自由曲面提供汽車、航太與冷凍空調業產品設計上極佳的造型能力，例如重要零組件渦輪葉片的幾何非常複雜，其加工製造過程多採用五軸切削的方式，最為關鍵的工作即是側銑葉片時的刀具路徑規劃。儘管先前文獻已探討此一問題，但大多透過調整單一刀具位置降低切削誤差，尚無考量曲面整體側銑誤差最小化的研究。有鑑於此，本論文深入探討如何減少曲面整體側銑誤差，根據動態規劃技巧，提出二項創新之最佳化側銑路徑產生演算法。透過適當參數組合，成功地將實際切削問題轉化成數學規劃問題，可搭配不同評估標準進行誤差之最小化。分別探討「刀具半徑」、「邊界曲線離散點數」、「可橫跨點數」、「曲面延伸比率」及「限制直紋線橫跨值」等參數對最佳解之影響。並由結果中歸納出曲面幾何形狀對最佳刀具路徑的影響。本研究提出不同簡化程度之「直紋線誤差估算」、「切線向量內積」及「近似體積誤差估算」評估標準，將對應最佳化路徑與模擬軟體的結果進行比較，驗證其於側銑路徑最佳化的實用性。最後以一直紋曲面為例，分別以「未延伸曲面之最佳路徑」、「延伸曲面之最佳路徑」及「傳統等參數直紋線刀具路徑」進行五軸加工實驗，並量測加工曲面之誤差值，進而驗證本研究方法論之可行性。本研究提出之方法論可自動產生五軸側銑之最佳路徑，提高加工表面精度，進而提升複雜幾何的製造技術水準。

Free form surfaces offer an excellent modeling capability of product design in automobile, aerospace, and air-conditioning industries. For example, one critical component in the industries, turbine blade, often contains such complex geometries. Its manufacturing process involves 5-axis CNC machining, in which the crucial task is tool path planning of the blade surface. Despite of previous studies concerning this problem, most of them independently adjusted individual tool positions for educing the machining error. Very few studies investigate optimization of the total deviation on the entire surface in an integrated fashion. To overcome this deficiency, this work aims at reducing the total machining error in 5-axis flank milling of ruled surfaces. Two novel methods based on dynamic programming techniques are proposed for generation of the optimized tool path. The machining problem is thus transformed into a mathematical programming task. The influences of important parameters: tool radius, the number of the discrete number on the boundary curves, the maximal span over the discrete points, the surface extension ratio, and the maximal tool contact length, are examined. This research discusses how the intrinsic properties of the surface affect the optimized tool path. In addition, three error evaluation criteria: approximating tool envelop, best matching of the curve tangents, and grid-height based volumetric error, with an increasing degree of simplification, are tested. The corresponding estimated errors are compared with the simulation results generated from commercial software to verify their practicality in the tool path optimization. A ruled-surface part is used as an example in 5-axis milling tests with the tool paths computed by different methods. The machining error is measured using a CMM for each finished part. The measure result indicates that the proposed method produces the best machining quality. It shows that this work provides effective methods for automatic generation of optimized tool path and improving the machining quality in 5-axis flank milling. The machining technology of complex geometries is thus enhanced.

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