An Algorithm of Adaptive Variable Spacing for Arc Fitting Non-Circular Curve

Abstract:

The Numerical Control (NC) systems are only linear and circular interpolation function, and the non-circular curve must be fitted with them before processed. There are many algorithms of fitting curve with arc, but most of them have some shortcomings, such as the numbers of fitting data points and arcs segments are too many, the error controlling are difficult in arc fitting , the programming are difficult to meet the real-time NC processing requirement and so on. This paper proposed a new algorithm, which could quickly and automatically determine the best node for fitting curve with arc according to the change of curvature and the machining error. It could ensure the machining precision and efficiency. The algorithm could be directly completed programming and processing by the NCs macro program function without any other auxiliary software. The detailed algorithm process and the application programming were given.

• Periodical: Advanced Materials Research (Volumes 753-755)
• Pages: 1960-1965
• DOI: https://doi.org/10.4028/www.scientific.net/AMR.753-755.1960
• Online since: August 2013
• Authors: Ying Hui Pan, Shi Yin Fang, Bo Guo
• Keywords: Arc Fitting, Error, Interpolation, Non-Circular Curve, Numerical Control (NC), Programming

References

[1] Shen Jigui: Optimal Method of Arc Fitting in NC Manufacturing. Chinese Journal of Mechanical Engineering, 1997, 33(6): 64-69.

[2] LI Ming-gui: Machining of Non-Circular Curved Surface. Journal of Xi＇an Shiyou University(Natural Science Edition) , 2004, 19(2): 54-57.

[3] WANG Xue-ying, REN Peng: Optimizing Algorithm of Equal Chord Length for CNC Machine Tools. Journal of Shenyang Normal University (Natural Science Edition), 2010, 28(4): 499-502.

[4] CAI Yong-Lin, XI Guang, SUN Wei-qing: A New Method for Obtaining Points from Plane Curve Interpolating by Arc. Journal of Engineering Graphics, 2002, 23(1): 97-103.

[5] TU Jiawen, XU Shoushi, TAN Yong: Method of Circular Arc Fragmented Curve-Fitting Based on Least Mean-Square Error. Computer Applications, 2001, 21(3): 48-50.

[6] CHEN Min, JIANG Xiaomin, TAO Tao, et al: Plane Parametric Curves Fitting in Numerical Control Processing. Machine Tool & Hydraulics, 2006, 23(4): 70-72.

[7] Cai Huilin, Dai Jianqiang: Calculation of Tangent-arc Under Polar Coordinates Approaching Non-circle Curve on GA.  Journal of Lanzhou Jiaotong University, 2007, 26(6): 5-8.

[8] GUO Wen-lan, ZHANG Tong: Biarc Fitting Algorithm and Application for Curve Equations.  Journal of Harbin University of Science and Technology, 2004, 9(6): 87-89.

[9] YUE Ying, HAN Qing-yao, WANG Zhang-qi: Least Squares Approximation for Non-Circular Curve In NC Machining.  Journal of North China Electric Power University (Natural Science Edition), 2006, 33(6): 102-104.

[10] Qie Shengqiang, Wang Xiankui: Symmetrical Variable Curvature Circular Arc Curve and Its Application in Circular Arc Spline Curve. Journal of Computer-Aided Design & Computer Graphics, 2002, 14(3): 222-224.

[11] YAO Bi-qiang, YAO Jin: The Method of Curve Fitting with Equal Length Arc Used for NC Processing.  Journal of Sichuan University (Engineering Science Edition), 2008, 40(1): 171-174.