Numerical analysis of stick-slip instability by a rate-dependent elastoplastic formulation for friction

In various fields of engineering, it is important to clarify friction-induced vibration, such as stick-slip motion, for a wide range of scales from microscopic elements to continental plates. In the present study, we apply a rate- and state-dependent friction model [30] (Hashiguchi and Ozaki, 2008), which can rationally describe the reciprocal transition between the static friction and the kinetic friction by a unified formulation, to the simulation of stick-slip instability for a one-degree-of-freedom spring-mass system under various conditions. It is verified that the various basic experimental findings on stick-slip motion can be pertinently described by the present approach. Moreover, the effect of the dynamic characteristics of the system, such as the mass, stiffness and driving velocity, is discussed, and parameters prescribing the rate of reciprocal transition of static-kinetic frictions and the preliminary microscopic sliding on the instability of the stick-slip motion are also discussed.     

Effects of weight on bit on torsional stick-slip vibration of oilwell drill string

The stick-slip phenomenon is a type of dysfunction detrimental to the drilling operation. Field application shows that stick-slip phenomenon is inclined to appear when using a large Weight on bit (WOB). In this paper, effects of the WOB on the stick-slip vibration are investigated. Based on a lumped torsional pendulum model of the drilling system, equation of motion of the drill bit is obtained. By using parameters commonly used in field applications, the bit dynamics are analyzed and the stick-slip vibrations are discussed. During the stick-slip motions, the negative damping effect occurs in the transition from the stick phase to the slip phase. With the increasing WOB, the bit behavior may change from the stable motion to the stick-slip vibration once the WOB reaches the critical value. In case of stick-slip vibration, the phase trajectory ultimately converges to a limit cycle which represents periodical bit motion. With increases in the WOB, the limit cycle enlarges. For cases without stick-slip vibrations, the drill bit vibrates damply and finally converges to a state of uniform motion. The results presented in this paper can be applied to interpret some of the field phenomena related to WOB.     

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.     

Coupled bending and torsional vibration of a rotor system with nonlinear friction

Unacceptable vibrations induced by the nonlinear friction in a rotor system seriously affect the health and reliability of the rotating machinery. To find out the basic excitation mechanism and characteristics of the vibrations, a coupled bending and torsional nonlinear dynamic model of rotor system with nonlinear friction is presented. The dynamic friction characteristic is described with a Stribeck curve, which generates nonlinear friction related to relative velocity. The motion equations of unbalance rotor system are established by the Lagrangian approach. Through numerical calculation, the coupled vibration characteristics of a rotor system under nonlinear friction are well investigated. The influence of main system parameters on the behaviors of the system is discussed. The bifurcation diagrams, waterfall plots, the times series, orbit trails, phase plane portraits and Poincaré maps are obtained to analyze dynamic characteristics of the rotor system and the results reveal multiform complex nonlinear dynamic responses of rotor system under rubbing. These analysis results of the present paper can effectively provide a theoretical reference for structural design of rotor systems and be used to diagnose selfexcited vibration faults in this kind of rotor systems. The present research could contribute to further understanding on the self-excited vibration and the bending and torsional coupling vibration of the rotor systems with Stribeck friction model.     

液压缸非线性约束下的轧机辊系振动行为

以四辊板带轧机为例,分析液压压下缸及弯辊缸在轧机辊系振动时表现出的分段弹性力和摩擦力两种非线性约束,建立液压缸非线性约束作用下的轧机辊系振动模型,并采用平均法求得振动系统的幅频响应。通过比较两种非线性作用下辊系振动速度和振动幅值的仿真曲线,研究辊系受分段弹性力和摩擦力影响时的行为特性。取不同分段弹性力和摩擦力,仿真分析两种非线性因素分别对轧机辊系幅频特性的影响规律。结果表明,轧机辊系振动速度受分段弹性力大小影响,系统不稳定频率区域随分段弹性力增大而变宽;摩擦力较小时,对辊系振动行为影响表现为阻尼特性,较大时,摩擦力的非线性成为影响辊系振动行为的主要特性。该结论为轧机辊系振动控制提供了理论参考。     

Acoustic output from stick-slip friction

An investigation into the correlation between the friction characteristics produced during stick-slip motion and the noise and vibration of a loading system caused by the frictional contact is presented. Various material combinations at the contact have produced distinctly different friction characteristics.Results show the presence of acoustic signals in some contact combinations and not in others. At this stage the reasons for this are not fully understood, but some common underlying trends are discussed.     

Pre-sliding friction control using the sliding mode controller with hysteresis friction compensator

Friction phenomenon can be described as two parts, which are the pre-sliding and sliding regions. In the motion of the sliding region, the friction force depends on the velocity of the system and consists of the Coulomb, stick-slip, Streibeck effect and viscous frictions. The friction force in the pre-sliding region, which occurs before the breakaway, depends on the position of the system. In the case of the motion of the friction in the sliding region, the LuGre model describes well the friction phenomenon and is used widely to identify the friction model, but the motion of the friction in the pre-sliding such as hysteresis phenomenon cannot be expressed well. In this paper, a modified friction model for the motion of the friction in the pre-sliding region is suggested which can consider the hysteresis phenomenon as the Preisach model. In order to show the effectiveness of the proposed friction model, the sliding mode controller (SMC) with hysteresis friction compensator is synthesized for a ball-screw servo system.     

The generation of dislocations in metals under a sliding contact and the dissipation of frictional energy

Observations on static friction behaviour under stick-slip vibration conditions are presented. A static contact-time model of static friction does not adequately describe the observed variation in static friction; the governing variable is the rate of increase of the tangential force coefficient.     

Elimination of Stick-Slip Motion in Sliding of Split or Rough Surface

Here, we present a mass-less quasi-static model of stick-slip phenomenon built exclusively on the difference between higher static and lower kinetic friction force. The model allows explaining the disappearance of stick-slip motion when elastic surface slid in contact with rigid counter-face bears large amount of small outgrowths. Adjusting the model parameters, it is also possible simulating systems with different transient responses. The results obtained may also be helpful in understanding the variety of sliding behavior of different materials.     

Effects of eccentricity defect on the nonlinear dynamic behavior of the mechanism clutch-helical two stage gear

This paper investigates the nonlinear dynamic behavior of an automotive clutch coupled with a helical two stage gear system. The nonlinear dynamic model is simulated by twenty seven degrees of freedom and including three types of nonlinearity: dry friction path, double stage stiffness and spline clearance. The utility of the proposed nonlinear model is illustrated by the industrial need to clearly identify the dynamic behavior of mechanical elements (shafts, bearings, gears, flywheel, pressure plate, hub of the clutch…) and reduce vibration. The governing nonlinear time varying motion equation formulated is resolved by the analytic Runge Kutta method.Then the modeling of the eccentricity defect located on the gear and the flywheel of the clutch is done. The effect of this defect on the nonlinear dynamic behavior of the system is investigated.     

黏滑驱动式小型精密运动平台

为满足微纳操作系统对精密驱动技术的需求,本文提出了一种基于黏滑原理的小型精密运动平台。该平台将柔性铰链、惯性质量块以及弹性元件结合为独立的定子基座,并与压电叠堆、陶瓷球固连为定子,安装在平台基座底部,通过螺钉调节弹性元件端部垂直方向的位置,就可以改变定子与移动台间的预压力,进而获得最佳的驱动力。为研究黏滑驱动的运动机理,分析各参数对平台运动的影响,进行了力学建模;而摩擦力作为黏滑驱动的关键因素,为了能准确地表达黏滑驱动的摩擦机理,在力学建模中引入了LuGre摩擦模型,并利用Matlab/Simulink软件进行了仿真分析。设计加工的黏滑驱动平台的整体尺寸为40mm×40mm×18mm,质量为32g。试验表明:该平台最小可实现10nm的运动步长,速度最高可达2.5mm/s,行程为22mm。     

离合器从动盘性能对汽车耸车的影响

为了研究离合器从动盘性能对汽车耸车振动的影响,建立了传动系统-汽车整车的11自由度非线性动力学模型。模型考虑了离合器从动盘的扭转特性、干摩擦阻尼、离合器接合黏滑特性以及变速器轮齿啮合刚度。利用建立的模型计算汽车起步过程系统动力学响应,通过实车测试验证模型的正确性,分析离合器从动盘性能参数对耸车振动的影响。结果表明:汽车的耸车现象发生在离合器完全接合之后;耸车振动频率与传动系第2阶固有频率相近;提高静摩擦因数,降低从动盘转动惯量和2级扭转刚度,可以降低汽车在起步过程中的耸车振动。本研究的建模和分析方法,可以用来计算与分析离合器从动盘结构性能参数对整车耸车振动特性的影响。     

Some considerations of slideway friction characteristics by observing stick-slip vibration

It is important to clarify the frictional characteristics of a slideway and to prevent unstable vibration, such as stick-slip vibration, for the improvement of kinematic performance and for precise positioning. In this research, the relations among the dynamic friction characteristics, the pitching motion or the floating up of the slider, the surface roughness of a slideway, and the lubricant property are investigated experimentally. As a result, some points necessary for the kinematic performance improvement of the slider are clarified.     

Thermal effect on piezoelectric stick-slip actuator systems

The piezoelectric stick-slip (PZT-SS) actuator is known to achieve motion with a theoretically unlimited range yet high resolution (several nanometers). In this type of actuator, friction plays an active role in producing a meaningful stick-slip motion. However, friction is a source of heat which may cause significant temperature rise, affecting the dynamic performance of the actuator. Our study aimed to measure temperature rise in the stick-slip motion and to understand whether such a rise could significantly affect the displacement of the stick-slip motion. In this study, a temperature measurement system was developed using the off-the-shelf components, with which the temperature rise up to 0.436 degrees C was successfully measured on a proprietary PZT-SS actuator. The experiment further shows that the temperature rise affects the displacement of the actuator when operating voltage is at the low end (approximately 6 V). Therefore, one of the design recommendations for such an actuator system is that the operating voltage should be at the high end (approximately 30 V). The study also measured the temperature rise (approximately 0.263 degrees C after the system worked for 6300 s) at the friction interface due to the piezoelectric element which is a part of the whole PZT-SS actuator. This means that temperature rise is due to both the friction at two interacting surface and the operation of the piezoelectric element.     

Stick-slip conditions in the general motion of a planar rigid body

In this paper we study combined translational and rotational (general) motion of planar rigid bodies in the presence of dry coulomb friction contact. Despite the cases where the body has pure translational/ rotational motion or can be assumed as a point mass, during the general motion, distinct points of the rigid body move in different directions which cause the friction force vector at each point to be different. Therefore, the direction and the magnitude of the overall friction force cannot be intuitively defined. Here the concept of instantaneous center of rotation is used as an effective method to determine the resultant friction force and moment. The main contribution of this paper is to propose novel stick-slip switching conditions for the general in-plane motion of rigid bodies. Simulation results for some combination of external forces are provided and some experimental tests are designed and conducted for practical verification of the proposed stick-slip conditions.     

Friction-induced vibration of oscillating multi-degree of freedom polymeric sliding systems

The purpose of this study is to investigate friction-induced vibration of oscillating systems. Special attention is focused on modeling polymer-on-metal systems. Past experimental and analytical friction results from non-oscillating or unidirectional translational sliding modes are extended into the oscillating sliding mode. Specifically, this refers to the incorporation of a representative functional shape of the friction–velocity relationships estimated from experimental results. Dependent on the relative sliding velocity between the frictionally coupled subsystems, the modeled system exhibits behavior such as a single stick–slip at the beginning of oscillatory motion, a single stick–slip at each motion reversal, or multiple stick-slip events during each half cycle of motion. Additionally, the boundary of incipient friction-induced vibration was identified via a rigorous definition of friction-induced vibration.     

Response of materials as a function of grinding angle on friction and transfer layer formation

Surface texture influences friction and transfer layer formation during sliding contact. In the present investigation, basic studies were conducted using an inclined pin-on-plate sliding apparatus to understand the effect of grinding mark directionality on the coefficient of friction and transfer layer formation. In the experiments, 080 M40 steel plates were ground to attain different surface roughness with unidirectional grinding marks. Pins consisting of soft materials (pure Al, pure Mg, and Al–4Mg alloy) were then slid against the prepared steel plates. The grinding angle (angle between direction of sliding and grinding marks) was varied between 0° and 90° in the tests. The experiments were conducted under both dry and lubricated conditions in an ambient environment. It was observed that the transfer layer formation and the coefficient of friction depend primarily on the directionality of the plate grinding marks. For the case of pure Mg pins, a stick-slip friction phenomenon was observed for all grinding angles under dry conditions and for grinding angles over 25° under lubricated conditions. In the case of Al pins, the stick-slip phenomenon was observed only under lubricated conditions for angles exceeding 25°. The stick-slip phenomena did not occur in any of the conditions studied with Al–4Mg alloy pins. Based on the results, it was concluded that the magnitudes of the friction and the stick-slip motion amplitude (for Al and Mg pins) were primarily controlled by changes in the level of plowing friction.     

Two dimensionless parameters controlling the occurrence of stick-slip motion in a 1-DOF system with Coulomb friction

The condition for the occurrence of stick-slip motion is examined analytically based on a 1-DOF system with Coulomb friction which includes seven independent parameters. There exist two dimensionless parameters which control the occurrence of stick-slip motion, one denotes the easiness for the occurrence of stick-slip motion and the other is the damping ratio acting to suppress the motion. A simple non-occurrence inequality of stick-slip motion is derived with the two dimensionless parameters through dimensionless analysis and numerical simulation, which has both high accuracy and high usability. Its validity is confirmed by the comparison with the experimental results reported by Singh.     

复杂接触运动下非线性摩擦力的求解

提出了复杂接触运动下求解接触非线性摩擦力的数值轨迹跟踪方法,利用该方法对几种复杂接触运动下的非线性摩擦力进行了计算。计算结果表明:数值方法在分析二维接触椭圆运动时可以得到更准确的结果;计算接触面摩擦力时不能忽略法向运动与切向运动之间的相位差,该相位差对接触状态的转变、摩擦力的大小以及迟滞回线的形状都有很大的影响;对于接触面的三维运动,必须同时考虑法向运动与接触面内两个方向切向运动之间的耦合;数值轨迹跟踪方法可以方便地求解一维、二维以及三维接触运动下的非线性摩擦力,为求解带干摩擦阻尼结构的动态响应提供了一种实用算法。     

盘式制动系统参数对制动颤振的影响分析

为了研究盘式制动系统参数对制动颤振的影响,建立了二自由度的动力学模型,利用Matlab进行数值仿真,分别研究了制动初速度、制动压力、阻尼和刚度等因素对制动系统动力学特性的影响。根据得到的位移曲线和相图可以看出:随着制动初速度的增大,系统黏滞阶段持续时间减少,并逐渐进入稳定运动状态;制动压力相对较小时,制动系统处于稳定状态,随着制动压力的增大,摩擦片和制动盘的振动幅值也随之增大,振动强度变大;在阻尼增大的过程中,摩擦片和制动盘均由起初的纯滑动运动状态进入稳定运动状态,且达到稳定运动状态的时间也逐渐缩短;摩擦片在相对较小的制动刚度下即可达到稳定状态,而制动盘则需要有较大的刚度才能达到稳定状态。