五軸切削技術已被廣泛應用於航太、汽車、能源與模具等產業，由於額外的刀具運動自由度，特別適用於複雜零件的製造。相較於傳統的三軸切削，不僅造型能力優越，亦可大幅提高生產效率。五軸側銑多半用於直紋曲面的加工，以刀柄接觸的材料移除率高，而加工誤差的控制則較為複雜，仍缺乏有效的做法。過往研究將側銑路徑規劃轉換成數學規劃問題，再以演化計算法則求解，實驗結果顯示能有效降低加工誤差，但由於計算效能欠佳，限制了其應用價值。本研究嘗試以三個面向的創新，改善五軸側銑之最佳化路徑規劃。首先探討起始解對於收斂結果的影響，根據粒子群演算法產生局部最佳刀具位置，以此結果做為全域最佳化的起始解。模擬結果顯示，其收斂解對應之加工誤差較佳，優於亂數隨機、或以啟發式演算法產生的起始解。接著提出多層次路徑規劃概念，根據前次加工後胚料做為輸入，重覆計算最佳化刀具路徑，持續降低切削誤差。並發展貪婪與非貪婪兩種規劃方法，比較個別計算上的效能。過往研究多以整個加工曲面做為計算參考，未能透過區域分解提高加工精度，故對此建構曲面分解路徑規劃方法，結合二分法搜尋與同步隨機擾動近似演算法，提供較佳的曲面分解。進階控制器允許以曲線方程式定義刀具運動，可簡化數值控制程式，同時提高加工精度，然而尚欠缺系統化的路徑規劃方法。故最後提出基於曲線插補之路徑規劃，以同步隨機擾動近似調整定義曲線的方程式係數，根據扭曲程度決定曲線個數，自動滿足加工誤差的限制。本研究提出創新的計算法則，改善過往五軸側銑路徑規劃的效能，擴大實際加工的應用價值。

5-axis machining technology has been widely applied in aerospace, automobile, energy, and mold industries. With two additional degrees of freedom in tool motion, this machining operation is highly suitable to manufacture of complex geometries. Compared to traditional 3-axis machining, it not only offers a good shaping capability, but also high productivity. 5-axis flank milling is normally used for producing ruled geometries. Its material removal rate is high due to the line contact of tool flank. Machining error control is highly complex and effective solutions are still lacking, though. Past research transformed the tool path planning in 5-axis flank milling into a mathematical programming problem and solved for the optimized tool path using evolutionary computation techniques. Experimental results show that this approach can effectively reduce the machining error. However, the computation efficiency is low and thus limits its practical value. This research improves optimized tool path planning in 5-axis flank milling from several aspects. First, the influence of initial solution on the quality of optimal solutions is analyzed. A PSO-based algorithm is proposed to produce local optimal solution, which is then used as the initiation solution in the later global optimization. Simulation results show that the machining error produced in this manner is lower than that of the initial solution randomly generated or the one computed by a heuristic method. Next, we propose a new concept of multi-pass tool path planning. The machined geometry at the current stage is used as the input to the next optimization stage. Greedy and non-greedy planning methods are proposed and compared. In addition, a multi-stage planning method is developed for dividing the surface to be machined into several strips. Binary search and SPSA methods are integrated and serve as a good mechanism of the surface subdivision. Finally, a novel path planning method is proposed for 5-axis flank milling based on CNC spline interpolation. The coefficients of the function that define the tool motion are alculated by SPSA. An adaptive scheme of surface subdivision is developed to guide the optimization process. In conclusion, this research proposes several new computation schemes to improve the effectiveness of the previous tool path planning methods. The practical value of the machining operation is this enhanced.
Keywords: 5-Axis machining, tool path planning, particle swarm optimization, spline interpolation, Simultaneous perturbation stochastic approximation

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