Search

A spatial quasi-static contact problem for a spherical hinge joint is considered. On one of the sliding surfaces, a thin polymer composite cover is coated. The polymer matrix is based on a C-2 phenylone and fillers in the form of fine F4MB fluoroplastic powders, tungsten-molybdenum blue, and a C-52 cylinder oil. To solve the problem, the finite-element method and the ANSYS software package were used. The Archard model was employed for describing the wear process. The stress-strain state of the joint was investigated, and the linear wear of the coating at the initial stage of interaction of faces was determined under the same loading conditions and coating thickness. It was found that, at the initial moment of time, the contact pressure and the equivalent stress in the interaction zone increased, which was associated with the “running-in” stage, when the contact was formed when the die unwinded. With reaching a stable rotation mode and a gradual increase in the area of contact patch, due to wear, these values decreased. The amount of wear at the initial stage changed almost linearly and directly depended on the wear factor. The volumetric wear was obtained for different coatings, which allowed us to calculate the rate and intensity of wear.

The features of the quantitative determination of the reliability of the results of the acoustic- emission (AE) method of monitoring and diagnostics are considered. It has been established that the traditional way of defining reliability via the probability of a controlled parameter falling into a certain interval sometimes suffers from informational underdetermination. It is shown that taking into account the probabilistic and information aspects of the assessment of reliability makes it possible to unambiguously link the concept of reliability of the results of testing and diagnostics with the amount of information obtained in the course of the inspection or diagnostics operation itself. Examples of practical determination of information reliability of the results of AE method are given.

The work presented is devoted to the axisymmetric contact problems on the interaction of a rigid stamp and an elastic layer fixed on a porous elastic half-space by using the Cowin–Nunziato model. It is assumed that the stamp basis has a flat or parabolic shape and friction is absent in the contact zone. With the help of the Hankel integral transform, the problems stated are reduced to solving integral equations for the unknown contact stress by using the collocation method. The values of contact stresses and the contact area in the case of a parabolic stamp are found. The normal stresses on the interface between the elastic layer and the poroelastic half-space are investigated. The relationship between the force acting on the stamp and the corresponding displacement, which is one of the main characteristics in determining the mechanical parameters of the material by the indentation method, is investigated. A comparative analysis of the values found for various parameters of the elastic layer and the poroelastic base is carried out. The numerical results are presented in a table and in the form of graphs.

In this article, we analyze axisymmetric contact problems on the interaction of a rigid stamp with a poroelastic layer using the equations of the Cowin–Nunziato theory of poroelastic bodies. It is assumed that the stamp base has a flat or parabolic shape and there is no friction in the contact zone. The posed problems are reduced to integral equations, the main kernel part of which is the delta function, by means of special function via which the contact stresses are expressed. Using a special approximation of the integral equation kernel transform, its asymptotic solution is constructed for the case of relatively large layer thicknesses. This approach to solving integral equations of contact problems was proposed by I.I. Vorovich and was further developed by his students. Expressions for the contact stresses and the contact area in the case of a parabolic stamp are obtained in a simple analytical form. Also, a relation between the force acting on the stamp and its displacement that is one of the main characteristics in determining the mechanical parameters of a material by the indentation method is found in terms of elementary expressions. A comparative analysis of the investigated quantities for various values ​​of the parameters of porosity and layer thickness is carried out.

The axially symmetric problem of a stamp excitation of torsional oscillations in a cylindrical waveguide with periodically changing mechanical properties along the longitudinal coordinate has been studied. A section of waveguide, corresponding to the minimal period of change in mechanical properties, can consist of any number of homogeneous regions (finite cylinders) with a different length and with various elastic constants. The method, related to the construction of the special “transition operator”, which allows finding the values of the displacement vector and stress tensors on one cross-section of a waveguide by their values on another. The distance between waveguide sections equals the value of the minimal period of changing properties of the waveguide. Relations for calculating the eigenvalues of the transition operator are obtained. The study of these eigenvalues allows defining the range of frequencies when both damping and continuous oscillations can propagate in the waveguide. Contact strains under a stamp are determined for relatively large radii of the cylinder.

Plane contact problem of interaction between rigid punch and elastic strip bonded to poroelastic half-plane is considered. Half-plane deformation is modeled on the base of Cowin-Nunziato poroelastic bodies equations. It is assumed that punch’s base is in the form of parabola, friction in the contact area is neglected. Using integral Fourier’s transformation, the problem is reduced to singular integral equation on unknown contact stress. The collocation method is utilized to solve equation. The values of contact stresses, the values of the contact area, and the relative deformation of the surface outside the punch were obtained. A comparative analysis of the investigated quantities for various values of the parameters of the elastic layer and the poroelastic foundation is carried out. Numerical results are present in the form of plots.

Introduction. The investigation of the contact problems for cylindrical bodies is urgent due to the engineering contact strength analysis on shafts, cores and pipe-lines. In the present paper, a new contact problem of elastostatics on the interaction between a rigid band and an infinite two-layered cylinder, which consists of an internal continuous cylinder and an outer hollow one, with a frictionless contact between the cylinders, is studied. The outer cylindrical band of finite length is press fitted. By using a Fourier integral transformation, the problem is reduced to an integral equation with respect to the unknown contact pressure.Materials and Methods. Different combinations of linearly elastic materials of the composite cylinder are considered. Asymptotics of the symbol function of the integral equation kernel at zero and infinity is analyzed. This plays an important role for the application of the analytical solution methods. A key dimensionless geometric parameter is introduced, and a singular asymptotic technique is employed to solve the integral equation.Research Results. On the basis of the symbol function properties, a special easily factorable approximation being applicable in a wide variation range of the problem parameters is suggested. The Monte-Carlo method is used to determine the approximation parameters. The asymptotic formulas are derived both for the contact pressure, and for its integral characteristic. Calculations are made for different materials and for various relative thickness of the cylindrical layer including thin-walled layers.Discussion and Conclusions. The asymptotic solutions are effective for relatively wide bands when the contact zone length is bigger than the diameter of the composite cylinder. It is significant that the method is applicable also for those cases when the outer cylindrical layer is treated as a cylindrical shell. The asymptotic solutions can be recommended to engineers for the contact strength analysis of the elastic barrels with a flexible coating of another material.

In the present work, frictional contact interaction between the tip and the shaft of the tail transmission of the MI-26 helicopter is considered in the framework of the linear theory of elasticity. The geometrical dimensions of the joint elements are taken from the design documentation. To set the profile of the tooth section, the necessary parametric equations were derived. To solve the tasks set, the finite element method and the ANSYS software were used. The main attention in the calculations was paid to the study of contact pressure q and effective (equivalent) stresses σe on the tip teeth surfaces that are in direct contact with the teeth of the cup. In accordance with one of the proposed ways to increase the operational life of the node under study, a thin coating with mechanical characteristics different from the teeth original material was designed placed on the contacting surface of the tip tooth. The stress-strain state of the node has been calculated for various geometrical and mechanical parameters of the coating.

The paper presents numerical and experimental burst pressure evaluation of the gas seamless hot-rolled steel pipe. The main goal was to estimate mechanical toughness of pipe wrapped with composite sleeve and verify selected sleeve thickness. The authors used a nonlinear explicit FE code with constitutive models which allows for steel and composite structure failure modelling. Thanks to the achieved numerical and analytical results it was possible to perform the comparison with data received from a capacity test and good correlation between the results were obtained. Additionally, the conducted analyses revealed that local reduction of pipe wall thickness from 6 mm to 2.4 mm due to corrosion defect can reduce high pressure resistance by about 40%. Finally, pipe repaired by a fibre glass sleeve with epoxy resin with 6 mm thickness turned out more resistant than an original steel pipe considering burst pressure.

Serviceability of metal-polymeric "dry-friction" sliding bearings depends on many parameters, including the rotational speed, friction coefficient, thermal and mechanical properties of the bearing system and, as a result, the value of contact temperature. The objective of this study is to develop a computational model for the metallic-polymer bearing, determination on the basis of this model temperature distribution, equivalent and contact stresses for elements of the bearing arrangement and selection of the optimal parameters for the bearing system to achieve thermal balance. Static problem for the combined sliding bearing with the account of heat generation due to friction has been studied in [1]; the dynamic thermoelastic problem of the shaft rotation in a single and double layer bronze bearings were investigated in [2, 3].

The serviceability of polymer dry sliding bearings is governed by a number of parameters, such as the rotational velocity of the shaft, the friction coefficient, еру thermal and mechanical properties of bearing members, and hence, the resulting contact temperatures. This work was aimed at developing a calculation model of the operation of a two-layer polymer dry sliding bearing, determining the temperatures distributions and the equivalent and contact stresses in bearing members, and choosing the optimum parameters of the bearing system for which heat balance is achieved.

The problem on indentation of elastic area with layered coating by cone shaped indenter is studied. Corresponding layers as well as material area are described using different models such as bilinear and Drucker-Prager model. As a result, the study covers materials of different nature described by completely different mechanical behavior under hydrostatic load. Various cases of elastoplastic properties for each layer are considered including the phenomena of residual stresses appearing after unloading and delaminating defects caused by stress concentration at the interface between layers.

The present paper is aimed at scrutinizing the contact interaction between the brake shoe and the railway wheel, taking into account the contacting surfaces friction and wear. The Archard’s model was used as a model describing the wear process. The solution to the problem was carried out applying the finite element method and the ANSYS software. The paper contains the results of calculations of wear and contact pressure intensity in the presence of a thin hardened layer on the shoe base, the survey of the influence of the mechanical properties of a layer on these values, as well as on the equivalent stress intensity at the boundary of the base material and the hardened layer. The performed calculations manifest that an entire set parameters must be considered when creating a hardened surface to increase the wear resistance of tribocontact parts.

The present paper deals with the spatial thermoelastic contact problem of the brake shoe pressing into the rotating roller with provision for friction and heat generation due friction and taking into account the reinforcing layer with other mechanical and thermophysical properties on the roller surface. The results of calculations of equivalent stresses and temperature fields are presented in relation to the thickness of the surface layer, its elasticity modulus and the rotation time. The simulation and calculation were performed by using the finite element method and the ANSYS software package. It is shown that the main changes of the temperature and the equivalent stresses take place at the depth of up to 1 mm from the friction surface. The presence of the reinforcing layer leads to decrease of the temperature on the surface. It is important to note that at the certain values of parameters the maximum value of temperature is achieved not on the friction surface out of the contact area, but at a certain depth.

The nonlinear static problem of FEM modeling of a damaged pipeline repaired by a composite material and subjected to internal pressure is considered. The calculation is carried out using plasticity theory for the pipeline material and considering the polymeric filler and the composite wrap. The level of stresses in various zones of the structure is analyzed. The most widespread alloy used for oil pipelines is selected as pipe material. The contribution of each component of the pipeline-filler-wrap system to the level of stresses is investigated. The effect of the number of composite wrap layers is estimated. The results obtained allow one to decrease the costs needed for producing test specimens.

Into framework of the linear theory of elasticity, the problem of the thermoelastic contact interaction of the brake disk and the pads studied. In the contact zone, the process of heat generation is realized due to friction forces. The friction coefficient is adopted as a function of temperature on the base of experimental data. The wear amount is calculated on the base of Archard model taking into account the dependency of model parameters on temperature. A number of calculation experiments is performed for various materials of braking pad.

In the modern petroleum industry it is vital to provide reliability and proper operation of transmitting pipelines, which are often subjected to various defects including volumetric surface defects (VSDs) arisen as a result of corrosion or erosion. In this, we consider a problem of computer simulation of pipeline fragment subjected to two VSDs and repaired by setting a composite wrap of a special structure. The algorithm of automatic finite-element model building based on the initial problem parameters is developed. The computational experiments on the influence of different parameters of the problem on a stress strain state of the pipe are conducted and discussed.

On the inside and/or outside surfaces of the steel pipes of the transmission lines intended for the transportation of hydrocarbons (petroleum, liquid petroleum products, natural gas, liquefied petroleum or natural gas) or other fluids (water, ammonia, etc.) clusters or colonies of volumetric surface defects (VSDs) can be generated. Each defect from such a colony can interact with the neighbouring defects, such that the stress concentration effects determined by a group/cluster of defects can be superior to the ones generated by the presence of individual defects. Therefore, the present chapter has the following goals: (i) definition of the factors that determine VSDs interaction: the characteristic dimensions of the pipeline (diameter and wall thickness); mechanical properties of the steel from which the pipeline containing the defects is manufactured (Young modulus, Poisson’s ratio, specified minimum yield strength, minimum tensile strength, minimum specified value of the percentage elongation, etc.); type, shape and characteristic dimensions of VSDs (length/axial extent, width/circumferential extent, maximum depth, etc.); distances between adjacent flaws/defects (in both axial and circumferential directions); complexity and intensity of the mechanical loads of the pipeline on which defects are placed (operating pressure and maximum intensities of other loads/forces and moments); (ii) comparative analysis of the criteria (from Norms presently in force: standards, codes, recommended practices, specifications, etc.) with which it can be assessed if adjacent defects from a VSD group or colony interact; (iii) description of the methods for the assessment of the shape and characteristic dimensions of the defect equivalent to a cluster of interacting VSDs; (iv) definition of the modalities for the evaluation of the effects of interacting VSDs groups upon the remaining mechanical strength of pipelines with such defects; (v) investigation of the influence of the interaction between two adjacent defects on the stress and strain states in the defects area by means of finite element analyses.

The present chapter describes an applied mathematical model aimed at assessing the strength properties of a damaged area of a transmission pipeline after repair works were performed using a composite material system. In the two-dimensional case, the problem of the stress–strain state in a pipe area with a long volumetric surface defect (VSD) has been considered. We have assumed that the repair work in the damaged area of the pipeline consisted of applying polymeric filler (in order to reconstruct the external configuration of the pipe in the VSD area) and then wrapping several layers of polymeric composite material, bonded with the help of a polymeric adhesive. We have also assumed that the VSD length (longitudinal extent) is considerably greater than its width (circumferential extent), which allows us to develop a two-dimensional analytical model. In our model, the effect of the composite material was taken into account by applying, on the pipeline outside surface, an additional normal stress, which is proportional to the tensile stresses from the composite wrap. These tensile stresses, in their turn, consist first of a pretension of the wounded composite layers, and second of the stresses arising from the circumferential deformation of the pipe. Such deformation, in the simplest case, can be described using Hooke’s law, as the product between the modulus of elasticity of the composite material in the circumferential direction and the circumferential strain of the pipe at its surface. Additional studies were conducted to evaluate the stress concentration effect at the corner points of the surface. To solve this problem, the whole area of the pipe cross-section has been divided into two subareas, each of which had its own stress function. Taking into account the symmetry of the field and external loads in each area, one stress function has been built in each subregion. All boundary conditions on the inner and outer surfaces of the pipe and on the symmetry axis are satisfied exactly. To obtain a closed system of equations, it was necessary to add two equations, including the condition of equality of the bending moment in the coupling zone and the proportionality condition of the radial and tangential displacements in the vertical direction for a solid body. Finally, we have obtained a closed system of 12 linear algebraic equations whose solution allowed us to obtain all the relevant characteristics of the problem. Numerical calculations have been conducted and von Mises combined stresses analyzed in the damaged pipe area as function of the VSD depth and compared with results obtained using a finite elements model.

The issue of stress state in coated bodies is a persistent problem in mechanical engineering and materials science that has congregated numerous efforts, both from experimental and fundamental points of view. The given paper concentrates on the contact problem considering the interaction between a punch and a dual-layered strip base that serves as a model of the interaction between loaded coating and the substrate. It also suggests strategies for applying analytical approaches and using the finite element method to solve the set of goals. The calculations and conducted study of the stress state in the base at the layer interface demonstrate that tensile normal stresses occur at the layer interface, which can lead to the top-layer delamination from the bottom one.

In the present study, we have considered several issues for a damaged pipeline with one or two volumetric surface defects, subjected to internal pressure loading. The problem of an optimal repair system for a pipe using a composite material wrap is considered. The analysis of the most efficient repair wrap properties was performed; some practical recommendations are provided.

In the current study, it is studied a problem of the simulations of stress state in the damaged section of the pipeline segment at its repair by introducing a composite band. The simulation was performed in ANSYS finite element software. Damage is modeled as single defect having a rectangular shape. The edges of the defect are rounded to the correct configuration with a specific radius R. Pipe model is loaded by internal pressure. It is taken into account X52 grade steel. The stress state of the pipe is studied for its two variants: (i) the model without defect and composite shell, (ii) the model of the defect with the filler and the composite shell (bandage). We studied the inhomogeneous stress field in the elastic deformation region. Stresses were calculated along two axes passing through the center of defect (the defect located on the main axis directed along the tube axis and in the radial direction). Modeling of stress state was performed for a defect imitating corrosive delamination of the layers. The delamination of corrosion in the defect area was modelled as a cavity of small volume. Corrosion is simulated as a detachment between the defect metal and composite filler.

We consider the plane contact problem of elasticity concerning the interaction between an absolutely rigid cylinder and the internal cylindrical surface of the cylindrical base, which consists of two circular cylindrical layers with different elastic constants. The base external surface is fixed, the layers are rigidly connected with each other, and the friction forces are absent in the contact region. Such problems sufficiently well model the operation of a composite cylindrical slider bearing, especially in the case of loads for which the angular dimension of the contact site is commensurable with the bearing width and the moduli of the insert liner and of the support are different and significantly less than the modulus of elasticity of the other details of the bearing.

The contact problem of a double-layer cylindrical base is discussed with account of friction forces. The problem is reduced to an integral equation of the first kind in relation to unknown contact stresses. A direct method of collocation is used to solve it, enabling us to obtain sufficiently accurate solutions for virtually any values of the parameters. The contact stresses and the contact-zone area are calculated for various material and geometrical parameters of the base layers.

Friction and antifriction composite materials of multilayer structure [1] have recently become very popular in the engineering industry. Antifriction materials are widely used in sliding bearings, and friction materials are widely used in brakes. In the first case, the friction forces between the contacting surfaces are negligible, but in the second case, they are rather large.

The calculation of temperature field for metal-polymeric tribosystem like “wheel-brake pad” of railway unit is performed. One of the methods used for calculation of temperature distribution in boundary layers is regularization of singularly perturbed problems. As a tool for simulation of problem for disc braking systems the finite element method is used. In the both cases, the fact of temperature maximum located under frictional surface is demonstrated. The experimental study confirms this fact, too. Such negative temperature gradient acts on physical, mechanical and tribological properties of metal-polymeric frictional units. This influence is studied and demonstrated.

The contact problem of the motion of a punch taking into account the heat released due to friction between the punch and a very thick elastic strip is considered. The contact problem of the theory of elasticity regarding a moving punch was previously investigated both ignoring [1, 2] and taking into account [3, 4] the forces of friction and the heat release. Here, unlike [3, 4], when solving the free quasistationary problem of thermoelasticity in a moving system of coordinates a relation is proposed between the coefficient of friction and the temperature. Particular attention is given to the problem of the possibility of a thermal explosion [5–11] or a sharp change (a bifurcation) in the contact temperatures. It is shown that a loss in the quasi-stationary thermoelastic stability occurs if the coefficient of friction increases linearly with the temperature. The proposed model can explain, to a first approximation, the avalanche-type wear of different moving components, for example, thin piston rings, due to their overheating.

Taking friction forces into account, we investigate the interaction between an elliptic-paraboloid die and a layer. The investigation concerns the effects of the Coulomb friction coefficient, die shape, elastic constants, and layer thickness on contact stresses, the dependence of the vertical die displacement on a pressing force, the dimensions and shape of the contact area, and the displacement of layer-surface points outside the contact area. It is discovered that the contact-area shape and displacements of the surface points are qualitatively different at small and large values of the Poisson ratio. We investigate the case of the limit equilibrium. Quasistatic die motion along the layer surface can be considered in a moving coordinate system in a similar way. The integral equation derived for the problem is solved by the method of nonlinear boundary integral equations [1, 2].

Fredholm integral equations of the second kind are obtained and investigated for various boundary conditions on one edge of a wedge which enables one to represent the corresponding Green's functions by integrals of Neumann series in powers of (1 − 2v). Contact problems of the action of a punch in the form of an elliptic paraboloid on an elastic spatial wedge are studied. The asymptotic method of “large λ” [1] is used to solve the integral equations of these problems. The results of the numerical analysis are compared with a well-known contact problem for a half-space [2, 3].