The paper describes an instability mechanism in a friction unit comprising a rotating flexible annular disk pressed to a rigid surface on the whole outer circumference. It is shown that for such a system, sliding friction forces set up a feedback between the orthogonal bending eigenmodes of the disk with the same form but different angular orientation. Due to axisymmetry, these modes have the same eigenfrequency. The feedback between the vibration modes with the same frequency leads to appearance of the circulation terms in the equations of motion and to instability. As a measure to suppress squeal, special apertures in the disk are suggested. The goal is to detach the paired eigenfrequencies to stabilize the system. The positioning of the apertures is discussed. The instability mechanism is investigated on the simple analytical model. More detailed finite-element analysis confirms the analytical prediction about the influence of the friction and axisymmetry on the instability and enables to prove the measures against friction induced vibrations.

References

References
1.
Ibrahim
,
R. A.
,
1994
, “
Friction-Induced Vibration, Chatter, Squeal, and Chaos—Part II: Dynamics and Modeling
,”
ASME Appl. Mech. Rev.
,
47
, pp.
227
253
.10.1115/1.3111080
2.
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
3.
Ouyang
,
H.
,
Nack
,
W.
,
Yuan
,
Y.
, and
Chen
,
F.
,
2005
, “
Numerical Analysis of Automotive Disc Brake Squeal: A Review
,”
Int. J. Veh. Noise Vib.
,
1
(
3/4
), pp.
207
231
.10.1504/IJVNV.2005.007524
4.
Shin
,
K.
,
Brennan
,
M. J.
,
Oh
,
J.-E.
, and
Harris
,
C. J.
,
2002
, “
Analysis of Disk Brake Noise Using a Two-Degree-of-Freedom Model
,”
J. Sound Vib.
,
254
, pp.
837
848
.10.1006/jsvi.2001.4127
5.
Hoffmann
,
N.
,
Fischer
,
M.
,
Allgaier
,
R.
, and
Gaul
,
L.
,
2002
, “
A Minimal Model for Studying Properties of the Mode-Coupling Type Instability in Friction Induced Oscillations
,”
Mech. Res. Commun.
,
29
, pp.
197
205
.10.1016/S0093-6413(02)00254-9
6.
Popp
,
K.
,
Rudolph
,
M.
,
Kroeger
,
M.
, and
Lindner
,
M.
,
2002
, “
Mechanisms to Generate and to Avoid Friction Induced Vibrations
,” VDI-Berichte 1736, VDI-Verlag, Düsseldorf, Germany, pp. 1–15.
7.
Brommundt
,
E.
,
1995
, “
Ein Reibschwinger mit Selbsterregung ohne fallende Reibkennlinie
,”
Z. Angew. Math. Mech.
,
75
(
11
), pp.
811
820
.10.1002/zamm.19950751202
8.
Von Wagner
,
U.
,
Hochlenert
,
D.
, and
Hagedorn
,
P.
,
2007
, “
Minimal Models for Disk Brake Squeal
,”
J. Sound Vib.
,
302
, pp.
527
539
.10.1016/j.jsv.2006.11.023
9.
Chakrabotry
,
G.
,
Jearsiripongkul
,
T.
,
von Wagner
,
U.
, and
Hagedorn
,
P.
,
2002
, “
A New Model for a Floating Caliper Disc-Brake and Active Squeal Control
,” VDI-Berichte 1736, VDI-Verlag, Düsseldorf, Germany, pp.
93
102
.
10.
Von Wagner
,
U.
,
Jearsiripongkul
,
T.
,
Vomstein
,
T.
,
Chakrabotry
,
G.
, and
Hagedorn
,
P.
,
2003
, “
Brake Squeal: Modeling and Experiments
,” VDI-Berichte 1749, VDI-Verlag, Düsseldorf, Germany, pp.
173
186
.
11.
Wauer
,
J.
, and
Heilig
,
J.
,
2001
, “
Dynamics and Stability of a Nonlinear Brake Model
,” ASME Design Engineering Technical Conferences (DETC'01), Pittsburgh, PA, September 9–12.
12.
Cao
,
Q.
,
Ouyang
,
H.
,
Friswell
,
M. I.
, and
Mottershead
,
J. E.
,
2004
, “
Linear Eigenvalue Analysis of the Disc-Brake Squeal Problem
,”
Int. J. Numer. Methods Eng.
,
61
(
9
), pp.
1546
1563
.10.1002/nme.1127
13.
Lou
,
G.
,
Wu
,
T. W.
, and
Bai
,
Z.
,
2004
, “
Disk Brake Squeal Prediction Using the ABLE Algorithm
,”
J. Sound Vib.
,
272
, pp.
731
748
.10.1016/S0022-460X(03)00416-4
14.
Tuchinda
,
A.
,
Hoffmann
,
N.
,
Ewins
,
D.
, and
Keiper
,
W.
,
2001
, “
Mode Lock-In Characteristics and Instability Study of the Pin-On-Disc System
,” 19th International Modal Analysis Conference (IMAC XIX), Kissimmee, FL, February 5–8, pp. 71–77, http://sem-proceedings.com/19i/sem.org-IMAC-XIX-190303-Mode-Lock-Characteristics-Instability-Study-Pin-disc-System.pdf
15.
Francisco
,
M.
,
Akay
,
A.
, and
Wickert
,
J.
,
1995
,
The Role of Mode Lock-In in Generating Brake Noise and Squeal
,
Society of Automotive Engineers Brake Colloquium
,
Philadelphia, PA
.
16.
Allgaier
,
R.
,
Keiper
,
W.
,
Gaul
,
L.
, and
Willner
,
K.
,
1999
, “
Mode Lock-in and Friction Modeling
,”
Computational Methods in Contact Mechanics IV
,
Southampton, WIT Press
,
Southampton, UK
, pp.
35
48
.
17.
Allgaier
,
R.
,
Gaul
,
L.
,
Keiper
,
W.
,
Willner
,
K.
, and
Hoffmann
,
N.
,
2002
, “
A Study on Brake Squeal Using a Beam-On-Disk Model
,”
Proceedings of the IMAC-XX
, Los Angeles, CA, February 4–7, pp.
528
534
.
18.
Massi
,
F.
,
Baillet
,
L.
, and
Culla
,
A.
,
2009
, “
Structural Modifications for Squeal Noise Reduction: Numerical and Experimental Validation
,”
Int. J. Veh. Des.
,
51
(
1–2
), pp.
168
189
.10.1504/IJVD.2009.027120
19.
Mottershead
,
J. E.
,
Ouyang
,
H.
,
Cartmell
,
M. P.
, and
Friswell
,
M. I.
,
1997
, “
Parametric Resonances in an Annular Disc, With a Rotating System of Distributed Mass and Elasticity; and the Effects of Friction and Damping
,”
Proc. R. Soc. London, Ser. A
,
453
, pp.
1
19
.10.1098/rspa.1997.0001
20.
Ouyang
,
H.
, and
Mottershead
,
J. E.
,
2004
, “
Dynamic Instability of an Elastic Disk Under the Action of a Rotating Friction Couple
,”
ASME J. Appl. Mech.
,
71
, pp.
753
758
.10.1115/1.1795815
21.
Hochlenert
,
D.
,
Spelsberg-Korspeter
,
G.
, and
Hagedorn
,
P.
,
2007
, “
Friction Induced Vibrations in Moving Continua and Their Application to Brake Squeal
,”
ASME J. Appl. Mech.
,
74
, pp.
542
549
.10.1115/1.2424239
22.
Spelsberg-Korspeter
,
G.
,
Hochlenert
,
D.
,
Kirillov
,
O.
, and
Hagedorn
,
P.
,
2009
, “
In- and Out-Of-Plane Vibrations of a Rotating Plate With Frictional Contact: Investigations on Squeal Phenomena
,”
ASME J. Appl. Mech.
,
76
, pp.
1
15
.10.1115/1.3112734
23.
Reik
,
W.
,
1998
, “
The Dual Mass Flywheel
,”
Proceedings of the 6th LuK Symposium
, Bühl, Germany, March 19–20, pp.
69
93
.
24.
Ryzhik
,
B.
,
2007
, “
Method for Reducing Vibrations in a Disc-Shaped Rotary Component Which is Rotatable About a Rotational Axis, and Rotary Component
,” Patent No. WO 2008/014744.
25.
Ryzhik
,
B.
,
2009
, “
Friction-Induced Vibrations of Squeal Type Due to Transverse Contraction in a Flexible Disk
,”
J. Sound Vib.
,
326
, pp.
623
632
.10.1016/j.jsv.2009.06.010
26.
Ryzhik
,
B.
,
2012
, “
Friction-Induced Vibrations of Squeal Type in Flexible Disks Sliding in Contact With Rigid Surfaces
,”
Proceeding of the ISMA2012
, Leuven, Belgium, September 17–19, pp.
957
970
.
27.
Millner
,
N.
,
1978
, “
An Analysis of Disc Brake Squeal
,”
SAE
Technical Paper No. 780332.10.4271/780332
28.
Nishiwaki
,
M.
,
Harada
,
H.
,
Okamura
,
H.
, and Ikeuchi, T.,
1989
, “
Study on Disc Brake Squeal
,”
SAE
Technical Paper No. 890864.10.4271/890864
29.
Fieldhouse
,
J. D.
,
Steel
,
W. P.
,
Talbot
,
C. J.
, and
Siddiqui
,
M. A.
,
2004
, “
Rotor Asymmetry Used to Reduce Disk Brake Noise
,”
SAE
Technical Paper No. 2004-01-2797.10.4271/2004-01-2797
30.
Spelsberg-Korspeter
,
G.
,
2010
, “
Structural Optimization for the Avoidance of Self-Excited Vibrations Based on Analytical Models
,”
J. Sound Vib.
,
329
, pp.
4829
4840
.10.1016/j.jsv.2010.04.004
31.
Spelsberg-Korspeter
,
G.
,
2012
, “
Eigenvalue Optimization Against Brake Squeal: Symmetry, Mathematical Background and Experiments
,”
J. Sound Vib.
,
331
, pp.
4259
4268
.10.1016/j.jsv.2012.04.026
32.
Birger
,
I. I.
, and
Panovko
,
Ya.
,
1968
,
Strength, Stability, Vibrations
, Vol.
3
,
Mashinostroenie
,
Moscow (in Russian)
.
33.
Timoshenko
,
S.
, and
Woinowsky-Krieger
,
S.
,
1959
,
Theory of Plates and Shells
,
McGraw-Hill
,
New York
.
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