Piecewise polynomial chaos expansion with an application to brake squeal of a linear brake system

Abstract

. Piecewise polynomial chaos expansion with an application to brake squeal of a linear brake system. Journal of Sound and Vibration, Elsevier, 2013, 332, pp.577-594. <10.1016/j.jsv.2012 AbstractThis paper proposes numerical developments based on polynomial chaos (PC) expansions to process stochastic eigenvalue problems efficiently. These developments are applied to the problem of linear stability calculations for a simplified brake system: the stability of a finite element model of a brake is investigated when its friction coefficient or the contact stiffness are modeled as random parameters. Getting rid of the statistical point of view of the PC method but keeping the principle of a polynomial decomposition of eigenvalues and eigenvectors, the stochastic space is decomposed into several elements to realize a low degree piecewise polynomial approximation of these quantities. An approach relying on continuation principles is compared to the classical dichotomy method to build the partition. Moreover, a criterion for testing accuracy of the decomposition over each cell of the partition without requiring evaluation of exact eigenmodes is proposed and implemented. Several random distributions are tested, including a uniform-like law for description of friction coefficient variation. Results are compared to Monte Carlo simulations so as to determine the method accuracy and efficiency. Some general rules relative to the influence of the friction coefficient or the contact stiffness are also inferred from these calculations.

Pitfalls in the frequency response represented onto Polynomial Chaos for random SDOF mechanical systems

“…Adaptive strategies can be implemented to recursively refine the partition based on a given criterion [12,34,35]. Here, the partition will be set a priori and the quality of the global expansion will be measured by .…”

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

“…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).…”

Friction-Induced Noise and Vibrations: Diagnosis and Prognosis

“…Brake noise is a largely elusive phenomenon, partly due to the stochastic features of friction and the relevant timevarying factors such as interface profile, wear, interface films. The theoretical stochastic models have been developed to address variability and uncertainty in brakes noise [25][26][27][28][29][30][31][32][33][34]. A typical study is reported in [26], which documented a robust design of a disc brake through structural optimization using the complex eigenvalue approach, considering the variation of friction coefficient, major elastic constants and the effect of material worn-off.…”

“…In [33], neural network method is used to predict disc brake performance. In [34], polynomial chaos expansions approach is used to tackle with stochastic eigenvalue problems with applications to linear stability calculations for a simplified brake system in which the stability of a finite element model of a brake is investigated when its friction coefficient or the contact stiffness are modeled as random parameters. Results are compared to Monte Carlo simulations.…”