Adaptive feedrate planning on parametric tool path with geometric and kinematic constraints for CNC machining

Feedrate planning is crucial for CNC systems to generate a smooth and fast movement, which is closely related to the machining quality and machining efficiency. In this paper, a new method for adaptive feedrate planning is proposed for parametric tool path with respecting geometric and kinematic constraints for CNC machining. The mathematic relationships between the prescribed constraints and tool tip feedrate are first formulated. Then the feedrate upper bound at any curve parameter is derived, and the tool path is adaptively discretized into discrete sampling positions and corresponding maximum feedrates are calculated. A linear mathematic model for linear programming is proposed to obtain the optimal square values of feedrates at each sampling position. After solving the linear model by a well-developed linear programming algorithm, the optimal feedrates at each sampling position can be calculated. Finally, the optimal discrete feedrate data are fitted to a smooth spline curve as the ultimate feedrate profile, which respects all prescribed constraints. Experiments are conducted on two parametric tool paths to show the merits of the proposed method. Results show that the proposed method are feasible and applicable, the generated feedrate profiles of the two tool paths respect all the prescribed constraints.