本文是探討煞車系統在運作時，煞車系統之動態穩定性，並探討煞車高頻異音的成因。在本研究中使用LS-Dyna進行煞車系統複數特徵值分析，藉此得到煞車系統之動態特性。為了確認有限元素模型之可靠度，利用理論模態分析與實驗模態分析進行模態驗證，以確保有限元素模型與實際結構一致性，並進而探討煞車系統中，各參數對煞車系統之動態特性之影響。經由參數變化複數特徵值分析結果可知，煞車系統的負阻尼受到摩擦係數的影響最大，其次是作動壓力，來令片摩擦材料厚度，最後是碟盤的轉速。為了探討煞車異音的聲學特徵，依據SAE J2521規範內容進行煞車異音試驗，並藉由麥克風與加速規紀錄煞車異音與結構振動時域訊號，利用短時傅立葉轉換進行時頻分析。吾人將實驗與分析結果進行比對，發現分析中的次大負阻尼與最大煞車異音頻率一致，進而提出方法的有效性。

This thesis investigates dynamic stability of a brake system and the cause of a brake squeal. This study used LS-Dyna to implement the Complex Eigenvalue Analysis (CEA) of a brake system to compute a brake system dynamic characteristic. The finite element model validity of the brake part was checked by modal verification. The dynamic stability of brake system was investigated through various the operating conditions in this thesis. The results obtained from various parameter complex eigenvalue analysis show that the brake system dynamic stability is most related with the change of friction coefficient. The other influence on the stability of brake system in order is the operating pressure, the thickness of linings, and rotation speed of the disc. To investigate the acoustic characteristic of squeal, we implement the SAE J2521 brake squeal testing. The testing sound and vibration time domain signal were recorded by microphone and accelerometer. The testing signal implements the time-frequency analysis through the Short-Time Fourier Transform (STFT). The comparison result obtained from the CEA and braking squeal frequency in the operating condition shows the submaximal frequency of negative damping same as maximum squeal frequency, and the validity of the proposed method can be confirmed.

[1] T. H. Oimao, I. N. Luginah and J. Bxer, "Cumulative effects of noise and odour annoyances on environmental and health related quality of life," Social Science & Medicine, vol. 146, pp. 191-203, 21 Oct 2015.
[2] S. A. Stansfeld and C. Clark, "Mental Health Effects of Noise," in Encyclopedia of Environmental Health, Amsterdam, Elsevier, 2019, pp. 287-294.
[3] A. Recio, L. Cristina, J. Ramón Banegas and J. Díaz, "Road Traffic Noise Effects on Cardiovascular, Respiratory, and Metabolic Health: An Integrative Model of Biological Mechanisms," Environmental Research, vol. 146, pp. 359-370, April 2016.
[4] 龐劍，2015，汽車車身噪聲與振動控制，北京: 機械工業出版社。
[5] V. P. Sergienko and S. N. Bukharov, Noise and Vibration in Friction Systems, New York: Springer International Publishing, 2015.
[6] F. Chen, C. Tan and R. Quaglia, Disc Brake Squeal: Mechanism, Analysis, Evaluation, and Reduction/Prevention, Warrendale, Pennsylvania: Society of Automotive Engineers, 2006.
[7] 鮑久聖，2015，盤式制動器摩擦學性能測試與智能預測技術，北京: 科學出版社。
[8] SAE International, "Disc and Drum Brake Dynamometer Squeal Noise Test Procedure J2521_200603," Society of Automotive Engineers, Warrendale, 2006.
[9] R. P. Jarvis and B. Mills, "Vibrations Induced by Dry Friction," in Proceedings of the Institution of Mechanical Engineers, 1963.
[10] 張力軍，吳軍，孟德健，2015，「模態耦合及摩擦系數一速度斜率與黏滑運動的 關係」 同濟大學學報(自然科學版)，第 43 卷，第 12，第 1850-1859 頁。
[11] X. C. Wang, B. Huang, R. L. Wang, J. L. Mo and H. Ouyang, "Friction-Induced Stick-Slip Vibration and its Experimental Validation," Mechanical Systems and Signal Processing, vol. 142, 2020.
[12] J. Kang, C. M. Krousgrill and F. Sadeghi, "Analytical formulation of mode-coupling instability in disc–pad coupled system," International Journal of Mechanical Sciences, vol. 51, no. 1, pp. 52-63, Jan 2009.
[13] T. S. Shi, O. Dessouki, T. Warzecha, W. K. Chang and A. Jayasundera, "Advances in Complex Eigenvalue Analysis for Brake Noise," Society of Automotive Engineers, Warrendale, 2001.
[14] R. S. Ballinger, "A Discussion of Complex Eigenvalue Analytical Method as They Relate to the Prediction of Brake Noise," Society of Automotive Engineers, Warrendale, 2016.
[15] S. Oberst and J. C. Lai, "Squeal Noise in Simple Numerical Brake Models," Journal of Sound and Vibration, vol. 352, pp. 129-141, 15 Sep 2015.
[16] X. Sui and Q. Ding, "Bifurcation and Stability Analyses for a Pad-on-Disc Frictional System," International Journal of Non-Linear Mechanics, vol. 107, pp. 112-125, 2018.
[17] M. Nishiwaki and M. Langthjem, "First Order Analysis of Disc Brake Noise-Relationship Between Low-Frequency Disc Brake Squeal and Moan Noise-," Society of Automotive Engineers, Warrendale, 2012.
[18] Y. Oura, Y. Kurita, Y. Nishizawa and K. Kosaka, "Influence of Brake Pad Thickness on Disc Brake Squeal," Journal of System Design and Dynamics, vol. 4, no. 6, pp. 970-982, 2010.
[19] J. Kang, "Squeal analysis of gyroscopic disc brake system based on finite element method," International Journal of Mechanical Sciences, vol. 51, no. 4, pp. 284-294, April 2009.
[20] Y. Du and Y. Wang, "Squeal Analysis of a Modal-Parameter-Based Rotating Disc Brake Model," International Journal of Mechanical Sciences, Vols. 131-132, pp. 1049-1060, Oct 2017.

[21] N. M. Ghazaly, S. A. Mohammed and A. M. Abd El Tawwab, "Understanding Mode-Coupling Mechanism of Brake Squeal Using Finite Element Analysis," International Journal of Engineering Research and Applications, vol. 2, no. 1, pp. 241-250, 2012.
[22] J.-J. Sinou and L. Jézéquel, "Mode coupling instability in friction-induced vibrations and its dependency on system parameters including damping," European Journal of Mechanics - A/Solids, vol. 26, no. 1, pp. 106-122, 2007.
[23] N. Kharate and S. Chaudhari, "Effect of Material Properties On Disc Brake Squeal And Performance Using FEM and EMA Approach.," in Materials Today: Proceedings, 2018.
[24] J. N. Eiras, C. Payan, S. Rakotonarivo and V. Garnier, "Experimental Modal Analysis and Finite Element Model Updating for Structural Health Monitoring of Reinforced Concrete Radioactive Waste Packages," Construction and Building Materials, vol. 180, pp. 531-542, 20 Aug 2018.
[25] R. J. Allemang and D. L. Brown, "A correlation coefficient for modal vector analysis," in Proceedings of the 1st International Modal Analysis Conference, Orlando, 1982.
[26] 王昭男，謝正昌，2007，「煞車系統之異音與振動分析」，中華民國音響學會年 會暨第二十屆論文發表會。
[27] J. S. Bendat and A. G. Piersol, Random data Analysus and Mearsurement Procedures Third edition, New York: A Wiley-Interscience Publication, 2000, pp. 200-214.
[28] R. D. Blevins, Formulas for natural frequency and shape, Florida: Krieger Publishing Company, 1979, pp. 250-251.
[29] R. K. Singhal, W. Guan and K. Willams, "Modal analysis of a thick-walled circular cylinder," Mechanical systems and signal processing, no. 16, pp. 141-153, 18 4 2001.
[30] Wikipedia, “維基百科-摩擦係數,” [線上]. Available: https://zh.wikipedia.org/wiki/摩擦系数. [存取日期: 15 08 2020].
[31] R. W. Clough and J. Penzien, Dynamic of Structures, Walnut Creek: Computers and Structures inc, 2010.
[32] D. J. Ewins, Modal Testing: Theory and Practice, Boston, Massachusetts: Research Studies Press, 1984, pp. 88-94.
[33] N. M. Newmark, "A Method of Computation for Structural Dynamics," Journal of the Engineering Mechanics Division, vol. 85, no. 3, pp. 67-94, 1959.
[34] A. Papinniemi, J. C. Lai, Z. Jiye and L. Loader, "Brake Squeal: a Literature Review," Applied Acoustics, vol. 63, no. 4, pp. 391-400, April 2002.
[35] S. S. Rao, Mechanical Vibrations 5th Edition, Upper Saddle River, New Jersey: Prentice Hall, 2011.