Occurrence limit of stick‐slip: dimensionless analysis for fundamental design of robust‐stable systems

In most practical mechanical systems, sliding surfaces are utilised under the assumption that they operate smoothly. Stick‐slip motion can therefore be a serious nuisance that interferes with achieving high performance in mechanical systems. The present paper describes the nature of stick‐slip based on an analysis of a 1‐DOF sliding system. The dimensionless parameters controlling the stick‐slip are clarified by deriving the dimensionless forms of the governing equations. For a friction model that considers the dependence of the kinetic friction coefficient on the relative velocity, we find three types of sliding systems with regard to stick‐slip: the unstable system, the stable system and the robust‐stable system. A criterion is proposed for the fundamental design of robust‐stable systems; if a sliding system is robust stable, no matter how large a disturbance is, the energy of the disturbance is dissipated perfectly, and steady sliding without any vibration is ensured. Copyright © 2009 John Wiley & Sons, Ltd.     

Stick‐slip with the slip phase as the starting point

In the literature, the stick‐slip phenomenon is always explained and modelled as starting from an initial stick phase. However, stick‐slip can also occur after a decrease in the imposed velocity, commencing above the critical (stick‐slip‐free) velocity. In this paper, it will be shown how stick‐slip can originate from a situation of pure sliding (without stick phases), if the slope of the friction force‐relative sliding velocity relation (F‐v_rel gradient) is negative. The F‐v_rel gradient used to study stick‐slip must, because of the interaction between the friction force and the dynamic behaviour of the mechanical system, be derived from velocity changes with the same time‐constant as the mechanical system of which the friction interface is part. It will also be shown that steady‐state friction data, and dynamic (non‐stationary) friction results obtained for relatively large (but fast) velocity variations, can lead to completely false conclusions related to stick‐slip.     

机械密封的黏滑分析

机械密封副磨损与黏滑引起的振动有关。以密封副动静环为摩擦副进行摩擦磨损试验,通过分析摩擦因数曲线的变化趋势以及机械密封副的磨损形貌,提出在动环与静环相对运动的过程中发生了黏滑振动。考虑动环刚度,构建密封副黏滑模型,通过仿真分析黏滑对密封副表面形貌的影响以及密封副的黏滑磨损机制。结果表明:动环在摩擦扭矩的作用下扭转导致黏滑;动环的最大转速在黏滑过程中达到转轴转速的2倍;黏滑在快速启动阶段并没有发生,仅在速度波动阶段出现,而当速度恢复稳定上升阶段,黏滑现象消失;黏滑最终造成密封副表面严重的黏着磨损。     

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.     

干摩擦阻尼叶片周期振动响应的解析计算

研究一个描述干摩擦阻尼器叶片振动的质量-弹簧-阻尼器振动系统。阻尼器摩擦力由黏滞模型描述,由接触面滑动或黏滞状态决定。将滞后摩擦力分为四个阶段,从而得到各个阶段上的线性振动系统,给出求干摩擦阻尼叶片周期响应的解析公式。计算表明,阻尼端压力取适当值时,阻尼器会处于最优的摩擦接触状态,获得较好减振效果。同时引入阻尼器处对叶片还起到调频作用,也可以起到使激振频率避开共振频率的作用,减小振动幅值。     

Study on dynamic friction characteristics in reciprocating friction drive system

The dynamic friction characteristics of a reciprocating friction drive system are investigated under conditions of dry contact using 0·45% carbon steel pair. Three friction modes are found during the operation, i.e. stick-slip, sticking and a transition region. The critical operating conditions in classifying these three modes are examined under various driver speeds, normal loads and spring constants. The critical values of driver speed and normal load increase with increasing spring constant. Generally, in the friction drive system the disappearance of the stick-slip results in smooth rolling. It is also found that the slope at the first period of slip on the traction force–relative slip velocity curve would have a transition from negative to positive value when the friction mode of stick-slip changes into sticking. Moreover, results show that the sticking mode gives the best positioning accuracy with the least wear on the contact surfaces. In addition, a transition from severe wear to mild wear is found when the friction mode is transferred from stick-slip to sticking only.     

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.     

Mechanism of self-excited torsional vibration of locomotive driving system

A single wheelset drive model and 2-DOFs torsional vibration model were established to investigate the self-excited torsional vibration of a locomotive driving system. The simulation results indicate that the self-excited torsional vibration occurs when the steady slip velocity is located at the descending slope of the adhesion coefficient curve. The principle of energy conservation was used to analyze the mechanism of the self-excited vibration. The factors affecting on the amplitude of the self-excited vibration are studied.     

考虑摩擦影响的重型车床横向进给伺服系统建模与分析

进给伺服系统的性能对数控(Computer numerical control,CNC)机床的跟踪及定位精度、零件加工表面质量等有着重要的影响。摩擦的非线性还会导致系统产生爬行行为。结合Karnopp摩擦模型的建模思想,对导轨接触面建立一种改进的Stribeck摩擦模型,针对闭环控制的某重型车床的横向进给系统,建立综合考虑轴的扭转刚度、齿轮的啮合刚度、丝杠螺母副接触刚度、丝杠轴和轴承轴向刚度、导轨接触面摩擦的进给伺服系统的多自由度力学模型和数学模型,研究低速进给下各个刚度变化对工作台输出的影响,找出机械传动系统中的刚度薄弱环节。现场试验测试工作台不同进给位置下的临界爬行速度,得出临界爬行速度与丝杠的轴向刚度的关系,理论分析与试验结果相吻合。所得结论可为该重型车床横向进给伺服系统的优化设计和性能预测提供理论支持。     

Macroscopic versus microscopic description of friction: from Tomlinson model to shearons

In this Letter we investigate the response of an embedded system that is subject to an external drive, which is chosen to be either a constant velocity or a harmonic shear. Two approaches are introduced that cover macroscopic and microscopic aspects of the problem and mimic recent measurements on friction using the surface forces apparatus. The first approach is based on the Tomlinson model and its generalization, and allows for the investigation of the coupled lateral–normal response to a lateral drive. We propose a method for analyzing both linear and nonlinear response of confined systems driven harmonically. The method provides a way to deduce the microscopic parameters responsible for dissipation. The second approach focuses on the microscopic level. The shear is shown to excite “shearons”, which are collective modes of the embedded system with well-defined spatial and temporal patterns that dominate the frictional properties of the driven system. We demonstrate that the slip relaxation in stick–slip motion and memory effects are well described in terms of the creation and/or annihilation of shearons.     

基于LuGre模型的气动位置伺服系统摩擦补偿控制

气动伺服系统的摩擦力/驱动之比较大,摩擦力模型复杂、受影响因素较多且存在一定的不确定性,导致精确建模比较困难;另一方面,摩擦力和气体的低刚度、弱阻尼特性相互作用导致爬行、黏滑振荡现象,严重影响了伺服系统的动态及稳态性能的提升。在综合考虑摩擦力特征、系统自身非线性、未建模动态不确定性及摩擦力和系统性能相互影响的基础上,结合LuGre摩擦模型,采用双观测器估计摩擦力模型中的部分不确定性参数,提出非线性自适应反步摩擦补偿控制方法。通过在低速和高速工况下分别进行试验验证,并与PID控制方法进行比较,结果表明非线性自适应反步摩擦补偿控制方法有效改善了起步阶段的动态滞后现象,减少了低速工况下爬行及高速工况下的黏滑振荡现象,提高系统的响应速度及跟踪精度。     

Stick-slip vibration of a moving oscillator on an axially flexible beam

This study investigates the stick-slip vibration between an axially flexible beam fixed at both ends and an oscillator moving on the beam. After deriving the equations of motion for the stick and slip states, the stick-slip vibrations between the oscillator and the beam are analyzed. In addition, to obtain the irregularly changed contact position due to the axial deformation of the beam and oscillator movement, a mathematical expression for the contact position is derived. It is found that the long-period stick-slip vibration is influenced mainly by the oscillator and the short-period vibration is influenced mainly by axial deformation of the beam. Furthermore, the dynamic responses show that even if a high damping ratio is applied to the oscillator, stick-slip vibration due to axial deformation of the beam can occur. Finally, the analysis shows that a kind of the internal resonance occurs between the oscillator and the beam when the harmonics of the natural frequency of the oscillator match the natural frequencies of the beam.

     

新型钻井振荡器工作原理与振动特性研究

提出了一种新型钻井振荡器。研究振荡器的工作机理,推导出了轴向脉冲激励函数,在此基础上建立了振荡器轴向振动分析模型,得到振荡器在振动下的位移、速度、加速度等关键参数;根据算例参数设计对应的室内实验,并将算例分析结果与实验结果进行对比,验证了振动分析模型的合理性,结果表明,振荡器可以产生平稳的高频微幅振动,使钻柱与井壁之间的静摩擦转化为动摩擦。研究结果对解决定向井、水平井钻进过程中钻压传递、钻柱磨损、粘卡等问题具有一定的参考意义。     

Dislocation Structure and Stick–Slip Phenomenon

Friction is a complex process involving multi-scale asperity contact and large plastic deformation associated with the development of a dislocation structure. Friction is closely associated with the stick–slip phenomenon. In spite of the large number of papers, dedicated to stick–slip effects, little effort has been directed toward elucidating the development of the dislocation structure during stick–slip phenomena. Here, we report some new systematic investigations into the dislocation nature of stick–slips during low-velocity friction of a lithium fluoride single crystal rubbed against a spherical diamond indenter. It is shown that the average velocity of the indenter in the stick phase is about 300 times lower than the maximal velocity in the slip. This difference in velocities leads to entirely different dislocation behavior and damage development in the stick and slips phases. The stick phase is mainly determined by time-dependent strain (creep) wherein, as in metals and alloys, three stages of creep are observed. Based on the analysis of the dislocation structure, a model of the dislocation distribution in the regions of stick (creep) and slip is proposed.     

干气密封滑动密封端面高频微幅摩擦振动研究

为揭示干气密封端面间摩擦振动规律,通过对密封端面在干摩擦状态下的微观形貌与受力进行分析,基于分形理论构建包含分形参数的密封端面法向位移激励,以及干气密封在干摩擦状态下的两自由度摩擦振动系统模型,并对摩擦振动系统模型的影响因素进行数值分析.研究结果表明:法向振动位移和速度随着分形维数与转速的增大先增大后减小;密封环面分形...     

Experimental verification of rate-dependent elastoplastic analogy friction model and its application to FE analysis

When two solid bodies in contact slide slowly past each other without lubrication, an intermittent vibration phenomenon might be observed. Such rate-dependent frictional behaviors are referred to as stick–slip motions, and such motions can impair the stability of machines and structures. The aim of this study is to propose a numerical approach for analyzing stick–slip motion; the approach is based on the finite element method implemented using a rate-dependent friction model. First, we demonstrate the capability of the rate-dependent friction model by comparing its results with experimental results obtained under various material and dynamic conditions. Then, a simple finite element analysis of rate-dependent frictional sliding behavior, including stick–slip motion, is carried out to examine the effect of the material and geometric properties and boundary conditions on the numerical results. The present numerical approach can consider not only the properties of friction and materials but also variations in boundary conditions.     

Kinetic friction characterizations of the tubular rubber seals

In this paper, both the kinetic friction characterizations and the stick–slip motion phenomena for the tubular rubber seals are studied. First, the kinetic friction model of the rubber seal is established to explain the kinetic friction mechanism of the tubular rubber seals. Second, both the measurement principle and the test instrument for the kinetic friction properties of the tubular rubber seals are developed, and then both the normal force curve and the friction force curve are obtained. Finally, the influences of the sliding velocity and the compressive displacement on the kinetic friction properties and the stick–slip motion of the tubular rubber seals are analyzed. The results will play an important role for designing and evaluating advanced rubber seal components.     

Mechanism of energy dissipation in mechanical system with dry friction

Determination of the energy dissipative mechanism in a mechanical system composed of two elastic structures in dry contact is presented. The analysis is based on the measurement of displacement ratio of the contacting elastic structures as a function of frequency due to light impulse excitation at a single point on any of the two elastic structures. The theoretical analysis depends on a very simple model of a two-degree-of-freedom system where two solid friction models are adopted in the analysis of the mathematical model. Several experiments are presented to illustrate the dominant friction mechanism of contacting surfaces within the micro slip regime in a frequency range of oscillation up to 400 Hz. It was shown experimentally that the solid friction model behaves in a way that is described as structural (hysteretic) damping. In other words, the energy dissipated due to dry friction during micro slip regime does not depend on the relative velocity between the two contacting surfaces but it is proportional to their relative displacements. The determination of the contact stiffness and damping loss factor in addition to their variation with the applied normal load was also shown.     

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.     

Pre-sliding Behaviour of Single Asperity Contact

The pre-sliding and static friction force behaviour at asperity level between a smooth ball and a smooth flat surface at different normal loads, as well as friction behaviour during full slip has been studied. The normal load dependence of the friction force and the preliminary displacement is discussed when the mean contact pressure is kept under 100 MPa. The theoretical model to calculate the shear stress and the preliminary displacement in the contact is discussed and the experimental data were used to verify the model. The results show that for low applied normal loads the adhesion force has an influence on the friction force measurements. Furthermore, the results for the friction force and preliminary displacement show good agreement with the theoretical trends. The experiments along with the model can be used to analyse the tangential traction in the contact and the behaviour of the stick–slip area. The measurement results along with the model were used to calculate the maximum shear stress at the point of sliding for different applied normal loads. It is also shown that at low applied normal loads the shear stress is not constant as compared to relatively high applied normal loads due to the presence of adhesion force.