Transfer matrix modeling on a longitudinal-bending coupled piezoelectric transducer with single-phase excitation: Analysis and verification

Surface-bonded type piezoelectric transducers have the advantages of simple structure, easy miniaturization, and flexible design and have been widely employed as the stator of ultrasonic motors. In order to simplify the control system, a surface-bonded type single-phase excited piezoelectric transducer operating in the longitudinal-bending coupling vibration is proposed, modeled, and validated in this study. Using the asymmetrical excitation effect, the longitudinal-bending coupled vibration is generated in the proposed piezoelectric transducer only applied with a single-phase electrical signal, leading to the production of the elliptical motion at its driving tip. The proposed transducer holds the advantages of compact structure, simple control system, and low manufacturing costs. The transfer matrix method, which is an efficient and fast semi-analytic computation solution, is employed to develop a dynamic model for the proposed transducer in this study in order to provide a general modeling method for surface-bonded type piezoelectric transducers operating with the longitudinal-bending coupled vibration. A novel longitudinal-bending coupled vibration transfer matrix is created first for surface-bonded type piezoelectric composite element. Then, a general semi-analytical electromechanical coupling model is developed to analyze dynamic behaviors of the proposed piezoelectric transducer. Finally, experimental validation is carried out on the prototype of the proposed piezoelectric transducer and compared with the calculation results using the developed transfer matrix model. Experimental results matched well with the calculation results, which confirmed the correctness of the transducer design and verified the feasibility of the developed transfer matrix model. The proposed piezoelectric transducer presents the potential application for linear ultrasonic motors.