Frequency Optimal Feed Motion Planning in Computer Numerical Controlled Machine Tools for Vibration Avoidance

This paper presents a novel trajectory generation technique, which has the capability to avoid excitation of inertial vibrations in precision manufacturing equipment. A major source of vibrations in fast moving precision manufacturing equipment is the inertial vibrations that are excited due to frequency content of reference motion commands (trajectory). In general practice, those inertial vibrations are avoided within the controller architecture through notch filtering. Or, input-shaping methods are utilized to attenuate critical frequency components of the reference trajectory so that lightly damped vibration modes of the structure are not excited. Instead of employing those postfiltering techniques that add unwanted delay to the coordinated motion, this paper introduces a direct trajectory generation technique with a shaped frequency content to suppress inertial vibrations. The time-stamped acceleration profile of the feed profile is defined as a ninth-order polynomial. Polynomial coefficients are solved through an optimization procedure where the objective function penalizes total frequency energy in a desired frequency band. As a result, generated reference acceleration commands do not contain any excitation near the vibration modes of the system and hence excitation of inertial vibrations is avoided. The proposed frequency optimal feed profiling (FOFP) system can be utilized to generate high-speed accurate point-to-point (P2P) trajectories as well as to interpolate continuous multi-axis coordinated motion. Effectiveness of the proposed FOFP scheme is evaluated through rigorous comparison against the well-known minimum jerk feed profiles (MJFP) technique through simulations and experiments. Experimental validation is performed on an in-house controlled machine tool with flexible structure.