Three-dimensional asperity model of rough surfaces based on valley–peak ratio of the maximum peak

Three-dimensional asperity model of rough surfaces is proposed using valley–peak ratio (VPR) of the maximum peak. Asperities of rough surfaces are reconstructed according to paraboloid asperity function, which is derived using least square method and asperity projection plane determined via VPR. The minimum profile deviation between reconstructed asperities and rough surface is calculated using simulated annealing method to optimize VPR. Effects of simulated mutation surfaces, measured surfaces, and different sampling intervals (SIs) on profile deviation are investigated. Compared with nine–point method, the proposed model demonstrates a smaller deviation of mutational rough surface, the absence of interference among asperities, and more stable surface parameters and contact mechanics performance at different SIs.

     

Elastic-plastic contact model for rough surfaces based on plastic asperity concept

A mathematical formulation for the contact of rough surfaces is presented. The derivation of the contact model is facilitated through the definition of plastic asperities that are assumed to be embedded at a critical depth within the actual surface asperities. The surface asperities are assumed to deform elastically whereas the plastic asperities experience only plastic deformation. The deformation of plastic asperities is made to obey the law of conservation of volume. It is believed that the proposed model is advantageous since (a) it provides a more accurate account of elastic-plastic behavior of surfaces in contact and (b) it is applicable to model formulations that involve asperity shoulder-to-shoulder contact. Comparison of numerical results for estimating true contact area and contact force using the proposed model and the earlier methods suggest that the proposed approach provides a more realistic prediction of elastic-plastic contact behavior.     

Strain gradient plasticity analysis of elasto-plastic contact between rough surfaces

From a microscopic point of view, the real contact area between two rough surfaces is the sum of the areas of contact between facing asperities. Since the real contact area is a fraction of the nominal contact area, the real contact pressure is much higher than the nominal contact pressure, which results in plastic deformation of asperities. As plasticity is size dependent at size scales below tens of micrometers, with the general trend of smaller being harder, macroscopic plasticity is not suitable to describe plastic deformation of small asperities and thus fails to capture the real contact area and pressure accurately. Here we adopt conventional mechanism-based strain gradient plasticity (CMSGP) to analyze the contact between a rigid platen and an elasto-plastic solid with a rough surface. Flattening of a single sinusoidal asperity is analyzed first to highlight the difference between CMSGP and J₂ isotropic plasticity. For the rough surface contact, besides CMSGP, pure elastic and J₂ isotropic plasticity analysis is also carried out for comparison. In all cases, the contact area A rises linearly with the applied load, but with a different slope which implies that the mean contact pressures are different. CMSGP produces qualitative changes in the distributions of local contact pressures compared with pure elastic and J₂ isotropic plasticity analysis, furthermore, bounded by the two.     

基于分子动力学-格林函数法的微凸体接触数值分析

表面接触是摩擦的先决条件,其真实接触面积、压应力大小、空间分布等一直是接触力学关注的核心问题.采用分子动力学-格林函数法(GFMD)模拟粗糙面的接触过程,验证了其在大规模接触分析中的高效及准确性,同时探讨了由微球体组成的粗糙面的接触力学特性,并分析了分子尺度下的结果和传统力学模型计算结果的差异.结果表明,单个微凸体接触结果和分子动力学-格林函数法模拟所得非常接近,误差在5%以内.数值模拟发现,在微凸体高度符合高斯分布的情况下,接触面积和接触力成线性关系;在相同接触面积下,微凸体模型得出的接触力偏高,是上限值.微凸体模型没有考虑微凸体间的相互影响,实际是高估了弹性体的刚度;实际接触过程中微凸体相互影响,微凸体对临域形变影响尤其大,使接触区域更加离散.GFMD模型可以准确计算数十亿量级别分子、原子接触过程中真实接触面积及分布,为后续摩擦、滑移等分析提供可靠的参考.     

固-液结合面法向动态接触刚度及阻尼的理论模型与实验分析

固-液接触状态广泛存在于机床核心单元关键零部件的接触运动副中,精确获得固-液结合面法向接触刚度及阻尼参数是高档数控机床产品在研发阶段就存在的一个关键理论与技术问题,并且仍然尚未根本解决.固-液结合面在介观层面上表现为两个粗糙表面的接触,在微观层面上表现为微凸体之间的接触,并在中/重载荷作用下微凸体可能会发生弹性/弹塑性...     

考虑粗糙结合面弹塑性接触的黏滑摩擦建模

提出一种同时考虑粗糙面上微凸体弹性变形和塑性接触的切向黏滑摩擦建模方法。采用Hertz弹性理论和Mindlin解描述弹性接触微凸体的切向载荷和相对变形的关系;采用AF(Abbott-Firstone)塑性理论和Fujimoto模型描述塑性接触微凸体切向载荷和相对变形的关系。再利用GW(Greenwood-Williamson)模型统计分析方法建立粗糙表面切向载荷和相对变形之间的关系。将模型与仅考虑微凸体弹性接触情况的模型进行对比,并研究了不同塑性指数对切向载荷和相对变形关系的影响。结果表明：与完全弹性接触模型相比,本文模型引入了塑性接触理论,能够更好地描述粗糙表面切向载荷和相对变形关系,并且考虑不同接触条件下弹性变形微凸体和塑性变形微凸体对切向接触载荷的贡献,在微滑移阶段,主要由弹性接触变形影响,而在进入宏观滑移阶段之后,切向行为主要由塑性变形影响。界面切向载荷由黏着和滑移接触作用共同决定,随着切向变形的增加,滑移接触力逐渐增加,而黏着接触力先增加后减少,反映了界面由微滑移逐渐向宏滑移演化的过程。随着塑性指数的增加,粗糙面上发生塑性接触的微凸体数目逐渐增加,切向黏滑行为主要受到塑性接触特征的控制。     

基于泛形理论的粗糙表面法向接触刚度研究

基于泛形理论和赫兹接触理论,通过泛形海岛分布描述粗糙表面的形貌从而建立结合面弹性接触模型,求解结合面的法向接触刚度。假设粗糙接触表面微凸体的高度满足高斯分布,通过赫兹接触理论建立单个微凸体的微观接触模型,利用粗糙表面的泛形复杂度D与面积度量尺码的最小下确界as确定表面形貌。泛形复杂度反映微凸体在粗糙表面上占据的空间大小程度;度量尺码下确界是接触过程中的最小接触面积。通过泛形复杂度和面积最小下确界推导出粗糙表面法向接触刚度的解析表达式。数值算例结果表明：在相同的面积尺度区间内,粗糙表面的法向接触刚度随着泛形复杂度的增加而增加,反之减小。当接触表面的泛形复杂度不变时,粗糙表面的法向接触刚度随最小下确界的减小而增大。泛形复杂度的较大时,最小下确界的变化对于接触刚度的影响更加明显。通过与已发表的文献结果对比分析之后,发现采用泛形海岛模型所得到的结合面接触刚度与文献中实验结果吻合较好。     

Hysteretic linear and nonlinear acoustic responses from pressed interfaces

An analysis of the linear and nonlinear acoustic responses from an interface between rough surfaces in elastoplastic contact is presented as a model of the ultrasonic wave interactions with imperfect interfaces and closed cracks. A micromechanical elastoplastic contact model predicts the linear and second order interfacial stiffness from the topographic and mechanical properties of the contacting surfaces during a loading–unloading cycle. The effects of those surface properties on the linear and nonlinear reflection/transmission of elastic longitudinal waves are shown. The second order harmonic amplitudes of reflected/transmitted waves decrease by more than an order of magnitude during the transition from the elastic contact mode to the elastoplastic contact mode. It is observed that under specific loading histories the interface between smooth surfaces generates higher elastoplastic hysteresis in the interfacial stiffness and the acoustic nonlinearity than interfaces between rough surfaces. The results show that when plastic flow in the contacting asperities is significant, the acoustic nonlinearity is insensitive to the asperity peak distribution. A comparison with existing experimental data for the acoustic nonlinearity in the transmitted waves is also given with a discussion on its contact mechanical implication.     

多粗糙峰弹塑性接触的有限元分析

采用具有一定数目圆形粗糙峰的刚性表面对弹塑性半元限体进行压下的模型来模拟多粗糙峰接触,并用有限元法对该模型进行了弹生分析,揭示了我地接触区应力状态的影响规律,发现中心接触区的变莆主要受到一定数目邻近粗糙峰的影响,而处于较远自找影响较小,同弹性接触相比,在弹塑性接触过程中有更多的邻近粗糙对中心接触区发生作用,改变粗糙的间距、曲率半径和压下深度都会对其产生影响。     

连接结构接触界面非线性力学建模研究

连接界面上存在的跨尺度、多物理场和非线性行为是引起结构复杂非线性动力学的主要原因。由于连接界面力学行为的复杂性,以及对连接界面进行直接试验观测的困难,连接界面的力学建模一直是非常具有挑战性的科学问题。本文首先从分析结合面的跨尺度物理机理入手,将名义的光滑平面视作凹凸不平的粗糙面,考虑单个微凸体的黏滑摩擦行为,建立接触载荷与变形的非线性关系,然后采用GW(Greenwood和Williamson, GW)模型数理统计方法建立整个粗糙界面的跨尺度力学模型,并与公开文献中试验结果进行对比。然后考虑连接界面典型非线性特征,提出一种改进的Iwan唯象模型,利用精细有限元方法获得非线性特征结果,采用系统辨识理论建立连接结构的降阶力学模型,并利用有限元结果进行模型验证。结果表明,本文提出的粗糙界面跨尺度模型在法向载荷较小时与试验结果吻合较好,改进的Iwan模型能够较好描述连接界面非线性特征,并与有限元结果吻合较好。      

Modeling of directional friction on a fully lubricated surface with regular anisotropic asperities

The modern surface technology now promises to fabricate surfaces with regular asperities. The regular asperity means that asperities, which are related to surface roughness in a conventional tribology, have similar shape and size, and their distribution over the surface is controllable. The regular asperity surface technology may have transformative impact to contemporary tribology. In this paper, we present a study of friction on the surface with regular anisotropic asperities (RAA) in a fully lubrication status. By anisotropic asperity, it is meant that the geometry of the asperity presents different to different motion directions, which is further speculated to have different friction behaviors along different motion directions. The primary goal of the study was to develop a model of friction force on the RAA surface in a fully lubrication status. The secondary goal was to exhibit the directional friction behavior based on our model. We employed Computational Fluid Dynamics (CFD) software to assist in the modeling and used the published data in the literature to validate our model. As a result, accuracy of our model was shown much better than that of the model reported in the current literature. With our model, we successfully demonstrated several interesting directional friction behaviors on the fully lubricated RAA surface.     

粗糙表面法向接触刚度的分形模型

提出了以往有关粗糙表面法向接触刚度理论研究工作的缺陷与不足,并在一定的前提假设下,基于球体与平面的接触理论和粗糙表面的分形接触理论,从理论上给出了具有尺度独立性的粗糙表面法向接触刚度分形模型,并进行了数字仿真研究。     

Contact mechanics of microscopically rough surfaces with graded elasticity

The well-known Greenwood and Williamson contact theory for microscopically homogeneous rough surfaces is generalized by considering functionally graded elastic rough surfaces. In particular, two distinct cases giving rise to a non-constant Young’s modulus with depth are considered: (I) an initially plane layered (or graded) solid which is non-uniformly eroded, so that the final product is a rough surface with asperities having an elastic modulus depending on the height; (II) an initially homogeneous rough surface which receives a surface treatment or a chemical degradation which modify the elastic properties of the asperities as a function of the depth from the exposed surface. These Functionally Graded Surfaces (FGS) can be observed both in biological systems and in mechanical components. The effects of graded elasticity on the relationship between real contact area versus applied load, and on the plasticity index are quantified and illustrated with numerical examples. It will be shown that the contact response may differ up to one order of magnitude with respect to that of a homogeneous surface. Comparison between Case I and Case II also shows that, for special surface properties, the two types of grading can provide the same mechanical response.     

单峰接触研究及其在分形表面接触中的应用

基于有限元方法,建立了弹塑性单峰的接触模型.粗糙峰为理想的弹塑性材料,为了考虑不同的材料特性对微凸体变形的影响,分别对9种不同的材料进行了分析.根据有限元计算结果,分析了接触面积,平均接触压力和接触力与变形干涉量之间的关系,并进行了经验公式的拟合.单峰接触所经历的4个不同的阶段,以及不同阶段之间的转化点均作了明确的表达.然后,根据分形理论,将单峰接触模型扩展到了三维的粗糙表面的接触,并提出了一个计算接触表面法向刚度的模型.通过与实验数据和以往模型的结果对比,证明本文中所提出的模型具有较高的精度.     

Lattice–Boltzmann simulations for analysing the detachment of micron-sized spherical particles from surfaces with large-scale roughness structures

Fully resolved numerical simulations of a micron-sized spherical particle residing on a surface with large-scale roughness are performed by using the Lattice–Boltzmann method. The aim is to investigate the influence of surface roughness on the detachment of fine drug particles from larger carrier particles for transporting fine drug particles in a DPI (dry powder inhaler). Often the carrier surface is modified by mechanical treatments for modifying the surface roughness in order to reduce the adhesion force of drug particles. Therefore, drug particle removal from the carrier surface is equivalent to the detachment of a sphere from a rough plane surface. Here a sphere with a diameter of 5 μm at a particle Reynolds number of 1.0, 3.5 and 10 are considered. The surface roughness is described as regularly spaced semi-cylindrical asperities (with the axes oriented normal to the flow direction) on a smooth surface. The influence of asperity distance and size ratio (i.e. the radius of the semi-cylinder to the particle radius, R_c/R_d) on particle adhesion and detachment are studied. The asperity distance is varied in the range 1.2 < L/R_d < 2 and the semi-cylinder radius between 0.5 < R_c/R_d < 0.75. The required particle resolution and domain size are appropriately selected based on numerical studies, and a parametric analysis is performed to investigate the relationship between the contact distance (i.e. half the distance between the particle contact points on two neighbouring semi-cylinders), the asperity distance, the size ratio, and the height of the particle centroid from the plane wall. The drag, lift and torque acting on the spherical particle are measured for different particle Reynolds numbers, asperity distances and sizes or diameters. The detachment of particles from rough surfaces can occur through lift-off, sliding and rolling, and the corresponding detachment models are constructed for the case of rough surfaces. These studies will be the basis for developing Lagrangian detachment models that eventually should allow the optimisation of dry powder inhaler performance through computational fluid dynamics.     

An adhesive wear model of fractal surfaces in normal contact

A generalized adhesive wear analysis that takes into account the effect of interfacial adhesion on the total load was developed for three-dimensional fractal surfaces in normal contact. A wear criterion based on the critical contact area for fully-plastic deformation of the asperity contacts was used to model the removal of material from the contact interface. The fraction of fully-plastic asperity contacts, wear rate, and wear coefficient are expressed in terms of the total normal load (global interference), fractal (topography) parameters, elastic–plastic material properties, surface energy, material compatibility, and interfacial adhesion characteristics controlled by the environment of the interacting surfaces. Numerical results are presented for representative ceramic–ceramic, ceramic–metallic, and metal–metal contact systems to illustrate the dependence of asperity plastic deformation, wear rate, and wear coefficient on global interference, surface roughness, material properties, and work of adhesion (affected by the material compatibility and the environment of the contacting surfaces). The analysis yields insight into the effects of surface material properties and interfacial adhesion on the adhesive wear of rough surfaces in normal contact.     

On the Iwan models for lap-type bolted joints

The paper presents mathematical modeling of the non-linear constitutive relation for bolted joints in the framework of the Kragelsky-Demkin theory of rough contact. It is shown that this approach, which maintains the tribology-related features of bolted joint interfaces, leads to a singular Iwan distribution density. In particular, we show that the Iwan density is expressed in terms of the height distribution density of the surface asperities, whereas its singular exponent is determined by the shape exponent of the surface asperities. Following this, constitutive relations for lap joints and the corresponding backbone (force-deflection) curves are obtained. Finally, Masing's hypothesis is applied and Goodman's relation for energy dissipation is recovered in order to describe the effects of cyclic loading. The two cases of a rough surface in contact with a flat surface and of two contacting rough surfaces are treated separately.     

Unloading an elastic-plastic contact of rough surfaces

A statistical model for the unloading of elastic-plastic contact of rough surfaces is presented for a single load-unload cycle. The hystereses of load-separation and load real contact area behavior are analyzed for a wide range of surface roughness and loading conditions. The residual topography of the unloaded rough surfaces is also analyzed and the new distribution functions of asperity heights and summit radii of curvature along with a corresponding GW residual plasticity index are presented. A new modified plasticity index (MPI) is suggested which considers the energy dissipation due to unrecovered plastic deformations. This MPI varies from zero for purely elastic contacts to unity for purely plastic contacts and hence, can better define the level of plasticity of contacting rough surfaces compared to the original GW plasticity index.     

基于微凸体接触压力分布的粗糙表面法向接触建模

提出一种考虑微凸体弹塑性接触变形影响的粗糙表面法向接触力学模型。采用有限元模拟微凸体弹塑性接触过程,分析不同塑性屈服条件对微凸体接触载荷和实际接触面积的影响。再根据微凸体接触面上压力分布的变化规律,将微凸体的接触状态分为完全弹性接触阶段、弹塑性接触阶段、完全塑性接触阶段。分析接触面压力变化规律对微凸体法向接触载荷-变形的影响,再利用GW模型的数理统计分析的方法得到粗糙表面的法向接触载荷。将本文提出的模型与完全弹性模型、CEB模型、ZMC模型、KE模型、JG模型进行对比,并且研究了塑性指数对粗糙面接触载荷-平均高度距离的影响。结果表明,本文提出的模型能够更好地描述微凸体法向接触载荷与接触变形的变化趋势,模型预测粗糙表面法向载荷与ZMC、KE模型具有较好的一致性;粗糙面接触载荷随着平均接触距离增加而减少,随着塑性指数的增加,不同模型预测的法向接触载荷差异逐渐增大。