Axisymmetric Contact Problem Research Articles

Axi-symmetric contact problem with frictional heating for thermally nonlinear sliders

The axi-symmetric contact problem for a sliding elastic sphere on a rigid foundation is considered. It is assumed that the work done against shearing tractions is the source of heat generation and all the heat is absorbed in one moving sphere. The effect of the temperature-dependent properties of the sphere material is investigated. The problem is reduced to the solution of nonlinear Fredholm type integral equations. The approximate solution of these equations is obtained. For a sphere of carbon graphite material it is established that the influence of the nonlinear thermal properties on the contact area, the contact pressure and temperature is essential.

Axisymmetric mixed boundary value problems for an elastic halfspace with a periodic nonhomogeneity

This paper examines certain axisymmetric contact, crack and inclusion problems related to a nonhomogeneous elastic medium where the two elastic parameters are periodic functions of the axial variable z. A general formulation of the equations governing the axisymmetric deformations of the medium is presented. It is shown that the mixed boundary value problems can be reduced to a set of two ordinary differential equations and a Fredholm integral equation of the second kind. The ordinary differential equations are solved in a numerical fashion, and these solutions are used to evaluate the kernel function of the Fredholm integral equation. The resulting integral equations governing the contact problem are also solved via a numerical technique to obtain the load-displacement relationship for a rigid circular indentor in smooth contact with a periodically non-homogeneous elastic halfspace region. The procedures are extended to examine the problems associated with a penny-shaped crack and a rigid disc inclusion embedded in such a non-homogeneous elastic medium.

Thermoelastic contact problem of two rotating bodies with frictional heat generation in annular region

An axisymmetric contact problem with frictional heating is considered in which a parabolic annular punch is pressed into a plane surface and rotates about its axis of symmetry at constant speed. The problem is formulated in terms of one governing equation with unknown pressure. This equation is solved numerically. The change of the geometry of the contact region and pressure has been investigated.

Approximate method for analysis of the contact temperature and pressure due to frictional load in an elastic layered medium

The present paper consists of two parts. The first part deals with the analysis of a temperature and the stress-strain state of the layered half-space by normal traction and is heated by heat flux distributed over the circle region of the top layer surface. The thermal and mechanical contact of the bodies is perfect. In the second part, the axisymmetric thermoelastic contact problem for the layered half-space with fractional heating is investigated. An approximate solution is obtained for a particular case in which the conductivity and rigidness of the thin layer is much less than that of the half-space.

Effect of a thin coating on the pressure distribution in contact problems involving frictional heat generation

A thermoelastic problem for a layer of finite thickness one of whose surfaces is subjected to the action of normal pressure and heat flux is studied. A relationship among vertical displacements of the surface of the layer, the surface temperature, and the disturbing factors is obtained. Corresponding relations are obtained for a layer of small thickness. An axisymmetric contact problem for a rigid heat-conducting base whose surface is coated with a thin elastic layer is studied as an example.

A general solution to the axisymmetric frictional contact problem of a thin bonded elastic layer

The configuration of a thin elastic layer bonded firmly to a rigid substrate and pressed by a spherical punch has been used as a model to many problems arising in the field of biomechanics. This work presents a rigorous analysis of a thin bonded layer indented by a punch of general profile in the presence of the radial tangential traction. The method is based on perturbation theory. Formulae for stresses, strains and deformations are derived in terms of layer thickness, material properties and surface tractions. The results are illustrated by the evaluation of the expressions for several simple punch shapes. The influence of friction on the results is also examined. Good agreement is found between the present solution and the results reported in the literature.

QUASISTATIC THERMOELASTIC CONTACT PROBLEM FOR INFINITE TWO-LAYER CIRCULAR CYLINDER UNDER FRICTION HEATING

An axisymmetric quasi-static thermoelastic contact problem for a two-layer isotropic infinite hollow circular cylinder with factional heating and thermal resistance on the contact surface is examined Based on the solution of the corresponding steady-state problem, the existing conditions are analyzed. In the transient problem, thermal expansion due to fictional heating modifies the contact pressure and can lead to instability resulting in seizure. The results received in the present study are adapted for the investigation of the critical angular velocity of such a system and can be used to project the cylindrical friction units while working in the conditions of dry friction.

The unsteady axisymmetric contact problem with heat generation

Unlike previous papers [1–3], where steady contact problems of thermoelasticity were investigated, an unsteady contact problem for a stiff finite cylinder with a plane base is considered. The cylinder is clamped to an elastic half-space and is rotated around its axis with constant angular velocity. Heat generation due to friction over the contact area, non-ideal thermal contact between the bodies and heat exchange with the surroundings from the free surface is assumed. A Laplace transformation with respect to the time coordinate, a Hankel transformation with respect to the radial coordinate for the half-space and the method of straight lines for the cylinder are used to solve the problem. The temperature and thermal flux fields in the cylinder and in the half-space, the contact stresses and the displacements of the half-space are determined. The problem is analysed for values of the input parameters which do not allow any change with time in boundary conditions.

Approximate solution of the thermoelastic contact problem with frictional heating in the general case of the profile shape

The steady-state thermoelastic contact problem in which heat is generated due to sliding friction at the interface between an axi-symmetric thermally conducting punch and non-conducting half-space has been considered by Barber [(1976) Some thermoelastic contact problems involving frictional heating. Quart. J. Mech. Appl. Math. 29, 1–13] and Yevtushenko and Kulchytsky-Zhyhailo [(1995) Determination of limiting radii of the contact area in axi-symmetric contact problems with frictional heat generation. J. Mech. Phys. Solids 43, 599–604]. It was shown that there exists some limiting value of the contact circle radius with increase of the total load. The present paper gives the approximate solution of this problem in the general case of the punch profile form. The approximate solution was developed based on the representation of the thermally deformed solid by a quadratic surface.

Mechanical Behaviors of Bolted Joint in Various Clamping Configurations.

In a bolted joint, failures usually initiate at the first root of the bolt thread. However, rupture around the bolt head is sometimes reported for a tap bolt because of high stresses produced by tightening torque applied to the bolt head. It is also well known that manufacturing errors of internal threads in a tapped hole are generally much larger than those of external threads. In this paper, mechanical behaviors of bolted joints in various clamping configurations are analyzed using FEM as an axisymmetric elastic contact problem, and the effects of nominal diameter, friction and pitch error upon stress concentrations are evaluated for through bolts, studs and tap bolts. In addition, the tightening process and strength of bottoming studs, which have seldom been studied despite of its good performance in preventing stress concentration at the runout of threads, are also investigated.

Determination of limiting radii of the contact area in axi-symmetric contact problems with frictional heat generation

Axi-symmetric contact problems for a half-space with frictional heat generation have been considered by Barber, [(1975) Thermoelastic contact of a rotating sphere and a half-space. Wear 35, 283–289; (1976) Some thermoelastic contact problems involving frictional heating. Q. J. Mech. Appl. Math. 29, 1–13], Generalov et al. [(1976) The contact problem of thermoelasticity for rotating bodies. Izvestija AN USSR. Mechanika Tverdogo Tela. 3, 46–52] and Grilitski and Kulchytsky-Zhyailo [(1991) The axi-symmetrical contact problem of thermoelasticity for the bodies of rotating. Physicochem. Mech. Mater. 3, 93–97]. The problems have been treated by different methods and their solutions included estimates of the critical values of the dimensionless contact area radius. The present paper gives closed form expressions for these limiting radii by the application of Atkinson's result [(1976) A Survey of Numerical Methods for the Solution of Fredholm Integral Equations of the Second Kind. SIAM, Philadelphia (SIAM Monograph)] to the governing Fredholm integral equations, rather than using a full solution as was done by previous authors.

Shrink fit of an elastic half-space with a cylindrical cavity

This paper deals with the axisymmetric contact problem for an elastic half-space with a cylindrical cavity when mixed boundary conditions are prescribed on the surface of the cavity. The problem is simplified to that of finding the solution of dual integral equations arising from the mixed boundary conditions. The solution is obtained by the series method, and quantities of physical interest are calculated.

The interaction of frictional heating and wear at a transient sliding contact

A solution of the axisymmetric contact problem for a half-space is obtained taking into account transient heat generation due to friction and wear, assuming a quadratic variation of the normal displacements along the radial coordinate. The problem is reduced to a non-linear Volterra integral equation in the dimensionless radius of the contact area. Asymptotic solutions of this equation are constructed for short and long periods of time, and a numerical algorithm is also developed for investigating it in the general case. The proposed mathematical methods enable the effect on the dimensions of the contact region of two processes of opposite kind, namely, frictional heating and wear, to be investigated.

Axisymmetric Contact Problem of an Elastic Half-Space with a Spherical Inclusion.

A solution is presented to an axisymmetric contact problem of a circular rigid punch penetrating an elastic half-space in which a spherical inclusion coaxial with the punch is embedded. By expressing the contact stress under the punch and the interface displacements and stresses between the half-space and the inclusion as appropriate series, the doubly mixed boundary-value problem is reduced to the solution of an infinite system of simultaneous equations. Numerical results are obtained for stress distributions under the punch and around the inclusion as well as for the force transmission underneath the punch due to the presence of the inclusion. Comparisons with the results in the absence of the inclusion are made in order to illustrate the effect of the presence of the inclusion on the stress field.

Interaction of rigid cylinder with elastic half-space by heat generation on the contact area

The axisymmetric contact problem of pressure of rotating the cylindrical punch into an elastic half-space with heat generation on the contact area is considered. The existence of the half-space separation zones from the punch are determined. The thermal fields, heat flows and contact stresses have been discovered.

Interaction between a rigid cylinder and elastic half space subject to heat generation on the contact area

The axisymmetric contact problem of thermoelasticity was first solved by Borodachev. Examination of the phenomenon of a delay between the plate and bed is critical in examining contact problems of thermoelasticity. As a rule, the heat-conduction equation for the plate is not resolved, and the temperature of the base of the plate or a heat flux is assigned. Consideration of friction-generated heat, which is done, significantly simplifies the statement of the contact problems and their solution.

On the indentation of a poroelastic layer

AbstractThe paper examines the axisymmetric contact problem related to the indentation of a fluid saturated poroelastic layer by a smooth rigid punch. The layer rests in bonded contact with a rigid impermeable base and the surface of the layer is considered to be either permeable or impermeable. The paper develops the integral equations governing the problem for the generalized case where the pore fluid exhibits compressibility. The numerical results presented in the paper illustrate the influence of the relative layer thickness, drainage conditions and the compressibility of the pore fluid on the degree of consolidation settlement of the indenting punch.

Axisymmetric Frictional Contact Problem for Elastic Half-Space with Surface Layer.

An axisymmetric contact problem between a rigid punch and an elastic layer bonded on an elastic half-space is solved. Coulomb-type friction is assumed on the contact surface. Using Boussinesq's stress functions for the layer and the half-space, the problem is reduced to solving simultaneous integral equations with respect to the tractions and displacements on the contact surface. The integral equations are discretized into a system of algebraic equations to obtain the numerical solution of the problem. Contact stresses and displacements have been computed for the case of rigid flat-ended punch. The stick-slip boundaries have also been determined for various combinations of parameters, namely, thickness of the layer, rigidity of the layer, and coefficient of friction.

Three benchmark examples for frictional contact modelling using finite element and boundary elements methods

Three benchmark examples for two-dimensional and axisymmetric contact problems with friction are presented using the finite element and boundary element methods. The examples have relatively simple geometries and boundary conditions, and involve frictional sticking and slipping modes at the interface according to Coulomb's law of friction. Results are presented in the form of normal contact stresses, shear stresses, relative tangential displacements, and the stick-slip partitioning of the contact interface.

Independent meshing of contacting surfaces using fictitious nodes in boundary element analysis

A boundary element solution method for two-dimensional and axisymmetric contact problems with friction using a fictitious-node approach is presented. The algorithm is based on an independent discretization of the contacting surfaces by using the element shape functions to distribute the geometry on each contact element and introducing fictitious nodes within the interface in order to apply the contact constraints exactly. Frictional slipping is modelled according to Coulomb's law of friction, and the contact iterations are performed through an automatic iterative procedure. The approach is developed for contact problems under static and proportional loading conditions. Several examples are presented to demonstrate the accuracy of the algorithm.