Analytical modeling and experimental validation of a V-shaped piezoelectric transducer with a flexible joint for generating an elliptical motion

Piezoelectric transducers are widely used for generating an elliptical motion in vibration-assisted machining and in a piezoelectric actuator. In this study, an analytical model of a V-shaped piezoelectric ultrasonic transducer with a flexible joint is proposed. The analytical model is used to optimize the structure, predict the performance, and design the controller and drive circuit. The longitudinal-bending mode is utilized for generating an elliptical motion at a drive foot. A vibration model of the V-shaped transducer is proposed. The vibration resonance frequency and mode shape are obtained by solving a set of differential equations of the balance force and continuous displacement. The energy method is then used to derive the displacement response based on Hamilton-Lagrange equations. Finally, three prototypes are fabricated to validate the model effectiveness. The resonance frequency, displacement response, and electric response of the analytical model are consistent with the experimental results. The results show that the vibration amplitude in the tangential direction X at the drive foot increases with the increase of the phase difference φ, and the amplitude in the normal direction Y decreases with the decrease of the phase difference φ. As the coupling angle θ increases, the amplitude in the tangential direction X increases and the amplitude in the normal direction Y decreases.