Low-Harmonic Corner Smoothing Algorithm Using Trajectory Pattern Method for High-Speed and Highprecision Machinery

Kinematic profiles with high-frequency harmonic contents can give rise to unwanted vibrations due to demand for higher-harmonic actuating forces / torques, which is a major source of inaccuracies in high-speed and high-precision machinery. In this paper, to synthesize low-harmonic kinematic profiles, a corner smoothing algorithm using Trajectory Pattern Method (TPM) is presented. The corner curve and axial kinematic profiles are constructed in one step by using the TPM with a specified fundamental frequency and its first three harmonics, which would minimize high harmonic contents in the required actuating forces / torques and avoid exciting natural modes of vibration of the machinery. These smooth trajectories are obtained by the boundary condition module, kinematic limitation control module and linear programming module, which would not exceed the dynamic response limitation of the actuation devices. The experimental analysis and comparison demonstrate that the proposed algorithm could achieve smooth kinematic profiles with low harmonic contents and cause minimal system vibration, therefore the machinery could be capable of operating at higher precision and speed.