Intelligent compensation of friction, ripple, and hysteresis via a regulated chatter

In this paper, a hybrid control scheme utilizing a PID feedback control with an additional regulated chatter signal is developed to compensate motion impeding influences such as the effects due to friction, force ripples, and hysteresis in linear piezoelectric motor. The regulated chatter signal is a pulse sequence superimposed on the PID control signal. It has a fixed amplitude, and a pulse width regulated via iterative learning control. As such, the scheme is expected to be useful for applications involving iterative motion sequences. An analysis of the closed-loop performance is presented in the paper. Simulation and experimental results are also furnished to demonstrate that the proposed control scheme can reduce tracking errors significantly.     

Simulation of transient friction of a cylinder between two planes

The need for good friction models for transient motions has increased as a consequence of the increased use of mechatronics and control engineering principles in precision mechanics. The machine elements in such equipment often involve rolling and sliding contacts. Most studies of friction in rolling and sliding contacts running under dry or boundary lubricated conditions have examined steady-state conditions.This paper describes simulations of the motion of a cylinder between two planes, first with a step change in velocity and then with an oscillating motion of the upper plane. The motion of the cylinder is determined by the friction in the contacts and the inertia. The friction in the rolling and sliding contacts is simulated with a brush model. The surfaces are assumed to be ideally smooth.For the step change in velocity, there is initially a period of complete sliding in the upper contact. During the sliding period, the friction force is the maximum possible, but it decreases as the complete sliding ends. The simulations show heavily damped oscillations, with frequencies corresponding to the natural translatory and torsional frequencies of the system. For the oscillating motions the sliding increases with the frequency of the motion, as expected.     

Rubber friction on rough and smooth surfaces

Some rigorous contact mechanics is used in a dynamic stiffness approach to generate a new theory for hysteresis sliding friction on some ideal peak shapes. These were the two- and three-dimensional projections: cylinder, wedge, sphere and cone, configured singly or as a periodic array. The theory is then extended for a ‘single roughness order’ i.e. identical peaks arranged with a randomly distributed envelope. A simple algebraic expression is obtained that is closely linked to the rubber complex modulus, with friction bandwidths extending over several decades. Several other secondary effects are introduced: multiple roughness orders, adhesion, stick-slip behaviour, friction magnification from either moments or atmospheric pressure, as these influence the observed friction bandwidth and amplitude. The sliding friction theory and secondary effects are compared to the measurements of Grosch [K.A. Grosch, The relation between the friction and the visco-elastic properties of rubber, Proc. Roy. Soc. Lond. A 274 (1963) 21–39] and Barquins et al. [M. Barquins, A.D. Roberts, Rubber friction variation with rate and temperature: some new observations, J. Phys. D: Appl. Phys. 19 (1986) 547–563], and are able to account for the friction amplitude and bandwidth for both gum and carbon loaded rubbers.     

基于预滑—动态摩擦力矩估计模型的自适应前馈补偿方法

根据数控交流伺服工作台进给系统从静止到宏观运动的过渡时间,和零速度时刻的指令加速度大小呈反比关系,区分摩擦力矩的预滑动区和滑动区,由此提出基于力矩值估计的摩擦补偿方法;在设定指令加速度后,基于命令力矩值的摩擦力矩模型,不需要测量速度就可以补偿工作台进给系统中的摩擦。同时,考虑到参数的不确定性,设计非线性摩擦自适应控制方案,对其稳定性进行理论证明。在交流伺服工作台进给系统上对基于摩擦力矩值估计的自适应前馈补偿方法进行验证。试验结果表明,基于预滑—动态摩擦力矩估计模型的自适应前馈补偿方法能实现在不同指令加速度下对期望轨迹的跟踪,并能大大提高系统的跟踪精度。     

Modeling of Dynamic Friction in Lubricated Line Contacts for Precise Motion Control

A simple dynamic friction model for an elastohydrodynamic lubrication sliding and rolling line contact has been developed. This model uses the technique introduced earlier by Harnoy and Friedland (1). The model includes low-velocity regions where friction is a combination of contact and elastohydrodynamic friction. The study shows that the lime-variable friction is not only a function of instantaneous sliding velocity, but is also a memory function of the velocity history. Simulation of the model for an oscillating velocity exhibits similar hysteresis effects in friction-velocity curves as observed earlier in several experimental studies. The model can be useful for friction compensation to enhance the precision of motion in control systems.     

Stick-Slip Motion in Boundary Lubrication

Using dynamical analysis for a pin-on-disk sliding system and the consideration of meniscus formation at the sliding interface, a wide range of experimental observations on stick-slip motion can be explained. It is shown that when the initial growth rate of the static friction force is larger than about half the product of the substrate speed and the spring constant, slick-slip motion occurs in that sliding system. The critical substrate speed or the critical spring constant, above which stick-slip motion ceases, can thus be determined. It is also shown that the saturation substrate speed, below which stick-slip motion retains its maximum stick-slip amplitude, is inversely proportional to the total growth time of the static friction force. The maximum stick-slip amplitude is proportional to the final difference between the static and kinetic friction force. For a thicker surface liquid-film, the initial growth rate and the final static friction force are larger but the total growth time is shorter, resulting in a larger critical speed, a larger stick-slip amplitude, and a larger saturation speed. For rougher contact surfaces, the initial growth rate is larger but the final static friction force and the total growth lime are smaller, resulting in a larger critical speed, a smaller stick-slip amplitude, and a larger saturation speed.     

摩擦噪声有限元预测

发展一种利用商业有限元软件进行摩擦系统全模型摩擦噪声预测的方法,可以对包括摩擦力和真实边界条件下的摩擦系统的复特征值进行分析,提出进行摩擦噪声预测的主要步骤.该方法能够大大提高摩擦噪声预测分析的精度和效率.利用该方法分析往复滑动摩擦系统的噪声发生趋势,获得系统特征方程的特征根及其变化特性,据此可判断摩擦系统自然频率和可能发生摩擦噪声的频率.计算结果表明,摩擦因数和滑动方向对系统摩擦噪声的形成有重要影响,摩擦噪声发生时摩擦系统具有振动模态重合的特点.将计算得到的系统可能发生摩擦噪声的频率与系统的试验噪声频率进行比较,发现有比较好的一致性.     

Contributions of adhesion and hysteresis to coefficient of friction between shoe and floor surfaces: effects of floor roughness and sliding speed

Abstract

Improving shoe–floor friction in order to reduce slip and fall accidents requires thorough understanding of the factors that contribute to friction. The friction between a sliding viscoelastic material (shoe) and a hard surface (floor) has two major components: adhesion and hysteresis. This study aimed to quantify the effects of floor roughness and sliding speed on adhesion and hysteresis to determine how each component contributes to the coefficient of friction. Experiments were conducted on a pin on disc tribometer using ceramic tiles with three levels of roughness, six sliding speeds, two common shoe materials and four liquid lubricants. Hysteresis was measured using a lubricant that minimised adhesion. Dry and lubricated adhesion was measured by subtracting hysteresis from the coefficient of friction. Analysis of variance regression models were used to determine the contributions of hysteresis, dry adhesion, sliding speed and fluid to lubricated coefficient of friction. Increased floor roughness led to increased hysteresis, while increased sliding speed reduced both adhesion and hysteresis. These findings are consistent with theory that states that larger asperities increase hysteretic deformation and that sliding speed affects deformation and real area of contact between a viscoelastic material and a hard surface. The model correctly predicted 83% of variation in coefficient of friction based on dry adhesion, hysteresis and fluid dependent constants. The sensitivity of hysteresis friction to shoe material and floor roughness indicates that optimising these parameters may be effective at reducing slip accidents on oily floor surfaces.     

Atomic-scale study of friction and energy dissipation

This paper presents an analysis of the interaction energy and various forces between two surfaces, and the microscopic study of friction. Atomic-scale simulations of dry sliding friction and boundary lubrication are based on the classical molecular dynamics (CMD) calculations using realistic empirical potentials. The dry sliding of a single metal asperity on an incommensurate substrate surface exhibits a quasi-periodic variation of the lateral force with two different stick-slip stage involving two structural transformation followed by a wear. The contact area of the asperity increases discontinuously with increasing normal force. Xe atoms placed between two atomically flat Ni surfaces screen the Ni-Ni interaction, decrease the corrugation of the potential energy as well as the friction force at submonolayer coverage. We present a phononic model of energy dissipation from an asperity to the substrates.     

The effect of longitudinal tangential vibrations on friction and driving forces in sliding motion

The main purpose of the work has been to qualitatively and quantitatively analyse the influence of longitudinal tangential vibrations on friction and driving forces in a sliding motion. Computational models were developed and implemented in a combined Matlab-Simulink environment. Both the dynamic Dahl's and the Dupont's and classical Coulomb's friction models were used. The influence of vibration velocity amplitude on the friction force in the presence of tangential longitudinal vibrations and on reduction of the driving force in sliding motion was analysed. It revealed that the commonly accepted view that the reduction of the average friction force is a consequence of cyclic changes in the sign of the friction force vector, only when the amplitude of vibration velocity is greater than the sliding motion velocity, is erroneous. The phenomenon was also observed without any changes in the sign of friction force vector. The results of simulations were compared with experimental data obtained with the use of a test rig specifically designed for the work. The Dahl's friction model led to the best correlation.     

Nonlinear shapes of steady-state vibrational oscillations of mechanical contact. Symmetrical tangential oscillations

A method of calculating nonlinear vibrational oscillations in mechanical contact systems with amplitude-dependent forces of hysteresis type is considered. The method is based on the representation of solutions of forced oscillation equation as nonlinear shapes corresponding to a model conservative system. Two-and three-dimensional dynamic characteristics of the principal and subharmonic modes of symmetrical tangential oscillations are obtained. Conditions under which friction contact oversteps the limits of the pre-sliding at force and kinematic vibrational loadings are specified. The results are compared to the Coulomb model of the friction force and this model is shown to be unsuitable for calculating contact oscillations with small amplitudes.     

Multi-layer models of friction between solids

Recent simulations of processes in surface layers of rubbing solids have shown the formation of a boundary layer, called quasi-fluid layer. To better understand the physical nature of the quasi-fluid layer, we investigate the processes occurring in the surface layer of rubbing solids in the frame of a simple multi-layer model, which also leads to the formation of a quasi-fluid layer. The multi-layer model can further be used to investigate how the friction force is determined by the material and loading parameters. It has been shown that the friction force and the thickness of the quasi-fluid layer depend on sliding velocity, the viscosity of the material and on a microscopic parameter (layer thickness). Subsequently, two different ways of extending the discussed model are proposed aiming at a model that can also predict the influence of normal pressure and surface topography on the friction force and on the formation of the quasi-fluid layer.     

Identification of pre-sliding and sliding friction dynamics: Grey box and black-box models

The non-linear dependence of pre-sliding and sliding friction forces on displacement and velocity is modelled using different physics-based and black-box approaches including various Maxwell-Slip models, neural networks, non-parametric (local) models and recurrent networks. The efficiency and accuracy of these identification methods is compared for an experimental time series where the observed friction force is predicted from the measured displacement and estimated velocity. All models, although varying in their degree of accuracy, show good prediction capability of friction. Finally, it is shown that better results can be achieved by using an ensemble of the best models for prediction.     

Nano-scale friction: A review

Frictional force is a resistant force that must be overcome to achieve relative motion between two components in contact. The economical and technological benefits of controlling friction and wear are tremendous. However, due to the complex nature of the phenomena, clear understanding of the mechanisms are yet to be achieved, particularly at the nano-scale where surface forces tend to dominate the tribological behavior of the system. In this paper the results of numerous theoretical, experimental, and numerical works on the fundamental mechanisms of friction at the nano-scale are reviewed. It is shown that friction coefficient values for nano-scale systems are quite varied depending on the conditions under which the system is investigated. As for the mechanism that causes friction at the nano-scale, interaction of the atoms plays a vital role. Furthermore, factors such as atomic radius, interatomic potential energy, and lattice parameters contribute to the degree of atomic interaction.     

Tribological behavior of reciprocating friction drive system under lubricated contact

The dynamic friction and wear behaviors are investigated in reciprocating friction drive system using a 0.45% carbon steel pair. The effects of various operating parameters on the traction force, stick and slip time, and friction modes are examined under the lubricated contacts. Moreover, the critical operating conditions in classifying three friction modes are also established. Results show that the fluid friction induced by the shearing of lubricant dominates the variation of traction force and produces the positive slope γ at the first period of slip in the traction force–relative sliding velocity curve. The γ value decreases at higher driver speed during stick-slip motion due to the thicker fluid film and shear thinning effect. The γ value increases due to the asperity interactions as the friction region is transferred from stick-slip to sticking with normal load from 196 to 980 N. Furthermore, it is also found that the static friction force is independent of stick time for the tangential loading rate ranged from 1.12 to 16.8 s⁻¹. The transition region produces the severest wear under the different driver speeds, but the wear is insensitive to the friction regions and the severe wear only occurs at higher normal load due to the action of Hertzian contact.     

Identification of the nonlinear excitation force acting on a bowed string using the dynamical responses at remote locations

For achieving realistic numerical simulations of bowed string instruments, based on physical modeling, a good understanding of the actual friction interaction phenomena is of great importance. Most work published in the field including our own has assumed that bow/string frictional forces behave according to the classical Coulomb stick-slip model, with an empirical velocity-dependent sliding friction coefficient. Indeed, the basic self-excited string motions (such as the Helmholtz regime) are well captured using such friction model. However, recent work has shown that the tribological behavior of the bow/string rosin interface is rather complex, therefore the basic velocity-dependent Coulomb model may be an over-simplistic representation of the friction force. More specifically, it was suggested that a more accurate model of the interaction force can be achieved by coupling the system dynamical equations with a thermal model which encapsulates the complex interface phenomena. In spite of the interesting work performed by Askenfelt [32], a direct measurement of the actual dynamical friction forces without disturbing the string motion is quite difficult. Therefore, in this work we develop a modal-based identification technique making use of inverse methods and optimization techniques, which enables the identification of the interface force, as well as the string self-excited motion, from the dynamical reactions measured at the string end supports. The method gives convincing results using simulated data originated from nonlinear computations of a bowed string. Furthermore, in cases where the force identifications are very sensitive to errors in the transfer function modal parameters, we suggest a method to improve the modal frequencies used for the identifications. Preliminary experimental results obtained using a basic bowing device, by which the string is excited with the stick of the bow, are then presented. Our identifications, from the two dynamical string reactions, are consistent as attested by the comparison of the two available versions of the string dynamical motion and of the friction force. Furthermore, the method seems adequate to investigate the interface force for the bowed string.     

Experimental study of air squeeze effect on high-frequency friction contact

A special tribometer was developed which was used to test sliding friction force between PTFE-based composites and bronze with normal (out-of-plane) or transverse (in-plane) high-frequency vibrations under three different environmental pressures. The influences of environmental pressure, vibration amplitude and sliding velocity on sliding friction coefficient were studied. The results show that the effect of environmental pressure on reduction of sliding friction is outstanding. With the increase of vacuum, the reduction of sliding friction by high-frequency vibrations decreased, especially the reduction of sliding friction by normal vibration. The sliding friction coefficient with high-frequency vibrations slowed down as the vibration amplitude increased. With increase of sliding velocity, the time-averaged friction coefficient with transverse vibration increased.     

Stick-slip algorithm in a tangential contact force model for multi-body system dynamics

Contact force of Multi-body dynamics (MBD) system can be classified two parts. First is a normal force and the other is a tangential force called friction force. And the friction force can be represented by two states such as stick and slip. The stick-slip phenomenon is simply described as a simple contact model which is a rigid body contacted on a sloped surface. If the calculated friction coefficient between the body and sloped surface is less than the static friction coefficient, the body should be stuck. If the calculated friction coefficient is greater than the static friction coefficient, the body will be sliding along the surface. The phenomenon is called as stick and slip state of friction, respectively. Usually many researchers and commercial MBD software used a coulomb friction force model which is defined with an only function of relative velocity. This kind of friction force model will be called a conventional friction force model in this paper. A big problem of the conventional model can not describe a stick state of friction phenomenon. In the case of conventional friction force model, the body will be sliding even though friction state is stick. Because, the relative velocity must have a non-zero value in order to generate the friction force. To solve this kind of problem, we propose a stick-slip friction force model including a spring like force. In the case of stick-slip friction force model, the body can be stuck on the sloped surface because the friction force will be a non-zero value, even though the relative velocity approaches zero. We defined a relative displacement variable called stiction deformation. In this paper, the stick-slip friction model is proposed and applied in the contact algorithm of MBD system. And then two friction models are compared with numerical examples. With the proposed stick-slip friction model, more realistic results are achieved.     

一个新的非线性迟滞隔振系统动力学模型

提出了一个新的非线性迟滞隔振系统的动力学模型,并导出了系统动力学模型的实用表达式。该模型由非线性刚度和非线性阻尼构造,迟滞非线性阻尼力被表示为位移的函数,从而使数值计算变得简单易行,试验中的测量工作减少。模型中的各个参数物理意义明晰,各阶刚度系数能很好地反映系统中存在的线性和非线性特性,而阻尼函数能很好地反映系统的迟滞和耗能特性,运用阻尼函数还可对隔振系统中可能存在的干摩擦阻尼、粘性阻尼及高阶阻尼等各种阻尼成分进行有效的识别。