| With the development of ultrasonic application, ultrasonic technology has been widely used in the fields of agriculture, industry, environment protection, medicine and national defense, and so on. Especially in the ultrasonic welding, ultrasonic cleaning, ultrasonic chemistry and ultrasonic extraction of Chinese herbal medicine and other applications, the transducers of single vibration mode cannot meet the requirements of some specific applications, and so, some power transducers with larger radiation area should be urgently needed. In order to improve power and increase ultrasonic radiation area, some mode-conversion ultrasonic transducers are often needed. In this paper, based on the mode-conversion theory, i.e. a vibration mode is converted into the other or more coupled vibration mode, the power ultrasonic transducers for longitudinal-flexural vibration mode-conversion and longitudinal-radial coupled vibration are developed and the main contents include as follows:(1) The design theory of the sandwich piezoelectric ultrasonic transducer (including the piezoelectric ceramic pile and variable cross section bar) is introduced, and its electro-mechanical equivalent circuit and resonance frequency equation are given. Then, taking vibrational displacement amplitude of the transducer's front end as the goal, the method and step of the optimization design are introduced by using the finite element software ANSYS, and the optimization results are given. It is expected that the theory of the sandwich piezoelectric ultrasonic transducer can provide a theoretical basis for the design of the following mode-conversion power ultrasonic transducers.(2) From the point of optimization design of flexural composite vibration system and longitudinal-flexural mode vibration system, for the distributed parameter system, the concept of lumped parameter is put forward. According to the equivalent principle of the kinetic energy and the potential energy for a distributed parameter system and another lumped parameter system, we give the lumped parameter equivalent mass and equivalent elasticity coefficient of the flexural vibration plate with the free boundary, and fixed boundary or simply supported boundary. From the point of radiation sound power, the radiation impedance is obtained. Then, the lumped parameter equivalent circuit is drawn and the resonance frequency equation is given. For the same dimension plate in the same order, resonant frequency with free boundary condition is larger than that with the simply supported boundary condition, but smaller than the resonance frequency with the fixed boundary condition. The theoretical values with three kinds of boundary conditions are consistent with the simulated ones. Therefore, these results can serve as a reference for designing flexural vibration systems and the theory is convenient to design the best working state.(3) The elastic metal cylinder and the piezoelectric ceramic cylinder with larger dimension are analyzed, and their equivalent circuits or frequency equations are obtained. Firstly, based on the apparent elasticity method, the equivalent circuit of metal cylinder is analyzed, which provides convenience for the design of ultrasonic vibration system by using electro-mechanical equivalent circuit method, but this situation is mainly suitable for thin-wall cylinder. Secondly, based on elastic dynamic equation and according to the boundary conditions of free-end annular elastic cylinder, the resonance frequency equation of annular cylinder with arbitrary dimension of longitudinal-radial coupled vibration is derived. The results show that the analytical resonance frequencies are in good agreement with the numerical results. This theory can serve as reference for the design of the longitudinal-radial composite vibrational systems. Finally, based on the analysis of the annular elastic cylinder, using the similar analytical method, the theory of the piezoelectric ceramic cylinder with large dimension is simply analyzed.(4) A new type of piezoelectric ultrasonic transducer for longitudinal-flexural vibrational mode-conversion is proposed. The mode-conversion transducer has a back metal mass, longitudinally polarized piezoelectric ceramic pile, and a circular metal plate. Based on the equivalent lumped parameters of the thin plate, the equivalent circuit and resonance frequency equation of the mode-conversion transducer are given. It can be seen from the frequency equation that the resonance frequencies and anti-resonance frequencies depend on the material parameters and the geometrical dimensions. This theory provides convenience for the design of this kind of transducer. Then, by using the finite element software ATILA, the vibration properties and sound radiation distribution of the whole transducer are analyzed. Finally, the vibrational mode-conversion transducers with the same simulated parameters and geometric dimensions are manufactured. The frequency characteristics and the amplitude distribution of the end surface of the transducers are measured by using Agilent Hp4294precision impedance analyzer and the scanning laser vibrometer Polytec PSV-400. It can be seen that the longitudinal vibration of the piezoelectric vibrator drives the circular metal plate to produce flexural vibration, i.e. the whole transducer is in longitudinal-flexural vibration mode, which increases the radiation area of the conventional sandwich transducer. The theory provides a design idea for high power transducers with large radiation area.(5) The longitudinal-radial coupled vibration of a cylindrical piezoelectric ultrasonic transducer with large geometrical dimensions is analyzed. The cylindrical transducer is composed of a longitudinal sandwich transducer, a metal tube and two metal radiation masses. According to the transmission line theory and Mason electro-mechanical equivalent model, by using force and velocity continuity of the transducer boundaries, the electro-mechanical equivalent circuit and the resonance frequency equation of the cylindrical transducer are derived. Then, the vibration performance of the transducer is analyzed and optimized by using the finite element software. Finally, the displacement and the sound pressure are analyzed. The front and the back metal radiation masses are driven to vibrate longitudinally by the inner sandwich longitudinal transducer, which causes the metal tube to produce longitudinal-radial coupled vibration. It can be seen that the axial vibrational displacements on the two end surfaces of the cylindrical transducer are basically uniformly distributed. On the other hand, the radial vibration on the side cylindrical surface is produced. And with the increase of radial-longitudinal ratio of the transducer, radial vibration displacement increases gradually. Compared with vibration distribution in air and sound pressure in water, resonance frequency and wall thickness of the cylindrical transducer have a close relationship. Therefore, if the right dimensions can be chosen, this kind of cylindrical transducer must be used as a three-dimensional ultrasonic radiator. At the same time, the cylindrical transducer can also produce the obvious longitudinal-radial coupled vibration at the second vibrational mode. Therefore, it is expected that the kind of transducer can also be used as a new type of multi-frequency radiator. |
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