Dry Friction Contact Research Articles

Aging of the frictional properties induced by temperature variations

The dry frictional contact between two solid surfaces is well known to obey Coulomb friction laws. In particular, the static friction force resisting the relative lateral (tangential) motion of solid surfaces, initially at rest, is known to be proportional to the normal force and independent of the area of the macroscopic surfaces in contact. Experimentally, the static friction force has been observed to slightly depend on time. Such an aging phenomenon has been accounted for either by the creep of the material or by the condensation of water bridges at the microscopic contact points. By studying a toy model, we show that the small uncontrolled temperature changes of the system can also lead to a significant increase of the static friction force.

Hybrid, Multiresolution Wires with Massless Frictional Contacts

We describe a method for the visual interactive simulation of wires contacting with rigid multibodies. The physical model used is a hybrid combining lumped elements and massless quasistatic representations. The latter is based on a kinematic constraint preserving the total length of the wire along a segmented path which can involve multiple bodies simultaneously and dry frictional contact nodes used for roping, lassoing, and fastening. These nodes provide stick and slide friction along the edges of the contacting geometries. The lumped element resolution is adapted dynamically based on local stability criteria, becoming coarser as the tension increases, and up to the purely kinematic representation. Kinematic segments and contact nodes are added, deleted, and propagated based on contact geometries and dry friction configurations. The method gives a dramatic increase in both performance and robustness because it quickly decimates superfluous nodes without loosing stability, yet adapts to complex configurations with many contacts and high curvature, keeping a fixed, large integration time step. Numerical results demonstrating the performance and stability of the adaptive multiresolution scheme are presented along with an array of representative simulation examples illustrating the versatility of the frictional contact model.

A 2D Lumped Parameter Model for Prediction of Temperature in C/C Composite Disk Pair in Dry Friction Contact

In applications involving substantial friction, surface failure is an inevitable phenomenon. Friction induced failure typically involves the generation of considerable heat. Existence of significant frictional force leads to relatively high interface temperature as a result of dynamic nature of flash temperatures at the contact areas. A first step in predicting friction induced failure is to develop an accurate thermomechanical model of the friction system. A thermomechanical model is developed in this paper based on a lumped parameter representation of a two-disk brake. A disk is viewed as consisting of three main regions: (1) the surface contact, (2) the friction interface, and (3) the bulk. The lumped parameter model is obtained by dividing a disk into a number of concentric rings and stacked layers. The friction layer contains both the interface and contact elements, each includes the equivalent thermal capacitance and conductive resistance. The contact capacitance and resistance are described in terms of the elastic contact interaction between the surfaces of the two disks. Therefore, they are obtained using the Greenwood and Williamson model for contact of rough surfaces. Each is described as a statistical summation of the micron-scale interaction of the surfaces.

Short-Time Dynamics of Frictional Strength in Dry Friction

We present an experimental study of the onset of local frictional motion along a long, spatially extended interface that separates two PMMA blocks in dry frictional contact. At applied shear forces significantly below the static friction threshold, rapid precursory detachment fronts are excited, which propagate at near sound speeds along the interface. These fronts initiate from the interface edge and arrest prior to traversing the entire sample length. Along the fronts’ path, we perform real-time measurements of the real contact area at every spatial point within the interface. In addition, the motion (slip) of the material adjacent to the interface is simultaneously measured at chosen locations. Upon their arrival at each spatial point along their path, these fronts instantaneously (within 4 μs) reduce the net contact area. Net slip is only initiated after this contact area reduction occurs. Slip is initially rapid and progresses at its initial velocity for a constant (60 μs) duration. Slip dynamics then undergo a sharp transition to velocities an order of magnitude slower, which remain nearly constant until slip arrest. We demonstrate that this scenario can be quantitatively explained by a model of interface weakening caused by instantaneous fracture-induced heating. Sustained rapid slip occurs in this weakened phase. Once the interface cools beneath its glass temperature the sharp transition to slow slip takes place. A similar fracture-induced weakening scenario might be expected in additional classes of materials.

Control of hysteretic instability in rotating machinery by elastic suspension systems subject to dry and viscous friction

Most of the undesired whirling motions of rotating machines can be efficiently reduced by supporting journal boxes elastically and controlling their movement by viscous dampers or by dry friction surfaces normal to the shaft axis, which rub against the frame. In the case of dry dampers, resonance ranges of the floating support configuration can be easily cut off by planning a motionless adhesive state of the friction surfaces. On the contrary, the dry friction contact must change automatically into sliding conditions when the fixed support resonances are to be feared. Moreover, the whirl amplitude can be restrained throughout the speed range by a proper choice of the suspension-to-shaft stiffness ratio and of the support-to-rotor mass ratio. This theoretical research deals firstly with the natural precession speeds and looks for Campbell plots in dependence on the shaft angular speed, for several rotor-suspension systems. Then, the steady response to unbalance is investigated, in terms of rotor and support orbits and of conical path of the rotor axis. In this search, the ranges of adhesive or sliding contact are identified in particular for system with dry friction damping. At last, the destabilizing influence of the shaft hysteresis in the supercritical regime is focalized and the counterbalancing effect of the other dissipative sources is verified. In the nonlinear case of dry friction dampers, the control of linear stability is fulfilled by a perturbation procedure, checking the magnitude of Floquet characteristic multipliers on the complex plane. Moreover, the nonlinear stability far from steady motion is tested by the direct numerical solution of the full motion equations. The comparison configuration of suspension systems with viscous dampers and no dry friction is examined through an analytical first approximation approach and closed-form results for stability thresholds are derived in particular for the symmetric case.

A MESHLESS METHOD ANALYSIS OF ELASTO-PLASTIC CONTACT PROBLEMS WITH FRICTION

We present a theoretical and numerical analysis of incremental elasto-plastic problems based on the meshless method and the mathematical programming. This study is done on an elasto-plastic material with isotropic hardening obeying to the von Mises criterion. The transformation method is adopted to impose the essential boundary condition. The Coulomb's dry friction contact is used to implement the frictional boundary conditions and is formulated by the bipotential method which leads to only one principle of minimum in displacement. The numerical analysis results obtained by the method proposed in this paper are in good agreement with those obtained by FEM.

Development of Al 2O 3 based ceramics for dry friction systems

Increasing requirements for friction systems such as smaller dimensions and greater power transmission lead to enhanced power density in dry frictional contact. Present organic based materials will be overloaded due to severe conditions and new friction materials are needed maybe on the basis of advanced ceramics. In the present study, ceramic composites were produced by embedding TiN particles into the surface of a commercial monolithic Al 2O 3 ceramic using a laser-assisted process. In this way multiphase microstructures were achieved in a surface layer of about 300 μm thickness. Tribological performance of the ceramic composites was studied in a pellet-on-disc tribometer by running consecutive short-time tests as function of the counterbody material, sliding speed, humidity and temperature. The results showed a substantially improved stability of friction coefficient compared with the monolithic alumina used for reference.

Wavelet Analysis of Stick-Slip Signals in Oscillators With Dry-Friction Contact

Wavelet transforms were compared between various simulated friction models and real stick-slip data. While simulations of several models produced stick-slip transition oscillations seen in the real data, the wavelet features of the compliant contact model with light damping best captured the characteristics of the experimental signal. The wavelet contours were also used to estimate the contact stiffness.

Modeling and Dynamics of Friction Wedge Dampers in Railroad Freight Trucks

A mechanical model for the vertical response of the bolster and friction-wedge suspension elements in a railroad freight truck is developed. The model incorporates linear stiffnesses and dry friction contact between rigid elements. Numerical bifurcation diagrams for sticking events, obtained for parameterizations of the amplitude and frequency of a harmonic track excitation, and for various friction laws, reveal distinct parameter-dependent dynamic responses: strongly nonlinear stick-slip oscillations, observed away from period-1 resonance; and weakly nonlinear, nearly harmonic responses, observed near the period-one resonance. The analytical method of harmonic balance is applied to develop a first order approximation for the period-1 response, and, as should be expected, is found to correspond well with the numerical results in the large amplitude limit and near the resonance location. Given that such weakly nonlinear, large amplitude, period-1 responses are not common for the speeds and system parameters of most freight vehicles, we conclude that friction-wedge models based on some form of equivalent linearization may be inadequate for simulating freight car dynamics in many cases of practical importance.

Numerical investigations into static and quasistatic problems of two-dimensional dry elastic frictional contact

A numerical-modelling method is developed to investigate the stress of the static-equilibrium state of the two-dimensional frictional contact problem achieved through a quasistatic process of increasing loading. The problem of relative tangential displacement between particles on the two contact surfaces is addressed. This scheme relies on solving each of the two contact solids in turn and iterating back and forth. The solutions for the two elastic bodies are connected through the surface traction and surface deformation. The contact surface is approximated by a cubic spline, and friction is modelled using the classical Coulomb friction law. Variational inequalities and finite-element methods are used to implement this scheme and are solved by an optimization method. In addition, the distinction between Cauchy stress and Piola–Kirchoff stress is taken into account and discussed. A numerical investigation is conducted into the stress dependence on the loading conditions and geometries of the solids. The results from the numerical examples deviate from Hertz theory and previous reports. Stress is shown to be sensitive to the loading distribution and geometry of contact solids. Therefore, it suggests that an accurate analysis of the dry frictional contact problem requires a refined knowledge of the loading conditions and the total geometry of both solids.PACS Nos.: 03.40D, 46.30P, 62.20P

Numerical analysis of a one-dimensional elastodynamic model of dry friction and unilateral contact

This paper deals with a numerical analysis of a one-dimensional dynamic purely elastic (i.e. hyperbolic) model with dry friction. Since we consider a Coulomb friction law with a slip velocity dependent coefficient, generally, the problem has more than one solution. A mass perturbation approach is developed to regain the uniqueness and to perform the numerical analysis. This study can be viewed as a first step in the numerical analysis of more elaborated dynamic purely elastic problems with dry friction.

The bipotential method: A constructive approach to design the complete contact law with friction and improved numerical algorithms

Nowadays, the concept of convex potential of dissipation is a powerful tool customarily used to model the constitutive dissipative laws. Unfortunately, it fails when applied to Coulomb's dry friction contact, which is shown in this paper by checking the cyclic monotony condition. Next, a new approach, the bipotential method, is presented and successfully applied to the contact law. This enables us to write it in a compact form and to uncover an implicit normality rule structure. The advantages of the new approach are numerous, among which is emphasized a pretty extension of the calculus of variation. Two minimum principles of the so-called bifunctional are presented for contact problems. Next, the bipotential method can be qualified as constitutive in the sense that it suggests improved numerical algorithms. In particular, it is proved that the complete contact law can be rewritten as a projection equation onto Coulomb's cone. Numerical examples show the feasibility of the algorithm and the computer time reduction with respect to other previous numerical approaches.

INVESTIGATIONS OF LOW FREQUENCY STICK–SLIP MOTION: EXPERIMENTS AND NUMERICAL MODELLING

Dry frictional contact between two steel surfaces in a harmonically forced spring–mass system is investigated both experimentally and numerically. The experimental set-up is somewhat novel in that the spring–mass system is excited through the frictional interface, facilitating detailed study of interactions between the system's dynamic characteristics and the stick–slip motion observed at the interface. A characterization of the effect of wear upon observed stick–slip is given, resulting in the identification of three sliding regimes displaying varying degrees of wear. Subsequent attention is focused primarily on the first of these regimes, the low wear regime, which features low frequency stick–slip oscillations that can be measured quite reliably. This work particularly emphasizes the nature of transients entering and exiting stick phases, with several representations given of the evolution of these transients as control parameters are changed. Multiperiod and chaotic motions of the mass are also observed, with routes to chaos being qualitatively similar for a wide range of system parameters. The work also presents some numerical results in support of the experimental work, utilizing a rate- and state-dependent friction model proposed previously by the authors. It is seen that this model yields significantly better predictions than can a simple Coulomb representation.

Vibration monitoring in sliding wear of plasma sprayed ceramics

Dry frictional contact between two surfaces, one made of plasma sprayed ceramic coatings of Al 2O 3 and Al 2O 3TiO 2 combination and the other made of steel, is analyzed. The experiments were conducted using a pin-on-disc set-up in the load range of 5–35 N and for sliding distances up to 14 km. The interactions between friction, wear and vibrations due to influence of normal load, sliding speed and system dynamics are investigated in the present paper. Two vibration parameters of pin in the load direction (vertical) are monitored, namely the r.m.s. acceleration and the kurtosis, which seem to be influenced considerably by the wear process and indicate correlation with wear mechanisms taking place such as stick-slip and grain pull-out, as evidenced by scanning electron microscopy of worn surfaces. The study shows that a range of frequency is to be utilized for vibration monitoring to include natural frequencis of the system consisting of pin in contact with disc. This could be estimated by a standard impulse hammer test. The pin acceleration decreases with increase in load and sliding distance, but with respect to sliding speed, the vibration level intially decreases but increases beyond the sliding speed of 1.5 m s −1. Among the three ceramic coatings, TiO 2 is found to be most wear resistant, exhibiting the lowest friction coefficient and a low vibration level. Variation in kurtosis with run-in wear indicates smoothing of Al 2O 3 due to grain pull out.

Dynamic Surface Solutions in Linear Elasticity and Viscoelasticity With Frictional Boundary Conditions

This paper presents a study on the dynamic stability of the steady frictional sliding of a linear elastic or viscoelastic half-space compressed against a rigid plane which moves with a prescribed nonvanishing tangential speed. The system of differential equations and boundary conditions that govern the small plane oscillations of the body about the steady-sliding state of deformation is established. It is shown that for large coefficient of friction and large Poisson’s ratio the steady-sliding of the elastic body is dynamically unstable. This instability manifests itself by growing surface oscillations which necessarily propagate from front to rear and which in a short time lead to situations of loss of contact or stick. Similarly to what has been found with various finite dimensional frictional systems, these flutter type surface instabilities result from the intrinsic nonsymmetry of dry friction contact laws. The effect of viscous dissipation within the deformable body is also assessed: when viscous dissipation is present larger coefficients of friction are required for the occurrence of surface solutions propagating and growing from front to rear.

Interactions Among Friction, Wear, and System Stiffness—Part 1: Effect of Normal Load and System Stiffness

Dry frictional contact between two metallic surfaces, one cast iron and the other steel, is analyzed. The experiments were conducted using a pin-on-disk setup instrumented with force and acceleration transducers. The interactions between friction, wear, and vibrations and their dependence on normal load and system stiffness are investigated. The results indicate that stiffness has a significant effect on the normal load at which transition takes place from mild to severe friction and wear. The variation of surface roughness with normal load for different stiffnesses is also examined. The different regimes of friction are observed, as the normal load is increased. They are characterized as steady state friction region, nonlinear friction region, region of transient friction with disturbances and region of self-excited vibrations. It is shown that the transition from the steady-state friction can be characterized by a sudden increase in the coefficient of friction and amplitude of slider oscillations.

Some aspects of improving abrasive resistance

A survey of literature on the structural and phase strengthening of alloys and steel is presented. Methods of strengthening such as mechanical riveting and expanding the length of intergrain boundaries do not increase abrasive wear resistance to hard particle attack. Alloying to increase the interatomic bond forces does not increase abrasive wear resistance. Thus there is a close connection between the modulus of normal elasticity of different metals and the wear resistance. The sharp decrease in dislocation mobility at the brittle transition temperature increases abrasive wear resistance. For a high carbon steel the resistance increases by a factor of 2.5. Increased resistance to attack by abrasive particles (by a factor of 2) can be achieved by preliminary friction treatment of the steel surface (especially by dry frictional contact against low carbon steel) because of the complex phase and structural transformations in the material of the surface that is subjected to frictional contact.

Non-linear analysis of stick/slip motion

The steady state relative motion of two masses with dry (Coulomb) friction contact is investigated. The bodies are assumed to have the same mass and stiffness and are subjected to harmonic excitation. By means of a combined analytical—numerical procedure, results are obtained for arbitrary values of Coulomb friction, excitation frequency, and natural frequencies of the bodies. For certain values of these parameters, multiple lockups per cycle are possible. In this respect, the problem investigated here is a natural extension of the one considered by Den Hartog, who in obtaining his closed form solution assumed a maximum of two lockups per cycle.

Surface Temperatures at Unlubricated Sliding Contacts

This is a theoretical paper concerned with the rise in the surface temperatures caused by frictional heating at sliding contacts. By taking into account in the theoretical model, the growth of junctions between contacting asperities due to the action of the friction force, a large improvement in the correlation with experimental surface temperature measurements at dry friction contacts has been obtained. These results are felt to support the use of the usual flash temperature technique for predicting the surface temperatures in lubricated or low friction conditions.