A corner smoothing algorithm using Trajectory Pattern Method (TPM) for high-speed and high-quality machining

In micro-line segments machining, transition curves with high harmonic components are more prone to causing vibration issues in the feed drive system, which affects machining efficiency and quality severely. To construct low harmonic trajectories, this paper proposes a corner smoothing algorithm that uses the Trajectory Pattern Method (TPM). The transition curve construction and axial motion scheduling are performed with a specified fundamental frequency in one step, which reduces the smoothing process time and avoids excitation of natural modes of vibration of the system. The synthesized trajectories and axial kinematic profiles are all smooth and only contain the selected fundamental frequency and its first two odd harmonics, which minimizes the number of high harmonic components in the required actuation forces/torques and avoids excitation of the system modes of vibration. Linear programming is used to synthesize the trajectories. The proposed algorithm is shown to achieve near time-optimal trajectories. The provided experimental analysis and comparisons demonstrate that the proposed algorithm achieves smooth axial kinematic profiles with low harmonic contents, which would improve machining efficiency and quality.