基于共轭梯度法和快速傅立叶变换的粗糙表面微动接触数值研究

实际工程表面多为粗糙表面,研究粗糙表面的表面形貌对微动接触中压力和应力的影响具有重要意义。本文研究接触过程中法向载荷保持不变,切向载荷为周期性的交变载荷。首先,建立接触算法和模型,算法核心是利用共轭梯度法CGM(Conjugate gradient method)计算微动接触中的表面压力及切向应力并利用快速傅里叶变换FFT(Fast Fourier transform)加快计算速度。然后,对单峰表面、正弦表面和随机粗糙表面的接触进行数值研究。结果表明,表面幅值对切向载荷-位移曲线以及接触过程中的能量耗散有影响,表面幅值越大,相同切向载荷作用下产生的切向位移越大,能量耗散也越大。     

Onset of Surface Damage in Modular Orthopedic Implants: Influence of Normal Contact Loading and Stress-assisted Dissolution

Surface damage at interfaces of modular implants results from repeated fretting contacts between metallic surfaces in a corrosive environment. As a first step in understanding this complex process, multi-asperity contact experiments were conducted to characterize roughness evolution due to action of contact loads and exposure to a reactive environment. Cobalt–chromium specimens with surface roughness similar to modular implant were first subjected to only contact loading and subsequently, to alternating contact loads and exposure to reactive environment. During repeated normal contact loading, amplitude of surface roughness reached a steady value after decreasing during the first few cycles. However during the second phase surface roughness amplitude continuously evolved—decreasing during contact loading and increasing on exposure to corrosive environment. The increase in roughness amplitude during surface reaction depended on the magnitude of applied contact loads. A damage mechanism that incorporates contact-induced residual stress development and stress-assisted dissolution is proposed to elucidate the measured surface roughness evolution.     

A friction contact stiffness model of fractal geometry in forced response analysis of a shrouded blade

To investigate the nonlinear vibration behavior of a shrouded blade with friction dynamic contact interface, a friction contact stiffness model is proposed to describe the friction force at different rough interfaces and different normal loads. In the proposed model, the friction contact interface is discretized to a series of friction contact pairs and each of them can experience stick, slip, or separate states. Fractal geometry is used to simulate the topography of contact surfaces. The contact stiffness is calculated using the Hertz contact theory and fractal geometry, which is related to contact interfaces parameters including normal load, roughness, Young??s modulus, and Poisson??s ratio. The trajectory tracking method is used to predict the friction force and it is not necessary to judge the transition condition among stick, slip, and separate states. It is suitable for complicated periodic motion of the contact interfaces. The forced response of a real shrouded blade is predicted using the proposed model and the multi-harmonic balance method. The effect of surface roughness, initial normal load, and contact area on the forced response of a shrouded blade is studied. It is shown that contact stiffness increases with normal load and fractal dimension. The resonant amplitude is sensitive to the initial normal load and contact surface roughness. The response can be influenced by the contact area, which is an important parameter for blade designers.     

General results for complete contacts subject to oscillatory shear

In this paper, we consider the general interfacial characteristics of a square elastic block, pressed onto an elastically similar half-plane by a constant normal force, and subjected to oscillatory shear. It is found that there is a critical coefficient of friction, 0.543, above which the contact is permanently stuck along its entire length for a shearing force below about 55% of that needed to cause sliding. For shearing forces above this, the contact interface will either shakedown to a fully adhered state (depending on the degree of reversal of the shear loading) or will exhibit cyclic slip at an interior point. If the coefficient of friction is below 0.543, the application of normal load alone will produce equal and opposite slip zones attached to the contact edges. The subsequent imposition of a shear force causes the leading edge slip zone to increase in length while the presence of residual slipping tractions at the trailing edge causes the trailing edge to lift off. Under oscillatory loading, the contact edges cycle between slip and separation over a minute region while an interior point may exhibit cyclic slip if the loading history is sufficiently demanding. The results found are of practical relevance to the study of fretting fatigue of complete contacts, such as some types of spline joint.     

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.     

基于Iwan模型的接合面切向响应建模

针对工程中常见预紧力作用下的搭接接头,研究其在小幅切向位移激励时的切向位移响应问题,为此提出一种新的基于实际表面形貌和材料性能参数的滑移力密度分布函数.应用该分布函数得到搭接接头切向响应本构模型,并获得单位加载周期内的迟滞曲线和能量耗散值, 通过与已出版的实验结果相对比,发现得到的模拟值与实验结果吻合, 证明该模型的合理性.在此基础上利用该分布函数研究了接合面切向位移与切向力、切向接触刚度及能量耗散之间的关系,结果表明: 建立的模型能很好地描述接合面间切向力与切向位移之间的关系,临界滑移力函数开始迅速上升, 到达最大值后迅速收敛到零;切线力与切向位移之间表现出非线性特性, 随着切向位移的增大,切向接触刚度表现出"软化"现象;初始切向刚度与法向载荷、粗糙度参数及塑性指数有关, 对于确定的接触表面,法向力越大, 初始切向刚度越大; 初始切向刚度同样也随着塑性指数的增大而增大.      

A slip-line plasticity analysis of sliding friction of rough surfaces exhibiting self-affine (fractal) behavior

A plasticity analysis of sliding friction of rough (fractal) surfaces sliding against smooth surfaces was developed based on a slip-line model of a rigid spherical asperity (wear particle) plowing and cutting through a soft semi-infinite medium. Solutions of the fraction of fully plastic asperity microcontacts responsible for the evolution of friction and energy dissipation were obtained in terms of the total normal load (global interference), interfacial adhesion characteristics, topography (fractal) parameters of the hard surface, and elastic–plastic material properties of the soft surface. This was accomplished by incorporating the slip-line model of a single microcontact into a friction analysis of sliding surfaces demonstrating multi-scale roughness. Numerical results provide insight into the effects of global interference (normal load), fractal parameters (surface roughness) of the hard surface, interfacial shear strength (adhesion), and material properties of the soft surface on plastic deformation at the microcontact level, global coefficient of friction, and frictional energy dissipated during sliding.     

粗糙度纹理对有限长线接触混合润滑影响

采用统一Reynolds方程建立有限长线接触混合润滑模型,研究横向、纵向和二维规则表面粗糙度的波长、幅值及工况变化对润滑影响.结果表明:波长、幅值与工况对三种表面粗糙度接触副的润滑影响类似;随着载荷增大,平均膜厚降低,摩擦系数、接触载荷比与接触面积比均增大;随着转速升高,平均膜厚增大,摩擦系数、接触载荷比与面积比均降低,其中摩擦系数随转速进一步增大而小幅升高.在润滑状态转换区域润滑特征参数变化显著,而其他润滑区域变化平缓.沿卷吸速度方向的压力与膜厚波动分布存在相位差,垂直方向则同相位;相同的工况和粗糙度参数时,纵向粗糙度分布更有利于接触润滑.     

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.     

Effect of phase on the frictional dissipation in systems subjected to harmonically varying loads

When contacting elastic systems are subjected to periodic loading, frictional slip occurs resulting in energy dissipation. Here we investigate the effect of the relative phase of harmonically varying tangential and normal loads on the frictional dissipation in a very simple uncoupled frictional system. We demonstrate that this effect is substantial when the system experiences periods of separation, but more modest when contact is continuous. The maximum dissipation occurs when the normal and tangential loads are approximately π/2 out of phase.     

Physics-based modeling for partial slip behavior of spherical contacts

A physics-based modeling approach for partial slip behavior of a spherical contact is proposed. In this approach, elastic and elastic–plastic normal preload and preload-dependent friction coefficient models are integrated into the Cattaneo–Mindlin partial slip solution. Partial slip responses to cyclic tangential loading (fretting loops) obtained by this approach are favorably compared with experiments and finite element results from the literature. In addition to load-deformation curves, tangential stiffness of the contact and energy dissipation per fretting cycle predictions of the models are also provided. Finally, the critical assumptions of elastically similar bodies, smooth contact surface and negligible adhesion, and limitations of this physics-based modeling approach are discussed.     

摩擦材料应用方式对超声波电机驱动特性的影响

摩擦材料是超声波电机的关键零件,其应用方式直接影响超声波电机的驱动特性.以行波超声波电机为研究对象,将摩擦材料分别应用到转子和定子上,与相应的定子和转子组合,模拟超声波电机的接触方式,研究了超声波电机的负载和磨损特性随摩擦材料应用方式的变化规律.借助于阻抗仪测试了摩擦材料应用到定子齿面前后的阻抗特性,采用精密粗糙度仪和金相显微镜评价了超声波电机定子和转子接触界面磨损前后的形貌变化及其磨损模式.结果表明:当摩擦材料应用到定子齿面时,定子的谐振频率略微降低;当2台超声波电机空载转速相同时,摩擦材料应用到定子齿面与金属转子配副时可获得较大的堵转力矩,定子摩擦材料表面呈现抛光的磨损特征,而当摩擦材料应用到转子表面与金属定子配副时,转子摩擦材料表面呈现较严重的犁沟磨损.     

磁电弹复合材料和刚性导电导磁圆柱压头的二维微动接触分析

本文求解平面应变状态下磁电弹复合材料半平面和刚性导电导磁圆柱压头的二维微动接触问题。假设压头具有良好的导电导磁性,且表面电势和磁势是常数。微动接触依赖载荷的加载历史,所以首先求解单独的法向加载问题,然后在法向加载问题的基础上求解循环变化的切向加载问题。整个接触区可以分为内部的中心粘着区和两个外部的滑移区,其中滑移区满足Coulomb摩擦法则。利用Fourier积分变换,磁电弹半平面的微动接触问题将简化为耦合的Cauchy奇异积分方程组,然后数值离散为线性代数方程组,利用迭代法求解未知的粘着/滑移区尺寸、电荷分布、磁感应强度、法向接触压力和切向接触力。数值算例给出了摩擦系数、总电荷和总磁感应强度对各加载阶段的表面接触应力、电位移和磁感应强度的影响。     

ENERGY DISSIPATION IN TAPPING MODE ATOMIC FORCE MICROSCOPY

原子力显微镜有多种成像模式,其中轻敲模式是最为常用的扫描方式.轻敲模式能获取样品表面形貌的高度信息和相位信息,其中相位信息具有更多的价值,如能反映样品的表面能、弹性、亲疏水性等.依据振动力学理论,相位与振动系统的能量耗散有关.探针样品间的能量耗散对于理解轻敲模式下原子力显微镜的成像机理至关重要,样品特性和测量环境会影响能量耗散.本文在不考虑毛细力影响下,基于JKR接触模型,给出了探针样品相互作用下的加卸载曲线,结合原子力显微镜力曲线实验,给出了探针-样品分离失稳点的位置,从而计算一个完整接触分离过程的能量耗散,进而讨论考虑表面粗糙度对能量耗散的影响.在轻敲模式下考虑毛细力影响,通过特征时间对比,证明挤出效应是液桥生成的主导因素,在等容条件下,用数值方法计算了不同相对湿度对能量耗散的影响.通过一维振子模型,简要说明原子力显微镜相位像与样品表面能、杨氏模量、表面粗糙度、相对湿度之间的关系.分析表明,表面粗糙度和环境湿度均会引起相位的变化,进而认为它们是引起赝像的因素.     

Frictional Hertzian contact problems under cyclic loading using static reduction

In this study we investigate an axisymmetric Hertzian contact problem of a rigid sphere pressing into an elastic half-space under cyclic loading. A numerical solution is sought to obtain a steady state, which demands a large amount of computer memory and computing speed. To achieve a tractable problem, the current numerical model uses a “static reduction” technique, which employs only a contact stiffness matrix rather than the entire stiffness of the problem and is more accurate than the approach used by most finite element codes. Investigation of the tendency of contact behavior in the transient and steady states confirms that a steady state exists, showing converged energy dissipation. The dependence of dissipation on load amplitude shows a power law of load amplitude less than 3, which may explain some deviations in the experimental findings.     

Effective macroscopic adhesive contact behavior induced by small surface roughness

In this paper we study a model contact problem involving adhesive elastic frictionless contact between rough surfaces. The problem's most notable feature is that it captures the phenomenon of depth-dependent-hysteresis (DDH) (e.g., see Kesari et al., 2010), which refers to the observation of different contact forces during the loading and unloading stages of a contact experiment. We specifically study contact between a rigid axi-symmetric punch and an elastic half-space. The roughness is represented as arbitrary periodic undulations in the punch's radial profile. These undulations induce multiple equilibrium contact regions between the bodies at each indentation-depth. Assuming that the system evolves so as to minimize its potential energy, we show that different equilibrium contact regions are selected during the loading and unloading stages at each indentation-depth, giving rise to DDH. When the period and amplitude of our model's roughness is reduced, we show that the evolution of the contact force and radius with the indentation-depth can be approximated with simpler curves, the effective macroscopic behavior, which we compute. Remarkably, the effective behavior depends solely on the amplitude and period of the model's roughness. The effective behavior is useful for estimating material properties from contact experiments displaying DDH. We show one such example here. Using the effective behavior for a particular roughness model (sinusoidal) we analyze the energy loss during a loading/unloading cycle, finding that roughness can toughen the interface. We also estimate the energy barriers between the different equilibrium contact regions at a fixed indentation-depth, which can be used to assess the importance of ambient energy fluctuations on DDH.     

船用凸轮-挺柱副摩擦润滑性能研究

随着船舶柴油机功率密度和转速等性能参数的不断提升,配气凸轮-挺柱副面临着更加严苛的工作环境,尤其是界面微观接触区的摩擦学特性,在瞬态载荷冲击、速度冲击、曲率变化及局部粗糙峰接触条件下,界面摩擦及闪温迅速突变,带来磨损和胶合等表面失效问题. 本研究中基于先进三维线接触混合润滑模型,考虑凸轮-挺柱副瞬态突变工况及几何变化、瞬态表面粗糙度影响以及润滑油非牛顿流体作用,采用稳定性好、收敛速度快的准系统数值分析方法开展凸轮-挺柱副摩擦闪温分析,揭示粗糙度参数、工况改变及几何结构对其润滑状态和摩擦闪温特性的影响规律,为船舶柴油机配气凸轮-挺柱副摩擦学优化设计及磨损胶合失效预测提供理论指导.      

Nonlinear Acoustic Interaction of Contact Interfaces

Nonlinear acoustic interactions at contact interfaces can be used to characterize defects or imperfect bonds at these interfaces. Most methods used to characterize nonlinear interactions consider only a portion of the nonlinear signature, such as nonlinearities caused by high-order harmonics or sidebands. We describe a signal processing algorithm that can extract three nonlinear indicators related to amplitude attenuation, phase shift, and harmonics. Two aluminum blocks were mounted together to form a contact interface and subjected to normal compressive loading. Experiments were conducted to investigate the nonlinear interactions between the ultrasonic waves and interfaces, with a focus on the influence of excitation levels, applied pressure, and surface roughness. The ultrasonic signals were then processed using the nonlinear feature extraction algorithm. We show that the nonlinear indicators can characterize the contact condition of interfaces, and that their sensitivities to pressure differ for interfaces of different roughness and over different pressure ranges.     

Effect of micropillar surface texturing on friction under elastic dry reciprocating contact

Surface texturing is considered to be a promising method to improve the tribological properties. Depending upon the experimental conditions, the effect of texturing varies from favourable to unnoticeable to detrimental. In this work, surfaces with micropillars are studied under elastic dry reciprocating contact. An array of micropillars with different pillar heights are generated on stainless steel using wire-cut electrical discharge machining. The effect of stiffness of the micropillars on friction is investigated, keeping the number of micropillars in contact with a flat aluminium alloy (Al6061) slider and contact geometry constant. Reciprocating experiments are carried out against a flat surface such that about 81 micropillars are in contact. From the experimental results, it is found that the coefficient of friction is independent of the stiffness of the texture elements. However, work done per cycle significantly varied with the stiffness of texture element and applied normal load. A lumped system model with Coulomb friction shows that the work done per cycle varies quadratically with the normal load. The experimental results agree with this simplified model except in the incipient sliding regime. These results show how the work done per cycle varies, for different contact stiffness under elastic contact even though the coefficient of friction remains constant. The implication of this study for a macroscopic measured coefficient of friction as a function of microscopic asperity level friction is discussed.     

载荷及位移幅值对DLC薄膜微动磨损行为的影响

为了提高TC4钛合金表面的抗微动磨损性能,在本文中采用非平衡磁控溅技术(Unbalanced Magnetron Sputtering)在TC4钛合金表面沉积了类金刚石(DLC)薄膜. 采用球/平面接触形式研究了DLC薄膜的微动摩擦磨损行为. 在不同法向载荷和位移幅值下,结合微动运行工况图研究了DLC薄膜滑移状态和损伤机理. 利用原子力显微镜、纳米压痕仪、激光拉曼光谱仪、激光共聚焦显微镜、场发射扫描电子显微镜和SRV-V微动摩擦磨损试验机等设备对DLC薄膜进行性能的表征和微动摩擦磨损性能测试. 通过微动图,摩擦耗散能,磨痕形貌、化学成分分析揭示其损伤机理. 结果表明:载荷和位移幅值对DLC薄膜微动摩擦磨损行为和损伤机理有显著影响. 当位移幅值为25 μm 时,微动运行于混合滑移(mixed slip regime,MSR)情形下,当位移幅值为100 μm时,微动运行于完全滑移(gross slip regime,GSR)情形下. 小位移幅值时,DLC薄膜磨损机理是磨粒磨损为主;大位移幅值时,DLC薄膜磨损机理是黏着磨损为主. 干摩擦条件下,DLC薄膜有良好的抗微动磨损性能,关键就在于其优异力学性能和自润滑特性.