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)     

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)     

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.     

Numerical evaluation of the temperature field of steady-state rolling tires

Rubber is the main component of pneumatic tires. The tire heating is caused by the hysteresis effects due to the deformation of the rubber during operation. Tire temperatures can depend on many factors, including tire geometry, inflation pressure, vehicle load and speed, road type and temperature and environmental conditions. The focus of this study is to develop a finite element approach to computationally evaluate the temperature field of a steady-state rolling tire. For simplicity, the tire is assumed to be composed of rubber and body-ply. The nonlinear mechanical behavior of the rubber is characterized by a Mooney–Rivlin model while the body-ply is assumed to be linear elastic material. The coupled effects of the inflation pressure and vehicle loading are investigated. The influences of body-ply stiffness are studied as well. The simulation results show that loading is the main factor to determine the temperature field. The stiffer body-ply causes less deformation of rubber and consequently decreases the temperature.     

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     

Frictional Contact of Rubber on rough Surfaces

The aim of this work is to investigate the frictional behaviour of rubber on rough rigid surfaces. Rubber friction is composed of hysteretic and adhesional effects. The main focus lies on the hysteresis theory which motivates rubber friction with the internal damping inside the viscoelastic material. It is necessary to perform a multiscale analysis to regard the roughness of the surface on all important length scales. The fractal surface is approximated by a superposition of harmonic functions. The simulations will start at the lowest wavelength and proceed to larger scales by replacing the smaller roughness with the ascertained friction law. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

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     

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     

On final motions of a Chaplygin ball on a rough plane

A heavy balanced nonhomogeneous ball moving on a rough horizontal plane is considered. The classical model of a “marble” body means a single point of contact, where sliding is impossible. We suggest that the contact forces be described by Coulomb’s law and show that in the final motion there is no sliding. Another, relatively new, contact model is the “rubber” ball: there is no sliding and no spinning. We treat this situation by applying a local Coulomb law within a small contact area. It is proved that the final motion of a ball with such friction is the motion of the “rubber” ball.     

Global stability conditions of a system with hysteresis nonlinearity

The paper discusses a two-dimensional automatic control system that contains a single hysteresis element of the general form. Systems of this type are mathematical models of real control systems and have been considered in many papers on this subject. In this paper, a system phase space, which is a manifold with a boundary, is constructed. The conditions under which the system is globally stable in a certain sense are formulated. The term sliding mode is used in the formulation ([15], Fig. 4).     

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.     

Dynamic responses of the impact drive mechanism modeled by the distributed parameter system

The piezoelectric actuator has been used for precision positioning from micro-meter down to nano-meter scale. In this paper, the impact drive mechanism (IDM) is designed to achieve a high accuracy and ability in precision positioning motion, where the frictional force is described by the Leuven model combined with the Bounc–Wen model of the hysteresis. The frictional model allows accurate dynamic modeling both in the sliding and the presliding regimes without using switching functions. The governing equations with the hysteresis effects of the distributed parameter system are formulated to obtain the dynamic responses. By using the finite element formulation, numerical solutions due to effects of the piezoelectric element (PE) are provided to compare between the distributed and lumped parameter systems of the IDM. It is shown that the neglect in the mass of the PE will cause the precision errors in the scale of tens nano-meters.     

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)     

Experimental investigations on the mechanical behavior of filled rubber

A lot of experimental results on the elastic as well as on the inelastic behavior of elastomer materials are known. However, so far now systematic examination on defined rubber mixtures has been reported. In this presentation the phenomenology of elastomer materials is characterized on the basis of extension and compression tests performed with dumbbell– and S2–specimen. Stiffness, upturn (stiffness at final deformation), hysteresis and remaining deformation have been analyzed for well defined rubber systems and environmental conditions. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Effect of liquid media on the deformation of the surface layers of a polymer-metal pair in sliding friction

The relation between the high-elastic component of polyurethane deformation and the deformation of the surface layers of metals has been investigated for sliding friction in various media. The surface layers of polymer and metal are plastically deformed. There is a certain correlation between the coefficient of friction and the amount of deformation.Kiev Institute of Civil Aviation Engineers. Translated from Mekhanika Polimerov, No. 1, pp. 147–149, January–February, 1970.     

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)     

A physically motivated model for filled elastomers including strain rate and amplitude dependency in finite viscoelasticity

A microstructure-based model of rubber reinforcement, the so-called dynamic flocculation model (DFM), is presented describing filler-induced stress softening and hysteresis by the breakdown and reaggregation of strained filler clusters [1]. An extension of this model allows to consider incomplete deformation cycles that occur in the simulation of arbitrary deformation histories [2]. Good agreement between measurement and the model is obtained for CB-filled elastomers like NR, SBR or EPDM, loaded along various deformation histories. One very important aspect is that the model parameters can be directly referred to the physical properties. This benefit is used to extend the model to further essential effects like time- and rate-dependent material behavior. In the limit range above the glass transition temperature these viscoelastic effects originate mainly from the filler-filler interactions. In the material model these interactions are characterized by two material parameters s_v and s_d, respectively. The parameter s_v defines the strength of the virgin filler cluster, whereas s_d represents the strength according to the broken or damaged filler clusters. Both parameters can be defined as functions of time s_v,d = ŝ_v,d(t), which can be motivated by physical meaning [3]. Due to this extension it is possible to capture the very complex strain rate and amplitude dependency during loading and relaxation. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)