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.     

Dynamic modeling of manipulation of micro/nanoparticles on rough surfaces

In this paper, the dynamic behavior of spherical micro/nanoparticles, while being pushed on rough substrates, is studied by means of an Atomic Force Microscope (AFM). For this purpose, first, the contact adhesion force, and the areas and penetration depths of rough surfaces are derived based on the Johnson-Kendall-Roberts (JKR) theory, the Schwarz method, and the Rumpf/Rabinovich models. Then, the dynamic model of particle manipulation on rough substrates is revised using the specified contact theory for rough surfaces. And finally, the pushing of spherical particles with 50, 100, 200, 500, and 10000 nm radii is simulated. The results show that the critical force and the critical time of manipulation decrease when the particles are pushed on the rough surfaces as compared to the smooth ones. It is also observed that the critical force for a rough substrate containing asperities of low height and large radius approaches a comparable critical force magnitude to the smooth substrate, as is expected. Also, when the asperity radius in the substrate is within the range of 0.5 < r < 5 nm, the critical force of pushing decreases; however, as the asperity radius becomes larger than 5 nm, the critical force begins to increase again. Furthermore, the critical values are generally more sensitive to the changes of the asperity radius than the height. It is also found that the difference between the critical values based on the Rumpf and Rabinovich models is negligible. However, the estimation of particles’ dynamic behavior using the Rumpf model could be wrong for the rough substrates with small radius asperities, which is considerable in the manipulation and assembly practices. Moreover, the dynamic behavior of particles of small radius (r < 500 nm) change during the pushing process on rough surfaces, and the rolling behavior could be possible on the surfaces that have small radius asperities. The probability of this occurrence is increased in the pushing of larger particles on rougher substrates.     

Nonlinear shear wave interaction at a frictional interface: energy dissipation and generation of harmonics

Analytical and numerical modeling of the nonlinear interaction of shear wave with a frictional interface is presented. The system studied is composed of two homogeneous and isotropic elastic solids, brought into frictional contact by remote normal compression. A shear wave, either time harmonic or a narrow band pulse, is incident normal to the interface and propagates through the contact. Two friction laws are considered and the influence on interface behavior is investigated: Coulomb's law with a constant friction coefficient and a slip-weakening friction law which involves static and dynamic friction coefficients. The relationship between the nonlinear harmonics and the dissipated energy, and the dependence on the contact dynamics (friction law, sliding, and tangential stress) and on the normal contact stress are examined in detail. The analytical and numerical results indicate universal type laws for the amplitude of the higher harmonics and for the dissipated energy, properly non-dimensionalized in terms of the pre-stress, the friction coefficient and the incident amplitude. The results suggest that measurements of higher harmonics can be used to quantify friction and dissipation effects of a sliding interface.     

Molecular dynamics investigations on polishing of a silicon wafer with a diamond abrasive

During the final stages of polishing silicon wafers, much of the interactions between silicon and diamond abrasive takes place at the silicon asperities. These interactions, leading to material removal, were investigated in a MD simulation of polishing of a silicon wafer with a diamond abrasive under dry conditions. Simulations were conducted with silicon asperities of different geometries, different abrasive configurations, and polishing speeds. Under the conditions of polishing, the silicon atoms from the asperities were found to bond chemically to the surface of the diamond abrasive. Continued transverse motion of the diamond abrasive (relative to the silicon asperity) leads to tensile pulling, necking, and ultimate separation of the silicon asperity material instead of conventional material removal in polishing (chip formation) involving cutting/ploughing, which takes place in the absence of chemical bonding between the abrasive and the asperity material. This phenomenon has not been reported previously in the literature. The thrust and cutting forces initially increase due to the increase in the number of asperity atoms affected finally reaching a maximum. This is followed by a decrease of these forces due to tensile pulling and formation of individual strings followed by ultimate separation or breakage of the final string. The ratio of thrust force (F _z ) to the cutting force (F _x ), i.e. |(F _z /F _x )| was found to increase continuously to a maximum of ～0.8 followed by continuous decrease to ～0.25. This is in contrast to a more or less constant value of ～2 in the case of tools with rounded radii or tools with large negative rake angles, where material is removed in the form of chips ahead of the tool. Three regions of the asperity have been identified that are useful in the development of a phenomenological model for polishing that enables computation of material removal rates: (1) the region directly in front of the abrasive for which the probability of the removal of an asperity atom is close to unity, (2) the distant region where this probability is nearly zero, and (3) an intermediate region from which the probability of removal is close to half.     

Crystalline misfit-angle implications for solid sliding

For the contact of two finite portions of interacting rigid crystalline surfaces, we compute the pinning energy barrier dependency on the misfit angle and contact area. This simple model allows us to investigate a broad contact-size and angular range, thus obtaining the statistical properties of the energy barriers opposing sliding for a single asperity. These data are used to generate the distribution of static frictional thresholds for the contact of polycrystals, as in dry or even lubricated friction. This distribution is used as the input of a master equation to predict the sliding properties of macroscopic contacts.     

Effects of a self-assembled monolayer on the sliding friction and adhesion of an Au surface

The friction and adhesion mechanisms with and without a self-assembled monolayer (SAM) in nanotribology were studied using molecular dynamics (MD) simulation. The MD model consisted of two gold planes with and without n-hexadecanethiol SAM chemisorbed to the substrate, respectively. The molecular trajectories, tilt angles, normal forces, and frictional forces of the SAM and gold molecules were evaluated during the frictional and relaxation processes for various parameters, including the number of CH₂ molecules, the interference magnitude, and whether or not the SAM lubricant was used. The various parameters are discussed with regard to frictional and adhesion forces, mechanisms, and molecular or atomic structural transitions. The stick–slip behavior of SAM chains can be completely attributed to the van der Waals forces of the chain/chain interaction. When the number of CH₂ molecules was increased, the SAM chains appeared to have bigger tilt angles at deformation. The magnitude of the strain energy that was saved and relaxed is proportional to the elastic deformable extent of the SAM molecules. The frictional force was higher for long chain molecules. With shorter SAM molecules, the adhesion force behavior was more stable during the compression and relaxation processes. A surface coated with a SAM can increase nano-device lifetimes by avoiding interface effects like friction and adhesion. PACS 52.65.Yy; 81.40.Pq; 81.16; 68.35.-p     

Plastic shear response of a single asperity: a discrete dislocation plasticity analysis

We investigate the plastic shear response during static friction of an asperity protruding from a large FCC single crystal. The asperity is in perfectly adhesive contact with a rigid platen and is sheared by tangentially moving the platen. Using discrete dislocation plasticity simulations, we elucidate the plastic shear behaviour of single asperities of various size and shape, in search for the length scale that controls the plastic behaviour. Since plasticity can occur also in the crystal, identification of the length scale that controls a possible size-dependent plastic behaviour is far from being trivial. It is found that scaling down the dimensions of an asperity results in a higher contact shear strength. The contact area is dominant in controlling the plastic shear response, because it determines the size of the zone, in and below the asperity, where dislocation nucleation can occur. For a specific contact area, there is still a dependence on asperity volume and shape, but this is weaker than the dependence on contact area alone.     

Regular and reverse nanoscale stick-slip behavior: Modeling and experiments

We recently proposed a new nanoscale friction model based on the bristle interpretation of single asperity contacts. The model is mathematically continuous and dynamic which makes it suitable for implementation in nanomanipulation and nanorobotic modeling. In the present paper, friction force microscope (FFM) scans of muscovite mica samples and vertically aligned multi-wall carbon nanotubes (VAMWCNTs) arrays are conducted. The choice of these materials is motivated by the fact that they exibit different stick-slip behaviors. The corresponding experimental and simulation results are compared. Our nanoscale friction model is shown to represent both the regular and reverse frictional sawtooth characteristics of the muscovite mica and the VAMWCNTs, respectively.     

Multipoint contact modeling of nanoparticle manipulation on rough surface

In this paper, the atomic force microscopy (AFM)-based 2-D pushing of nano/microparticles investigated on rough substrate by assuming a multipoint contact model. First, a new contact model was extracted and presented based on the geometrical profiles of Rumpf, Rabinovich and George models and the contact mechanics theories of JKR and Schwartz, to model the adhesion forces and the deformations in the multipoint contact of rough surfaces. The geometry of a rough surface was defined by two main parameters of asperity height (size of roughness) and asperity wavelength (compactness of asperities distribution). Then, the dynamic behaviors of nano/microparticles with radiuses in range of 50–500 nm studied during their pushing on rough substrate with a hexagonal or square arrangement of asperities. Dynamic behavior of particles were simulated and compared by assuming multipoint and single-point contact schemes. The simulation results show that the assumption of multipoint contact has a considerable influence on determining the critical manipulation force. Additionally, the assumption of smooth surfaces or single-point contact leads to large error in the obtained results. According to the results of previous research, it anticipated that a particles with the radius less than about 550 nm start to slide on smooth substrate; but by using multipoint contact model, the predicted behavior changed, and particles with radii of smaller than 400 nm begin to slide on rough substrate for different height of asperities, at first.     

Definition of road roughness parameters for tire vibration noise control

Road roughness plays an important role in the generation of tire vibration noise. However, it is unclear which kinds of road roughness parameters should be controlled to reduce the noise. In this paper, we define the essential road roughness parameters that govern tire tread vibration and provide information on tire/road noise abatement. The detailed effects of road roughness parameters on tire tread vibration are estimated using a tire/road contact model. The results reveal that pavement asperity height itself is not an essential parameter, but asperity height unevenness, asperity radius, and asperity spacing are important for the abatement of tire vibration noise.     

Ice internal friction: Standard theoretical perspectives on friction codified,adapted for the unusual rheology of ice,and unified

Sea ice contains flaws including frictional contacts. We aim to describe quantitatively the mechanics of those contacts, providing local physics for geophysical models. With a focus on the internal friction of ice, we review standard micro-mechanical models of friction. The solid's deformation under normal load may be ductile or elastic. The shear failure of the contact may be by ductile flow, brittle fracture, or melting and hydrodynamic lubrication. Combinations of these give a total of six rheological models. When the material under study is ice, several of the rheological parameters in the standard models are not constant, but depend on the temperature of the bulk, on the normal stress under which samples are pressed together, or on the sliding velocity and acceleration. This has the effect of making the shear stress required for sliding dependent on sliding velocity, acceleration, and temperature. In some cases, it also perturbs the exponent in the normal-stress dependence of that shear stress away from the value that applies to most materials.

We unify the models by a principle of maximum displacement for normal deformation, and of minimum stress for shear failure, reducing the controversy over the mechanism of internal friction in ice to the choice of values of four parameters in a single model. The four parameters represent, for a typical asperity contact, the sliding distance required to expel melt-water, the sliding distance required to break contact, the normal strain in the asperity, and the thickness of any ductile shear zone.     

Molecular dynamics investigation on the atomic-scale friction behaviors between copper(0 0 1) and diamond(1 1 1) surfaces

Classical molecular dynamics (MD) simulations are conducted to examine the atomic-scale friction behavior of an infinite flat-flat contact between copper(0 0 1) and diamond(1 1 1) surfaces. Two types of diamond surface, namely H-free and hydrogenated, are constructed and on each of them the copper counterface is brought to slide along the [1 1 −2] and [1 −1 0] crystallographic directions with a variety of loads. The simulation results demonstrate that the hydrogen atoms chemisorbed to the diamond surface can to large extent eliminate the directional dependency of its friction behavior with copper. Under pressures less than 30 GPa, the sliding between copper and hydrogenated is wearless. In this period, the shear stress of them just slightly increases to 0.6 GPa. Between 30 GPa and 32 GPa, copper atoms near the interface begin to be worn and incorporate into the diamond substrate and this causes a sharp shift from 0.6 GPa to 2.7 GPa in their shear stress. In contrast, the sliding process between copper and H-free diamond is always wearless even under pressure beyond 40 GPa. The H-free [1 −1 0] model exhibits much higher shear stress than H-free [1 1 −2] under pressures less than 35 GPa. Beyond 35 GPa, they present nearly consistent shear stress evolution. Moreover, the simulations for hydrogenated diamond models suggest that their friction behavior is independent on sliding velocity only under wearless sliding regime.     

Effect of substrate dimensions on dynamics of ultrasonic consolidation

An FEM model is developed for a fundamental study of the time-dependent mechanical behavior of the substrate and its dimensions on ultrasonic consolidation. The simulation shows that for a given vibration condition, the amplitude of contact friction stress and displacement stabilizes to a saturated state after certain number of ultrasonic cycles. With the increased substrate height, the amplitude of contact frictional stress decreases, while that of contact interface displacement increases. The reason for the decrease in the frictional stress at the contact interface for certain substrate heights is the complicated wave interference occurring in the substrate. An analytical wave model has been built to validate the FEM model. A specific substrate geometry (height:width = 1.0) generates a minimum frictional strain state at the interface as a result of wave superposition. Such minimum strain state is believed to have produced the “lack of bonding” defect for the geometry. The energy density and transfer coefficient at the contact interface with different substrate heights is used as an indicator to correlate with the bond formation in ultrasonic bonding.     

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.     

Molecular dynamics simulations of diffusion of carbon into iron

Molecular dynamics (MD) simulations of diffusion couple tests were conducted between carbon (diamond/graphite) and iron at three different temperatures (300, 800 and 1600 K) and contact times (0, 40 and 80 ps) to investigate the chemical interaction between carbon and iron. Two different carbon structures, namely, diamond (cubic) and graphite (hexagonal), were considered. Diffusion of carbon into iron was observed only when a graphite interlayer was added to the diamond surface. When diamond alone was used, no diffusion was observed. This result provides corroborating evidence that diamond tool wear in the machining of iron occurs via a mechanism that involves an initial graphitization of diamond followed by diffusion of the newly formed graphite into the iron workpiece.     

Influence of nanometer scale film structure of ZDDP tribofilm on Its mechanical properties: A computational chemistry study

We investigated the influence of a nanometer scale film structure of a tribofilm generated from zinc dialkyldithiophosphate (ZDDP) anti-wear additive on its mechanical properties using a combined molecular dynamics (MD) and finite element (FE) method. The frictional behavior of an interface between a native iron oxide layer on steel surface and zinc metaphosphate - regarded as a model material of ZDDP tribofilm - was firstly studied using the MD method. The results showed that the iron atoms in the oxide layer diffused into the phosphate layer during the friction process. The zinc atoms in the phosphate layer also diffused into the oxide layer. Significant interdiffusion of iron and zinc atoms was observed with increasing simulation time. Thus, metallic phosphate with a gradient composition of iron and zinc atoms was formed on the phosphate/oxide interface. We then constructed an axisymmetric nanoindentation simulation model from the MD-derived structures at a certain simulation time and carried out a FE calculation. As a result, we found that the rubbed ZDDP tribofilm, including the phosphate with the gradient composition of metallic atoms, showed larger contact stiffness and hardness. The combined MD/FE simulation indicates that the tribofilm becomes stiffer and harder due to the interdiffusion of iron and zinc atoms on the tribofilm/oxide interface. We have found that the gradient composition formation in ZDDP tribofilm during friction process influences on its mechanical properties.     

Ageing of a microscopic sliding gold contact at low temperatures

Nanometer-scale friction measurements on a Au(111) surface have been performed at temperatures between 30 and 300?K by means of atomic force microscopy. Stable stick slip with atomic periodicity is observed at all temperatures, showing only weak dependence on temperature between 300 and 170?K. Below 170?K, friction increases with time and a distortion of the stick-slip characteristic is observed. Low friction and periodic stick slip can be reestablished by pulling the tip out of contact and subsequently restoring the contact. A comparison with molecular dynamics simulations indicates that plastic deformation within a growing gold junction leads to the observed frictional behavior at low temperatures. The regular stick slip with atomic periodicity observed at room temperature is the result of a dynamic equilibrium shape of the contact, as microscopic wear damage is observed to heal in the sliding contact.     

Planarization process of single crystalline silicon asperity under abrasive rolling effect studied by molecular dynamics simulation

In the chemical mechanical polishing (CMP) process, the complex behaviors of abrasive particles play important roles in the planarization of wafer surface. Particles embedded in the pad remove materials by ploughing, while particles immersed in the slurry by rolling across the wafer surface. In this paper, processes of the particle rolling across a silicon surface with an asperity under various down forces and external driving forces were studied using molecular dynamics (MD) simulation method. The simulations clarified the asperity shape evolution during the rolling process and analyzed the energy changes of the simulation system and the interaction forces acted on the silica particle. It was shown that both the down force and the driving force had important influences on the amount of the material removed. With relatively small down forces and driving forces applied on the particle, the material removal occurred mainly in the front end of the asperity; when the down forces and driving forces were large enough, e.g., 100?nN, the material removal could take place at the whole top part of the asperity. The analysis of energy changes and interaction forces provided favorable explanations to the simulation results.     

Contact mechanics analysis of oscillatory sliding of a rigid fractal surface against an elastic–plastic half-space

Oscillatory sliding contact between a rigid rough surface and an elastic–plastic half-space is examined in the context of numerical simulations. Stick-slip at asperity contacts is included in the analysis in the form of a modified Mindlin theory. Two friction force components are considered – adhesion (depending on the real area of contact, shear strength and interfacial adhesive strength) and plowing (accounting for the deformation resistance of the plastically deformed half-space). Multi-scale surface roughness is described by fractal geometry, whereas the interfacial adhesive strength is represented by a floating parameter that varies between zero (adhesionless surfaces) and one (perfectly adhered surfaces). The effects of surface roughness, apparent contact pressure, oscillation amplitude, elastic–plastic properties of the half-space and interfacial adhesion on contact deformation are interpreted in the light of numerical results of the energy dissipation, maximum tangential (friction) force and slip index. A non-monotonic trend of the energy dissipation and maximum tangential force is observed with increasing surface roughness, which is explained in terms of the evolution of the elastic and plastic fractions of truncated asperity contact areas. The decrease of energy dissipation with increasing apparent contact pressure is attributed to the increase of the elastic contact area fraction and the decrease of the slip index. For a half-space with fixed yield strength, a lower elastic modulus produces a higher tangential force, whereas a higher elastic modulus yields a higher slip index. These two competing effects lead to a non-monotonic dependence of the energy dissipation on the elastic modulus-to-yield strength ratio of the half-space. The effect of interfacial adhesion on the oscillatory contact behaviour is more pronounced for smoother surfaces because the majority of asperity contacts deform elastically and adhesion is the dominant friction mechanism. For rough surfaces, higher interfacial adhesion yields less energy dissipation because more asperity contacts exhibit partial slip.     

A dynamic Lagrangian frequency-time method for the vibration of dry-friction-damped systems

A new frequency-time domain procedure, the dynamic Lagrangian mixed frequency-time method (DLFT), is proposed to calculate the non-linear steady state response to periodic excitation of structural systems subject to dry friction damping. In this formulation, the dynamic Lagrangians are defined as the non-linear contact forces obtained from the equations of motion in the frequency domain, with the adjunction of a penalization on the difference between the interface displacements calculate by the non-linear solver in the frequency domain and those calculated in the time domain from the non-linear contact forces, thus accounting for Coulomb friction and non-penetration conditions. The dynamic Lagrangians allow one to solve for the non-linear forces between two points in contact without using artifacts such as springs. The new DLFT method is thus particularly well suited to handling finite element models of structures in frictional contact, as it does not require a special model for the contact interface. Dynamic Lagrangians are also better suited to frequency-domain friction problems than the traditional time-domain method of augmented Lagrangians. Furthermore, a reduction of the non-linear system to relative interface displacements is introduced to decrease the computation time. The DLFT method is validated for a beam in contact with a flexible dry friction element connected to ground, for frictional constraints that feature two-dimensional relative motion. Results are also obtained for a large-scale structural system with a large number of one-dimensional dry-friction dampers. The DLFT method is shown to be accurate and fast, and it does not suffer from convergence problems, at least in the examples studied.