Existence and analytical predictions of periodic motions in a periodically forced,nonlinear friction oscillator

The grazing bifurcation, stick phenomena and periodic motions in a periodically forced, nonlinear friction oscillator are investigated. The nonlinear friction force is approximated by a piecewise linear, kinetic friction model with the static force. The total forces for the input and output flows to the separation boundary are introduced, and the force criteria for the onset and vanishing of stick motions are developed through such input and output flow forces. The periodic motions of such an oscillator are predicted analytically through the corresponding mapping structure. Illustrations of the periodic motions in such a piecewise friction model are given for a better understanding of the stick motion with the static friction. The force responses are presented, which agreed very well with the force criteria. If the fully nonlinear friction force is modeled by several portions of piecewise linear functions, the periodically forced, nonlinear friction oscillator can be predicted more accurately. However, for the fully nonlinear friction force model, only the numerical investigation can be carried out.     

载荷对壁虎刚毛束的摩擦各向异性特性影响的实验研究

用离体壁虎刚毛阵列在自制微黏附摩擦测试台上对预加载荷对刚毛摩擦与黏着的各向异性特性的影响进行了实验研究.实验结果表明,在逆壁虎刚毛自然弯曲方向卷出实现脱附时, 刚毛所受摩擦力与法向力成正比,摩擦系数为0.6;沿顺刚毛自然弯曲方向卷入实现黏附时, 随预载荷增加摩擦力增加,法向力由黏附力变为斥力.在同等预载荷下,卷入方向的摩擦力是卷出方向的2倍以上. 本文提出了摩擦各向异性特征参数,对壁虎刚毛的黏着与摩擦各向异性进行了定量表征, 这种特性是由刚毛的弯曲及多等级结构决定的. 关键词： 壁虎刚毛 黏着 摩擦 各向异性     

Influence of the normal force and contact geometry on the static force of friction of an oscillating sample

The paper is devoted to an experimental and theoretical investigation of the static friction force between a rapidly oscillating sample and a steel plate. The static frictional force is studied experimentally as function of the oscillating amplitude, the normal force and the contact geometry. A simplest model of tangent contact with a constant friction coefficient is proposed and shows a good agreement with experiment. The static friction force is proved to be a universal function of the ratio of the oscillation amplitude, the indentation depth and to the friction coefficient.     

Simulation of the Burridge-Knopoff model of earthquakes with variable range stress transfer

Simple models of earthquake faults are important for understanding the mechanisms for their observed behavior, such as Gutenberg-Richter scaling and the relation between large and small events, which is the basis for various forecasting methods. Although cellular automaton models have been studied extensively in the long-range stress transfer limit, this limit has not been studied for the Burridge-Knopoff model, which includes more realistic friction forces and inertia. We find that the latter model with long-range stress transfer exhibits qualitatively different behavior than both the long-range cellular automaton models and the usual Burridge-Knopoff model with nearest-neighbor springs, depending on the nature of the velocity-weakening friction force. These results have important implications for our understanding of earthquakes and other driven dissipative systems.     

Correlation mechanism between force chains and friction mechanism during powder compaction

The relation between friction mechanism and force chains characteristics has not yet been fully studied in the powder metallurgy research area.In this work,a uniaxial compression discrete element model is established based on the compaction process of ferrous powder.Furthermore,the correlation mechanism between force chains and the friction mechanism during powder compaction is investigated.The simulation results reveal a strong correlation between the variation of the friction coefficient and the evolution of force chains.During the powder compaction,the friction coefficient would eventually tend to be stable,a feature which is also closely related to the slip ratio between particles.The side wall friction and the friction between particles would have an important effect on the direction of force chain growth in about one-third of the area near the side wall.The research results provide theoretical guidance for improving the densification process of the powder according to the force chain and friction.     

摩擦力的实验研究与设计

设计了3个研究摩擦力的实验,直观地演示了摩擦力的特点和性质.     

Influence of ultrasonic surface acoustic waves. on local friction studied by lateral force microscopy

We studied dynamic friction phenomena introduced by ultrasonic surface acoustic waves using a scanning force microscope in the lateral force mode and a scanning acoustic force microscope. An effect of friction reduction was found when applying surface acoustic waves to the micro-mechanical tip-sample contact. Employing standing acoustic wave fields, the wave amplitude dependent friction variation can be visualized within a microscopic area. At higher wave amplitudes, a regime was found where friction vanishes completely. This behavior is explained by the mechanical diode effect, where the tip's rest position is shifted away from the surface in response to ultrasonic waves.     

Static friction of sinusoidal surfaces: a discrete dislocation plasticity analysis

Discrete dislocation plasticity simulations are carried out to investigate the static frictional response of sinusoidal asperities with (sub)-microscale wavelength. The surfaces are first flattened and then sheared by a perfectly adhesive platen. Both bodies are explicitly modelled, and the external loading is applied on the top surface of the platen. Plastic deformation by dislocation glide is the only dissipation mechanism active. The tangential force obtained at the contact when displacing the platen horizontally first increases with applied displacement, then reaches a constant value. This constant is here taken to be the friction force. In agreement with several experiments and continuum simulation studies, the friction coefficient is found to decrease with the applied normal load. However, at odds with continuum simulations, the friction force is also found to decrease with the normal load. The decrease is caused by an increased availability of dislocations to initiate and sustain plastic flow during shearing. Again in contrast to continuum studies, the friction coefficient is found to vary stochastically across the contact surface, and to reach locally values up to several times the average friction coefficient. Moreover, the friction force and the friction coefficient are found to be size-dependent.     

Instability criteria for a motion of a vortex subject to a non-linear friction force

Here we study the instability of the vortex motion caused by non-monotonous dependence of the friction force on the vortex velocity in the presence of a gyroforce. The analysis is done within the frameworks of “minimal” model for the elastic string subject to friction force and gyroforce. We demonstrate that even a weak gyroforce renders the condition for onset of instability more strict than for a vortex not subject to gyroforce: either the friction force must exceed a threshold, or its non-monotonic velocity dependence must be a rather steep function.     

Effect of the electric current on the Casimir force between graphene sheets

The dependence of the thermal component of the Casimir force and Casimir friction between graphene sheets on the drift velocity of charge carriers in one of the sheets has been analyzed. It has been shown that the drift motion results in the measurable change in the thermal Casimir force owing to the Doppler effect. The thermal Casimir force, as well as Casimir friction, increases strongly in the case of resonant photon tunneling, when the energy of an emitted photon coincides with the excitation energy of an electron-hole pair. In the case of resonant photon tunneling, the dominant contribution to the Casimir friction even at temperatures above room temperature comes from quantum friction caused by quantum fluctuations. Quantum friction can be detected in an experiment on the friction drag between graphene sheets in a high electric field.     

纳米级随机粗糙表面微观滑动摩擦力的计算研究

表面形貌很大程度上决定了摩擦副的摩擦性能, 而所有的表面都不可能是绝对光滑的.由于摩擦表面形貌的随机性, 决定了实际的摩擦过程具有随机性的特点, 因此为了获得与随机形貌对应的摩擦特性, 建立合理的随机摩擦模型是必要的. 本文基于Lennard-Jones势能建立了纳米级随机粗糙表面和原子级光滑的刚性平面间的随机摩擦模型; 模型中, 界面势能由法向载荷和界面间平衡距离决定.通过数值计算的方法, 推导了微观滑动摩擦力的计算公式和摩擦力与法向载荷之间的关系. 研究结果表明摩擦力随着法向载荷的增加而增加, 但不是线性增长. 结果也说明界面间的表面势能可能是微观摩擦力的本质起源. 关键词： 随机粗糙表面 Lennard-Jones势能 微滑动摩擦力 微摩擦     

Casimir friction force between a SiO<Subscript>2</Subscript> probe and a graphene-coated SiO<Subscript>2</Subscript> substrate

The possibility of mechanical detection of Casimir friction with the use of a noncontact atomic force microscope is discussed. A SiO₂ probe tip located above a graphene-coated SiO₂ substrate is subjected to the frictional force caused by a fluctuating electromagnetic field produced by a current in graphene. This frictional force will create the bend of a cantilever, which can be measured by a modern noncontact atomic force microscope. Both the quantum and thermal contributions to the Casimir frictional force can be measured using this experimental setup. This result can also be used to mechanically detect Casimir friction in micro- and nanoelectromechanical systems.     

Ultrasonic excitation affects friction interactions between food materials and cutting tools

In the food industry, ultrasonic cutting is used to improve separation by a reduction of the cutting force. This reduction can be attributed to the modification of tool–workpiece interactions at the cutting edge and along the tool flanks because of the superposition of the cutting movement with ultrasonic vibration of the cutting tool. In this study, model experiments were used to analyze friction between the flanks of a cutting tool and the material to be cut. Friction force at a commercial cutting sonotrode was quantified using combined cutting–friction experiments, and sliding friction tests were carried out by adapting a standard draw-off assembly and using an ultrasonic welding sonotrode as sliding surface. The impact of material parameters, ultrasonic amplitude, and the texture of the contacting food surface on friction force was investigated. The results show that ultrasonic vibration significantly reduces the sliding friction force. While the amplitude showed no influence within the tested range, the texture of the contact surface of the food affects the intensity of ultrasonic transportation effects. These effects are a result of mechanical interactions and of changes in material properties of the contact layer, which are induced by the deformation of contact points, friction heating and absorption heating because of the dissipation of mechanical vibration energy.     

Tribological behavior of micro/nano-patterned surfaces in contact with AFM colloidal probe

In effort to investigate the influence of the micro/nano-patterning or surface texturing on the nanotribological properties of patterned surfaces, the patterned polydimethylsiloxane (PDMS) surfaces with pillars were fabricated by replica molding technique. The surface morphologies of patterned PDMS surfaces with varying pillar sizes and spacing between pillars were characterized by atomic force microscope (AFM) and scanning electron microscope (SEM). The AFM/FFM was used to acquire the friction force images of micro/nano-patterned surfaces using a colloidal probe. A difference in friction force produced a contrast on the friction force images when the colloidal probe slid over different regions of the patterned polymer surfaces. The average friction force of patterned surface was related to the spacing between the pillars and their size. It decreased with the decreasing of spacing between the pillars and the increasing of pillar size. A reduction in friction force was attributed to the reduced area of contact between patterned surface and colloidal probe. Additionally, the average friction force increased with increasing applied load and sliding velocity.     

摩擦力演示装置

为了辅助摩擦力的教学,自制了摩擦力演示装置,通过模拟电路与数字电路的转换可以直接显示出滑块与传送带间的摩擦力.该装置不仅可以探究静摩擦力和滑动摩擦力,而且还可直观地显示出物体间摩擦力的渐变过程.     

Heavy-ion friction force from a gas-kinetic model

A friction force is derived from the two-body collisions of projectile nucleons with target nucleons in the overlap region of their densities. We treat the diffuse surfaces of the heavy ions as Fermi gases. A certain average of the resulting friction force turns put to be identical in structure with the phenomenological Tsang-Swiatecki linear force. In our approach, the strength coefficient of the latter force can be calculated from the free two-nucleon scattering cross section without adjustable parameters. We obtain a strength which agrees well with the value found by Siwek-Wilczyńska and Wilczyński from an empirical fit.     

Delayed feedback for controlling the nature of bifurcations in friction-induced vibrations

We analyse the control of friction-induced vibrations using time-delayed displacement feedback. We have used the exponential model for the drooping characteristics of the friction force for which the bifurcation is subcritical in nature. With an appropriate choice of the control parameters we have managed to change the nature of the bifurcation to supercritical along with increasing the stability boundaries. A nonlinear controller is required when the control force is applied in a direction parallel to the friction force. In contrast, a linear time-delayed displacement feedback applied in a direction normal to the friction force achieves our dual objective of controlling the nature of the bifurcation as well as quenching the vibrations. We also consider a dynamic friction model (the LuGre model) and observe that the qualitative change in the nature of the bifurcation is independent of the complexity considered in modeling the friction force.     

摩擦——一个古老而时髦的话题

介绍了在原子力显微镜基础上发展起来的摩擦力显微镜的原理,应用摩擦力显微可以测量原子级的摩擦力,从而为从微观上理解摩擦这一最为普遍的宏观物理象奠定了基础。同时,不评述了近十年严这一分为二或理论和实验两方面的研究进展。     

What does friction really depend on? Robust governing parameters in contact mechanics and friction

It is known that the coefficient of friction generally depends on a large number of system and loading parameters. Already Coulomb presented experimental evidence that the static coefficient of friction may depend on time, on normal force, on the contact size, on the nature of contacting materials, and on the presence of intermediate lubricant layers. For the sliding coefficient of friction, he observed the dependence on the sliding velocity as well as the force and size dependencies. Later research has shown that the friction coefficient is very sensitive to the presence of oscillations (including self-excited vibrations). In spite of the practical importance of the problem, no generalized laws of friction or empirical procedures for measuring and representing the law of friction have been developed so far, which included at least the following four parameters: contacting body velocity, normal force, shape (and thus implicitly size), and time. In the present paper, we discuss the question of how the dimension of space of governing parameters can be reduced and if a small set of “robust governing parameters” of friction can be identified. We argue that one of such robust governing parameters is the indentation depth (or relative approach) of contacting bodies and discuss further candidates for the role of robust governing parameters.     

直观显示摩擦力实验的改进

对文献^[1]中用弹簧秤直观显示摩擦力的实验进行了改进，成功地解决了原实验在滑动摩擦力的测量过程中不易读数的问题。