How Do Nonlinearities Influence Brake Squeal?

Brake squeal is usually investigated using linearized models and the eigenvalues of the linear equations of motion. Eigenvalues with positive real parts are interpreted as the onset of squeal. Nonlinearities are commonly neglected due to the high effort associated with the corresponding calculations. Following the linear theory, the vibration amplitude should increase exponentially. On the other hand experimental results and overall experience show, that brake squeal is a stationary or quasi-stationary vibration phenomenon with approximately constant amplitude. This can only be explained by introducing nonlinearities into the model. These nonlinearities are limiting the increasing vibration amplitudes to a stationary limit cycle. Considering experimentally identified material properties of the brake lining as the main source of nonlinearities in the system a nonlinear disk brake model is introduced. Using the eigenvalues and eigenvectors of the linearized system, the bifurcation of the nonlinear system is investigated by normal form theory. This complements the stability boundary obtained from an analysis of the linearized system. It is shown that the linear model can result in incorrect stability boundaries even with perfectly identified parameters. On the other hand, the nonlinear model predicts stability boundaries that are consistent with experimental results.