# Prise en compte des comportements viscoélastiques dans la simulation dynamique des systèmes de freinage

1 LISMMA - Laboratoire d-Ingénierie des Systèmes Mécaniques et des MAtériaux 2 Bosch Chassis Systems Brakes

Abstract : Dynamic computation of braking systems including viscoelastic behaviours. In the context of brake system simulation, the highlight of phenomenon like squeal needs specific methods. We will focus on stability analysis by complex modal analysis. The use of damping system called shims for squeal noise reduction implies that simulations take into account the damping of materials. To do this, we use parametric viscoelastic models and particularly the generalised Maxwell model. Work consisted in tools choice and validation viscoelastic models, finite elements formulations,

. and in simulation method implementation. It was divided in several steps. In a first step, we have selected, among several mathematical models able to describe viscoelasticity, the best for damping modelisation in brake systems. We studied the complex modulus model, the Kelvin-Voigt model and the generalised Maxwell model. In a second step, we sought a formulation of the finite element problem adapted to the modal analysis. We then used a state space model formulation. A capital hypothesis on the equality of the pole of the generalised Maxwell model permits to reduce the size of the model and in the same time to simplify its formulation. Finally, the developed methods have been applied to simulate a pad and a full brake system. The influence of the number of modes used in model reduction and the order of the Maxwell model has been quantified in parametric studies. In the pad case, we performed a complex modal analysis with friction material considered as viscoelastic. The objective was to update the pad frequencies and damping according to FRF measures. In the brake case, we performed a complex modal analysis with the two friction materials and one shim considered as viscoelastic. This model has also been used to exhibit the link between the strain energy distribution in the brake and the damping level obtained by complex modal analysis. To conclude, we developed a simulation method using Abaqus and Matlab for the complex modal analysis with viscoelasticity effects and Python to make data exchange between Abaqus and Matlab possible. This method permits to perform stability analysis with several viscoelastic materials, on large models, without degradation of computation time.

Keywords : generalized Maxwell damping brake strain energy Viscoelasticity complex modal analysis

Author: Sylvain Thouviot - Gaël Chevallier - Franck Renaud - Jean-Luc Dion - Rémi Lemaire -

Source: https://hal.archives-ouvertes.fr/