Effects of Anisotropy and Substrate Shape on Atomic Friction Force in Two-Dimensional Model

We investigate the effect of the shape potential on the frictional behavior transitions. The Tomlinson parameter for the deformable substrate potential is calculated theoretically and its influence on friction force is studied. Futhermore, effects of temperature and substrate shape on the tip jump probability are presented. We find two critical times, which characterize the tip dynamics. The first critical time is the time spent by the tip to reach next potential minimum and the second is the time at which the tip exhibits an equiprobability of forward and backward jump. We show that these critical times depend strongly on the substrate shape as well as on the temperature.

We study thermomechanical deformations of a thermally softening viscoplastic thick target impacted at normal incidence by a cylindrical rod made of a material considerably harder than the target material. Thus we regard the penetrator to be rigid and analyze the effect of the penetrator nose shape and the frictional force at the target/penetrator interface on target's deformations. In the postulated expression for the frictional force, the coefficient of friction, defined as the ratio of the tangential force at a point to the normal force there, is a function of the relative speed of sliding between the two bodies. The computed depth of penetration is found to match very well with that observed in experiments by Forrestal et al. For each nose shape studied, the consideration of frictional forces reduces significantly the computed penetration depth. For the same kinetic energy of the penetrator, the penetrator with a sharp nose gives higher values of the penetration depth as compared to that obtained with a blunt nose.

ABSTRACTWe have used the surface forces apparatus to measure the structural and frictional force profiles between opposing, solvated brush layers as a function of temperature. Two different polyvinylpyridine-polystyrene [PVP-PS] diblock copolymers were used to make PS brushes. The molecular weights (in thousands) of these PVP-PS materials were [114/103]k, [30/70]k, respectively. Structural and frictional force profiles in toluene and cyclohexane were measured, and the cyclohexane experiments were conducted at temperatures ranging from the theta-point to 50°C. In toluene the PS brushes needed to be compressed to ∼1/5th of their equilibrium height before frictional forces were measured, but this onset of frictional forces was detected at a much lower level of compression in near-theta cyclohexane. In cyclohexane the structural force profiles were basically insensitive to the temperature change, but the frictional forces depended strongly on the solvent temperature. When the cyclohexane temperature was raised, the onset of frictional forces decreased toward the good-solvent onset. We also discuss the dependence of frictional force on shearing parameters.

This thesis comes within the scope of tribology studies at the nanometer scale. The experimental techniques used in this work are essentially related to atomic force microscopy, which gives a direct access to the topography and forces of the studied systems. Two principal aspects of the nanotribology have kept our attention. They are the nanofriction and the nanomechanics. These two domains divide the thesis in two main parts that remain however intimately bound. The first experimental part of the thesis describes the friction of a nanoscopic tip sliding on hydrophilic surfaces. The dependence of the friction force on the sliding velocity is studied for various applied normal loads and surrounding relative humidity levels. We found a logarithmic dependence of the friction force on both the scanning velocity and the relative humidity. For the first time, a transition from a positive to a negative slope of the friction force versus the logarithm of the sliding velocity has been observed for the very same tip-surface contact, by varying the relative humidity. The role of the relative humidity on the friction force has then been studied more deeply, leading to a two-thirds power law dependence of the capillary force on the normal load. Finally, analytical expressions for the friction phenomenon and the capillary condensation between the asperities of the tip and the surface have been developed to explain the phenomenological behaviors. The second experimental part describes themechanics of carbon nanotubes and tobacco mosaic viruses. In order to stay in the linear elasticity regime, small indentation amplitudes have been applied in the radial direction of multiwalled carbon nanotubes adsorbed on a silicon oxide surface. Using a theory based on the Hertz model, the radial stiffness has been evaluated and compared to molecular dynamics simulations. We found a radial Young modulus strongly decreasing with increasing radius and reaching an asymptotic value of 30 ± 10 GPa. The tobacco mosaic viruses have been adsorbed on a polyimide porous membrane. Evidence for the softness of the viruses has been obtained by imaging the tubes with the atomic force microscope in non-contact mode. Viruses hanging like ropes over the pores of the surface served as basis to measure their bending Young modulus. Using a model of a clamped beam loaded by a discrete gradient of van der Waals forces, we found a bending Young modulus of 3.1 ± 0.1 MPa.

The lateral modulation friction force microscopy (LM-FFM) technique was used to investigate the tribological characteristics of a longitudinal magnetic recording medium (hard disk). The load dependence of the frictional force between the hard disk and the Si tip should be influenced by the dynamic elasticity of the tip. Very slight wear of the hard disk due to scanning of the tip was observed and the wear depth increased linearly with increasing load. The frictional force in areas which were significantly deformed increased due to scanning of the tip. The frictional force decreased in the first stage of repeated scanning and then increased with the number of scans under a load of 1.5 or 3.5 µ N. For a load of 130 nN, the frictional force between the tip and the sample increased with the number of scans.

Layered materials are the most important class of solid lubricants. Friction on their surfaces has complex origins. Most experimental methods so far only give total friction force and cannot separate contributions from different origins. Here, we report a method to separate anisotropic and isotropic friction forces on atomically flat surfaces such as ${\mathrm{MoS}}_{2}$, graphite, h-BN, and mica by combining a two-dimensional friction force microscope technology and a two-dimensional friction model. We found that the friction force of most atomically flat surfaces is anisotropic, the total force on the tip misaligns with the scan direction, and the friction anisotropy vanishes under low sliding velocity. Our two-dimensional friction model explains experimental observations. It reveals the existence of elemental hopping combinations and the isotropic component in total friction. The misalignment angle can be used to calculate the ratio of anisotropic and isotropic friction components and the ratio of resistance forces from different lattice directions. The separation of anisotropic and isotropic friction forces will offer an avenue for studying the properties of individual friction components, which can boost the study of friction mechanisms in the future and benefit the application of solid lubricants.

The operation and accuracy of industrial robotic arms can be negatively affected by significant fluctuations in friction forces within their joints, potentially resulting in financial and operational losses. To mitigate these issues, an online model-free reinforcement learning controller specifically designed to handle high variations in joints’ friction forces. To the best of our knowledge this is the first time where reinforcement learning controller is used to handle high friction variations in a robotic arm. Initially, the dynamic equations of the robotic arm are derived, verified and validated to ensure an accurate representation of real-world behaviour. The stability of the closed-loop system is analyzed using the Lyapunov second method. The performance of the proposed controller in terms of position tracking is compared against four commonly used controllers found in literature for similar applications: (i) nonlinear model-based computed torque controller, (ii) proportional-derivative controller, (iii) adaptive iterative learning controller and (iv) radial basis function neural network adaptive controller. Simulation results demonstrate that the reinforcement learning controller outperforms the other controllers in terms of tracking performance, even in the presence of significant variations in joint friction forces.

Using molecular dynamics simulations and a coarse-grained model of ionic liquids (ILs), we study mechanisms of electrotunable friction measured in friction force microscopy experiments, where only one layer of IL is present between the tip and the electrode (substrate). We show that the variation of the friction force with the electrode surface charge density is determined by the regime of motion of the confined IL relative to the substrate and tip. The latter depends on the strengths of the ion–substrate and ion–tip interactions and on the commensurability between the characteristic ion dimensions and lattice spacings of the substrate and tip surfaces. Related with those factors, our simulations predict two strictly different scenarios for the variation of the friction force with the electrode surface charge. Revealing mechanisms of frictional energy dissipation in nanoscale IL films offers a way for controlling friction by tuning ion–substrate interactions and electrical polarization of sliding surfaces.

We have used an ultrahigh vacuum atomic-force microscope to study the variation in contact radius and friction with applied force between a silicon tip and a ${\mathrm{NbSe}}_{2}$ sample. The data are compared to the Maugis-Dugdale theory, which is the appropriate continuum mechanics model for the properties and size of the tip-sample contact. The lateral stiffness of the tip-sample contact is related to the radius of the tip-sample contact through the shear moduli of the materials and we have used this relationship to measure directly the variation in contact radius with applied load. The contact radius measured in this way is found to be in agreement with the Maugis-Dugdale theory using the bulk values of the shear moduli. We also measured the variation in friction force with applied load using the same silicon tip. The variation in friction force with applied normal force is found to follow the variation of the contact area as predicted by the Maugis-Dugdale theory [D. Maugis, J. Colloid Interface Sci. 150, 243 (1992)], which supports the hypothesis that for a single asperity contact, the frictional shear stress \ensuremath{\tau} is constant. The value of the shear stress is found to be \ensuremath{\tau}\ensuremath{\approx}6\ifmmode\times\else\texttimes\fi{}${10}^{8}$ N/${\mathrm{m}}^{2}$, which is comparable to the estimated theoretical shear strength of ${\mathrm{NbSe}}_{2}$.

Presented paper concerns a new mathematical form of stochastic theory of hydrodynamic friction forces occurring on the real cooperating surfaces in computer micro bearing fan and computer microbearing in hard disc driver HDD. This paper presents particularly a new-review of stochastic analytical considerations realized by the authors for friction forces estimation during hydrodynamic lubrication performed on the ground of the measurements of the gap height between two roughness surfaces. After numerous experimental measurements directly follows that the random unsymmetrical increments and decrements of the gap height of computer microbearings have important influence on the load carrying capacities and finally on the friction forces and wear of cooperating surfaces. The main topic demonstrates the influence of the variations of expectancy values and standard deviation of the computer microbearing gap height on the friction forces occurring in the HDD and microbearing fan. Moreover, it is observed the evident connection between the apparent dynamic viscosity and the features of the microbearing superficial surface. Hence after abovementioned remarks follows the corollary that the influence of the microbearing gap height stochastic variations connected with the surface roughness tend moreover indirect from the apparent viscosity into the friction forces variations. The synthetic, complex elaboration of obtained results indicates finally the influence of the random roughness in micro and nano level of microbearing surfaces on the friction forces distribution. A new results contained in this paper are obtained taking into account 3D variations of dynamic viscosity of the non-Newtonian lubricant, particularly variations crosswise the film thickness and influences of surface superficial layer features on the lubricant apparent viscosity.

A three-dimensional model of a Cold Gas Dynamic Spray system with a peripheral nonaxisymmetric powder feeder is studied in this work. It is found that the stagnation pressure alternates for different substrate standoff distances due to the nature of the supersonic flow interaction with the substrate. One can find the optimum substrate location for any given operating condition, which results in minimum pressure buildup on the substrate. The three-dimensional analysis sheds more light on the complex gas and particle flow fields generated due to the three-dimensional particle injection process. In addition, the three-dimensional model allows us to further investigate the effect of practical substrate shapes (such as convex and concave) on the flow field and consequently to determine the optimum conditions to deposit coating particles.

Friction-type reinforcing members(FRM) to enhance the resistance to wind loads of a transmission tower through both stiffness strengthening and damping increase are energy dissipation devices that utilize bending deflection of a tower leg. In this paper, the hysteretic behavior of the transmission tower structure with FRMs was experimentally investigated through cyclic loading tests on a half scale substructure model. Firstly, the variation of friction forces and durability of the FRM depending on the type of friction-inducing materials used in the FRM were examined by performing the cyclic loading tests on the FRM. Secondly, cyclic loading tests of a half-scale two-dimensional substructure model of a transmission tower with FRMs were conducted. Test results show that the FRM, of which desired maximum friction force is easily regulated by adjusting the amplitude of the torque applied to the bolts, have stable hysteretic behaviors and it is found that there exists the optimum torque depending on a design load by investigating the amount of energy dissipation of the FRMs according to the increase of torque.

Coarse-grained, metallic materials undergo microstructure refinement during tribological loading. This in turn results in changing tribological properties, so understanding deformation under tribological load is mandatory when designing tribological systems. Single-trace experiments were conducted to understand the initiation of deformation mechanisms acting in various tribological systems. The main scope of this work was to investigate the influence of normal and friction forces as well as crystal orientations on the dominating deformation mechanism in a face-centred cubic concentrated solid solution. While varying the normal force is easily realised, varying friction forces were achieved by using several counter body materials paired against CoCrFeMnNi. The subsurface deformation layer was either mediated through dislocation slip or twinning, depending on the grain orientation and on the tribological system. A layer dominated by dislocation-based deformation is characterised by lattice rotation, the formation of a dislocation trace line or subgrain formation. Such behaviour is observed for tribological systems with a low friction coefficient. For systems dominated by deformation twinning, three types of twin appearance were observed: small twins interacting with the surface, large twins and grains with two active twin systems. Two different twinning mechanisms are discussed as responsible for these characteristics.

A high velocity accessory for friction force microscopy measurements for velocities up to the mm/s range was developed for a commercial stand-alone atomic force microscope (AFM). The accessory consists of a shear piezo element, which rapidly displaces the sample in the lateral direction, perpendicular to the main axis of the AFM cantilever. Friction forces, which are acquired via conventional optical beam deflection detection, can thus be measured as a function of velocity and load in controlled environment (0–40% relative humidity and 0–40°C). Using the accessory, a broad range of velocities up to several mm/s can be accessed independent of the lateral scan size up to a maximum scan size of 1000nm. The velocity dependence of friction forces and coefficients was measured on organic [poly(methylmethacrylate)], as well as inorganic [oxidized Si(100)] samples to demonstrate the feasibility and underline the importance of high velocity nanotribology using this accessory.

The friction between a hard steel indenter and a soft elastomer is studied experimentally. To investigate the influence of roughness, a series of experiments was conducted utilizing an indenter with varying degrees of surface roughness. There is a strong adhesive interaction between the contacting bodies and the friction force is proportional to the real contact area. It has been shown that as the amplitude of roughness increases, the friction force initially rises due to the deformable elastomer filling the gaps between the roughness features, thereby increasing the real contact area. An increase in the roughness amplitude results in a more regular dependence of the friction force on the tangential displacement of the indenter. High-amplitude roughness prevents the propagation of elastic deformation waves (Schallamach waves) within the contact, which are responsible for the establishment of a “stick–slip” type of friction regime. The results of this study are of interest for technical applications in mechanical engineering, particularly those involving the production of rubber seals.