Polymer friction

The results of research on the antifriction properties of polymeric materials and expressions for calculating their coefficient of friction are presented. The effect of the mechanical properties of the materials on their antifriction characteristics is discussed.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 3, pp. 421–429, May–June, 1975.     

Antifriction and mechanical properties of polymer compositions based on silicone adhesives

A comparative investigation has been made of the antifriction and mechanical properties of polymer compositions based on K-400 silicone adhesive and fillers in the form of finely dispersed powdered polymers (tetrafluoroethylene, Kapron, polyethylene), graphite, sawdust, B-83 babbitt, and a lubricant^–US-2 grease. The antifriction properties of these materials are not inferior to those of some common nonferrous metals (B-83 babbitt, TsAM9-1.5 zinc alloy, OTsS5-5-5 bronze). The rational range of application of the compositions investigated is indicated.Rostov-on-Don Institute of Railroad Transport Engineers. Translated from Mekhanika Polimerov, No. 5, pp. 937–940, September–October, 1969.     

Investigation of polytetrafluorethylene surface texture

Results are given of an X-ray investigation of the formation of a textured surface layer on polytetrafluorethylene (PTFE) film and its dependence on external mechanical factors — unit load and sliding speed. It is established that the thickness of the surface texture of PTFE is determined by the relation between the processes of texture formation under the influence of frictional forces and its destruction by wear. These processes, in turn, are determined by the working parameters of the moving joint. Data on the kinetics of polymer surface texture formation in the presence of friction are extremely useful in relation to the design of efficient antifriction materials.Mekhanika Polimerov, Vol. 1, No. 2, pp. 129–132, 1965     

Investigation of the fatigue properties of rigid polymers used in making harmonic drives

The fatigue properties of rigid polymers used for making harmonic drive components have been investigated. Certain data on the fatigue of flexible shells under complex loading conditions have been obtained. The effect of the polymer structure on the fatigue properties of a series of compounds with various antifriction fillers and plasticizing additives is evaluated.Translated from Mekhanika Polimerov, No. 6, pp. 1014–1019, November–December, 1970.     

Some features of the frictional behavior of polymeric crystalline materials

The coefficients of friction for thin polymeric films are calculated, and it is shown that the coefficient of friction of the films is much less than that of a homogenous block. This may be due to some features of the antifriction properties of polymeric crystalline materials.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 6, pp. 1053–1058, November–December, 1972.     

Polypropylene reinforced with aramid and glass fibers

The effect of the chemical nature of the aramid fibers Phenylone, Terlon, Armos, and SVM on the mechanical, thermophysical, and antifriction properties of reinforced polypropylene was investigated. It was found that the composite filled with SVM fibers based on a stiff-chain polymer has high tensile strength and bending modulus. Reinforcement of polypropylene with Phenylone stiff-chain fibers produces a composite with a high impact viscosity. Organoplastics based on polypropylene and aramid fibers have a low density and friction coefficient and high durability. Reinforcement of polypropylene with aramid (SVM) and glass fibers increases the technological properties of the composites. The glass-filled organoplastics developed can be used in instrument making, radio engineering, and machine building as antifriction and construction materials.Ukrainian State Chemical Technological University, Dnepropetrovsk, Ukraine. Translated from Mekhanika Kompozitnykh Materialov, No. 1, pp. 106–110, January–February, 1996.     

Study of the thermophysical and antifriction properties of polyethylene-based compositions

The mechanical and antifriction properties of polyethylene filled with various, relatively hard fillers are determined. Filling with oxides and silicates produces the greatest increase in wear resistance. The coefficient of friction decreases with increase in the stiffness of the compositions.Mekhanika Polimerov, Vol. 3, No. 6, pp. 1070–1077, 1967     

Supermolecular structure of teflon and its role in the manufacture of metal-polymer antifriction materials

The question of the formation of supermolecular structures in teflon is considered. It is shown that during processing they become oriented, causing anisotropy of the material properties. The realtive rheological characteristics of the anisotropic materials are given as a function of the directionality of the force field. Specimens are obtained on the basis of the experimentally determined laws and certain properties of a polymer-metal antifriction material consisting of a high tin, porous bronze impregnated with teflon are investigated.Institute of the Chemistry of High Molecular Compounds, AS UkrSSR, Kiev. Translated from Mekhanika Polimerov, Vol. 4, No. 6, pp. 1122–1124, November–December, 1968.     

Polyformaldehyde as an antifriction material

The antifriction properties of polyformaldehyde have been studied on the velocity interval from 4 · 10^–4 to 10 m/sec and at loads to 300 kgf/cm². Tests were conducted with and without lubrication on laboratory friction machines of various types and under service conditions. Steel, emery cloth, and polyformaldehyde were used as the second member of the friction pair. The values of the coefficients of friction, temperatures and performance limits for polyformaldehyde are compared with those for polycaprolactam.All-Union Scientific Research Institute of Railroad Transport, Moscow. Translated from Mekhanika Polimerov, No. 5, pp. 850–856, September–October, 1969.     

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     

The limit of the partial sums process of spatial least squares residuals

We establish a functional central limit theorem for a sequence of least squares residuals of spatial data from a linear regression model. Under mild assumptions on the model we explicitly determine the limit process in the case where the assumed linear model is true. Moreover, in the case where the assumed linear model is not true we explicitly establish the limit process for the localized true regression function under mild conditions. These results can be used to develop non-parametric model checks for linear regression. Our proofs generalize ideas of a univariate geometrical approach due to Bischoff [W. Bischoff, The structure of residual partial sums limit processes of linear regression models, Theory Stoch. Process. 8 (24) (2002) 23–28] which is different to that proposed by MacNeill and Jandhyala [I.B. MacNeill, V.K. Jandhyala, Change-point methods for spatial data, in: G.P. Patil, et al. (Eds.), Multivariate Environmental Statistics. Papers Presented at the 7th International Conference on Multivariate Analysis held at Pennsylvania State University, University Park, PA, USA, May 5–9 1992, in: Ser. Stat. Probab., vol. 6, North-Holland, Amsterdam, 1993, pp. 289–306 (in English)]. Moreover, Xie and MacNeill [L. Xie, I.B. MacNeill, Spatial residual processes and boundary detection, South African Statist. J. 40 (1) (2006) 33–53] established the limit process of set indexed partial sums of regression residuals. In our framework we get that result as an immediate consequence of a result of Alexander and Pyke [K.S. Alexander, R. Pyke, A uniform central limit theorem for set-indexed partial-sum processes with finite variance, Ann. Probab. 14 (1986) 582–597]. The reason for that is that by our geometrical approach we recognize the structure of the limit process: it is a projection of the Brownian sheet onto a certain subspace of the reproducing kernel Hilbert space of the Brownian sheet. Several examples are discussed.     

Physico-mechanical properties of polymer materials and the friction problem

Aspects of the friction behavior of polymer materials associated with their molecular structure and responsible for the relatively small value of the modulus of elasticity as compared with the ultimate strength are examined. It is shown that, in view of the important influence of hydrostatic pressure on the mechanical properties of polymer materials, the mechanical characteristics obtained from uniaxial testing cannot be used in calculating the contact area and the forces of friction. Formulas are presented for calculating the mechanical characteristics under these conditions. The results of indentation experiments designed to simulate contact processes are discussed. It is shown that the resistance to deformation of the asperities on the surface of polymer materials is of the order of the yield stress, and not two or three times greater, as with metals. The results of contact creep studies are described and evaluated. The results of investigations of the mechanical and antifriction properties of filled polymer materials show that the forces of friction are inversely proportional to the modulus of elasticity, while the thermophysical characteristics are a function not only of the thermophysical characteristics of the filler and the base, but also depend to a great extent on the shape of the filler particles; thus, when a fibrous filler with a low coefficient of linear expansion is used, the thermal stability of the friction material can be considerably improved. The results of a study of the adhesion interaction of polymer materials under conditions of omnidirectional nonuniform compression and simultaneous deformation are presented. It is shown that the adhesion interaction is strong even at room temperature. Aspects of the mechanical properties of lubricants that determine their effectiveness in polymer friction are considered.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, Vol. 5, No. 2, pp. 303–314, March–April, 1969.     

The Gerber–Shiu discounted penalty functions for a risk model with two classes of claims

In this paper, we consider the ruin problems for a risk model involving two independent classes of insurance risks. We assume that the claim number processes are independent Poisson and generalized Erlang(n) processes, respectively. When the generalized Lundberg equation has distinct roots with positive real parts, both of the Gerber–Shiu discounted penalty functions with zero initial surplus and the Laplace transforms of the Gerber–Shiu discounted penalty functions are obtained. Finally, some explicit expressions for the Gerber–Shiu discounted penalty functions with positive initial surplus are given when the claim size distributions belong to the rational family.     

Thermodynamic Potential of a System of Electrons and Phonons in a Disordered Alloy

We obtain a cluster expansion for the two-time retarded Green's functions and the thermodynamic potential of a disordered crystal taking the electron–phonon and electron–electron interactions into account. The electron states of the system are described in the framework of a multiband tight-binding model. The calculations are based on the diagram techniques for the temperature Green's functions. The coherent potential approximation is chosen as a zeroth-order one-site approximation in this cluster expansion method. We show that the contributions from the processes of scattering of elementary excitations on clusters decrease as the number of sites in the cluster increases in accordance with certain small parameters. Analytic estimates of the influence of the electron–phonon interaction on the energy spectrum of electrons of an alloy being ordered are obtained in a one-band model. The applicability of these results to describing the influence of strong electron correlations on the electron structure and properties of alloys of transition metals with narrow energy bands is illustrated with the example of the Fe–Ti alloy.     

Generalized z-Distributions and Related Stochastic Processes

The class of generalized z–distributions is defined and their properties are investigated. Ornstein–Uhlenbeck–type and self–similar generalized z–processes are constructed and described. Esscher transforms of the generalized z–processes and the mixed generalized z–processes are characterized. Finally, construction and some properties of generalized z–diffusions are also discussed.     

A numerical computation of a non-dimensional form of stream water quality model with hydrodynamic advection–dispersion–reaction equations

Mathematical models of water quality assessment problems often arise in environmental science. The modelling often involves numerical methods to solve the equations. In this research, two mathematical models are used to simulate pollution due to sewage effluent in the nonuniform flow of water in a stream with varied current velocity. The first is a hydrodynamic model that provides the velocity field and elevation of the water flow. The second is a dispersion model, where the commonly used governing factor is the one-dimensional advection–dispersion–reaction equation that gives the pollutant concentration fields. In the simulation processes, we used the Crank–Nicolson method system of a hydrodynamic model and the backward time central space scheme for the dispersion model. Finally, we present a numerical simulation that confirms the results of the techniques.     

Thermodynamic determination of the shift factor

The determination of the shift factor is examined on the basis of the thermodynamics of irreversible processes assuming a closed homogeneous system. It is shown that for any internal state the shift factor is equal to the product of the temperature and stress shift factors. An equation in which the nonequilibrium character of the processes is taken into account is obtained for the temperature shift factor.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 6, pp. 1001–1010, November–December, 1973.     

Information Criteria in Model Selection for Mixing Processes

We present information criteria for statistical model evaluation problems for stochastic processes. The emphasis is put on the use of the asymptotic expansion of the distribution of an estimator based on the conditional Kullback–Leibler divergence for stochastic processes. Asymptotic properties of information criteria and their improvement are discussed. An application to a diffusion process is presented.     

Theory of one-dimensional waves in nonlinear dissipative media

A unified approach is made to the construction of mathematical models describing discontinuous processes, and their analogs in the region of continuous solutions are presented; this makes it possible to distinguish between idealized and actual discontinuities and to classify media on the basis of model equations. The media considered are characterized by physical and geometric nonlinearity and by dissipation due to either viscosity or to the coupling of strain and temperature fields.Institute of Cybernetics, Academy of Sciences of the Estonian SSR, Tallin. Translated from Mekhanika Polimerov, No. 1, pp. 41–48, January–February, 1976.     

Influence of natural convection on the crystallization of pseudobinary compounds

The solution of the problem concerning the influence of intrinsic convection on the crystallization rate of pseudobinary compounds in an ampul by the method of vertical-directed crystallization is considered. A mathematical model of the physical processes occurring in the apparatus for the growth of semiconducting structures is outlined. An algorithm for numerical realization of the proposed model is constructed. The significant influence of natural convection in the melt/solution on the rate of crystal growth is shown.Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 19, pp. 94–98, 1988.