Improved time-optimal B-spline feedrate scheduling for NURBS tool paths in CNC machining

Feedrate scheduling in computer numerical control (CNC) machining is of great importance to fully develop the capabilities of machine tools while maintaining the motion stability of each actuator. Smooth and time-optimal feedrate scheduling plays a critical role in improving the machining efficiency and precision of complex surfaces considering the irregular curvature characteristics of tool paths and the limited drive capacities of machine tools. This study develops a general feedrate scheduling method for non-uniform rational B-splines (NURBS) tool paths in CNC machining aiming at minimizing the total machining time without sacrificing the smoothness of feed motion. The feedrate profile is represented by a B-spline curve to flexibly adapt to the frequent acceleration and deceleration requirements of machining along complex tool paths. The time-optimal B-spline feedrate is produced by continuously increasing the control points sequentially from zero positions in the bidirectional scanning and sampling processes. The required number of knots for the time-optimal B-spline feedrate can be determined using a progressive knot insertion method. To improve the computational efficiency, the B-spline feedrate profile is divided into a series of independent segments and the computation in each segment can be performed concurrently. The proposed feedrate scheduling method is capable of dealing with not only the geometry constraints but also high-order drive constraints for any complex tool path with little computational overhead. Simulations and machining experiments are conducted to verify the effectiveness and superiorities of the proposed method.