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研究生:周義閔
研究生(外文):Yi-MingChou
論文名稱:拓樸最佳化設計方法於單車鏈條外鏈片設計之研究
論文名稱(外文):Topology Optimization Methods for Design of the Outer Plate of Bicycle Chain
指導教授:劉至行
指導教授(外文):Chih-Hsing Liu
學位類別:碩士
校院名稱:國立成功大學
系所名稱:機械工程學系
學門:工程學門
學類:機械工程學類
論文種類:學術論文
論文出版年:2016
畢業學年度:104
語文別:中文
論文頁數:107
中文關鍵詞:拓樸最佳化雙向演進式結構最佳化方法滾子鏈條外鏈片
外文關鍵詞:Topology optimizationroller chainouter plate
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由於滾子鏈條具有高傳輸效率與低成本的優點,因此在廣泛的被應用在動力傳輸的領域。本研究利用雙向演進式結構最佳化方法(Bi-Evolutionary Structural Optimization)對滾子鏈條之外鏈片進行結構最佳化設計,在與現有外鏈片相同體積條件下,以其剛性最大化為設計目標,利用BESO方法找出強度較高的外鏈片拓樸結構。本研究並提出等體積雙向演進式結構最佳化方法(Bi-Evolutionary Structural Optimization with Constant Volume,BESOCV),BESOCV方法之特色為起始體積與目標體積相等,且運算過程會一直維持相同目標體積直到收斂。透過三個測試範例中,BESO與BESOCV拓樸結果皆相同。兩方法最大的差別在運算時間與疊代次數,在3種測試問題中BESOCV減少之運算時間為21%~42%,疊代次數為14%~43%。
本研究成功利用BESO與BESOCV方法找出相同之外鏈片拓樸結構,且設計出5種新型外鏈片結構,BESOCV方法減少之運算時間為57%~78%,疊代次數減少54%~80%。本研究挑選其中較好的3種設計與傳統鏈片做進一步比較,透過ANSYS模擬,在結構之最大應力值與總應變能皆小於現有鏈片外型,最大應力值改善量有59%~66%,總應變能改善量為67%~68%,整體改善量來說,新型設計鏈片是優於現有設計鏈片的。在實驗驗證方面,本研究利用相同材料,實際製作3種新型與傳統外鏈片,並透過拉伸試驗驗證鏈片之強度,實驗方式利用外鏈片在相同力量下,產生的位移量愈小,代表結構強度愈好,實驗結果也證明新型3種設計鏈片也是優於傳統鏈片的,且位移量之改善量為49%~52%。
This study presents a new topology optimization method, Bi-directional Evolutionary Structural Optimization with Constant Volume (BESOCV) method, for design of continuum structures. The special characteristic of the BESOCV method is that the volume fraction remains the same throughout the optimization process. Three analysis cases are provided as the benchmark examples in this study. The objective function is to minimize the strain energy. The results show that BESOCV method can obtain similar results as the traditional BESO method but with better computational efficiency. Both BESO and BESOCV methods are used to design the outer plate of the bicycle chain. Three topology optimized designs of the outer plate are proposed and are analyzed by the finite element analysis. By comparing the total strain energy, maximum von Mises stress and the maximum displacement of the topology optimized designs with the traditional outer plate, the results show that the topology optimized designs are with better performance in overall. The optimal designs are prototyped by using aluminum material. The experimental results agree with the numerical simulations.
摘要 i
ABSTRACT ii
誌謝 xi
目錄 xii
表目錄 xv
圖目錄 xvii
符號說明 xxi
第一章 緒論 1
1-1 前言 1
1-2 文獻回顧 3
1-3 研究目的 5
1-4 本文架構 6
第二章 拓樸最佳化方法介紹 7
2-1 演進式結構最佳化方法 7
2-1-1 設計區間與設計變數 8
2-1-2 目標函數、目標體積、靈敏度 9
2-1-3 計算步驟與流程圖 10
2-1-4 範例說明 11
2-2 雙向演進式結構最佳化方法 16
2-2-1 濾化演算法(Filter scheme) 16
2-2-2 元素填補與挖除 18
2-2-3 收斂準則 20
2-2-4 雙向演進式結構步驟與最佳化流程圖 20
2-2-5 使用BESO方法之改善結果 22
2-3 等體積雙向演進式結構最佳化方法 23
2-3-1 等體積方法 23
2-3-2 等體積方法之二分法疊代流程 24
2-3-3 BESO方法與BESOCV方法之比較 26
2-4 範例測試與討論 27
2-4-1 範例一 27
2-4-2 範例二 33
2-4-3 範例三 38
2-5 本章小結 43
第三章 外鏈片設計 44
3-1 最佳化目標函數與目標體積 44
3-1-1 元素剛性矩陣 44
3-1-2 目標函數與元素靈敏度 45
3-1-3 目標體積與設計區間 48
3-2 外鏈片之最佳化邊界條件 50
3-2-1 外鏈片的分佈力 50
3-2-2 固定自由度之邊界條件 52
3-3 拓樸最佳化結果 53
3-3-1 最佳化非設計區間 54
3-3-2 固定不同環厚度之最佳化結果 56
3-3-3 不同元素量下之拓樸結構 60
3-4 傳統方法與等體積方法結果比較 63
3-4-1 疊代過程與運算時間比較 63
3-4-2 目標函數值比較 66
3-4-3 不同拓樸結構之目標函數值比較 70
3-5 本章小結 72
第四章 外鏈片模擬分析與實驗驗證 73
4-1 ANSYS模擬之前處理步驟 73
4-1-1 模型建立 73
4-1-2 材料性質測試 76
4-1-3 Mapped mesh方法網格化結構 80
4-1-4 邊界條件 81
4-2 模擬結果 83
4-2-1 應力分析結果 83
4-2-2 目標函數結果 87
4-2-3 位移結果 91
4-2-4 元素量收斂性分析 94
4-3 實作驗證 95
4-3-1 鏈片加工 95
4-3-2 實驗流程設計 96
4-3-3 實驗結果與模擬驗證 97
4-4 本章小結 102
第五章 結論與建議 103
5-1 結論 103
5-2 建議 104
參考文獻 105
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