Oliviero Giannini

Brake squeal as dynamic instability: An experimental investigation

This paper presents an experimental analysis performed on a simplified brake apparatus. In past years a common approach for squeal prediction was the complex eigenvalues analysis. The squeal phenomenon is treated like a dynamic instability: when two modes of the brake system couple at the same frequency, one of them becomes unstable, leading to increasing vibration. The presented experimental analysis is focused on correlating squeal characteristics with the dynamic behavior of the system. The experimental modal identification of the setup is performed and different squeal conditions and frequencies are reproduced and analyzed. Squeal events are correlated with the modal behavior of the system as a function of the main parameters. A clear distinction between squeal events involving the dynamics of the pad and squeal events involving the dynamics of the caliper is performed. The effect of the adding of damping is also investigated on the squeal phenomenon. Two opposite roles of the modal damping are described: a large modal damping can either prevent the rise of squeal instabilities or enlarge the squeal propensity of the brake apparatus. The robustness of the obtained squeal events permits a further analysis on the triggering mechanism of the squeal instability during braking.

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.

High frequency vibration analysis by the complex envelope vectorization

The complex envelope displacement analysis (CEDA) is a procedure to solve high frequency vibration and vibro-acoustic problems, providing the envelope of the physical solution. CEDA is based on a variable transformation mapping the high frequency oscillations into signals of low frequency content and has been successfully applied to one-dimensional systems. However, the extension to plates and vibro-acoustic fields met serious difficulties so that a general revision of the theory was carried out, leading finally to a new method, the complex envelope vectorization (CEV). In this paper the CEV method is described, underlying merits and limits of the procedure, and a set of applications to vibration and vibro-acoustic problems of increasing complexity are presented.

Crack detection in beam-like structures by nonlinear harmonic identification

The dynamic behavior of beam-like structures with fatigue cracks forced by harmonic excitation is characterized by the appearance of sub and super-harmonics in the response even in presence of cracks with small depth. Since the amplitude of these harmonics depends on the position and the depth of the crack, an identification technique based on such a dependency can be pursued: the main advantage of this method relies on the use of different modes of the structure, each sensitive to the damage position in its peculiar way. In this study the identification method is detailed through numerical examples tested on structures of increasing complexity to evaluate the applicability of the method to engineering applications. The amount of data to obtain a unique solution and the optimal choice of the observed quantities are discussed. Finally, a robustness analysis is carried out for each test case to assess the influence of measuring noise on the damage identification.

Nonlinear Harmonic Identification of Cracks in Structures

The dynamic behavior of structures with breathing cracks forced by harmonic excitation is characterized by the appearance of sub and super-harmonics in the response even in presence of cracks with small depth. Since the amplitude of these harmonics depends on the position and the depth of the crack, an identification technique is developed based on such a dependency. The main advantage of the proposed method relies on the use of different modes of the structure, each sensitive to the damage position in its peculiar way. In this paper the identification is tested against structure of increasing complexity to evaluate the applicability of the method to engineering applications. In particular, a robustness analysis is carried out for each test case to assess the influence of measuring noise on the damage identification.

Experimental Analysis of the Transition Between Veering and Crossing on a Two-Beam System

When there is a parameter varying in a system, so that one natural frequency approaches another one, the phenomenon of veering is generally found and highly coupled modes are the emerging characteristic of this dynamic behavior. It is far more difficult to find systems that instead of a veering present crossing between modes, and the crossing phenomenon is almost unreported in the scientific literature, unless the case of uncoupled modes is considered.In this paper, the two-modes interaction is presented. In particular, mode veering and mode crossing are introduced and investigated through a simple analytic 2-dof model that allows for closed-form solution. Then, an experimental setup, appropriately designed to study the two-modes veering and crossing is presented and experimental evidences of both phenomena are measured showing the main characteristics of such modal interaction..Copyright

Nonlinear dynamics of piecewise smooth systems and damage identification

This paper addresses the study of the nonlinear dynamics of non-smooth systems representative of beams with breathing cracks. The aim is to use the nonlinear characteristics of the system response to identify the damage in cracked structures that behave similarly to bilinear systems and hence exhibit nonlinear phenomena in the dynamic response even for low damage levels. The idea is supported by the study of a piecewise smooth 2-DOF model where a wide variety of nonlinear phenomena has been evidenced, which include among others the bifurcations of super-abundant modes and a number of resonances greater than the system degrees of freedom. All these phenomena are strongly dependent on the stiffness discontinuity which is governed by the damage parameter. A novel method able to detect crack severity and position through measurements of the system nonlinear response has been developed and a cantilever beam with a breathing crack is considered as a numerical test case. The inverse procedure is tested by identifying the position and depth of a crack using pseudo-experimental data; the results show a strong robustness of the method even in the case when the data are affected by measurement errors.Copyright

Squeal suppression through a tuned fuzzy damper: a numerical study

Despite over a century of research on brake squeal, an effective solution for its suppression has not yet been achieved. The scientific community agrees that squeal is caused by a coupling between modes of the rotor with modes of the pads, however, the complexity of commercial brakes represents an obstacle to design an effective solution to this problem. For this reason several researchers focused their study on the beam-on-disk that exhibit a similar instability. This paper proposes an innovative passive damper, based on the theory of pseudo damping, that completely suppress squeal occurrence on the beam-on-disk.

Free and Forced Response of a Piecewise Linear 2-DOF System: Analysis and Experiments

The present paper analyzes the free and forced dynamics of a 2-DOF mechanical system with piecewise linear restoring force, by means of analytical/numerical and experimental investigations. This oscillator is roughly representative of an asymmetrically cracked cantilever beam vibrating in bending and hence exhibiting a bilinear stiffness, depending on whether the crack is open or closed. A parametric analysis of the NNMs has been performed for a wide range of the damage parameter: the influence of damage on the nonlinear frequencies has been investigated and bifurcations characterized by the onset of superabundant modes with or without internal resonance, have been revealed. The dynamic behavior of the system under harmonic base excitation has been numerically investigated assuming both low and high damping. It has been found that the NNMs of the free motion play a key role in the system forced response. Finally, a test set-up has then been built to investigate the validity of the proposed model for technical applications: the experimental measurements qualitatively and quantitatively capture the basic bifurcation scenarios anticipated by the model while a strong robustness of the phenomena pointed out by the theoretical analyses has been revealed in the experiments.Copyright

Application of the Complex Envelope Vectorization to a Boundary Element Formulation

The complex envelope vectorization (CEV) is a recent method that has been successfully applied to structural and internal acoustic problems. Unlike other methods proposed in the last two decades to solve high frequency problems, CEV is not an energy method, although it shares with all the other techniques a variable transformation of the field variable. By such transformation involving a Hilbert transform, CEV allows the representation of a fast oscillating signal through a set of low oscillating signals. Thanks to such transformation it is possible to solve a high frequency dynamic problem at a computational cost that is lower than that required by finite elements. In fact, by using finite elements, a high frequency problem usually implies large matrices. On the contrary the CEV formulation is obtained by solving a set of linear problems of highly reduced dimensions. Although it was proved that CEV is in general a successful procedure, it was shown that it is particularly appropriate when the modes of the system have a negligible role on the solution. Moreover, the numerical advantage of the CEV formulation is much more pronounced when full matrices are used. Thus, for the first time it is applied to a boundary element formulation (BEM). Both external and internal acoustic fields of increasing complexity are considered: the internal and external field generated by a pulsating sphere; the external field of a forced box, where the velocity field is determined by finite elements; a set of 4 plates that form an open cavity. The results are compared with those obtained by a BEM procedure (SYSNOISE), highlighting the good quality of the proposed approach. An estimate of the computational advantage is also provided. Finally it is worthwhile to point out that the reduction of the BE matrices allows for an in-core solution even for large problems.Copyright