Time-optimal feedrate scheduling with actuator constraints for 5-axis machining

Cycle time minimization is one of the major goals to achieve in manufacturing. Maximizing feedrate is the direct solution; however, physical motions need to be under the specified motion limits to avoid high-frequency vibration, causing machining error. In this paper, a time-optimal feedrate scheduling approach with corner smoothing for 5-axis G1 toolpaths is presented for 5-axis machining. One key feature of the proposed method is to describe the orientation toolpath in the spherical coordinate system (SCS), instead of the commonly used unit sphere. With this, the position and orientation of the 5-axis toolpath are integrated to become a hyper-curve in a 5-dimensional (5-D) space. The feedrate scheduling and corner smoothing are designed for this 5-D hyper-curve. Thus, no synchronization of position and orientation feedrate scheduling is needed, making the feedrate scheduling easier. A quintic B-spline corner smoothing method is utilized to smoothen sharp corners in the toolpath. Then, the S-shape feedrate profile of each block is optimized under the actuator motion constraints, with the objective of minimizing the cycle time. Particle swarm optimization (PSO) is used to provide the optimized solution. Experiments are conducted to validate the proposed approach, and the results are compared with two other existing approaches. It is found that the proposed method can achieve shorter cycle time and less contour errors, showing the effectiveness of the proposed approach.