Instability prediction of brake squeal by nonlinear stability analysis

ABSTRACT Prediction of brake squeal as unwanted high frequency noise above 1 kHz remains a challenging problem despite substantial research efforts in the past two decades. Brake squeal, triggered by friction-induced self-excited vibration, can be caused by many different and interacting mechanisms with nonlinear origins in material properties and boundary conditions. Although brake squeal is essentially a nonlinear phenomenon, the standard industrial practice for prediction of brake squeal relies on the linear complex eigenvalue analysis which may under-predict or over-predict the number of unstable vibration modes. Brake squeal can be considered in nonlinear dynamics terms to be caused by a friction-induced self-excitation driven into instability and oscillating in a limit cycle through super-critical Andronov-Hopf bifurcations. In this paper, a nonlinear stability analysis that may be applied to a full brake system is examined using an unforced 4-DOF friction oscillator with cubic nonlinearity. The local bifurcation behaviour of this model is studied using the normal form theory and the nonlinear stability boundary is evaluated. Differences between results of linear and nonlinear analyses are discussed and the limitations of the linear analysis are highlighted. The energy provided by friction and consumed by damping is calculated by multiple scales method to provide a physical explanation for instability generation.