The Study On The Design Theory Of Ultrasonic Transducer

The ultrasound transducer is widely used in many engineering applications, such as ultrasonic welding, ultrasonic machining, ultrasonic cleaning, etc. An ultrasonic transducer is taken as the key part of ultrasonic machining system. Due to lack of high performance, reliable, cheap and durable of the transducer, that impeded the wide applications of the ultrasonic transducer. Generally, the design of the ultrasound transducer is based on the one-dimensional longitudinal vibration theory. Its frequency equation is obtained by the boundary conditions. This design method is that the remaining dimensions are calculated through the frequency equation, setting the size of some parts according the design requirements or experience. This method is an approximate calculation because of ignoring some minor factor, which will cause large errors. Therefore, the optimization problem of ultrasonic transducer is raised. Design the excellent performance of ultrasonic transducer by the optimization methods.This paper describes the basic design theory of ultrasonic transducer, including transducer types, material selection, structural analysis, and thin electrode ultrasonic transducer vibrator frequency equation. For the optimization of the ultrasonic transducer, this paper analyzed four transducer’s models:Nonparametric Model, Continuum Model, Finite Element Model and Lumped Parameter Models. Ultimately, the continuum model is used as the mathematical model of the transducer. The behavior of piezoelectric transducers is modeled using the transfer matrix method based on analytical models. The design problem is a constrained multi-objective optimization problem, involving continuous and discrete variables. The maximum vibration and the minimum electrical input power are considered as optimization objectives. Multi-objective evolutionary algorithms are applied in the optimization process and a set of Pareto-optimal design is obtained. In order to determine the final design, there’re two methods. One is the use of pseudo-weight vector method; the other one is to use clustering techniques to narrow the number of optimal solutions, according to the evaluation criteria (piezoelectric quality factor, coupling factor, etc.) to determine the final design.Finally, building finite element model for the optimal design, resonance frequency and vibration mode are obtained by means of modal analysis and harmonic analysis with ANSYS. For these two types of transducers, modal analysis showed that there is a very small error of0.2%in natural frequency. The output amplitude of stepped-horn transducer is between11μm and12μm, which meet the requirement of ultrasonic machining.