以複數特徵值分析浮動卡鉗動態之不穩定與噪音

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研究生：	普德古 Unggul Teguh Prasetyo
論文名稱：	以複數特徵值分析浮動卡鉗動態之不穩定與噪音 Dynamic Instability Analysis of Floating Caliper Brake Based on Complex Eigenvalue Extraction: A Parametric Study of Low and High-Frequency Squeal
指導教授：	黃以玫 Yi Mei Huang 黃以玫 Yi Mei Huang
口試委員:
學位類別：	碩士 Master
系所名稱：	工學院 - 機械工程學系 Department of Mechanical Engineering
論文出版年：	2020
畢業學年度：	108
語文別：	英文
論文頁數：	91
中文關鍵詞：	卡鉗噪音、卡鉗的不穩定性、複數特徵值分析、有限元素法
外文關鍵詞：	brake squeal, instability, complex eigenvalue analysis, finite element method
相關次數：	點閱：21 下載：0
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在車輛煞車至停止前的一瞬間往往是卡鉗的高頻噪音
(1 16kHz)的來源，雖然噪音
對於煞車效能僅有些微的影響，但卻與產品的品質保證與消費者的滿意度有莫大的關聯，
雖然此現象複雜且無法完全了解，多項研究仍推斷此現象發生的原因為系統的不穩定
性。
本次研究使用有限元素法萃取複數的特徵值進而分析系統，當特徵值實部為正時，
代表系統存在著負的阻尼，此時系統會變的不穩定，進而產生尖銳煞車噪音。本研究使
用 MSC Nastran 2018 進行複數特徵值的分析。研究發現對於所分析的特定卡鉗在低
頻範圍中 2.9kHz會出現最大不穩定性與噪音，而高頻範圍則是 9.9kHz 會出現最大不穩
定性與噪音。本研究也討論變更設計的參數研究其對於系統的影響，其結果顯示摩擦係
數、來令片背板的勁度、接觸面積、來令片形狀、阻尼隔音層對於系統的不穩定性甚為
顯著。而噪音可經由減少摩擦係數達到抑制當來令片背板越硬，則噪音會越大來令
片楊氏模數在低頻範圍的噪音中臨界值為 180GPa 而高頻範圍其不穩定區間為 140GPa至 280GPa 不僅如此，減少來令片與煞車碟盤接觸面積或者改變來令片的形狀也可以
減少噪音最後，煞車噪音也可以藉著增加阻尼隔音層而減少。

Brake squeal results from high frequency vibration (1 16 kHz) during the vehicle braking that occurs just a moment before stopping. Brake squeal has little effect on braking performance. However, this audible noise relates to customer dissatisfaction and high warranty cost. Although this phenomenon is complicated and remains unclear, several previous studies presumed that it is due to system instability.
In this study, the finite element method was used to analyze the system by extracting and examining the complex eigenvalues. The system is unstable if the real part of the eigenvalue is positive, which indicates the existence of negative damping. Complex eigenvalue calculation was done using MSC Nastran 2018. In this the present work, the dominant instability occurs at 2.9 kHz for the low frequency squeal and 9.9 kHz for the high frequency squeal. The effects of varying several parameters were studied. The results of friction coefficient, rotational speed and hydraulic pressure, back pad stiffness, contact area, lining pad shape, and adding a damping layer are significant to the instability.

摘要 .    i
Abstract    ii
Preface    iii
Table of Contents    iv
List of Figures    vii
List of Tables    xi
Chapter 1. Introduction and Literature Review    1
1.    Background    1
2.    Classification of the vehicle system    2
3.    Classification of brake system    4
4.    Brake squeal mechanism    5
4.1.    Stick-slip mechanism    5
4.2.    Sparg-slip mechanism    6
4.3.    Mode coupling mechanism    7
5.    The investigation into brake squeal    8
5.1.    Experimental approach    8
5.2.    Theoretical approach    9
5.3.    Finite element approach    11
Chapter 2. Formulation and Computational Methods    15
1.    Complex eigenvalue extraction    15
2.    Finite element modeling    16
3.    Complex eigenvalue analysis using MSC Nastran    19
Chapter 3. Results and Discussion    22
1.    Verification of model and analysis procedure    22
1.1.    Natural frequency extraction    22
1.2.    Validation of analysis procedure    24
2.    Complex eigenvalue analysis results    25
3.    Modal assurance criteria (MAC) analysis    27
4.    Parametric studies    29
4.1.    Influence of rotational speed    29
4.2.    Influence of hydraulic pressure    29
4.3.    Influence of friction coefficient    32
4.4.    Influence of back pad stiffness    35
4.5.    Influence of reduced contact area    38
4.6.    Influence of lining pad shape    44
4.7.    Influence of damping layer    46
5.    Parametric optimization and prediction opportunity    51
5.1.    Model fitting    52
5.2.    Optimization opportunity    56
Chapter 4. Conclusions and Future Works    60
1.    Conclusions    60
2.    Suggestions for future works    60
Bibliography    62
APPENDIXES    66
Appendix A: Procedure of brake squeal analysis    67
   Import the finite element (FE) model to MSC Patran and define materials.    67
   Set up coordinate 1 and 2    68
   Set up multi-point constrain (MPC)  RB2    68
   Apply the loading    70
   Determine the analyzed group    71
   Choose the solution pack and set the output    72
   Create subcase (1st load step: non-linear static analysis)    73
   Create subcase (2nd load step: complex eigenvalue analysis)    74
   Run both subcases in one execution    75
   Edit *.bdf file manually and run with MSC Nastran    76
   Processing the data (complex eigenvalue)    77
Appendix B: Nastran input file    78
Appendix C: Neural network (NN) curve fitting code by Mathlab    82
Appendix D: Genetic algorithm (GA) codes by Python    84

                                

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