Stability Analysis with an NVH Minimal Model for Brakes under Consideration of Polymorphic Uncertainty of Friction

Abstract

In brake systems, some dynamic phenomena can worsen the performance (e.g., fading, hot banding), but a major part of the research concerns phenomena which reduce driving comfort (e.g., squeal, judder, or creep groan). These dynamic phenomena are caused by specific instabilities that lead to self-excited oscillations. In practice, these instabilities can be investigated using the Complex Eigenvalues Analysis (CEA), in which positive real parts of the eigenvalues are identified to characterize instable regions. Measurements on real brake test benches or tribometers show that the coefficient of friction (COF), μ , is not a constant, but dynamic, system variable. In order to consider this aspect, the Method of Augmented Dimensioning (MAD) has been introduced and implemented, which couples the mechanical degrees of freedom of the brake system with the degrees of freedom of the friction dynamics. In addition to this, instability prediction techniques can often determine whether a system is stable or instable, but cannot eliminate the instability phenomena on a real brake system. To address this, the current work deals with the quantification of the relevant polymorphic uncertainty of the friction dynamics, wherein the aleatory and epistemic uncertainties are described simultaneously. Aleatory uncertainty is concerned with the stochastic variability of the friction dynamics and incorporated with probabilistic methods (e.g., a Monte Carlo simulation), while the epistemic uncertainty resulting from model uncertainties is modeled via fuzzy methods. The existing measurement data are collected and processed through Data Driven Methods (DDM) for the identification of the dynamic friction models and corresponding parameters. Total Variation Regularization is used for the evaluation of derivatives within noisy data. Using an established minimal model for brake squealing, this paper addresses the question of probabilities for instabilities and the degree of certainty with which this conclusion can be made. The focus is on a comparison between the conventional Coulomb friction model and a dynamic friction model in combination with the MAD. This shows that the quality of the predictive accuracy improves dramatically with the more precise friction model.

Cascade architecture for nonlinear control of transient and stationary regimes of friction-induced vibrations

“…and its damping coefficient ξ * 1 is defined by the relation (20) is the positive solution of the second-order polynomial equation…”

“…In fact, FIV are known to be submitted to parameter uncertainty. The friction coefficient is one of the most influential parameters on FIV ( [20,10,18,57,44,37]. Furthermore, this parameter is submitted to dispersion.…”

“…These minimal models give the key advantage to faithfully represent the mechanism generating friction-induced vibrations through considering mechanical systems with small numbers of degree-of-freedom. Numerous studies have developed such models within different frameworks especially the brake squeal framework, by considering different objectives namely the analysis and prediction [23,28,29,41,56], the uncertainty propagation [20,60,35], and passive and active control [46,8,53,42,43].…”

Abstract Methods on Mesoscopic Scales of Friction

“…In Fig. 15 an uncertainty calculation has been carried out in the complex eigenvalue analysis of a simple brake model [14].…”

“…Fig. 15 Comparison of the Coulomb friction model and the Ostermeyer friction model with respect to polymorphic uncertainty and stability analysis [14]…”