Abstract:

Dynamic instability of structures in frictional contact : Application on TGV disc brake squeal

TGV disc brake squeal is a particularly embarrassing high-pitched noise produced during the arrival of the train in railway station. This work is aimed at understanding this phenomenon in order to reduce or even to abolish the noise emission. This acoustical phenomenon have a vibratory origin : the squeal of disc brakes results from self-sustaining vibrations of the different components induced by the friction of the pads with the disc. This friction is linked to the surface asperity and it enhances a two-scale-problem where a phenomenon appearing in the microscopic scale creates vibrations in a disc of macroscopic scale (the amplitude of disc vibrations is of the order of some micrometers). Brake noise phenomena, of which squeal is part, are complex various and have different origins according to the working points of the mechanism. A state of art on different modelling studies shows that an instability of stationary equilibrium said to be geometric or by mode coupling allows to mobilize modes of vibration responsible for squeal and this with a constant friction coefficient.

From a modelling point of view, these observations have led us to a model of deformable continuum mechanics in the hypothesis of small perturbations. Numerous works on self-sustained vibrations are interested in the stability of equilibrium but make one quick shortcut between frequencies of unstable modes and transient evolutions. Numerical studies dealing with the characterization of these transient evolutions have underlined strongly non linear events under the zone of contact (as the adhesion or separation caused by unilateral contact). A first objective of this work is the study of the evolution of disturbances close to equilibrium towards transient solution. This study allows us to enhance links between the characteristic frequencies of this transient resolution (frequencies of squeal) and the frequencies of modes of stability. The particular case of a three-dimensional simplified disc-brake mechanism is chosen. The transition between the evolution of disturbances close to equilibrium and transient evolution is studied thanks to an original projection method on stability modes. It allows the space and temporal study of the vibration field resolutions. Its application on the simplified disc brake model is made possible thanks to an eulerian formulation of the problem. From a computational point of view, transient solutions were determined thanks to well adapted algorithms and numerical strategies allowing to take into account the non regular character of the behavior of the unilateral frictional contact in the dynamic frame (such as in shock situations).

The instability of equilibrium by mode coupling is the generating mechanism of self-sustained vibrations which is favoured in the literature. What about the TGV brake mechanism ? This question led us at first to observe the behaviour of the real mechanism thanks to experimental campaigns. In a second step, we propose a realistic model of TGV brake. The study of the stability of equilibrium allowed us to predict the measured frequencies of squeal. It also allowed us to specify the physical mechanism of the mode coupling as well as its dependency on the pad physical characteristics. The knowledge of this physical mechanism is a clue in the research of noise reduction solutions.

 

Xavier LORANG / October 2007 / Ecole Polytechnique