五軸加工比傳統的三軸加工增加了兩個旋轉的自由度，被廣泛應用於複雜曲面的成型，包括汽車、航太、模具與能源等產業。以往研究將五軸側銑之路徑產生轉換成數學規劃問題，並使用全域最佳化演算法求解，以降低曲面的加工誤差。但因轉換後的問題具有高維度、高度非線性的特性，導致求解過程的計算效率與收斂解的品質均不佳。此外由於獨立調整個別刀具位置，無法保持最後路徑的連續性，造成加工表面精度不佳。本研究基於對刀具路徑重新編碼，針對直紋曲面的五軸側銑精加工，發展連續型調整刀具路徑的計算方法。研究目的包括持續改善最佳化演算法的計算效率，以及提升最佳化路徑品質，並透過連續型編碼的限制，改善刀具路徑產生的加工表面精度，另外也嘗試將最佳化過程從工件座標系轉移至機器座標系，探討在不同座標系進行最佳化的差異。分別完成「連續型五軸側銑路徑編碼」、「動態增加變數之機制」、「改良篩選變化解類電磁演算法」、「探討不同座標系最佳化差異」以及「模擬驗證加工曲面之表面粗糙度」等具體工作內容。最後根據代表性曲面產生對應之刀具路徑，進行切削模擬測試，模擬結果驗證了提出方法的效能。本研究兼具創新與應用價值，發揮基於全域最佳化之五軸側銑路徑規劃的優勢，不僅有效控制加工曲面的誤差，提升計算效率，亦提供新穎的連續型路徑規劃模式，提升複雜幾何的製造技術水準。

Five-axis CNC flank machining has been commonly used in various industries for shaping complex geometries. This advanced machining operation offers highly flexible tool motion with two rotational degrees of freedom. It produces a greater material removal rate than 5-axis point machining because of a larger contact area of the cutter. Previous studies have developed tool path planning methods for reducing machining errors in 5-axis flank finishing cut of ruled surface. Most methods independently adjust individual cutter locations of a tool path by an optimization process. This usually results in a high-dimensional solution space difficult to search for optimal solutions. In addition, the continuity of the resultant tool path is not guaranteed in those methods. An excessive change between consecutive cutter locations may deteriorate the machined surface quality. To overcome these problems, we propose a novel optimization scheme that optimally adjusts a tool path subject to higher-order continuity constraints. The scheme encodes both the translational and rotational tool motions in compact curve representations. As a result, the number of optimization variables, determined by the curve control points, is largely reduced. A curve subdivision mechanism is applied to adaptively increase the control points until the machining accuracy satisfies a given tolerance. Simulation results have validated the effectiveness of the proposed scheme on reducing geometrical errors on the machined surface. Not only is the efficiency in optimization enhanced, but preserving the tool path continuity also improves the finished surface quality. This work provides a computational approach to increasing the practical value of 5-axis CNC flank machining by tool path optimization.

摘要 2
Abstract 3
誌謝 4
目錄 5
第一章 緒論與文獻探討 11
1.1 研究背景 11
1.2 文獻探討 13
1.2.1 刀具路徑規劃 14
1.2.2 刀具路徑編碼 14
1.2.3 過往研究限制 16
1.3 研究目的 17
第二章 刀具路徑編碼 19
2.1 連續型刀具路徑編碼 19
2.1.1 貝茲曲線 19
2.1.2 刀具中心點軌跡編碼 20
2.1.3 刀具軸向編碼 21
2.2 增加變數之機制 26
2.2.1 增加變數之方法 26
2.2.2 增加變數之時機 28
第三章 誤差計算與演算法 31
3.1 切削誤差估計 31
3.2 最佳化演算法 33
3.2.1 同步擾動近似演算法 33
3.2.2 篩選變化解類電磁演算法 34
3.3 演算法之虛擬碼 36
第四章 實作結果與模擬測試 40
4.1 設計曲面與誤差計算參數 40
4.2 結果分析 41
4.5 模擬測試 51
第五章 改良式篩選變化解類電磁演算法 54
第六章 最佳化刀具路徑於不同座標系 58
6.1 逆運動轉換 58
6.2 非線性誤差 59
6.3 結果分析 61
第七章 表面粗糙度 63
7.1 十點平均粗糙度 63
7.2 結果分析 64
第八章 結論與未來工作 67
8.1結論 67
8.2 未來工作 68
參考文獻 69
附錄一 測試曲面 72
附錄二 測試曲面控制點座標 73

 

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