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。     

A novel nonlinear contact stiffness model of concrete–steel joint based on the fractal contact theory

The heavy-duty machine tool is usually assumed in the concrete foundation, in which the machine tool-foundation joints have a critical effect on the working accuracy and life of heavy-duty machine tool. This paper proposed a novel contact stiffness model of concrete–steel joint based on the fractal theory. The topography of contact surface exist in concrete–steel joint has a fractal feature and can be described by fractal parameters. Asperities are considered as elastic, plastic deformation in micro-scale. However, the asperities of concrete surface will be crushed when the stress is larger than their yield limit. Then, the force balance of contact surfaces will be broken. Here, an iteration model is proposed to describe the contact state of concrete–steel joint. Because the contact asperities cover a very small proportion (less than 1%), the load on crushed asperities is assumed carried by other no contact asperities. This process will be repeated again and again until the crushed asperities are not being produced under external load. After that, the real contact area, contact stiffness of the concrete–steel joint can be calculated by integrating the asperities of contact surfaces. Nonlinear relationships between contact stiffness and load, fractal roughness parameter G, fractal dimension D can be revealed based on the presented model. An experimental setup with concrete–steel test-specimens is designed to validate the proposed model. Results indicate that the theoretical vibration mode shapes agree well with the experimental variation mode shapes. The errors between theoretical and experimental natural frequencies are less than 4.18%. The presented model can be used to predict the contact stiffness of concrete–steel joint, which will provide a theoretical basis for optimizing the connection characteristic of machine tool-concrete foundation.     

弹塑性微凸体侧向接触相互作用能耗

传统的结合面研究多基于光滑刚性平面与等效粗糙表面接触假设,忽略了结合面上微凸体侧向接触及相邻微凸体之间的相互作用,这导致理论模型与实际结合面存在较大出入.针对承受法向静、动态力的机械结合面,从微观上研究了微凸体侧向接触及相互作用的接触能耗.将法向静、动态力分解为法向分力和切向分力,获取弹性/弹塑性/塑性阶段考虑微凸体侧接触及相互作用的加、卸载法向分力-变形和切向分力-位移的关系.通过力的合成定理,从而获取加、卸载法向合力与总变形之间的关系,由于法向分力产生的塑性变形及切向分力产生的摩擦,导致加载、卸载法向合力-总变形曲线存在迟滞回线.通过对一个加、卸载周期内的法向合力-总变形曲线积分,获得一个周期的微凸体接触能耗,包括应变能耗及摩擦能耗.仿真分析表明:微凸体在3个阶段的能耗均随变形的增大而非线性增大.微凸体侧向接触角度越大,能耗越大,且在弹性阶段最为明显.在弹性阶段,仅存在侧向的摩擦能耗,故结合面在低载荷作用下必须采用双粗糙表面假设.在塑性阶段,由于微凸体接触能耗为应变能耗,且接触角对其能耗影响甚微,故结合面在大载荷作用下可采用单平面假设对其进行研究.相对于KE和Etsion模型,本文提出的模型与Bartier的实验结果更吻合.     

机械结合面切向接触阻尼计算模型

针对两粗糙表面在法向力和切向力共同作用下相互接触时结合面切向阻尼的问题进行了研究。首先,根据KE模型对单个微凸体在弹性、弹塑性、塑性变形阶段的切向接触行为进行了分析,获得了微凸体在三个变形阶段的黏滑特性;然后,基于GW统计模型建立了一种在微凸体法向弹性、弹塑性和塑性变形机制基础上,考虑微凸体黏滑摩擦行为的机械结合面切向接触阻尼统计模型;最后,分别讨论了机械结合面的法向预载荷、切向激振频率和切向动态位移幅值对机械结合面切向阻尼的影响。研究表明:结合面切向接触阻尼系数随着结合面法向载荷的增大而增大,随着切向激振频率和切向动态位移幅值的增大而减小;在高频率、大幅值下,结合面切向接触阻尼系数几乎与动态位移幅值和激振频率无关。为了验证模型的准确性,构建了动态切向力作用下的结合面切向阻尼试验,其试验结果与理论仿真变化规律与量级基本一致,从而证明了本文所提出的切向阻尼模型的有效性。      

磨削粗糙表面法向接触刚度研究

为更加准确地描述机械磨削表面的接触刚度,本文在现有统计分析理论的基础上,提出了一种新的粗糙表面接触模型。模型针对接触表面微凸体形貌,将原有的球体假设采用cos函数曲线回转体代替,在假设形貌的基础上重新解算了微凸体弹塑性变形的临界压入深度,推导出了接触区域真实接触压力与接触刚度关系表达式。通过数值仿真方法得到了不同塑性指数下平均距离、接触刚度与接触压力之间的变化关系。对比结果显示,随着塑性指数的增大,本文模型的平均距离与球形模型的平均距离之间的差值逐渐增大。在接触刚度方面,本文模型相比球形模型更加贴近实验结果,并且随着塑性指数的增加,球形模型与本文模型之间的差值越来越大。本文模型结果与实验数据的相对偏差能够控制在5%以内,从而验证了本文模型的正确性,为更加准确地描述磨削表面零件的接触行为提供理论基础。     

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。     

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...     

Elasto-plastic contact of rough surfaces: a mixed-lubrication model for the textured surface analysis

An improved asperity contact model for two rough surfaces with misalignment is presented in this study. The contact model is statistical and can account for the elasto-plastic behavior of interacting asperities. By combining the improved asperity contact model and the average flow Reynolds equation together, a mixed-lubrication model is developed to understand the effect of surface texturing. By comparing with the results of the purely elastic asperity contact model, it is found that the improved asperity contact model can predict the contact force and actual contact area more accurately, particularly under high load conditions. Moreover, comparing with the elasto-plastic model with an equivalent rough surface against a plane, the improved contact model can consider the effect of permitting misalignment of two rough surfaces. This is beneficial for analyzing the performance of the textured piston ring/liner system, especially when asperities contact and wear happen.     

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.     

考虑摩擦系数和微凸体相互作用的粗糙表面接触热导分形模型

基于三维分形理论,建立了考虑摩擦系数和微凸体相互作用的粗糙表面接触热导分形模型,并且考虑了微凸体的弹性变形、弹塑性变形和完全塑性变形. 通过该模型,分析了摩擦系数、分形维数、分形粗糙度和接触载荷对热接触热导的影响. 研究结果表明:接触热导随着摩擦系数和分形粗糙度的增大而减小,随着分形维数和接触载荷的增大而增大. 该研究为开展接合面的热传递提供了一定的理论基础.      

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。     

两圆柱体结合面的接触热导分形模型研究

基于三维分形理论,在考虑微凸体的弹性变形、弹塑性变形和塑性变形的基础上,建立了两圆柱体结合面接触热导分形模型。通过数值仿真,分析了分形维数,分形尺度参数、圆柱体曲率半径和接触类型对接触热导的影响。研究结果表明：接触热导随着分形维数的增大而增大,随着分形尺度参数的增大而减小;相同参数下,内接触比外接触的接触热导要大;此外,当固定其中一个圆柱体的曲率半径时,随着另一个圆柱体曲率半径的增大,接触热导增大。该模型为开展齿轮等曲面接触热导的研究提供了理论基础。     

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.

     

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.     

三维轮轨法向接触力学行为弹塑性理论分析

基于Hertz接触理论和双线性强化模型,建立了轮轨法向接触弹塑性理论分析模型,分析了轮轨法向接触力学响应特征,讨论了轴重对接触压力和接触变形的影响规律。同时,基于三维轮轨接触有限元模型模拟了轮轨接触力学行为,并引入理论误差系数分析了弹性模型和双线性强化模型对轮轨接触力学响应预测结果的差异性。结果表明,轮轨最大接触压力和接触变形量均随轴重的增大而增大;双线性强化模型的理论误差系数较小,采用双线性强化分析模型能较准确地预测轮轨接触弹塑性力学行为。研究结果可为轮轨系统安全服役和损伤评估提供理论和技术支持。     

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.     

A model for simulation of friction phenomenon between dies and workpiece

Based on the interaction of asperities and upperbound approach a mathematical model for simulation of friction phenomenon between dies and workpiece is proposed. Optimizing the mathematical model with respect to several variables it is found that in addition to adhering, tearing, ploughing, etc., asperities workpiece can move wave-like along the surface layer and under certain circumstances they may disappear. If the asperities wavily move along the surface layer the friction coefficient depends on the geometry of asperities. However, the bonding strength of asperities has no significant influence on friction coefficient. The depth of the plastic deformation layer is related to the geometry of asperities, too. The soundness of the prerequisite of the proposed model and some analytical results were verified by experiments.Department of Materials Engineering, Northwestern Polytechnical UniversityThis is a project of the cooperative program between the Department of Materials Engineering of Northwestern Polytechnical University of the People's Republic of China and the Institute for Metal Forming at Lehigh University of the United States of America.     

A multi-scale constitutive model for the sintering of an air-plasma-sprayed thermal barrier coating, and its response under hot isostatic pressing

A micromechanical model is developed for the sintering of an air-plasma-sprayed, thermal barrier coating, and is used to make predictions of microstructure evolution under free sintering and under hot isostatic pressing. It is assumed that the splats of the coating are separated by penny-shaped cracks; the faces of these cracks progressively sinter together at contacting asperities, initially by the mechanism of plastic yield and subsequently by interfacial diffusion. Diffusion is driven by the reduction in interfacial energy at the developing contacts of the cracks and also by the local contact stress at asperities. The contact stress arises from the remote applied stress and from mechanical wedging of the rough crack surfaces. Sintering of the cracks leads to an elevation in both the macroscopic Young's modulus and thermal conductivity of the coating, and thereby leads to a degradation in thermal performance and durability. An assessment is made of the relative roles of surface energy, applied stress and crack face roughness upon the sintering response and upon the evolution of the pertinent mechanical and physical properties. The evolution in microstructure is predicted for free sintering and for hot isostatic pressing in order to provide guidance for experimental validation of the micromechanical model.     

粗糙表面的弹塑性接触研究

建立了综合载荷作用下粗糙表面弹塑性接触的确定性模型,考虑了微凸峰接触的弹塑性变形阶段,数值求解得到实际接触面积、压力分布和微凸峰塑性形变.分析了实际接触面积与法向载荷的关系,并研究了点接触的椭圆参数对上述关系的影响.建立了结点增长模型,分析了结点增长与滑动摩擦系数的关系以及滑动摩擦系数随椭圆参数的变化.结果表明:随着法向载荷增大,实际接触面积与法向载荷之间的非线性关系愈加显著;椭圆参数越大,实际接触面积越小,选择较小的椭圆参数可降低平均接触压力;结点增长的速率随滑动摩擦系数增大而增大;表面剪切作用力使最大Mises应力值升高,疲劳裂纹的发生源向表面靠近;重载时选择较小的滚动轴承沟曲率半径系数有利于减小摩擦功耗.