Friction-induced vibration and the noise or wear it causes are everlasting problems in the design of dynamical mechanical systems. The most common way to analyze friction-induced vibration is to determine the borders of linear stability. In that framework, the present study focuses on robustness concepts of systems prone to friction-induced vibration. Here, robustness is defined on two different levels. First, robustness will be considered in a global design perspective, giving an answer to the question of how many realizations within an overall ensemble of possible designs will show instability and if a given stability characteristic remains robust under parameter variations. Second, robustness will be understood with respect to the sensitivity of the system’s eigenvalues against parameter variations in general, focusing on the questions of how single eigenvalues react to parameter variation and if the real parts of the system’s eigenvalues give a measure for changes of stability characteristics under parameter variation. To answer the posed questions, dynamical model systems subject to friction-induced vibration are generated on the basis of specified random processes and evaluated in statistical terms. It shows that the size of the real parts of the eigenvalues, i.e., the growth or decay rates of the linear modes, which are in practice often used as decisive values in the interpretation of stability calculations, cannot be used as a well defined indicator for any kind of the considered robustness concepts. We, thus, suggest a novel measure taking into account variance properties to rate the robustness of systems subject to friction-induced vibration.
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December 2013
Research-Article
On the Robustness of Instabilities in Friction–Induced Vibration
Sebastian Kruse,
Sebastian Kruse
1
Audi AG,
Development Foundation Brake,
Ingolstadt 85045, Germany;
Structural Dynamics Group,
Mechanical Engineering,
Hamburg 21073,
e-mail: sebastian.kruse@audi.de
Development Foundation Brake,
Ingolstadt 85045, Germany;
Structural Dynamics Group,
Mechanical Engineering,
Hamburg University of Technology
,Hamburg 21073,
Germany
e-mail: sebastian.kruse@audi.de
1Corresponding author.
Search for other works by this author on:
Norbert P. Hoffmann
Norbert P. Hoffmann
Structural Dynamics Group,
Mechanical Engineering,
Hamburg 21073,
Dynamics of Machines and Structures Group,
London SW7 2AZ,
e-mail: norbert.hoffmann@tuhh.de
Mechanical Engineering,
Hamburg University of Technology
,Hamburg 21073,
Germany
;Dynamics of Machines and Structures Group,
Imperial College London
,London SW7 2AZ,
UK
e-mail: norbert.hoffmann@tuhh.de
Search for other works by this author on:
Sebastian Kruse
Audi AG,
Development Foundation Brake,
Ingolstadt 85045, Germany;
Structural Dynamics Group,
Mechanical Engineering,
Hamburg 21073,
e-mail: sebastian.kruse@audi.de
Development Foundation Brake,
Ingolstadt 85045, Germany;
Structural Dynamics Group,
Mechanical Engineering,
Hamburg University of Technology
,Hamburg 21073,
Germany
e-mail: sebastian.kruse@audi.de
Norbert P. Hoffmann
Structural Dynamics Group,
Mechanical Engineering,
Hamburg 21073,
Dynamics of Machines and Structures Group,
London SW7 2AZ,
e-mail: norbert.hoffmann@tuhh.de
Mechanical Engineering,
Hamburg University of Technology
,Hamburg 21073,
Germany
;Dynamics of Machines and Structures Group,
Imperial College London
,London SW7 2AZ,
UK
e-mail: norbert.hoffmann@tuhh.de
1Corresponding author.
Contributed by the Design Engineering Division of ASME for publication in the Journal of Vibration and Acoustics. Manuscript received December 8, 2012; final manuscript received June 30, 2013; published online August 6, 2013. Assoc. Editor: Steven W Shaw.
J. Vib. Acoust. Dec 2013, 135(6): 061013 (8 pages)
Published Online: August 6, 2013
Article history
Received:
December 8, 2012
Revision Received:
June 30, 2013
Citation
Kruse, S., and Hoffmann, N. P. (August 6, 2013). "On the Robustness of Instabilities in Friction–Induced Vibration." ASME. J. Vib. Acoust. December 2013; 135(6): 061013. https://doi.org/10.1115/1.4024939
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