Frictional duality observed during nanoparticle sliding

One of the most fundamental questions in tribology concerns the area dependence of friction at the nanoscale. Here, experiments are presented where the frictional resistance of nanoparticles is measured by pushing them with the tip of an atomic force microscope. We find two coexisting frictional states: While some particles show finite friction increasing linearly with the interface areas of up to 310 000 nm(2), other particles assume a state of frictionless sliding. The results further suggest a link between the degree of surface contamination and the occurrence of this duality.     

Numerical study of the stress response of two-dimensional dense granular packings

We investigate the Green function of two-dimensional dense random packings of grains in order to discriminate between the different theories of stress transmission in granular materials. Our computer simulations allow for a detailed quantitative investigation of the dynamics which is difficult to obtain experimentally. We show that both hyperbolic and parabolic models of stress transmission fail to predict the correct stress distribution in the studied region of the parameters space. We demonstrate that the compressional and shear components of the stress compare very well with the predictions of isotropic elasticity for a wide range of pressures and porosities and for both frictional and frictionless packings. However, the states used in this study do not include the critical isostatic point for frictional particles, so that our results do not preclude the fact that corrections to elasticity may appear at the critical point of jamming, or for other sample preparation protocols, as discussed in the main text. We show that the agreement holds in the bulk of the packings as well as at the boundaries and we validate the linear dependence of the stress profile width with depth.     

Random packings of frictionless particles

We conduct numerical simulations of random packings of frictionless particles at T = 0. The packing fraction where the pressure becomes nonzero is the same as the jamming threshold, where the static shear modulus becomes nonzero. The distribution of threshold packing fractions narrows, and its peak approaches random close packing as the system size increases. For packing fractions within the peak, there is no self-averaging, leading to exponential decay of the interparticle force distribution.     

Elasticity from the force network ensemble in granular media

Transmission of forces in static granular materials is studied within the framework of the force network ensemble, by numerically evaluating the mechanical response of hexagonal packings of frictionless grains and rectangular packings of frictional grains. In both cases, close to the point of application of the overload, the response is nonlinear and displays two peaks, while at larger length scales, it is linear and elasticlike. The crossover between these two behaviors occurs at a depth that increases with the magnitude of the overload and decreases with increasing friction.     

A method to determine dynamic loads on spur gear teeth and on bearings

A method is described which can be used to calculate dynamic gear tooth force and bearing forces. The model includes elastic bearings. The gear mesh stiffness and the path of contact are determined using the deformations of the gears and the bearings. This gives contact outside the plane-of-action and a time-varying working pressure angle. In a numerical example it is found that the only important vibration mode for the gear contact is the one where the gear tooth deformation is dominant. The bearing force variation, however, will be much more affected by the other vibration modes. The influence of the friction force is also studied. The friction has no dynamic influence on the gear contact force or on the bearing force in the gear mesh line-of-action direction. On the other hand, the changing of sliding directions in the pitch point is a source for critical oscillations of the bearings in the gear tooth frictional direction. These bearing force oscillations in the frictional direction appear unaffected by the dynamic response along the gear mesh line-of-action direction.     

Frictional effect of ultrasonic-vibration on upsetting

The ultrasonic-vibration ring compression test and finite element analysis were performed on aluminum alloy specimens to explore the frictional effect of superimposing ultrasonic-vibration during upsetting. The extrapolated compression test was first adopted to obtain the frictionless material properties for finite element analysis. Experimental results of extrapolated compression test also indicate that ultrasonic-vibration can reduce the compressive force when friction is eliminated and can increase the temperatures of a material at the same time.The following results of the hot extrapolated compression test and the hot ring compression test reveal that increasing temperature by ultrasonic-vibration may reduce the flow stress and increase the interfacial friction. Finally, finite element analysis was conducted to derive the friction calibration curves and to evaluate the friction factor.     

Lateral force microscopy in low normal force limit

We have studied frictional force between SiN tip and Si surface by using lateral force microscopy. The cantilever we have used has very low stiffness of 0.006 N/m, and the normal force acting on the surface was much lower than the attractive force such as van der Waals force. In this low normal force limit, it was found that the frictional force did not depend on the normal force. We suggest a calibration method to estimate the attractive force from the lateral force data in this limit. The estimated attractive force between Si sample and SiN tip with radius of 10 nm was 0.4 nN in flat region and 0.65 nN at the corner of a rectangular hole.     

Nonlinear mobility of a driven system: Temperature and disorder effects

We consider the dissipative nonlinear dynamics of a model of interacting atoms driven over a substrate potential. The substrate parameters can be suitably tuned in order to introduce disorder effects starting from two geometrically opposed ideal cases: commensurate and incommensurate interfaces. The role of temperature is also investigated through the inclusion of a stochastic force via a Langevin molecular dynamics approach. Here, we focus on the most interesting tribological case of underdamped sliding dynamics. For different values of the chain stiffness, we evaluate the static friction threshold and consider the depinning transition mechanisms as a function of the applied driving force. As experimentally observed in QCM frictional measurements of adsorbed layers, we find that disorder operates differently depending on the starting geometrical configuration. For commensurate interfaces, randomness lowers considerably the chain depinning threshold. On the contrary, for incommensurate mating contacts, disorder favors static pinning destroying the possible frictionless (superlubric) sliding states. Interestingly, thermal and disorder effects strongly influence also the occurrence of parametric resonances inside the chain, capable of converting the kinetic energy of the center-of-mass motion into internal vibrational excitations. We comment on the nature of the different dynamical states and hysteresis (due to system bi-stability) observed at different increasing and decreasing strengths of the external force.     

Complex force network in marginally and deeply jammed solids

This paper studies the force network properties of marginally and deeply jammed packings of frictionless soft particlesfrom the perspective of complex network theory. We generate zero-temperature granular packings at different pressures by minimizing the inter-particle potential energy. The force networks are constructed as nodes representing particles and links representing normal forces between the particles. Deeply jammed solids show remarkably different behavior from marginally jammed solids in their degree distribution, strength distribution, degree correlation, and clustering coefficient. Bimodal and multi-modal distributions emerge when the system enters the deep jamming region. The results also show that small and large particles can show different correlation behavior in this simple system.     

基于耦合振子模型的摩擦力计算研究

以界面摩擦为研究对象,探讨了基于耦合振子模型(coupled-oscillator model)的滑动摩擦微观机理,分析了滑动过程中的能量耗散问题. 采用Maugis-Dugdal接触模型替代界面摩擦中的Lennard-Jones势能,并将该模型融入耦合振子模型之中,通过计算振子在一个周期内的能量增加值,推导出了界面摩擦力的理论计算公式. 理论分析表明,对于探针-试样接触系统,滑动摩擦力近似随着法向载荷的2/3次方增加,这与纳米摩擦学经典理论是相符的.理论计算结果与超高真空原子力显微镜镀铜探针在Cu(111)晶面扫描实验结果符合良好,表明本文提出的理论和方法可行. 关键词： 耦合振子模型 界面摩擦 摩擦力 法向载荷     

Force distribution in an inhomogeneous sandpile

The force perturbation field in a two-dimensional pile of frictionless gravity-loaded discs or spheres arising from lattice distortions is derived to first order. The starting point is the model proposed by Liffman et al. (Powder Technology (1992) pp. 255-267) and Hong (Phys. Rev. E 47, 760-762 (1993)) in which discs of uniform size are arranged on a regular lattice: this predicts a uniform normal stress distribution at the base of the pile. The analysis is applied to two problems: (i) deformable (rather than rigid) grains that undergo Hertzian deformation at the points of contact; (ii) a pile containing a gradient in particle size from the centre to the free surfaces. The former results in the classical pressure dip at the centre; the latter also produces a dip if the larger particles are at the centre. Received 29 January 1998 and Received in final form 7 September 1998     

Measurement of the frictional forces in fretting fatigue

This paper presents the results of a study of the frictional forces associated with the tangential harmonic displacements of a slider in the frequency range from 20 to 1000 Hz.On the basis of our experiments, we establish that the frictional interaction creates a normal periodic force which, in turn, creates normal vibrations leading to a change in the actual load and hence in the peak value of the force of friction.A change in the force of friction with the frequency of the tangential displacements has also been noted elsewhere [1]; however, the causes of this behavior have not previously been ascertained.We show that the force of friction depends significantly not only on the amplitude of the normal vibrations but also on the phase-frequency-relations between the vibrations in the normal and tangential directions.     

发动机喷流对火箭气动特性影响

开展了考虑底部发动机喷流影响的火箭气动特性CFD仿真设计,比较了有/无喷流时火箭附近流场结构、表面压力分布、整体气动力/力矩特性在亚/超声速段的差异,结果显示,发动机喷流对火箭亚声速段的轴向力、法向力和俯仰力矩特性均有较为显著的影响,且有减小尾部空气舵气动控制力矩的影响,而超声速段的影响仅限于轴向力。该仿真结果与飞行试验气动辨识结果较为一致。基于仿真分析结果,可建立一种折中考虑喷流影响的气动特性设计方法,供火箭精细化气动特性设计参考使用。      

Dynamic tangential contact of rough surfaces in stick-slip microdrives: Modeling and validation using the method of dimensionality Reduction

The dynamic tangential contact of rough surfaces of frictional elements of a stick-slip microdrive is theoretically investigated. By applying the method of dimensionality reduction, the contact areas of the frictional partners are modeled such that the physical properties of the contact can be fully considered and the influence of the roughness is taken into account. The dynamics of the microscopic rough contact is combined with a macroscopic movement of the drive’s runner in a hybrid dynamic simulation. The numerical results show a good agreement with experimental data. Furthermore, an analytical relation between maximal tangential contact displacement and normal force applied to the contact is analyzed, allowing the contact behavior to be theoretically predicted.     

塑压接触平面上之长程滑动与短程滑动(等倾陡线规律)

塑压接触面之质点滑动线称“摩擦线”。滑动现象有两种基本类型,一为“长程滑动”,摩擦线为质点之长程连续轨迹,如抽拔,挤压,冲压等塑性过程中之滑动;一为“短程滑动”,质点仅在摩擦线上滑动一微小距离,如锻,轧,压力实验等过程中之滑动(小压缩时)。过去对这两种滑动现象之规律未曾分别处理。本文将摩擦力接纯力学关系视为一切应力,即压应力p与摩擦应力τ,以边界平衡关系,相系于一应力函数F: τ=Fp, F=((l₁²p₁²+l₂²p₂²+l₃²p₃²)/(l₁²p₁+l₂²p₂+l₃²p₃)²)^1/2-1, p₁,p₂,p₃为内部主应力; l₁,l₂, l₃为p对p₁,p₂,p₃之夹角余弦。除视τ为p之函数τ=τ(p)外,对摩摩力之物理性质不作规定。在此基础上,以住意质点滑动之最小摩阻功为基本条件分析滑向规律,一如任意质点滑动之最小摩阻力条件之于“陡线规律”。如此,则问题类于古典变分问题,变分方程引出两结论:在短程滑动中,滑向规律为已知之陡线规律;在长程滑动中为以下将提出之“等倾陡线规律”。并得到几个有关重要推论。     

Influence of the alignment of load and oscillation on the frictional shakedown of an elastic rolling contact with Coulomb friction

We examine frictional shakedown of a three dimensional elastic rolling contact. Slight oscillatory rolling of one contacting body varies the normal pressure distribution. In turn this causes incremental sliding processes and a macroscopic rigid body motion. We consider two settings: tangential force and rolling direction aligned parallel and perpendicular to each other. In both cases, the slip ceases after the first few periods and a safe shakedown occurs if the oscillation is sufficiently small. Otherwise ratcheting occurs and the accumulated slip leads to a continuing rigid body motion.Numerical simulations with Kalker’s and Vollebregt’s software CONTACT show that the rolling direction leads to differences in the contact region and the traction distribution. Using the method of dimensionality reduction we derive the analytical shakedown limits for the tangential load and the oscillation amplitude. The results show strong agreement with experimental data and allow the accurate prediction of the shakedown displacement and the maximum tangential load capacity in the shakedown state. It shows that a perpendicular alignment of force and rolling direction increases the final displacement in case of shakedown as well as the incremental shift in case of ratcheting.     

Numerical Study of Fin-and-Tube Heat Exchanger in Low-Pressure Environment: Air-Side Heat Transfer and Frictional Performance,Entropy Generation Analysis,and Model Development

Heat transfer and frictional performance at the air-side is predominant for the application and optimization of finned tube heat exchangers. For aerospace engineering, the heat exchanger operates under negative pressure, whereas the general prediction models of convective heat transfer coefficient and pressure penalty for this scenario are rarely reported. In the current study, a numerical model is developed to determine the air-side heat transfer and frictional performance. The influence of air pressure (absolute pressure) is discussed in detail, and the entropy generation considering the effect of heat transfer and pressure drop are analyzed. Furthermore, prediction models of air-side thermal and frictional factors are also developed. The results indicate that both the convective heat transfer coefficient and pressure penalty decrease significantly with decreasing air pressure, and the air-side heat transfer coefficient is decreased by 64.6~73.3% at an air pressure of 25 kPa compared with normal environment pressure. The entropy generation by temperature difference accounts for the highest proportion of the total entropy generation. The prediction correlations of Colburn j-factor and friction factor f show satisfactory accuracy with the absolute mean deviations of 7.48% and 9.42%, respectively. This study can provide a reference for the practical application of fined tube heat exchangers under a negative pressure environment.     

Instabilities in the sliding of continua with surface inertias: An initiation mechanism for brake noise

This paper presents a model for friction-induced vibration in brake systems, which takes a homogeneous tribological layer on the brake pad into account. The derived model consists of two flat elastic bodies sliding against each other with a constant coefficient of friction. In brake tribology, like in most tribological processes, a surface structure is observed, which can be modeled as an additional film of homogenized mass distribution bonded on the moving continua. The developed mechanical model and its analytical solution show an excitation mechanism that bases on the interaction of normal and frictional shear force and on the elastic coupling of spatial directions. The derived solution allows to study stability and eigenforms of the sliding process: on the frictional plane traveling surface waves are generated, with stability properties depending on parameters of the tribological layer. A parameter study analyzes the frictional couple of brake disk and pad and the related surface state. It is found that increasing inertias of surface structures on the pad strengthen instabilities of the sliding system. A comparison with experiments suggests a similar dependency between surface state and stability as observed by the model under discussion.     

Considerations on the determining factors of the angular distribution of emitted particles in laser ablation

Simulations of particles which are emitted in laser ablation have been performed by the method of Direct Simulation Monte Carlo to investigate the deposition profiles of the emitted particles. The influences of the temperature, pressure and stream velocity of the initial evaporated layer formed during laser ablation process on the profile of the deposited film have been examined. It is found that the temperature gives a minor influence on the deposition profile, whereas the stream velocity and the pressure of the initial evaporated layer have a greater impact on the deposition profile. The energy in the direction of surface normal (E_⊥) and that in the parallel direction of the surface (E_||) are shown to increase and decrease, respectively after the laser irradiation due to collisions between the emitted particles, and this trend is magnified as the pressure increases. As a consequence, the stream velocity in the direction of surface normal increases with the increase in the pressure. A mechanism of the phenomenon that a metal with a lower sublimation energy shows a broader angular distribution of emitted particles is presented. It is suggested that low density of evaporated layer of a metal with a low sublimation energy at its melting point decreases the number of collisions in the layer, leading to the low stream velocity in the direction of surface normal, which results in the broader deposition profile of the emitted particles.     

Fast frictionless expansion of an optical lattice

We investigate fast frictionless expansion of an optical lattice with dynamically variable spacing (accordion lattice). We design an expansion trajectory that yields a final state identical to the initial state up to an irrelevant phase factor. We discuss the effect of additional force and nonlinear interaction on the fast frictionless expansion.