Design and experimental study of longitudinal-torsional ultrasonic transducer with helical slots considering the stiffness variation

The ultrasonic transducer employing helical slots to generate longitudinal-torsional (L&T) ultrasonic vibration is popular in the field of hard and brittle material machining. However, the design approach for this type of L&T ultrasonic transducer is not well established. An improved design model combining equivalent circuit theory and material parameter equivalent method based on stiffness variation was proposed in this study. The structure parameters of the transducer can be obtained according to given resonance frequency and nodal position. The model can further predict electrical characteristics and mechanical responses under specific excitation. For the preliminary verification of this theoretical model and the optimization of the transducer, finite element analyses were carried out to investigate the influences of slot structure parameters on dynamic performances in terms of resonance frequency, frequency separation, and amplitude of L&T vibration. After that, a prototype was manufactured according to the design results, and the measurements of impedance curve and vibration amplitude were conducted. The experimental results indicate that this prototype resonates at 24,920 Hz with an effective electromechanical coupling coefficient of 0.19. Meanwhile, the vibration amplitude in longitudinal direction is 8.1 μm and that in tangential direction is 5.6 μm under 70-V sinusoidal voltage excitation, which are consistent with the theoretical design and simulation results. Furthermore, machining tests demonstrate that surface roughness reduction and surface quality improvement can be gained by adopting this L&T ultrasonic transducer, compared to using the longitudinal vibration transducer. The proposed design approach was validated and this study can provide guidelines for the design of L&T ultrasonic transducer for rotary ultrasonic machining (RUM).