Analytical time constant design for jerk-limited acceleration profiles to minimize residual vibration after positioning operation in NC machine tools

The positioning operation of the axes of numerically controlled (NC) machine tools is essential before initiating their machining operation. Residual vibration following the positioning operations of the axes deteriorates the cycle time and quality of the machined parts. This study aims to develop a novel acceleration and deceleration design method to suppress the residual vibration during the high-speed positioning of NC machine tools. The proposed method suppresses the vibration by appropriately designing the jerk-limited acceleration profile during acceleration and deceleration. To design the jerk profile, the amplitude map that can represent the relationships between the acceleration parameters and the estimated vibration amplitude is developed. The proposed method suppresses the vibration amplitude without changing the total positioning time. To evaluate the effectiveness of this method, the residual vibration following the high-speed positioning motions was measured and simulated. The results confirm that the proposed method can effectively suppress the residual vibration.