A [formula omitted] continuous B-spline transition algorithm for CNC machining with jerk-smooth feedrate scheduling along linear segments

Abstract

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.