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.     

Friction and wear of certain thermoplastic materials in physiological solution

The wear resistance of certain thermoplastics has been subjected to comparative investigation together with the velocity dependence of the coefficients of friction at various pressures and after various periods of contact with a model physiological solution.Priorov Central Scientific-Research Institute of Traumatology and Orthopedics. Moscow Technological Institute of the Food Industry. Second Moscow Pirogov State Medical Institute. Translated from Mekhanika Polimerov, No. 6, pp. 1116–1119, November–December, 1971.     

Influence of temperature on frictional properties of highly elastic materials in vacuum under high normal pressures

Experimental results obtained by the rubbing of cross-linked rubbers against smooth steel surfaces in vacuum under volume compression conditions at high normal pressures are examined. The influence of volume compression on the frictional properties of highly elastic materials at various temperatures is explained. Basic rules of temperature functions of specific frictional force at high normal pressures in vacuum and in atmosphere are established.V. I. Lenin Moscow State Pedagogical Institute, Problem Laboratory for Polymer Physics. Translated from Mekhanika Polimerov, No. 1, pp. 91–97, January–February, 1972.     

Contact Dehn surgery, symplectic fillings, and Property P for knots

These are notes of a talk given at the Mathematische Arbeitstagung 2005 in Bonn. Following ideas of Özbağcı–Stipsicz, a proof based on contact Dehn surgery is given of Eliashberg's concave filling theorem for contact 3-manifolds. The role of the theorem in the Kronheimer–Mrowka proof of Property P for nontrivial knots is sketched.     

The stress-deformed state of a packet of cylindrical shells taking account of friction

We propose a method of determining the contact pressures between the shells in a packet under the influence of nonlinear internal and constant external pressure. Using the equations of the general moment theory of shells we determine the stress-deformed state of a packet of finite cylindrical shells taking account of frictional forces on the contacting surfaces. One table. Bibliography: 10 titles.Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 30, 1989, pp. 94–98.     

An Ozsváth–Szabó Floer homology invariant of knots in a contact manifold

Using the knot Floer homology filtration, we define invariants associated to a knot in a three-manifold possessing non-vanishing Floer co(homology) classes. In the case of the Ozsváth–Szabó contact invariant we obtain an invariant of knots in a contact three-manifold. This invariant provides an upper bound for the Thurston–Bennequin plus rotation number of any Legendrian realization of the knot. We use it to demonstrate the first systematic construction of prime knots in contact manifolds other than S³ with negative maximal Thurston–Bennequin invariant. Perhaps more interesting, our invariant provides a criterion for an open book to induce a tight contact structure. A corollary is that if a manifold possesses contact structures with distinct non-vanishing Ozsváth–Szabó invariants, then any fibered knot can realize the classical Eliashberg–Bennequin bound in at most one of these contact structures.     

The Harnack Estimate for the Yamabe Flow on CR Manifolds of Dimension 3

We deform the contact form by the amount of the Tanaka–Webstercurvature on a closed spherical CR three-manifold.We show that if a contact form evolves with free torsion from initial datawith positive Tanaka–Webster curvature, then a certainHarnack inequality for the Tanaka–Webster curvature holds.     

Determination of contact stresses in problems on bending of a package of transversely isotropic bars

A mechanomathematical model for bending of packages of transversely isotropic bars of rectangular cross section is proposed. Adhesion, slippage, and separation zones between the bars are considered. The resolving equations for deflections and tangential displacements are supplemented with a system of linear differential equations for determining the normal and tangential contact stresses, and boundary conditions are formulated. A scheme for analytical solution of two contact problems—a package under the action of a distributed load and a round stamp—is considered. For these packages, a transition is performed from the initial system of differential equations for determining the contact stresses, where the unknown functions are interrelated by recurrent relationships, to one linear differential equation of fourth order and then to a system of linear algebraic equations. This transition allows us to integrate the initial system and get expressions for the contact stresses.Translated from Mekhanika Kompozitnykh Materialov, Vol. 40, No. 6, pp. 761–778, November–December, 2004.     

Static friction of metal - polymer pairs under vacuum conditions

The static friction of a series of polymer — steel friction pairs has been investigated as a function of the stationary contact time at temperatures from –150°C to +200°C. The experimental technique is described and the results of the experiments are evaluated.Novocherkassk Sergo Ordzhonikidze Polytechnic Institute. Translated from Mekhanika Polimerov, No. 6, pp. 1065–1069, November–December, 1970.     

Investigation of the starting conditions of rolling thixotropic polymeric systems

The solution of the problem of flow in the roll gap of a polymeric system whose rheological behavior is described by Leonov's thixotropic model is presented. Analytical expressions are obtained for specific pressures, thrusts, and torques under transient rolling conditions, which permitted developing a method of calculating the maximum values of the energy and force characteristics.Lensovet Leningrad Technological Institute. Translated from Mekhanika Polimerov, No. 1, pp. 133–140, January–February, 1972.     

Tribological periodic processes exhibited by acceleration or braking of a shaft–pad system

A new one-dimensional thermoelastic frictional pair contact model of a shaft–bush system is proposed. The assumed model includes a study of vibration processes and contact characteristics exhibited by a relative velocity between the two mentioned bodies, contact temperature, pressure and wear. Some important conclusions are formulated.     

Valuations with Crofton formula and Finsler geometry

Valuations admitting a smooth Crofton formula are studied using Geometric Measure Theory and Rumin's cohomology of contact manifolds. The main technical result is a current representation of a valuation with a smooth Crofton formula. A geometric interpretation of Alesker's product is given for such valuations. As a first application in Finsler geometry, a short proof of the theorem of Gelfand–Smirnov that Crofton densities are projective is derived. The Holmes–Thompson volumes in a projective Finsler space are studied. It is shown that they induce in a natural way valuations and that the Alesker product of the k-dimensional and the l-dimensional Holmes–Thompson valuation is the (k+l)-dimensional Holmes–Thompson valuation.     

Vibration of a Reissner–Mindlin–Timoshenko plate–beam system

In this paper, we consider a plate–beam system in which the Reissner–Mindlin plate model is combined with the Timoshenko beam model. Natural frequencies and vibration modes for the system are calculated using the finite element method. The interface conditions at the contact between the plate and beams are discussed in some detail. The impact of regularity on the enforcement of certain interface conditions is an important feature of the paper.     

Study of the autoadhesion of polyethylene -polyisobutylene compositions

The autoadhesion of polyethylene-polyisobutylene compositions is shown to depend importantly on contact pressure. The introduction of a filler may increase or reduce the autoadhesion of the composition. The experimental results are explained in terms of the diffusion theory of autoadhesion.Moldavian Scientific-Research Institute of the Food Industry, Kishinev. Translated from Mekhanika Polimerov, No. 3, pp. 532–534, May–June, 1971.     

Effect of a vacuum on the adhesion of rubbers to metal

The effect of a vacuum on the adhesion of rubbers to metals has been investigated both when the joints are formed in the vacuum and when joints formed under normal conditions are transferred to a vacuum. A method of estimating the effect of the vacuum, independently of the duration of contact and the contact temperature and pressure used in forming the joint, is described. The results obtained (a sharp increase in adhesion under vacuum) correspond to the theoretical notions of Bikerman concerning weak boundary layers.Central Scientific-Research Laboratory of Chemical Packaging, Moscow. Translated from Mekhanika Polimerov, No. 6, pp. 1036–1041, November–December, 1973.     

Effect of gaseous oxygen pressure on the kinetics of accumulation of residual deformation in resins

The authors studied changes in the properties of resins in the static deformed state under the effect of gaseous oxygen pressures of up to 200 atm at 25, 50, and 70° C for 20–500 days, depending on the experimental conditions. It was shown that an increase in gaseous oxygen pressure significantly affects the process of accumulation of residual deformation up to 30–40 atm while a further pressure rise has practically no effect on changes in the accumulation rate of residual deformation.Scientific-Research Institute of the Resin Industry, Moscow. Translated from Mekhanika Polimerov, Vol. 9, No. 3, pp. 552–554, May–June, 1973.     

Contact creep as the principal source of the losses associated with the rolling of a plastic ball

An engineering method is proposed for calculating the contact creep of plastic balls used in rolling bearings. The method is based on empirical expressions relating the relative creep strain with the specific load and its duration of action. The complex contact-creep characteristics of the material are obtained by means of simple laboratory tests.Moscow Bauman Higher Technical College. Translated from Mekhanika Polimerov, No. 3, pp. 498–504, May–June, 1969.     

Contact problems for beams and plates with low shear stiffness

The low shear stiffness and strength of unidirectionally reinforced plates and beams predetermines the choice of calculation model in specific problems [4]. The contact problem is considered for a glass-reinforced plastic plate resting on a Winkler foundation; the deformation properties of the plate are described by the equations of an orthotropic material; the investigation is based on generalized applied theories of the Timoshenko and Ambartsumyan types [5–8], which permit the high shear compliance of thin-walled structures to be taken into account.L'vov Polytechnic Institute; Ivan Franko Institute of Petroleum and Gas. Translated from Mekhanika Polimerov, No. 4, pp. 715–720, July–August, 1970.     

Method of nonlinear boundary equations in problems of contact of several elastic bodies

The method of nonlinear boundary equations is applied to develop new formulations of contact problems with unknown contact regions. Our formulation is free from inequality constraints, which enter the method of variational inequalities and the standard formulations of contact problems. Methods of the theory of operator equations are applied to prove that the problems are well-posed.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 61, pp. 62–70, 1987.     

Stability of the momentum state of a three-layer orthotropic cylindrical casing at uniform and nonuniform external pressures

The effect of the momentum subcritical state on the stability of three-layer orthotropic cylindrical casings at external pressures was investigated. The problem is solved by means of equations that take into account transversal shear. It is shown that in some cases the effect of the subcritical state momentum on the critical load parameter is significant.Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Mekhanika Polimerov, No. 5, pp. 874–879, September–October, 1972.