A G4 continuous B-spline transition algorithm for CNC machining with jerk-smooth feedrate scheduling along linear segments

• Published in: Computer aided design Vol. 115; pp. 231 - 243
• Main Authors: Zhang, Yong, Zhao, Mingyong, Ye, Peiqing, Zhang, Hui
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier Ltd 01.10.2019; Elsevier BV
• Subjects: [formula omitted] continuity; Acceleration; Algorithms; CNC machine tools; Computer simulation; Curvature; G01 linear segments; Jerk-smooth feedrate scheduling; Machining; Mathematical analysis; Motion planning; Numerical controls; Quintic B-spline; Scheduling; Segments; G4 continuity; Quintic B-spline; Jerk-smooth feedrate scheduling; G01 linear segments; CNC machine tools
• ISSN: 0010-4485; 1879-2685
• DOI: 10.1016/j.cad.2019.04.004

Toolpath is always presented as a combination of G01 linear segments in practical computer numerical control (CNC) machining. However, the inherent tangent discontinuity at junctions will lead to uncontinuous feedrate, acceleration (i.e. the change rate of feedrate), jerk (i.e. the change rate of tangential acceleration), making it difficult to realize higher machining efficiency and better machining quality. In recent studies, the improvement of practical feedrate profile continuity is beneficial to overcome the drawbacks above, especially when smooth jerk is satisfied. In this paper, it is proved that in order to obtain smooth jerk along toolpath, G4 continuous toolpath and jerk-smooth feedrate scheduling process are both essential. On this basis, a path-smoothing algorithm is proposed to generate G4 continuous toolpath via a quintic B-spline curve. In addition, the transition curve is optimized by curvature variation energy (CVE) to produce better machining quality. Meanwhile, the chord error is constrained seriously and the curvature extreme, occurring at the middle of transition curves, can be calculated analytically. In motion planning stage, based on the bidirectional scanning algorithm, a look-ahead method is utilized to determine the reachable transition feedrate extreme and a jerk-smooth feedrate scheduling scheme is also developed. Finally, simulations and experiments are conducted to demonstrate the feasibility and efficiency of the proposed method compared to point-to-point (P2P) motion, constant feedrate strategy, G2 and G3 methods respectively. •A new path-smoothing algorithm is proposed to generate G4 continuous toolpath.•The curvature of transition curve is proved to be monotonous, and curvature extreme occurs exactly at the middle of B-spline curve analytically.•The relationship between trajectory continuity and feedrate profile continuity is illustrated.•A scanning algorithm is performed in feedrate scheduling, and jerk-smooth feedrate is achieved.