Research Papers

Stability Analysis and Improvement of Uncertain Disk Brake Systems With Random and Interval Parameters for Squeal Reduction

[+] Author and Article Information
Hui Lü

State Key Laboratory of Advanced Design
and Manufacturing for Vehicle Body,
Hunan University,
Changsha, Hunan 410082, China

Dejie Yu

State Key Laboratory of Advanced Design
and Manufacturing for Vehicle Body,
Hunan University,
Changsha, Hunan 410082, China
e-mail: djyu@hnu.edu.cn

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received August 25, 2014; final manuscript received March 6, 2015; published online April 27, 2015. Assoc. Editor: Corina Sandu.

J. Vib. Acoust 137(5), 051003 (Oct 01, 2015) (11 pages) Paper No: VIB-14-1314; doi: 10.1115/1.4030044 History: Received August 25, 2014; Revised March 06, 2015; Online April 27, 2015

Stability analysis and improvement of disk brake systems for squeal reduction have been investigated by automotive manufacturers for decades. However, most of the researches have not considered uncertainties. For this case, a practical approach for analyzing and improving the stability of uncertain disk brake systems is proposed in this paper. In the proposed approach, a hybrid uncertain model with random and interval parameters is introduced to deal with the uncertainties existing in a disk brake system. The parameters of brake pressure, densities of component materials, and thickness of back plate are treated as random variables; whereas the parameters of frictional coefficient and Young's modulus of component materials are treated as interval variables. Attention is focused on stability analysis of the disk brake system for squeal reduction, and the stability is investigated via complex eigenvalue analysis (CEA). The dominant unstable mode is extracted by performing CEA based on a linear finite element (FE) model, and the negative damping ratio corresponding to the dominant unstable mode is selected as the indicator of system stability. To improve the efficiency of analysis, response surface methodology (RSM) is used to replace the time-consuming FE simulations. Based on RSM and CEA, the stability analysis model of the disk brake system is constructed, in which reliability analysis, hybrid uncertain analysis and sensitivity analysis are applied to deal with the uncertain problems. The analysis results of a numerical example demonstrate the effectiveness of the proposed approach, and show that the stability and robustness of the uncertain disk brake system can be improved effectively by increasing the stiffness of back plate.

Copyright © 2015 by ASME
Topics: Stability , Disks , Brakes
Your Session has timed out. Please sign back in to continue.


Nishiwaki, M. R., 1990, “Review of Study on Brake Squeal,” JPN Soc. Automob. Eng. Rev., 11(4), pp. 48–54.
Yang, S., and Gibson, R. F., 1997, “Brake Vibration and Noise: Reviews, Comments, and Proposals,” Int. J. Mater. Prod. Technol., 12(4–6), pp. 496–513. [CrossRef]
Nishiwaki, M., 1993, “Generalized Theory of Brake Noise,” Proc. Inst. Mech. Eng., Part H, 207(3), pp. 195–202. [CrossRef]
Papinniemi, A., Lai, J. C. S., Zhao, J., and Loader, L., 2002, “Brake Squeal: A Literature Review,” Appl. Acoust., 63(4), pp. 391–400. [CrossRef]
Kinkaid, N. M., O'Reilly, O. M., and Papadopoulos, P., 2003, “Automotive Disc Brake Squeal: A Review,” J. Sound Vib., 267(1), pp. 105–166. [CrossRef]
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. [CrossRef]
AbuBakar, A. R., and Ouyang, H., 2006, “Complex Eigenvalue Analysis and Dynamic Transient Analysis in Predicting Disc Brake Squeal,” Int. J. Veh. Noise Vib., 2(2), pp. 143–155. [CrossRef]
Liles, G. D., 1989, “Analysis of Disc Brake Squeal Using Finite Element Methods,” SAE Paper No. 891150. [CrossRef]
Chargin, M. L., Dunne, L. W., and Herting, D. N., 1997, “Nonlinear Dynamics of Brake Squeal,” Finite Elem. Anal. Des., 28(1), pp. 69–82. [CrossRef]
Ouyang, H., Li, W., and Mottershead, J. E., 2003, “A Moving-Load Model for Disc-Brake Stability Analysis,” ASME J. Vib. Acoust., 125(1), pp. 53–58. [CrossRef]
Guan, D., Su, X., and Zhang, F., 2006, “Sensitivity Analysis of Brake Squeal Tendency to Substructures' Modal Parameters,” J. Sound Vib., 291(1–2), pp. 72–80. [CrossRef]
Fritz, G., Sinou, J. J., Duffal, J. M., Jézéquel, L., 2007, “Investigation of the Relationship Between Damping and Mode-Coupling Patterns in Case of Brake Squeal,” J. Sound Vib., 307(3–5), pp.591–609. [CrossRef]
Liu, P., Zheng, H., Cai, C., Wang, Y. Y., Lu, C., Ang, K. H., and Liu, G. R., 2007, “Analysis of Disc Brake Squeal Using the Complex Eigenvalue Method,” Appl. Acoust., 68(6), pp. 603–615. [CrossRef]
Junior, M. T., Gerges, S. N. Y., and Jordan, R., 2008, “Analysis of Brake Squeal Noise Using the Finite Element Method: A Parametric Study,” Appl. Acoust., 69(2), pp. 147–162. [CrossRef]
Dai, Y., and Lim, T. C., 2008, “Suppression of Brake Squeal Noise applying Finite Element Brake and Pad Model Enhanced by Spectral-Based Assurance Criteria,” Appl. Acoust., 69(3), pp. 196–214. [CrossRef]
Nouby, M., Mathivanan, D., and Srinivasan, K., 2009, “A Combined Approach of Complex Eigenvalue Analysis and Design of Experiments (DOE) to Study Disc Brake Squeal,” Int. J. Eng. Sci. Technol., 1(1), pp. 254–271.
Chittepu, K., 2011, “Robustness Evaluation of Brake Systems Concerned to Squeal Noise Problem,” SAE Paper No. 2011-26-0059. [CrossRef]
Sarrouy, E., Dessombz, O., and Sinou, J. J., 2013, “Piecewise Polynomial Chaos Expansion With an Application to Brake Squeal of a Linear Brake System,” J. Sound Vib., 332(3–4), pp. 577–594. [CrossRef]
Stefanou, G., 2009, “The Stochastic Finite Element Method: Past, Present and Future,” Comput. Methods Appl. Mech. Eng., 198(9–12), pp. 1031–1051. [CrossRef]
Moore, R., and Lodwick, W., 2003, “Interval Analysis and Fuzzy Set Theory,” Fuzzy Set. Syst., 135(1), pp. 5–9. [CrossRef]
Baş, D., and Boyacı, İ. H., 2007, “Modeling and Optimization I: Usability of Response Surface Methodology,” J. Food Eng., 78(3), pp. 836–845. [CrossRef]
Mayers, R. H., and Montgomery, D. C., 2002, Response Surface Methodology: Process and Product Optimization Using Designed Experiments, Wiley, New York.
Kruse, S., and Hoffmann, N. P., 2013, “On the Robustness of Instabilities in Friction-Induced Vibration,” ASME J. Vib. Acoust., 135(6), p. 061013. [CrossRef]
Gao, W., Wu, D., Song, C., Tin-Loi, F., and Li, X., 2011, “Hybrid Probabilistic Interval Analysis of Bar Structures With Uncertainty Using a Mixed Perturbation Monte Carlo Method,” Finite Elem. Anal. Des., 47(7), pp. 643–652. [CrossRef]
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. [CrossRef]
Papila, M., 2001, “Accuracy of Response Surface Approximations for Weight Equations Based on Structural Optimization,” Ph.D., thesis, University of Florida, Gainesville, FL.
Fu, J., Zhao, Y., and Wu, Q., 2007, “Optimising Photoelectrocatalytic Oxidation of Fulvic Acid Using Response Surface Methodology,” J. Hazard. Mater., 144(1–2), pp. 499–505. [CrossRef] [PubMed]
Joglekar, A. M., and May, A. T., 1987, “Product Excellence Through Design of Experiments,” Cereal Foods World, 32, pp. 857–868.
Kim, H. K., Kim, J. G., Cho, J. D., and Hong, J. W., 2003, “Optimization and Characterization of UV-Curable Adhesives for Optical Communications by Response Surface Methodology,” Polym. Test., 22(8), pp. 899–906. [CrossRef]
Hou, J., Guo, X. X., and Tan, G. F., 2009, “Complex Mode Analysis on Disc-Brake Squeal and Design Improvement,” SAE Technical Paper No. 2009-01-2101. [CrossRef]
Butlin, T., and Woodhouse, J., 2010, “Friction-Induced Vibration: Quantifying Sensitivity and Uncertainty,” J. Sound Vib., 329(5), pp. 509–526. [CrossRef]
Melchers, R. E., and Ahammed, M., 2004, “A Fast Approximate Method for Parameter Sensitivity Estimation in Monte Carlo Structural Reliability,” Comput. Struct., 82(1), pp. 55–61. [CrossRef]


Grahic Jump Location
Fig. 1

The model of a simplified disk brake system

Grahic Jump Location
Fig. 4

The distribution of the complex eigenvalues of the brake system for some groups of samples

Grahic Jump Location
Fig. 2

The FE model of a simplified disk brake

Grahic Jump Location
Fig. 3

Constraints and loading of the brake system

Grahic Jump Location
Fig. 5

The sensitivities of ζd(x) to system parameters: (a) sensitivity of ζd(x) to f; (b) sensitivity of ζd(x) to p; (c) sensitivity of ζd(x) to E1; (d) sensitivity of ζd(x) to E2; (e) sensitivity of ζd(x) to E3; (f) sensitivity of ζd(x) to ρ1; (g) sensitivity of ζd(x) to ρ2; (h) sensitivity of ζd(x) to ρ3; and (i) sensitivity of ζd(x) to h1



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In