Determining growth rates of instabilities from time-series vibration data: Methods and applications for brake squeal
In this work, a novel and generic methodology to derive instability growth rates from vibration time-series data is introduced. Spectral filtering using Fourier and wavelet transforms is employed to obtain the amplitude evolution of the major vibration frequency from the raw vibration signal. Then, the transient phase, i.e. the temporal regime in which the vibrations grow rapidly, is found and extracted. An exponential fit is applied to the amplitude series to estimate the local instability growth rate. A statistical framework is introduced by variation of the fitting regime and definition of fitting errors in order to obtain a robust growth rate estimate from a multitude of fits. Using this methodology, growth rates are extracted from time-series vibration signals for a large set of laboratory data from commercial passenger car testing for the first time. Specifically, self-excited brake system vibrations, commonly known as brake squeal, are studied in this research. Two different brake systems exhibiting various squeal instabilities are analyzed. Results show that the proposed approach is robust and applicable in a highly automated fashion to large data sets. The data analysis reveals that the final acoustical squeal intensity develops independently of the instability growth rates. Loading conditions which lead to squeal are extracted from the testing data. These loading conditions are then studied to illustrate growth rate dependencies on operational parameters and link results to the existing understanding of bifurcations and nonlinear dynamics in self-excited friction brake systems.