A polynomial chaos approach to the robust analysis of the dynamic behaviour of friction systems

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. Key word: Dry friction systems, Nonlinear dynamic systems, stability, limit cycle, robustness, uncertainty propagation, polynomial chaos, Lyapunov function, SOS programming.