Structural Optimization Study on a Three-Degree-of-Freedom Piezoelectric Ultrasonic Transducer

A three-degree-of-freedom (3-DOF) piezoelectric ultrasonic transducer is a critical component in elliptical and longitudinal ultrasonic vibration-assisted cutting processes, with its geometric structure directly influencing its performance. This paper proposes a structural optimization method based on a convolutional neural network (CNN) and non-dominated sorting genetic algorithm II (NSGA2). This method establishes a transducer lumped model to obtain the electromechanical coupling coefficients (X-ke and Z-ke) and thermal power (X-P) indicators, evaluating the bending and longitudinal vibration performance of the transducer. By creating a finite element model of the transducer with mechanical losses, a dataset of different transducer performance parameters, including the tail mass, piezoelectric stack, and dimensions of the horn, is obtained. Training a CNN model with this dataset yields objective functions for the relationship between different transducer geometric structures and performance parameters. The NSGA2 algorithm solves the X-ke and Z-ke objective functions, obtaining the Pareto set of the transducer geometric dimensions and determining the optimal transducer geometry in conjunction with X-P. This method achieves simultaneous improvements in X-ke and Z-ke of the transducer by 22.33% and 25.89% post-optimization and reduces X-P to 18.97 W. Furthermore, the finite element simulation experiments of the transducer validate the effectiveness of this method.