應用曲線擬合技術於CNC插補器小線段路徑平滑化之研究
Other Title
Application of Curve Fitting Technology for Short Line Segment Trajectory of CNC Interpolator
Journal
機械工業雜誌
Journal Issue
516
Start Page
13
End Page
23
ISSN
0255-0075
Date Issued
2026-03
Author(s)
Abstract
CNC工具機控制器的關鍵技術為插補器，插補器會依照輸入的路徑進行命令規劃，當給予的命令出現瑕疵時會使控制器在插補時產生異常加減速，除了會造成異常降速延長加工時間之外，也會使加工品質不佳。因此，本文提出將曲線擬合技術應用於小線段路徑平滑化，在該項技術中除了具備曲線擬合的技術之外，也透過路徑的幾何進行分段並結合近似迭代擬合技術（Least Square Progressive Iterative Approximation, LSPIA）使路徑在平滑的過程中可以維持公差。與傳統僅使用LSPIA的擬合結果在相同的公差設定下可減少80%以上的迭代次數並獲得較好的NURBS（Non-Uniform Rational B-splines）曲線擬合精度。
The key technology of CNC machine tool controllers lies in the interpolator, which plans motion trajectory based on the input tool path. When flaws or irregularities exist in the provided path commands, the interpolator may produce abnormal acceleration and deceleration during interpolation. This not only leads to undesirable speed reductions but also degrades machining quality, thereby increasing the overall machining time. To address this issue, this article proposes applying curve-fitting techniques to smooth short line segment tool paths. In addition to employing conventional curve-fitting principles, the method further performs geometric segmentation of the path and integrates the Least-Square Progressive Iterative Approximation (LSPIA) technique to ensure that the path maintains the required tolerance throughout the smoothing process. Given the required tolerance, the proposed approach could reduce the number of iterations by more than 80% compared with conventional LSPIA-only fitting, while achieving superior NURBS (Non-Uniform Rational B-splines) curve-fitting accuracy.
Subjects
曲線擬合
幾何分段
控制點最佳化
NURBS curve fitting
Geometric segmentation
Control point optimization
Type
journal article