Mathematical model of the stick-slip phenomenon

A mathematical model of the stick-slip phenomenon is presented which is related to the characteristic changes of the friction forces as a function of the slip speed. The model leads to simple differential equations without the necessity of using distribution equations. It can be utilized in a simple way to describe actual friction nodes.     

Multiple Slips in Atomic-Scale Friction: An Indicator for the Lateral Contact Damping

The occurrence of multiple jumps in 2D atomic-scale friction measurements is used to quantify the viscous damping accompanying the stick–slip motion of a sharp tip in contact with a NaCl(001) surface. Multiple slips are observed without apparent wear for normal forces between 13 and 91 nN. For scans parallel to [100] directions, the tip jumps between minima of the substrate corrugation potential in a zigzag fashion. An algorithm is applied to determine histograms of lateral force jumps which characterize multiple slips. The same algorithm is used to classify multiple slips occurring in calculated lateral force maps. Comparisons between simulations and experiments indicate that the nanometer-sized contact is underdamped at intermediate loads (13–26 nN) and becomes slightly overdamped at higher loads. The proposed procedure is a novel way to estimate the lateral contact damping which plays an important role in the interpretation of measurements of the velocity and temperature dependence of friction, of slip duration, and of the reduction of friction by applied perpendicular or parallel oscillations.     

纳观纹理表面相关参数对滑动摩擦过程的影响

采用分子动力学方法研究了半球形刚性压头在单晶铜纹理表面上的纳观黏着滑动摩擦过程。对不同纹理密度下纹理形状和纹理深度对黏滑摩擦性能的影响进行了全面研究,通过对比分析不同纹理参数下的滑动摩擦力和基体变形,揭示了上述参数对纹理表面黏滑摩擦的影响规律。模拟结果表明:在相同的纹理密度下,柱状纹理表面的滑动摩擦力小于矩形纹理表面。相比矩形纹理,柱状纹理表面的结构稳定性较差,但纹理表面的结构稳定性随着纹理密度的增加而加强。在相同的纹理密度下,矩形纹理表面的滑动摩擦力随着纹理深度的增加而减小。     

Stick-slip algorithm in a tangential contact force model for multi-body system dynamics

Contact force of Multi-body dynamics (MBD) system can be classified two parts. First is a normal force and the other is a tangential force called friction force. And the friction force can be represented by two states such as stick and slip. The stick-slip phenomenon is simply described as a simple contact model which is a rigid body contacted on a sloped surface. If the calculated friction coefficient between the body and sloped surface is less than the static friction coefficient, the body should be stuck. If the calculated friction coefficient is greater than the static friction coefficient, the body will be sliding along the surface. The phenomenon is called as stick and slip state of friction, respectively. Usually many researchers and commercial MBD software used a coulomb friction force model which is defined with an only function of relative velocity. This kind of friction force model will be called a conventional friction force model in this paper. A big problem of the conventional model can not describe a stick state of friction phenomenon. In the case of conventional friction force model, the body will be sliding even though friction state is stick. Because, the relative velocity must have a non-zero value in order to generate the friction force. To solve this kind of problem, we propose a stick-slip friction force model including a spring like force. In the case of stick-slip friction force model, the body can be stuck on the sloped surface because the friction force will be a non-zero value, even though the relative velocity approaches zero. We defined a relative displacement variable called stiction deformation. In this paper, the stick-slip friction model is proposed and applied in the contact algorithm of MBD system. And then two friction models are compared with numerical examples. With the proposed stick-slip friction model, more realistic results are achieved.     

A frictional force microscope controlled with an electromagnet

Frictional forces are usually measured by detecting spring displacement. To obtain high-resolution measurements of frictional force distributions, a sharp tip and a light load are required. In measuring frictional force on relatively rough surfaces, using very sharp tips (submicron radii), significant stick-slip motions are observed, and continuously varying dynamic frictional forces can not be measured. To measure continuous friction distributions between sharp tips and surfaces with light loads, a new frictional force microscope (FFM) is developed. This FFM has an electromagnet to maintain the tip suspension spring in a non-deflected position. The frictional force is then measured from the magnet current. Using this FFM, continuous friction distributions between 0·1 μm radius diamond tips and magnetic disk surfaces with light loads (less than 10 μN) are obtained.     

Friction-induced vibration of oscillating multi-degree of freedom polymeric sliding systems

The purpose of this study is to investigate friction-induced vibration of oscillating systems. Special attention is focused on modeling polymer-on-metal systems. Past experimental and analytical friction results from non-oscillating or unidirectional translational sliding modes are extended into the oscillating sliding mode. Specifically, this refers to the incorporation of a representative functional shape of the friction–velocity relationships estimated from experimental results. Dependent on the relative sliding velocity between the frictionally coupled subsystems, the modeled system exhibits behavior such as a single stick–slip at the beginning of oscillatory motion, a single stick–slip at each motion reversal, or multiple stick-slip events during each half cycle of motion. Additionally, the boundary of incipient friction-induced vibration was identified via a rigorous definition of friction-induced vibration.     

Nanomechanical characteristics at an ultra-small particle-surface contact interface

Atomic force microscopy (AFM) measurements have shown that nanoscale interfaces in sliding contact frequently exhibit atomic lattice stick-slip friction. Using various material surfaces and AFM tips, including colloidal probes, and systematically varying applied load and lever stiffness, it is demonstrated that transitions can be repeatedly observed from smooth sliding to single unit-cell slips and then multiple slips. The behavior is dependent on the interplay between the stiffness of the contact zone, the measurement system (i.e., the AFM cantilever), and the interfacial potential. Atomic lattice stick-slip occurs with colloidal particle tip orders of magnitudes larger than those previously used. Stable atomically corrugated sliding in ambient conditions that cannot be seen elsewhere is reported. The generality of these conditions suggests that atomic-scale stick-slip behavior may be far more prevalent than previously appreciated. In addition, the friction-stiffness maps of various material surfaces in contact with a colloidal particle were reported, and the complex effects of system stiffness and pressure were discussed for chemical-mechanical polishing applications.     

Simultaneous measurement of normal and friction forces using a cantilever-based optical interfacial force microscope

We measured normal and friction forces simultaneously using a recently developed cantilever-based optical interfacial force microscope technique for studies of interfacial structures and mechanical properties of nanoscale materials. We derived how the forces can be incorporated into the detection signal using the classical Euler equation for beams. A lateral modulation with the amplitude of nanometers was applied to create the friction forces between tip and sample. We demonstrated its capability by measuring normal and friction forces of interfacial water at the molecular scale over all distance ranges.     

Effects of higher oscillation modes on TM-AFM measurements

The finite element method and molecular dynamics simulations are used for modeling the AFM microcantilever dynamics and the tip-sample interaction forces, respectively. Molecular dynamics simulations are conducted to calculate the tip-sample force data as a function of tip height at different lateral positions of the tip with respect to the sample. The results demonstrate that in the presence of nonlinear interaction forces, higher eigenmodes of the microcantilever are excited and play a significant role in the tip and sample elastic deformations. Using comparisons between the results of FEM and lumped models, how some aspects of the system behavior can be hidden when the point-mass model is used is illustrated.     

Effects of weight on bit on torsional stick-slip vibration of oilwell drill string

The stick-slip phenomenon is a type of dysfunction detrimental to the drilling operation. Field application shows that stick-slip phenomenon is inclined to appear when using a large Weight on bit (WOB). In this paper, effects of the WOB on the stick-slip vibration are investigated. Based on a lumped torsional pendulum model of the drilling system, equation of motion of the drill bit is obtained. By using parameters commonly used in field applications, the bit dynamics are analyzed and the stick-slip vibrations are discussed. During the stick-slip motions, the negative damping effect occurs in the transition from the stick phase to the slip phase. With the increasing WOB, the bit behavior may change from the stable motion to the stick-slip vibration once the WOB reaches the critical value. In case of stick-slip vibration, the phase trajectory ultimately converges to a limit cycle which represents periodical bit motion. With increases in the WOB, the limit cycle enlarges. For cases without stick-slip vibrations, the drill bit vibrates damply and finally converges to a state of uniform motion. The results presented in this paper can be applied to interpret some of the field phenomena related to WOB.     

Microscopic Friction Studies on Metal Surfaces

Atomically flat and clean metal surfaces exhibit a regime of ultra-low friction at low normal loads. Atomic force microscopy, performed in ultra-high vacuum on Cu(100) and Au(111) surfaces, reveals a clear stick-slip modulation in the lateral force but almost zero dissipation. Significant friction is observed only for higher loads (∼4–6 nN above the pull-off force) together with the onset of wear. We discuss the minor role of thermal activation in the low friction regime and suggest that a compliant metallic neck between tip and surface is formed which brings upon the low, load-independent shear stress.     

Observation of controlled,electrochemically induced friction force modulations in the nano-Newton range

The local chemical properties of the contacting asperities in a real tribosystem are of crucial importance for the resulting macroscopic tribo-behavior. Thus, the lateral forces acting on the tip of a standalone scanning force and friction microscope have been investigated as a function of controlled surface chemistry, realized by potentiostatic control of the sample. The results obtained show a clear dependence of nanoscale friction behavior upon changes in the electrochemical state of the system.     

On the motion of the structure varying multibody systems with two-dimensional dry friction

In the present paper the dynamics of the structure varying multibody systems caused by stick-slip motion with two-dimensional dry friction are analyzed. The methods to determine friction force both in stick and slip states are described. The direct method of considering the wagon bogie system as a structure varying system was used to consider two dimensional friction at the wheelset-side frame connection. The concept of friction direction angle used to determine the friction force components of two-dimensional dry friction both in the stick and slip motion states was used. A speed depended friction coefficient was used and described approximately by hyperbolic secant function. All switch conditions were derived and friction forces both for stick and slip states. Some simulation results are provided.     

Velocity dependent friction laws in contact mode atomic force microscopy

Friction forces in the tip–sample contact govern the dynamics of contact mode atomic force microscopy. In ambient conditions typical contact radii between tip and sample are in the order of a few nanometers. In order to account for the large interaction area the dynamics of contact mode atomic force microscope (AFM) is investigated under the assumption of a multi-asperity contact interface between tip and sample. Thus, the kinetic friction force between tip and sample is the product of the real contact area between both solids and the interfacial shear strength. The velocity strengthening of the lateral force is modeled assuming a logarithmic relationship between shear-strength and velocity. Numerical simulations of the system dynamics with this empirical model show the existence of two different regimes in contact mode AFM: steady sliding and stick–slip where the tip undergoes periodically stiction and kinetic friction. The state of the system depends on the scan velocity as well as on the velocity dependence of the interfacial friction force between tip and sample. Already small viscous damping contributions in the tip–sample contact are sufficient to suppress stick–slip oscillations.     

Nanoscale Mapping of Frictional Anisotropy

Friction hodographs contain all the information related to the intensity and symmetry of the friction phenomenon. We show how an atomic force microscope can be used to collect friction hodographs at the nanoscale and how to carry out data interpretation to unravel the friction–surface structure relationship. As a model system, we analyzed the basal plane of orthorhombic β-alanine single crystals, and interpreted the data in terms of a constitutive model of orthotropic friction with slip direction-dependent friction coefficients.     

Effect of MoS2 and WS2 Nanotubes on Nanofriction and Wear Reduction in Dry and Liquid Environments

Nano-objects in dry and liquid conditions have shown reductions in friction and wear on the macroscale. Studies in low viscosity liquids with nanoparticles and nanotubes made of lubricating materials such as molybdenum disulfide (MoS₂) and tungsten disulfide (WS₂) are limited. In this research, MoS₂ and WS₂ nanotubes with spherical gold (Au) nano-objects as a control are studied on the nanoscale under dry and low viscosity liquid environments for their effect on friction and wear reduction. Atomic forces microscopy (AFM) experiments on the nanoscale are performed in single-nano-object contact with an AFM tip, where nano-objects are laterally manipulated and multiple nano-object contact with a tip attached to a glass sphere sliding over several nano-objects. Wear tests were performed on the nanoscale by means of AFM as well as on the macroscale using a ball-on-flat tribometer to relate friction and wear reduction on both scales. Results indicate that nano-objects such as MoS₂ and WS₂ nanotubes contribute to friction and wear reduction due to the reduced contact area and the possible rolling and sliding on the nanoscale. On the macroscale, reductions in friction and wear occur due to possible exfoliation of outer layers in addition to other mechanisms just mentioned.     

界面黏滑摩擦现象的研究进展

从宏观尺度和微观尺度两个方面介绍了界面黏滑摩擦的研究进展,重点概述了宏观黏滑现象及其摩擦特性、微观黏滑现象及其摩擦特性、黏滑摩擦的建模以及黏滑实验研究进展,分析了现阶段界面黏滑摩擦研究中的重点问题。最后指出,从微观和介观尺度上研究界面摩擦行为是黏滑摩擦的未来发展方向。     

Study on dynamic friction characteristics in reciprocating friction drive system

The dynamic friction characteristics of a reciprocating friction drive system are investigated under conditions of dry contact using 0·45% carbon steel pair. Three friction modes are found during the operation, i.e. stick-slip, sticking and a transition region. The critical operating conditions in classifying these three modes are examined under various driver speeds, normal loads and spring constants. The critical values of driver speed and normal load increase with increasing spring constant. Generally, in the friction drive system the disappearance of the stick-slip results in smooth rolling. It is also found that the slope at the first period of slip on the traction force–relative slip velocity curve would have a transition from negative to positive value when the friction mode of stick-slip changes into sticking. Moreover, results show that the sticking mode gives the best positioning accuracy with the least wear on the contact surfaces. In addition, a transition from severe wear to mild wear is found when the friction mode is transferred from stick-slip to sticking only.     

带在轮系上的横向运动问题

本文所提出的关于带在轮系上的横向运动的理论,牵涉到带轮装置的一系列问题。它概括了这些似无联系的问题,使之系统化成为一个较完整的体系,澄清了有关的某些模糊和错误的认识,并为一系列实验所证实。带在轮系上的横向运动,应分为横向移动与横向滑动。两者在其产生的原因、对工作的影响、分析的方法和应采取的措施等方面,都有着根本的区别。横向移动是由于受到摩擦支持的斜缠绕作用而引起的,并且肯定是不平稳的。“装带定律”就是为防止出现斜缠绕。不仅半交叉的而且包括开口的带轮装置在内的各种带轮装置,都必须遵守这一定律。分析横向移动问题时,应从带的应力和变形分析入手,找出带在进入轮时的实际方向,才能最后正确判定带横向移动的趋向。中凸鼓形轮是稳定带的横向位置、防止带从轮上由于斜缠绕而掉落的有效措施。横向运动的另一种形式是横向滑动。横向滑动可以是平稳的,也可以是不平稳的。它是由于带的接触段所受到的横向外力而引起的。横向滑动的存在,会使带轮装置的负载能力与传动效率降低。轮缘挡边可用以防止带从轮上滑落。     

环境湿度下硅材料表面的粘滑行为及其抑制

通过自行开发的微摩擦测试仪,分别研究了小载荷湿度环境下光洁硅片、物理形貌修饰表面和OTS膜修饰表面的微摩擦行为。实验结果表明,OTS膜表面和凹坑形貌修饰表面在高湿度环境下可以有效地抑制粘滑现象的发生。通过对湿度环境下液桥作用机制的研究,初步认为摩擦力来自于工作间隙的固固、固液和液液3个接触面间相互作用,并且高湿度下是否出现粘滑现象取决于这3种界面间力的竞争关系。