High Speed Machining for Linear Paths Blended with G3 Continuous Pythagorean-Hodograph Curves

doi:10.1007/s11424-022-0258-x

Journal of Systems Science and Complexity ›› 2022, Vol. 35 ›› Issue (4): 1586-1607.DOI: 10.1007/s11424-022-0258-x

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High Speed Machining for Linear Paths Blended with G3 Continuous Pythagorean-Hodograph Curves

ZHAO Kai^1,2, LI Shurong³

1. College of Control Science and Engineering, China University of Petroleum (East China), Qingdao 266580, China;
2. College of Computer Science and Information Engineering, Anyang Institute of Technology, Anyang 455000, China;
3. School of Artificial Intelligence, Beijing University of Posts and Telecommunications, Beijing 100876, China

Received:2020-10-13 Revised:2021-07-08 Online:2022-08-25 Published:2022-08-02
Contact: LI Shurong,Email:lishurong@bupt.edu.cn
Supported by:
This research was supported by the National Natural Science Foundation of China under Grant No. 61573378; The authors also appreciate the supports from Henan Province Programs for Science and Technology Development under Grant No. 212102210391 and Anyang Institute of Technology Research and Cultivation Fund under Grant No. YPY2020012.

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ZHAO Kai, LI Shurong. High Speed Machining for Linear Paths Blended with G3 Continuous Pythagorean-Hodograph Curves[J]. Journal of Systems Science and Complexity, 2022, 35(4): 1586-1607.

Previously, many studies have illustrated corner blend problem with different parameter curves. Only a few of them take a Pythagorean-hodograph (PH) curve as the transition arc, let alone corresponding real-time interpolation methods. In this paper, an integrated corner-transition mixing-interpolation-based scheme (ICMS) is proposed, considering transition error and machine tool kinematics. Firstly, the ICMS smooths the sharp corners in a linear path through blending the linear path with G3 continuous PH transition curves. To obtain optimal PH transition curves globally, the problem of corner smoothing is formulated as an optimization problem with constraints. In order to improve optimization efficiency, the transition error constraint is deduced analytically, so is the curvature extreme of each transition curve. After being blended with PH transition curves, a linear path has become a blend curve. Secondly, the ICMS adopts a novel mixed interpolator to process this kind of blend curves by considering machine tool kinematics. The mixed interpolator can not only implement jerk-limited feedrate scheduling with critical points detection, but also realize self-switching of two interpolation modes. Finally, two patterns are machined with a carving platform based on ICMS. Experimental results show the effectiveness of ICMS.

Key words: Bézier control polygon, corner transition, jerk-limited scheduling, mixed interpolation, pythagorean-hodograph curve

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