On the dependence of the static friction force between a rigid,randomly rough fractal surface and a viscoelastic body on the normal force

The present investigation is based on the assumption that the static coefficient of friction can be characterized roughly by the rms value of the surface gradient in the contact region. We numerically investigate the contact between a rigid, randomly rough surface and an elastic half-space and determine the dependence of the rms slope in the contact region on the normal force. For fractal surfaces with a Hurst exponent of H ≈ 1, the rms slope can be approximated very well by a logarithmic function of the normal force. Parameters of the approximation have been determined as functions of the Hurst exponent. The rms value of the slope always increases with the normal force, which indicates that the coefficient of friction should be an increasing function of the normal force.     

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     

Finite element simulation of nanostructuring burnishing

Dynamics simulation of burnishing of a thin steel layer beneath an indenter applied with a constant force and then moving with a constant velocity was performed by the finite element method in the plane strain approximation. The indenter was modeled by a perfectly rigid body, and the steel was modeled by an elastoplastic body with isotropic hardening according to an experimentally defined law. The regularities of changes in the stressstrain state of the material near the treated surface were studied and mechanisms of the formation of a nanostructured layer were disclosed. The effect of the friction coefficient and the burnishing force on the height of a bulge of edged material was analyzed. The results of studies agree well with experimental data.     

摩擦导致的聚合物表层微观结构改变

应用大规模分子动力学方法, 模拟了锥形探头在非晶态聚合物薄膜表面的滑动摩擦过程, 研究了摩擦导致的聚合物薄膜表层微观结构改变, 以及探头与基体间黏着作用、滑动速度和分子链长度对基体表层微观结构改变的影响. 当探头与基体之间为黏着作用时, 摩擦导致基体表面滑痕区域的键取向沿滑动方向重新取向, 导致表层分子链回转半径沿滑动方向伸长, 并且这些表层微观结构的改变程度随滑动速度的减小而增大. 在摩擦导致结构改变的过程中, 链端单体和链中单体的贡献作用不同, 形成了不同的分子链拉伸变形机制. 当样本缠结度较大或探头滑动速度较小时, 相比于链中单体, 探头对链端单体的拖曳作用使更多分子链发生拉伸变形. 研究还发现, 在探头与聚合物薄膜系统中, 使薄膜表层微观结构发生改变是摩擦能量耗散的重要途径.     

Dynamics of the coefficient of friction between a rigid conical indenter and a viscoelastic foundation under step-wise change of sliding velocity

We numerically calculated the coefficient of friction between a rigid cone and a viscoelastic Kelvin body under step-wise change of the velocity of sliding. The time dependence of the coefficient of friction has been empirically approximated. We show that the transition process has different character for the cases of increasing and decreasing of the sliding velocity.     

Prediction of sound reflection by corrugated porous surfaces

The coupled mode (CM) and finite-element methods (FEMs) are developed and used to predict the acoustic reflection coefficient of a semi-infinite porous medium with closely spaced two-dimensional (2D) periodical corrugations. These methods are also applied to predict the reflection coefficient of a periodic array of porous corrugations installed on an acoustically rigid surface. It is shown that the predictions by the both methods agree closely. The reflection coefficient and Brewster angle of total refraction for the corrugated semi-infinite medium predicted with these methods are compared against that predicted by the Biot/Tolstoy/Howe/Twersky and extended Twersky models. A similar analysis is carried out for porous corrugations set on a rigid backing. The behavior of the reflection coefficient and the pole in the expression for the reflection coefficient located close to grazing incidence is studied.     

Coefficient of friction between a rigid conical indenter and a model elastomer: Influence of local frictional heating

We investigate the coefficient of friction between a rigid cone and an elastomer with account of local heating due to frictional dissipation. The elastomer is modeled as a simple Kelvin body and an exponential dependency of viscosity on temperature is assumed. We show that the coefficient of friction is a function of only two dimensionless variables depending on the normal force, sliding velocity, the parameter characterizing the temperature dependence as well as shear modulus, viscosity at the ambient temperature and the indenter slope. One of the mentioned dimensionless variables does not depend on velocity and determines uniquely the form of the dependence of the coefficient of friction on velocity. Depending on the value of this controlling variable, the cases of weak and strong influence of temperature effects can be distinguished. In the case of strong dependence, a generalization of the classical “master curve” procedure introduced by Grosch is suggested by using both horizontal and vertical shift factors.     

An acoustic model of diffusion in gases [1]

Principles of macroscopic acoustical theory are applied to the calculation of the friction constant of a dilute gas of rigid spheres. In the model molecular motions are perturbed by acoustic disturbances arising from the occurrence of density fluctuations in the equilibrium fluid. The friction constant calculated is found to have the same parametric form but a substantially lower numerical coefficient when compared with the result of Chapman and Enskog.     

Investigation of Transfer Behaviors of Embedded Polytetrafluoroethylene in Different Metal Substrates

Transfer behaviors of molded polytetrafluoroethylene (PTFE) blocks embedded in metal substrates were studied using a DFPM reciprocating tribometer under designed conditions. The substrate properties markedly affected the embedded PTFE transfer behaviors. For instance, the surface friction coefficient when embedded in AISI-1045 steel had evident fluctuations even after 1000 cycles although the friction coefficient decreased with the increase of the sliding cycles. On the other hand, the friction coefficient when the PTFE was embedded in 2024Al was remarkably reduced during the first 200 cycles, reaching a low and stable state. The loads played different roles in the transfer process; a higher load was advantageous for the steel-PTFE embedded composites, but it resulted in the opposite result for the Al-PTFE embedded composites. The motion direction of the GCr15 tribometer steel ball had no remarkable effect on the transfer behaviors. The worn surface of the substrates and the steel ball were observed and analyzed using scanning electron microscopy (SEM) and energy dispersive spectrometer (EDS). The results indicate that the efficiency of second transfer film formation on the 2024Al substrate was better than for the AISI-1045 steel. The adhesion properties of Al enhanced the mechanical transfer of PTFE during the friction process.     

Towards a statistical theory of solid dry friction

Wearless dry friction of an elastic block of weight N, driven by an external force F over a rigid substrate, is investigated. The slider and substrate surfaces are both microscopically rough, interacting via a repulsive potential that depends on the local overlap. The model reproduces Amontons’s laws which state that the friction force is proportional to the normal loading force N and independent of the nominal surface area. In this model, the dynamic friction force decays for large velocities and approaches a finite static friction for small velocities if the surface profiles are self-affine on small length scales.     

Changes in surface properties of nitrogen-implanted AISI316L stainless steel

The effect of nitrogen ion implantation with an energy of 125 keV and doses of 1 × 10¹⁷–1 × 10¹⁸ at/cm² on such tribological characteristics of AISI316L stainless steel as the friction coefficient, wear resistance, and microhardness was studied. The steel surface layer composition was studied by the methods of RBS, XRD, GXRD, SEM, and EDX. The friction coefficient and abrasion resistance of AISI316L stainless steel were measured in air, oxygen and argon atmospheres, and in vacuum. An increase in the abrasion resistance after implantation was detected, which was different for various media. The largest increase in the wear resistance was observed during testing in air. The largest decrease in the friction coefficient was observed for all implanted samples in argon atmosphere. Tribological tests resulted in an increase in nitrogen, carbon, and oxygen concentrations in worn sample fragments in comparison with their concentrations in surface layers immediately after implantation.     

On the stability of the flow and heat transfer over a moving thin needle with prescribed surface heat flux

The steady flow and heat transfer over a moving thin needle with prescribed surface heat flux is studied. The similarity equations are obtained by using similarity transformation technique. The problem is solved numerically using the boundary value problem solver (bvp4c) in Matlab software. The plots of the skin friction coefficient and the local Nusselt number as well as the velocity and temperature profiles are presented and their behaviors are discussed for different values of the needle size and the velocity ratio parameter. Results show that the decreasing of the needle size enhance the skin friction coefficient and the local Nusselt number on the needle surface. It is found that dual solutions exist (upper and lower branches) for a certain range of the velocity ratio parameter. A stability analysis of the solutions are performed and it shows that the upper branch solution is stable, while the lower branch solution is unstable.     

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.     

Frenkel-Kontorova模型中垫底势对最大静摩擦力的影响

用一维Frenkel-Kontorova模型,对相互接触的两个单原子分子链具有相对运动趋势时所产生的最大静摩擦力进行了研究.分别在相邻原子的距离与周期势场的周期比b/a为可公度(commensurate)、黄金分割(golden mean)、螺旋分割(spiral mean)三种情况下,描述了特殊垫底势力的振幅A与分子链静摩擦力的关系,在特殊垫底势力的作用下上层原子链弹性系数K对静摩擦力的影响.研究表明,垫底势力的形式对静摩擦力的大小有很重要的影响.     

Frenkel-Kontorova模型中垫底势对最大静摩擦力的影响

用一维Frenkel-Kontorova模型,对相互接触的两个单原子分子链具有相对运动趋势时所产生的最大静摩擦力进行了研究.分别在相邻原子的距离与周期势场的周期比b/a为可公度(commensurate)、黄金分割(golden mean)、螺旋分割(spiral mean)三种情况下,描述了特殊垫底势力的振幅A与分子链静摩擦力的关系,在特殊垫底势力的作用下上层原子链弹性系数K对静摩擦力的影响.研究表明,垫底势力的形式对静摩擦力的大小有很重要的影响. 关键词： Frenkel-Kontorova模型 静摩擦力     

Wave pattern motion and stick-slip limit cycle oscillation of a disc brake

This paper examines the dynamic response of a rotating squealing disc brake subject to distributed nonlinear contact stresses where two brake pads are assumed to be stationary and rigid. The friction stresses produce high-frequency vibrations that exhibit standing or traveling waves on the disc surface. The wave pattern resulting from the binary flutter mechanism of one transverse doublet mode pair is studied here. The results show that the wave pattern is associated with mode-coupling character. For a steady-squealing mode, the stick zone of the contact area is determined by a smooth friction-velocity curve having both negative and positive slopes.     

Multiscale simulation of friction with normal oscillations in the method of reduction of dimensionality

In the framework of the method of reduction of dimensionality, the dependence of the kinetic coefficient of friction of elastomers with linear rheology on normal loads with a static and an oscillatory part has been examined. It is shown that the sinusoidal excitation leads to a reduction of the coefficient of friction by up to 20 % for a sliding velocity range of two orders of magnitude. The largest reduction of the coefficient of friction occurs at a velocity, which is proportional to the characteristic wave length of the surface and the frequency of the acting normal force.     

Block Elements in Contact Problems with a Variable Friction Coefficient

Contact problems on the surface interaction of rigid stamps with a deformed layered medium are considered provided that the variable friction coefficients arise in the contact zone as a function of the coordinate under the horizontal motion of stamps. The cause of the variable friction coefficients arising may be surface phenomena induced by a complex rheology of the deformed-medium surface, the chemical reactions proceeding, or a change in the properties of the contact surface of the stamps, for example, as a result of the presence of separate particles of the wear contact surface of the stamp and the base.     

Impact of substrate corrugation on the sliding friction levels of adsorbed films

We report a quartz crystal microbalance (QCM) study of sliding friction for solid xenon monolayers at 77 K on Cu(111), Ni(111), graphene/Ni(111), and C(60) substrates. Simulations have predicted a strong dependence of phononic friction coefficient (eta) on surface corrugation in systems with similar lattice spacing, eta approximately U(2)(0), but this has never before been shown experimentally. In order to make direct comparisons with theory, substrates with similar lattice spacing but varying amplitudes of surface corrugation were studied. QCM data reveal friction levels proportional to U(2)(0), validating current theoretical and numerical predictions. Measurements of Xe/C(60) are also included for comparison purposes.     

Energy dissipation in solid friction

Dissipation in solid friction is studied as a function of the elastic properties of the two sliding surfaces. The two surfaces have been constructed by embedding macroscopic asperities in an elastic layer. It is shown that when the surfaces are rigid the energy dissipation is smaller than in the elastic case. The scaling of the friction force as a function of the asperity number is also studied. Received 9 November 1998