Identification of Iwan distribution density function in frictional contacts

Mechanical contacts affect structural responses, causing localized nonlinear variations in the stiffness and damping. The physical behaviors of contact interfaces are quite complicated and almost impossible to model at the micro-scale. In order to establish a meaningful understanding of the friction effects and to predict the contact behavior, a robust parametric friction model is usually employed. This paper employs an Iwan-type model to predict the nonlinear effects of a frictional contact interface. The Iwan model is characterized by its distribution density function which is commonly identified by double differentiation of the experimentally obtained joint interface restoring force. Direct measurement of restoring forces at the contact interface is impractical and estimating it using an inverse approach introduces considerable uncertainties in identification of the density function. This paper develops a more reliable procedure in identification of the Iwan model by relating the density function to the joint interface dissipated energy. The energy dissipated in a contact interface is easily obtained from measurement and it is shown that the dissipation is uniquely defined using the density function and the vibration amplitude. In an experimental case study Iwan distribution density function in a frictional contact is obtained using measured dissipations at different vibration levels.     

Frictional dissipation in stick-slip sliding

The time variation of the frictional force between two surfaces, undergoing stick-slip sliding across a molecularly thin film of a confined model liquid, was examined at high time and force resolution, showing clearly that dissipation of energy occurs both during the slip, and at the instant of stick (via transfer of residual momentum). Detailed analysis indicates that, in marked contrast to earlier suggestions, of order 90% or more of the dissipation occurs by viscous heating of the confined shear-melted film during the slip, and only a small fraction of the energy is dissipated at the instant of stick.     

Stick-slip friction and energy dissipation in boundary lubrication

Shearing of a simple nonpolar film, right after the liquid-to-solid phase transition under nanometer confinement, is studied by using a liquid-vapor molecular dynamics simulation method. We find that, in contrast with the shear melting and recrystallization behavior of the solidlike phase during the stick-slip motion, interlayer slips within the film and wall slips at the wall-film interface are often observed. The ordered solidified film is well maintained during the slip. Through the time variations of the frictional force and potential energy change within the film, we find that both the friction dissipation during the slip and the potential energy decay after the slip in the solidified film take a fairly large portion of the total energy dissipation.     

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.     

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.     

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.     

Dynamics of a 3dof torsional system with a dry friction controlled path

A three-degrees of freedom semi-definite torsional system representing an automotive driveline is studied in presence of a torque converter clutch that manifests itself as a dry friction path. An analytical procedure based on the linear system theory is proposed first to establish the stick-to-slip boundaries. Smoothened and discontinuous Coulomb friction formulations are then applied to the nonlinear system, and the differential governing equations are numerically solved given harmonic torque excitation and a mean load. Time domain histories illustrating dry friction-induced stick–slip motions are predicted for different saturation torques and system parameters. Approximate analytical solutions based on distinct states are also developed and successfully compared with numerical studies. Analysis shows that the conditioning factor associated with the smoothened friction model (hyperbolic tangent) must be carefully selected. Then nonlinear frequency responses are constructed from cyclic time histories and the stick–slip boundaries predictions (as yielded by the linear system theory) are confirmed. In particular, the effect of secondary inertia is analytically and numerically investigated. Results show that the secondary inertia has a significant influence on the dynamic response. A quasi-discontinuous oscillation is found with the conventional bi-linear friction model in which the secondary inertia is ignored. Finally, our methods are successfully compared with two benchmark analytical and experimental studies, as available in the literature on two-degrees of freedom translational systems.     

Frictional shear cracks

We discuss crack propagation along the interface between two dissimilar materials. The crack edge separates two states of the interface, “stick” and “slip.” In the slip region, we assume that the shear stress is proportional to the sliding velocity; i.e., the linear viscous friction law is valid. In this picture, the static friction appears as the tile Griffith threshold for crack propagation. We calculate the crack velocity as a function of the applied shear stress and find that the main dissipation comes from the macroscopic region and is mainly due to the friction at the interface. The relevance of our results to recent experiments, Baumberger et al., Phys. Rev. Lett. 88, 075509 (2002), is discussed.     

Simulation of frictional energy dissipation in a fiber contact subjected to normal and tangential oscillation

This paper presents a numerical study on the frictional contact between two crossed fibers subject to both normal and tangential oscillation. The results from simulation using the method of dimensionality reduction show that the frictional energy dissipation increases firstly with coefficient of friction, and then almost symmetrically decreases to a constant. The fiber aspect ratio has an important effect on the energy dissipation and this effect becomes more significant for larger coefficient of friction. The simulation results for very large coefficient of friction show a good agreement with the analytical solution for the case of infinite coefficient of friction.     

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.     

Influence of velocity in nanoscale friction processes

Force-microscopy images of boric acid crystals were obtained experimentally and simulated with the use of a two-dimensional mechanical model. An analysis of the stick and slip movement of the microscope tip shows that the energy-dissipation mechanism is strongly influenced by the non-linear dynamics of the sliding system. The contributions of stick and viscous forces on the energy dissipation (or friction forces) are studied as a function of the relative scanning velocity. At low relative velocities, the stick forces are shown to be responsible for the energy dissipation. This energy is velocity-dependent, due to the coupling between the two degrees of freedom of the sliding system. As the scanning velocity increases the stick forces are damped; the viscous force is then predominant in the energy-dissipation process. Received: 30 October 2001 / Accepted: 17 May 2002 / Published online: 22 November 2002 RID="*" ID="*"Corresponding author. Fax: +55-21/2295-9397, E-mail: prioli@vdg.fis.puc-rio.br     

An analytical particle damping model

Particle damping is a passive vibration control technique where multiple auxiliary masses are placed in a cavity attached to a vibrating structure. The behavior of the particle damper is highly non-linear and energy dissipation, or damping, is derived from a combination of loss mechanisms. These loss mechanisms involve complex physical processes and cannot be analyzed reliably using current models. As a result, previous particle damper designs have been based on trial-and-error experimentation. This paper presents a mathematical model that allows particle damper designs to be evaluated analytically. The model utilizes the particle dynamics method and captures the complex physics involved in particle damping, including frictional contact interactions and energy dissipation due to viscoelasticity of the particle material. Model predictions are shown to compare well with test data.     

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.     

Experimental and numerical investigation of friction-induced vibration of a beam-on-beam in contact with friction

The vibrations generated by friction are responsible for various noises such as squealing, squeaking and chatter. Although these phenomena have been studied for a long time, it is not well-understood. In this study, an experimental and numerical study of friction-induced vibrations of a system composed of two beams in contact is proposed. The experimental system exhibits periodic steady state vibrations of different types. To model and understand this experimental vibratory phenomenon, complex eigenvalue and dynamic transient analyses are performed. In the linear complex eigenvalue analysis, flutter instability occurs via the coalescence of two eigenmodes of the system. This linear study provides an accurate value of the experimental frequency of vibration. To understand what happens physically during friction-induced instability, a dynamic transient analysis that takes account of the non-linear aspect of a frictional contact is performed. In this analysis, friction-induced instability is characterized by self-sustained vibrations and by stick, slip and separation zones occurring at the surface of the contact. The results stemming from this analysis show that good correlation between numerical and experimental vibrations can be obtained (in time and frequency domains). Moreover, time domain simulations permit understanding the physical phenomena involved in two different vibratory behaviours observed experimentally.     

Interface stress effect tuning and enhancing the energy dissipation of staggered nanocomposites

ABSTRACT

Natural biological composites and artificial biomimetic staggered composites with nanoscale internal structures can exhibit extraordinary energy dissipation, compared with conventional composites. It is believed that the interface stress effects of the interfaces between hard platelets and a viscous matrix play an important role in the extraordinary damping properties of such nanocomposites. In this study, a viscoelastic model is established to investigate the mechanism of the influence that the interface stress effect has on the damping properties, based on the Gurtin-Murdoch interface model and the tension-shear chain model. An explicit analytical solution of the effective dynamic moduli characterising the damping properties is obtained by using the correspondence principle, which is also validated by comparison with a finite element analysis. From the obtained analytical solution, an interface factor is abstracted to characterise the synergistic effect of the feature size and material parameters on the damping properties. Based on the model established, the optimal size of the platelets and the optimal loading frequency can be designed to achieve superior energy dissipation, when the staggered nanocomposites bear the dynamic load. Therefore, the findings of the present study not only reveal the damping mechanism of biological structures at nanoscale but also provide useful guidelines for the design of biomimetic nanocomposites from the nanoscale to the macroscopic scale.     

Vibration damping in bolted friction beam-columns

In this paper we examine the use of dynamic friction within a bolted structure to improve damping properties of the structure. The structure considered for this paper consists of two steel beam-columns bolted together allowing dynamic friction to occur at the interface. This paper presents an analysis of the behaviour of the structure and the effect of friction on its dynamics. It also presents an analysis of the energy dissipation in the structure by means of friction and the optimization of the bolt tension in order to dissipate the maximum vibration energy. We define analytical expressions for the vibration behaviour before and after slip occurs as well as the condition at which the slip-stick transition occurs. An experiment, in which the measurements of the bolt tension, the slip within the structure and the bending velocity are made, is used to validate the model. The theoretical analysis gave very close agreement with the experimental results and the effective damping of the structure was increased by a factor of approximately 10 through the use of dynamic friction.     

In situ observation of interfacial debonding process induced by matrix crack propagation in two-dimensional unidirectional model composites

Interfacial debonding behavior is studied for unidirectional fiber reinforced composites from both experimental and analytical viewpoints. A new type of two-dimensional unidirectional model composite is prepared using 10 boron fibers and transparent epoxy resin with two levels of interfacial strength. In situ observation of the internal mesoscopic fracture process is carried out using the single edge notched specimen under static loading. The matrix crack propagation, the interfacial debonding growth and the interaction between them are directly observed in detail. As a result, the interfacial debonding is clearly accelerated in specimens with weakly bonded fibers in comparison with those with strongly bonded fibers. Secondary, three-dimensional finite element analysis is carried out in order to reproduce the interfacial debonding behavior. The experimentally observed relation between the mesoscopic fracture process and the applied load is given as the boundary condition. We successfully evaluate the mode II interfacial debonding toughness and the effect of interfacial frictional shear stress on the apparent mode II energy release rate separately by employing the present model composite in combination with the finite element analysis. The true mode II interfacial debonding toughness for weaker interface is about 0.4 times as high as that for a stronger interface. The effect of the interfacial frictional shear stress on the apparent mode II energy release rate for the weak interface is about 0.07 times as high as that for the strong interface. The interfacial frictional shear stress and the coefficient of friction for weak interface are calculated as 0.25 and 0.4 times as high as those for strong interface, respectively.     

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.