Multimode Active Control of Friction,Dynamic Ratchets and Actuators

Active control of friction by ultrasonic vibration is a well-known effect with numerous technical applications ranging from press forming to micromechanical actuators. Reduction of friction is observed with vibration applied in any of the three possible directions (normal to the contact plane, in the direction of motion and in-plane transverse). In this work, we consider the multi-mode active control of sliding friction, where phase-shifted oscillations in two or more directions act at the same time. Our analysis is based on a macroscopic contact-mechanical model that was recently shown to be well-suited for describing dynamic frictional processes. For simplicity, we limit our analysis to a constant, load-independent normal and tangential stiffness and two superimposed phase-shifted harmonic oscillations, one of them being normal to the plane and the other in the direction of motion. As in previous works utilizing the present model, we assume a constant local coefficient of friction, with reduction of the observed force of friction arising entirely from the macroscopic dynamics of the system. Our numerical simulations show that the resulting law of friction is determined by just three dimensionless parameters. Depending on the values of these parameters, three qualitatively different types of behavior are observed: (a) symmetric velocity-dependence of the coefficient of friction (same for positive and negative velocities), (b) asymmetric dependence with respect to the sign of the velocity, but with zero force at zero velocity, and (c) asymmetric dependence with nonzero force at zero velocity. The latter two cases can be interpreted as a "dynamic ratchet" (b) and an actuator (c).     

Coefficient of friction between a rigid conical indenter and a model elastomer: Influence of local frictional heating

We investigate the coefficient of friction between a rigid cone and an elastomer with account of local heating due to frictional dissipation. The elastomer is modeled as a simple Kelvin body and an exponential dependency of viscosity on temperature is assumed. We show that the coefficient of friction is a function of only two dimensionless variables depending on the normal force, sliding velocity, the parameter characterizing the temperature dependence as well as shear modulus, viscosity at the ambient temperature and the indenter slope. One of the mentioned dimensionless variables does not depend on velocity and determines uniquely the form of the dependence of the coefficient of friction on velocity. Depending on the value of this controlling variable, the cases of weak and strong influence of temperature effects can be distinguished. In the case of strong dependence, a generalization of the classical “master curve” procedure introduced by Grosch is suggested by using both horizontal and vertical shift factors.     

Dependence of the kinetic force of friction between a randomly rough surface and simple elastomer on the normal force

The force of friction between a self-affine fractal rough surface and an elastomer with the simplest linear rheology is simulated with the method of reduction of dimensionality. The coefficient of friction increases with normal force approximately according to logarithmic law.     

What does friction really depend on? Robust governing parameters in contact mechanics and friction

It is known that the coefficient of friction generally depends on a large number of system and loading parameters. Already Coulomb presented experimental evidence that the static coefficient of friction may depend on time, on normal force, on the contact size, on the nature of contacting materials, and on the presence of intermediate lubricant layers. For the sliding coefficient of friction, he observed the dependence on the sliding velocity as well as the force and size dependencies. Later research has shown that the friction coefficient is very sensitive to the presence of oscillations (including self-excited vibrations). In spite of the practical importance of the problem, no generalized laws of friction or empirical procedures for measuring and representing the law of friction have been developed so far, which included at least the following four parameters: contacting body velocity, normal force, shape (and thus implicitly size), and time. In the present paper, we discuss the question of how the dimension of space of governing parameters can be reduced and if a small set of “robust governing parameters” of friction can be identified. We argue that one of such robust governing parameters is the indentation depth (or relative approach) of contacting bodies and discuss further candidates for the role of robust governing parameters.     

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.     

The method of reduction of dimensionality and its application to simulation of elastomer friction under complex dynamic loads

The paper reports on basic ideas of the method of reduction of dimensionality and demonstrates its efficiency in simulation of friction of elastomers having arbitrary linear rheology and a rigid rough surface with fractal relief. The fixation time of elastomer on a rigid surface before the onset of tangential motion is studied as a parameter affecting the static friction coefficient. It is also studied how the friction coefficient in steady-state sliding is affected by harmonic oscillations of normal pressing force.     

Very low friction for natural diamond in water of different pH values

Very high reductions in the friction coefficient are reported for natural diamond sliding upon natural diamond when water is introduced at the interface of contact. This reduction is found to depend on the pH value of the water, the load and the sliding velocity. The results are interpreted in terms of the reduction of adhesion due to adsorption of the liquid on the surface, and of graphitisation occurring during sliding, with graphite acting as a lubricant. Received 15 September 1999     

基于非连续能量耗散的滑动摩擦系数计算模型

分析了界面摩擦状态下能量非连续耗散过程,建立了简化条件下晶体材料界面摩擦滑动摩擦系数计算模型.结果表明:在弹性接触状态下,滑动摩擦系数与载荷及实际接触面积无关,当实际接触面积接近名义接触面积时,滑动摩擦系数随载荷增加而减小.在缓慢滑动时,滑动摩擦系数随滑动速度的增高而缓慢增大,相对滑动速度愈高,滑动摩擦系数增大趋势愈显著.滑动摩擦系数随晶格常数的增加而降低,而当晶格常数较大时,其变化对滑动摩擦系数影响较小.同时,滑动摩擦系数随原子的可能温升增加而增大.研究结论对工程应用及相关的理论研究具有一定的参考意义. 关键词： 滑动摩擦系数 非连续能量耗散 界面摩擦     

Friction and wear of a spherical indenter under influence of out-of-plane ultrasonic oscillations

This paper presents an experimental and theoretical investigation of friction and wear of a spherical indenter. With the pin-on-disc-tribometer the out-of-plane oscillations are applied to the sliding indenter. Oscillations lead to a decrease of the coefficient of friction, and this effect is also related to the sliding velocity and oscillation amplitude. During the sliding movement, the contact area of indenter increases due to the wear of material. This radius of the worn spherical cap is measured after each sliding period. It is found that the radius of the wear flat increases with sliding distance according to a power law with the power 1/4 and is independent of the sliding velocity. It further is practically insensitive to the presence of oscillations. A theoretical analysis and a numerical simulation based on the method of dimensionality reduction are carried out, both describing the experimental data very well.     

The wire drawing process with axial ultrasonic vibration of the die

The influence of ultrasound on the behaviour of metals drawn through a conical converging die has been analysed by means of an energy method. The effect of the ultrasonic field is considered on the basis of experimental data and used to determine the drawing stress, the coefficient of friction, the viscosity coefficient, the drawing velocity effects, the area reduction and the die geometry. Results obtained by the given formulae used to calculate the drawing stress, are in good agreement with the experimental data. A detailed treatment is given for the drawing of aluminium through vibrated die.     

Model of Nanostructuring Burnishing by a Spherical Indenter Taking into Consideration Plastic Deformations

A dynamic model of the nanostructuring burnishing of a surface of metallic details taking into consideration plastic deformations has been suggested. To describe the plasticity, the ideology of dimension reduction method supplemented with the plasticity criterion is used. The model considers the action of the normal burnishing force and the tangential friction force. The effect of the coefficient of friction and the periodical oscillation of the burnishing force on the burnishing kinetics are investigated.     

Study of AFM-based nanometric cutting process using molecular dynamics

Three-dimensional molecular dynamics (MD) simulations are conducted to investigate the atomic force microscope (AFM)-based nanometric cutting process of copper using diamond tool. The effects of tool geometry, cutting depth, cutting velocity and bulk temperature are studied. It is found that the tool geometry has a significant effect on the cutting resistance. The friction coefficient (cutting resistance) on the nanoscale decreases with the increase of tool angle as predicted by the macroscale theory. However, the friction coefficients on the nanoscale are bigger than those on the macroscale. The simulation results show that a bigger cutting depth results in more material deformation and larger chip volume, thus leading to bigger cutting force and bigger normal force. It is also observed that a higher cutting velocity results in a larger chip volume in front of the tool and bigger cutting force and normal force. The chip volume in front of the tool increases while the cutting force and normal force decrease with the increase of bulk temperature.     

Rolling friction for hard cylinder and sphere on viscoelastic solid

We calculate the friction force acting on a hard cylinder or spherical ball rolling on a flat surface of a viscoelastic solid. The rolling-friction coefficient depends non-linearly on the normal load and the rolling velocity. For a cylinder rolling on a viscoelastic solid characterized by a single relaxation time Hunter has obtained an exact result for the rolling friction, and our result is in very good agreement with his result for this limiting case. The theoretical results are also in good agreement with experiments of Greenwood and Tabor. We suggest that measurements of rolling friction over a wide range of rolling velocities and temperatures may constitute a useful way to determine the viscoelastic modulus of rubber-like materials.     

Dynamics of the coefficient of friction between a rigid conical indenter and a viscoelastic foundation under step-wise change of sliding velocity

We numerically calculated the coefficient of friction between a rigid cone and a viscoelastic Kelvin body under step-wise change of the velocity of sliding. The time dependence of the coefficient of friction has been empirically approximated. We show that the transition process has different character for the cases of increasing and decreasing of the sliding velocity.     

A model for the characterization of friction contacts in turbine blades

Stresses produced by the forced vibrations can lead to a significant reduction of the life of turbo engine blades. To predict the vibration amplitudes of this components an accurate dynamic analysis is necessary. The forced response calculation of these dynamic systems is strongly affected by the presence of the contact interfaces (i.e., underplatform dampers, shrouds, root joints). Different contact models are available in literature. These models make use of contact parameters, contact stiffness and friction coefficient to evaluate the damping and stiffness related to the contact interfaces. In this paper a model is proposed to characterize friction contact of non-spherical contact geometries obeying the Coulomb friction law with constant friction coefficient and constant normal load. The hysteresis curves of the oscillating tangential contact forces vs. relative tangential displacements and the dissipated energy at the contact are obtained for different contact geometries. The developed model is suitable to be implemented in numerical solvers for the calculation of the forced response of turbine blades with embedded friction contacts.     

Density inversion in rapid granular flows: the supported regime

This paper presents numerical findings on rapid 2D and 3D granular flows on a bumpy base. In the supported regime studied here, a strongly sheared, dilute and agitated layer spontaneously appears at the base of the flow and supports a compact packing of grains moving as a whole. In this regime, the flow behaves like a sliding block on the bumpy base. In particular, for flows on a horizontal base, the average velocity decreases linearly in time and the average kinetic energy decreases linearly with the travelled distance, those features being characteristic of solid-like friction. This allows us to define and measure an effective friction coefficient, which is independent of the mass and velocity of the flow. This coefficient only loosely depends on the value of the micromechanical friction coefficient whereas the infuence of the bumpiness of the base is strong. We give evidence that this dilute and agitated layer does not result in significantly less friction. Finally, we show that a steady regime of supported flows can exist on inclines whose angle is carefully chosen.     

Static friction of sinusoidal surfaces: a discrete dislocation plasticity analysis

Discrete dislocation plasticity simulations are carried out to investigate the static frictional response of sinusoidal asperities with (sub)-microscale wavelength. The surfaces are first flattened and then sheared by a perfectly adhesive platen. Both bodies are explicitly modelled, and the external loading is applied on the top surface of the platen. Plastic deformation by dislocation glide is the only dissipation mechanism active. The tangential force obtained at the contact when displacing the platen horizontally first increases with applied displacement, then reaches a constant value. This constant is here taken to be the friction force. In agreement with several experiments and continuum simulation studies, the friction coefficient is found to decrease with the applied normal load. However, at odds with continuum simulations, the friction force is also found to decrease with the normal load. The decrease is caused by an increased availability of dislocations to initiate and sustain plastic flow during shearing. Again in contrast to continuum studies, the friction coefficient is found to vary stochastically across the contact surface, and to reach locally values up to several times the average friction coefficient. Moreover, the friction force and the friction coefficient are found to be size-dependent.     

DEM simulation of small particles clogging in the packing of large beads

The percolation of small particles through a periodic random loose packing of large beads is studied numerically with the Distinct Element Method. The representativity of periodic mono-sized sphere packing of varying system size was first studied by comparing their pore size distributions and tortuosities with those of a larger system, considered as an infinite medium. The results show that a periodic packing of size as low as 4-grain diameters gives a reasonable representation of the porous medium and allows reducing considerably the number of particles that has to be used in the simulations. The flow and clogging of small particles of varying concentrations and friction coefficients flowing through the former packing are then studied numerically. Results show that a steady state is rapidly reached where the mean velocity and mean vertical velocity of small particles are both constant. These mean velocities decrease with an increase in friction coefficient and in small particle concentration. The influence of the friction coefficient μ is much less marked for values of μ larger than or equal to 0.5. The distribution of small particles throughout the crossed packing becomes rapidly heterogeneous. Small particles concentrate in some pores where their velocity vanishes and where the density can reach values larger than the density of the random loose packing. The proportion of particles blocked in these pores varies linearly with concentration. Finally, the narrow throats of the porous medium responsible for blocking are identified and characterized for different values of the friction coefficient.     

New Equation for Predicting Pipe Friction Coefficients Using the Statistical Based Entropy Concepts

In general, this new equation is significant for designing and operating a pipeline to predict flow discharge. In order to predict the flow discharge, accurate determination of the flow loss due to pipe friction is very important. However, existing pipe friction coefficient equations have difficulties in obtaining key variables or those only applicable to pipes with specific conditions. Thus, this study develops a new equation for predicting pipe friction coefficients using statistically based entropy concepts, which are currently being used in various fields. The parameters in the proposed equation can be easily obtained and are easy to estimate. Existing formulas for calculating pipe friction coefficient requires the friction head loss and Reynolds number. Unlike existing formulas, the proposed equation only requires pipe specifications, entropy value and average velocity. The developed equation can predict the friction coefficient by using the well-known entropy, the mean velocity and the pipe specifications. The comparison results with the Nikuradse’s experimental data show that the R2 and RMSE values were 0.998 and 0.000366 in smooth pipe, and 0.979 to 0.994 or 0.000399 to 0.000436 in rough pipe, and the discrepancy ratio analysis results show that the accuracy of both results in smooth and rough pipes is very close to zero. The proposed equation will enable the easier estimation of flow rates.     

Influence of the normal force and contact geometry on the static force of friction of an oscillating sample

The paper is devoted to an experimental and theoretical investigation of the static friction force between a rapidly oscillating sample and a steel plate. The static frictional force is studied experimentally as function of the oscillating amplitude, the normal force and the contact geometry. A simplest model of tangent contact with a constant friction coefficient is proposed and shows a good agreement with experiment. The static friction force is proved to be a universal function of the ratio of the oscillation amplitude, the indentation depth and to the friction coefficient.