A microslip friction model with normal load variation induced by normal motion

A two-dimensional microslip friction model with normal load variation induced by normal motion is presented in this paper. The model is a distributed parameter model, which characterizes the stick-slip-separation of the contact interface and determines the resulting friction force, including its time variance and spatial distribution, between two elastic structures. When the relative motion is simple harmonic motion, the stick-slip-separation transition angles associated with any point in the contact area can be analytically determined within a cycle of motion. In addition, if the relative motion is given, stick-slip-separation transition boundaries inside the contact area and their time variances can be determined. Along with an iterative multi-mode solution approach utilizing harmonic balance method (HBM), the developed model can be employed to determine the forced response of frictionally constrained structures. In the approach, the forced response is constructed in terms of the free mode shapes of the structure; consequently, it can be determined at any excitation frequency and for any type of normal load distribution. Two examples, a one-dimensional beam like damper and a more realistic blade to ground damper, are employed to illustrate the predictive abilities of the developed model. It is shown that while employing a single mode model, transition boundaries for the beam like damper agrees with the results given in the literature, the developed method identifies the phase difference along the slip to stick transition boundary when a multi-mode model is employed. Moreover, while partial slip is illustrated in the two examples, typical softening and hardening effects, due to separation of the contact surface, are also predicted for the blade to ground damper.     

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.      

双材料单伸臂叠合梁的界面滑移与自振特性分析

将叠合梁划分为接触区和分离区,接触区界面间的摩擦作用会对叠合梁的滑移、刚度和自振频率产生影响.本文给出了单伸臂叠合梁在均布荷载和集中力作用下,考虑叠合界面摩擦作用的滑移应变和滑移分布的表达式;推导了考虑叠合界面间摩擦力及摩擦力产生的抵抗弯矩共同作用下的截面刚度.假设梁按等波长和等刚度两种形式自由振动,运用传递矩阵法推导...     

考虑摩擦因素的结合面切向接触刚度分形预估模型及其仿真分析

为建立更完善和精确的结合面接触刚度模型,本文根据分形理论和摩擦学原理,从微观角度建立了考虑摩擦因素的结合面切向接触刚度分形预估模型.通过数值仿真分析研究了接触载荷、分形维数、摩擦系数和接触面积等因素对结合面切向接触刚度的影响.分析结果表明:结合面切向接触刚度随法向载荷和分形维数的增加而增大,而随分形尺度参数的增大而减小;摩擦系数对结合面切向接触刚度的影响较大,不同实际接触面积下的切向刚度相差较大;当分形维数较小时,摩擦系数对结合面切向刚度的影响将降低.这些研究对于进一步开展结合面的动力学特性研究具有重要意义.     

依据各向异性分形理论的固定结合面椭圆弹塑性法向接触刚度建模及仿真分析

依据各向异性分形几何理论,将结合面接触点拓展为椭圆形,结合微凸体接触点面积大小分布函数以及概率论相关理论获得关于椭圆形接触点接触面积以及离心率的二维联合分布密度函数,应用赫兹接触理论,进而建立了依据各向异性分形理论的结合面椭圆弹塑性法向接触刚度模型,并采用MATLAB软件对影响结合面法向刚度的相关因素进行了数值仿真及结...     

Transition from stick to slip in Hertzian contact with “Griffith” friction: The Cattaneo–Mindlin problem revisited

Classically, the transition from stick to slip is modelled with Amonton–Coulomb law, leading to the Cattaneo–Mindlin problem, which is amenable to quite general solutions using the idea of superposing normal contact pressure distributions – in particular superposing the full sliding component of shear with a corrective distribution in the stick region. However, faults model in geophysics and recent high-speed measurements of the real contact area and the strain fields in dry (nominally flat) rough interfaces at macroscopic but laboratory scale, all suggest that the transition from ‘static’ to ‘dynamic’ friction can be described, rather than by Coulomb law, by classical fracture mechanics singular solutions of shear cracks. Here, we introduce an ‘adhesive’ model for friction in a Hertzian spherical contact, maintaining the Hertzian solution for the normal pressures, but where the inception of slip is given by a Griffith condition. In the slip region, the standard Coulomb law continues to hold. This leads to a very simple solution for the Cattaneo–Mindlin problem, in which the “corrective” solution in the stick area is in fact similar to the mode II equivalent of a JKR singular solution for adhesive contact. The model departs from the standard Cattaneo–Mindlin solution, showing an increased size of the stick zone relative to the contact area, and a sudden transition to slip when the stick region reaches a critical size (the equivalent of the pull-off contact size of the JKR solution). The apparent static friction coefficient before sliding can be much higher than the sliding friction coefficient and, for a given friction fracture “energy”, the process results in size and normal load dependence of the apparent static friction coefficient. Some qualitative agreement with Fineberg's group experiments for friction exists, namely the stick–slip boundary quasi-static prediction may correspond to the arrest of their slip “precursors”, and the rapid collapse to global sliding when the precursors arrest front has reached about half the interface may correspond to the reach of the “critical” size for the stick zone.     

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.     

基于LuGre摩擦模型的接触约束法旋转柔性梁斜碰撞研究

基于接触约束法和LuGre摩擦模型对在重力场作用下作大范围旋转运动的柔性梁系统和斜坡发生含摩擦斜碰撞的动力学问题进行研究.首先运用刚柔耦合的多体系统动力学理论对大范围运动的柔性梁进行离散化和动力学建模,在碰撞时采用冲量动量法求出跳跃速度,其次在法向上引入接触约束求解出碰撞力,在切向上采用LuGre摩擦模型分两种方式求解...     

Modeling and dynamic analysis of bolted joined cylindrical shell

Based on Sanders shell theory, modeling and dynamic analysis of bolted joined cylindrical shell were studied in this paper. When subjected to external excitations, contact state such as stick, slip and separation may occur at those locations of bolts. Considering these three contact states, an analytical model of cylindrical shell with a piecewise-linear boundary was established for the bolted joined cylindrical shell. First, the model was verified by the simplified line system, and the effects of stiffness in connecting interface and the number of bolts on natural frequency and mode shape were investigated. Then, through the response under instantaneous excitation, damping characteristic of the system was proved which is caused by the friction model. Last, the effects of external load frequency, response location, excitation amplitude and connecting parameters including stiffness and preload were numerically investigated and fully explained by 3-D frequency spectrum. The results indicated that periodic motion, times periodic motion and even chaotic motion were observed based on different parameters.     

A slip-line plasticity analysis of abrasive wear of a smooth and soft surface sliding against a rough (fractal) and hard surface

Abrasive wear of a soft and smooth surface sliding against a rough (fractal) and hard surface was analyzed by the slip-line theory of plasticity. The analysis is based on a slip-line model of a rigid spherical asperity (wear particle) plowing through a soft surface and removing material by microcutting. Integration of this single-contact model into a three-dimensional contact mechanics analysis of an abrasive surface exhibiting multi-scale roughness described by fractal geometry yielded relationships of the abrasive wear rate and wear coefficient in terms of the interfacial shear strength (adhesion), topography (fractal) parameters of the hard/rough surface, elastic–plastic material properties of the soft/smooth surface, and total normal load. Analytical results from the single-contact analysis provide insight into the deformation of a perfectly plastic material caused by the abrasive action of a rigid asperity/wear particle under different normal load and interfacial friction (adhesion) conditions. The dependence of the abrasive wear rate and wear coefficient on normal load (global interference), roughness of the abrasive surface, elastic–plastic material properties of the abraded surface, and interfacial shear strength (lubrication effect) is interpreted in the context of numerical results obtained for representative ceramic/ceramic, ceramic/metallic, and metal/metal sliding systems.     

Passive control of vibration of thin-walled gears: advanced modelling of ring dampers

Vibrations on gears are mainly induced by the gear mesh contact. Resonance conditions of the gear may occur during service if the mesh frequency is close to the natural frequencies of the system at the designed speed of the shaft. Since detuning is not always possible in gears, the response level must be reduced by increasing the damping of the system. In this paper, a passive approach based on the application of a ring damper to reduce the vibration level is presented. The ring damper is placed in a groove underneath the outer rim of the gear. The contact is guaranteed by the preload due to the elasticity of the ring damper itself and above all by the centrifugal force that presses the damper against the groove during rotation. The relative motion of the two components at the contact interface dissipates energy by friction, and hence damping is generated. The vibration amplitude is reduced by optimizing the material and geometrical properties of the ring damper. One of the most important parameters in the determination of the amount of damping due to friction phenomena is the static normal load at the contact, which depends on the mass, the shape, and the material of the ring damper. A numerical method is presented, which couples the static and dynamic equilibrium equations of the assembly. The core of the proposed method is the contact element that takes into account local stick–slip–lift off of the contact and determines the contact forces in terms of static and dynamic loads, which are then used to solve the coupled static and dynamic equilibrium. Since the ring damper has a cut that breaks its continuous circular shape in order to be fitted on the groove, the hypothesis of cyclic symmetry for the gear/ring–damper assembly fails. As a consequence, an appropriate reduced-order modeling is presented to allow the forced response calculations. The algorithm is applied to a dummy bevel gear and to a ring damper having a flat punch contact area. The forced response calculations are performed to highlight the nonlinear interaction between the gear and damper by varying the parameters that mainly affect the amount and distribution of the contact forces and therefore the response level.     

粘着摩擦系数的分形几何研究

计及作用于接触斑点上的切向力，通过比较作用于接触斑点上的法向弹性载荷与法向塑性载荷，确定了区分弹性接触与塑性接触区域的临界接触斑点面积．总的粘着摩擦系数被表示为弹性接触区与塑性接触区的粘着摩擦系数的组合．假设屈服压力及局部粘着摩擦系数不依赖于接触斑点且等于塑性接触区中的平均值，则总的粘着摩擦系数可用简单的表达式描述．分形几何参数及归一接触面积对于粘着摩擦系数的效应已通过算例表明，研究中，分别考虑了忽略与计及接触斑点的微粒间的相互作用，两种情况的结果完全不同．     

An example of stick–slip and stick–slip–separation waves

The dynamical problem of a brake-like mechanical system composed of an elastic cylindrical tube with Coulomb's friction in contact with a rigid and rotating cylinder is considered. This model problem enables us to give an example of non-trivial periodic solutions in the form of stick–slip or stick–slip–separation waves propagating on the contact surface. A semi-analytical analysis of stick–slip waves is obtained when the system of governing equations is reduced by condensation to a simpler system involving only the contact displacements. This reduced system, of only one space variable in addition to time, can be solved almost analytically and gives some interesting informations on the existence and the characteristics of stick–slip waves such as the wave numbers on the circumference, stick and slip proportions, wave celerities, tangential and normal forces. It is shown in particular that the stick–slip–separation solutions would occur for small normal pressures or high rotational speeds. Since the analytical discussion becomes cumbersome in this case, a second approach based on numerical analysis by the finite element method is performed. The existence and the characteristics of stick–slip and stick–slip–separation waves are discussed numerically.     

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.     

包含几何误差的机械结合面法向刚度研究

对包含几何误差的机械结合面进行离散化,离散后的微表面的基准平面高度满足结合面几何误差分布.每个微表面内,微凸体的高度只受粗糙度的影响.基于接触理论建立了微表面的法向刚度模型,通过对微表面模型集成获得了结合面的法向刚度模型.通过对所建模型的数值仿真,揭示了结合面法向刚度与间隙的非线性关系,几何误差的幅值和波长对法向刚度的影响以及非线性刚度对结合面振动特性的影响.计算结果表明:法向刚度随着间隙的减少而迅速增加,几何误差会导致结合面宏观上的局部接触和应力集中;在相同干涉量下,法向刚度随着几何误差幅值的增加而增加,但与结合面的波长没有关系;非线性刚度会导致结合面固有频率的下降和振动位移的不对称.     

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。     

考虑弹塑性变形阶段的干气密封接触模型

为探究干气密封摩擦界面在变形全阶段的接触特性,基于分形接触理论及微观接触力学理论,充分考虑微凸体变形的3个阶段,通过余弦函数构建干气密封全阶段接触模型,并分别与GW模型、KE模型和ZMC模型三种经典接触模型及相关文献的试验数据作对比,验证本文中接触模型的合理性与正确性.最后对干气密封摩擦界面接触特性的主要影响因素进行探究.模型研究结果表明：干气密封摩擦界面的接触特性与分形维数、特征尺度及两表面的真实接触面积有关.接触特性与分形维数和两表面真实接触面积呈正相关,与特征尺度呈负相关.分形维数越大,接触载荷与接触刚度的数量级就越大,且接触载荷变化范围相对较大.当特征尺度每次以1个数量级递增时,接触载荷与接触刚度的变化范围较小,都在1个数量级内.     

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.     

基于三维各向异性分形理论的固定机械结合面法向接触刚度建模研究

将结合面接触点拓展为椭圆形,基于KE有限元模型,类比球形微凸体在弹塑性接触变形阶段法向载荷、接触面积以及变形量之间的关系,采用代入法得到了表征椭圆抛物面形微凸体弹塑性接触变形机制的对应关系式.假设结合面接触点离心率分布与接触点面积分布相互独立,根据概率论以及接触点的面积大小分布函数,获得了关于结合面接触点面积与离心率的...     

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.