Fast Transient Analysis for Locally Nonlinear Structures by Recursive Block Convolution, #79

Journal of Vibration and Acoustics, 2001

This paper introduces the velocity-dependent friction with the Stribeck effect into the moving load model for the vibration of a car disc brake. By solving its corresponding eigenvalue problem, a bounded region of instability is obtained for the rotating speed of the disc versus the friction coefficient at the disc/pads interface, which is compatible with observed squeal phenomenon of a car disc brake.

International Journal for Numerical Methods in Engineering, 2004

This paper presents a numerical method to calculate the unstable frequencies of a car disc brake and suggests a suitable analysis procedure. The stationary components of the disc brake are modelled using finite elements and the disc as a thin plate. The separate treatments of the stationary components and the rotating disc facilitate the modelling of the disc brake squeal as a moving load problem. Some uncertain system parameters of the stationary components and the disc are tuned to fit experimental results. A linear, complex-valued, asymmetric eigenvalue formulation is derived for the friction-induced vibration of the disc brake. Predicted unstable frequencies are compared with experimentally established squeal frequencies of a real car disc brake.

Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering, 2003

This paper presents a method for analysing the unstable vibration of a car disc brake, and numerical results are compared with squeal frequencies from an experimental test. The stationary components of the disc brake are modelled using many thousands of solid and special nite elements, and the contacts between the stationary components and between the pads and the disc are considered. The disc is modelled as a thin plate and its modes are obtained analytically. These two parts (stationary and rotating) of the disc brake are brought together with the contact conditions at the disc/pads interface in such a way that the friction-induced vibration of the disc brake is treated as a moving load problem. Predicted unstable frequencies are seen to be close to experimental squeal frequencies.

Journal of Sound and Vibration

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 show that a sufficiently fast ramp loading can destabilize a stable configuration and generate nonlinear vibrations. Moreover, the fast ramp loading applied for the two unstab...

International Journal of Vehicle Design, 2009

The focus of this article is to show and discuss the nonlinear dynamical behaviors of brake system subjected to friction-induced vibration that can be generated due to the co-existence of multi-unstable modes. A finite element model with friction coupling is used to analyze the stability of the brake system and the stationary nonlinear oscillations for squeal noise prediction. The mechanism of squeal instability considers a mode coupling phenomenon that is classically referred to as coalescence.

Journal of Sound and Vibration, 2005

In this paper, we examine the dynamics of a simple model for a braking process. The 4 dof model is designed to capture some of the dynamics of a set of brake pads halting a rotor. We find from our model that the motion of the system transverse to the direction of braking experiences a sharp change in excitation when the slip velocity in the braking direction is low. This change results in a complicated vibration which occurs at low slip speeds. In addition, there is often no correlation between the frequencies of the resulting vibration and the natural frequencies of system in the absence of friction. Based on the results from our numerical investigations we are able to propose a new mechanism for disc brake squeal. This mechanism is similar to previously proposed mechanisms in that we view squeal as a friction-induced phenomenon. However, in contrast to the majority of these mechanisms, we are able to encompass the transient, dissipative nature of a braking process. r

International Journal of Vehicle Noise and Vibration, 2006

There are typically two different methodologies that can be used to predict squeal in a disc brake, i.e., complex eigenvalue analysis and dynamic transient analysis. The positive real parts of complex eigenvalues indicate the degree of instability of the disc brake and are thought to associate with squeal occurrence or noise intensity. On the other hand, instability in the disc brake can be identified as an initially divergent vibration response using transient analysis. From the literature it appears that the two approaches were performed separately, and their correlation was not much investigated. In addition, there is more than one way of dealing the frictional contact in a disc brake. This paper explores a proper way of conducting both types of analyses and investigates the correlation between them for a large degree-of-freedom disc brake model. A detailed three-dimensional finite element model of a real disc brake is developed. Three different contact regimes are examined in order to assess the best correlation between the two methodologies.

Journal of Sound and Vibration, 2015

Non-stationary effects in the friction-induced dynamics of a two-degree-of-freedom brake model are examined in this paper. The belt-spring-block model is designed to take into account variations of the normal load during the braking process. It is shown that due to the adiabatically slowing down velocity of the belt, the system response experiences specific qualitative transitions that can be viewed as simple mechanical indicators for the onset of squeal phenomenon. In particular, the creep-slip leading to a significant widening of the spectrum of the dynamics is observed at the final phase of the process. & 2015 Elsevier Ltd. All rights reserved. phases [25]. This leads to widening spectrum of the dynamics, which can provide the possibility of interaction with acoustical modes in real brake systems. Such effects obtained experimental proof based on the rig designed in [9,21], however, theoretical considerations of the present work are conducted on a new model, which accounts for the influence of gravity and geometrical nonlinearity. Friction-induced vibrations in physical systems based on the mass-damper-spring modeling have been widely considered in the literature for many years. In particular, such models have been used extensively as deterministic Contents lists available at ScienceDirect

Mechanics Research Communications, 2010

This paper outlines the non-linear transient and stationary dynamics due to friction-induced vibrations in a disc brake model. Using a finite element model and the Continuous Wavelet Transform, the contributions of fundamental frequencies and harmonic components in non-linear transient and stationary dynamics are investigated for disc brake system subjected to single and multi-instabilities. Results from these non-linear analyses demonstrate the complexity of the contributions of different harmonic components in transient friction-induced vibrations with the coexistence of multi-unstable modes. One of the most important contributions of this study is to illustrate the limitation of stability analysis related to transient and stationary non-linear behaviors. Stability analysis around an equilibrium point can only be used as the first step in providing information on the onset and increase of self-excited disc brake vibrations. Consequently, a complete non-linear analysis is necessary to fully predict non-linear vibration and the contribution of unstable modes. This study shows that an under-estimation of the unstable modes observed in the non-linear time simulation can be calculated by the stability analysis. During transient vibrations, an additional unstable mode can appear. This instability is not predicted by the complex eigenvalues analysis due to the fact that linear conditions (i.e. the linearized stability around an initial equilibrium point) are not valid during transient and stationary oscillations. So new fundamental frequencies (linked to the appearance of the new unstable mode) can emerge in the signals due to the non-linear contact and loss of contact interactions at the frictional interface. Therefore, non-linear transient and stationary self-excited vibrations can become very complex and include more unstable modes than those predicted by a linearized stability analysis around a non-linear equilibrium point.

Journal of Sound and Vibration, 2009

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.