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TECHNICAL PAPERS

An Efficient Approach to Estimate Critical Value of Friction Coefficient in Brake Squeal Analysis

[+] Author and Article Information
Jinchun Huang

School of Mechanical Engineering, Purdue University, 585 Purdue Mall, West Lafayette, IN 47907-2088huangjinchun@tsinghua.org.cn

Charles M. Krousgrill

School of Mechanical Engineering, Purdue University, 585 Purdue Mall, West Lafayette, IN 47907-2088krousgri@ecn.purdue.edu

Anil K. Bajaj

School of Mechanical Engineering, Purdue University, 585 Purdue Mall, West Lafayette, IN 47907-2088bajaj@ecn.purdue.edu

J. Appl. Mech 74(3), 534-541 (Jun 13, 2006) (8 pages) doi:10.1115/1.2423037 History: Received March 30, 2005; Revised June 13, 2006

Automotive brake squeal generated during brake applications has become a major concern in automotive industry. Warranty costs for brake noise related complaints have been greatly increasing in recent years. Brake noise and vibration control are also important for the improvement of vehicle quietness and passenger comfort. In this work, the mode coupling instability mechanism is discussed and a method to estimate the critical value of friction coefficient identifying the onset of brake squeal is presented. This is achieved through a sequence of steps. In the first step, a modal expansion method is developed to calculate eigenvalue and eigenvector sensitivities. Different types of mode couplings and their relationships with possible onset of squeal are discussed. Then, a reduced-order characteristic equation method based on the elastically coupled system eigenvalues and their derivatives is presented to estimate the critical value of friction coefficient. The significance of this method is that the critical value of friction coefficient can be predicted accurately without the need for a full complex eigenvalue analysis, making it possible to determine the sensitivity of system stability with respect to design parameters directly.

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Copyright © 2007 by American Society of Mechanical Engineers
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Figures

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Figure 1

A typical occurrence of mode merging for a pair of modes that leads to “coupled-mode” instability. The frequency loci for the two frequencies as a function of the friction coefficient μ merge at μ=μcr and beyond this point, the two frequencies are a complexconjugate pair. Here, only the real part of the two frequencies is shown.

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Figure 2

Frequency loci and inner products of eigenvectors as a function of the lining stiffness k, showing curve crossing for modes r and s. This corresponds to the case where Eksr=Ekrs=0 in eigenvalue expressions in Eqs. (17) and (18).

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Figure 3

Frequency loci and inner products of eigenvectors as a function of the lining stiffness k, showing “curve veering away” for modes r and s when Eksr=Ekrs≠0 in Eqs. 17,18

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Figure 4

Examples of eigenfrequency loci interactions for two modes as the friction coefficient μ is varied: (a) curve crossing, (b) veering away, and (c) veering towards

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Figure 5

Estimates of μcr by the power series expansion approach. Here μcr is defined by the intersection of approximations to the two eigenfrequency loci.

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Figure 6

Variation of the frequencies of modes 27 to 32 with μ for a drum brake model (See Ref. 10)

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Figure 7

Estimate of μcr by the reduced-order characteristic equation for modes 30 and 31 in Fig. 6 for the drum brake system (see Ref. 10). The exact results are from the complex eigenvalue analysis, whereas the approximate eigenfrequency loci are based on approximation in Eq. 29.

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Figure 8

Estimate of μcr by the reduced-order characteristic equation for the drum brake model in Ref. 10 with increased lining stiffness. k=1.3.

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Figure 9

Exact and estimated stability boundaries as a function of the lining stiffness for the drum brake system in Ref. 10. The stability boundaries are for different combinations of modes that merge.

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