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Journal of Applied Mechanics | Volume 74 | Issue 3 | TECHNICAL PAPERS
TECHNICAL PAPERS

Friction Induced Vibrations in Moving Continua and Their Application to Brake Squeal

[+] Author and Article Information
Daniel Hochlenert1

Department of Mechanical Engineering, Dynamics and Vibrations Group, Technische Universität Darmstadt, Hochschulstrasse 1, 64289 Darmstadt, Germanyhochlenert@dyn.tu-darmstadt.de

Gottfried Spelsberg-Korspeter

Department of Mechanical Engineering, Dynamics and Vibrations Group, Technische Universität Darmstadt, Hochschulstrasse 1, 64289 Darmstadt, Germanyspeko@dyn.tu-darmstadt.de

Peter Hagedorn

Department of Mechanical Engineering, Dynamics and Vibrations Group, Technische Universität Darmstadt, Hochschulstrasse 1, 64289 Darmstadt, Germanypeter.hagedorn@dyn.tu-darmstadt.de

Due to the symmetry of the system, the circumferential position of the pads is arbitrary, i.e., it is always possible to transform the equations of motion to the described form.

1

Corresponding author.

J. Appl. Mech 74(3), 542-549 (Jun 22, 2006) (8 pages) doi:10.1115/1.2424239 History: Received September 14, 2005; Revised June 22, 2006
Article
References
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Citing Articles

Considerable effort is spent in the design and testing of disk brake systems installed in modern passenger cars. This effort can be reduced if appropriate mathematical–mechanical models are used for studying the dynamics of these brakes. In this context, the mechanism generating brake squeal in particular deserves closer attention. The present paper is devoted to the modeling of self-excited vibrations of moving continua generated by frictional forces. Special regard is given to an accurate formulation of the kinematics of the frictional contact in two and three dimensions. On the basis of a travelling Euler–Bernoulli beam and a rotating annular Kirchhoff plate with frictional point contact the essential properties of the contact kinematics leading to self-excited vibrations are worked out. A Ritz discretization is applied and the obtained approximate solution is compared to the exact one of the traveling beam. A minimal disk brake model consisting of the discretized rotating Kirchhoff plate and idealized brake pads is analyzed with respect to its stability behavior resulting in traceable design proposals for a disk brake.
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References

1
Kinkaid, N. M., O’Reilly, O. M., and Papadopoulos, P., 2003, “Automotive Disc Brake Squeal,” J. Sound Vib.  [CrossRef], 267 , pp. 105–166.
2
Ibrahim, R. A., 1994, “Friction-Induced Vibration, Chatter, Squeal, and Chaos, Part II: Dynamic and Modeling,” Appl. Mech. Rev., 47 (7), pp. 227–253.
3
Ouyang, H., and Mottershed, J. E., 2004, “Dynamic Instability of an Elastic Disk under the Action of a Rotating Friction Couple,” J. Appl. Mech.  [CrossRef], 71 , pp. 753–758.
4
Ono, K., Chen, J., and Bogy, D. B., 1991, “Stability Analysis for the Head-Disk Interface in a Flexible Disk Drive,” J. Appl. Mech., 58 , pp. 1005–1014.
5
Kinkaid, N. M., O’Reilly, O. M., and Papadopoulos, P., 2005, “On the Transient Dynamics of a Multi-Degree-of-Freedom Friction Oscillator: A New Mechanism for Brake Noise,” J. Sound Vib.  [CrossRef], 287 (4–5), pp. 901–917.
6
von Wagner, U., Hochlenert, D., and Hagedorn, P., “Minimal Models for the Explanation of Disk Brake Squeal,” J. Sound Vib., in press.
7
Wickert, J. A., and Mote, C. D., 1990, “Classical Vibration Analysis of Axially Moving Continua,” J. Appl. Mech., 57 , pp. 738–744.
8
Chakraborty, G., and Mallik, K., 2000, “Wave Propagation in and Vibration of a Travelling Beam With and Without Non-Nonlinear Effects,” J. Sound Vib.  [CrossRef], 236 (2), pp. 277–290.
9
Karapetjan, A. V., 1975, “The Stability of Nonconservative Systems,” Vestn. Mosk. Univ., Ser. 1: Mat., Mekh., 30 (4), pp. 109–113.
10
Lakhadanov, V. M., 1975, “On the Stability of Nonlinear Systems,” J. Appl. Math. Mech.  [CrossRef], 39 (1), pp. 53–58.
11
Leissa, A., 1969, “Vibration of Plates,” NASA SP-160, Washington, D.C.
12
Jearsiripongkul, T., 2005, “Squeal in Floating Caliper Disk Brakes: A Mathematical Model,” Ph.D. thesis, Technische Universität Darmstadt, Germany.
13
von Wagner, U., Hochlenert, D., Jearsiripongkul, T., and Hagedorn, P., 2004, “Active Control of Brake Squeal via Smart Pads,” "Proceedings of the 22nd Annual Brake Colloquium", Anaheim, CA, SAE Paper 2004-01-2773.
14
Hochlenert, D., and Hagedorn, P., 2006, “Control of Disc Brake Squeal—Modelling and Experiments,” "Structural Control and Health Monitoring", Wiley, New York, 13 , pp. 260–276.

Figures

Grahic Jump Location
+Axially moving beam
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Axially moving beam
Figure 1

Axially moving beam

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+Kinematics and forces acting on the beam and on the pads
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Kinematics and forces acting on the beam and on the pads
Figure 2

Kinematics and forces acting on the beam and on the pads

Grahic Jump Location
+Comparison of the exact (lines) and the approximate solution (×)
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Comparison of the exact (lines) and the approximate solution (×)
Figure 3

Comparison of the exact (lines) and the approximate solution (×)

Grahic Jump Location
+Comparison of the exact and the approximate solution for varying v¯
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Comparison of the exact and the approximate solution for varying v¯
Figure 4

Comparison of the exact and the approximate solution for varying v¯

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+Rotating Kirchhoff plate: model (left) and top view (right)
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Rotating Kirchhoff plate: model (left) and top view (right)
Figure 5

Rotating Kirchhoff plate: model (left) and top view (right)

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+Kinematics of the plate (section in eφ-ez- and er-ez-plane)
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Kinematics of the plate (section in eφ-ez- and er-ez-plane)
Figure 6

Kinematics of the plate (section in eφ-ez- and er-ez-plane)

Grahic Jump Location
+Root locus for varying Ω (only eigenvalues with pos. imag. part)
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Root locus for varying Ω (only eigenvalues with pos. imag. part)
Figure 7

Root locus for varying Ω (only eigenvalues with pos. imag. part)

Grahic Jump Location
+Critical speed for varying k
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Critical speed for varying k
Figure 8

Critical speed for varying k

Grahic Jump Location
+Critical speed for varying μ and N0 but constant braking torque (r0=0.13m)
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Critical speed for varying μ and N0 but constant braking torque (r0=0.13m)
Figure 9

Critical speed for varying μ and N0 but constant braking torque (r0=0.13m)

Grahic Jump Location
+Critical speed for varying r0 and N0 but constant braking torque (μ=0.6)
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Critical speed for varying r0 and N0 but constant braking torque (μ=0.6)
Figure 10

Critical speed for varying r0 and N0 but constant braking torque (μ=0.6)

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