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

  • Yu Pang
  • Pingfa Feng
  • Jianfu ZhangEmail author
  • Yuan Ma
  • Qiaoli Zhang


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.


Longitudinal-torsional vibration Rotary ultrasonic machining Mode conversion frequency coupling design Face milling Cutting force 


Funding information

The authors gratefully acknowledge the financial support provided to this study by the National Natural Science Foundation of China (Grant Nos. 51761145103 and 51875311) and the Shenzhen Fundamental Research and Discipline Layout project (Grant No. JCYJ2016042818191622).


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Copyright information

© Springer-Verlag London Ltd., part of Springer Nature 2020

Authors and Affiliations

  • Yu Pang
    • 1
  • Pingfa Feng
    • 1
    • 2
  • Jianfu Zhang
    • 2
    Email author
  • Yuan Ma
    • 1
  • Qiaoli Zhang
    • 2
  1. 1.Graduate School at ShenzhenTsinghua UniversityShenzhenChina
  2. 2.Department of Mechanical EngineeringTsinghua UniversityBeijingChina

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