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 study focuses on the kriging based metamodeling for the prediction of parameter-dependent mode coupling instabilities. The high cost of the currently used parameter-dependent Complex Eigenvalue Analysis (CEA) has induced a growing need for alternative methods. Hence, this study investigates capabilities of kriging metamodels to be a suitable alternative. For this aim, kriging metamodels are proposed to predict the stability behavior of a four-degree-of-freedom mechanical system submitted to friction-induced vibrations. This system is considered under two configurations defining two stability behaviors with coalescence patterns of different complexities. Efficiency of kriging is then assessed on both configurations. In this framework, the proposed kriging surrogate approach includes a mode tracking method based on the Modal Assurance Criterion (MAC) in order to follow the physical modes of the mechanical system. Based on the numerical simulations, it is demonstrated by a comparison with the reference parameter-dependent CEA that the proposed kriging surrogate model can provide efficient and reliable predictions of mode coupling instabilities with different complex patterns.

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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.