Abstract
Different from the existing equivalent circuit analysis method of the transducer, based on the vibration theory of the mechanical system and combined with the constitutive equation, this paper analyzes the radial vibration characteristics of the transducer. The piezoelectric ceramic composite ultrasonic transducer is simplified as a mechanical model of a composite thick wall tube composed of a piezoelectric ceramic tube and a metal prestressed tube. The mathematical model of radial vibration of the transducer is established, which consists of the wave equation of radial coupling vibration of the piezoelectric ceramic tube and the metal prestressed tube, the continuity conditions, and the boundary conditions of radial vibration of composite thick wall tube. The characteristic equation and the mode function of radial vibration are derived. The calculated results of natural frequency are in good agreement with the existing experimental results. Based on the analytical method and the difference method, the numerical simulation models of radial vibration are established, and the amplitude-frequency characteristic curves and the displacement responses are given. The simulation results show that the amplitude-frequency characteristic curves and the displacement responses of the two methods are the same, which verifies the correctness of simulation results. Through the simulation analysis, the influence rule of the transducer’s structure sizes on its radial vibration natural frequency is given: when the thickness of the metal prestressed tube and the piezoelectric ceramic tube are constant, the natural frequency decreases with the increase of the inner diameter of the piezoelectric ceramic tube; when the outer diameter of the metal prestressed tube and the inner diameter of the piezoelectric ceramic tube are constant, the natural frequency decreases with the increase of the thickness-to-wall ratio. The calculation method of natural frequency based on elastic vibration theory is clear in concept and simple in calculation, and the simulation models can analyze the mechanical vibration of the transducer.
Highlights
Ultrasonic transducer is one of the most important parts of an ultrasonic vibration system
Piezoelectric ceramic composite ultrasonic transducer is composed of a piezoelectric ceramic tube and a metal prestressed tube along radial direction, and the assembling method is the temperature difference method [7, 8]
Based on the analytical method and the difference method, the numerical simulation models of the radial vibration of the transducer are established, and the amplitude-frequency characteristic curves and the displacement responses of the radial vibration are given. e relationship between the natural frequency of radial vibration and structure sizes was discussed. is paper will provide some guidance for the design and application of the transducer
Summary
Ultrasonic transducer is one of the most important parts of an ultrasonic vibration system. Based on the theory of elasticity, the vibration and stress in the length and radius direction of the thin walled piezoelectric ceramic short tube are ignored; references [11, 12] discussed the natural frequency of transducer through its equivalent circuit. According to the principle of electromechanical analogy, reference [14] studied a kind of composite piezoelectricity ultrasonic transducer and obtained the equivalent circuit and frequency equation of the system. E mathematical model of radial vibration of the transducer is established, which consists of the wave equation of radial coupling vibration of the piezoelectric ceramic tube and the metal prestressed tube, the continuity conditions, and the boundary conditions of radial vibration of composite thick wall tube. Based on the analytical method and the difference method, the numerical simulation models of the radial vibration of the transducer are established, and the amplitude-frequency characteristic curves and the displacement responses of the radial vibration are given. e relationship between the natural frequency of radial vibration and structure sizes was discussed. is paper will provide some guidance for the design and application of the transducer
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