CNC運動控制器之NURBS曲線擬合與插值器設計

Design of Curve Fitting and Interpolator of NURBS for CNC Motion Controller

朱智煒(Chih-Wei Chu)

指導教授 ： 陳金聖 ； 賴炎生

國立臺北科技大學/機電學院/自動化科技研究所/碩士(2013年)

摘要

本論文提出應用於CNC運動控制器之NURBS曲線擬合與插值器設計的方法。此方法包括：(1)離散點資訊處理，(2)NURBS曲線擬合，(3)NURBS速度規劃， (4)NURBS曲線插值器。首先，在獲取經由CAM演算法產生近似於原工件輪廓的加工資訊時，即存在許多誤差，會使得工件在加工時產生偏移或刀痕，為了降低這兩種不良的影響，本論文利用離散點資訊處理流程改善。其次，將處理完之離散點資訊做數學建模獲取擬合所需之參數，利用最小平方法進行曲線擬合，其擬合曲線品質未必滿足精度要求，通常需進行疊代修改。本論文不僅使用傳統之全域調整法也提出局部調整法，能依據誤差和微分誤差較大線段直接調整，可加快曲線擬合的速度。曲線規劃則是藉由擬合產生NURBS曲線資訊，在考量機械性能條件下，使用適應性進給率進行速度估測並令區域曲率最大之位置為分段點，再利用最低速優先規劃法依序在各區段利用S-Curve 或S-L-Curve做加減速規劃。接著透過改良式補償式插值器計算出每一取樣時間準確的位置命令。最後，透過運動控制卡結合串列式伺服機構實際驗證本論文所提方法的可行性。

關鍵字

NURBS ； 刀具路徑 ； 改良式補償式插值器

並列摘要

This thesis proposes the systematic design of NURBS curve fitting and interpolator for CNC motion controller, which includes: (1) Data processing of discrete points, (2) NURBS curve fitting (3) NURBS curve federate planning and (4) NURBS curve interpolator. Firstly, the data coming from CAM yields the contouring error and non-continuity. Furthermore, the roughness of workpiece will be degraded when these datum are applied to generate the cutting path. This thesis proposes an effective data progressing method to filter out the linear segments and smooth the curve segments. The parameters of NURBS curve are selected by mathematical model and the discrete datum after processing. And then, the curve fitting is iteratively used by the least squares method to get the fitted NURBS curve satisfying the specification of chord error. In this thesis, using not only the traditional global modification method but also proposed local modification method to locally adjust the segments owing big chord error and differential error, that will speed up the efficiency of curve fitting. The NURBS curve is separated into many segments by break points which have the maximum curvature, and the estimated feedrate in these break points will be the initial starting and ending feedrates in these segments. The feedrate planning for NURBS motion trajectory considering motion dynamics including maximum feedrate and the limitations of acceleration and jerk are further designed. In addition, a compensated interpolator is proposed to control the federate command accuracy to generate the servo position command. These methods are evaluated on a multi-axis servo mechanism with the IMP motion controller, which is made by ITRI. Experimental results have illustrated that these techniques are effective to reduce the contouring error and improve the machining efficiency and quality.

並列關鍵字

NURBS ； Tool Paths ； Modified Compensated Interpolator

參考文獻

[26] 賴政賢，考量機械性能之NURBS曲線速度規劃運用於補償式插值器，碩士論文，國立臺北科技大學自動化科技研究所，台北，2011。

[30] 工業技術研究所，IMP Series單機模式使用者導引，2010。

[31] 工業技術研究所，IMP-2硬體使用手冊，2010。

[3] W. Ma and J. P. Kruth, "NURBS curve and surface fitting for reverse engineering," International Journal Advanced Manufacturing Technology, vol. 14, 1998, pp. 918-927.

[4] 高天一，多維NURBS曲線擬合及考量加減速之插值器實現，碩士論文，國立臺北科技大學自動化科技研究所，台北，2009。