To cite this version:Lyes Nechak, Sébastien Berger, Evelyne Aubry. A polynomial chaos approach to the robust analysis of the dynamic behaviour of friction systems. Abstract-This paper presents a dynamic behaviour study of non-linear friction systems subject to uncertain friction laws. The main aspects are the analysis of the stability and the associated non-linear amplitude around the steady-state equilibrium. As friction systems are highly sensitive to the dispersion of friction laws, it is necessary to take into account the uncertainty of the friction coefficient to obtain stability intervals and to estimate the extreme magnitudes of oscillations. Intrusive and nonintrusive methods based on the polynomial chaos theory are proposed to tackle these problems. The efficiency of these methods is investigated in a two degree of freedom system representing a drum brake system. The proposed methods prove to be interesting alternatives to the classic method such as parametric studies and Monte Carlo based techniques.

This paper is devoted to the stability analysis of uncertain nonlinear dynamic dry friction systems. The stability property of dry friction systems is known to be very sensitive to the variations of friction laws. Moreover, the friction coefficient admits dispersions due to the manufacturing processes. Therefore, it becomes necessary to take this uncertainty into account in the stability analysis of dry friction systems to ensure robust predictions of stable and instable behaviours. The generalized polynomial chaos formalism is proposed to deal with this challenging problem treated in most cases with the prohibitive Monte Carlo based techniques. Two equivalent methods presented here combine the non-intrusive generalized polynomial chaos with the indirect Lyapunov method. Both methods are shown to be efficient in the estimation of the stability and instability regions with high accuracy and high confidence levels and at lower cost compared with the classic Monte Carlo based method.

The optimization of wiper systems under various conditions and the creation of a product which is as robust as possible are the main objectives for an equipment supplier. However, in certain conditions, instabilities can appear and generate wiping defects due to the rubber-glass contact. To improve wiping quality and to reduce the number of test stages for design, this study proposes a wiper system modeling method. The wiper system is represented by a rigid blade holder on which a rubber blade is fitted. This rigid blade system is used on a flat test bench at constant wiping velocity. The model is based on modal synthesis methods and will be validated through comparison with experimental tests under various conditions. The right correlation obtained allows the same modelling method to be applied to the new generation of flexible wiper blades which take account of the degree of freedom of the wiper blade flexions. So, a new computation tool will be developed and validated through experimentation on a specific test bench.

The prediction of self friction-induced vibrations is of major importance in the design of dry friction systems. This is known to be a challenging problem since dry friction systems are very complex nonlinear systems. Moreover, it has been shown that the friction coefficients admit dispersions depending in general on the manufacturing process of dry friction systems. As the dynamic behavior of these systems is very sensitive to the friction parameters, it is necessary to predict the friction-induced vibrations by taking into account the dispersion of friction. So, the main problem is to define efficient methods which help to predict friction-induced vibrations by taking into account both nonlinear and random aspect of dry friction systems. The multi-element generalized polynomial chaos formalism is proposed to deal with this question in a more general setting. It is shown that, in the case of friction-induced vibrations obtained from long time integration, the proposed method is efficient by opposite to the generalized polynomial chaos based method and constitutes an interesting alternative to the prohibitive Monte Carlo method.

Flexible polyurethane foam is widely used in numerous applications such as seats and mattresses, due to its low stiffness and its ability to absorb deformation energy. The main objective of this article is to model the quasi-static mechanical behavior of three types of polyurethane foam in large deformation and to compare these three foams with three proposed models. The uniaxial compression/ decompression tests at three different strain rates were performed. The test results show that the three foams present different plateau stresses, maximum stresses, and abilities to absorb energy. Moreover, polyurethane foam also presents a nonlinear hyperelastic behavior and a viscoelastic behavior in large deformation. Three viscohyperelastic models which include a hyperelastic component and a memory component are proposed to model these behaviors. Model parameters were identified using the experimental data and a proper identification method. These models were validated on these three types of foam with the aim to present comparison results. The comparison results show that Ogden's viscoelastic model best agrees with the experimental results. POLYM. ENG. SCI., 55:1795SCI., 55: -1804SCI., 55: , 2015