基於電腦繪圖晶片運算之五軸側銑刀具路徑規劃最佳化

規則自由曲面提供了複雜之產品造型能力，已大量被應用於如航空、汽車與模具零件等。以能源與冷凍空調產業之渦輪葉片為例，外型幾何設計涉及尖端流體力學，而其製造工作則由專業加工廠負責，通常使用五軸數值控制加工技術，需要專精的電腦輔助製造與切削經驗，渦輪葉片的開發能力被視為工業水準之重要指標之一。　　現今刀具規劃方法多沿著曲面直紋線進行加工，其切削誤差並非最佳化之結果，故已有研究為此提出改善方法。然而大多數工作僅能產生局部最佳化之刀具路徑，或是計算效率不彰，使得路徑規劃難以獲得符合精度要求之切削曲面。有鑑於此，本研究提出一項具高度創新性的方法，運用電腦繪圖晶片（Graphic Processing Unit, GPU）於五軸側銑誤差之計算。此項晶片技術擁有卓越之大量平行處理運算能力，與中央處理器相比，處理浮點數運算更為快速，近來已被用於一般用途之計算工作。本研究首先成功地應用此項技術於五軸加工規劃，具相當高的原創性。此外，本研究考量工具機切削時可能遭遇之實際物理限制，例如刀具進給速度、角度變異等，根據四角片區塊進行切削規劃，藉以求得切削誤差最小之最佳化刀具路徑。首先將複雜之刀具路徑規劃問題建構成一網路圖，以各刀具運動造成之誤差作為節點間連線之權重，再以最短路徑求得最佳解。但隨著問題之複雜度提高，網路圖變得龐大，最佳解的計算相當費時，因此再利用基因演算法（Genetic Algorithm, GA），結合繪圖晶片之平行運算能力，大量且迅速地進行交配並篩選較佳解。除了考量實際切削時刀具路徑間的線性插補，並設計全新的突變及交配編碼方式，以符合實際刀具路徑之需求。最後以商用軟件進行模擬，並進行實際切削實驗與量測，以驗證本研究方法之正確性。結果顯示本研究成功地結合數種創新概念，提供一種於運算效率、精密度及路徑規劃彈性皆能有突破之五軸刀具路徑計算方法。

關鍵字

五軸側銑；直紋曲線；切削誤差；基因演算法；繪圖晶片

並列摘要

Ruled surfaces provide a good capability of complex product modeling. Such geometry has been widely used in the aero-space, automobile, and mold industries. For example, turbine blade is a key component in energy and air-conditioning applications. The shape design involves advanced fluid mechanics. The manufacturing task is generally performed by companies specialized in five-axis CNC machining. It requires computer-aided manufacturing (CAM) technology and cutting experiences. The development of turbine blade is considered an indicator of industrial competence. In current practice, the cutter goes along the rulings of a ruled surface, thus finishing the machining job. However, this machining method does not produce optimal machining quality. Thus, several studies had attempted to improve it. Most of the adopt local optimization approaches or heuristic algorithms, which do not guarantee globally best result. Their computational efficiency is poor. As a result, the tool path planning of five-axis flank milling is highly limited. The machining quality cannot be precisely controlled. To overcome this deficiency, this research proposes a novel computational scheme that estimates the machining error using general-purpose graphic processing unit (GPGPU) in five-axis flank milling. GPGPU provides excellent functionality of parallel processing. The processing speed of floating number is faster than CPU. This computing technology has been applied to many engineering problems in addition to computer graphics. This research is one pioneering work that applies GPGPU in five-axis tool path planning. It cooperates physical limitations into the path planning such as feed, rotation angles, and cutting length. Quadrilateral patches are used for generation of optimal tool path in terms of minimal machining error. We convert a geometric problem into a math programming task. First, a network is constructed for modeling feasible solution of tool motions. The machining errors induced by individual tool motions become the weights between the nodes of the network. It thus transforms into a shortest path problem and can be easily solved by the Dijkstra’s algorithm. For complex machining conditions, we employ GA (Genetic Algorithm) for searching optimal tool path empowered by the parallel processing provided by GPGPU. The resultant GA algorithm can perform cross-over and mutation operations rapidly. It also considers linear interpolation between tool motions. Efficient encoding/decoding schemes are developed to fulfill the actual requirements of 5-axis machining. Simulation result produced by commercial software is obtained for verification purpose. Finally, a real cutting experiment is conducted to validate the effectiveness of the proposed scheme. CMM measure of the machining part shows that it significantly improves the machining quality of 5-axis flank milling. This work provides advantages on computational efficiency, machined quality, and planning flexibility for 5-axis flank milling of complex ruled geometry.

並列關鍵字

five-axis CNC machining ； ruling line ； machining error ； Genetic Algorithm ； GPGPU

參考文獻

[8] 李宇尉 (2007)，基於動態規劃之五軸側銑路徑最佳化，碩士論文，清華大學工業工程與工程管理研究所。

[2] 黃煒能 (2006)，含分離葉片離心式渦輪之整合性刀具路徑規劃架構，碩士論文，清華大學工業工程與工程管理研究所。

[1] G. B. Vickers and K. W. Guan (1989), “Ball-Mills Versus End-Mills for Curved Surface Machining,” ASME Journal of Engineering for Industry, Vol. 111, pp. 22-26.

[3] X. W. Liu (1995), “Five-axis NC cylindrical milling of sculptured surfaces,” Computed-Aided Design, Vol. 27, No. 12, pp. 887-894.

[4] C. Lartigue, E. Duc. And A Affouard (2003), “Tool path deformation in 5-axis flank milling using envelop surface,” Computer-Aided Design, Vol. 35, pp. 375-382.

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基於電腦繪圖晶片運算之五軸側銑刀具路徑規劃最佳化

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