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.     

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.     

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.     

Squeal and chatter phenomena generated in a mountain bike disc brake

This paper examines squeal and chatter phenomena generated experimentally in mountain bike disc brakes. There are two kinds of frictional self-excited vibrations in the bike disc brakes, called squeal with frequency of 1 kHz and chatter with frequency of 500 Hz. In order to reproduce the squeal and chatter, a bench test apparatus using an actual bike was set up to determine the associated frequency characteristics experimentally. The results show the frequencies to be independent of pad temperature and disc rotating speed. Squeal is shown to be in-plane vibration in the direction of the disc surface which is caused by the frictional characteristics having negative slope with respect to the relative velocity in the vibrating system, which includes brake unit, spokes and hub. Chatter is generated within a limited high temperature region. Again, it is frictional vibration in which the squeal and out-of-plane vibration of the disc due to Coulomb friction combine through the internal resonance relation between in-plane and out-of-plane nonlinear vibration caused by the temperature increase of the disc during braking.     

Numerical study of friction-induced instability and acoustic radiation – Effect of ramp loading on the squeal propensity for a simplified brake model

This paper presents a numerical study of the influence of loading conditions on the vibrational and acoustic responses of a disc brake system subjected to squeal. A simplified model composed of a circular disc and a pad is proposed. Nonlinear effects of contact and friction over the frictional interface are modelled with a cubic law and a classical Coulomb?s law with a constant friction coefficient. The stability analysis of this system shows the presence of two instabilities with one and two unstable modes that lead to friction-induced nonlinear vibrations and squeal noise. Nonlinear time analysis by temporal integration is conducted for two cases of loadings and initial conditions: a static load near the associated sliding equilibrium and a slow and a fast ramp loading. The analysis of the time responses shows that a sufficiently fast ramp loading can destabilize a stable configuration and generate nonlinear vibrations. Moreover, the fast ramp loading applied for the two unstable cases generates higher amplitudes of velocity than for the static load cases. The frequency analysis shows that the fast ramp loading generates a more complex spectrum than for the static load with the appearance of new resonance peaks. The acoustic responses for these cases are estimated by applying the multi-frequency acoustic calculation method based on the Fourier series decomposition of the velocity and the Boundary Element Method. Squeal noise emissions for the fast ramp loading present lower or higher levels than for the static load due to the different amplitudes of velocities. Moreover, the directivity is more complex for the fast ramp loading due to the appearance of new harmonic components in the velocity spectrum. Finally, the sound pressure convergence study shows that only the first harmonic components are sufficient to well describe the acoustic response.     

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.     

Analysis of brake squeal noise using the finite element method: A parametric study

Brake squeal noise has been under investigation by automotive manufacturers for decades due to consistent customer complaints and high warranty costs. J.D. Power surveys consistently show brake noise as being one of the most critical vehicle quality measurements. Furthermore, the development of methods to predict noise occurrence during the design of a brake system has been the target of many researchers in recent years.This paper summarizes the application of complex eigenvalue analysis in a finite element model of a commercial brake system. The effect of the operational parameters (friction coefficient, braking pressure and brake temperature) and wear on the dynamic stability of the brake system is examined. After identifying unstable frequencies and the behavior of the brake system under different conditions, the performance of some control methods are tested. Changes in material properties and the application of brake noise insulators are presented and their effects discussed.The results show that the effect of brake temperature changes the coupling mechanisms between rotor and pad, which in some cases can be useful in order to reduce the instabilities and generated noise. Wear is an operational condition that has an strong effect on the system instability, since stiffness properties of brake pads are influenced by the changes on geometry and on the friction material, leading to high-frequency noise generation when the system is in the end of its lifetime. Application of brake insulators requires a detailed investigation of the system since, for some cases, an increase on the system damping does not balance changes on stiffness, leading the system to instability and noise.     

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.     

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.     

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.     

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.     

LINING-DEFORMATION-INDUCED MODAL COUPLING AS SQUEAL GENERATOR IN A DISTRIBUTED PARAMETER DISC BRAKE MODEL

A distributed-parameter model of a disc brake is developed, which is used for simulation of friction-induced vibrations in the form of high-frequency squeal. The effect of different squeal generation mechanisms is investigated. The comparison of measured and calculated frequencies shows a good agreement and this study indicates that lining-deformation-induced modal coupling can act as a squeal generator in disc brakes.     

Effect of damping on the propensity of squeal instability: an experimental investigation

Friction induced vibrations in automotive brakes is recognized as a major problem in industry. Squeal is a difficult subject because of its unpredictability caused by a not completely understood sensitivity to variation of the system parameters. In the literature several analytical and numerical studies deal with the relationship between damping and system propensity to have instability. These studies highlight the existence of a nonintuitive effect of damping distribution on modal coupling that gives rise to the unstable vibrations. The complexity of commercial brakes and the difficulties to identify the values of modal damping in brake assemblies lead to the necessity to rely on experimental analysis using simplified test rigs. This paper presents an experimental investigation of the relationship between the distribution of modal damping and the propensity to develop squeal in a beam-on-disk setup, which reliably reproduces squeal events with easy control and measurement of the damping of the disk and the beam, respectively. The experiments highlight the key role played by the modal damping distribution on squeal: A nonuniform repartition of the modal damping causes an increase of the squeal propensity.     

Recurrence analysis and phase space reconstruction of irregular vibration in friction brakes: Signatures of chaos in steady sliding

Irregular friction brake vibration data have been collected with sampling rates of up to 200 kHz. The measured time series have been subjected to recurrence analysis and phase space reconstruction. The recurrence analysis indicates that irregular vibration states of friction brakes are strongly dominated by intermittency phenomena. Phase space reconstruction suggests that this intermittency is dominated by low-dimensional irregular deterministic dynamics rather than by high-dimensional stochastic processes.     

Brake squeal reduction of vehicle disc brake system with interval parameters by uncertain optimization

An uncertain optimization method for brake squeal reduction of vehicle disc brake system with interval parameters is presented in this paper. In the proposed method, the parameters of frictional coefficient, material properties and the thicknesses of wearing components are treated as uncertain parameters, which are described as interval variables. Attention is focused on the stability analysis of a brake system in squeal, and the stability of brake system is investigated via the complex eigenvalue analysis (CEA) method. The dominant unstable mode is extracted by performing CEA based on a linear finite element (FE) model, and the negative damping ratio corresponding to the dominant unstable mode is selected as the indicator of instability. The response surface method (RSM) is applied to approximate the implicit relationship between the unstable mode and the system parameters. A reliability-based optimization model for improving the stability of the vehicle disc brake system with interval parameters is constructed based on RSM, interval analysis and reliability analysis. The Genetic Algorithm is used to get the optimal values of design parameters from the optimization model. The stability analysis and optimization of a disc brake system are carried out, and the results show that brake squeal propensity can be reduced by using stiffer back plates. The proposed approach can be used to improve the stability of the vehicle disc brake system with uncertain parameters effectively.     

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.     

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。     

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.