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.     

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.     

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.     

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.     

Finite element modelling for the investigation of in-plane modes and damping shims in disc brake squeal

Squeal propensity of the in-plane modes and the constrained-layer type damping shims for disc brake system is investigated by using the finite element method. Theoretical formulation is derived for a rotating disc in contact with two stationary vibrating pads attached to the damping shim components. By the conversion from the theoretical to FE brake model, the full equations of motion for the actual disc brake system describes the disc rotation, the in-plane friction characteristics and damping shims in association with squeal vibration. It is concluded from the results that the in-plane torsion modes can be generated by the negative friction slope, but they cannot be controlled by the damping shims. The in-plane radial mode is also investigated and found to be very insensitive in squeal generation.     

A note on safety-relevant vibrations induced by brake squeal

Brake squeal is mostly considered as a comfort problem only but there are cases in which self-excited vibrations of the brake system not only cause an audible noise but also result in safety-relevant failures of the system. In particular this can occur if lightweight design rims having very low damping are used. Considering the special conditions of lightweight design rims, a minimal model for safety-relevant self-excited vibrations of brake systems is presented. It is shown that most of the knowledge emanated from investigations of the comfort problem can be used to understand and avoid safety-relevant failures of the brake system.     

Modal Amplitude Stability Analysis and its application to brake squeal

In the present study, a new approach is proposed to predict the occurrence of squeal in brake systems. This strategy, called Modal Amplitude Stability Analysis (MASA), is based on the calculation of the first harmonic state-space system of nonlinear original equations using a specific linearization of the nonlinear contact forces at the frictional interfaces. An estimation of the occurrence and generation of increasing self-excited vibration is proposed on the basis of monitoring and the evolution of the real parts of the dynamic system considered as a function of modal amplitudes.     

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.     

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 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.     

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.     

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.     

Wave pattern motion and stick-slip limit cycle oscillation of a disc brake

This paper examines the dynamic response of a rotating squealing disc brake subject to distributed nonlinear contact stresses where two brake pads are assumed to be stationary and rigid. The friction stresses produce high-frequency vibrations that exhibit standing or traveling waves on the disc surface. The wave pattern resulting from the binary flutter mechanism of one transverse doublet mode pair is studied here. The results show that the wave pattern is associated with mode-coupling character. For a steady-squealing mode, the stick zone of the contact area is determined by a smooth friction-velocity curve having both negative and positive slopes.     

Brake squeal: a literature review

Brake squeal, which usually falls in the frequency range between 1 and 16 kHz, has been one of the most difficult concerns associated with automotive brake systems since their inception. It causes customer dissatisfaction and increases warranty costs. Although substantial research has been conducted into predicting and eliminating brake squeal since the 1930s, it is still rather difficult to predict its occurrence. In this paper, the characteristics and current difficulties encountered in tackling brake squeal are first described. A review of the analytical, experimental and numerical methods used for the investigation of brake squeal is then given. Some of the challenges facing brake squeal research are outlined.