Linear and Non-linear Stability Analysis of a Fixed Caliper Brake During Forward and Backward Driving

[+] Author and Article Information
Oliver Stump

Daimler AG, Brake Development, Group Research & MBC Development, Sindelfingen, Germany

Ronaldo Nunes

Daimler AG, Brake Development, Group Research & MBC Development, Sindelfingen, Germany

Karl Häsler

Daimler AG, Brake Development, Group Research & MBC Development, Sindelfingen, Germany

Wolfgang Seemann

Institute of Engineering Mechanics, Karlsruhe Institute of Technology (KIT), Germany

1Corresponding author.

ASME doi:10.1115/1.4042393 History: Received July 12, 2017; Revised December 18, 2018


The parking manoeuvre 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 manoeuvre. The contact area at the caliper is under a large change during a forward and backward driving manoeuvre. The measurements motivate linear and non-linear 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 non-linear system shows a possible stable limit cycle, when the brake pad moves from the leading to the trailing side, like in a parking manoeuvre. This growth of amplitude is not anticipated from the complex eigenvalue analysis, because no instable eigenvalue is found in the linearised equation of motion at that working point. This subcritical flutter-type behaviour 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 linearisation cannot be neglected. Furthermore, different initial conditions are analysed 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 behaviour.

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