Abstract The current ultrasonic milling tool holders are relatively long in structure, and the tool is susceptible to generating detrimental radial vibrations during high-speed rotation. To achieve high-quality milling of difficult-to-machine materials, a longitudinal-torsional ultrasonic oscillator suitable for BT40 tool holders has been proposed, which can generate a large amplitude while maintaining a compact length. A longitudinal vibration ultrasonic transducer with an exponential front cover is designed using the analytical method. Based on the principle of acoustic wave reflection, four spiral grooves are introduced on the exponential variable cross-section bar to convert the longitudinal vibration into longitudinal-torsional composite vibration. The effects of groove width, groove depth, and spiral angle on the longitudinal-torsional resonance were analyzed using the single-factor method in finite element software, and the optimal spiral groove parameter combination was determined. The longitudinal-torsional ultrasonic transducer is assembled with the BT40 tool holder to construct a longitudinal-torsional ultrasonic tool holder model, and modal analysis was performed. The resonant frequency was determined to be 22, 845 Hz. An experimental platform was established to carry out impedance analysis and amplitude testing on the longitudinal-torsional ultrasonic tool holder. The results show that its resonant frequency is 22, 152 Hz, which is slightly different from the simulation value. The tool holder’s maximum longitudinal amplitude is 11.2 μm, and the maximum torsional amplitude is 4.3 μm, with a torsional-to-longitudinal ratio of 0.38. The performance of the longitudinal-torsional ultrasonic tool holder meets the processing requirements of most ultrasonic milling applications, and the correctness of the design method is verified.
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