Modeling and simulation of trajectory smoothing and feedrate scheduling for vibration-damping CNC machining

Abstract

The mathematical models of tool path smoothing and feedrate scheduling in Computer Numerical Control (CNC) system are critical for high-precision manufacture. Inthe existing studies, G2/G3 (curvature-continuous/-smooth) trajectory smoothing, and jerk-limited/-continuous feedrate scheduling schemes have been developed. Nonetheless, there are exist some requirements that cannot be satisfied simultaneously, including confined chord error, G01 points interpolated, analytical curvature extremum, real-time performance, kinematic time-optimality, and the smoothness of tool-path and feedrate profile. Recently the scholars found the potentials of the tool path with high-order geometric continuity and the feedrate with high-order kinematic constraints, respectively in increasing the smoothness of tool path and reducing the impact caused by axis actuators during the process. Aiming to reduce the vibration and guarantee high machining efficiency, this work proposes G4 (curvature-variation-smooth) interpolative trajectory model with confined chord error and analytical curvature extrema for trajectory smoothing, and employs jerk-smooth (jerk-differentiable) feedrate mode to perform time-optimal feedrate scheduling. Finally, a real-time tool path processing strategy under various geometric and kinematic constraints is developed. The simulation shows approximation error, curvature extrema, and feedrate fluctuation are reduced compared with G2 transition and G3 interpolation schemes. The experimental results demonstrate advantages of the proposed method in vibration damping, surface quality, compared with the previous works.