以Double NURBS為基礎之擺線加工路徑生成

陳明辰(Ming-Chen Chen)

指導教授 ： 姚宏宗

國立中正大學/工學院/機械工程學系/碩士(2014年)

摘要

本研究提出創新的以Double NURBS曲線為基底之擺線加工路徑生成演算法，傳統的擺線路徑在實際加工時，為了符合現有的控制器要求，必須被拆解成大量的短線段，再到控制器內進行加減速規劃進而延伸出許多種複雜的問題。為了克服此問題，本研究提出以Double NURBS曲線為基底之創新擺線數學模型。在擺線路徑產生中，可以區分為一條引導曲線與一條沿著此引導曲線的偏擺線。在計算幾何中，此引導曲線即為物體內部的中軸線，且中軸線上一點所允許的最大圓之半徑即為該為點的偏擺半徑。因此本研究使用曲線擬合技術，將中軸線擬合成一條連續的NURBS曲線。在偏擺線上，本研究以一個三階的NURBS曲線表示一個圓。因此當引導曲線上前進一個進給量時，刀具會在此圓上旋轉一圈，完成一個擺線路徑。透過這樣的機制，可以建立引導曲線與偏擺線的關係。完成以Double NURBS曲線為基底之擺線加工路徑生成演算法。本研究考量到實際加工的需求，針對不同材質之加工狀態，推導出適應性的進給量，最後規劃出合適的擺線加工路徑。至此，本研究主要著重於Double NURBS曲線為基底之擺線加工路徑生成演算法發展，並且以模擬驗證本研究提出之Double NURBS曲線為基底之擺線加工路徑之正確性。
預期透過本研究提出的方法，能有效縮短加工時間，提升加工機之加工效率，在CAD/CAM系統與CNC控制器之間的資料傳輸上更為精簡，有效降低CNC控制器之負擔。

關鍵字

曲線插補 ； NURBS曲線 ； 加工路徑生成 ； 擺線加工 ； 粗加工 ； 材料移除率

並列摘要

The purpose of this study is to propose the innovation of using double NURBS curve as the base of trochoidal tool path generation algorithm, when using the traditional of cycloid path for processing, in order to meet the requirements of the controller, a large number of short segments must be broken down in order for the controller to program its acceleration and deceleration, this whole process extends to many complex issues.
To overcome this problem, this study proposes a mathematical model using double NURBS curve as the base of trochoidal tool path generation algorithm. During the production of the cycloid path, two lines will be divided, a guide curve and a partial cycloid that runs along this guide curve. In computational geometry, the partial cycloid that runs along the guide curve is the medial axis of the object, while the radius of the biggest circle that the medial axis point can occur is the trochoidal radius. In the study, a curve fitting technique is used, medial axis is curve fitted into a continuous NURBS curve. On the partial cycloid, a third-order NURBS curve is used to represent a circle, thus, when a guide curve progresses a step, the tool will rotate itself along the circle, completing a trochoidal tool path. Through this mechanism, the relationship between the guide curve and the partial cycloid can be established, completing using a double NURBS curve as the bases of the trochoidal tool path generation algorithm. In this study, the actual needs during processing is taken into accountant, due to the different processing status of different materials, an adaptability step is derived, finally, a suitable trochoidal tool path will be set. Therefore, the purpose of this study is based on using double NURBS curve as the base of trochoidal tool path generation algorithm; moreover, simulation is used to verify if the innovation of using double NURBS curve as the base of trochoidal tool path generation algorithm proposed in this study is correct.
The method proposed in this study is expected to shorten the processing time needed for manufacturing and enhance the processing efficiency, while simplifying the data transfer between the CAD/CAM system and the CNC controller, reducing the load of the CNC controller effectively.

並列關鍵字

tool path generation ； curve interpolation ； NURBS curve ； trochoidal milling ； Rough milling ； material removal rate

參考文獻

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