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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
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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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Copyright © 2007 by American Society of Mechanical Engineers
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+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

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+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 (×)

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+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)

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+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)

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+Critical speed for varying k
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Critical speed for varying k
Figure 8

Critical speed for varying k

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+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)

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+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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