Minimizing brake squeal is one of the most important issues in the development of high performance braking systems. Furthermore, brake squeal occurs due to the changes in unpredictable factors such as the friction coefficient, contact stiffness, and pressure distribution along the contact surfaces of the brake disk and brake pads. This paper proposes a conceptual design method for disk brake systems that specifically aims to reduce the occurrence of low frequency brake squeal at frequencies below 5 kHz by appropriately modifying the shapes of brake system components to obtain designs that are robust against changes in the above unpredictable factors. A design example is provided and the validity of the obtained optimal solutions is then verified through real-world experiments. The proposed optimization method can provide useful design information at the conceptual design stage during the development of robust disk brake systems that maximize the performance while minimizing the occurrence of brake squeal despite the presence of unpredictable usage factors.

References

1.
Mills
,
H. R.
, 1938, “
Brake Squeal
,” Institution of Automobile Engineers, Technical Report No. 9000 B.
2.
Blok
,
H.
, 1940, “
Fundamental Mechanical Aspects of Boundary Lubrication
,”
SAE J.
,
46
(
2
), pp.
56
68
.
3.
Watari
,
A.
, and
Sugimoto
,
T.
, 1963, “
Vibrations Caused by Dry Friction
,”
Trans. Jpn. Soc. Mech. Eng.
,
29
(
200
), pp.
769
782
(in Japanese).
4.
Chen
,
G. X.
,
Zhou
,
Z. R.
,
Kapsa
,
P.
, and
Vincent
,
L.
, 2003, “
Experimental Investigation Into Squeal Under Reciprocating Sliding
,”
Tribol. Int.
,
36
, pp.
961
971
.
5.
Spurr
,
R. T.
, 1961, “
A Theory of Brake Squeal
,”
Proc. Inst. Mech. Eng.: Automob. Div.
,
15
(
1
), pp.
33
52
.
6.
North
,
M. R.
, 1972, “
Disc Brake Squeal—A Theoretical Model
,” Motor Industry Research Association, Research Report, Warwickshire, England, pp.
1
33
.
7.
Millner
,
N.
, 1978, “
An Analysis of Disk Brake Squeal
,” SAE Paper No. 780332.
8.
Murakami
,
H.
,
Tsunada
,
N.
, and
Kitamura
,
T.
, 1984, “
A Study Concerned With a Mechanism of Disc Brake Squeal
,” SAE Paper No. 841233.
9.
Brooks
,
P. C.
,
Crolla
,
D. A.
,
Lang
,
A. M.
, and
Schafer
,
D. R.
, 1993, “
Eigenvalue Sensitivity Analysis Applied to Disc Brake Squeal
,”
Braking of Road Vehicles
,
Institution of Mechanical Engineers, Mechanical Engineering Publications Limited, Bury St. Edmunds
,
England
, pp.
135
143
.
10.
Nishiwaki
,
M.
, 1993, “
Generalized Theory of Brake Noise
,”
Proc. Inst. Mech. Eng., Part D
,
207
, pp.
195
202
.
11.
Hulten
,
J.
, and
Flint
,
J.
, 1999, “
An Assumed Modes Method Approach to Disc Brake Squeal Analysis
,” SAE Paper No. 1999–01–1335.
12.
El-Butch
,
A. M.
, and
Ibrahim
,
I. M.
, 1999, “
Modeling and Analysis of Geometrically Induced Vibration in Disc Brakes Considering Contact Parameters
,” SAE Paper No. 1999–01–0143.
13.
Rudolph
,
M.
, and
Popp
,
K.
, 2001, “
Friction Induced Brake Vibrations
,”
Proceedings of DECT’01 ASME 2001 Design Engineering Technical Conference and Computer and Information in Engineering Conference
, DETC2001/VIB-21509.
14.
Kinkaid
,
N. M.
,
O’Reilly
,
O. M.
, and
Papadopoulos
,
P.
, 2003, “
Review Automotive Disc Brake Squeal
,”
J. Sound Vib.
,
267
, pp.
105
166
.
15.
Liles
,
G. D.
, 1989, “
Analysis of Disk Brake Squeal Using Finite Element Methods
,” SAE Paper No. 891150.
16.
Kido
,
I.
,
Kurahachi
,
T.
, and
Asai
,
M.
, 1996, “
A Study on Low-Frequency Brake Squeal Noise
,” SAE Paper No. 960993.
17.
Matsushima
,
T.
,
Nishiwaki
,
M.
,
Masumo
,
H.
, and
Ito
,
S.
, 1997, “
FEM Analysis of Low-Frequency Disc Brake Squeal (in Case of Opposed Type Caliper)
,” SAE Paper No. 973020.
18.
Dihua
,
G.
, and
Dongying
,
J.
, 1998, “
A Study on Disc Brake Squeal Using Finite Element Methods
,” SAE Paper No. 980597.
19.
Matsushima
,
T.
,
Masumo
,
H.
,
Ito
,
S.
, and
Nishiwaki
,
M.
, 1998, “
FE Analysis of Low-Frequency Disc Brake Squeal (in Case of Floating Type Caliper)
,” SAE Paper No. 982251.
20.
Chung
,
C.-H.
,
Steed
,
W.
,
Kobayashi
,
K.
, and
Nakata
,
H.
, “
A New Analysis Method for Brake Squeal Part I: Theory for Modal Domain Formulation and Stability Analysis
,” SAE Paper No. 2001–01–1600.
21.
Lou
,
G.
,
Wu
,
T. W.
, and
Bai
,
Z.
, 2004, “
Disk Brake Squeal Prediction Using the ABLE Algorithm
,”
J. Sound Vib.
,
272
, pp.
731
748
.
22.
Joo
,
S. D.
,
Hun Han
,
J.
,
Park
,
K. W.
, and
Kim
,
Y. J.
, 2006, “
Reducing Brake Squeal Through FEM Approach and Parts Design Modifications
,” SAE Paper No. 2006–01–3206.
23.
Fritz
,
G.
,
Sinou
,
J.-J.
,
Duffal
,
J.-M.
, and
Jezequel
,
L.
, 2007, “
Effects of Damping on Brake Squeal Coalescence Patterns—Application on a Finite Element Model
,”
Mech. Res. Commun.
,
34
, pp.
181
190
.
24.
Soh
,
H. J.
, and
Yoo
,
J. H.
, 2010, “
Optimal Shape Design of a Brake Caliper for Squeal Noise Reduction Considering System Instability
,”
Proc. Inst. Mech. Eng., Part D
,
224
, pp.
909
925
.
25.
Yetis
,
F. A.
, and
Saitou
,
K.
, 2002, “
Decomposition-Based Assembly Synthesis Based on Structural Considerations
,”
ASME J. Mech. Des.
,
124
, pp.
593
601
.
26.
Lee
,
B.
, and
Saitou
,
K.
, 2003, “
Decomposition-Based Assembly Synthesis for In-Process Dimensional Adjustability
,”
ASME J. Mech. Des.
,
125
, pp.
464
473
.
27.
Lyu
,
N.
, and
Saitou
,
K.
, 2003, “
Decomposition-Based Assembly Synthesis for Structural Stiffness
,”
ASME J. Mech. Des.
,
125
, pp.
452
463
.
28.
Nakagawa
,
T.
,
Nishigaki
,
H.
,
Tsurumi
,
Y.
, and
Kikuchi
,
N.
, 2000, “
First Order Analysis for Automotive Body Structure Design
,”
Proceedings of DECT’00 ASME2000 Design Engineering Technical Conference and Computer and Information in Engineering Conference
, DECT2000/DAC-14533.
29.
Nishigaki
,
H.
,
Amago
,
T.
,
Sugiura
,
H.
,
Kojima
,
Y.
,
Nishiwaki
,
S.
, and
Kikuchi
,
N.
, 2004, “
First Order Analysis for Automotive Body Structure Design—Part 1: Overview and Applications
,” SAE Paper No. 2004–01–1658.
30.
Tsurumi
,
Y.
,
Nishigaki
,
H.
,
Nakagawa
,
T.
,
Amago
,
T.
, and
Furusu
,
K.
, 2004, “
First Order Analysis for Automotive Body Structure Design—Part 2: Joint Analysis Considering Nonlinear Behavior
,” SAE Paper No. 2004–01–1659.
31.
Nishigaki
,
H.
, and
Kikuchi
,
N.
, 2004, “
First Order Analysis for Automotive Body Structure Design—Part 3: Crashworthiness Analysis Using Beam Elements
,” SAE Paper No. 2004–01–1660.
32.
Nakagawa
,
T.
,
Nishigaki
,
H.
,
Tsurumi
,
Y.
, and
Kikuchi
,
N.
, 2004, “
First Order Analysis for Automotive Body Structure Design—Part 4: Noise and Vibration Analysis Applied to a Subframe
,” SAE Paper No. 2004–01–1661.
33.
Lyu
,
N.
, and
Saitou
,
K.
, 2006, “
Decomposition-Based Assembly Synthesis of Space Frame Structures Using Joint Library
,”
ASME J. Mech. Des.
,
128
, pp.
57
65
.
34.
Takezawa
,
A.
,
Nishiwaki
,
S.
,
Izui
,
K.
, and
Yoshimura
,
M.
, 2006, “
Structural Optimization Using Function-Oriented Elements to Support Conceptual Designs
,”
ASME J. Mech. Des.
,
128
, pp.
689
700
.
35.
Ma
,
W. Y.
,
Wang
,
D. L.
, and
Ting
,
K.-L.
, 2010, “
Characteristic Matrices and Conceptual Design of Hydraulic Systems
,”
ASME J. Mech. Des.
,
132
, p.
031005
.
36.
Saitou
,
K.
,
Izui
,
K.
,
Nishiwaki
,
S.
, and
Papalambros
,
P.
, 2005, “
A Survey of Structural Optimization in Mechanical Product Development
,”
ASME J. Comput. Inf. Sci. Eng.
,
5
, pp.
214
226
.
37.
Yu
,
J. C.
, and
Ishii
,
K.
, 1998, “
Design for Robustness Based on Manufacturing Variation Patterns
,”
ASME J. Mech. Des.
,
120
, pp.
196
202
.
38.
Gunawan
,
S.
, and
Azarm
,
S.
, 2004, “
Non-Gradient Based Parameter Sensitivity Estimation for Single Objective Robust Design
,”
ASME J. Mech. Des.
,
126
, pp.
395
402
.
39.
Gunawan
,
S.
, and
Azarm
,
S.
, 2005, “
A Feasibility Robust Optimization Method Using Sensitivity Region Concept
,”
ASME J. Mech. Des.
,
127
, pp.
858
865
.
40.
Li
,
M.
,
Azarm
,
S.
, and
Boyars
,
A.
, 2006, “
A New Deterministic Approach Using Sensitivity Region Measures for Multi-Objective Robust and Feasibility Robust Design Optimization
,”
ASME J. Mech. Des.
,
128
, pp.
874
883
.
41.
Beyer
,
H.-G.
, and
Sendhoff
,
B.
, 2007, “
Robust Optimization—A Comprehensive Survey
,”
Comput. Methods Appl. Mech. Eng.
,
196
, pp.
3190
3218
.
42.
Lu
,
X. J.
,
Li
,
H.-X.
, and
Chen
,
C. L. P.
, 2010, “
Variable Sensitivity-Based Deterministic Robust Design for Nonlinear System
”,
ASME J. Mech. Des.
,
132
, p.
064502
.
43.
Matsushima
,
T.
,
Nishiwaki
,
S.
,
Yamasaki
,
S.
,
Izui
,
K.
, and
Yoshimura
,
M.
, 2007, “
An Optimal Design Method for Reducing Brake Squeal in Disc Brake Systems
,”
Proceedings of DECT’07 ASME2007 International Design Engineering Technical Conference and Computer and Information in Engineering Conference
, DECT2007–34708.
44.
Kurita
,
Y.
, and
Oura
,
Y.
, 2009, “
Influence of Distributed Stiffness in Contact Surface on Disk Brake Squeal
,”
J. Jpn. Soc. Tribol.
,
54
, pp.
646
651
.
45.
Chakraborty
,
U. K.
, and
Janikow
,
C. Z.
, 2003, “
An Analysis of Gray Versus Binary Encoding in Genetic Search
,”
Inf. Sci.
,
156
(
3–4
), pp.
253
269
.
46.
Miller
,
B. L.
, and
Goldberg
,
D. E.
, 1995, “
Genetic Algorithms, Tournament Selection, and the Effects of Noise
,”
Complex Syst.
,
9
(
3
), pp.
193
212
.
47.
Goldberg
,
D. E.
, 1989,
Genetic Algorithms in Search, Optimization, and Machine Learning
,
Addison-Wesley
,
Boston
.
You do not currently have access to this content.