The destabilization paradox applied to friction-induced vibrations in an aircraft braking system

Mechanisms of friction are known as an important source of vibrations in a large variety of engineering systems, where the emergence of oscillations is noisy and can cause severe damage to the system. The reduction or elimination of these vibrations is then an industrial issue that requires the attention of engineers and researchers together. Friction-induced vibrations have been the matter of several investigations, considering experimental, analytical, and numerical approaches. An aircraft braking system is a complex engineering system prone to friction-induced vibrations, and is the subject herein. By considering experimental observations and by evaluating the mechanisms of friction involved, a complete nonlinear model is built. The nonlinear contact between the rotors and the stators is considered. The stability analysis is performed by determining the eigenvalues of the linearized system at the equilibrium point. Parametric studies are conducted in order to evaluate the effects of various system parameters on stability. Special attention will be given to the understanding the role of damping and the associated destabilization paradox in mode-coupling instabilities.     

渐变段倾角对渐变复合腔特性影响的分析

 利用模式耦合理论，在考虑多模耦合的情况下，对渐变结构复合腔进行了冷腔分析，计算了H₅₁-H₅₂模式对下，各个模式的耦合及场幅值分布情况，分析了渐变段的倾角对渐变复合腔的Q值及场幅值分布的影响。研究表明：渐变段的倾角对渐变结构复合腔的高频特性有很大的影响，特别是各模式的场分布及Q值，合适地选择渐变角度，能使场幅值放大率比较大，这将有利于提高注-波互作用效率。     

How can automotive friction-induced noises be related to physical mechanisms?

Three main physical mechanisms are found in the literature to explain the occurrence of friction-induced noises: the stick–slip, the sprag-slip and the mode-coupling instabilities. In order to improve the understanding of the automotive friction-induced noises and regarding the variety of these noises and the systems concerned, the consideration of these three physical mechanisms in a unique model, called phenomenological model, is proposed. The relationships between the mechanisms at the origin of friction-induced noises and the different kinds of friction-induced noises that can be perceived in a vehicle are particularly investigated. First, a simple classification of automotive-friction induced noises is proposed and highlights three noise categories: squeal, squeak and creak noises. Time simulations carried out on the phenomenological model show the qualitative reproduction of the vibrational behaviors at the origin of these three noise categories. Conditions are then proposed to define the three noise categories, based on the contact states ratios encountered in the time response. In order to understand the relationships between the three physical mechanisms and the three noise categories, a fullfact design of experiments is carried out with the phenomenological model. A system with realistic dynamic properties is used and submitted to a large number of conditions of use, allowing the appearance of a wide diversity of responses. The results show that the three mechanisms as well as the three noise categories can be obtained on a same dynamic system. They also show that creak is caused by a stick–slip phenomenon, squeal is mainly due to a mode-coupling phenomenon, while squeak can be caused either by mode-coupling or stick–slip phenomena. Finally, the occurrence of each mechanism and noise category is independently analyzed for the given dynamic system, giving quite significant trends towards model parameters. These trends highlight some interesting design levers to reduce the propensity of noise for an automotive structure.     

Mode-coupling theory for purely diffusive systems

A mode-coupling formalism is developed for multicomponent systems of particles performing diffusive motion in a uniform host medium. The mode-coupling equations are derived from a set of nonlinear fluctuating diffusion equations by expanding the concentration-dependent diffusion constants about their equilibrium values. From the mode-coupling equations the dominant long time behavior of current-current and super-Burnett correlation functions is derived. As specific applications I consider the long time behaviors of these correlation functions for collective and tracer diffusion in a one-component lattice gas with particle-conserving stochastic dynamics. The results agree with those from exactly solvable models and computer simulations.     

A statistical-mechanical theory of slow dynamics near the glass transition

A statistical-mechanical theory of slow dynamics near the glass transition in two kinds of glass-forming systems, (M) molecular systems and (S) suspensions of colloids, is presented from a unified point of view based on the Tokuyama-Mori projection operator method. The exact diffusion equations for the coherent- and the incoherent-intermediate scattering functions are first derived, whose memory functions are convolutionless in time and contain the correlation effects due to the hydrodynamic interactions in (S). The analytic expressions of the memory functions are then calculated within the mode-coupling theory (MCT) approximation and are shown to coincide with the conventional ones obtained by MCT. Alternative mode-coupling equations are thus obtained in (M) and (S) separately. Self-diffusion is also discussed. Alternative equations for the mean-square displacement and the non-Gaussian parameter are also derived within MCT approximation. All results in both the systems are compared with those obtained by MCT.     

Time-dependent Diffusion Coefficient and Conventional Diffusion Constant of Nanoparticles in Polymer Melts by Mode-coupling Theory (cited: 2)

Time-dependent diffusion coefficient and conventional diffusion constant are calculated and analyzed to study diffusion of nanoparticles in polymer melts. A generalized Langevin equa-tion is adopted to describe the diffusion dynamics. Mode-coupling theory is employed to calculate the memory kernel of friction. For simplicity, only microscopic terms arising from binary collision and coupling to the solvent density fluctuation are included in the formalism. The equilibrium structural information functions of the polymer nanocomposites required by mode-coupling theory are calculated on the basis of polymer reference interaction site modelwith Percus-Yevick closure. The effect of nanoparticle size and that of the polymer size are clarified explicitly. The structural functions, the friction kernel, as well as the diffusion coefficient show a rich variety with varying nanoparticle radius and polymer chain length. We find that for small nanoparticles or short chain polymers, the characteristic short time non-Markov diffusion dynamics becomes more prominent, and the diffusion coefficient takes longer time to approach asymptotically the conventional diffusion constant. This constant due to the microscopic contributions will decrease with the increase of nanoparticle size, while increase with polymer size. Furthermore, our result of diffusion constant from mode-coupling theory is compared with the value predicted from the Stokes-Einstein relation. It shows that the microscopic contributions to the diffusion constant are dominant for small nanoparticles or long chain polymers. Inversely, when nanonparticle is big, or polymer chain is short, the hydrodynamic contribution might play a significant role.     

Oscillation pattern of stick-slip vibrations

This paper studies the stick-slip oscillations of discrete systems interacting with translating energy source through a non-linear smooth friction curve. The stick-slip limit cycle oscillations of a single degree-of-freedom model are examined by means of numerical time-integration and analytical methods. Similar approaches are also applied to the model of the coupled friction oscillator. Particularly, it is found that the steady-state response of the coupled oscillator can be divided into two different forms of oscillation (mode-merged and mode-separated oscillations) according to the frequency separation of two modes. The oscillation pattern of the steady-state response is shown to depend on system parameters such as detuning factor, energy source speed, and normal contact load.     

模耦合理论计算纳米粒子在聚合物熔体中的含时扩散系数与常规扩散常数 (cited: 2)

分析和计算了纳米粒子在聚合物熔体中的含时扩散系数与常规扩散常数. 采用广义朗之万方程描述扩散动力学,并通过模耦合理论计算摩擦记忆内核.为简单起见,只考虑了来自两体碰撞和溶剂密度涨落耦合作用两类微观因素对摩擦记忆内核的贡献. 采用聚合物参考作用点模型以及Percus-Yevick闭合条件计算了聚合物-纳米粒子复合溶液的平衡态结构信息函数;详尽分析了纳米粒子的尺寸与聚合物链的尺寸对扩散动力学的影响. 揭示了结构函数、摩擦记忆内核以及扩散系数等随着纳米粒子半径和聚合物链长的变化关系. 结果表明,对于小尺寸的纳米粒子或者短链的聚合物,短时间的非马尔可夫扩散 动力学特征比较显著,含时扩散系数需要更长的时间弛豫到常规扩散常数. 微观因素对扩散常数的贡献随着纳米粒子尺寸的增加而减小,却随着聚合物链长的增加而增大. 此外,模耦合理论得到的扩散常数与Stokes-Einstein关系的预测值进行比较,发现对于小尺寸的纳米粒子或者长链的聚合物,微观因素对扩散常数的的贡献占主导地位. 相反,当纳米粒子较大或者聚合物链长较短时,流体力学的贡献会发挥重要作用.     

Mode-Coupling Theory for Glass Transition of Active-Passive Binary Mixture?

Collective behaviours of active particle systems have gained great research attentions in recent years. Here we present a mode-coupling theory (MCT) framework to study the glass transition of a mixture system of active and passive Brownian particles. The starting point is an effective Smoluchowski equation, which governs the dynamics of the probability distribution function in the position phase space. With the assumption of the existence of a nonequilibrium steady state, we are able to obtain dynamic equations for the intermediate scattering functions (ISFs), wherein an irreducible memory function is introduced which in turn can be written as functions of the ISFs based on standard mode-coupling approximations. The effect of particle activity is included through an effective diffusion coefficient which can be obtained via short time simulations. By calculating the long-time limit of the ISF, the Debye-Waller (DW) factor, one can determine the critical packing fraction η_c of glass transition. We find that for active-passive (AP) mixtures with the same particle sizes, η_c increases as the partial fraction of active particle x_A increases, which is in agreement with previous simulation works. For system with different active/passive particle sizes, we find an interesting reentrance behaviour of glass transition, i.e., η_c shows a non-monotonic dependence on x_A. In addition, such a reentrance behaviour would disappear if the particle activity is large enough. Our results thus provide a useful theoretical scheme to study glass transition behaviour of active-passive mixture systems in a promising way.