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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姓名	普德古(Unggul Teguh Prasetyo) 查詢紙本館藏	畢業系所	機械工程學系
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)
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摘要(中)	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。
摘要(英)	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.
關鍵字(中)	★ 卡鉗噪音 ★ 卡鉗的不穩定性 ★ 複數特徵值分析 ★ 有限元素法	關鍵字(英)	★ brake squeal ★ instability ★ complex eigenvalue analysis ★ finite element method
論文目次	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 1.1. Background 1 1.2. Classification of the vehicle system 2 1.3. Classification of brake system 4 1.4. Brake squeal mechanism 5 1.4.1. Stick-slip mechanism 5 1.4.2. Sparg-slip mechanism 6 1.4.3. Mode coupling mechanism 7 1.5. The investigation into brake squeal 8 1.5.1. Experimental approach 8 1.5.2. Theoretical approach 9 1.5.3. Finite element approach 11 Chapter 2. Formulation and Computational Methods 15 2.1. Complex eigenvalue extraction 15 2.2. Finite element modeling 16 2.3. Complex eigenvalue analysis using MSC Nastran 19 Chapter 3. Results and Discussion 22 3.1. Verification of model and analysis procedure 22 3.1.1. Natural frequency extraction 22 3.1.2. Validation of analysis procedure 24 3.2. Complex eigenvalue analysis results 25 3.3. Modal assurance criteria (MAC) analysis 27 3.4. Parametric studies 29 3.4.1. Influence of rotational speed 29 3.4.2. Influence of hydraulic pressure 29 3.4.3. Influence of friction coefficient 32 3.4.4. Influence of back pad stiffness 35 3.4.5. Influence of reduced contact area 38 3.4.6. Influence of lining pad shape 44 3.4.7. Influence of damping layer 46 3.5. Parametric optimization and prediction opportunity 51 3.5.1. Model fitting 52 3.5.2. Optimization opportunity 56 Chapter 4. Conclusions and Future Works 60 4.1. Conclusions 60 4.2. Suggestions for future works 60 Bibliography 62 APPENDIXES 66 Appendix A: Procedure of brake squeal analysis 67 1. Import the finite element (FE) model to MSC Patran and define materials. 67 2. Set up coordinate 1 and 2 68 3. Set up multi-point constrain (MPC)  RB2 68 5. Apply the loading 70 6. Determine the analyzed group 71 7. Choose the solution pack and set the output 72 8. Create subcase (1st load step: non-linear static analysis) 73 9. Create subcase (2nd load step: complex eigenvalue analysis) 74 10. Run both subcases in one execution 75 11. Edit *.bdf file manually and run with MSC Nastran 76 12. 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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指導教授	黃以玫黃以玫(Yi Mei Huang Yi Mei Huang)	審核日期	2020-7-24
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