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研究生：	徐力崴 Hsu, Li-Way
論文名稱：	基於靜態與平均動態撓性之汽車引擎腳拓樸最佳化設計 Topology Optimization of Automotive Engine Mounts based on Static and Average Dynamic Compliance
指導教授：	劉至行 Liu, Chih-Hsing
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：	2021
畢業學年度：	109
語文別：	英文
論文頁數：	162
中文關鍵詞：	拓樸最佳化、平均動態撓性、靜態剛性限制、動態剛性、引擎腳、光固化3D列印
外文關鍵詞：	Topology optimization , Average dynamic compliance, Static stiffness constraint, Dynamic stiffness, Engine mount, SLA 3D printing
相關次數：	點閱：219 下載：0
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本研究以平均動態撓性作為目標函數提出兩套用於設計汽車引擎腳之拓樸最佳化流程，並介紹靜態剛性限制方法，使最佳化設計能同時滿足設計規範中垂直與水平方向之目標與限制範圍。在第一套拓樸最佳化的流程中，本研究同時使用兩種方向的靜態剛性限制以滿足設計需求；而在第二套拓樸最佳化的流程中，以調整目標體積率的方法取代垂直方向的靜態剛性限制來進行設計。本研究選定樹脂材料作為製造引擎腳模型的材料，並對於樹脂材料進行拉伸與鬆弛的材料試驗，用以獲得超彈性與黏彈性的非線性材料參數。在模型製造上，本研究使用光固化3D列印的方式搭配樹脂材料進行模型的製造，並對其進行靜態剛性與動態剛性的實驗以驗證本研究在拓樸流程中，對於引擎腳在靜態與動態剛性模擬結果的準確性。在引擎腳拓樸設計的部分，根據最佳化的方向，可以從這兩套拓樸最佳化的流程中分成三種情形進行引擎腳設計，並根據在每種情形下給定的4種厚度，總共可以得到12種滿足設計規格中靜態剛性限制的設計結果。最後，本研究針對拓樸最佳化流程中的靜態剛性限制進行測試，探討其對於結果的約束力以及對於滿足不同設計規範的能力。

In this study, two topology optimization procedures based on the static and average dynamic compliance are proposed to design automotive engine mounts. In the topology optimization process, the average dynamic compliance is chosen as the objective function to optimize the dynamic stiffness of engine mount. Moreover, in order to satisfy the static stiffness values in the vertical and lateral directions, the method of static stiffness constraint is introduced to limit the static stiffness value within the acceptable range according to the design specification. The first topology optimization procedure utilizes the static stiffness constraint in both directions to design engine mounts, and the second topology optimization procedure replaces the vertical static stiffness constraint with the method of adjusting the target volume ratio. The elastic resin is selected as the material to produce the prototype of engine mount by SLA 3D printing. The material experiments of the resin material are performed to obtain the nonlinear material properties, i.e., hyperelasticity and viscoelasticity. Furthermore, the experimentally and simulation obtained static and dynamic stiffnesses are compared to verify the designs. Finally, with the two topology optimization procedures, twelve design results of engine mount are obtained through three different cases.

ABSTRACT	i
摘要	ii
Acknowledgments	iii
Contents	iv
List of Tables	vii
List of Figures	ix
Nomenclatures	xiii
Chapter 1	Introduction	1
1	Introduction of Engine Mounts	1
2	Optimization Designs of Engine Mount	5
3	Topology Optimization	13
4	Introduction of Stereolithography 3D Printing	16
5	Research Motivation	18
6	Outline of the Thesis	19
Chapter 2	Topology Optimization Theory	20
1	Introduction	20
2	Topology Optimization Procedure	21
3	Finite Element Analysis	22
3.1	Numerical Model Establishment	23
3.2	Sensitivity Analysis	26
3.3	Static and Dynamic Problems	28
4	Objective Function	30
5	Element Sensitivity	33
6	MMA Theory	34
7	Static Stiffness Constraint	39
8	Filter Algorithm	40
9	Convergence Criteria	43
10	Topology Optimization Procedures for Engine Mount Design	44
11	Chapter Summary	54
Chapter 3	Experimental Analysis of Resin Material	55
1	Introduction	55
2	Material Experiments of Elastic Resin	56
2.1	Tensile Test	56
2.2	Relaxation Test	59
3	Experimental Data Analysis	61
3.1	Curve Fitting of Material Models	62
3.2	Models Verification	73
4	Chapter Summary	78
Chapter 4	Experimental and Simulation Results of Engine Mount	79
1	Introduction	79
2	Experimental Test	79
2.1	Static Stiffnesses Experiments	82
2.2	Dynamic Stiffness Experiment	87
3	Finite Element Simulation	90
3.1	Static Stiffnesses Simulations	93
3.2	Dynamic Stiffness Simulation	96
4	Verification and Discussion	101
5	Chapter Summary	104
Chapter 5	Topology Optimization Design of Engine Mount	105
1	Introduction	105
2	Material Model, Design Domain and Boundary Condition	105
2.1	Rubber Material Model	106
2.2	Design Domains and Boundary Conditions	107
3	Topology Optimization Design of Engine mount	110
3.1	First Optimization Procedure: Maximize Average Dynamic Compliance	111
3.2	First Optimization Procedure: Minimize Average Dynamic Compliance	117
3.3	Second Optimization Procedure	123
3.4	Results Discussion	130
4	Grading Standard and Results	133
4.1	Min-max Normalization Method	133
4.2	Grading Results	135
4.3	Comparison with Commercial Product	137
5	The Effectiveness of the Static Stiffness Constraint	138
6	Topology Optimization Design with Different Target Stiffness Values	144
7	Chapter Summary	152
Chapter 6	Conclusions and Suggestions	153
1	Conclusions	153
2	Suggestions	155
References	158
                                    

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