On contact interaction between a moving massive body and a linear elastic half space

We study a class of problems involving the motion of a linear elastic body in frictional contact with a linear elastic half space. The dynamic effects considered are the inertial properties of the body regarded as rigid. We study only those regimes of contact interaction for which the slip velocity with the body taken as absolutely rigid and the time rate of change of the elastic displacements of points of the body and the half space that are on the contact surface are of the same order of magnitude. This work generalizes previous work on similar problems in that we simultaneously consider inertia forces of the body and the convective term in the slip-velocity due to the rigid-body velocity of the slider/indentor. Thus regimes of contact interaction investigated include rolling/sliding and shift-torsion type. We propose a variational formulation of the following two problems: (a) finite contact area and shift-torsion type of contact kinematics, (b) local contact area and general kinematics at the contact surface. Results for an elastic cylinder contacting an elastic half-plane are also given.     

Coupled rocking and sliding vibration response of a structure to harmonic horizontal ground motion

For a strip wall erected on a rigid strip foundation and supported by the surface of the ground, the dynamic soil-structure interaction under the action of the horizontal ground motion is investigated. The ground motion is idealized as vertically propagating, horizontal steady-state motion. Because the horizontal ground motion brings about the sliding vibration of the foundation as well as the rocking vibration, the coupled rocking and sliding vibration of the soil-structure system is considered in the present paper. For the contact between the ground and foundation, the following assumptions are made: 1) the contact is assumed to be welded, that is to say, the motion of the foundation is consistent with the ground; 2) the horizontal translation at each point on the bottom surface of the foundation is equal to a constant; 3) the distribution of the normal displacements under the foundation remains to be linear in the rocking vibration. For comparison, the case of uncoupled vibration is considered also. The use of Fourier transform method yields dual integral equations (for the case without coupling effect) or simultaneous dual integral equations (for the case with coupling effect). Both of them are solved by means of infinite series of orthogonal functions, the Jacobi polynomials. The numerical results show that there is a significant difference between the displacements of the foundation, the relative displacements of the top of the wall with respect to its base, and the distribution of contact stresses beneath the foundation, for the cases with and without coupling effect.     

Modeling of friction at different scale levels

We construct a model for studying the common influence of the imperfect elasticity of actual bodies, the microgeometry of their surfaces, and their adhesive interaction on the contact characteristics (the contact pressure distribution, the region of actual contact) and on the sliding friction force. The model is based on the solution of a plane contact problem of sliding of a rigid body with a regular relief on the boundary of a viscoelastic foundation with surface molecular attraction in the gap between the surfaces taken into account. We analyze the influence of the surface microgeometry parameters at different scale levels on the character of the surface interaction (the saturated or discrete contact) and the friction force for different sliding velocities of the contacting bodies.     

Vibrations of a Rigid Body with Cylindrical Surface on a Vibrating Foundation

The analytic solution of the problem of forced vibrations of a rigid body with cylindrical surface on a horizontal foundation is given. It is assumed that the dry friction force acts at the point of contact between the cylindrical surface of the body and the foundation and the foundation moves by a harmonic law in the horizontal direction perpendicularly to the cylindrical surface element. The averaging method is used to determine the forced vibration mode near the natural frequency of the body vibrations on the fixed foundation. The results are presented as amplitude-frequency and phase-frequency characteristics.     

Constant velocity motion of a strip die on the boundary of a viscoelastic base

We consider a contact problem on the interaction of a rigid strip die with the boundary of a viscoelastic base. We assume that the die moves at a constant velocity on this boundary and is indented into it by a constant normal force. Friction in the die—surface contact region is neglected. The die base is corrugated in the direction perpendicular to the direction of motion. At the first stage, we determine the displacement of the base boundary due to the normal load applied to it. Then, at the second stage, we derive the integral equation of the contact problem for determining the contact pressure. At the third stage, we construct an approximate solution of this integral equation by using the modified Multhopp—Kalandiya method.     

Winkler地基模型上功能梯度材料涂层的摩擦接触问题

研究Winker地基模型上功能梯度材料涂层在一刚性圆柱形冲头作用下的摩擦接触问题。功能梯度材料涂层表面作用有法线向和切线向集中作用力。假设材料非均匀参数呈指数形式变化,泊松比为常量,利用Fourier积分变换技术将求解模型的接触问题转化为奇异积分方程组,再利用切比雪夫多项式对所得奇异积分方程组进行数值求解。最后,给出了功能梯度材料非均匀参数、摩擦系数、Winker地基模型刚度系数及冲头曲率半径对接触应力分布和接触区宽度的影响情况。     

Contact interaction of a rigid heat-conducting punch with an elastic layer involving nonstationary frictional heating

A mathematical formulation is given and a solution is found to the quasistatic contact problem of thermoelasticity for a rigid heat-conducting punch moving over an elastic layer with fixed base. The interaction is accompanied by heating due to frictional forces obeying Amonton’s law. The problem is reduced to a system of integral equations with time-varying limits of integration. The structure of these equations depends on the type of thermal and physical conditions on the contact surface. An algorithm is proposed for the numerical solution of this kind of equations. The variation in the contact pressure and contact area with time is studied __________ Translated from Prikladnaya Mekhanika, Vol. 41, No. 12, pp. 35–46, December 2005.     

Surface topography formation in a region of plate collision: Mathematical modeling

The collision of earth’s crustal plates is modeled mathematically based on a numerical solution of the equations of deformable solid mechanics using a finite element method with the MSC software. The interaction of the plates with each other and with the mantle is described by the solution of the contact problem with an unknown contact boundary between the solids considered. The mantle material is assumed to be ideal elastic-plastic with the Huber-Mises yield surface, and the properties of the plate material are described using an elastic-plastic model with the Drucker-Prager parabolic yield function which takes into account fracture in the tensile stress region. The results of the mathematical modeling show that the surface profiles of the plates in the region of their collision are consistent, both qualitatively and quantitatively, to the surface topography observed in nature under similar conditions.     

Thermoelastic contact instability of a functionally graded layer and a homogeneous half-plane

The conductive heat transfer between two elastic bodies in the static contact can cause the system to be unstable due to the interaction between the thermoelastic distortion and pressure-dependent thermal contact resistance. This paper investigates the thermoelastic contact instability of a functionally graded material (FGM) layer and a homogeneous half-plane using the perturbation method. The FGM layer and half-plane are exposed to a uniform heat flux and are pressed together by a uniform pressure. The material properties of the FGM layer vary exponentially along the thickness direction. The characteristic equation governing the thermoelastic stability behavior is obtained to determine the stability boundary. The effects of the gradient index, layer thickness and material combination on the critical heat flux are discussed in detail through a parametric study. Results indicate that the thermoelastic stability behavior can be modified by adjusting the gradient index of the FGM layer.     

基于基底长度的粗糙表面分形接触模型的构建与分析

为建立更为精确的粗糙表面接触模型,根据微凸体变形特征、分形理论以及摩擦的作用,从微观角度基于基底长度建立了粗糙表面分形接触模型.通过与其他粗糙表面接触模型和实验数据的比较,验证了本文模型的正确与合理,并由数值仿真分析了分形维数、接触载荷与真实接触面积之间的相互关系.分析结果表明:特征尺度一定时,要维持一定的真实接触面积,分形维数越大,所需要的力也越大;分形维数与特征尺度一定时,随着载荷的增加,接触面积也在增加;特征尺度与接触力一定时,随着分形维数的增大,真实接触面积在减小.该模型的建立为进一步研究粗糙表面的摩擦、磨损与润滑提供了理论依据.     

Axisymmetric contact between an annular rough punch and a surface nonuniform foundation

The axisymmetric contact problem of interaction between a two-layer foundation and a rigid annular punch is considered under the assumption that the surface nonuniformity of the upper layer and the shape of the punch base are described by rapidly varying functions. The integral equation of the problem containing two rapidly varying functions is derived, and two versions of the problem are considered. Their solutions were first constructed by the generalized projection method. As an illustration, the model problem is analyzed numerically to demonstrate the high efficiency of the method.     

强夯作用下成层地基的表面接触应力分布特征

结合夯锤的刚体运动方程和成层弹性地基空间轴对称动力问题的传递矩阵法,导出了强穷的接触应力沿锤底的应力分布在变换域中的解析式,通过Ｌａｐｌａｃｅ－Ｈａｎｋｅｌ联合反交换求得了接触应力分布及沉降的时域解,确定了接触应力时间,并将数值结果与现场测试规律作了比较,结果表明：本文方法较好地解决了夯锤冲击成层地基的接触应力分布特征,为确定强夯的表面接触应力提供了帮助．     

Stress analysis of a layered elastic solid in contact with a rough surface exhibiting fractal behavior

A contact stress analysis is presented for a layered elastic half-space in contact with a rough surface exhibiting self-affine (fractal) behavior. Relationships for the mean contact pressure versus representative strain and the real half-contact width versus elastic properties of the layer and the substrate, asperity radius, layer thickness, and truncated half-contact width were derived from finite element simulations of a layered medium compressed elastically by a rigid cylindrical asperity. These relationships were incorporated in a numerical algorithm that was used to obtain the contact pressure distributions and stresses generated by the asperity contacts formed at the interface of the layered medium and the fractal surface. Analytical solutions illustrate the significance of the elastic material properties, layer thickness, and surface topography (roughness) on global parameters such as normal load and real contact area. Results for the contact pressure distribution and the surface and subsurface stresses provide insight into the initiation of yielding and the tendency for cracking in the layered medium. It is shown that cracking at the surface and the layer/substrate interface is more likely to occur in the case of a stiff layer, whereas surface cracking is more prominent for a relatively compliant layer.     

Thermoelastic Contact of a Shroud Ring and a Cylinder under Unsteady Friction-Induced Heat Release

Mathematical formulation is performed and a solution is found for a quasi-static thermoelastic problem of contact interaction of an elastic shroud ring and a hollow circular cylinder inserted into this ring, which are compressed by a load varied along the axis of the system, under the condition of an unloaded contact over the ring surface or over the circumference contour. The radial displacements of the contact surface of the shroud ring are approximated by displacements of the surface of a long circular hollow cylinder. Unsteady friction-induced heat release caused by the action of friction forces owing to shroud ring rotation over the cylinder with a time-dependent low angular velocity is taken into account. The problem is reduced to a system of integral equations whose structure is determined by the form of thermophysical contact conditions. A numerical algorithm of the solution is proposed, and the influence of the problem parameters on the contact pressure and temperature distributions is considered. Based on an analysis of results, a conclusion is made that the character of axial variation of the compressing load has a significant effect on the distribution of contact pressure in describing the kinematic condition of interaction of bodies in accordance with Hertz’s theory.__________Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 4, pp. 161–178, July– August, 2005.     

On Indentation of a System of Irregularly Shaped Rigid Punches into a Coated Foundation

We consider the contact problem of interaction between a coated viscoelastic foundation and a system of rigid punches in the case where the punch shape is described by rapidly varying functions. A system of integral equations is derived, and possible versions of the statement of the problem are given. The analytic solution of the problem is constructed for one of the versions.     

Influence of surface topography in the boiling mechanisms

The present paper addresses the qualitative and quantitative analysis of the pool boiling heat transfer over micro-structured surfaces. The surfaces are made from silicon chips, in the context of pool boiling heat transfer enhancement of immersion liquid cooling schemes for electronic components. The first part of the analysis deals with the effect of the liquid properties. Then the effect of surface micro-structuring is discussed, covering different configurations, from cavities to pillars being the latter used to infer on the potential profit of a fin-like configuration. The use of rough surfaces to enhance pool boiling mainly stands on the arguments that the surface roughness will increase the liquid–solid contact area, thus enhancing the convection heat transfer coefficient and will promote the generation of nucleation sites. However, one should not disregard bubble dynamics. Indeed, the results show a strong effect of bubble dynamics and particularly of the interaction mechanisms in the overall cooling performance of the pair liquid–surface. The inaccurate control of these mechanisms leads to the formation of large bubbles and strong vertical and horizontal coalescence effects promote the very fast formation of a vapor blanket, which causes a steep decrease of the heat transfer coefficient. This effect can be strong enough to prevail over the benefit of increasing the contact area by roughening the surface. For the micro-patterns used in the present work, the results evidence that one can reasonably determine guiding pattern characteristics to evaluate the intensity of the interaction mechanisms and take out the most of the patterning to enhance pool boiling heat transfer, when using micro-cavities. Instead, it is far more difficult to control the appearance of active nucleation sites and the optimization of the patterns allowing a reasonable control of the interaction mechanisms and in particular of horizontal coalescence, when dealing with the patterns based on micro-pillars. Hence, providing an increase of the liquid contact area by an effective increase of the roughness ratio is not enough to assure a good performance of the micro-structured surface. Despite it was not possible to clearly evidence a pin–fin effect or of an additional cooling effect due to liquid circulation between the pillars, the results show a significant increase of the heat transfer coefficient of about 10 times for water and 8 times for the dielectric fluid, in comparison to the smooth surface, when the micro-patterning based on pillars is used.     

The effect of tangential elasticity of the contact layer between stator and rotor in travelling wave ultrasonic motors

In travelling wave ultrasonic motors the elliptical motion of material points of the stator drives the rotor due to frictional mechanisms. The motor characteristic strongly depends on the mechanical properties of the components stator, rotor and contact layer. In order to predict the motor behaviour, a model for the contact between stator and rotor has been developed. The goal of the present paper is to point out the importance of the tangential elasticity of the contact layer which is responsible for the formation of stick zones and also for the amount of friction losses and overall efficiency. Therefore a comparison with a model with a contact layer rigid in tangential direction is given. Based on a visco-elastic foundation model for the contact layer, torque-speed curves as well as torque-efficiency curves are computed. Experimental investigations for identification of parameters, check of assumptions and model validation are carried out. Finally, the model is used to show the results of parameter variations for normal force, vibration amplitude and modulus of elasticity of the contact layer.     

Static analysis of a two-member linkage interacting with a given surface

Summary The static interaction of a two-member linkage with a given surface is investigated. Dry friction acts at the point of contact of the linkage with the surface. The linkage has two drives generating torques at its joints. The optimal distribution of the joint torques is determined to maximize the friction force at the point of contact. The dependence of this maximal force on the lengths of the links and on the linkage configuration is investigated. The results obtained can be applied to the analysis and optimization of various robotic systems, in particular, manipulators interacting with rough surfaces and walking machines, especially tube-crawling robots. Received 21 December 1998; accepted for publication 25 February 1999     

A thermodynamical approach to contact wear as application of moving discontinuities

The propagation of a moving surface inside a body is analysed within the framework of thermomechanical couplings when the moving surface is associated with an irreversible change in mechanical properties. The moving surface is a surface of heat sources and of entropy production whose intensities are related to particular energy release rates defined in terms of Hamiltonian gradients. For example, we analyse the wear process. Wear phenomena due to contact and relative motion between two solids depend on the loading conditions and material mechanical properties. Friction between contacting bodies induces damage of materials, producing surface and subsurface cracks. Particles are detached from sound solids when some local criteria are satisfied at the boundary. As wear occurs, geometrical changes take place and contact conditions are modified, and the particle induces a specific layer with particular properties. Then the interface between the bodies is a complex medium made of detached particles, eventually a lubricant fluid, and damaged zones. We propose to describe the evolution of the interface using a framework developed earlier for inducing the general form of a wear law.     

The effect of the time structure of laser pulse on the temperature distribution in homogeneous body with coating

In the present paper an analytical solution of the transient heat conduction problem for the nonhomogeneous body, consisting of bulk foundation and thin coating of different material, is presented. This body is heated through the outer surface of coating by heat flux generated due to absorption of pulsed laser radiation. The dependence of nonstationary temperature on the thermophysical properties of the foundation and coating were studied.