Investigation into the Mechanism of Tool Path Effects on Cutting Forces in Longitudinal-Torsional Ultrasonic-Assisted End Milling

This study presents a systematic investigation into the variation of cutting forces in longitudinal–torsional ultrasonic vibration-assisted milling, focusing on the coupling mechanism between tool path geometry and ultrasonic vibration. A cutting force modeling approach integrating path features and ultrasonic parameters is proposed and validated through comparative experiments involving linear and arc tool paths. The results show that, in linear paths, vibration amplitude exerts a moderate influence on cutting forces, while in arc paths, variations in tool path curvature dominate the force characteristics due to changes in instantaneous cutting conditions. The ultrasonic vibration modulates the tool’s instantaneous displacement and rotational angle, thereby affecting the uncut chip thickness (UCT) and ultimately altering the magnitude and distribution of cutting forces. The findings highlight the critical role of path geometry in ultrasonic-assisted machining and offer theoretical guidance for cutting force control and path optimization in complex trajectory milling, with significant engineering application potential.