A new treatment for predicting the self-excited vibrations of nonlinear systems with frictional interfaces: The Constrained Harmonic Balance Method,with application to disc brake squeal

Brake squeal noise is still an issue since it generates high warranty costs for the automotive industry and irritation for customers. Key parameters must be known in order to reduce it. Stability analysis is a common method of studying nonlinear phenomena and has been widely used by the scientific and the engineering communities for solving disc brake squeal problems. This type of analysis provides areas of stability versus instability for driven parameters, thereby making it possible to define design criteria. Nevertheless, this technique does not permit obtaining the vibrating state of the brake system and nonlinear methods have to be employed. Temporal integration is a well-known method for computing the dynamic solution but as it is time consuming, nonlinear methods such as the Harmonic Balance Method (HBM) are preferred. This paper presents a novel nonlinear method called the Constrained Harmonic Balance Method (CHBM) that works for nonlinear systems subject to flutter instability. An additional constraint-based condition is proposed that omits the static equilibrium point (i.e. the trivial static solution of the nonlinear problem that would be obtained by applying the classical HBM) and therefore focuses on predicting both the Fourier coefficients and the fundamental frequency of the stationary nonlinear system.The effectiveness of the proposed nonlinear approach is illustrated by an analysis of disc brake squeal. The brake system under consideration is a reduced finite element model of a pad and a disc. Both stability and nonlinear analyses are performed and the results are compared with a classical variable order solver integration algorithm.Therefore, the objectives of the following paper are to present not only an extension of the HBM (CHBM) but also to demonstrate an application to the specific problem of disc brake squeal with extensively parametric studies that investigate the effects of the friction coefficient, piston pressure, nonlinear stiffness and structural damping.     

Analysis of disc brake squeal using the complex eigenvalue method

A new functionality of ABAQUS/Standard, which allows for a nonlinear analysis prior to a complex eigenvalue extraction in order to study the stability of brake systems, is used to analyse disc brake squeal. An attempt is made to investigate the effects of system parameters, such as the hydraulic pressure, the rotational velocity of the disc, the friction coefficient of the contact interactions between the pads and the disc, the stiffness of the disc, and the stiffness of the back plates of the pads, on the disc squeal. The simulation results show that significant pad bending vibration may be responsible for the disc brake squeal. The squeal can be reduced by decreasing the friction coefficient, increasing the stiffness of the disc, using damping material on the back plates of the pads, and modifying the shape of the brake pads.     

基于车用电涡流缓速器温度场分析控制系统设计

随着车辆向大型化,高速化的发展趋势,车辆正常行驶制动能量增加,传统的摩擦制动器已经难以满足使用要求,很容易诱发一些故障。电涡流缓速器以其非接触无摩擦,响应时间短,无明显时间滞后,工作时噪声很小,能够提供车辆正常行驶85%的制动功率等优点成为新型的车辆辅助制动系统。本文采用ANSYS软件实现电涡流缓速器转子盘的二维温度场分析,对不同宽度的转筒式电涡流缓速器的温度分布进行数据采集,建立转筒式电涡流缓速器转筒的二维模型,采用虚拟边界法进行简化处理,然后根据系统不同的载荷和约束条件进行温度场控制系统建模。最后本文做了大量的仿真实验,模拟了依据不同的制动力矩,不同的磁路结构以及转子盘温升来分析对汽车制动性的影响。     

Suppression of brake squeal noise applying finite element brake and pad model enhanced by spectral-based assurance criteria

An enhanced dynamic finite element (FE) model with friction coupling is applied to analyze the design of disc brake pad structure for squeal noise reduction. The FE model is built-up from the individual brake component representations. Its interfacial structural connections and boundary conditions are determined by correlating to a set of measured frequency response functions using a spectral-based assurance criterion. The proposed friction coupling formulation produces an asymmetric system stiffness matrix that yields a set of complex conjugate eigenvalues. The analysis shows that eigenvalues possessing positive real parts tend to produce unstable modes with the propensity towards the generation of squeal noise. Using a proposed lumped parameter model and eigenvalue sensitivity study, beneficial pad design changes can be identified and implemented in the detailed FE model to determine the potential improvements in the dynamic stability of the system. Also, a selected set of parametric studies is performed to evaluate numerous design concepts using the proposed dynamic FE model. The best pad design attained, which produces the least amount of squeal response, is finally validated by comparison to a set of actual vehicle test results.     

Modeling of automotive drum brakes for squeal and parameter sensitivity analysis

Many fundamental studies have been conducted to explain the occurrence of squeal in disc and drum brake systems. The elimination of brake squeal, however, still remains a challenging area of research. Here, a numerical modeling approach is developed for investigating the onset of squeal in a drum brake system. The brake system model is based on the modal information extracted from finite element models for individual brake components. The component models of drum and shoes are coupled by the shoe lining material which is modeled as springs located at the centroids of discretized drum and shoe interface elements. The developed multi degree of freedom coupled brake system model is a linear non-self-adjoint system. Its vibrational characteristics are determined by a complex eigenvalue analysis. The study shows that both the frequency separation between two system modes due to static coupling and their associated mode shapes play an important role in mode merging. Mode merging and veering are identified as two important features of modes exhibiting strong interactions, and those modes are likely candidates that lead to coupled-mode instability. Techniques are developed for a parameter sensitivity analysis with respect to lining stiffness and the stiffness of the brake actuation system. The influence of lining friction coefficient on the propensity to squeal is also discussed.     

INVESTIGATION OF AUTOMOTIVE CREEP GROAN NOISE WITH A DISTRIBUTED-SOURCE EXCITATION TECHNIQUE

Creep groan is a high-intensity, low-frequency noise and vibration problem that affects road vehicles at very low speeds. It usually persists for short periods of time, but a “skilled” driver can deliberately make it last several seconds by tuning the force exerted on the brake pedal. The original cause is considered to be a self-induced vibration of the brake components, due to the friction material characteristics that make the system prone to a stick-slip behaviour. No clear evidence upon the creep groan and how it is perceived inside the passenger cockpit has yet been analyzed in the literature and no formal methods are yet available for its analysis. The present study focuses on the transmission of the vibration from the brake component regions to the ears of the vehicle occupants. Characterization of the calliper acceleration and noise inside the cockpit are described for a test vehicle. Distributed-source noise excitation via the standard vehicle hi-fi system is proposed as a practical but less rigorous particular application of the exact reciprocity method. Virtual groan (in which sound power is delivered by means of a loudspeaker) dismisses the airbone path and shows that the phenomenon is structure-borne. On the examined vehicle, front brakes contribute more strongly than rear. Groan frequency close to cavity acoustic resonance constitutes the worst case scenario, and has to be avoided.     

Analysis of friction and instability by the centre manifold theory for a non-linear sprag-slip model

This paper presents the research devoted to the study of instability phenomena in non-linear model with a constant brake friction coefficient. Indeed, the impact of unstable oscillations can be catastrophic. It can cause vehicle control problems and component degradation. Accordingly, complex stability analysis is required. This paper outlines stability analysis and centre manifold approach for studying instability problems. To put it more precisely, one considers brake vibrations and more specifically heavy trucks judder where the dynamic characteristics of the whole front axle assembly is concerned, even if the source of judder is located in the brake system. The modelling introduces the sprag-slip mechanism based on dynamic coupling due to buttressing. The non-linearity is expressed as a polynomial with quadratic and cubic terms. This model does not require the use of brake negative coefficient, in order to predict the instability phenomena. Finally, the centre manifold approach is used to obtain equations for the limit cycle amplitudes. The centre manifold theory allows the reduction of the number of equations of the original system in order to obtain a simplified system, without loosing the dynamics of the original system as well as the contributions of non-linear terms. The goal is the study of the stability analysis and the validation of the centre manifold approach for a complex non-linear model by comparing results obtained by solving the full system and by using the centre manifold approach. The brake friction coefficient is used as an unfolding parameter of the fundamental Hopf bifurcation point.     

Minimal models for disk brake squeal

Numerous publications on the modeling of disk brake squeal can be found in the literature. Recent publications describe the onset of disk brake squeal as an instability of the trivial solution resulting from the non-conservative friction forces even for a constant friction coefficient. Therefore, a minimal model of disk brake squeal must contain at least two degrees of freedom. A literature review of minimal models shows that there is still a lack of a minimal model describing the basic behavior of disk brake squeal which can easily be associated to an automotive disk brake.Therefore, a new minimal model of a disk brake is introduced here, showing an obvious relation to the technical system. In this model, the vibration of the disk is taken into account, as it plays a dominant role in brake squeal. The model is analyzed with respect to its stability behavior, and consequences in using it in the optimization of disk brake systems are discussed.     

Influence of magnetic powders on the tribological performance of a novel magnetic brake material

By adding magnetic powders into matrix material, it has been proved to be a creative approach to improve tribological properties of brake materials. In this paper, a novel magnetic brake material with Nd–Fe–B and nano-Fe₃O₄ was developed, and the influential mechanism of these two magnetic powders and their content on the friction and wear performance was deeply discussed. Firstly, some experiments were carried out to investigate the tribological performance and influential mechanisms of four groups of brake pad samples with different magnetic powders. Furthermore, based on these results, further experiments for investigating the influence that Nd–Fe–B contents have on the tribological properties were conducted. According to the theoretical analysis about experiments, it was concluded that nano-Fe₃O₄ is beneficial to promote the formation of friction film and has certain lubricant effects. However, Nd–Fe–B has double effects on the formation of friction film. It will have positive effects when its content is less than a certain value. Otherwise, it will destroy the structure of friction film. Conclusively, it is believed that this study will be significantly valuable and meaningful for developing new brake materials and improving safety reliability of mechanical brakes.     

The method of feed-in energy on disc brake squeal

Brake squeal is studied in this paper by feed-in energy analysis. Based on the brake closed-loop coupling model, a calculation method of feed-in energy for squeal mode is derived. Result of the feed-in energy indicates squeal tendency of the brake system, while formula for calculating it discloses the relation among brake squeal phenomenon and structural parameters, such as frictional coefficient, geometric shape of brake pads, elastic modulus of frictional material, substructure modal shape, etc. The method also helps to analyze the effectiveness of various structural modification schemes attempted to eliminate the squeal noise. Finally, this method is illustrated by application to a typical squealing disc brake.     

Structural damage detection of controlled building structures using frequency response functions

If a building structure requires both a vibration control system and a health monitoring system, the integration of the two systems will be cost-effective and beneficial. One of the key problems of this integrated system is how to use control devices to enhance system identification and damage detection. This paper presents a new method for system identification and damage detection of controlled building structures equipped with semi-active friction dampers through model updating based on frequency response functions. The two states of the building are first created by adding a known stiffness using semi-active friction dampers. A scheme based on the frequency response functions of the two states of the building is then presented to identify stiffness parameters of structural members in consideration of structural connectivity and transformation information. By applying the proposed model updating scheme to the damaged building, a damage detection scheme is proposed based on the identified stiffness parameters of structural members of both the original and damaged buildings. The feasibility of the proposed schemes is finally demonstrated through a detailed numerical investigation in terms of an example building, in which the effects of measurement noise and excitation conditions are discussed. The numerical results clearly show that the proposed method can locate and quantify damage satisfactorily even though measurement noise is taken into consideration.     

Eigenvalue optimization against brake squeal: Symmetry,mathematical background and experiments

Brake squeal is still a challenge for design engineers and scientists. Due to cost reasons for the avoidance of brake noise only passive measures are meaningful for a broad industrial range. Many countermeasures against squeal are based on the introduction of damping, for example by using shims. In the literature on the modeling of brake squeal, the structural properties of the brake disc are most often not considered. It has however been shown analytically and experimentally that the stiffness properties of the disc are important and that splitting of double modes of the disc has a stabilizing effect. This knowledge can be used for structural optimization of brake rotors. The goal of this paper is to exploit the potential and to discuss some mathematical difficulties. Furthermore, experimental evidence for the relation of rotor asymmetry and squeal is given.     

基于AMESim的制动钳动态所需液量检测仿真研究

制动钳所需液量检测是制动钳性能检测中十分重要的一部分,目前关于制动钳动态所需液量检测研究缺乏理论和仿真依据,无法结合实际检测实现制动钳故障诊断,针对这一问题,在研究主缸位移差值法动态所需液量检测系统数学模型的基础上搭建AMEsim仿真模型,对主缸活塞速度和钳体结构因素进行仿真分析,并通过实验验证模型的正确性。结果表明：主缸活塞速度对动态所需液量检测影响较小;回位弹簧刚度、制动间隙和摩擦块、橡胶密封圈硬度对动态所需液量曲线有不同程度的影响,可以根据曲线特征实现制动钳故障诊断。     

Noise temperature distribution of superconducting hot electron bolometer mixers

We report on the investigation of optimal bias region of a wide-band superconducting hot electron bolometer(HEB)mixer in terms of noise temperature performance for multi-pixel heterodyne receiver application in the 5-meter Dome A Terahertz Explorer(DATE5) telescope. By evaluating the double sideband(DSB) receiver noise temperature(Trec) across a wide frequency range from 0.2 THz to 1.34 THz and with a large number of bias points, a broad optimal bias region has been observed, illustrating a good bias applicability for multipixel application since the performance of the HEB mixer is uniquely determined by each bias point. The noise temperature of the HEB mixer has been analyzed by calibrating the noise contribution of all RF components, whose transmissions have been measured by a time-domain spectroscopy. The corrected noise temperature distribution shows a frequency independence relation. The dependence of the optimal bias region on the bath temperature of the HEB mixer has also been investigated, the bath temperature has limited effect on the lowest receiver noise temperature until 7 K, however the optimal bias region deteriorates obviously with increasing bath temperature.     

Chaos in brake squeal noise

Brake squeal has become an increasing concern to the automotive industry because of warranty costs and the requirement for continued interior vehicle noise reduction. Most research has been directed to either analytical and experimental studies of brake squeal mechanisms or the prediction of brake squeal propensity using finite element methods. By comparison, there is a lack of systematic analysis of brake squeal data obtained from a noise dynamometer. It is well known that brake squeal is a nonlinear transient phenomenon and a number of studies using analytical and experimental models of brake systems (e.g., pin-on-disc) indicate that it could be treated as a chaotic phenomenon. Data obtained from a full brake system on a noise dynamometer were examined with nonlinear analysis techniques. The application of recurrence plots reveals chaotic structures even in noisy data from the squealing events. By separating the time series into different regimes, lower dimensional attractors are isolated and quantified by dynamic invariants such as correlation dimension estimates or Lyapunov exponents. Further analysis of the recurrence plot of squealing events by means of recurrence quantification analysis measures reveals different regimes of laminar and random behaviour, periodicity and chaos-forming recurrent transitions. These results help to classify brake squeal mechanisms and to enhance understanding of friction-related noise phenomena.     

Local control of noise and vibration with KELTRACK™ friction modifier and Protector trackside application: an integrated solution

Wheel squeal is a source of continuing concern for many railroads and transits, as well as for their neighbours. The underlying mechanism for squeal noise has been well understood in the literature for some time. However an integrated abatement method addressing the underlying cause of the problem has not previously been reported.This paper describes practical experience using a water-based liquid Friction Modifier (KELTRACK™) applied using a top of rail trackside applicator (Portec Protector^®). The Friction Modifier and delivery equipment have been co-developed to provide an optimized product/delivery system that gives significant reduction of wheel squeal in curves.Wheels experiencing lateral creep in curves are subject to roll-slip oscillations as a result of the frictional characteristics of the interface layer between the wheel and rail. These roll-slip oscillations are amplified in the wheel web leading to the familiar squeal. Providing a thin film of material between the wheel and rail with positive friction characteristics can both in theory and practice greatly reduce the magnitude of these oscillations. The controlled intermediate friction characteristics of KELTRACK™ allow the material to be delivered to the top of both rails without compromising traction or braking.The positive friction aspects of the friction modifier are illustrated by published laboratory studies. Delivery of KELTRACK™ to the contact patch is achieved with a proprietary top of rail electric trackside applicator, the Portec Protector^®. The material is delivered to the top of both rails for optimum friction control.The integrated product/equipment technology is now successfully controlling noise at more than twenty transit sites. Typical sound level reduction is 10-15 dB, in some cases as high as 20 dB, depending on the initial sound level. Two case studies are presented illustrating the technology.     

Sensitivity of friction-induced vibration in idealised systems

Friction-induced vibration occurs in many contexts: vehicle brake squeal in particular remains surprisingly unpredictable and poorly understood. Testing theory against measurements has been hindered by the difficulty in obtaining repeatable results suggesting that the phenomenon is sensitive to small changes in parameters. This paper explores highly idealised cases as a starting point to understanding sensitivity. Using a stability criterion based on the roots of the characteristic equations of the system, the sensitivity of predictions to parameter changes is studied, focussing on a single-mode model. The effects of contact stiffness, non-proportional damping and a velocity-dependent coefficient of friction are considered. It is found that each physical effect can significantly alter predictions; each physical effect can lead to extreme sensitivity; and high sensitivity can sometimes occur when modal amplitudes are small such that they might normally be considered insignificant. With a large body of literature focussing on reduced-order models this study provides an important warning when interpreting their results.