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.

References

References
1.
Akay
,
A.
,
2002
, “
Acoustics of Friction
,”
J. Acoustic Society of America, Vol. J. Acoust. Soc. Am.
,
111
(
4
), pp.
1525
1548
.10.1121/1.1456514
2.
Turrin
,
S.
,
Hanss
,
M.
, and
Gaul
,
L.
,
2006
, “
Fuzzy Arithmetical Vibration Analysis of a Windshield With Uncertain Parameters
,”
Proc. of the IX International Conference on Recent Advances in Structural Dynamics—RASD 2006
, Southampton, UK, July 17–19.
3.
Gauger
,
U.
,
Hanss
,
M.
, and
Gaul
,
L.
,
2006
, “
On the Inclusion of Uncertain Parameters in Brake Squeal Analysis
,”
IMAC-XXIV: Conference & Exposition on Structural Dynamics
, St. Louis, MO, January 30–February 2.
4.
Butlin
,
T.
, and
Woodhouse
,
J.
,
2009
, “
Sensitivity Studies of Friction-Induced Vibration
,”
Int. J. Vehicle Design
,
51
(
1/2
), pp.
238
257
.10.1504/IJVD.2009.027124
5.
Butlin
,
T.
, and
Woodhouse
,
J.
,
2010
, “
Friction-Induced Vibration: Quantifying Sensitivity and Uncertainty
,”
J. Sound Vib.
,
329
, pp.
509
526
.10.1016/j.jsv.2009.09.026
6.
Bathe
,
K.-J.
,
2002
,
Finite Elemente Methoden
,
Springer-Verlag
,
Berlin
.
7.
Müller
,
P. C.
,
1977
,
Stabilität und Matrizen
,
Springer-Verlag
,
Berlin
.
8.
Voss
,
H.
,
2010
,
Iterative Projection Methods for Large Scale Nonlinear Eigenvalue Problems, Computational Technology Review
, Vol. 1,
Saxe-Coburg Publications
,
Stirlingshire, UK
.
9.
Kinkaid
,
N. M.
,
O’Reilly
,
O. M.
, and
Papadopoulos
,
P.
,
2003
, “
Automotive Disc Brake Squeal
,”
J. Sound Vib.
,
267
, pp.
105
166
.10.1016/S0022-460X(02)01573-0
10.
AbuBakar
,
A. R.
, and
Ouyang
,
H.
,
2006
, “
Complex Eigenvalue Analysis and Dynamic Transient Analysis in Predicting Disc Brake Squeal
,”
Int. J. Vehicle Noise Vib.
,
2
(
2
), pp.
143
155
.
11.
Ghazaly
,
N. M.
,
Mohammed
,
S.
, and
Abd-El-Tawwab
,
A. M.
,
2012
, “
Understanding Mode-Coupling Mechanism of Brake Squeal Using Finite Element Analysis
,”
Int. J. Eng. Res. Appl.
,
2
(
1
), pp.
241
250
.
12.
Kung
,
S W.
,
Dunlap
,
K. B.
, and
Ballinger
,
R. S.
,
2000
, “
Complex Eigenvalue Analysis for Reducing Low Frequency Brake Squeal
,” SAE, Warrendale, PA, Technical Report 2000-01-0444.
13.
Popp
,
K.
, and
Rudolph
,
M.
,
2004
, “
Vibration Control to Avoid Stick-Slip Motion
,”
J. Vib. Contr.
,
10
, pp.
1585
1600
.10.1177/1077546304042026
14.
Hoffmann
,
N.
,
Fischer
,
M.
,
Allgaier
,
R.
, and
Gaul
,
L.
,
2002
, “
A Minimal Model for Studying Properties of the Mode-Coupling Instability in Friction Induced Oscillations
,”
Mech. Res. Commun.
,
29
(
4
), pp.
197
205
.10.1016/S0093-6413(02)00254-9
15.
Hoffmann
,
N.
, and
Gaul
,
L.
,
2003
, “
Effects of Damping on Mode-Coupling Instability in Friction Induced Oscillations
,”
ZAMM
,
83
(
8
), pp.
524
534
.10.1002/zamm.200310022
16.
Hetzler
,
H.
,
2008
, Zur Stabilität von Systemen Bewegter Kontinua mit Reibkontakten am Beispiel des Bremsenquietschens, Schriftenreihe des Instituts für Technische Mechanik, Band 8, Universitätsverlag Karlsruhe, Karlsruhe, Germany.
17.
Madras
,
N.
,
2002
, “
Lectures on Monte Carlo Methods
,”
Fields Institute Monographs 16
, American Mathematical Society, Providence, RI.
18.
Huang
,
J. C.
,
Krousgrill
,
C. M.
, and
Bajaj
,
A. K.
,
2009
, “
An Efficient Approach to Estimate Critical Value of Friction Coefficient in Brake Squeal Analysis
,”
ASME J. Appl. Mech.
,
74
, pp.
534
541
.10.1115/1.2423037
You do not currently have access to this content.