應用拓樸優化技術於工具機結構設計

Application of topology optimization technology in machine tool structural design

江俊蔚(Jun-Wei Jiang)

指導教授 ： 柯文俊

國立臺灣大學/工學院/工程科學及海洋工程學研究所/碩士(2016年)

https://doi.org/10.6342/NTU201600459

摘要

拓樸優化(Topology optimization)技術為有限元素法(Finite element method)結合數學非線性規劃法(Nonlinear program algorithm)而形成優化設計方法。此方法目前已經廣泛應用於各種產品設計上，例如:減重設計、性能改善、造型設計等產品設計。運用此方法進行結構優化設計，不僅能大幅地降低開發成本與時間，亦可提供創新產品設計概念。
首先根據工具機編碼、構型碼以及根樹狀圖三者常見工具機編碼系統。重新歸納並統整出一套新編碼系統，用以描述工具機外型特徵與構件之運動關係並建立一對一參數化命名規則。增加工具機構件模組化之概念，則可由新編碼系統反向建立出立式工具機幾何構型。
接著將考慮業界常用之實際立式三軸工具機形式，分別定義靜力分析、模態分析等不同工況條件，進行有限元素分析(Finite Element Analysis)，並將其分析之結果作為工具機結構優化設計之基準值。根據其對應之新編碼系統與相應之尺寸，透過模組化概念可建立簡易工具機幾何模型。完成設計變數、目標函數與限制條件等三大拓樸優化相關設定後，即可開始進行工具機拓樸優化迭代計算。
最後則依序進行單一零部件拓樸優化以及整機拓樸優化，並比較其拓樸優化前、後之結構參數(例如:質量、靜剛度、自然頻率等)以及拓樸優化後工具機所提升之性能百分比。期望建立一套工具機拓樸優化設計流程，將此流程導入工具機結構設計開發前期。

關鍵字

拓樸優化 ； 工具機 ； 有限元素分析 ； 幾何構型 ； 結構設計

並列摘要

Topology optimization technology is one of design method which combined with mathematical nonlinear program algorithm and finite element method. This method have been widely used in variety of product design, such as: weight loss design, improved performance, shape design and other product design. Using this method for structural optimization design, not only can significantly reduce development costs and time, but also provide innovative product design concepts.
First, according to the machine tool code, configuration code, and the rooted tree this three kind of common machine tool coding system. Integration and re-induction of a new coding system that can describe the motion of the machine tool and characteristics of compoment relationship, and also establishment one by one parametric naming rules. With the concept of modular that can be reversed by the new coding system to establish machine tool geometry configuration.
Next, considering the actual vertical 3-axis machine tool type for industry used. Using finite element analysis can define corresponding value for static analysis, modal analysis, or other loadcases. As the results of the analysis, those value can be the baseline of machine tool. According to modular concept can build a simple machine tool geometry configuration which corresponds to the new coding system and machine tool dimension. After the completion of three topology optimization settings, include design variables, objective function and constraints function, then machine tool start to topology optimization iteration.
Finally, compare the topology optimization result of structural parameters (for example: mass, stiffness, natural frequency, etc.), as well as the percentage for each part and whole machine. Hope establish the topology optimization design process, then import this process into early development of machine tool structure design.

並列關鍵字

Topology optimization ； Machine tool ； FEA ； Configuration ； Structure design

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