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Nonlinear stability analysis of a disk brake model

Hochlenert, Daniel (2009):
Nonlinear stability analysis of a disk brake model.
58, In: Nonlinear Dynamics, (1-2), Springer, pp. 63-73, [Article]

Abstract

It has become commonly accepted by scientists and engineers that brake squeal is generated by friction-induced self-excited vibrations of the brake system. The noise-free configuration of the brake system loses stability through a flutter-type instability and the system starts oscillating in a limit cycle. Usually, the stability analysis of disk brake models, both analytical as well as finite element based, investigates the linearized models, i.e. the eigenvalues of the linearized equations of motion. However, there are experimentally observed effects not covered by these analyses, even though the full nonlinear models include these effects in principle. The present paper describes the nonlinear stability analysis of a realistic disk brake model with 12 degrees of freedom. Using center manifold theory and artificially increasing the degree of degeneracy of the occurring bifurcation, an analytical expression for the turning points in the bifurcation diagram of the subcritical Hopf bifurcations is calculated. The parameter combination corresponding to the turning points is considered as the practical stability boundary of the system. Basic phenomena known from the operating experience of brake systems tending to squeal problems can be explained on the basis of the practical stability boundary.

Item Type: Article
Erschienen: 2009
Creators: Hochlenert, Daniel
Title: Nonlinear stability analysis of a disk brake model
Language: English
Abstract:

It has become commonly accepted by scientists and engineers that brake squeal is generated by friction-induced self-excited vibrations of the brake system. The noise-free configuration of the brake system loses stability through a flutter-type instability and the system starts oscillating in a limit cycle. Usually, the stability analysis of disk brake models, both analytical as well as finite element based, investigates the linearized models, i.e. the eigenvalues of the linearized equations of motion. However, there are experimentally observed effects not covered by these analyses, even though the full nonlinear models include these effects in principle. The present paper describes the nonlinear stability analysis of a realistic disk brake model with 12 degrees of freedom. Using center manifold theory and artificially increasing the degree of degeneracy of the occurring bifurcation, an analytical expression for the turning points in the bifurcation diagram of the subcritical Hopf bifurcations is calculated. The parameter combination corresponding to the turning points is considered as the practical stability boundary of the system. Basic phenomena known from the operating experience of brake systems tending to squeal problems can be explained on the basis of the practical stability boundary.

Journal or Publication Title: Nonlinear Dynamics
Volume: 58
Number: 1-2
Publisher: Springer
Divisions: 16 Department of Mechanical Engineering
16 Department of Mechanical Engineering > Dynamics and Vibrations
Date Deposited: 19 Sep 2012 06:45
Identification Number: doi:10.1007/s11071-008-9461-0
Alternative keywords:
Alternative keywordsLanguage
Friction, Self-excited vibrations, Brake squeal, Nonlinear stability analysis, Center manifold, Hopf bifurcationUNSPECIFIED
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