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.

On the interrelation of equilibrium positions and work of friction forces on brake squeal

“…2 and [8]. As already described, in [5] large deviations of equilibrium positions are encountered for forward and backward driving. Nevertheless, following the state of the art in FE simulations, the linear equations of motion are obtained by linearizing with respect to the one determined equilibrium position, and all subsequent steps are therefore based on this solely considered equilibrium position.…”

“…This means that a large number of tests must be carried out in order to take each parameter combination into account. As described, for example, in [4][5][6], the difficult situation is further complicated by the fact that, despite identical operation parameters, squealing sometimes occurs and sometimes not. In [4,5], this is related to forward/backward driving and corresponding positions of the brake components, while other reasons like subcritical Hopf bifurcations as, for example, in [6] are also possible.…”

On the Influence of Multiple Equilibrium Positions on Brake Noise

“…[4]. The situation becomes more complicated by the fact that there is a possibility for squealing to sometimes occur and sometimes not even during the tests with the identical operation parameters [5][6][7]. Ref.…”

“…Ref. [6] mainly considers thereby changes in the direction in which the brake components obviously capture significantly different positions as well as the corresponding influence on the squealing behavior.…”

A Hybrid Model for Predicting Steering Brake Squeal Based on Multibody Dynamics and Finite Element Methods

“…e frictional force is introduced by the CEA method into the friction pair such that the stiffness matrix becomes asymmetric and generates complex eigenvalues, which can be used to predict brake squeal propensity, and is widely used in automotive brake squeal research. Stump et al [30] showed that the restraint conditions of the pad and caliper are different, which is the reason for the brake squeal under forward and backward conditions. erefore, in the process of FE modeling, we should focus on the physical parameters of the chassis corner restraint conditions.…”