Global time-optimal B-spline feedrate scheduling for a two-turret multi-axis NC machine tool based on optimization with genetic algorithm

Abstract

Feedrate scheduling is of great significance in numerical control machining for the improvement of the surface finish and machining efficiency. For multi-axis machine tools with more than two rotary axes, the feedrate scheduling issue considering the geometry and drive constraints is highly complicated due to the nonlinear kinematic relationship between the cutter location and drive axes. In this paper, a general optimization-based time-optimal feedrate scheduling method for two-turret machine tools with three-rotary axes and one short linear axis is proposed. The closed-form solution for the inverse kinematics of the machine tool is developed to analytically determine the preferable motion of each drive axis for a desired motion of the cutter. By using the B-spline method to represent the feedrate profile, the optimization-based feedrate scheduling model is built, where the control points and knot vector are designated as the decision variables. Two alternative operations, namely the progressive knot insertion and genetic-algorithm-based optimization, are conducted to determine the knot vector and control points for a time-optimal feedrate, respectively. To improve the robustness and computational efficiency of the algorithm, a feedrate profile segmentation criteria is established for concurrent computing. Without any simplification of the constraints, the proposed method can be employed to produce a global time-optimal feedrate efficiently. Typical simulation cases and experiments are carried out to verify the effectiveness and time-optimality of the proposed method.