Position-velocity-acceleration-timemethod for time-dependent polishing under dynamic constraints

The time-dependent processes, such as bonnet polishing and magnetorheological finishing, utilize the dwell time map to guide material removal distribution. To account for machine dynamic limits and interpolator effects, converting dwell time points to a velocity profile is essential. Current velocity scheduling methods, using trapezoidal velocity planning or cubic splines, do not consider machine dynamic limits and continuous acceleration. Sudden changes in acceleration cause the controller to alter the path to protect the machine, resulting in trajectory deviations from the dwell time requirements. This research proposes a scheduler that uses the position-velocity-acceleration-time (PVAT) mode in the motion controller. First, the velocity scheduling principle of the PVAT-based velocity scheduler is proposed. Second, simulations of the raster, maze, and Hilbert paths demonstrate that this scheduler can ensure accuracy while achieving better continuity compared to the position-velocity-time (PVT) method. Finally, dry-run and magnetorheological figuring experiments were conducted. Using the proposed scheduler, the root mean square (RMS) error of the fused silica sample surface was reduced to 3.115 nm. Additionally, combining the scheduler with the maze path during processing improved the performance in terms of middle spatial frequency (MSF) errors.