Squeal analysis of a modal-parameter-based rotating disc brake model

Abstract

Many squeal studies of brake system finite element (FE) model neglected the disc rotation effect. This paper, based on modal theory and FE modal result, presents a novel method to construct a disc brake model that concerns disc rotation and analyzes its dynamic instability. The rotation effect is embodied in velocity-dependent rotating disc equivalent modal parameters, which are derived through time-space and coordinate transformation and proved to be orthogonal with respect to system matrices in state-space. Through modal synthesis with stationary components, system eigenfunction is formulated in modal space. A comprehensive squeal analysis concerning both rotation and friction negative slope effect is then conducted through complex eigenvalue analysis and modal composition analysis. The result shows the dependency of system instability on rotation speed. Under constant friction, disc rotation is a destabilizing factor to the system as it not only raises the squeal propensity and strengthens the split of eigenvalue loci of mode-merging instability, but also gives rise to additional squeal modes that cannot be generated by mode-merging. Velocity-dependent friction model with negative slope character is proved to generate negative damping and destabilize the system at low speed range. Over high speed range, however, the system becomes more stable due to the decline of friction magnitude. Mechanisms responsible for the squeal are discussed, it is demonstrated that mode-merging induced by the friction coupling is the major mechanism for brake squeal. The destabilizing effects on the system which stems from the split of repeated-root modes caused by rotation, as well as the negative damping effect caused by velocity-dependent negative slope friction, are relatively limited.