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.     

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.     

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.     

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.     

Effectiveness of multilayer viscoelastic insulators to prevent occurrences of brake squeal: A numerical study

The purpose of this publication is to give an overview of the actual role of multi-layered viscoelastic parts, so called “shims”, to prevent squeal noises of automotive brake systems. Since shear stress is usually used to damp thin structures in their bending modes it is commonly believed to be the largest underwent by shims. To check this assumption and considering that stresses underwent by shims cannot be measured experimentally, the authors have computed them with the help of a detailed and realistic finite element model. Contrary to what shims manufacturers say, this study exhibits the fact that shims are almost uniquely solicited in their normal direction in brake systems. Secondly, the study focuses on the added damping and stiffening induced by the viscoelastic materials. In order to take into account these materials, a realistic frequency dependent viscoelastic behavior has been integrated in the simulations. Finally, the study shows certains eigenmodes for which the viscoelastic behavior of the shims reveals instabilities that would not exist without it. It is shown that this is due to coalescence phenomenon.     

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.     

Structural optimization of an asymmetric automotive brake disc with cooling channels to avoid squeal

Brake squeal is still a major issue in the automotive industry due to comfort complaints of passengers and resulting high warranty costs. Many measures to avoid squeal have been discussed in the engineering community reaching from purely passive measures like the increase of damping, e.g. by the application of shims, to the active or semiactive suppression of squeal. While active measures can be effective but are elaborate and therefore more expensive, passive measure are less complex in most cases. This leads to the necessity to develop passive, economic and robust measures to avoid squeal. Asymmetry of the brake rotor has been proposed to achieve this goal and the resulting split of all double eigenfrequencies of the brake rotor has lately been shown to stabilize the system.     

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.     

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 DISC BRAKE NOISE USING A TWO-DEGREE-OF-FREEDOM MODEL

Although a brake pad and disc have many modes of vibration, when it is unstable and hence noisy then frequently only a single mode of the complete system contributes to the vibration. In this condition, only a few modes are required to model the system. In this paper, a two-degree-of-freedom model is adopted where the disc and the pad are modelled as single modes connected by a sliding friction interface. Using this model, the interaction between the pad and the disc is investigated. Stability analysis is performed to show under what parametric conditions the system becomes unstable, assuming that the existence of a limit cycle represents the noisy state of the disc brake system. The results of this analysis show that the damping of the disc is as important as that of the pad. Non-linear analysis is also performed to demonstrate various limit cycles in the phase space. The results show that the addition of damping to either the disc or the pad alone may make the system more unstable, and hence noisy.     

EXPERIMENTAL ACTIVE CONTROL OF AUTOMOTIVE DISC BRAKE ROTOR SQUEAL USING DITHER

This paper presents an experimental investigation into the application of “dither” control for the active control and suppression of automobile disc brake squeal. Dither control is characterized by the application of a control effort at a frequency higher than the disturbance to be controlled. In the particular system considered here, a vibro-acoustic analysis of a disc brake system during squeal determined the acoustic squeal signature to be emanating from the brake rotor. This squeal was eliminated, and could even be prevented from occurring, through the application of a harmonic force with a frequency higher than the squeal frequency. The harmonic force was generated by a stack of piezoelectric elements placed within the brake's caliper piston. The harmonic force represented a small variation about the mean clamping force exerted by the brake upon the rotor. The high-frequency vibration in the brake system due to the action of the control system was not heard if an ultrasonic control frequency was used. More importantly, the active control system is shown to be able to prevent squeal from even occurring. This gives rise to a possible active control system integrated into the brake system of automobiles to prevent squeal.     

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.     

Performances of some reduced bases for the stability analysis of a disc/pads system in sliding contact

The complex eigenvalue analysis is a widely used technique to investigate the stability of a dynamical system with frictional contact. In the case of brake systems, it is the most frequently employed method to study the propensity of the brake to generate squeal noise. When finite element models are considered, iterative solvers are needed to calculate the complex modes and eigenvalues with good precision. In practice, reduced real bases are often used in order to reduce the computational times. However, great attention should be focused on the errors introduced by the reduction, which is rarely done. In this paper, the performances of some reduced bases are investigated in the case of a simple disc/pads system. Bases composed of real coupled modes and bases provided by Component Mode Synthesis (CMS) techniques are tested. An enrichment of these bases is proposed in order to improve the precision of the results. In particular, new rubbing attachment modes are proposed to adapt free-interface CMS techniques to frictional contact. When real coupled modes are used, it is suggested to complete the basis by the static response to a first-order approximation of the friction forces. Applied to the disc/pads model, the different enrichment options allow a reduction of the errors on frequencies, divergence rates and mode shapes by a factor comprised between 10 and 100 without significantly increasing the computational times.     

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.     

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.     

Automotive disc brake squeal

Disc brake squeal remains an elusive problem in the automotive industry. Since the early 20th century, many investigators have examined the problem with experimental, analytical, and computational techniques, but there is as yet no method to completely suppress disc brake squeal. This paper provides a comprehensive review and bibliography of works on disc brake squeal. In an effort to make this review accessible to a large audience, background sections on vibrations, contact and disc brake systems are also included.     

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.