Squeal occurrence classification using a harmonic balance vector signal model

Abstract

Brake squeal is an instability that generates self-excited limit cycles that, in real experiments, vary with time and operating conditions. To analyze test results, it is proposed to use a Harmonic Balance Vector (HBV) signal model, that combines the space-time decomposition of the Harmonic Balance Method, where spatial distribution of each harmonic is described by a complex vector and frequency is common to all sensors, with analytic signal methodologies, where quantities are assumed to be slowly varying in time. Synchronous demodulation and principal coordinate definitions are combined in a multistep algorithm that provides an HBV estimation. % On an industrial brake test matrix, the method is shown to be robustly applicable. The HBV signal being slowly varying, sub-sampling reduces the volume of test data by two orders of magnitude. Limit cycle frequency, amplitude and shapes can thus be added to the parallel coordinates containing operating parameters: pressure, velocity, temperature, torque, disk position, disk/bracket distance, ... This opens a path to a range of analyzes otherwise difficult to perform. Classification of occurrences is first discussed showing pressure and amplitude dependence. The effect of amplitude on both frequency and shape is then demonstrated. The entry and exit of instability when parameters change are then analyzed by proposing a transient root locus built from test. Thus squeal test results are related to the classical complex eigenvalue analysis. Intermittent growth/decay events are shown to be correlated with wheel position. Furthermore, distance measurements indicate that disk shape variations of a few microns play a clear parametric role. Parametric testing and clustering are then used to map the instability region and its edges. Pressure is shown to have an effect dominating other variations. Prospective uses of these results to combine test results and finite element models are discussed last.