction force, an equation is written for the balance of the mechanical energy for the punch - elastic base system considered. It is shown that the equality of the work of the external force in displacing the punch to the losses due to friction and the change in the shape of the foundation due to wear is satisfied when the work done by the contact stresses on the increments of the boundary displacements is equal to zero, and the frictional losses must be determined taking into account the non-uniformity of the distributions of the shear contact stresses and the sliding velocity in the contact area. Two special cases of the foundation in the form of a wide and narrow strip are considered, for which the total coefficient of friction is calculated, taking into account the deformation component of the friction force.     

Friction of polymeric materials. 4. effect of temperature and relative sliding velocity on the coefficient of friction of flastomers

The relationship between the coefficient of friction of elastomers and the temperature and sliding velocity has been calculated for various specific pressures on the assumption that the frictional force is low and that heating up of the surface of the bodies rubbing against each other can be neglected. Qualitative agreement with experimental results was obtained. The changes in the coefficient of friction observed are explained in terms of the temperature dependence of the volumetric properties of the elastomer, Young's modulus, and the shearing strength. A formula is proposed for calculating the rate of deformation of the material in the contact zone, which depends on the radius of curvature of the hump and the sliding velocity.     

Some laws of plastics friction

The dependence of the actual contact area S of plastics on temperature, specific load, and sliding speed has been investigated. The value of S increases exponentially with the specific load, the maximum value at large specific loads being less than the nominal contact area. The temperature dependence of S under static conditions between 20 and 130° C is attributable to the decrease in the static modulus of elasticity of the plastic near the glass transition point and to the development of high-elastic and plastic deformations at elevated temperatures. There is practically no change in S as the sliding speed varies from 10^–3 to 10 cm/min; at the same time the force of friction increases slightly.Mekhanika Polimerov, Vol. 3, No. 6, pp. 1078–1081, 1967     

Temperature dependence of the actual contact area and friction force of high-elasticity materials

An investigation of the temperature dependence of the actual contact area (under static conditions and during friction at a given sliding speed) of materials based on butadienenitrile rubber in a wide temperature interval is described. Measurements of the friction force were also made. It was established that the temperature dependence of the contact area is associated with corresponding changes in the elasticity modulus (nonequilibrium static modulus for contacts at rest and dynamic modulus for nonstationary contacts). The friction constant c decreases linearly with rising temperature and does not depend on the applied load.Mekhanika Polimerov, Vol. 3, No. 4, pp. 726–729, 1967     

The sliding of viscoelastic bodies whenthere is adhesion

The plane contact problem of the sliding without friction of a rigid cylinder over a viscoelastic half-space when there is adhesion is solved, neglecting the inertial properties of the half-space. The distribution of the contact pressure, the size and position of the contact area, and the deformation force of resistance to motion of the cylinder are investigated as a function of the adhesion properties of the surfaces, the mechanical characteristics of the half-space and the sliding velocity of the cylinder.     

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)     

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)     

Deformation of polymers under friction loading

A study has been made of the laws of distribution of elastic and residual deformations in the surface layers of polymers subjected to friction. The dependence of these deformations on normal pressure, sliding velocity, and duration of loading has been determined. A relation between deformation and antifriction characteristics has been established, and the relative effect of normal and tangential loads on surface-layer deformation determined.Mekhanika Polimerov, Vol. 3, No. 3, pp. 539–543, 1967     

Formation of the true contact area between high-elastic materials and a hard smooth surface

The change in the true contact area between rubber and glass on passing from static to dynamic friction has been studied experimentally. The extent of this change depends on the applied normal load and the contact time. The change of friction force is determined by the conditions of formation of the true contact area under the action of normal and tangential forces.Mekhanika Polimerov, Vol. 2, No. 2, pp. 263–268, 1966     

Rubber wear during friction against a metallic surface (with reference to packing glands for high-speed machine elements)

The wear of rubber in sliding against a metallic surface at high sliding velocities, which causes temperatures at the point of contact of the order of 100–250°C, has been studied. The theoretical equation obtained relates the wear of rubber during sliding against a metallic surface to its elastic-strength and friction properties and to the geometrical characteristics of the metal surface. Satisfactory agreement between theory and experiment is found.Mekhanika Polimerov, Vol. 1, No. 6, pp. 120–126, 1965     

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.     

A dynamically consistent model of the contact stresses in the plane motion of a rigid body

The problem of determining dry friction forces in the case of the motion of a rigid body with a plane base over a rough surface is discussed. In view of the dependence of the friction forces on the normal load, the solution of this problem involves constructing a model of the contact stresses. The contact conditions impose three independent constraints on the kinematic characteristics, and the model must therefore include three free parameters, which are determined from these conditions at each instant. When the body is supported at three points, these parameters (for which the normal stresses can be taken) completely determine the model, while indeterminacy arises in the case of a larger number of contact points and, in order to remove this, certain physical hypotheses have to be accepted. It is shown that contact models consistent with the dynamics possess certain new qualitative properties compared with the traditional quasi-static models in which the type of motion of the body is not taken into account. In particular, a dependence of the principal vector and principal moment of the friction forces on the direction of sliding or pivoting of the body, as well as on the magnitude of the angular velocity, is possible.     

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)     

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     

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)     

Friction of polymeric materials

The case of contact of polymer and metallic surface has been examined. A formula is proposed for calculating the contact area as a function of time of holding the compression surface under load and for calculating the coefficient of friction, the dependence of Young's modulus and shear strength on temperature, deformation rate, and average force on the contact surface being taken into account. The nature of deformation of irregularities on the surfaces of polymeric materials under the action of normal and tangential loading has been examined.See [1] for Communication 1.Institute for Polymer Mechanics, Academy of Sciences of the Latvian SSSR, Riga. Translated from Mekhanika Polimerov, No. 5, pp. 809–815, September–October, 1972.