Side-contact of sharp indenters, including the effects of friction

When a sharp-edged indenter is pressed into a half-plane material in the half-plane is displaced and ‘laps around’ the edges of the punch, possibly making contact with the side faces. This phenomenon is quantified within (coupled) half-plane theory, and applied first to an idealised indenter having the cross section of a trapezium, and then to a semi-infinite indenter. The latter allows an asymptotic form to be found which, through a generalised stress intensity factor may be collocated into the edge of any notionally sharp-edged indentation problem.     

Note on the complete contact between a flat rigid punch and an elastic layer attached to a dissimilar substrate

The contact pressure distribution is found for a square ended rigid punch, pressing normally onto an elastic layer, itself attached to an elastically dissimilar half-plane, under plane deformation. Each interface may be either frictionless or adhesive, and it is shown that the shear traction assumption has only a very small influence on the contact pressure, which is found as a perturbation on the classical Flamant half-plane solution. For thin layers the contact pressure distribution is only weakly dependent on the pad aspect ratio.     

The derivation and application of a semi-infinite flat and rounded asymptotic frictionless contact

The solution is found for the contact pressure distribution between a semi-infinite flat and rounded, frictionless, elastic punch pressed onto an elastically similar half-plane. This is used to obtain an asymptotic form of wide-ranging applicability, for finding the near-edge contact pressure in a contact which is nearly complete in character, and this is illustrated by example.     

Hysteretic friction in the small velocity approximation

A general expression, based on a solution of the equations of linear viscoelasticity, is given for the coefficient of hysteretic friction of a smooth rigid punch moving across a viscoelastic half-plane at very low velocities. It is valid for general punch shapes, provided the curvature of the punch is not too large in the region of contact. The simplicity of the formula and its generality could result in its being of some experimental interest. It should also prove useful as a means of incorporating hysteretic friction effects into stochastic models of surface contact. Some initial attempts in this direction are described.     

A contact problem for an elastic half-plane with rigid coating

Solution of contact problems on soft or rigid coatings of an elastic half-plane is of great practical interest. The present paper is aimed at considering the problem of interaction between a rigid biquadratic die and an elastic half-plane through a thin rigid coating. We have derived an integral equation for the problem under study and constructed its approximate solution by an asymptotic method.     

Complete solutions of plasticity theory in the task of pressing a flat rigid punch into a surface plastic layer adhered to a hard base

A complete solution of the mathematical plasticity theory on pressing a flat rigid punch into a surface, relatively soft, plastic layer has been obtained. The solution finds practical application for calculating the load-carrying ability of a friction bearing. The slip-line fields and the velocity hodographs satisfying the problem boundary conditions have been defined. Extreme contact pressures were determined, and a graph of how the numerical values depend on the relative length of the contact area has been plotted.     

Deformation component of friction force in a wavy elastic contact subjected to wear

The problem of frictional interaction between a wavy punch subjected to wear and an elastic strip is discussed. The contact of the punch and strip is assumed to cover the whole its lengths (complete contact). An analytic solution of the problem is presented, based on which the formula for the deformation component of the friction force is derived. Analysis of this formula enables us to represent visually certain features of the deformation component of the friction force, particularly in relation to its behavior in time.     

Steady sliding of a circular cylinder over a dissimilar thermally conducting half-plane

The problem of a thermally conducting cylinder sliding steadily over the surface of an elastic half-plane with different thermal properties was analyzed. Appropriate Green's functions are used to reduce the problem to an integral equation which is solved numerically. Thermoelastic distortion due to frictional heating causes the contact patch to be smaller than that predicted for isothermal (Hertzian) contact although solutions assuming a single, perfectly conducting contact patch are not found for all values of parameters.     

Determination of surface deformation of a bonded elastic layer indented by a rigid cylinder using the Chebyshev series method

The surface deformations due to the pressure applied by a frictionless rigid cylindrical punch upon an elastic layer, of finite thickness, attached to a rigid substrate (bonded layer) are calculated numerically. The numerical results show excellent agreement with the analytic solution when the layer becomes a half-plane. The influence of the layer thickness and Poisson ratio on the obtained results is examined.     

Stress analysis in elastic joint structures

A new inverse problem approach is introduced to analyse the stresses in the overlap elastic joint structures consisting of two adherents and an adhesive interlayer. Displacements in the elements of a joint are expressed in terms of some initially unknown contact stresses by solving the boundary-value problem for each element considered separately. The contact stresses are calculated from the matching continuity conditions for the displacements. Contact tearing and shear stresses, three-dimensional stress distribution in the bulk of adhesive interlayer, and the maximum stress values are calculated for different ratios of thicknesses and material properties of the adherents and the adhesive interlayer. The present study represents a new alternative modelling approach to stress analysis in the elastic joint structures.     

An approximate solution for the contact area and elastic compliance of a smooth punch of arbitrary shape

An approximate solution is developed for the contact area and the load-penetiation relation for frictionless indentation of the elastic half-space by a punch of arbitrary profile. The method makes use of a previous result to the effect that the contact area in this problem is that which maximizes the total indenting force. An estimate of this force is obtained by applying the reciprocal theorem to the solution for indentation by a flat punch of the same plan-form, for which an approximate solution has recently been developed by Fabrikant. The method is illustrated using an example, the results of which are compared with a direct numerical solution using Hartnett's algorithm.     

Investigation of friction-induced thermal processes for some non-hertzian fast-moving plane contacts

A method is described for deducing the stresses induced in a half-plane by an symmetrical indentor, fast-sliding over the surface of an half-plane. The heat is generated by the friction and it is assumed that the indentor is an insulator and that all of the heat flows into the half-plane. The form of the contacting profile of the indentor is represented by a power series. The influence on the yielding of material due to the contact temperature are investigated. An associated wear mechanism controlled by plastic deformation is introduced, and a wear control approach is presented.     

Analysis of the elastic punch-substrate contact under fretting: Monotonic and cyclic loading of the punch

The object of this paper is to analyze the elastic behaviour of a 2-D contact problem between a right-angled flat punch and a semi-infinite substrate, subjected to a constant normal compressive load and a cyclic shear load using a finite element code. The knowledge of the stress and strain fields produced close to the corners of the punch under different loading conditions as a function of the friction coefficient will allow insight to be gained into the fretting fatigue problem associated to this cyclic loading. In order to better understand the behaviour and analyze the possibility of using fracture mechanics approaches to study the stress field close to the punch corners, two different models have been compared to each other: one without continuity solution between the punch and the substrate and the other with a couple of contact surfaces between them. Using the continuous model, a particularization of the general analytic solutions of Williams has been proposed. The complete stress field around the corners of the punch for this model has been obtained for any values of the punch size, normal and shear loads. Some general guides for understanding and systematizing the punch-substrate behaviour have been extracted from the above solution and that of a sliding wedge, provided by the literature, which enable a systematic numerical analysis of the problem. Further on, a more detailed study of the slip between punch and substrate, as well as of the stress field, has been accomplished using finite element analysis guided by the previous semi-analytical results. The study has been completed for the whole load process: compressive normal load, monotonic shear load, and cyclic shear load.     

On the plane contact problem of a functionally graded elastic layer loaded by a frictional sliding flat punch

This article is concerned with the contact mechanics of a functionally graded layer loaded by a frictional sliding flat punch. The coefficient of friction is assumed to be constant and the lower side of the graded layer is firmly attached to a rigid foundation. The graded, nonhomogeneous property of the medium is represented in terms of an exponential variation of the shear modulus, while Poisson’s ratio is taken to be constant. Based on the use of plane elasticity equations and the Fourier integral transform technique, the formulation of the current contact mechanics problem lends itself to a Cauchy-type singular integral equation of the second kind for the unknown contact pressure, which is solved numerically. As a result, the effects of several parameters, i.e., the material nonhomogeneity, the friction coefficient, the punch width, and Poisson’s ratio, on the distributions of the contact pressure and the in-plane surface stress component are presented.     

考虑界面端应力奇异性的螺栓连接支承面接触压力计算模型

将螺栓连接支承面接触问题简化为集中载荷和力矩耦合作用的有限刚度平头压模接触问题,利用BOGY特征值方程,分析双材料界面端应力奇异性发生的几何条件;依据GLADWELL接触力学理论,构建集中载荷和力矩耦合作用下平头压模接触压力计算模型,利用此模型分析螺栓预紧力、装配间隙和被连接件材料对螺栓连接支承面接触压力分布的影响规律。结果表明：在规定预紧力范围、装配等级和常用被连接件材料下,螺栓连接支承面不会发生退让接触,而界面端部出现明显的应力奇异性,其中预紧力变化对界面端应力奇异性强度影响不明显,但装配间隙和被连接件材料的变化对界面端应力奇异性强度影响显著;当被连接件材料弹性模量大于螺栓材料时,支承面内侧应力奇异性强度大于外侧,反之内侧应力奇异性强度明显小于外侧。此外,以平头压模为算例,采用有限元法验证了构建模型的准确性。     

Flat and rounded fretting contact problems incorporating elastic layers

The problem of plane elastic contact between a thin strip and symmetric flat and rounded punches is studied. This geometry has recently been used by a number of researchers to assess life of various mechanical couplings undergoing fretting fatigue. Most of the experimental fixtures used do not allow the problem to be treated using the conventional half-plane approximation. Here we propose a numerical approach, which enables the solution of configurations characterised by finite strip thickness, avoiding the use of finite element analyses. Various loading regimes and contact configurations are treated in detail and both surface tractions and internal stresses are derived.     

Plane contact problems involving frictional heating for wavy half-space

Contact problems of a rigid punch sliding over the wavy thermoelastic half-space are studied. The punch geometry is considered to be parabolic or flat-ended. It is assumed that the contact between bodies occurs within a finite number of separated contour areas. The frictional heating in these regions is involved. The problem is reduced to the non-linear system of algebraic equations, which is solved iteratively. The effects of the boundary waviness on the heat generation are studied and presented in diagrams.     

轧机圆锥滚子轴承载荷的边界元法解析及实验研究

针对滚动轴承接触的特点,在轴承边界元法中采用赫兹接触理论对滚动体与轴承内、外圈的接触宽度进行修正。编制了三维有摩擦弹性接触的专用轴承边界元法计算程序,对轧机圆锥滚子轴承的载荷分布进行了数值模拟。采用轴承座直接测量法对轧机圆锥滚子轴承的径向和轴向载荷进行测试,并与数值模拟的结果进行了对比,实验测试结果与数值模拟的轴承载荷的分布规律基本一致,证明了边界元方法求解轴承载荷分布的正确性和有效性。     

轴承套圈锻造过程的计算机仿真研究

本文运用MSC-Marc软件对轴承锻造加工过程进行了计算机仿真.以金属成形理论和有限元方法基本原理为基础,建立了热力偶合刚粘塑性轴承锻造模型.包括对材料特性进行了完整的描述,确定了成形模拟中体积不可压缩实现方法.以二代轮毂轴承外圈锻造为例进行模拟分析.模拟分析中进行了冲头力的计算及对两次预成形模型的实验和模拟结果的对比;提出了产生过大冲头力的一个原因是最终成形阶段工件在模腔内分布不均使变形速率急剧增加;分析了工件应力和模具结构的关系及其优化问题,对冲头的倒角圆弧半径作了优化;对温度效应、表面质量和金属流线等锻造设计有关问题作了讨论.提出了预成形坯的设计优化准则,以此设计了二代轮毂轴承外圈的优化的预成形结构,冲头力比原设计下降了一半以上.     

Influence of the microprojection geometry on the elastic contact of surfaces with regular microrelief

The influence of surface microprojections—their shape and additional harmonics—on the elastic contact of a flat surface and a surface with regular microrelief is considered on the basis of the elastic contact of a half-plane and an undulatory surface. It is shown that the contact-pressure curve depends on the surface gradient of the microprojection and the mutual influence of adjacent microprojections.