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.

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