Prediction of Random Self Friction-Induced Vibrations in Uncertain Dry Friction Systems Using a Multi-Element Generalized Polynomial Chaos Approach

Abstract

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.

Kriging Surrogate Models for Predicting the Complex Eigenvalues of Mechanical Systems Subjected to Friction-Induced Vibration

“…However, it may present some limits when the number of uncertain parameters is relatively high and/or when high chaos orders are required in particular for functions that are strongly nonlinear in the random space. In this last case, surrogate models based on the multielement GPC can be useful [20]. The response surface methodology (RMS) is also proposed in [21] to deal with the stability, reliability, and sensitivity analysis of brake systems submitted to interval and random uncertainties.…”

Stochastic study of a non-linear self-excited system with friction

“…To this end, a constrained harmonic balance method is proposed. This modified harmonic balance method overcomes the problem of dealing with an unknown cycle period and long term integration problems that arise when using a time integration scheme as in (Nechak et al, 2012). The proposed method suits both deterministic and stochastic cases.…”

“…Multi-Element generalized Polynomial Chaos (MEgPC) (Wan and Karniadakis, 2005) to demonstrate stability of equilibria of stochastic systems using the Lyapunov function (Fisher and Bhattacharya, 2008;Nechak et al, 2011) or to compute limit cycles in the time domain (Nechak et al, 2012) when the equilibrium loses stability. Recent papers propose evaluation of Hopf bifurcation point (when stability changes) using MEgPC for a system with dry friction when one parameter (the friction coefficient) varies but does not investigate the non-linear effects in the unstable range (see (Nechak et al, 2013) for a 2-dofs system and (Sarrouy et al, 2013) for a finite element model of a brake).…”

Prediction of the dynamic behavior of an uncertain friction system coupled to nonlinear energy sinks using a multi-element generalized polynomial chaos approach

“…Uncertainties due to friction in gear system have been investigated using the gPC in Guerine et al (2016). Moreover, the ME-gPC is shown to be very efficient to predict the friction-induced vibrations in a nonlinear uncertain dry friction system Nechak et al (2011Nechak et al ( , 2012. More recently in Trinh et al (2016), the ME-gPC has been used to perform stability analysis of a clutch system, a significant reduction of the computational cost in comparison with the standard gPC has been highlighted.…”