刀具是製造工業非常重要的技術工具，刀具的性能和品質的優劣對於切削加工的精度、效率和產品品質都有直接而嚴重的影響，刀具產業的振興，首先需徹底研究引進新技術，進一步加強基礎研究與應用，提昇研發能力，掌握現代先進產品之新技術，方能使技術理論化，打破經驗的侷限性，開創屬於本國特色的刀具技術體系。
刀具的幾何模型研究包括兩方面，一是從切削理論和使用性能出發，討論新型刀具開發或最佳刀具參數設計問題；二是由已知理想刀具的結構和設計參數要求，尋求其幾何形態的數學描述，稱為幾何建模。幾何建模是實現刀具CAD技術的關鍵，無疑是刀具設計，加工理論研究的首要前提，是加工干涉檢查和加工誤差分析的基礎。
現代刀具設計與製造技術結合了基礎數學理論，電腦輔助應用技術現代設計方法，材料科學與加工技術等各領域學門的研究成果，數學理論的發展更是推動技術進步的主要關鍵，是應用電腦輔助設計技術解決實際問題之重要橋樑，因此本文應用微分幾何，共軛嚙合理論、座標系轉換、數值方法等理論基礎，來探討特種迴轉銑刀的設計製造、模擬與補償，透過數學建模建立可行，而有效的系統化製造模型並利用動力訊號分析及田口方法來探討不同刀刃曲線設計對鎳基超合金加工特性之影響，綜合全文，主要可歸結於以下幾點結果：
1.探討球頭端銑刀，錐球頭銑刀，帶角圓錐形銑刀，刃口曲線，溝槽設計模型，進而根據包絡反問題求解原理導出磨製溝槽的砂輪截形和砂輪相對銑刀的位置和NC加工中的相對運動，並就實得溝槽曲面的求解模型和具體電腦模擬方法進行探討還就模擬中所見殘留迴轉面和局部無刃帶問題進行補償，從而為NC加工特種迴轉銑刀提供了參考。
2.藉出田口實驗法L9之實驗計畫表，分別設計錐球頭銑刀，平面型，S型，傳統型的刃口曲線，以分析不同刀具刃口曲線對Inconel 718加工特性之影響，同時找出其最佳的加工條件，以建立此航太材料的加工技術資訊，並建立基本數據資料庫作為自動化加工時的參考。
3.探討旋轉銼與一般迴轉銑刀的設計、製造中的刃口曲線、溝槽曲面、砂輪底角設計及相關幾何模型的差異，並針對三軸聯動NC加工這類刀具的相對運動進給及實得刃口曲線之探討。

The cutter is a fundamental machine tool used extensively throughout manufacturing industries. The performance and quality of the cutter have a direct influence upon the cutting precision, product quality and production rate. Invigorating the domestic cutter industry and establishing a characteristic syscxtem of cutter technology requires that new technology be imported, the constraints of previous experience be overcome, a fundamental research and development capability be developed and new machine tool materials be adopted
Two basic approaches exist when considering geometrical models of the cutter. In the first approach, developing new cutters and establishing an optimal set of cutter design parameters is performed in accordance with general cutting theory and the operational functions of the machine tool. Meanwhile, in the second approach, the structural requirements and design parameters of an ideal cutter are used to establish a geometrical cutter model which describes the various contours of the cutter. Developing an accurate geometrical model is an essential prerequisite to realizing the com-puter-aided design of a cutter, and is necessary in order to apply the theory of cutter design and manufacturing theory to the practical manufacturing proc-ess. Moreover, the geometrical model provides the basis for interference checking and manufacturing error analysis.
Modern cutter design and manufacturing technologies integrate the results from a diverse range of previous studies, including those performed within the fields of fundamental mathematical theory, computer-aided ap-plication technology, modern design technology, material science and manufacturing technology. In each field, technological progress is reliant upon the development of mathematical theory. In the present study, differen-tial geometry, conjugate theory, engagement relationship theory, coordinate transfer and numerical methods are used to develop a systematic method for the design, simulation, manufacturing and compensation of special revolving cutters. Using the proposed mathematical models, this paper presents real-izable and effective manufacturing models for these revolving cutters. Fur-thermore, the Taguchi method and power signal analysis techniques are em-ployed to investigate the effects of different cutting-edge curves on the cut-ting characteristics of Inconel tool material. The basic research activities performed within the present study can be summarized as follows:
1.The study develops geometrical models for the cutting-edge curves and flute designs of ball-end cutters, truncated-cone ball-end cutters and toroid-cone shape cutters. Applying the inverse-envelope theory, a geometrical model for the cross-section of the grinding wheel used to grind the required helical groove on the cutter is developed. Further-more, the relative positions and velocities of the grinding wheel and workpiece during the NC manufacturing of the cutter are developed and investigated via a process of computer simulation. Finally, a compensation method is developed which resolves the problems of residual revolution surface and localized non-existence of the cutting-edge. The theoretical models and results provide a valuable source of reference for the NC manufacturing of revolving cutters.
2.A series of experiments are performed to investigate the effects of the cutting-edge geometry on the machining performance when machining Inconel 718. The Taguchi method is adopted to determine the set of optimal machining parameters for a variety of cutting-edge types, in-cluding those of the truncated-cone ball-end cutter, the plane type, the S type and the traditional type. The results of these experiments serve as a valuable reference for the automated machining of aero-materials.
3.Study the design and manufacture of the cutting-edge curve, flute sur-face and the coning angle of the grinding wheel for both the rotating burr and the revolving cutter, and discuss the difference of the related geometrical models. Also, the practical cutting-edge curve and the feeding rate of the relative movement for the cutter of the two and half axes processes of the NC machine have been discussed.

總 目 錄
總目錄 i
圖目錄 iv
表目錄 vii
符號說明 viii
論文摘要(中文) xii
論文摘要(英文) xiv
第一章 緒論
1.1 研究動機及目的 1
1.2 文獻回顧 3
1.3 研究內容 12
1.4 論文組織與章節 13
1.5 研究步驟 15
第二章 迴轉銑刀的設計與NC加工模型
2.1 前言 16
2.2 理想刀刃曲線 19
2.3 溝槽截形設計 40
2.4 磨用砂輪截形設計 44
2.5 實施NC加工徑向運動速度修正與實得溝槽模型 48
2.6 電腦實體切削模擬補償與實體加工 61
2.7 結論 69
第三章 刀刃曲線對Inconel 718加工特性之影響
3.1 前言 70
3.2 圓錐面刀刃曲線 71
3.3 球頭平面刀刃曲線 75
3.4 具負前角錐球面銑刀前刀面的製造模型 82
3.5 具正前角錐球頭端銑刀前刀面 89
3.6 S型刃口曲線 92
3.7 傳統型刃口曲線 93
3.8 計實例與刀具實體切削模擬 95
3.8.1模擬設計所得之刃口曲線 95
3.8.2刀具實體切削摸擬 100
3.9 實驗設備與步驟 104
3.10 實驗設計與田口分析 105
3.11 結論 115
第四章 旋轉銼的設計與製造問題之研究
4.1 前言 117
4.2 刃口設計及其特殊點 118
4.3 砂輪底角設計 121
4.4 實得刃口曲線 123
4.5 實例模擬 125
4.6 結論 126
第五章 結論與建議
5.1 結論 127
5.2 建議 128
參考文獻 130
著作目錄 139
作者簡介 140

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