ULTRASONIC TRANSDUCERS WITH VIBRATING PIEZOELECTRIC PLATES

Transcription

1 JOURNAL DE PHYSIQUE Colloque C6, supplément au no 11-12, Tome 33, Novembre-Décembre 1972, page 258 ULTRASONIC TRANSDUCERS WITH VIBRATING PIEZOELECTRIC PLATES W. PAJEWSKI Institute of Fundamental Technological Research. Warszawa, Swietokrzyska 21, Pologne Résumé. - La communication présente les résultats d'études des transducteurs piézoélectriques composés de plaques métalliques et de plaques piézoélectriques, vibrant en modes différents. On a constaté l'influence de la réactance des plaques métalliques sur les paramètres du réseau équivalent électromécanique du transducteur, ainsi que sur les coefficients de rendement et de puissance. Les idées exposées dans la communication permettent de perfectionner la construction des émetteurs ultrasonores de puissance. Abstract. - This communication covers the results of investigations on piezoelectric transducers made of metal and piezoelectric plates, vibrating in different modes. We investigated the influence of the reactance of the metal plates on the parameters of the electromechanical equivalent circuit of the transducer, as well as on the efficiency and power ratios. The ideas reported in this communication allow improvements in the design of power ultrasonic generators. 1. Introduction. - For some application of ultrasound in laboratories and industry an intensity of hundreds and even thousands of watts per cm2 is needed. Such intensity can by obtained only through the increase of the transducer's radiating surface and focusing of ultrasonic energy. As the power produced by a single piezoelectric ceramic element is practicllay limited to about 100 W, an increase of the total power of a transducer can be obtained by the application of several vibrating elements. Transducers with an enlarged radiating surface composed of many piezoelectric elements were constructed already during the World War 1 by Langevin. These transducers were composed of two steel plates with small quartz elements inserted between them. Such a transducer, called Langevin's transducer, was radiating considerable power for frequencies of some tens of khz. Some present solutions of mosaic transducers are based on small piezoelectric elements connected electrically in parallel. The piezoelectric elements are immerged in oil and separated from the fluid medium into which they are radiating ultrasonic energy, by means of a pc rubber diaphragm transparent for the ultrasound [6], [7]. Thin or half-wave metal plates are also used as an intermediate element between the radiating transducer and the fluid medium. The ultrasound radiating systems with half-wave plates are used for frequencies above 100 khz. The advantages of application of half-wave plate are : a good cooling of piezoelectric elements and protection of their surface against corrosion. The construction of transducers composed of a concave half-wave plate excited by several piezoelectric elements is still requiring further investigations for obtaining optimum efficiency and power factor. 2. Half-wave plate excited by a set of piezoelectric elements. - An important increase of the radiated ultrasound power in the range above 100 khz can be obtained by means of a set of piezoelectric elements fixed to a half-wave plate as was suggested by Rosenberg. The increase of the number of piezoelectric driving elements decreases however the transducer's efficiency [Il. The low efficiency of transducers of this type is caused, it seems, through the mutual coupling of piezoelectric elements across the plate what impairs the total radiating resistance of the transducer. It is also-difficult to match precisely the resonant frequencies of piezoelectric elements and at the same time their mechanical parameters : mass, resistance, elasticity modulus, etc. These differencies between piezoelectric elements are impairing their driving action as the asymmetry of the excitation induces the differences of phases on the vibrating surface as well as the cancelling of a part of the generated energy. Observations of the displacement patterns for resonant vibrations of the plate excited with a single piezoelectric element fixed in the middle show many Article published online by EDP Sciences and available at

2 ULTRASONIC TRANSDUCERS WITH VIBRATING PIEZOELECTRIC PLATES C6 259 modes of vibrations [2]. Radial vibrations are corresponding to lower frequencies whereas thickness vibrations and coupled vibrations - to higher frequencies. When the plate is excited by several elements the displacement patterns are more complicated (Fig. 1). shape to the driving element shape as well as restrains couplings between piezoelectric elements across the half-wave plate [l]. Each segment work separately like the resonator in the energy trapping filters. The segmented plate of a transducer of watts power with seven driving elements is presented in figure 2. Measurements are revealing an increased efficiency of such a transducer in comparison with f KHz f KHz mm-. FIG Displacement patterns for the resonante vibration or plate excited with seven piezoelectric elements. 3. Concave piezoelectric transducer with a plate dîvided into segments. - The division of the plate into segments allows a better matching of segment FIG Concave segmented transducer. FIG. 3. -The pattern of the acoustical pression in a focus plane of the concave transducer : a) frequency 295 khz ; b) frequency 287 khz.

3 C6-260 W. PAJEWSKI a solid half-wave plate transducer. The efficiency was about 75 % and the intensity in focus area about fifty W/cm2, while the total power delivered to the transducer was 100 VA. There is a self controlling mechanism which is opposed to focusing energy. As is known from the theory of focusing systems the increasing of the angle of the bowl decreases the focus area and increases the intensity in focus. But as is known from experiments 133 in this case a strong side lobes of radiation pressure appears which affects the focus where the intensity cannot increase much. Moreover, in the case of a concave transducer a strong acoustical coupling between segments exists through Iiquid medium. This coupling increases the acoustical reactance of the transducer and limits the real of radiated part acoustical energy. The pattern of acoustic pressure in focus plane of the segmented concave transducer (Fig. 3) shows strong side lobes (- 5 db) which is not convenient for application where the most important factor is energy density. On the figure 4 the acoustical pression on the axis of the transducer is presented. An improvement of the transducer focusing properties can be obtained by appropriated distribution of piezoelectric elements and by adjusting, their vibration amplitudes. In order to obtain a maximum efficiency the segment dimensions should be matched to the dimen- FIG The acoustical pression on the axis of the concave transducer (frequency 295 khz). sions of piezoelectric elements. The ratio of the corresponding should be not inferior than the ratio of ultrasound velocities in the driving element and in the plate. 4. The electrical properties of the concave transducer. - Some of interesting electrical properties of the transducer can be deduced from the admittance diagram for not loaded and loaded transducer, presented in the figure 5. The diagram is not a circle fc=288,100 khz R-lOQ 20 - R=36Q cos <9=0,83 FIG. 5. -The admittance diagram of the transducers with piezoelectric plates : a) in air ; b) in water.

4 ULTRASONIC TRANSDUCERS WITH VIBRATING PIEZOELECTRIC PLATES C6-261 as usually, because the piezoelectric elements were not well adjusted to the common resonante frequency. The part of the diagram near the resonance is deformed and has a band of frequencies with constant resistance, like in the pass-band filter. The transducer mentioned above has three different main resonant frequencies 286.0,289.6 and 295 khz, but work, as experiments show, on the frequency 295 and 286 khz. The resonance at khz being practically not important. It is very interesting that the transducer works better on the resonant frequency 295 khz that in this case we get a good concentration of the ultrasonic energy in spite of strong side lobes (- 5 db) (Fig. 3). For resonant frequency 286 khz the patterns are better, the central lobe is stronger than side lobes (+ 15 db) but the total power is weaker. Explanation of a such phenomenon can be based on figure 5 and figure 6. the situation is improved because the transistorized generators can work well with low resistance load. Moreover, we have the possibility to change the electrical resistance of the loaded transducer by changing the thickness of the face plate. The formula for calculation the electrical resistance of the transducer as a function of an acoustical radiation and loss resistance R is Where a> : ratio of electromechanical transformer ; a : coefficient which is equal 0.25 in the case when the plates are just half wave each. In the table 1 the coefficient a is presented in function of thickness -dd of face plate in the case resonance of the system. Dependence of the coeficient a from the thickness and material of the face plate of the transducer elecfrical egurvalent circuit of fhe transducer 6) f, - 294,I kiiz f, = k ~ z noload woier l O ad 6/70 R Frç The electrical equivalent circuit of the transducer : a) two resonance in air (no load) ; b) second resonance in air (no load) ; c) second resonance with water load. d dd Material (2) (Ad> a Aluminium PZT O Steel PZT O Titan PZT The capacity of the transducer in vicinity of the PZT second resonance is compensated by the inductivity of the first resonance circuit ; as a result the power factor of the transducer working at the second resonance frequency is greater and greater real power is delivered to the transducer circuit. This idea is in good agreement with the experiment, but it is not clear why the feedback-compled generator selects this frequency for work. May be in the second case the condition for better electrical coupling and matching exist, because the resistance of the transducer for this frequency is greater (and the experiment was carried out with valve generator). The low resistivity of the loaded transducer limits the influence of it's capacity and increases the power factor. From another side the low resistivity is not convenient for electronic generators. - These two conditions are opposed to each other. Recently FIG Concave transducer at work.

5 C6-262 W. PAJEWSKI As can be seen from the table 1 it is possible to increase the electrical resistance nearly two times for dd = 0.6 Ad in the case of an aluminium plate. The use of the face plate reduced also the effective electromechanical coupling factor of the transducer, because with the face plate we introduced the additional stiffness to the system and increased the mechanical Q-factor. The potential energy stored in the stiffness of the plate does not participates in coupling process. Theoretically only in the case when the thickness of the plates are half a wave there is no degradation of coupling factor. 5. Conclusion. - On the base of measurements carried out for transducers with metal segmented bowl it can be stated that the problem of focusing of ultrasonic energy and geting the high power of ultrasound is very complicated. The theory of focusing systems is not sufficient to solve al1 the problems connected with the application of high intensity ultrasound. References [l] PAJEWSKI W., Piezoelectric transducer, Pat. PRL, Nr (1968). [2] PAJEWSKI W., Etude de rayonnement des transductures à céramiques piézoélectriques. Se Congr. Inter. dyacoust. Liège (1965) com [3] PAJEWSKI W., Acoustic focusing systems with non uniform particles velocity distribution VI1 Int. Congr. on Acoustics, Budapest (1971), com. 19, p. 8. [4] PAJEWSKI W., GAZANH-ES Cl., GARNIER J. L., Champ ultrasonore de disques de titanate de baryum et de quartz émettant dans un liquide. C. R. Acad. Sci. Paris, 262 (1966), [5] ROSENBERG L. D., SIROTIUK M. G., Ustanowka dla poluczenia fokusirowannogo ultrazwuka wysokoj intensiwnosti, Akust. Zh., 5 (1959), [6] Ross E. D., Underwater transducers, Patent USA , J. Acoust. Soc. Am., 22 (1950), 318. [7] WILLIAMS A. LW, Electroacoustic device, Patent USA Nr , septembre 1950, J. Acoust. Soc. Am., 25 (1953), 1220.