Linear and Nonlinear Stability Analysis of a Fixed Caliper Brake During Forward and Backward Driving

Abstract

The parking maneuver of a passenger car is known by bench and vehicle testers to sometimes produce brake squeal, even though the brake system is otherwise quiet. This phenomenon is examined in this work. Pressure foil measurements at the pad caliper contact and acceleration measurements are done on a real break system in order to better understand the mechanisms of the forward–backward driving maneuver. The contact area at the caliper is under a large change during a forward and backward driving maneuver. The measurements motivate linear and nonlinear simulations. A proposal has been made to include the linear effects of parking into the standard robustness analysis with the complex eigenvalues calculation. A time integration of the full nonlinear system shows a possible stable limit cycle, when the brake pad moves from the leading to the trailing side, like in a parking maneuver. This growth of amplitude is not anticipated from the complex eigenvalue analysis (CEA), because no instable eigenvalue is found in the linearized equation of motion at that working point. This subcritical flutter-type behavior is known for small models in the literature and is examined in this paper with a more realistic brake system. It is found that the resulting error of the linearization cannot be neglected. Furthermore, different initial conditions are analyzed to narrow the zone of attraction of the stable limit cycle and the decrease of the critical friction value due to this kind of bifurcation behavior.