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.     

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.     

Wear resistance of filled epoxypolyamide composites in aggressive media

The authors investigate the influence of certain aggressive media (toxic chemicals) on the wear resistance of filled epoxypolyamide composites. The presence of toxic chemicals in the zone of friction causes a sharp fall in the wear of the polymers. The maximum wear resistance is displayed by epoxypolyamide composites filled with iron powder, cement, or graphite.     

The wear contact problem with partial slippage

A method of analysing the variation in the stress state and shape of wearable bodies, subjected to the action of an oscillating shear load with partial slippage of the surface in the contact area is proposed. The method is based on the introduction of two time scales: the time of a single cycle of variation in the shear load and the time corresponding to a specified number of cycles. To estimate the shape variation of the surface due to wear a linear relation between the wear rate and the contact pressure and velocity of relative slippage is used. Cases of complete or partial removal of the wear particles from the friction zone are considered. As an example, the kinetics of the variation in the stress state in the contact of an elastic indentor, having a flat base and rounded edges, with an elastic half-space of the same material, is investigated. Analytical expressions for calculating the asymptotic values of the stresses and shape of the worn surface are obtained.     

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     

An analysis of contact deformation of auxetic composites

The adaptive mode of frictional interaction has been studied as a self-locking effect upon contact deformation of isotropic and anisotropic auxetic materials with a negative Poisson ratio. This effect manifests itself in the fact that the bearing capacity of the joint rises with increasing shear load. In particular, the parameters of stress state (contact load, tangential stresses, slippage, etc.) were determined for a double-lap joint under conditions of compression with or with out shear. The contact interaction was analyzed by the finite-element method for three profiles of symmetrically located contact elements (plane, cylindrical, and wedge-shaped). The Poisson ratio was varied within the range theoretically admissible for isotropic elastic media. Analogous calculations were also performed for a joint with a deformed element made of an anisotropic auxetic composite, whose reinforcement angle was varied. The maximum loads, tangential stresses, and slippage are obtained as nonlinear functions of Poisson ratio (in the isotropic case) and reinforcement angle of the composite material. The stress concentration and the increased ultimate shear forces are also estimated. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 42, No. 5, pp. 681–692, September–October, 2006.     

Effect of internal stresses on the wear resistance of epoxy coatings

The results of wear tests on ED-5 epoxy coatings are used to derive a relation between internal stresses, modulus of elasticity, and wear resistance. During wear the internal tensile stresses diminish, the rate of decrease depending on the initial stress state, the material of the abrading body, and the test conditions. The thickness of the coating affects wear resistance up to a certain value; for ED-5 the limiting thickness is 500 microns.Mekhanika Polimerov, Vol. 1, No. 2, pp. 123–128, 1965     

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.     

A solution of the problem of oscillations of a die on a two-phase base under a seismic impact

A method of studying nonstationary seismic oscillations of a cylindrical die on a two-phase base is developed, which is modeled with an application of the theory of M. Bio-Ya. I. Frenkel'—V.N. Nikolaevskii. In the solution of the problem integral transforms are used in combination with the method of orthogonal polynomials for a representation of required contact stresses. Numerical results are given, which characterize a change of coefficients of expansion of the series of contact stresses with respect to time, including their resultant, under different masses of the die. Transformations of the projection diagram of normal contact stresses are shown as time passes.Translated from Dinamicheskie Sistemy, No. 7, pp. 32–41, 1988.     

Wear and fluid-solid-thermal transient coupled model for journal bearings

In this study, the transient interactions between the sliding wear behaviour and fluid–solid–thermal (FST) characteristics of journal bearings are revealed using an established mathematical model. The calculated temperature distribution is validated by a comparison with experimental results from the literature. Furthermore, a wear test for lubricated journal bearings is conducted to verify the predicted wear rate. The time-varying wear and FST performances of the journal bearing, including the wear rate, wear depth, fluid pressure, contact pressure, and maximum temperature are calculated numerically. Through numerical simulations, the effects of the boundary friction coefficient and surface roughness on the wear and FST performances are evaluated. To demonstrate the importance of considering the three-dimensional (3D) thermal effect during the wear analysis of lubricated journal bearings, the numerical results predicted by the isothermal model and the thermal model are compared systematically within a wide range of operating conditions. The numerical results reveal that the worn surface profile slightly decreases the maximum temperature. Additionally, the worn region is primarily located at both edges of the bearing, and the time-varying worn surface profile may be beneficial for improving the hydrodynamic effect. Furthermore, the effect of the 3D thermal characteristics on the wear prediction of journal bearings cannot be ignored when the external load, boundary friction coefficient, surface roughness are relatively large.     

Thermoelastic rolling contact problem with temperature dependent friction

The paper is concerned with the numerical solution of a thermoelastic rolling contact problem with wear. The friction between the bodies is governed by Coulomb law. A frictional heat generation and heat transfer across the contact surface as well as Archard's law of wear in contact zone are assumed. The friction coefficient is assumed to depend on temperature. In the paper quasistatic approach to solve this contact problem is employed. This approach is based on the assumption that for the observer moving with the rolling body the displacement of the supporting foundation is independent on time. The original thermoelastic contact problem described by the hyperbolic inequality governing the displacement and the parabolic equation governing the heat flow is transformed into elliptic inequality and elliptic equation, respectively. In order to solve numerically this system we decouple it into mechanical and thermal parts. Finite element method is used as a discretization method. Numerical examples showing the influence of the temperature dependent friction coefficient on the temperature distribution and the length of the contact zone are provided. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On wheel–rail contact problem with material properties varying with depth

Numerous laboratory experiments indicate that the use of a layer or a coating material attached to the conventional steel body reduce the magnitude of contact stress. Therefore in this paper we solve numerically the wheel–rail contact problem with friction and wear assuming the existence of a small elastic layer on the rail surface. Material properties of this layer are changing with its depth. The friction between the bodies is governed by Coulomb law. In contact zone Archard's law of wear is assumed. We take special features of this rolling contact problem and use so-called quasistatic approach to solve this contact problem. Finite element method is used as a discretization method. The numerical results including the distribution of normal stress along the contact boundary are provided and discussed. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Contact problems of the theory of elasticity in the presence of wear : PMM vol.40, n 6, 1976, pp. 981–986

The solutions of the contact problems of the theory of elasticity in the presence of wear is given for two cases. In Sect. 1 we consider the problems in which an initially curved beam comes in contact with a half-plane. One of the initial assumptions is that the distance between certain directrices along which the body in contact is sliding and the boundary of the half-plane remains constant. In Sect. 1 the contact between the curved beam and the half-plane is discussed at the assumption that the half-plane is subject to wear. As the result of the wear, the pressure between the beam and the half-plane is gradually reduced. It is naturally assumed that the pressure at the terminal points of the contact area will, in this case, be zero. The conditions characterizing the pressure at these terminal points can be established for various types of contact problems only under certain additional assumptions; this will be discussed below.     

Analytical modelling for static stress analysis of pin-loaded lugs with bush fitting

Pin-loaded connections are widely used in the industry. Connecting rods of reciprocating engines in automotive applications or pin-loaded lugs of landing gears and airframe structures can be cited as examples. These systems are subject to thermomechanical cyclic loadings and fatigue mechanisms are often observed. The calculation of stresses in the lug is crucial in view of a fatigue lifetime analysis. Analytical modelling may be very helpful in the early design stage, by allowing fast parametric studies and the identification of the most influent parameters on the response in stresses. In this paper, we propose analytical models for bush fitting and pin-loading conditions, leading to the complete calculation of the stress distribution in the lug. In each case, the analytical solutions are compared with finite element simulations. In the last part, we perform a sensitivity analysis as an application of the presented analytical tools.     

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.     

A differential variational inequality in the study of contact problems with wear

We start with a mathematical model which describes the sliding contact of a viscoelastic body with a moving foundation. The contact is frictional and the wear of the contact surfaces is taken into account. We prove that this model leads to a differential variational inequality in which the unknowns are the displacement field and the wear function. Then, inspired by this model, we consider a general differential variational inequality in reflexive Banach spaces, governed by four parameters. We prove the unique solvability of the inequality as well as the continuous dependence of its solution with respect to the parameters. The proofs are based on arguments of monotonicity, compactness, convex analysis and lower semicontinuity. Then, we apply these abstract results to the mathematical model of contact for which we deduce the existence of a unique solution as well as the existence of optimal control for an associate optimal control problem. We also present the corresponding mechanical interpretations.     

Towards a Standardised Method for Visualisation of Stress Distribution at the Cartilage-Bone Interface

The degeneration of articular cartilage is one of the most common causes of pain and disability in middle-aged and older people. In this context, osteoarthritis is a well-known clinical syndrome related to cartilage degeneration. The degeneration of normal articular cartilage is not simply the result of aging and mechanical wear. Pathological loads may also increase the risk of degeneration of normal joints, and individuals who have an abnormal joint anatomy or inadequate muscle strength probably have a greater risk of degenerative joint disease. The goal of this contribution is to investigate the influence of cartilage degeneration on the stress pattern at the cartilage-bone interface. In this connection, articular cartilage is described as a highly anisotropic and heterogeneous charged biphasic solid-fluid aggregate in the framework of the Theory of Porous Media (TPM). After calibration of the model under physiological loading conditions, the results of a sensitivity analysis of the model parameters are presented. Realistic boundary conditions are applied on the cartilage surface of the femoral head obtained from multibody dynamics calculations. Use is made of the Hertzian contact theory for the contact pressure distribution. The applicability of a new rendition technique to visualise simulation results based on a standardised stereographic projection of the von Mises stresses along the curved cartilage-bone interface is introduced. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A solution method for the sub-surface stresses and local deflection of a semi-infinite inhomogeneous elastic medium

This paper proposes analytical Fourier series solutions (based on the Airy stress function) for the local deflection and subsurface stress field of a two-dimensional graded elastic solid loaded by a pre-determined pressure distribution. We present a selection of numerical results for a simple sinusoidal pressure which indicates how the inhomogeneity of the solid affects its behaviour. The model is then adapted and used to derive an iterative algorithm which may be used to solve for the contact half width and pressure induced from contact with a rigid punch. Finally, the contact of a rigid cylindrical stamp is studied and our results compared to those predicted by Hertzian theory. It is found that solids with a slowly varying elastic modulus produce results in good agreement with those of Hertz whilst more quickly varying elastic moduli which correspond to solids that become stiffer below the surface give rise to larger maximum pressures and stresses whilst the contact pressure is found to act over a smaller area.     

A non-linear wear-contact problem for a Winkler foundation with an increasing contact area

A wear-contact problem for a Winkler foundation is considered in the case when the rate of wear depends nonlinearly on the contact pressure and the contact area increases. The corresponding integral and differential equations are obtained. A successive approximation procedure is proposed which enables an exact solution of the problem in the space of continuous functions to be found. The property of non-negativity of the contact pressure when it has non-negative initial values is established. It is shown, using a qualitative analysis and calculations, that the non-linearity of the wear law can have a considerable effect on the behaviour of the contact pressure during the wear process.     

Stress-strain state and stability of composite sandwich shells with a scaling zone between the core and facings

A finite element model is presented for analyzing the strength and stability of sandwich shells of arbitrary configuration with an adhesion failure zone between the core and one of the facings. The model is based on the assumptions that both facings are laminated Timoshenko-type composite shells, only transverse shear stresses in the core and normal stresses in the thickness direction have nonzero values, a free slip in the tangential plane in the adhesion failure zone and unilateral contact along the normal are possible, and the prebuckling state in the stability problem is linear. Biquadratic nine-node approximations for all functions and numerical integration were used. The displacements and rotation angles of the normals toward the facings as well as stresses in the core are taken as global degrees of freedom. The algebraic problem is solved using a special step-by-step procedure of determining the contact area in the scaling zone and employing unilateral constraints for some of the unknowns. Numerical examples are also given.Translated from Mekhanika Kompozitnykh Materialov, Vol. 29, No. 5, pp. 640–652, September–October, 1993.