Friction and wear of polymer-based composites

Polymeric materials containing different fillers and/or reinforcements are frequently used for applications in which friction and wear are critical issues. This overview describes how to design high temperature-resistant thermoplastics, e.g., filled with carbon fibers and internal lubricants, for operation under low friction and wear at elevated temperatures as sliding elements in, e.g., textile drying machines. Further information will be given on the systematic development of continuous fiber/polymer composites with high wear resistance, and on attempts for the prediction of their load-bearing capacity using a finite element approach. Finally, the application of such composites in thermoplastic filament-wound journal-bearings is discussed.Presented at the 10th International Conference on the Mechanics of Composite Materials (Riga, April 20–23, 1998).Institute of Composite Materials (IVW), University of Kaiserslautern, D-67663 Kaiserslautern, Germany. Published in Mekhanika Kompozitnykh Materialov, Vol. 34, No. 6, pp. 717–732, November–December, 1998.     

Determination of wear coefficient in mixed lubrication using FEM

In a line or point contact with an elastohydrodynamic lubricant oil film, solid-to-solid contacts are common and wear will occur at these places. Given that there is only a portion of the load is supported by the direct interaction of roughness asperities, the wear coefficient should be less than that for dry contacts and account for the effect of surface roughness and oil film. Since it is difficult to obtain the wear coefficient value at different oil film thickness by experiments, this paper presents the methodology of determination of wear coefficient in mixed lubrication using finite element method (FEM). In this method, the roughness of contact surfaces is characterized as fractal surfaces by the Weierstrass–Mandelbrot (W–M) function, the sliding wear in mixed lubrication is simulated by the Coupled-Eulerian–Lagrangian (CEL) method and the wear volume is calculated according to the solid–solid contact load. Then the wear coefficient can be determined and the simulation example shows that the wear coefficient decreases nonlinearly with the increasing of oil film thickness and dynamic viscosity in mixed lubrication.     

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.     

Effect of character of counterbody roughness on the wear resistance of composites based on polyethylene

Conclusions 1. The magnitude of the mean-square deviation in heights of irregularities is not a comprehensive characteristic of the starting roughness of the counterbody for evaluating the wear of polymeric composites. The characteristic of the steel counterbody surface in magnitude of the mean radius of curvature of the peaks of the irregularities is very important.2. On the basis of a study of profilograms of the friction surfaces and results obtained in a study of the wear of composites containing fillers of various hardnesses and dispersities which have been presented in this and preceding articles [3], it has been shown that the presence of filler particles leads to a significant change in the profile of the surface of the steel counterbody (peaks of irregularities are smoothed out, and the mean radius of curvature of the peaks of irregularities increases considerably, by a factor of severalfold). The harder the filler and the coarser the filler particles of a given type, the faster an optimum roughness is created, which ensures the lowest wear of the composite.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 3, pp. 479–485, May–June, 1977.     

Comparison of the mass spectra of the volatile products liberated from polymers in the course of mechanical destruction and thermal degradation

The compositions of the volatile products liberated from polymers in the course of mechanical destruction and thermal degradation have been studied and compared by means of mass spectrometry. For those polymers in which in both cases breakdown of the macromolecules begins with the basic chain, the volatile products are the same. For polymers in which breakdown of the molecules in thermal degradation begins with the stripping of side groups, the volatile products of thermal and mechanical degradation are different. This confirms and extends the ideas of the kinetic theory of fracture concerning the relationship between the processes of mechanical fracture and thermal degradation of polymers.Mekhanika Polimerov, Vol. 3, No. 1, pp. 80–88, 1967     

On non-Newtonian lubrication with the upper convected Maxwell model

A long-standing theoretical and practical problem, whether the viscoelasticity can have a measurable and beneficial effect on lubrication performance characteristics, is readdressed in this paper. The upper convected Maxwell model is chosen to study the influence of viscoelasticity on lubricant thin film flows. By employing characteristic lubricant relaxation times in an order of magnitude analysis, a perturbation method is developed for analysing the flow of a Maxwell lubricant between two narrow surfaces. The effect of viscoelasticity on the lubricant velocity and pressure is examined, and the influence of minimum film thickness on lubrication characteristics is investigated. An order of magnitude analysis reveals that the pressure distribution is significantly affected by the presence of fluid viscoelasticity when the minimum film thickness is sufficiently small. This mechanism suggests that viscoelasticity does indeed enhance the lubricant pressure field and produce a beneficial effect on lubrication performance, which is consistent with some experimental observations.     

Preservation and destruction of periodic orbits by symplectic integrators

We investigate what happens to periodic orbits and lower-dimensional tori of Hamiltonian systems under discretisation by a symplectic one-step method where the system may have more than one degree of freedom. We use an embedding of a symplectic map in a quasi-periodic non-autonomous flow and a KAM result of Jorba and Villaneuva (J Nonlinear Sci 7:427–473, 1997) to show that periodic orbits persist in the new flow, but with slightly perturbed period and an additional degree of freedom when the map is non-resonant with the periodic orbit. The same result holds for lower-dimensional tori with more degrees of freedom. Numerical experiments with the two degree of freedom Hénon–Heiles system are used to show that in the case where the method is resonant with the periodic orbit, the orbit is destroyed and replaced by two invariant sets of periodic points—analogous to what is understood for one degree of freedom systems.     

Existence and numerical results of a transient lubrication problem with cavitation

This work is devoted to an existence result of a transient lubrication problem with a time dependent velocity and in the presence of cavitation which is modeled by the Elrod–Adams method. The existence of a solution is based on the time semi-discretization method which yields to a sequence of a second kind variational inequalities. We also give some numerical results for a journal bearing system.     

On a problem of the theory of lubrication governed by a variational inequality

The hydrodynamic lubrication of a complete journal bearing of finite width is studied using the theory of variational inequalities: we deal mainly with existence, uniqueness and regularity of the solution.     

Crossed products by finite group actions with the Rokhlin property

We prove that a number of classes of separable unital C*-algebras are closed under crossed products by finite group actions with the Rokhlin property, including: (a) AI algebras, AT algebras, and related classes characterized by direct limit decompositions using semiprojective building blocks. (b) Simple unital AH algebras with slow dimension growth and real rank zero. (c) C*-algebras with real rank zero or stable rank one. (d) Simple C*-algebras for which the order on projections is determined by traces. (e) C*-algebras whose quotients all satisfy the Universal Coefficient Theorem. (f) C*-algebras with a unique tracial state. Along the way, we give a systematic treatment of the derivation of direct limit decompositions from local approximation conditions by homomorphic images which are not necessarily injective.     

Numerical investigation of the generalized lubrication equation

Explicit, implicit-explicit and Crank-Nicolson implicit-explicit numerical schemes for solving the generalized lubrication equation are derived. We prove that the implicit-explicit and Crank-Nicolson implicit-explicit numerical schemes are unconditionally stable. Numerical solutions obtained from both schemes are compared. Initial curves with both zero and finite contact angles are considered.     

Rolling Contact Problem with the Generalized Coulomb Friction

This paper deals with the numerical solution of the wheel - rail rolling contact problems. The unilateral dynamic contact problem between a rigid wheel and a viscoelastic rail lying on a rigid foundation is considered. The contact with the generalized Coulomb friction law occurs at a portion of the boundary of the contacting bodies. The Coulomb friction model where the friction coefficient is assumed to be Lipschitz continuous function of the sliding velocity is assumed. Moreover Archard's law of wear in the contact zone is assumed. This contact problem is governed by the evolutionary variational inequality of the second order. Finite difference and finite element methods are used to discretize this dynamic contact problem. Numerical examples are provided. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the Asymptotic Behavior of Mechanical Systems with Friction

Siberian Mathematical Journal - We study the asymptotic behavior of systems with the Coulomb friction expressed as Lagrange’s equations of the second kind with solutions in the sense of...     

Shape Optimization in 2D Contact Problems with Given Friction and a Solution-Dependent Coefficient of Friction

The paper deals with shape optimization of elastic bodies in unilateral contact. The aim is to extend the existing results to the case of contact problems, where the coefficient of friction depends on the solution. We consider the two-dimensional Signorini problem, coupled with the physically less accurate model of given friction, but assume a solution-dependent coefficient of friction. First, we investigate the shape optimization problem in the continuous, infinite-dimensional setting, followed by a suitable finite-dimensional approximation based on the finite-element method. Convergence analysis is presented as well. Next, an algebraic form of the state problem is studied, which is obtained from the discretized problem by further approximating the frictional term by a quadrature rule. It is shown that if the coefficient of friction is Lipschitz continuous with a sufficiently small modulus, then the algebraic state problem is uniquely solvable and its solution is a Lipschitz continuous function of the control variable, describing the shape of the elastic body. For the purpose of numerical solution of the shape optimization problem via the so-called implicit programming approach we perform sensitivity analysis by using the tools from the generalized differential calculus of Mordukhovich. The paper is concluded first order optimality conditions.     

Representing products of polyhedra by products of edge-colored graphs

Given an (m + 1)-colored graph ( Γ γ′) and an (n + 1)-colored graph (, γ″), representing two polyhedra P′, P″ respectively, we present a direct construction of an (m + n+1)-colored graph ( Γ ′? Γ ″, γ′ ? γ″), which represents the product P ′ × P ″. Some examples, applications, and conjectures about the genus of manifold products are also presented. © 1993 John Wiley & Sons, Inc.     

Flow of polyethylene melts with steadystate and recurrent deformation

Results are presented of studies on melts of batches of polyethylene differing in overall molecular weight and branching. For high-density polyethylene, unlike the low-density material, the ratios between the tangential and normal stresses and between the constituents of the composite dynamic shear modulus are independent of temperature. A close agreement has been found between the total and net viscosity with cyclic vibration frequencies equal to the steady shear rate.