ANALYTICAL SOLUTION FOR ROTATIONAL RUBBING PLATE UNDER THERMAL SHOCK

提出了热冲击和碰摩故障共同作用下的旋转悬臂板系统动力特性解析解法. 基于变分原理,推导出考虑碰摩力沿宽度方向差异性的薄板系统运动微分方程,将该方程的解分解为热冲击悬臂板准静态解和碰摩薄板热冲击动力解. 通过计算旋转悬臂板的模态特性和温度分布函数,获得了碰摩叶片旋转悬臂板模型的热冲击振动解析解,讨论分析得出热冲击和碰摩故障对薄板振动的影响规律. 研究表明:碰摩振动表现为复杂的多频率耦合振动,高频振动较为显著;热冲击振动表现为简单的低频振动形式,强烈的热冲击导致碰摩薄板趋于低频振动. 碰摩引起的振动形式较热冲击故障更加复杂,更容易引起叶片的破坏. 增大的摩擦系数加剧了碰摩引起的振动,利用减小表面粗糙程度等方法降低摩擦系数,可以达到减小碰摩破坏程度的目的.     

旋转碰摩板热冲击振动的解析法研究

提出了热冲击和碰摩故障共同作用下的旋转悬臂板系统动力特性解析解法. 基于变分原理,推导出考虑碰摩力沿宽度方向差异性的薄板系统运动微分方程,将该方程的解分解为热冲击悬臂板准静态解和碰摩薄板热冲击动力解. 通过计算旋转悬臂板的模态特性和温度分布函数,获得了碰摩叶片旋转悬臂板模型的热冲击振动解析解,讨论分析得出热冲击和碰摩故障对薄板振动的影响规律. 研究表明:碰摩振动表现为复杂的多频率耦合振动,高频振动较为显著;热冲击振动表现为简单的低频振动形式,强烈的热冲击导致碰摩薄板趋于低频振动. 碰摩引起的振动形式较热冲击故障更加复杂,更容易引起叶片的破坏. 增大的摩擦系数加剧了碰摩引起的振动,利用减小表面粗糙程度等方法降低摩擦系数,可以达到减小碰摩破坏程度的目的.      

Vibrations of a Rigid Body with Cylindrical Surface on a Vibrating Foundation

The analytic solution of the problem of forced vibrations of a rigid body with cylindrical surface on a horizontal foundation is given. It is assumed that the dry friction force acts at the point of contact between the cylindrical surface of the body and the foundation and the foundation moves by a harmonic law in the horizontal direction perpendicularly to the cylindrical surface element. The averaging method is used to determine the forced vibration mode near the natural frequency of the body vibrations on the fixed foundation. The results are presented as amplitude-frequency and phase-frequency characteristics.     

干摩擦控制振动的应用

干摩擦能衰减机械振动的现象早为人们所熟悉。但是很长一段时期,干摩擦应用到控制振动上的例子不多见。这是由于干摩擦的性能不好掌握和干摩擦会使系统变为非线性,设计、计算就很复杂。 干摩擦振动系统是非线性系统。以振动系统中的一个干摩擦接头来说明。当接头上的力     

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．     

Nonlinear dynamics of mistuned bladed disks with ring dampers

In turbomachinery applications, rotating bladed disks (blisks) are often subject to high levels of dynamic loading, such as traveling wave excitations, which result in large response amplitudes at resonance. To prevent premature high cycle fatigue, various dry friction dampers are designed for blisk systems to reduce the forced responses. Ring dampers are located in the disk, underneath the blades, and are held in contact with the blisk by centrifugal loading. Energy is dissipated by nonlinear friction forces when relative motions between the ring damper and the blisk take place. To investigate the dynamic responses of blisk–damper systems in the presence of the nonlinear frictional contacts, conventional methods based on numerical time integration are not suitable since they are computationally expensive. This paper presents a reduced-order modeling technique to efficiently capture the nonlinear dynamic responses of the blisk–damper systems. Craig–Bampton component mode synthesis (CB-CMS) serves as the first model reduction step. A novel mode basis that mimics the contact behavior under sliding and sticking conditions is developed to further reduce the CB-CMS model while maintaining its accuracy. The resulting reduced nonlinear equations of motion are solved by a hybrid frequency/time domain (HFT) method. In the HFT method, the contact status and friction forces are determined in the time domain by a three-dimensional contact model at each contact point, whereas the reduced equations of motion are solved in the frequency domain according to a harmonic balance formulation. Moreover, to investigate the effects of blade mistuning, which can lead to drastic increase of forced responses, an extension of the reduced-order models (ROMs) is developed based on component mode mistuning. Forced responses computed by the proposed ROMs are validated for both tuned and mistuned systems. A statistical analysis is performed to study the effectiveness of ring dampers under random blade mistuning patterns.     

The effect of friction reduction in the presence of in-plane vibrations

A reduction of friction by vibrations has been observed in various experiments. This effect can be applied to actively control frictional forces by modulating vibrations. Moreover, common methods of controlling friction rely on lubricants and suitable material combinations. The superimposition of vibrations can further reduce the friction force. This study presents a theoretical approach based on the Dahl friction model that describes the friction reduction observed in the presence of the tangential vibrations at an arbitrary angle. Analysis results indicated that the tangential compliance should be considered in modeling the effect of vibrations in reducing friction. At any vibration angle, the tangential compliance of the contacts reduces the friction reduction effect. The vibrations parallel to the macroscopic velocity are most effective for friction reduction.     

Analysis of the non-periodic oscillations of a self-excited friction-damped system with closely spaced modes

Nonlinear Dynamics - It is widely known that dry friction damping can bound the self-excited vibrations induced by negative damping. The vibrations typically take the form of (periodic) limit cycle...     

Self-vibration-induced wear of a friction pair

We study rotational self-excited vibrations of two frictionally coupled disks and consider the case of self-excited vibrations arising in the presence of dry friction, where the disk relative velocity periodically changes sign passing through the point of discontinuity of the friction law. We show that if there are resonances in the system, then undulatory wear arises either on the driving disk or on the driven disks. We find the existence and stability conditions for the corresponding modes.     

On longitudinal impact III

Summary The graphodynamical method which was introduced and applied to elastic longitudinal impact in the first two articles of this series is here used to study the transmission of a rectangular compressive pulse along a system consisting of a bar which is joined by friction to a stiff anvil or to a co-axial elastic tube. Some of these cases will in the next article be used as models of pile driving. The influence of the frictional force, of the dimensions of the pulse (the dimensions and impact velocity of the hammer) and of the area and length of the tube on the sign and magnitude of the slide at a concentrated friction joint and on the associated energy loss is determined, and the results are illustrated by diagrams. The results of a few simple experiments agree reasonably well with the theory. The theory is extended to a model of a pile with constant friction per length unit, and it is found that a light hammer with great impact velocity gives better penetration than a heavy hammer with the same energy and thus smaller velocity.     

Dynamics of windscreen wiper blades: Squeal noise,reversal noise and chattering

The motion of a windshield wiper blade is modelled by a mass-spring-damper system on a moving frictional surface. The system dynamics is time-varying, since three different regimes of motion, characterized by different degrees of freedom, are possible. Indeed the system, which schematizes a blade cross-section, can experience stick and slip motions when it is in contact with the glass surface, and free-flight motion when it is detached. The contact between the system and the surface is governed by Stribeck׳s friction law and Poisson׳s impact law, which make the dynamics non-smooth. The model is numerically implemented in an event-driven code, and simulations are performed which reproduce the three basic classes of undesired oscillations observed in the motion of real windscreen wipers, i.e., squeal, reversal and chattering noises. Attention is focused on the causes of these vibrations, and remedies for reducing or avoiding them are proposed.     

Nonlinear friction dynamics on fibrous materials,application to the characterization of surface quality. Part I: global characterization of phase spaces

The diversity and the complexity of fibrous materials (woven fabrics, nonwovens or knitted fabrics) make the control of surface qualities very difficult. The control and the comprehension of the tribological phenomena generated by a dynamic friction are of major importance. Whereas the traditional investigations such as measurements of average parameters like roughness or friction coefficient quickly find their limits on such deformable, heterogeneous and flexible fibrous surfaces with very heterogeneous relief, this series of two publications proposes a new manner of observing the interactions of friction. Our laboratory has developed a patented method of measurements, called MODALSENS, which aims at rubbing a very fine and flexible blade on the analyzed surface. Dynamic friction with the contact generates nonlinear vibrations, and the response of the sensor is analyzed in its phase space using the tools of nonlinear analysis of time series. Then, when the evaluated surfaces change, this first part endeavors to characterize the portraits of phases related to the nonlinear vibrations of MODALSENS in a global way, by quantifying its invariants such as dimensions, Shannon entropies, diameters of attractors and largest Lyapunov exponents. From this first part, a classification of studied fibrous surfaces is built and is expected to give rise to new estimators for the surface quality analysis of fibrous media.     

Stick-Slip Vibrations Induced by Alternate Friction Models

In the present paper a simple and efficient alternate friction model is presented to simulate stick-slip vibrations. The alternate friction model consists of a set of ordinary non-stiff differential equations and has the advantage that the system can be integrated with any standard ODE-solver. Comparison with a smoothing method reveals that the alternate friction model is more efficient from a computational point of view. A shooting method for calculating limit cycles, based on the alternate friction model, is presented. Time-dependent static friction is studied as well as application in a system with 2-DOF.     

摩擦力和摩擦振动的分形行为研究

在不同的摩擦磨损试验机上提取了摩擦磨损过程中摩擦力和摩擦振动的时间序列信号,采用关联维数方法研究了摩擦力和摩擦振动的分形行为．结果表明：摩擦力和摩擦振动信号具有分形特征;随着摩擦磨损过程的进行,信号分形维数的变化出现规律性的递增或递减;对于“收敛”或磨合磨损过程,不同阶段摩擦信号的分形维数趋于增大;对于“发散”的摩擦磨损过程,不同阶段的摩擦信号的关联维数趋于减小．摩擦力和摩擦振动的分形维数的变化规律同摩擦磨损过程中表面形貌分形维数的变化规律相似。     

摩擦诱发的事件相关电位认知成分特征研究

本研究旨在讨论人在探索物体表面时由物体表面摩擦属性的影响而引起的脑电变化.而事件相关电位技术是观测这一变化的理想手段.试验通过Neuroscan 64导事件相关电位采集系统来采集脑电信号,采用Oddball范式来诱发P300电位,并观察摩擦诱发的事件相关电位的认知成分P300的潜伏期和峰值特点.样本为摩擦系数不一样但其他属性基本一致的三种纸类.受试者通过手指主动触摸的方式判断物体表面摩擦力大小,观察此过程中的事件相关电位.试验发现,摩擦系数大样本诱发的P300的潜伏期小,峰值大.摩擦系数小的样本诱发的P300潜伏期大,峰值小.     

The effect of longitudinal high-frequency in-plane vibrations on a 1-DoF friction oscillator with compliant contact

Nonlinear Dynamics - The effect of vibrational smoothing of dry friction has been studied intensively in the past. High-frequency vibrations have been shown to reduce average friction forces and...     

锯切过程中花岗石与金刚石间的摩擦效应

通过测量锯切力和计算锯切比能,获得了多种条件下的比能与单颗磨粒平均载荷的试验,从能量角度探讨了花岗石的锯石的锯切机理,并建立了单颗磨粒平均载荷与磨粒纵向切削面积平均值之间,单位宽度功率消耗与滑擦面积之间的对应关系。结果表明,锯切过程中能量主要消耗于花岗石与金刚石间的摩擦,由于单颗磨粒向切削面积平均值同时包含了磨粒切削深度与弧长的影响,更适用于描述锯切过程。锯切中锯切深度和材料去除率等因素的影响均可     

Bifurcation phenomena of the reversal behavior of an automobile wiper blade

Reducing the noise generated by windshield wipers during reversal is desirable. As a fundamental first step in exploring the cause of this noise, the present study attempts to theoretically and experimentally clarify the dynamics of the behavior of the wiper blade near the reversal point. First, an experiment is conducted to observe the reversal behavior using the cross sectional model of the blade rubber. In order to theoretically explain the experimentally observed phenomena, an analytical link model of the wiper blade is introduced. The reversal behavior of a blade is theoretically investigated through the bifurcation analysis by considering Coulomb??s friction during reversal. Then we show the continuous variation of the angle of blade rubber, and predict a rapid variation of the normal force, which can cause reversal noise, acting to the blade rubber.     

Effects of the local resonance in bending on the longitudinal vibrations of reticulated beams

This work investigates the dynamic behaviour of reticulated beams obtained by repeating a unit cell made up of interconnected beams or plates forming an unbraced frame. As beams are much stiffer in tension–compression than in bending, the longitudinal modes of such structures (governed by tension–compression at the macroscopic scale) can appear in the same frequency range as the bending modes of the elements. The condition of scale separation being respected for compression, the homogenization method of periodic discrete media is used to rigorously derive the macroscopic behaviour at the leading order. In the absence of bending resonance, the longitudinal vibrations of the structure are described at the macroscopic scale by the usual equation for beams in tension–compression. When there is resonance, the form of the equation is unchanged but the real mass of the structure is replaced by an effective mass which depends on the frequency. This induces an abnormal response in the neighbourhood of the natural frequencies of the resonating elements. This paper focuses on the consequences on the modal properties and the transfer function of the reticulated structure. The same macroscopic mode shape can be associated with several natural frequencies of the structure (but the deformation of the elements at the local scale is different). Moreover the vibrations are not transmitted when the effective mass is negative. These phenomena are first evidenced theoretically and then illustrated with numerical simulations.