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Submitted on 1 Jan 1972
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ULTRASONIC TRANSDUCERS WITH VIBRATING PIEZOELECTRIC PLATES
W. Pajewski
To cite this version:
W. Pajewski. ULTRASONIC TRANSDUCERS WITH VIBRATING PIEZOELECTRIC PLATES.
Journal de Physique Colloques, 1972, 33 (C6), pp.C6-258-C6-262. �10.1051/jphyscol:1972655�. �jpa-
00215173�
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 trans- ducers 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 trans- ducer and the fluid medium. The ultrasound radiat- ing systems with half-wave plates are used for fre- quencies 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 Rosen- berg. 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 http://dx.doi.org/10.1051/jphyscol:1972655
ULTRASONIC TRANSDUCERS WITH VIBRATING PIEZOELECTRIC PLATES C6 259
modes of vibrations [2]. Radial vibrations are corres- ponding to lower frequencies whereas thickness vibrations and coupled vibrations - to higher fre- quencies.
When the plate is excited by several elements the displacement patterns are more complicated (Fig. 1).
f
-
295 KHzf
-
319 KHzshape 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 100-500 watts power with seven driving elements is presented in figure 2. Measurements are revealing an increased efficiency of such a transducer in comparison with
mm-.
FIG. 1. - 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. 2. - 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.
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 experi- ments 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 pres- sion on the axis of the transducer is presented.
An improvement of the transducer focusing pro- perties can be obtained by appropriated distribution of piezoelectric elements and by adjusting, their vibration amplitudes.
In order to obtain a maximum efficiency the seg- ment dimensions should be matched to the dimen-
FIG. 4. - 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
286.9
55 -
50 -
45 -
40 -
35 - 30 -
1 fc=288,100
kHz R - l O Q 20 -
R = 3 6 Q cos
<9=0,83
FIG. 5. -The admittance diagram of the transducers with piezoelectric plates : a) in air ; b) in water.
ULTRASONIC TRANSDUCERS WITH VIBRATING PIEZOELECTRIC PLATES C6-261 as usually, because the piezoelectric elements were
not well adjusted to the common resonante fre- quency. 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 diffe- rent 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 289.6 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 ultra- sonic 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.
elecfrical egurvalent
