Micro/macro-slip damping in beams with frictional contact interface

Friction in contact interfaces of assembled structures is the prime source of nonlinearity and energy dissipation. Determination of the dissipated energy in an assembled structure requires accurate modeling of joint interfaces in stick, micro-slip and macro-slip states. The present paper proposes an analytical model to evaluate frictional energy loss in surface-to-surface contacts. The goal is to develop a continuous contact model capable of predicting the dynamics of friction interface and dissipation energy due to partial slips. To achieve this goal, the governing equations of a frictional contact interface are derived for two distinct contact states of stick and partial slip. A solution procedure to determine stick–slip transition under single-harmonic excitations is derived. The analytical model is verified using experimental vibration test responses performed on a free-frictionally supported beam under lateral loading. The theoretical and experimental responses are compared and the results show good agreements between the two sets of responses.     

A numerical study on stick-slip motion of a brake pad in steady sliding

A numerical model for an elastic brake pad sliding under constant load and with constant velocity over a rigid surface is investigated by finite element analysis. The geometry is taken to be two-dimensional, the contact is assumed to follow the laws of continuum mechanics and temporal and spatial resolution are such that dynamical effects localized at the interface are resolved. It turns out that at the contact interface localized slip events occur either in the form of long-lasting slip pulses, or in the form of brief local relaxations. Macroscopically steady sliding, macroscopic stick-slip motion or slip-separation dynamics occurs, depending on the macroscopic relative velocity. While structural oscillations of the brake pad do not seem to play a significant role during steady sliding at least one structural oscillation mode becomes synchronized with the interfacial dynamics during stick-slip or slip-separation motion. Assuming a given friction law for the interface, the macroscopically observed friction coefficient depends considerably on the underlying dynamics on the interface.     

Transverse shear oscillator investigation of boundary lubrication in weakly adhered films

We investigate the boundary lubrication in weakly adhered molecularly thin films deposited between a sphere and a plane, below the sliding threshold. The shear contact stiffness and interfacial dissipation at the micrometer scale are determined with a high-frequency quartz oscillator. Two distinct behaviors are found as a function of the shear oscillation: a linear viscoelastic response at low amplitude and a nonlinear frictional microslip at high amplitude. A friction model is proposed to analyze the data, which allows evaluating the shear strength, the friction coefficient, and the interfacial viscosity at different solid interfaces under low load.     

Atomistic simulations of the lubricative mechanism of a nano-alkane lubricating film between two layers of Cu-Zn alloy

We describe simulations of lubrication by a hexadecane molecular lubricating film during the shearing process of a Cu-Zn alloy performed using the atomistic method. The results indicate that with increasing Zn contents, the interface slip between the alloy wall and the lubricating film first decreases and then increases, according to variations of the radius distribution function (RDF), while the interface slip reaches its lowest value of 0.12 during the shearing of CuZn30 alloy. We also discuss the relationship between interface roughness and the lubricating film. During film lubrication, the interface's roughness effectively inhibits interfacial slip. For the convex contact model, the presence of the hexadecane lubricating film reduces the interfacial contact pressure from 11.9 GPa to 8.7 GPa and the friction coefficient from 0.81 to 0.52.     

A numerical investigation of curve squeal in the case of constant wheel/rail friction

Curve squeal is commonly attributed to self-excited vibrations of the railway wheel, which arise due to a large lateral creepage of the wheel tyre on the top of the rail during curving. The phenomenon involves stick/slip oscillations in the wheel/rail contact and is therefore strongly dependent on the prevailing friction conditions. The mechanism causing the instability is, however, still a subject of controversial discussion. Most authors introduce the negative slope of the friction characteristic as a source of the instability, while others have found that squeal can also occur in the case of constant friction due to the coupling between normal and tangential dynamics. As a contribution to this discussion, a detailed model for high-frequency wheel/rail interaction during curving is presented in this paper and evaluated in the case of constant friction. The interaction model is formulated in the time domain and includes the coupling between normal and tangential directions. Track and wheel are described as linear systems using pre-calculated impulse response functions that are derived from detailed finite element models. The nonlinear, non-steady state contact model is based on an influence function method for the elastic half-space. Real measured wheel and rail profiles are used. Numerical results from the interaction model confirm that stick/slip oscillations occur also in the case of constant friction. The choice of the lateral creepage, the value of the friction coefficient and the lateral contact position on the wheel tread are seen to have a strong influence on the occurrence and amplitude of the stick/slip oscillations. The results from the interaction model are in good qualitative agreement with previously published findings on curve squeal.     

Transition from static to kinetic friction: insights from a 2D model

We describe a 2D spring-block model for the transition from static to kinetic friction at an elastic-slider-rigid-substrate interface obeying a minimalistic friction law (Amontons-Coulomb). By using realistic boundary conditions, a number of previously unexplained experimental results on precursory microslip fronts are successfully reproduced. From the analysis of the interfacial stresses, we derive a prediction for the evolution of the precursor length as a function of the applied loads, as well as an approximate relationship between microscopic and macroscopic friction coefficients. We show that the stress buildup due to both elastic loading and microslip-related relaxations depends only weakly on the underlying shear crack propagation dynamics. Conversely, crack speed depends strongly on both the instantaneous stresses and the friction coefficients, through a nontrivial scaling parameter.     

On the origin of why static or breakloose friction is larger than kinetic friction, and how to reduce it: the role of aging, elasticity and sequential interfacial slip

We discuss the origin of static friction and show how it can be reduced towards kinetic friction by the appropriate design of the sliding system. The basic idea is to use elastically soft solids and apply the external forces in such a way that different parts of the contacting interface start to slip at different times during the (tangential) loading process. In addition, the local slip must be large enough in order to result in a strong drop in the static friction force. We illustrate the theoretical predictions with the results of a simple model experiment.     

Mechanism analysis and improved model for stick-slip friction behavior considering stress distribution variation of interface

Studying the evolution of interface contact state, revealing the "black box" behavior in interface friction and establishing a more accurate friction model are of great significance to improve the prediction accuracy of mechanical system performance. Based on the principle of total reflection, a visual analysis technology of interface contact behavior is proposed. Considering the dynamic variation of stress distribution in interface contact, we analyze the nonlinear characteristics of contact parameters in different stages of stick-slip process using the above-mentioned experimental technology. Then, we find that the tangential stiffness of the interface is not a fixed value during the stick-slip process and the stress distribution variation is one of the important factors affecting the tangential stiffness of interface. Based on the previous experimental results, we present an improved stick-slip friction model, considering the change of tangential stiffness and friction coefficient caused by the stress distribution variation. This improved model can characterize the variation characteristics of contact parameters in different stages of stick-slip process, whose simulation results are in good agreement with the experimental data. This research may be valuable for improving the prediction accuracy of mechanical system performance.     

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.     

Shakedown and induced microslip of an oscillating frictional contact

Using the method of reduction of dimensionality, we calculate the microslip motion of a tangentially loaded frictional contact between an elastic sphere and a rigid base. An oscillating rotation of the sphere with a small amplitude leads to a creep motion of the rigid base. Depending on the amplitude and the tangential force, two possible scenarios may occur. For oscillation amplitudes smaller than a critical value, the rigid body shakes down in the sense that the frictional slip ceases after a limited number of rotation cycles. Otherwise, the rigid base starts to slip with a constant mean velocity, which depends on the static displacement and the rotational amplitude.     

Scaling of dynamic contact angles in a lattice-Boltzmann model

We study the origins of the dynamic contact angle in a two-dimensional lattice-Boltzmann model of immiscible fluids. We show that the dynamic contact angle changes as a function of capillary number as observed in laboratory experiments and explain how this dependence arises in the lattice-Boltzmann model. We also explain how the fluid-fluid interface can move while retaining its shape. The interface has an apparent slip length. The apparent slip follows the classical Navier slipping rule where the velocity of the fluid at the wall is proportional to the viscous stress at the wall. This apparent slip length is proportional to the viscous length scale associated with the spurious flow induced by uncompensated stress at the three-phase contact point.     

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.     

Complete boundary element formulation for normal and tangential contact problems

The boundary element method as a numerical tool in contact mechanics is widely used and allows for surface roughness to be investigated with very fine grids. However, for every two grid points, influence coefficients have to be employed for every force-displacement combination. In this paper, we derive the matrixes of influence coefficients for the deformation of an elastic half space, starting from the classical solutions of Boussinesq and Cerruti. We show how to overcome complexity problems by using FFT-based fast convolution. A comprehensive algorithm is given for solving the case of dry Coulomb friction with partial slip. The resulting computer program can be used effectively in iterative schemes also in similar problems, such as mixed lubrication and notably improves the applicability of the boundary element method in contact mechanics.     

Relationship between the real contact area and contact force in pre-sliding regime

The pre-sliding regime is typically neglected in the dynamic modelling of mechanical systems. However, the change in contact state caused by static friction may decrease positional accuracy and control precision. To investigate the relationship between contact status and contact force in pre-sliding friction, an optical experimental method is presented in this paper.With this method, the real contact state at the interface of a transparent material can be observed based on the total reflection principle of light by using an image processing technique. A novel setup, which includes a pair of rectangular trapezoidal blocks, is proposed to solve the challenging issue of accurately applying different tangential and normal forces to the contact interface. The improved Otsu's method is used for measurement. Through an experimental study performed on polymethyl methacrylate(PMMA), the quantity of contact asperities is proven to be the dominant factor that affects the real contact area. The relationship between the real contact area and the contact force in the pre-sliding regime is studied, and the distribution of static friction at the contact interface is qualitatively discussed. New phenomena in which the real contact area expands along with increasing static friction are identified. The aforementioned relationship is approximately linear at the contact interface under a constant normal pressure, and the distribution of friction stress decreases from the leading edge to the trailing edge.     

Experimental study of different modes of block sliding along interface. Part 2. Field experiments and phenomenological model of the phenomenon

The paper reports the results of field experiments on studying different modes of gravitational sliding of a block on the natural fault surface. Various materials were used as interface filler to model the whole range of deformation events that can be arbitrarily divided into three groups: accelerated creep, slow slip, and dynamic slip. The experiments show that the type of modeled deformation events is defined by both structural parameters of contact between blocks and material composition of the contact filler.Foundations for a new geomechanical model of occurrence of different-type dynamic events were developed. The model is based on the idea that “contact spots” form subnormally to the crack edges during shear deformation; the “spots” are clusters of force mesostructures whose evolution governs the deformation mode. The spatial configuration of “contact spots” remains unchanged during the entire “loading-slip” cycle but changes after the dynamic event occurrence. The destroyed force mesostructures can be replaced by similar structures under intergranular interaction forces when the external influence is fully compensated. Unless “contact spots” are incompletely destroyed, the deformation process dynamics is defined by their rheology. The migration of “contact spots” during deformation of a crack filled with heterogeneous material causes changes in deformation parameters and transformation of the mode itself due to changing rheology of local contact areas between blocks.It is found by fractal analysis that in order for dynamic slip to occur, spatially structured “contact spots” characterized by low fractal dimension must be formed; slow slip events can exist only in a certain parametric domain called the “dome of slow events”. It is found that the probability of slow slip occurrence is higher on fault regions characterized by maximum fractal dimension values: fault tips, fault branching and fault intersection zones.     

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.     

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.     

Effects of partial slip on axisymmetric flow of an electrically conducting viscoelastic fluid past a stretching sheet

The entrained flow of an electrically conducting non-Newtonian, viscoelastic second grade fluid due to an axisymmetric stretching surface with partial slip is considered. The partial slip is controlled by a dimensionless slip factor, which varies between zero (total adhesion) and infinity (full slip). Suitable similarity transformations are used to reduce the resulting highly nonlinear partial differential equation into an ordinary differential equation. The issue of paucity of boundary conditions is addressed, and an effective numerical scheme has been adopted to solve the obtained differential equation even without augmenting the boundary conditions. The important findings in this communication are the combined effects of the partial slip, magnetic interaction parameter and the second grade fluid parameter on the velocity and skin friction coefficient. It is observed that in presence of slip, the velocity decreases with an increase in the magnetic parameter. That is, the Lorentz force which opposes the flow leads to enhanced deceleration of the flow. Moreover, it is interesting to find that as slip increases in magnitude, permitting more fluid to slip past the sheet, the skin friction coefficient decreases in magnitude and approaches zero for higher values of the slip parameter, i.e., the fluid behaves as though it were inviscid.