Optimal Feed-Rate Scheduling for High-Speed Contouring

The majority of efforts to improve the contouring performance of high-speed CNC systems has focused on advances in feedback control techniques at the single-axis servo level. Regardless of the dynamic characteristics of an individual system, performance will inevitably suffer when that system is called upon to execute a complex trajectory beyond the range of its capabilities. The intent of the present work is to provide a framework for abstracting the capabilities of an individual multiaxis contouring system, and a methodology for using these capabilities to generate a time-optimal feed-rate profile for a particular trajectory on a particular machine. Several constraints are developed to drive the feed-rate optimization algorithm. First, simplified dynamic models of the individual axes are used to generate performance envelopes that couple the velocity versus acceleration capabilities of each axis. Second, bandwidth limitations are introduced to mitigate frequency related problems encountered when traversing sharp geometric features at high velocity. Finally, a dynamic model for the instantaneous following error is used to estimate the contour error as a function of the instantaneous velocity and acceleration state. We present a computationally efficient algorithm for generating a minimum-time feed-rate profile subject to the above constraints, and demonstrate that significant improvements in contouring accuracy can be realized through such an approach. Experimental results are presented on a conventional two-axis $X−Y$ stage executing a complex trajectory.