Linear Interpolation of machining tool-paths with robust vibration avoidance and contouring error control

Abstract

This paper presents a reference trajectory (command) generation scheme to robustly avoid residual vibrations that occur due to rapid acceleration of machine axes in high-speed machining and positioning tasks. A robust Finite impulse response (FIR) filter is designed to generate reference motion commands for accurate real-time interpolation of linear toolpaths along point-to-point (P2P) and non-stop contouring trajectories. The designed FIR filter generates reference acceleration profiles with wide attenuation bands in the frequency spectrum to avoid unwanted vibrations. Design and tuning principles for the robust FIR filter are presented, and kinematics of the generated reference trajectories are analyzed. Contour errors that occur during rapid non-stop linear interpolation are estimated from the filter dynamics. A feedrate scheduling method is introduced to analytically confine those interpolation contour errors within user specified tolerances. Effectiveness of the proposed trajectory generation scheme is validated in actual machining tests, and it is benchmarked against the state-of-the-art technique. It is shown that developed FIR-based trajectory generator can robustly avoid unwanted inertial vibrations to produce smoother surfaces without elongating cycle times.