A comprehensive study on the behavior of a rigid block on an oscillating ground with friction,elastic and viscous forces

This paper investigates the behavior of a non-linear mechanical model where a block is driven by an oscillating ground through Coulomb friction, a linear viscous damper and a linear spring. The governing equation is solved analytically for different partial configurations: friction only, friction with viscous damping, friction with a linear restoring force, and for the complete model. Using dimensionless groups, the analysis of the block motion provides a comprehensive set of information on the motion regime (stick, stick-slip or permanent sliding), on the dominant energies or forces, on the resonance and on the amplification of the ground oscillation by the system. The limit between the stick-slip regime and the permanent slipping regime is found either analytically or numerically. It is also shown that there exists a set of parameters for which the friction force, the viscous dissipative force and the elastic restoring force are equal.     

Study of a piezo-electric actuated vibratory micro-robot in stick-slip mode and investigating the design parameters

Nonlinear Dynamics - In this paper, the stick-slip motion of a new type of micro-robot with two perpendicular vibratory actuators is studied which is based on the friction drive principle. The...     

Comparison and analysis of two Coulomb friction models on the dynamic behavior of slider-crank mechanism with a revolute clearance joint

The objective of this study is to investigate the effects of the Coulomb dry friction model versus the modified Coulomb friction model on the dynamic behavior of the slider-crank mechanism with a revolute clearance joint. The normal and tangential forces acting on the contact points between the journal and the bearing are described by using a Hertzian-based contact force model and the Coulomb friction models, respectively. The dynamic equations of the mechanism are derived based on the Lagrange equations of the first kind and the Baumgarte stabilization method. The frictional force is solved via the linear complementarity problem (LCP) algorithm and the trial-and-error algorithm. Finally, three numerical examples are given to show the influence of the two Coulomb friction models on the dynamic behavior of the mechanism. Numerical results show that due to the stick friction, the slider-crank mechanism may exhibit stick-slip motion and can balance at some special positions, while the mechanism with ideal joints cannot.     

Nonlinear motions of a flexible rotor with a drill bit: stick-slip and delay effects

In this article, a discrete model of a drill-string system is developed taking into account stick-slip and time-delay aspects, and this model is used to study the nonlinear motions of this system. The model has eight degrees-of-freedom and allows for axial, torsional, and lateral dynamics of both the drill pipes and the bottom-hole assembly. Nonlinearities that arise due to dry friction, loss of contact, and collisions are considered in the development. State variable dependent time delays associated with axial and lateral cutting actions of the drill bit are introduced in the model. Based on this original model, numerical studies are carried out for different drilling operations. The results show that the motions can be self-exited through stick-slip friction and time-delay effects. Parametric studies are carried out for different ranges of friction and simulations reveal that when the drill pipe undergoes relative sticking motion phases, the drill-bit motion is suppressed by absolute sticking. Furthermore, the sticking phases observed in this work are longer than those reported in previous studies and the whirling state of the drill pipe periodically alternates between the sticking and slipping phases. When the drive speed is used as a control parameter, it is observed that the system exhibits aperiodic dynamics. The system response stability is seen to be largely dependent upon the driving speed. The discretized model presented here along with the related studies on nonlinear motions of the system can serve as a basis for choosing operational parameters in practical drilling operations.     

High-velocity operation of piezoelectric inertia motors: experimental validation

Piezoelectric inertia motors use the inertia of a body to drive it by means of a friction contact in a series of small steps. It has been shown previously in theoretical investigations that higher velocities and smoother movements can be obtained if these steps do not contain phases of stiction (“stick-slip” operation), but use sliding friction only (“slip-slip” operation). One very promising driving option for such motors is the superposition of multiple sinusoidal signals or harmonics. In this contribution, the theoretical results are validated experimentally. In this context, a quick and reliable identification process for parameters describing the friction contact is proposed. Additionally, the force generation potential of inertia motors is investigated theoretically and experimentally. The experimental results confirm the theoretical result that for a given maximum frequency, a signal with a high fundamental frequency and consisting of two superposed sine waves leads to the highest velocity and the smoothest motion, while the maximum motor force is obtained with signals containing more harmonics. These results are of fundamental importance for the further development of high-velocity piezoelectric inertia motors.     

Dynamic Study of a Structure with Flexion-Torsion Coupling in the Presence of Dry Friction

In aero engines, blade vibrations are frequently reduced by centrifugal flyweights, which exert a dry friction force per unit length under blade platforms. The response of this system to a periodic load has been analysed experimentally and theoretically. From a model having mode shapes similar to those of a blade, and a dry friction link per unit length, we show that the presence of the dry friction link is very effective in reducing vibrations for a range of excitation loads. The theoretical analysis is based on the Craig and Bampton mode synthesis, the rigid movement of the platform in its plane and the replacing of the linear dry friction link by several discrete parallel systems. Direct integration of the equations of motion is carried out by using the Newmark method. The comparison with experimental results is good. This method can easily be extended to more complex structures and shows that the dry friction link is effective when stick-slip occurs in the contact zone by limiting the energy provided to the system.     

三相驱动下非光滑振动驱动系统的动力学分析

可移动式机器人已成为机器人研究领域的重要分支,为实现其在狭小特殊环境中的运动, 学者们提出并研究了振动驱动移动系统.本文基于二维LuGre摩擦模型和拉格朗日方程,给出了一类振动驱动系统在各向同性摩擦环境中的动力学建模方法和数值算法.这类振动驱动系统结构简单且密封性好,依靠箱体与地面间的摩擦力实现自身的定向运动.该系统由一个外部箱体和两个内部质量块构成,两个质量块在箱体内的两个平行轨道上作三相振动驱动,箱体通过三个刚性支撑足与地面保持接触. 二维LuGre摩擦模型的利用,可有效避免库伦摩擦模型的不连续性给动力学方程的数值求解带来的困难,且可有效揭示该系统在运动过程中的黏滞-滑移切换现象. 数值仿真结果表明,通过调整其内部质量块的驱动参数,可实现箱体的直线平移、定轴转动和平面一般运动,且箱体在移动和转动过程中会出现擦滑、穿滑、回滑和不黏等4种现象; 另外,通过调节驱动参数, 不仅可以改变箱体移动和转动的快慢,还可以改变箱体形心运动轨迹的曲率半径.      

KINETICS ANALYSIS OF NON-SMOOTH VIBRATION-DRIVEN SYSTEM WITH THREE-PHASE CONTROL 1)

可移动式机器人已成为机器人研究领域的重要分支,为实现其在狭小特殊环境中的运动, 学者们提出并研究了振动驱动移动系统.本文基于二维LuGre摩擦模型和拉格朗日方程,给出了一类振动驱动系统在各向同性摩擦环境中的动力学建模方法和数值算法.这类振动驱动系统结构简单且密封性好,依靠箱体与地面间的摩擦力实现自身的定向运动.该系统由一个外部箱体和两个内部质量块构成,两个质量块在箱体内的两个平行轨道上作三相振动驱动,箱体通过三个刚性支撑足与地面保持接触. 二维LuGre摩擦模型的利用,可有效避免库伦摩擦模型的不连续性给动力学方程的数值求解带来的困难,且可有效揭示该系统在运动过程中的黏滞-滑移切换现象. 数值仿真结果表明,通过调整其内部质量块的驱动参数,可实现箱体的直线平移、定轴转动和平面一般运动,且箱体在移动和转动过程中会出现擦滑、穿滑、回滑和不黏等4种现象; 另外,通过调节驱动参数, 不仅可以改变箱体移动和转动的快慢,还可以改变箱体形心运动轨迹的曲率半径.     

伴随变阻尼作用的干摩擦下的车辆系统非线性动力学分析

对分段线性阻尼和干摩擦共同作用下的车辆悬挂系统进行了非线性动力学分析研究，阐述了判定系统周期运动稳定性的理论方法；利用数值模拟方法分析了具有不同阻尼参数组合的系统对简谐激励的振动响应，并分析了由干摩擦引起的粘-滑振动行为．结果表明：提高摩擦力对抑制响应有利，但车辆系统在低速下运行时会出现复杂的粘-滑振动，轮轨之间产生较大的瞬时刚性冲击；而通过增加轮对与侧架的弹性悬挂可以有效减弱这种瞬时刚性冲击．     

Vibrational self-alignment of a rigid object exploiting friction

In this paper, one-dimensional self-alignment of a rigid object via stick-slip vibrations is studied. The object is situated on a table, which has a prescribed periodic motion. Friction is exploited as the mechanism to move the object in a desired direction and to stop and self-align the mass at a desired end position with the smallest possible positioning error. In the modeling and analysis of the system, theory of discontinuous dynamical systems is used. Analytic solutions can be derived for a model based on Coulomb friction and an intuitively chosen table acceleration profile, which allows for a classification of different possible types of motion. Local stability and convergence is proven for the solutions of the system, if a constant Coulomb friction coefficient is used. Next, near the desired end position, the Coulomb friction coefficient is increased (e.g. by changing the roughness of the table surface) in order to stop the object. In the transition region from low friction to high friction coefficient, it is shown that, under certain conditions, accumulation of the object to a unique end position occurs. This behavior can be studied analytically and a mapping is given for subsequent stick positions.     

Analytical study of nonlinear synchronous full annular rub motion of flexible rotor–stator system and its dynamic stability

The nonlinear synchronous full annular rub motion of a flexible rotor induced by the mass unbalance and the contact-rub force with rigid and flexible stator is studied analytically. The nonlinear property is due to the dry friction force between stator and rotor. The exact solutions of the synchronous full annular rub motion and its run speed regions are obtained. The stability of the synchronous full annular rub motion is discussed analytically. The stability criterion and the stability regions of the synchronous full annular rub motion are obtained. A simplified approximate criterion formula for dynamic stability is also derived under the conditions of large impact stiffness, small damping and small friction. The simplified criterion formula can be used conveniently in engineering and matches the real situations of industry.     

Experimental investigation of a single-degree-of-freedom system with Coulomb friction

This paper presents an experimental investigation of the dynamic behaviour of a single-degree-of-freedom (SDoF) system with a metal-to-metal contact under harmonic base or joined base-wall excitation. The experimental results are compared with those yielded by mathematical models based on a SDoF system with Coulomb damping. While previous experiments on friction-damped systems focused on the characterisation of the friction force, the proposed approach investigates the steady response of a SDoF system when different exciting frequencies and friction forces are applied. The experimental set-up consists of a single-storey building, where harmonic excitation is imposed on a base plate and a friction contact is achieved between a steel top plate and a brass disc. The experimental results are expressed in terms of displacement transmissibility, phase angle and top plate motion in the time and frequency domains. Both continuous and stick-slip motions are investigated. The main results achieved in this paper are: (1) the development of an experimental set-up capable of reproducing friction damping effects on a harmonically excited SDoF system; (2) the validation of the analytical model introduced by Marino et al. (Nonlinear Dyn, 2019. https://doi.org/10.1007/s11071-019-04983-x) and, particularly, the inversion of the transmissibility curves in the joined base-wall motion case; (3) the systematic observation of stick-slip phenomena and their validation with numerical results.     

受限颗粒体对制动系统非线性振动的影响

制动系统在工作时,往往受到沙粒、尘土以及磨屑等受限颗粒体的影响,这些受限颗粒体在摩擦副中的高度分布具有较强的随机性,一定程度诱发了制动系统的非线性振动. 本文中基于制动片切向振动模型,引入了新的受限颗粒体摩擦模型,提出了用波动系数来描述受限颗粒体高度分布随机性的强弱. 发现在特定参数下,当此系数为0时,制动片切向振动为周期运动;但是当此系数不为0时,制动片切向振动呈现拟周期或混沌运动,此时的切向振动分岔特性图的稳定轨道也会出现数量或分布的变化,甚至表现出混沌特性. 同一时变信号内,受限颗粒体引发制动片切向非线性振动包括发散、收敛以及拟周期运动等多种形式.      

Stability and response of a self-amplified braking system under velocity-dependent actuation force

Wedge brakes, featuring self-amplification, inspire good opportunity to obtain large normal force by small actuation force. A single degree of freedom torsional model with harmonic excitation for a driveline with a wedge brake is developed to investigate the effect of velocity-dependent actuation force. The stability analysis indicates that instability can occur even with a constant friction coefficient and is greatly influenced by the slope of the actuation force. Three bifurcation points are found: one stable, one unstable, and the other one Hopf. Phase portraits, time domain responses, Poincaré maps, and frequency spectra are provided by nonlinear computation. Three motions are observed: unidirectional stick-slip, bidirectional stick-slip, and non-stick-slip. Due to the self amplification, the wedge brake leads to more stick motions and more side bands compared with the conventional brake. By varying the slope, the dynamic response of the driveline can be synchronous or irregular multi-periodic motion. The dynamics at negative slope is studied further considering three other influencing factors, i.e., the initial actuation force, excitation frequency, and wedge angle. The results are provided by the comparison with those of the driveline with a conventional brake.     

Analytical approximations for stick-slip vibration amplitudes

The classical “mass-on-moving-belt” model for describing friction-induced vibrations is considered, with a friction law describing friction forces that first decreases and then increases smoothly with relative interface speed. Approximate analytical expressions are derived for the conditions, the amplitudes, and the base frequencies of friction-induced stick-slip and pure-slip oscillations. For stick-slip oscillations, this is accomplished by using perturbation analysis for the finite time interval of the stick phase, which is linked to the subsequent slip phase through conditions of continuity and periodicity. The results are illustrated and tested by time-series, phase plots and amplitude response diagrams, which compare very favorably with results obtained by numerical simulation of the equation of motion, as long as the difference in static and kinetic friction is not too large.     

Coupled axial-torsional dynamics in rotary drilling with state-dependent delay: stability and control

Nonlinear motions of a rotary drilling mechanism are considered, and a two degree-of-freedom model is developed to study the coupled axial-torsional dynamics of this system. In the model development, state-dependent time delay and nonlinearities that arise due to dry friction and loss of contact are considered. Stability analysis is carried out by using a semi-discretization scheme, and the results are presented in terms of stability volumes in the three-dimensional parameter space of spin speed, cutting depth, and a cutting coefficient. These stability volume plots can serve as a guide for choosing parameters for rotary drilling operations. A control strategy based on state and delayed-state feedback is presented with the goal of enlargening the stability region, and the effectiveness of this strategy to suppress stick-slip oscillations is illustrated.     

Analytical investigation of stick-slip motions in coupled brake-driveline systems

In this paper, we investigate the brake creep-groan problem by formulating the issues in terms of two dynamic sub-systems that are coupled at the friction interface, and thus, experience stick-slip motions. Thorough examination of the nature of discontinuous solutions using numerical methods is a useful prelude to analytical studies. We examine such dynamics through parametric studies for magnitude and rate of brake release, where the vehicle is initially at rest and under low constant drive torque. Dependency on the initial conditions and solution flow before reaching the orbit will thus be illustrated. Four types of motions (one steady sliding and three stick-slip) are found based on extensive studies. Our formulation and analysis should lead to a better understanding of the brake groan phenomenon and systems coupled by interfacial friction.     

Stick-slip instability analysis

A theoretical investigation of friction-induced self-excited oscillations for systems with one degree of freedom is proposed. The friction force is assumed as an odd function of the relative sliding velocity with a jump discontinuity at a value of zero for the relative sliding velocity. The friction characteristic is approximated with a piecewise linear function, i.e. straight line segments with a suitable slope. For the generic system belonging to the class in question, the stick-slip instability region is located on a suitable dimensionless map.

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Sommario Viene proposta un'indagine teorica sulle oscillazioni autoeccitate indotte dall'attrito per sistemi ad un grado di libertà. La forza d'attrito viene assunta come funzione dispari della velocità relativa tra le superfici accoppiate, con una discontinuità di prima specie in corrispondenza del valore nullo della velocità. La caratteristica d'attrito viene approssimata mediante una funzione lineare a tratti con segmenti di opportuna pendenza. Per il generico sistema appartenente alla classe in esame, si perviene all'individuazione, su opportuna mappa adimensionale, della regione di instabilità da stick-slip.

     

基于LuGre摩擦模型的接触约束法旋转柔性梁斜碰撞研究

基于接触约束法和LuGre摩擦模型对在重力场作用下作大范围旋转运动的柔性梁系统和斜坡发生含摩擦斜碰撞的动力学问题进行研究. 首先运用刚柔耦合的多体系统动力学理论对大范围运动的柔性梁进行离散化和动力学建模, 在碰撞时采用冲量动量法求出跳跃速度, 其次在法向上引入接触约束求解出碰撞力, 在切向上采用LuGre摩擦模型分两种方式求解摩擦力, 第一种是在滑动时摩擦力由摩擦系数和碰撞力计算得出, 黏滞状态下引入切向约束计算拉格朗日乘子反应实际摩擦力, 根据黏滞/滑动切换判断计算出碰撞过程摩擦力(与Coulomb摩擦模型计算摩擦力一致); 第二种根据LuGre摩擦模型摩擦系数和法向碰撞力计算其摩擦力, 从而在碰撞时无需黏滞/滑动切换, 采用相同的摩擦力计算公式. 通过与Coulomb摩擦模型对比发现, LuGre摩擦模型描述碰撞切向摩擦过程更精确, LuGre摩擦模型黏滞时建立约束方程和碰撞采用统一的摩擦力公式这两种建模方式描述的斜碰撞动力学特性没有区别, 进而说明采用法向接触约束和LuGre摩擦模型具有满足碰撞非嵌入情况、避免黏滞/滑动切换、描述摩擦力相对准确的优势.      

振动驱动移动机器人直线运动的滑移分岔

近年来,随着移动型机器人设计技术水平的不断提高,其运动形式日趋多样. 借助于仿生学的思想,模仿蚯蚓等动物的蠕动成为不少机器人设计者所追求的目标. 为了实现这一目标,学者们提出并研究了振动驱动系统. 本文研究了各向同性干摩擦下,单模块三相振动驱动系统的粘滑运动. 考虑到库伦干摩擦力的不连续性,振动驱动系统属于Filippov 系统. 基于此,运用Filippov 滑移分岔理论,分析了振动驱动系统不同的粘滑运动情况. 根据驱动参数的不同,系统运动的滑移区域被分成4 种基本情形. 对这些情形分类讨论,得到系统的6 种运动情况. 然后对这6 种运动情况进行归纳,最终得出系统一共存在4 种不同的粘滑运动,而且也解析地给出了发生这4 种粘滑运动的分岔条件. 分岔条件包含系统的3 个驱动参数,通过变化这些参数,得到了系统运动的分岔图. 借助分岔图,详细分析了随着驱动参数的变化,系统如何实现不同粘滑运动类型之间的切换,并从分岔角度给出了相应的物理解释. 最后,通过数值方法直接求解原运动方程,数值解法得到的4 种运动图像与理论分析一致,验证了系统运动分岔研究的正确性.