Optimal curvature-smooth transition and efficient feedrate optimization method with axis kinematic limitations for linear toolpath

Abstract

In industrial areas, the machining performance with linear G01 code is a crucial indicator to evaluate the computer numerical control (CNC) systems and many researchers have presented various methods to deal with the corner tracking issue. However, the axis jerk limitations are not satisfied well and the different axis kinematic limitations are not considered in most researches, which will reduce the machining efficiency and machining quality simultaneously. In this paper, a novel method including trajectory planning, feedrate scheduling, and interpolating is proposed to obtain better machining quality and higher machining efficiency. In trajectory planning, a B-spline curve is utilized to smooth the linear toolpath and obtain a curvature-smooth trajectory, which is third-order geometry continuous. Thereby, a time-optimal method for the geometric continuous trajectory is proposed based on linear programming algorithm in the feedrate scheduling and the bounded multi-constraints, including axis velocity, axis acceleration, axis jerk, and feedrate. Moreover, it can be seen that the proposed method is near Bang-bang control. To reduce the computation time of the optimal numerical method, an efficient method with a look-ahead window around the transition B-spline curve is applied. In the interpolation stage, a novel interpolation method about arc-length is proposed to improve computation efficiency. Finally, simulation and experiment are conducted to show superiorities of the proposed method to the already existing approaches. The results show that the cycling time of the proposed method is reduced by more than 7% than G2 method and 20% than G3 method with better contour performance.