現今企業為了在全球的激烈競爭下求生存，對於每一項作業或任務都必須追求最佳效率，並且在最短的時間生產滿足顧客所需要的產品或服務。高速切削工具機產業為了保持競爭力，也須縮短產品設計階段在找尋最佳設計變數的時間，本研究以蟻群最佳化（Ant Colony Optimization）演算法作為加速搜尋最佳解的方法。
蟻群最佳化演算法在解決一些困難的組合最佳化問題（Combinatorial Optimization Problems）已有相當的成效。在1991年被Dorigo等學者將ACO演算法成功的應用在旅行者問題之後，陸續有更多的學者引用此方法應用在不同的困難組合最佳化問題上，並得到相當不錯的績效。
本研究主要藉由蟻群最佳化演算法為設計架構，在分析高速主軸系統之軸承位置對於第一自然頻率的影響，並以隨機區域搜尋的方式搜尋第一自然頻率，依據每一次的遞迴所產生的最佳解來當作下一次遞迴的初始值來達到加速最佳化設計變數的產生進而縮短產品開發時間。
在本研究數值分析結果發現，本研究之MACO演算法在搜尋四個設計變數的組合最佳化問題，探討五個模式所搜尋的第一次自然頻率以及總時間，所得最佳的設計數據依序為162.93、286.16、552.21與568.21mm，最佳解為1009.860 Hz，且軸承位置對於FMNF幾乎沒有交互作用的產生。並根據敏感度分析結果顯示，增加初始預負荷將可提高FMNF的值。

Nowadays the enterprise in order to strives for the survival under the global steep competition, they must pursue the best efficiency regarding each work or the duty, and the production satisfies the product or the service which the customer needs in the shortest time. The high-speed cutting machine industry in order to maintain the competitive ability must shorten time of products design phase look for optimum design parameter, This research develops the algorithm by the ant colony optimization to take the acceleration search best solution.
The Ant Colony Optimization algorithm solves some difficult combinatorial optimization problems having a suitable effect already. After being applied ACO algorithm successfully to traveling salesperson problem by such scholars as Dorigo,etc. on the 1991 year, more scholars quote and use this method getting the pretty good performance on different difficulty combinatorial optimization problems.
Research perform by ant colony optimization algorithm as project construction, and analyse bearing position of high-speed motorized spindle systems influence in first mode natural frequency, and search the first mode natural frequency by the way of searching in the random area, the starting value which hands over has the best solution treats as which based on each next time, achieved the acceleration optimization design variable the production then reduces the product development time.
This research numerical analysis result discovery, MACO algorithms of this research performs in the combinatorial optimization problem of searching four design parameters, and discusses five patterns searches for first mode nature frequency and total time, and obtained the best design data in order is 162.93, 286.16, 552.21 and 568.21 mm, and the best solution is 1009.860 Hz. And the bearing position nearly does not have the correlation regarding FMNF the production. Demonstrated according to the sensitivity analysis result that increase initial preload might enhance FMNF’s value.

中文摘要 ..................................................i
英文摘要 .................................................ii
誌謝 ....................................................iii
目錄 .....................................................iv
表目錄 ..................................................vii
圖目錄 .................................................viii
符號彙編 .................................................ix
第一章 緒論 ..............................................1
1.1 研究背景 .............................................1
1.2 研究動機 .............................................2
1.3 研究目的 .............................................2
1.4 研究流程架構 .........................................3
第二章 文獻探討 ..........................................5
2.1 工具機設計相關文獻 ...................................5
2.2 主軸系統動態模型 .....................................6
2.3 最佳化設計 ...........................................7
2.4 螞蟻族群最佳化演算法 .................................9
第三章 高速主軸系統 .....................................14
3.1 高速主軸系統 ........................................14
3.1.1 FEM整合模型 ......................................14
3.2 設計變數對動態特性的影響 ............................17
第四章 研究方法 .........................................20
4.1 ACO通用啟發式演算法 .................................20
4.2 MACO演算法架構說明 ..................................21
4.2.1 費洛蒙更新規則 ...................................23
第五章 最佳化模型建立 ...................................24
5.1 最佳化問題定義 ......................................24
5.1.1 目標函數 .........................................25
5.1.2 設計變數 .........................................25
5.1.3 限制條件 .........................................26
5.2 建構最佳化模式 ......................................27
第六章 數值分析與驗證 ...................................29
6.1 設計變數對FMNF的影響 ................................29
6.2 MACO演算法搜尋最佳FMNF ..............................32
6.2.1 模式一：MACO演算法搜尋Max FMNF ...................32
6.2.2 模式二：MACO演算法之每次迴圈降低最大跳躍距離 .....34
6.2.3 模式三：MACO演算法之迴圈次數增加至20次 ...........36
6.2.4 模式四：MACO演算法之螞蟻數量增加至625隻 ..........38
6.2.5 模式五：MACO演算法之變更初始值位置 ...............40
6.2.6 結論 .............................................41
6.3 敏感度分析 ..........................................42
第七章 結論與未來研究方向 ...............................44
7.1 結論 ................................................44
7.2 未來研究方向 ........................................44
參考文獻 .................................................46
附錄ㄧ ...................................................51
附錄二 ...................................................56
作者簡介 .................................................58

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