Thermoelastic Contact of a Rotating Inertial Cylinder with a Bush under the Conditions of Friction Self-Oscillations

We construct the solution of the problem of thermoelastic contact of an inertial cylinder with a rigid bush under the conditions of friction heating and wear. It is assumed that the friction coefficient depends on the relative velocity of contacting bodies. We analyze the stability of stationary solutions, determine contact parameters in the process of nonuniform rotation of the cylinder, and demonstrate the possibility of friction self-oscillations.     

Inverse Problem of Evaluation of the Coefficient of Friction of Layers According to the Data of Measurements of the Surface Displacements

We consider a one-dimensional model of friction contact of two layers of different nature. The lower surface of the first layer is elastically fixed and the second layer is pressed to the upper surface of the first layer and moves along this surface with variable velocity. As a result of friction, heat is produced on the contact surface according to the Amonton's law. For known boundary and initial conditions, we pose the problem of evaluation of the friction coefficient and the intensity of friction heat flux according to given values of the vertical displacements of the upper surface of the second layer. The posed problem is reduced to the inverse contact problem of thermoelasticity described by the Volterra integral equation of the first kind. The solution of the problem obtained by the method of averaging of functional corrections enables us to study the time behavior of the indicated quantities for the entire period of interaction of the bodies and establish the dependence of the friction coefficient on the basic parameters of the process (sliding velocity, contact pressure, and temperature of the contact surface). The solution of the direct contact problem of thermoelasticity is used to perform the numerical verification of the proposed method for the solution of the inverse problem.     

Determination of the Maximum Temperature of the Friction Pad in a One-Disk Clutch

Materials Science - We obtain the exact solution of the thermal problem of friction for a one-disk clutch with regard for the power law of variation of the friction torque with time. The evolution...     

Cracks with bonding between the lips in bushings of friction couples

We study the problem of contact deformation of a bushing of friction couple. The friction surface of the bushing contains rectilinear cracks with end zones characterized by the presence of interaction between the crack lips. In the case of repeated reciprocal motion of a plunger, the material of the bushing finally fails as a result of contact interaction. The boundary-value problem of equilibrium of the bushing of friction couple with cracks whose lips are interacting is reduced to the solution of a system of nonlinear singular integro-differential equations with Cauchy-type kernel. The solution of this system is used to find the normal and tangential forces in the bonds. The condition of limiting equilibrium of a crack with end zone is formulated with regard for the criterion of ultimate length of the bonds in the material. __________ Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 42, No. 2, pp. 53–61, March–April, 2006.     

Analysis of frictional contact problem using boundary element method and domain decomposition method

In this paper, we study the bilateral or unilateral contact with Coulomb friction between two elastic solids, using a domain decomposition method coupled with the boundary element method. The decomposition method we have selected is the Schur complement method, a non‐overlapping technique. It enables to reduce the solution of the global problem to the solution of a problem defined only on the contact surface. Moreover, its principal advantage is that computing is done separately on each solid. We have chosen to associate it with the boundary element method. Indeed, it only requires the discretization of the boundaries of solids. This technique of coupling reduces the number of unknowns and the time of computing. We have applied it to the study of indentation of an elastic foundation by an elastic flat punch and a sphere. In this last case, our results are in conformity with the Hertz theory and the analytical solution of Spence. Moreover, we have shown the influence of friction on the size of the contact radius and on the normal pressure at centre. Copyright © 1999 John Wiley & Sons, Ltd.     

水工钢闸门滚轮的滚动摩擦力臂计算方法

为了解决水工钢闸门滚轮在受载荷作用时产生的滚动摩擦力臂的计算方法问题,将滚轮与钢轨的接触问题简化为圆柱与圆柱座之间的接触问题,并以接触线为底作半圆,假设接触线上各点的压力与此半圆在该点的高度成正比。同时根据无限半平面Boussinesq问题的解法推导出滚动摩擦力臂的解析解。最后采用ANSYS建立滚轮全模型与钢轨进行接触分析来验证滚动摩擦力臂解析解的正确性。结果表明该滚动摩擦力臂计算公式简化合理,计算精度能够满足实际要求。     

Thermoelastic contact of a rotating shaft with a rigid bush in conditions of bush wear and stick-slip movements

The nonlinear problem of thermoelastic contact of a rotating shaft with a rigid bush fixed to the base elastically (springs) is investigated using both Laplace transform and perturbation methods. A friction coefficient is assumed to be a nonlinear function of a relative velocity. The solution to the problem is reduced to the system of nonlinear differential and integral equations. Zones of steady-state solution stability and friction self-excited oscillations existence are established. The numerical analysis is carried out and some important conclusions are given.     

Iterative Algorithms for the Solution of Quasistatic Unilateral Problems of Thermal Friction

We present the differential and variational statements of unilateral quasistatic problems of thermal friction for anisotropic thermoelastic bodies within the framework of the generalized model of linear dissipative mechanism of sliding in the case of imperfect thermal contact in the region of actual interaction. It is shown that these statements are equivalent for sufficiently smooth solutions. We also construct an alternative iterative algorithm for the solution of the problem, obtain estimates of the rate of its convergence similar to those established earlier for the constructive algorithm, and determine sufficient conditions for the convergence of both these algorithms in the corresponding norms to the solution of the analyzed problem (in particular, to the unique solution).     

Pressure with friction of a perfectly rigid die upon an elastic half space with cracks

We study the interaction of a rigid die with a base of any shape and the surface of an elastic half space containing cracks in the presence of friction in the contact zone. The solution of the plane contact problem of the theory of elasticity is obtained by the method of singular integral equations. The detailed analysis of the problem is performed for the case where the base of the die is parabolic and a crack is rectilinear and appears on the surface of half space. We also investigate the effects of the friction coefficient, crack length, its orientation, and location on stress intensity factors KI and KII at the crack tip and the distribution of contact stresses under the die.     

A mode II crack problem with sliding contact in an orthotropic strip

The problem of a centrally cracked, linear elastic orthotropic strip loaded in bending by three point forces is analyzed and discussed. Coulomb friction is assumed between the crack faces to study the influence of the friction coefficient on the strain energy release rate. Under certain simplifying assumptions the problem is reduced to the solution of a singular integral equation which is evaluated numerically. The results are compared with the solution of the same problem obtained using the beam theory; limits of the application of beam theory for the reduction of experimental data are discussed.     

An incremental procedure for friction contact problems with the boundary element method

The contact problem between deformable bodies with the presence of friction is not a problem that can be solved linearly. The uncertainty of the final contact zone and/or the irreversible character of the friction itself are the causes of the nonlinearity. An incremental procedure is proposed to deal with this kind of problem, without restriction in the application of the load. The algorithm has been implemented using as solution tool the Boundary Element Method. The use of discontinuous elements makes the applications of boundary and contact conditions easier.     

Couette flow of rigid/hardening solids

Steady Couette-type flow of rigid/linear-hardening solids is investigated. Material behaviour is governed by the von-Mises flow rule. The general flow problem is reduced to a semi-coupled system of two partial differential equations. A few possible boundary conditions are suggested. An exact solution for the plane strain problem is derived. That solution is used, in conjunction with average stress boundary data, for simulating a simple Couette-type flow problem through a curved tube with a rectangular cross section. It is shown that wall friction induces plastic boundary layers into the material. The essential features of these boundary layers are discussed.     

Plane-strain deformation of an elastic material compressed in a rough rectangular cavity

Deformation and stress distributions in a linear elastic solid, confined to a rigid cavity with rough walls and subjected to uniform compression from one end, are examined. Wall roughness is modeled by Coulomb friction. At the rigid walls, one boundary condition involves deformation and the other stresses, and this renders the problem non-standard. A Laplace transformation solution is constructed for a semi-infinite cavity, and a computational solution for a cavity with finite length. Agreement between the two solutions is good, and improves with increasing cavity lengths and higher coefficients of friction. There exists a critical value of the coefficient of friction below which the axial displacements decay monotonically with distance from the loaded end and the material points stay in contact with the rough walls. For supercritical values of the coefficient of friction, displacements and stresses on the rough walls exhibit oscillatory behavior in the axial direction. The material loses contact with the walls, and the analytical solution presented here loses validity.     

Nonstationary frictional heat production in the course of sliding of a composite layer over the surface of a half space

We obtain the analytic solution of a nonstationary thermal problem of friction for a system formed by a composite plane-parallel layer and a homogeneous semiinfinite base. The layer slides over the surface of the base with a constant velocity. Due to the action of friction forces, the bodies are heated. In the course of interaction, convective heat transfer with the environment takes place on the outer surface of the layer. For the rectangular shape of the cross section of composite fibers, we study the influence of the thermal properties of the materials of the fiber and the matrix on the distribution of temperature in the tribosystem.     

Interior point surrogate dual algorithm for unilateral problems

Summary. A unilateral problem is one kind of variational inequality problems; it can be discretized with the finite element method and converted to an inequality constrained nonsmooth optimization problem with the potential energy of the structure acting as the objective and unilateralization as the constraints. One characteristic in the optimization problem is that the number of constraints is much smaller than the dimension of the problem; therefore dual methods are often adopted. This paper focuses on the more complicated unilateral problems, the frictional contact problems. First, it is investigated that the value of the Coulomb friction coefficient has great influence on the property of the optimization problem; the friction orientation constraint is accordingly introduced in the solution procedure for treating the problems resulting from the larger friction coefficient. Then, the primal optimization problem is converted to an explicit surrogate dual problem which can be solved by a Karmarkars interior point based method. Finally, the method is verified by two typical frictional contact examples.     

Analysis of crack closure problem using the dual boundary element method

A numerical procedure of the crack closure problem solved by the dual boundary element method is developed in this paper. The dual boundary element method is used to allow for the solution to a general mixed-mode crack problem with a single regional formulation. The frictional contact problem on the crack surface is formulated with the complementary problem adapting the Coulomb's friction law. Several examples are shown to demonstrate the validity of the present procedure.     

Influence of turbulent pr number on friction and heat transfer at a plate immersed in a turbulent gas stream

A solution is offered to the problem of determining the friction and heat transfer coefficients for a plate immersed in a turbulent gas stream, using the approximate dependence of heat content on velocity given in reference [1]. The influence of Pr_T on friction and heat transfer is evaluated.     

Minimization of the thermal state of the hub of a friction pair

Theoretical analysis for defining the function of displacements of a hub’s external contour points and the microgeometry of the friction surface, ensuring minimization of the thermal state of the hub of a friction pair, is performed based on the model of rough friction surfaces and minimax criterion. A closed system of algebraic equations is constructed, allowing the solution to the problem of the optimal design of the friction pair to be obtained, depending on geometric and thermophysical characteristics of the hub and plunger. The resulting functions of displacements of the hub’s external contour points and microgeometry of the friction surface ensure the increased serviceability of the friction pair.     

Slow vertical motions of an elliptic punch on an elastic half-space

The dynamic contact problem for a homogeneous, isotropic elastic half-space and a punch of an arbitrary base shape is studied. During the motion of the punch it is assumed that the contact area is fixed and there is no friction under the punch. An approximate solution to the problem is obtained under the assumption that the contact pressure under the punch is slightly varied during the time of travel of the Rayleigh wave along the distance equal to the diameter of the contact area. The solution of the problem of slow motions of a punch on an elastic half-space is reduced to the solution of the recurrent system of integral equations of the static contact problem. Asymptotic models of vertical motions of a flat-ended punch with an arbitrary base are constructed. The case of an elliptic punch is considered in detail.