臺灣博碩士論文加值系統

在現今如此快速工業化的時代，電腦數值控制Computer (Numerical Controller)工具機簡稱CNC扮演相當重要的角色，然而傳統CNC之加工方式，是將由Computer-Aided Design (CAD)系統所設計的曲面經由Computer-Aided Manufacturing (CAM)以連續短線段(Continuous Short Block, CSB)或圓弧來近似曲線，並產生其加工路徑傳送至CNC。CNC在根據此連續短線段進行速度規劃與伺服控制。此方法會產生一些問題，例如：需要較大的記憶體來儲存龐大的加工程式；資料傳輸會增加CNC在計算量；進給率抖動及速度不連續等問題，故無法達到高速高精度的加工。要克服上述問題可利用曲線參數式插補來取代傳統的直線/圓弧插補。
本論文提出以Bezier曲線來擬合連續短線段的插補架構，利用三階的Bezier曲線來擬合連續短線段，已達到曲線C2連續。透過預視弁?look-ahead function)來偵測出曲率變化較大處，並針對其整體進給率進行加減速規劃。最後，利用傳統的插補方式與本論文所提出之插補方式進行比較，並模擬伺服控制系統來驗證本文所提出之插補器。
關鍵詞:電腦數值控制、Bezier曲線、預視、插補器。

A computer numerical controller (CNC) plays an important role in machine tools. In traditional manufacturing system, a free-form curve or surface are designed with computer-aided design (CAD) systems. Then computer-aided manufacturing (CAM) system uses continuous short block (CSB) or small circular blocks to approximate the free-form curve and send the codes into CNC machine tools. However, this approach has some problems such as large volume data transmission which might cause the loading of the CNC; feedrate fluctuation and velocity discontinuous. It is difficult to achieve high-speed and high-precision under the CSB approach. To overcome the problems, the parametric interpolation is used as the substitute for the conventional interpolation.
In this thesis, the CSB fitting scheme with Bezier curve is proposed. By using a look-ahead technique, the sensitivity curvature of curves can be detected and the acceleration/deceleration motion planning is applied for feedrate profiles. Finally, the proposed interpolation is compared with the traditional interpolation. The simulation results show that the proposed interpolation scheme can achieve better tracking and contour accuracies than the conventional interpolation approach.
Keywords: CNC, Bezier Curve, Look-Ahead, interpolation .

第一章 緒 論 1
1-1 前言 1
1-2 研究動機與目的 1
1-3 文獻回顧 3
1-4 研究方法 6
1-5 論文架構 8
第二章 參數式曲線數學理論與擬合設計原理 9
2-1 Bezier曲線參數式及數學理論 9
2-2 Bezier曲線參數式擬合設計原理 11
2-2-1 Bezier Curve 擬合設計法概述 11
2-3 連續短線段(CSBs)擬合 16
第三章 Bezier 曲線之預視插補器加減速規劃 19
3-1 Bezier曲線插補法概述 19
3-1-1 Bezier Curve 曲線插補法概述 19
3-1-2 Bezier Curve 曲線插補演算法 19
3-2 加減速規劃 23
3-2-1 加減速規劃類型 23
3-2-2 插補器加減速架構法則 24
3-3 Look-Ahead 插補器設計 26
3-3-1 連續短線段Look-Ahead插補設計 26
3-3-2 連續擬合線段Sharp Corner Detection Module 33
第四章 動態模擬結果 38
4-1 模擬控制器系統簡介 38
4-2 模擬結果 39
第五章 結論與未來研究發展方向 49
5-1 結論 49
5-2 未來研究發展方向 50
附錄 54
文 獻 回 顧 55

[1]M. Shpitalni, Y. Koren, C.-C. Lo, “Realtime curve interpolators,” Computer-Aided Design, Vol.26, No.11, pp.832-838, 1994.
[2]D.C.H. Yang, T. Kong, “Parametric interpolator versus linear interpolator for precision CNC machining,” Computer Aided Design, Vol.26, No.3, pp. 225-2341, 1994.
[3]D. II. Kim, J. II. Song and S. Kim, “Dependence of machine accuracy on acceleration/deceleration and interpolation methods in CNC machine tools”, Industry Applications Society Annual Meeting,Vol.3 ,pp. 1898-1905, 1994.
[4]J.T. Huang, D.C.H. Yang,, “A generalized interpolator for command generation of parametric curves in computer controlled machines”, ASME Japan/USA Symposium on Flexible Automation, Vol.1, pp.393-399, 1992.
[5]R.T. Farouki, Y.F. Tsai, “Exact Taylor series coefficients for variable-feedrate CNC curve interpolators”, Computer-Aided Design , pp.155-165,2001.
[6]S.-S. Yeh and P.-L. Hsu, “Adaptive-feedrate interpolation for parametric curves with a confined chord error,” Computer-Aided Design, Vol. 34, pp. 229-237, 2002
[7]X.-G. Guo, D.-C. Wang, C.-X. Li and Y.-D. Liu, “A rapid and accurate positioning with linear deceleration in servo system,” International Journal of Machine Tools & Manufacture, Vol. 42, pp. 851-861, 2002
[8]G. C. Han, D. I. Kim, H. G. Kim, K. Nam, B. K. Choi and S. K. Kim, “A high speed machining algorithm for CNC machine tools,”Industrial Electronics Society, 1999. IECON ’99 Proceedings. The 25th Annual Conference of the IEEE, Vol. 3, pp. 1493-1497, San Jose, CA, USA, 1999.
[9]D. Kiritsis, “High precision interpolation algorithm for 3D parametric curve generation”, Computer-Aided Design, Vol. 26, No. 11, pp. 850-856, 1994.
[10]X. Zhiming, C. Jincheng, F. Zhengjin, Performance evaluation of a real-time interpolation algorithm for NURBS curves, International Journal of Advanced Manufacturing Technology Vol.20,pp.270-276,2002.
[11]S.S. Yeh, P.L. Hsu, Adaptive-feedrate interpolation for parametric curves with a confined chord error, Computer-Aided Design Vol.34, pp. 229-237,2002.
[12]Ming-Tzong Lin, Meng-Shiun Tsai, Hong-Tzong Yau, “Development of A Dynamics-based NURBS Interpolator with Real-time Look-Ahead Algorithm,” International Journal of Machine Tools & Manufacture, Vol. 47, pp. 2246–2262, 2007.
[13]黃允伸，CNC運動控制加減速法則之研究，國立中正大學機械工程研究所碩士論文，1996。
[14]林明宗，WindowsNT環境下PC-Based即時控制架構之發展與應用，國立中正大學機械工程研究所碩士論文，2000。
[15]Hong-Tzong Yau, Jun-Bin Wang,”Fast Bezier interpolator with real-time lookahead function for high-accuracy machining”, 2007,International Journal of Machine Tools & Manufacture,vol. 47, pp.1518-1529,2007.
[16]Hong-Tzong Yau, Jun-Bin Wang, Chien-Yu Hsu and Chih-Hua Yeh,” PC-based Controller with Real-time Look-ahead NURBS Interpolator”, Computer-Aided Design & Applications, Vol. 4, Nos. 1-4, pp. 331-340,2007.
[17]Chou, J.J, Yang, D.C.H, “Command Generation for Three Axis CNC Machining”, Journal of Engineering for Industry, Transactions of the ASME, Vol.113, No.3, pp.305-310, 1991.
[18]T. Yong and R. Narayanaswami, “A parametric interpolator with confined chord errors, acceleration and deceleration for NC machining”, Computer-Aided Design, Vol. 35, pp. 1249-1259, 2003.
[19]廖家賢，「NURBS插補器在PC-Based CNC之設計與實現」，國立中央大學機械工程研究所碩士論文，2002。
[20]Nakamura S., “Applied numerical methods in C. Prentice- Hall”, New Jersey,1993.
[21]M.-Y. Cheng and C.-C. Lee, “On real-time contour error estimation for contour following tasks,” Proceedings of IEEE/ASME International Conference on Advanced Intelligent Mechatronics, pp. 1047-1052, Monterey, California, USA, 24-28 July, 2005.
[22]H.-T. Yau and M.-J. Kuo,” NURBS machining and feed rate adjustment for high-speed cutting of complex sculptured surfaces”, International Journal of Production Research, Vol. 39, No. 1, pp.21- 41,2001