盘-销摩擦系统摩擦接触力测试与特性分析

测量分析动态摩擦接触力是研究摩擦振动与噪声发生机理的关键.本文中建立了盘-销系统摩擦尖叫试验台架,成功再现了摩擦尖叫.采用三向力传感器对有无摩擦尖叫条件下的动态摩擦接触力进行了测量,并利用小波信号分解、概率密度函数、功率谱密度函数、时频分析等方法进行了分析和讨论.研究发现:在发生摩擦尖叫时,动态摩擦力和法向力发生高频波动,是系统噪声的激励源;无摩擦尖叫时的摩擦力和法向力的动态分量为典型的白噪声随机过程,呈非高斯分布;有摩擦尖叫时的摩擦力和法向力为窄带高频类谐波信号,摩擦力呈非高斯分布,而法向力近似为高斯分布;模态耦合是导致盘-销系统发生动态接触力高频波动以及摩擦尖叫的原因.     

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.     

深部煤岩界面超低摩擦时变模型及能量转化研究

深部煤岩超低摩擦型冲击地压实质是巨量煤岩体沿煤岩界面发生失稳滑动的时变过程,期间煤岩界面摩擦力和摩擦系数随时间变化,同时伴随煤岩界面摩擦力做功向煤岩冲击动能释放能量转化特征.为定量描述煤岩界面能量转化规律,引入量纲分析法,实验测定了煤岩弹性系数、阻尼系数和待定系数,给出了深部煤岩界面摩擦系数表达式.以沈阳红阳三矿为研究对象,通过实验研究和工程实际相结合,定义了冲击动能转化率新指标,验证了所建模型可靠性,定量描述了煤岩界面摩擦力做功向煤岩冲击动能转化规律.研究结果表明:深部煤岩界面摩擦系数随冲击载荷幅值增大而线性降低,随冲击载荷频率增大而线性增加.深部煤岩界面摩擦力的降幅和降低速率变化急剧,当冲击载荷幅值为5000 N、冲击载荷频率为500 Hz时,深部煤岩界面摩擦力降幅为97%、降低速率为38.9 kN/ms～41.38 kN/ms时发生超低摩擦效应.首次从摩擦力降低幅值和降低速率定量表征超低摩擦效应.结合实验和工程实际分析发现,能耗比实验结果均值为0.441,红阳三矿“11.11”冲击地压计算结果为0.488,两者较为接近,进一步证明所建模型合理性.     

Analytical parametric study of bi-linear hysteretic model of dry friction under harmonic,impulse and random excitations

Hysteretic behavior due to some nonlinear sources is a common phenomenon in many dynamical systems. One of the sources of this behavior in mechanical systems is dry friction. Dry friction in bolted or riveted joints of mechanical structures makes their dynamic behavior hysteretic. Bi-linear hysteresis is one of the models that can be used to study these systems which is used in this paper. A SDOF system containing a bi-linear hysteretic element called Jenkins element under harmonic, impulse and random excitations is considered. For all three types of excitations, the effects of system and excitation parameters on the defined equivalent system parameters and the response specifications are studied. Harmonic balance method is employed for harmonic excitation studies, and optimum friction threshold for minimizing response amplitude is obtained versus other system parameters and response amplitude. Energy balance method is used for impulse excitation through which the desired decaying ratio can be achieved by tuning the friction threshold, depending on stiffness ratio. System under random excitation is investigated by equivalent linearization technique in two steps. At the first step, equivalent properties are obtained versus instantaneous amplitude of response. In this step, the paper contains the parametric study of system in which the variations of equivalent parameters are described when physical parameters of system or input intensity vary. Overall variance of system response is determined in the second step, and optimum sliding threshold is obtained to have minimum overall variance of system response.     

Dynamics of a gravity stonewall

Treated is the dynamics of a gravity stonewall. The wall is excited by a transient damped periodic oscillation simulating an earthquake. The model adopts a stick-slip friction constitutive law. Sensitivity of energy dissipation to parameters such as number of blocks, friction coefficient, sticktion and slipping stiffness and excitation amplitude and frequency is determined. A 2-D model of the monolithic wall is also analyzed to compare displacement and shear stress of the two constructions.     

Evolution of a Small Distortion of the Spherical Shape of a Gas Bubble under Strong Expansion-Compression

The evolution of a small distortion of the spherical shape of a gas bubble which undergoes strong radial expansion-compression upon a single oscillation of the ambient liquid pressure under a harmonic law are analyzed by numerical experiments. It is assumed that the distortions of the spherical bubble shape are axisymmetric and have the form of individual spherical surface harmonics with numbers of 2–5. Bubble-shape oscillations prior to the beginning of expansion are taken into account. Generally, the distortion value during bubble expansion-compression depends on the phase of bubble-shape oscillation at the beginning of the expansion (initial phase). Emphasis is placed on the dependence of the maximum distortions in the initial phase at certain characteristic times of bubble expansion-compression on the amplitude of the external excitation, liquid viscosity, and distortion mode (harmonic number). The parameters of the problem are typical of the stable periodic sonolumiescence of an individual air bubble in water at room temperature. An exception is the liquid pressure oscillation amplitude, which is varied up to values that are five times the static pressure. That large excitation amplitudes are beyond the stability threshold of periodic oscillations of spherical bubbles. Their consideration is of interest from the point of view of increasing the compression ratio of the bubble gas, i. e., increasing the maximum temperature and density achievable in the final compression stage.__________Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 4, pp. 17–28, July–August, 2005.     

Turbulent drag reduction by spanwise wall oscillations

In the present work a technique is numerically investigated, which is aimed at reducing the friction drag in turbulent boundary layers and channel flows. A cyclic spanwise oscillation of the wall with a proper frequency and amplitude is imposed, allowing a reduction of the turbulent drag of up to 40%. The present work is based on the numerical simulation of the Navier-Stokes equations in the simple geometry of a plane channel flow. The frequency of the oscillations is kept fixed at the most efficient value determined in previous studies, while the choice of the best value for the amplitude of the oscillations is evaluated not only in terms of friction reduction, but also by taking into consideration the overall energy balance and the power spent for the motion of the wall. The analysis of turbulence statistics allows to shed some light on the way oscillations interact with wall turbulence, as illustrated by visual inspection of some instantaneous flow fields. Finally, a simple explanation is proposed for this interaction, which leads to a rough estimate of the most efficient value for the frequency of the oscillations.     

参外联合激励下的簇发振荡及其机理

当周期激励频率远小于系统固有频率时,会存在快慢耦合效应,与单项激励不同,参外联合激励不仅会导致快子系统平衡曲线和分岔行为的复杂化,也会产生一些特殊的非线性现象,为此,本文以两耦合Hodgkin-Huxley细胞模型为例,引入周期参外联合激励,探讨在频域不同尺度耦合时该系统的簇发振荡的特点及其分岔机制．通过建立相应的快慢子系统,得到慢变参数变化下的快子系统的各种分岔模式以及相应的分岔行为,结合转换相图,揭示耦合系统随激励幅值变化时的动力学行为及其机理．研究表明,在激励幅值较小时,系统表现为概周期振荡,两频率分别近似于快子系统平衡曲线由Hopf分岔引起的两稳定极限环的振荡频率．概周期解随激励幅值的增加进入簇发振荡,导致这些簇发振荡的主要原因是在慢变参数变化的部分区间内,存在唯一稳定的平衡曲线,使得系统的轨迹逐渐趋向该平衡曲线,产生沉寂态,并随着慢变参数的变化,由分岔进入激发态．同时,快子系统中参与簇发振荡的稳定吸引子随激励幅值的变化也会不同,导致不同形式的簇发振荡．另外,与单项激励下的情形不同,联合激励时快子系统的部分稳定吸引子掩埋在其它稳定吸引子内,从而失去对簇发振荡的影响．     

Amplitude reduction of primary resonance of nonlinear oscillator by a dynamic vibration absorber using nonlinear coupling

The paper presents the characteristics of a new type of nonlinear dynamic vibration absorber for a main system subjected to a nonlinear restoring force under primary resonance. The absorber is connected to the main system by a link in order to be excited with twice the frequency of the motion of the main system. The natural frequency of the absorber is tuned to be twice the natural frequency of the main system, in contrast to autoparametric vibration absorber, whose natural frequency is tuned to be one-half the natural frequency of the main system. The presented absorber is not excited through the autoparametric resonance, i.e., no trivial equilibrium state exists. Therefore, the absorber always oscillates because of the motion of the main system and cannot be trapped by Coulomb friction acting on the absorber, in contrast to the autoparametric vibration absorber. Under small excitation amplitude, this absorber does not produce an overhang in the frequency response curve, which occurs because of the use of the conventional autoparametric vibration absorber; the overhang renders the response amplitude larger than that in the case without an absorber. In addition, the absorber removes the hysteresis in the frequency response curve caused by the nonlinearity of the restoring force acting on the main system. Regarding large excitation amplitude, the response amplitude in the main system can be decreased by increasing the damping of the absorber, but that decrease is limited by the nonlinearity in the restoring force acting on the main system. This paper also describes experimental validation of the absorber under small excitation amplitude using a simple apparatus.     

Detection and description of non-linear phenomena in experimental modal analysis via linearity plots

Ground vibration tests (GVTs) on aircraft prototypes are mainly performed to experimentally identify the structural dynamic behaviour in terms of a modal model. This assumes a linear dynamic behaviour of the structure. However, in the practice of ground vibration testing it is often observed that structures do not behave in a perfectly linear manner. Non-linearities can be determined, for example, by free play in junctions, hydraulic systems in control surfaces, or friction. This paper compiles measured, typical, non-linear phenomena from various GVTs on large aircraft. The standard procedure in GVTs nowadays is the application of the Harmonic Balance method which linearizes the dynamic behaviour on the level of excitation. The procedure requires a harmonic excitation of the structure which is usually performed during phase resonance testing. The non-linear behaviour is investigated in terms of linearity plots in which the resonance frequency of a mode is plotted as a function of the excitation level. The experimental data is then compatible with all post-processing procedures for the measured results, e.g. updating of the finite element model or flutter calculations. This paper shows measured linearity plots for some typical non-linear phenomena. In the second part of the paper analytical linearity plots for different non-linear stiffness and damping models are considered in order to investigate whether the type of non-linearity can be identified from measured linearity plots. The analytical linearity plots are discussed with respect to their application limits. The analytical linearity plots are used to interpret the experimental linearity plots stemming from various GVTs on different aircraft prototypes. Finally, the observability of non-linear stiffness and non-linear damping characteristics via linearity plots is assessed.     

Map of regimes of pressure oscillations induced by absorption during gas jet injection through a submerged nozzle

Map of regimes of pressure oscillations induced by absorption during rapid injection of a soluble gas jet through a submerged nozzle into liquid, namely, oscillations during absorption, bubbling, internal chugging and small chugging, is suggested. Boundaries between various pressure oscillations regimes occurring when rapidly soluble gas is absorbed in water are investigated theoretically. It is showed that these boundaries are determined by four equations. It is showed that regime of high-frequency pressure oscillations during absorption occurs due to gas bubble oscillations, and other regimes of oscillations occur due to pressure oscillations in the whole system comprising the header, vent tubes and gas bubble. The conditions for excitation of high-frequency and low-frequency oscillations and boundaries between different regimes of pressure pulsations are determined. In a case when Henri's law for soluble gases is valid the developed model predicts that oscillations during absorption are not excited.     

Escape of a harmonically forced particle from an infinite-range potential well: a transient resonance

The paper considers a transient process of escape of a classical particle from a one-dimensional potential well. We address a particular model of the infinite-range potential well that allows independent adjustment of the well depth and of the frequency of small oscillations. The problem can be conveniently reformulated in terms of action-angle variables. Further averaging provides a nontrivial conservation law for the slow flow. Then, one can consider the problem in terms of averaged transient dynamics on primary 1:1 resonance manifold. This simplification allows efficient analytic exploration of the escape process. As a result, one obtains a theoretical prediction for minimal forcing amplitude required for the escape, as a function of the excitation frequency. This function exhibits a single sharp minimum for a certain intermediate frequency value, below the frequency of small free oscillations. This result conforms to earlier numeric and semi-analytic estimations for similar escape models, considered, in particular, in connection with problems of ship capsize and dynamic pull-in in microelectromechanical systems. The results presented in the paper allow conjecturing the generic dynamical mechanism, responsible for these regularities. In particular, the aforementioned sharp minimum in the frequency–amplitude domain is related to formation of heteroclinic connection between the saddle points on the resonance manifold. Numeric simulations are in complete qualitative and reasonable quantitative agreement with the theoretical predictions.     

Sliding friction in the presence of ultrasonic oscillations: superposition of longitudinal oscillations

Summary  It was often observed that friction forces can be reduced significantly if ultrasonic oscillations are superposed to the macroscopic sliding velocity. This phenomenon can be used to improve machining processes by addition of ultrasonic vibration to tools or workpieces, and forms the basis for many processes of ultrasonic machining. On the other hand, ultrasonic vibrations can be used to generate motion. The thrusting force of ultrasonic motors is provided to the rotor through friction. In the present paper, a simple theoretical model for friction in the presence of ultrasonic oscillations is derived theoretically and validated experimentally. The model is capable of predicting the reduction of the macroscopic friction force as a function of the ultrasonic vibration frequency and amplitude and the macroscopic sliding velocity. Received 22 November 2000; accepted for publication 6 February 2001     

钛珠涂层和羟基磷灰石涂层与皮质骨界面的切向微动损伤研究

通过体外模拟切向微动行为,探究两种生物固定材料-钛珠涂层和羟基磷灰石涂层与皮质骨界面之间的微动摩擦磨损机理,建立钛珠涂层和羟基磷灰石涂层与骨组织生物固定界面的微动-松动-骨损伤的关系.结果表明,界面处于部分滑移区时,弹塑性协调作用起主导,固定界面不易产生松动,皮质骨表面损伤以剥落为主,表面损伤较小.增大微动位移幅值,界面摩擦系数增大,皮质骨的损伤增大.同时,划分出了钛珠涂层和羟基磷灰石涂层部分滑移区的工况分界线.通过对比两种材料的摩擦磨损机理,钛珠涂层与皮质骨界面固定效果较好,羟基磷灰石涂层与皮质骨界面损伤较小.结果对人工关节生物固定起到一定的参考作用.     

A polynomial chaos approach to the robust analysis of the dynamic behaviour of friction systems

This paper presents a dynamic behaviour study of non-linear friction systems subject to uncertain friction laws. The main aspects are the analysis of the stability and the associated non-linear amplitude around the steady-state equilibrium. As friction systems are highly sensitive to the dispersion of friction laws, it is necessary to take into account the uncertainty of the friction coefficient to obtain stability intervals and to estimate the extreme magnitudes of oscillations. Intrusive and non-intrusive methods based on the polynomial chaos theory are proposed to tackle these problems. The efficiency of these methods is investigated in a two degree of freedom system representing a drum brake system. The proposed methods prove to be interesting alternatives to the classic methods such as parametric studies and Monte Carlo based techniques.     

On one mechanism of formation of tornado‐like vortices in a rotating fluid

It is shown that during excitation of forced, resonant, inertial oscillations of large amplitude in a rigidly rotating fluid, the mechanism of formation of tornadolike vortices is primarily of a kinematic nature($advection of circulation of the azimuthal component velocity and stretching of vortex lines by the poloidal components of the velocity field that arise from excitation of inertial oscillations). The main parameters of the vortices are obtained by solutions of model problems. To excite such oscillations, it is necessary to deliver energy far exceeding the initial energy of the rotating fluid. Therefore, inertial oscillations by themselves cannot lead to the occurrence of intense atmospheric vortices. Nevertheless, such oscillations can apparently play the role of a trigger mechanism that activates more complex processes of vortex formation related to instability of the atmosphere.     

Inelastic impact dynamics of ships with one-sided barriers. Part I: analytical and numerical investigations

This two-part paper deals with impact interaction of ships with one-sided ice barrier during roll dynamics. The first part presents analytical and numerical studies for the case of inelastic impact. An analytical model of a ship roll motion interacting with ice is developed based on Zhuravlev and Ivanov non-smooth coordinate transformations. These transformations have the advantage of converting the vibro-impact oscillator into an oscillator without barriers such that the corresponding equation of motion does not contain any impact term. Such approaches, however, account for the energy loss at impact times in different ways. The present work, in particular, demonstrates that the impact dynamics may have qualitatively different response characteristics to different dissipation models. The difference between localized and distributed equivalent damping approaches is discussed. Extensive numerical simulations are carried out for all initial conditions covered by the ship grazing orbit for different values of excitation amplitude and frequency of external wave roll moment. The basins of attraction of safe operation are obtained and reveal the coexistence of different response regimes such as non-impact periodic oscillations, modulation impact motion, period added impact oscillations, chaotic impact motion and rotational motion. The second part will consider experimental validations of predicted results.     

盘式制动器摩擦噪声特性的试验分析

盘式制动器制动时产生的摩擦噪声不仅影响车辆的驾乘舒适性,还会带来严重的环境噪声污染. 摩擦噪声具有瞬时性与不确定性的特点,至今尚未形成对制动器摩擦噪声机理的统一论断. 基于盘式制动器声振试验台,研究了摩擦系数、摩擦力波动系数和等效A声级三个参数在不同制动压力和制动初速度下的变化规律,结合对摩擦片微观特性的试验分析,从摩擦学角度揭示了盘式制动器摩擦噪声的发生规律及机理. 结果表明:摩擦噪声随制动初速度的增大而减小,随制动压力的增加而先增大后减小;制动摩擦噪声由于摩擦系统不稳定而产生,其产生原因是因为摩擦副表面的沟壑与黏着引起,沟壑与黏着程度与噪声的声压与频率呈正相关关系. 研究结果对于解释制动器摩擦噪声发生机理、控制制动器噪声污染具有重要理论意义和实际价值.      

One-to-two global-local interaction in a cable-stayed beam observed through analytical, finite element and experimental models

The mechanism of cable end angle-variation induced oscillations in the non-linear interactions between beams and cables in stayed-systems is first explained by a proposed analytical model. It is then verified by both experimental and finite element models. The non-linear interaction maximizes its effects for cable oscillations when inherent quadratic coupling between local and global modes produces energy transfer from low to high frequency vibrations by means of a one-to-two global-local autoparametric resonance. The response of the analytical model is fully described using a continuation method applied directly to the reduced two degree of freedom discrete model showing that, for a selected one-to-two global-local resonant system, primary harmonic excitation of the global mode produces large oscillations of the local mode at twice the excitation frequency. Detailed comparisons between the responses of the analytical model, experimental results and finite element simulations show excellent agreement both in the qualitative behaviour and in the calculated/measured response amplitudes.     

Nonlinear structural dynamics of a new sliding-mode triboelectric energy harvester with multistability

A new sliding-mode triboelectric energy harvester in the form of a cantilever beam with a tip mass that is acted upon by both magnetic and friction forces is modelled and simulated. A numerical scheme based on the trapezoidal rule with the second-order backward difference formula (TR-BDF2) method is introduced to solve the combined non-smooth mechanical and stiff electrical system. This is the first study of the structural dynamics of the sliding-mode triboelectric energy harvesting; additionally, a magnetic field that induces multistability is present. A comparison between the coupled and uncoupled electromechanical models suggests that the electrostatic force between the electrodes can be ignored, which makes the uncoupled model preferable in the dynamical analysis. The influence of the non-conservative force (the friction force) on the multistability of the system is investigated. It is found that the distribution of the multistability on the parametric plane changes even when a small amount of friction is involved, and the areas of bistability and tristability shrink while that of the monostability expands. A comparison among these three types of stability reveals the superiority of invoking bistability as it facilitates broadband energy harvesting. The excitation level plays an important role in inducing the snap-through motion (the interwell oscillation) by enabling the crossing of the energy barriers between wells. The increase in the friction shrinks the frequency band of interwell oscillations from high frequencies down to low frequencies on the discrete frequency sweep. An analysis of the basins of attraction finds that at low frequencies the bistable system can undergo only interwell oscillations, while the tristable system can merely experience intrawell oscillations. The basins can intermingle with each other in both bistable and tristable systems. Finally, an increase in the excitation level can break the basins into discrete pieces and/or points.