Frequency coupling design of ultrasonic horn with spiral slots and performance analysis of longitudinal-torsional machining characteristics

Longitudinal-torsional (L-T) vibration in rotary ultrasonic machining (RUM) can further reduce the cutting force and improve the machining efficiency compared with the single longitudinal vibration in RUM. In this study, an ultrasonic step horn with spiral slots using the principle of mode conversion was designed to realize L-T vibration. The torsional amplitude to longitudinal amplitude (AT/AL) ratio is proposed to quantify the efficiency of mode conversion. Moreover, a simulation method was used to carry out the frequency coupling design of the ultrasonic horn with spiral slots. The influence of the step position and slot position with a spiral angle of 52° on the resonant frequency and amplitude of the ultrasonic horn were analyzed, respectively. Based on the simulation results, ultrasonic horns with different AT/AL were designed and fabricated. Finally, the results obtained through experiments with milling glass plane revealed that the cutting force was reduced by 48–73%, while the surface quality improved compared with single longitudinal vibration when the torsional vibration is coupled with the longitudinal vibration in RUM. The reasonable AT/AL ratio could effectively reduce the cutting force when the synthetic amplitude was the same. This indicates that the L-T vibration changes the trajectories of the diamond abrasives, which improves the machining performance.