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Selecting passive and active materials for 1.3 composite power transducers
Ultrasonics 40 (2002) 895–901 www.elsevier.com/locate/ultras
Selecting passive and active materials for 1.3 composite power transducers C. Richard *, L. Goujon, D. Guyomar, H.S. Lee, G. Grange Laboratoire de G enie Electrique et Ferro electricit e, INSA Batiment G. Ferri e, 20 Avenue A. Einstein, 69621 Villeurbanne Cedex, France
Abstract 1.3 PZT-polymer composites were fabricated using the dice and fill method with various PZT types and volume fractions. These composites were evaluated for power underwater transducer applications with an air backed and no matching layer configuration. Electrical input and acoustical output powers were monitored as a function of the drive level. Total acoustic power densities of 30 W/cm2 were obtained with a P189/epoxy piezocomposite vibrating at 350 kHz with a low duty cycle (1–5%) and with a 90% efficiency. Power densities up to 20 W/cm2 were measured with a 50% duty cycle. Evolution and destruction of the transducers were monitored versus increasing averaged power. It was observed that better efficiencies were obtained with low volume fraction configurations allowing natural acoustic impedance matching to water. It was found that hard PZT type (Navy III) are optimal compositions even for piezocomposite transducers. It is shown that, unlike a common belief, the polymer mechanical losses are comparable to those of the active ceramic justifying that 1.3 piezocomposites are suited for low-cost power applications. In fact, the main limitation induced by the polymer phase is a strong thermal breakdown when the temperature of the transducer approaches the glass transition region of the polymer. Measurements of the polymer losses as a function of the temperature were obtained confirming this point and offering interesting new alternatives for future composite power transducers. Ó 2002 Elsevier Science B.V. All rights reserved. Keywords: Piezoelectric composite; Ultrasonic transducer; Efficiency; Thermal modeling
1. Introduction A 1.3 connectivity piezocomposite consists of several PZT rods embedded in a polymer matrix [1]. This kind of structure allows to associate the electromechanical properties of the ceramic to the low acoustic impedance of the polymer for improving the transducer acoustic properties that can be tuned to the desired application by adjusting the composite phases. They have been widely used for medical imaging and non-destructive testing. This paper deals with the study of piezocomposite for underwater power applications in the 300–400 kHz frequency range. The objective of this work is to determine among different PZT types and volume fractions, the suitable configuration for power emission in the case of a transducer with no matching layer and an air backed configuration.
*
Corresponding author. Tel.: +33-472-43-82-86; fax: +33-472-4385-13. E-mail address: [email protected] (C. Richard).
In Section 2, the experimental transducers and the measurement conditions will be described. Then the results for low electrical input will be presented in Section 3 and compared with those obtained theoretically with the KLM model [2]. The one dimensional character of the vibration of the composite with regard to the massive case will especially be discussed. The measurement results under high electrical input and low duty cycle (up to 40 W/cm2 at 1% duty cycle) will be presented in Section 4. They show that hard PZT type based piezocomposites present the lowest mechanical losses and that best efficiencies are obtained with low to medium volume fractions of PZT. Piezocomposites appear to be more promising than bulk transducers for high power applications in water. An interpretation of this adequation to high power sources will be given using a KLM modeling of the transducer with losses. The results obtained when the duty cycle is increased, while keeping constant the drive level are presented in Section 5. The role of the polymer in the destruction of the composites by excessive heating will be pointed out.
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A method for a proper characterization of the polymer phase is discussed and examples of various polymer behaviors with the temperature are given. Finally, by mean of thermal finite element modeling, the early destruction of low PZT volume fraction composites when increasing the total power is explained in Section 6 by smaller thermal exchanges with the water because of the low thermal conductivity of the polymer. A trade-off between thermal exchange with water and efficiency is pointed out as a key factor for the design of power piezocomposites.
2. Experimental set-up The PZT materials used in this study are P188 (Navy type II), P762 (Navy I), and P189 (Navy III), made by Saint-Gobain-Quartz (Nemours–France). The polymer is an epoxy resin (Araldite D with HY956 hardener from Ciba Specialties). The composite acoustic transducers, 36 mm in diameter, are fabricated with the ‘‘dice and fill’’ method, from a poled ceramic disk. Due to the periodicity of the structure, lateral modes take place in the frequency range of interest. Their resonance frequencies can be predicted with various dynamic models [3,4]. To avoid interference with these resonant modes, the dicing of the various samples has been tailored according to Ref. [4]. As a basis for comparison, bulk ceramic transducers have also been built. The transducers thicknesses, have been adapted in order to get antiresonance frequencies near 400 kHz. For temperature measurements, a thermocouple is installed at the periphery of the transducers, and the transducer radiating face is encapsulated with a thin layer of polyurethane for electrical insulation. The transducer samples are mounted in a housing, ensuring air backing condition and one radiating face. This face is located in the center of the housing front face, large enough to be considered as an infinite rigid baffle. The housing is immersed in a 2 m 1 m 1 m water tank. In the frequency range of interest, these dimensions allow far field condition measurements. The transducers are driven with monochromatic sinusoidal low duty cycle tone bursts with a maximum length of 60 periods, ensuring free field radiation conditions. The sound pressure level is measured with a broad band (up to 1.5 MHz) lead titanate based hydrophone, which has been calibrated by a comparison method [5] with a GEC-Marconi Y-33-7638 hydrophone. The acoustic pressure is measured 40 ls after the beginning of the burst where the transient regime is died out and no echos against the hydrophone’s holder spoils the signal. If the receiver is in the far field the total acoustic power radiated is calculated [5] with
Pr ¼
4p po2 Zo Rh
ð1Þ
Rh is the directivity index, computed by integration of the full directivity pattern measured at low level. Zo is the acoustic impedance of water, po is the measured rms pressure taken at 1 m in the axis of the transducer and k is the acoustic wavelength. At high pressure level, harmonic generation due to non-linear wave propagation was observed on the hydrophone signal. It has at least two consequences on the output power measurements. First, part of the energy is transferred to higher frequency overtones for which the attenuation in water is greater. This energy transfer leads to a saturation of the radiated power. Secondly, the most important error arises from the fall of the directivity index when increasing the radiated pressure. A measurement of the directivity pattern for a total radiated power of 350 W, with a 53% PZT-polymer transducer, allowed to evaluate the error as a 2 dB maximum underestimate of the acoustic power.
3. Low-level measurements The transmitting voltage response (TVR), the 3 dB relative bandwidth and the 3 dB beamwidth have been measured for each transducer. Since the resonant frequencies are close together, these measurements have shown that the TVR and the bandwidth were only dependent on the PZT volume fraction. The beamwidth, which only depends on the frequency and the geometry, is near 8° for each transducer vibrating on a pure mode. Experimental results are summarized in Table 1 and are compared to theoretical predictions made with a lossless KLM model. The relative bandwidth decreases while the transmitting sensitivity globally increases with the PZT volume fraction. Theoretical and measurement results are in good agreement for piezocomposites. It is not the case with massive PZT samples for which the discrepancies are obvious. This is illustrated on Fig. 1 where the theoretical and experimental TVR, as a function of frequency, are represented for a 53% piezocomposite (D4A) and a bulk PZT (D2B) transducer. The experimental plot clearly shows ‘‘spurious’’ modes on the bulk ceramic disk measurement. The directivity pattern of the bulk PZT transducer is also strongly affected by these ‘‘spurious’’ motions. For piezocomposite disks, the radial vibration is completely uncoupled and no parasitic mode is observed. The vibration has globally a one dimensional behavior, and justify that the monodimensional KLM modeling is well suited to predict the performances of piezocomposite transducers.
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Table 1 Composite transducer data and low-level acoustic properties Transducer ref.
PZT type
PZT (%)
Freq. Fs (kHz)
Max. TVR (dB ref. 1 lPa/V) Experiment
Theory
Experiment
Theory
D1A, D2A D4A D2B D5A, D6A D5B D12A D7A, D8A D7B
P762 P762 P762 P188 P188 P189 P189 P189
31 53 100 53 100 20 53 100
346 331 364 301 380 365 340 380
174 176 175 177 179 171 177 176
172 176 180 177 179 170 177 182
14.5 9.3 5.5 10 4.8 13 8.0 4.4
13.5 10.0 4.0 11.5 5.0 16 9.0 4.0
Fig. 1. Experimental (thick lines) and theoretical (thin lines) TVR of bulk P762 PZT (D2B) and 53% P762 composite (D4A) transducers.
Relative bandwidth (%)
Fig. 2. Total losses (instantaneous) in a 53% piezocomposite transducer. Measured for various instantaneous input power and 1% duty cycle (constant transducer temperature), for P188 based (––), P762 based ( ), and P189 based transducers ( ).
4. High level––short burst 4.1. Measurements It was shown in the low driving level regime (Section 3) that the PZT type has a small influence on the transducer TVR. This parameter has no direct energetic meaning, and is essentially representative of the transducer impedance and coupling, more affected by the PZT volume fraction and transducer geometry, than by the PZT type itself. The losses or the efficiency are the main parameters that control the transducer performance in the high driving regime. The transducers losses, versus instantaneous input power at 1% duty cycle, are represented on Fig. 2 for the 53% piezocomposite transducers made with different PZT materials. Despite the presence of the viscoelastic polymer (tan dm ffi 4%), this shows that the PZT type still has a strong influence on the composites performances. So, for high power applications of piezocomposites, hard PZT like P189 or new fluoridated PZT [6], are still of major interest. For input powers above 250 W, the losses increase abnormally. This effect is due to
harmonic generation and its consequences on the directivity index as mentioned in Section 2. The output power is undervalued and then the losses over estimated. The losses of P762 based transducers are plotted on Fig. 3 for the different PZT volume fractions and as a function of the input power. It appears that the global losses increase with the PZT volume fraction. For a 53% piezocomposite, it is noticeable that the losses are about twice smaller than those of the massive transducer. Similar results are observed for Navy III composite transducers (P189). Hence, despite a lower TVR, piezocomposites with low to medium PZT volume fractions have to be preferred for high electrical input because of higher efficiencies. For the different transducers, the efficiencies measured at 10 W/cm2 of input power density have been summarized in Table 2. The best configurations for short burst measurements are the P189 based piezocomposites with 53% and 20% PZT volume fraction where efficiencies reach up the 92–95% range. They are closely followed by the 31% P762 based, with an efficiency of 91%.
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Fig. 3. Losses in the same conditions as in Fig. 2 for composite transducers with various PZT P762 volume fractions: 100% (––), 53% ( ) and 31% ( ).
Table 2 1.3 composite transducer efficiencies PZT volume fraction (%)
PZT Type P762 (Navy I)
P188 (Navy II)
P189 (Navy III)
100 53 31 20
71% 84% 91% –
67% 67% – –
80% 92–95% – 92%
Fig. 4. Theoretical piezocomposite mechanical loss angle (thin lines) and efficiencies (thick lines) as a function of the PZT volume fraction for various PZT types. Losses are computed with a simple homogeneization model and efficiency is obtained with a KLM model with losses.
tions are greater when the loss angle of the PZT is important showing that the PZT material losses can be largely comparable to the polymer ones. So there is a trade-off between these effects, which is favorable to the low to medium volume fraction composites made with hard PZT materials.
5. High level––long burst 4.2. Interpretation 5.1. Measurements Fig. 4 shows the composite theoretical mechanical loss angles (thin lines) and the efficiencies (thick lines) versus the PZT volume fraction for P189, P188 and P762. The transducer efficiencies have been computed using the KLM model. The input parameters including the loss angles have been obtained with a classic homogenization approach in which losses were introduced with imaginary parts on the stiffness and permittivity matrixes of both the PZT and the polymer. PZT losses introduced in the model are measured on rods using usual methods and are inaccurate to predict losses of massive disk shaped transducers. The higher volume fraction (above 80%) results shown in Fig. 4 are then not truly representative. The polymer losses are measured with the method described in Section 5. Despite the steady rise of the loss angle while decreasing the PZT volume fraction, the efficiency of piezocomposites presents a maximum for a 10–30% PZT volume fraction. As the PZT volume fraction decreases, the rise of the loss angle is compensated by a better acoustic impedance matching to water. Fig. 4 points out that this second effect is preponderant as long as the global losses are small enough. The global losses varia-
The instantaneous input power is in this case set at 250 W and the total input power is increased by increasing the burst length, while the burst rate is kept constant (100 Hz). The axial radiated pressure and the peripheral transducer temperature are measured when the thermal equilibrium is reached (a few minutes after the power step). The duty cycle is then increased and this process is repeated until the transducer destruction is reached, which looks like a thermal avalanche process (Fig. 5). Fig. 6 shows the equilibrium temperature of the transducer versus the duty cycle. These plots are nearly straight with a slope representative of the losses. The curves are interrupted by the transducer destruction figured with a square marker. For all of them, the destruction begins in the 50–65 °C temperature range. The axial pressure is rather steady up to the failure and then drops suddenly. The principal mode of destruction is the debonding of the electrode layer as a consequence of the generated heat. Among piezocomposites, the P189/epoxy type presents the best performances, since 50% duty cycle is reached without significant damages.
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fraction, allowing higher duty cycle operation. Now, even if the 31% P762 piezocomposite presents an efficiency close to the P189 53% composite, as the area of ceramic in contact with the water is smaller, thermal exchanges are lower, this raises the temperature and precipitates the transducer failure. For this reason, bulk transducers can work under higher duty cycle (about 70%) and higher temperatures than piezocomposites. 5.2. Epoxy phase characterization
Fig. 5. Variation of the composite temperature with time during the high-level long burst evaluation of a 50% P189/epoxy piezocomposite (D7A). Instantaneous input power is 250 W and the duty cycle is increased by 5% steps.
Fig. 6. Piezocomposite transducer working temperature as a function of the burst duty cycle. The instantaneous power is 250 W. The squares represent the last steady regime prior breakdown. The dashed temperature area is the beginning of the polymer glass–rubber transition zone.
The temperature of the transducers, which causes their destruction, is in fact determined both by the losses and by the thermal exchange with the water. These exchanges are dependent both on the thermal conductivity of the materials (about 2 W/m2 °C for the PZT and 0.2 W/m2 °C for the polymer) and their respective areas in contact with the water. For piezocomposites of the same volume fraction, exchange areas or the thermal resistance are nearly the same. So, only the losses in the materials will differentiate them. Therefore, for a given duty cycle, the P189 based piezocomposite, which presents lower losses, has a temperature lower than the other piezocomposites with the same PZT volume
The increase of the polymer losses near the glassy transition zone is responsible for the transducer failures. To have a representation of it, the polymer mechanical losses have been evaluated as a function of the temperature. A parallelepipedic 25% P189/epoxy piezocomposite sample has been made. The sample is 3 mm wide, 14.6 mm long and 3.9 mm thick with the rods oriented along the thickness. Its first lateral resonance mode (approximately 60 kHz) quality factor has been monitored at low signal level as a function of the temperature. Because of the composite anisotropy and of the low PZT volume fraction and losses (tan d ffi 0:08%), mechanical losses on this mode are mainly due to the polymer (mechanically in series connection with the PZT) and the PZT contribution is ignored, therefore a direct measurement of the polymer losses is obtained. This assumption has been checked at room temperature by a measurement of the polymer losses with an ultrasonic method [7] which gave a value of 3.9% at 25 °C, instead of the 3.1% obtained by the composite resonance way. Fig. 7 shows the evolution of the loss angle of different polymers as a function of temperature. As expected for the Ciba Specialties Resin D used in the previous experiments, the loss angle which rises steadily below 60 °C, increases drastically above this temperature
Fig. 7. Mechanical losses (tan d) of various polymer resins as a function of temperature (measured at 60 kHz).
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when reaching the glass–rubber transition zone. If in the low increase rate region, the piezocomposite temperature always reaches an equilibrium, when the loss increase is steep, the heating of the polymer increases even more the losses of the transducer up to its destruction. In order to make composite transducers for higher power rates, a better stability of the passive materials is needed and especially to shift up the thermal avalanche zone, resins with a higher transition temperature are required. Also plotted on Fig. 7 are the losses for two polymer candidates (Resins 1 and 2) evaluated in the same way and which are also interesting since they exhibit a low viscosity and rather low curing temperatures. As shown in Fig. 7, the failure temperature can be moved higher than 130 °C, making them promising materials for power piezocomposite design.
6. Thermal analysis The thermal behavior of bulk and composite transducers in the permanent regime, has been simulated using finite element modeling [7,8]. The transducer model is constituted of a bulk or composite disk, surrounded by epoxy and polyurethane rings as in the experimental case. Five PZT volume fractions have been studied: 100%, 53%, 31%, 25% and 9%. Due to symmetry considerations, only one eighth of the structure was meshed. Boundary conditions outcome from the experimental set-up. The water is considered as an purely diffusive infinite medium and we assume that no thermal convection take place which is reasonable for low temperatures. Consequently, the temperature is constant on the radiating face. The good thermal conductivity of the metallic housing surrounding the structure and which is in contact to water allows also to assume a constant temperature on the peripheral face. Finally, no thermal exchanges between the rear transducer face and air are considered, therefore, the heat flow through this face is null. The heat sources are the PZT rods and the polymer matrix losses that can be obtained through the transducer efficiency and input or radiated power. It was shown that as the thermal diffusion scale is large compared to the composite pitch, the results are quite independent on the distribution of the losses between the PZT and the matrix. This was shown by the isothermal plots which were found to be parallel to the transducer front face, and the thermal gradients due to the PZT rods or the polymer strips were very weak, showing a piezocomposite as a rather homogeneous medium from a thermal point of view. For computations, the global losses were consequently equally distributed between both phases. Fig. 8 represents the computed temperature increase of P762 and P189 based piezocomposites as a function
Fig. 8. Theoretical temperature elevation (obtained with thermal FEM modeling) of a piezocomposite disk radiating a 20 W acoustic power in water as a function of the PZT volume fraction for P762 and P189 materials.
of the PZT volume fraction for a constant radiated power of 20 W (i.e. 200 W with a 10% duty cycle). Both curves show a minimum, one near 50% for P189 based piezocomposites, the other near 30% for P762 based piezocomposites. Because a higher heating means an early destruction when increasing the duty cycle, Fig. 9 shows that among piezocomposites, the best suited configuration is close to 50% P189/epoxy, as experimentally observed. The minimum heating shown in Fig. 8 is representative of a trade-off between the thermal exchange resistance which decreases and the total losses which increases in the same time with the PZT volume fraction.
7. Conclusion 1.3 piezocomposites made with different PZT type and various PZT volume fractions have been tested under high driving signals. The measurements for high instantaneous input power (up to 40 W/cm2 ) and low duty cycle have shown that 1.3 piezocomposites are more adapted to high power applications than bulk transducers because of their higher efficiencies. This results from the better impedance matching to water. The efficiency is governed by a trade-off between the loss angle and the characteristic impedance of the composite, which is to some extend favorable to low to medium PZT volume fractions. Losses in piezocomposites are strongly dependent on the PZT material type and hard PZT are optimal compositions even for piezocomposite transducers.
C. Richard et al. / Ultrasonics 40 (2002) 895–901
At low duty cycle (1%), the best configurations were obtained with a 53% and a 20% P189/epoxy piezocomposite vibrating at 350 and 365 kHz respectively with a total efficiency of 92–95%. Output power densities of 30 W/cm2 have been achieved. It is shown that the glass rubber transition of the polymer induces a strong limitation especially for low PZT volume fractions in long burst applications. Then using polymers with higher transition temperatures could bring great improvements in the composite transducers performances. Finally, it is pointed out that a power piezocomposite design is governed by a second trade-off between efficiency and thermal exchanges. Numerical modeling have shown that 50% P189 based piezocomposite is the best suited configuration for high power applications.
901
References [1] R.E. Newnham, L.J. Bowen, K.A. Klicker, L.E. Cross, Material in Engineering 2 (1980) 93. [2] D.A. Leedom, R. Krimholtz, G.L. Matthaei, IEEE Transactions on Sonics and Ultrasonics SU-18 (3) (1971) 128. [3] Q.M. Zhang, X. Geng, Journal of Applied Physics 76 (10) (1994) 6014. [4] C. Richard, D. Guyomar, L. Eyraud, in: Proceedings of the 10th IEEE-ISAF Symposium, vol. 1, 1996, p. 39. [5] R.J. Bobber, Underwater Electroacoustic Measurements, Peninsula Publishing, 1988. [6] L. Eyraud, M. Boisrayon, P. Eyraud, F. Eyraud, D. Audigier, Ferroelectric Perovskite––US Patent no. 5,683,613, November 4, 1997. [7] L. Goujon, Study of 1-3 piezoelectric composites for electroacoustic underwater application, Ph.D. Thesis, Insa Lyon, December 1999 (in French). [8] MODULEF, A modular finite element software, Rocquencourt (France): INRIA, 1985 (in French).
Selecting passive and active materials for 1.3 composite power transducers C. Richard *, L. Goujon, D. Guyomar, H.S. Lee, G. Grange Laboratoire de G enie Electrique et Ferro electricit e, INSA Batiment G. Ferri e, 20 Avenue A. Einstein, 69621 Villeurbanne Cedex, France
Abstract 1.3 PZT-polymer composites were fabricated using the dice and fill method with various PZT types and volume fractions. These composites were evaluated for power underwater transducer applications with an air backed and no matching layer configuration. Electrical input and acoustical output powers were monitored as a function of the drive level. Total acoustic power densities of 30 W/cm2 were obtained with a P189/epoxy piezocomposite vibrating at 350 kHz with a low duty cycle (1–5%) and with a 90% efficiency. Power densities up to 20 W/cm2 were measured with a 50% duty cycle. Evolution and destruction of the transducers were monitored versus increasing averaged power. It was observed that better efficiencies were obtained with low volume fraction configurations allowing natural acoustic impedance matching to water. It was found that hard PZT type (Navy III) are optimal compositions even for piezocomposite transducers. It is shown that, unlike a common belief, the polymer mechanical losses are comparable to those of the active ceramic justifying that 1.3 piezocomposites are suited for low-cost power applications. In fact, the main limitation induced by the polymer phase is a strong thermal breakdown when the temperature of the transducer approaches the glass transition region of the polymer. Measurements of the polymer losses as a function of the temperature were obtained confirming this point and offering interesting new alternatives for future composite power transducers. Ó 2002 Elsevier Science B.V. All rights reserved. Keywords: Piezoelectric composite; Ultrasonic transducer; Efficiency; Thermal modeling
1. Introduction A 1.3 connectivity piezocomposite consists of several PZT rods embedded in a polymer matrix [1]. This kind of structure allows to associate the electromechanical properties of the ceramic to the low acoustic impedance of the polymer for improving the transducer acoustic properties that can be tuned to the desired application by adjusting the composite phases. They have been widely used for medical imaging and non-destructive testing. This paper deals with the study of piezocomposite for underwater power applications in the 300–400 kHz frequency range. The objective of this work is to determine among different PZT types and volume fractions, the suitable configuration for power emission in the case of a transducer with no matching layer and an air backed configuration.
*
Corresponding author. Tel.: +33-472-43-82-86; fax: +33-472-4385-13. E-mail address: [email protected] (C. Richard).
In Section 2, the experimental transducers and the measurement conditions will be described. Then the results for low electrical input will be presented in Section 3 and compared with those obtained theoretically with the KLM model [2]. The one dimensional character of the vibration of the composite with regard to the massive case will especially be discussed. The measurement results under high electrical input and low duty cycle (up to 40 W/cm2 at 1% duty cycle) will be presented in Section 4. They show that hard PZT type based piezocomposites present the lowest mechanical losses and that best efficiencies are obtained with low to medium volume fractions of PZT. Piezocomposites appear to be more promising than bulk transducers for high power applications in water. An interpretation of this adequation to high power sources will be given using a KLM modeling of the transducer with losses. The results obtained when the duty cycle is increased, while keeping constant the drive level are presented in Section 5. The role of the polymer in the destruction of the composites by excessive heating will be pointed out.
0041-624X/02/$ - see front matter Ó 2002 Elsevier Science B.V. All rights reserved. PII: S 0 0 4 1 - 6 2 4 X ( 0 2 ) 0 0 2 2 1 - 4
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A method for a proper characterization of the polymer phase is discussed and examples of various polymer behaviors with the temperature are given. Finally, by mean of thermal finite element modeling, the early destruction of low PZT volume fraction composites when increasing the total power is explained in Section 6 by smaller thermal exchanges with the water because of the low thermal conductivity of the polymer. A trade-off between thermal exchange with water and efficiency is pointed out as a key factor for the design of power piezocomposites.
2. Experimental set-up The PZT materials used in this study are P188 (Navy type II), P762 (Navy I), and P189 (Navy III), made by Saint-Gobain-Quartz (Nemours–France). The polymer is an epoxy resin (Araldite D with HY956 hardener from Ciba Specialties). The composite acoustic transducers, 36 mm in diameter, are fabricated with the ‘‘dice and fill’’ method, from a poled ceramic disk. Due to the periodicity of the structure, lateral modes take place in the frequency range of interest. Their resonance frequencies can be predicted with various dynamic models [3,4]. To avoid interference with these resonant modes, the dicing of the various samples has been tailored according to Ref. [4]. As a basis for comparison, bulk ceramic transducers have also been built. The transducers thicknesses, have been adapted in order to get antiresonance frequencies near 400 kHz. For temperature measurements, a thermocouple is installed at the periphery of the transducers, and the transducer radiating face is encapsulated with a thin layer of polyurethane for electrical insulation. The transducer samples are mounted in a housing, ensuring air backing condition and one radiating face. This face is located in the center of the housing front face, large enough to be considered as an infinite rigid baffle. The housing is immersed in a 2 m 1 m 1 m water tank. In the frequency range of interest, these dimensions allow far field condition measurements. The transducers are driven with monochromatic sinusoidal low duty cycle tone bursts with a maximum length of 60 periods, ensuring free field radiation conditions. The sound pressure level is measured with a broad band (up to 1.5 MHz) lead titanate based hydrophone, which has been calibrated by a comparison method [5] with a GEC-Marconi Y-33-7638 hydrophone. The acoustic pressure is measured 40 ls after the beginning of the burst where the transient regime is died out and no echos against the hydrophone’s holder spoils the signal. If the receiver is in the far field the total acoustic power radiated is calculated [5] with
Pr ¼
4p po2 Zo Rh
ð1Þ
Rh is the directivity index, computed by integration of the full directivity pattern measured at low level. Zo is the acoustic impedance of water, po is the measured rms pressure taken at 1 m in the axis of the transducer and k is the acoustic wavelength. At high pressure level, harmonic generation due to non-linear wave propagation was observed on the hydrophone signal. It has at least two consequences on the output power measurements. First, part of the energy is transferred to higher frequency overtones for which the attenuation in water is greater. This energy transfer leads to a saturation of the radiated power. Secondly, the most important error arises from the fall of the directivity index when increasing the radiated pressure. A measurement of the directivity pattern for a total radiated power of 350 W, with a 53% PZT-polymer transducer, allowed to evaluate the error as a 2 dB maximum underestimate of the acoustic power.
3. Low-level measurements The transmitting voltage response (TVR), the 3 dB relative bandwidth and the 3 dB beamwidth have been measured for each transducer. Since the resonant frequencies are close together, these measurements have shown that the TVR and the bandwidth were only dependent on the PZT volume fraction. The beamwidth, which only depends on the frequency and the geometry, is near 8° for each transducer vibrating on a pure mode. Experimental results are summarized in Table 1 and are compared to theoretical predictions made with a lossless KLM model. The relative bandwidth decreases while the transmitting sensitivity globally increases with the PZT volume fraction. Theoretical and measurement results are in good agreement for piezocomposites. It is not the case with massive PZT samples for which the discrepancies are obvious. This is illustrated on Fig. 1 where the theoretical and experimental TVR, as a function of frequency, are represented for a 53% piezocomposite (D4A) and a bulk PZT (D2B) transducer. The experimental plot clearly shows ‘‘spurious’’ modes on the bulk ceramic disk measurement. The directivity pattern of the bulk PZT transducer is also strongly affected by these ‘‘spurious’’ motions. For piezocomposite disks, the radial vibration is completely uncoupled and no parasitic mode is observed. The vibration has globally a one dimensional behavior, and justify that the monodimensional KLM modeling is well suited to predict the performances of piezocomposite transducers.
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Table 1 Composite transducer data and low-level acoustic properties Transducer ref.
PZT type
PZT (%)
Freq. Fs (kHz)
Max. TVR (dB ref. 1 lPa/V) Experiment
Theory
Experiment
Theory
D1A, D2A D4A D2B D5A, D6A D5B D12A D7A, D8A D7B
P762 P762 P762 P188 P188 P189 P189 P189
31 53 100 53 100 20 53 100
346 331 364 301 380 365 340 380
174 176 175 177 179 171 177 176
172 176 180 177 179 170 177 182
14.5 9.3 5.5 10 4.8 13 8.0 4.4
13.5 10.0 4.0 11.5 5.0 16 9.0 4.0
Fig. 1. Experimental (thick lines) and theoretical (thin lines) TVR of bulk P762 PZT (D2B) and 53% P762 composite (D4A) transducers.
Relative bandwidth (%)
Fig. 2. Total losses (instantaneous) in a 53% piezocomposite transducer. Measured for various instantaneous input power and 1% duty cycle (constant transducer temperature), for P188 based (––), P762 based ( ), and P189 based transducers ( ).
4. High level––short burst 4.1. Measurements It was shown in the low driving level regime (Section 3) that the PZT type has a small influence on the transducer TVR. This parameter has no direct energetic meaning, and is essentially representative of the transducer impedance and coupling, more affected by the PZT volume fraction and transducer geometry, than by the PZT type itself. The losses or the efficiency are the main parameters that control the transducer performance in the high driving regime. The transducers losses, versus instantaneous input power at 1% duty cycle, are represented on Fig. 2 for the 53% piezocomposite transducers made with different PZT materials. Despite the presence of the viscoelastic polymer (tan dm ffi 4%), this shows that the PZT type still has a strong influence on the composites performances. So, for high power applications of piezocomposites, hard PZT like P189 or new fluoridated PZT [6], are still of major interest. For input powers above 250 W, the losses increase abnormally. This effect is due to
harmonic generation and its consequences on the directivity index as mentioned in Section 2. The output power is undervalued and then the losses over estimated. The losses of P762 based transducers are plotted on Fig. 3 for the different PZT volume fractions and as a function of the input power. It appears that the global losses increase with the PZT volume fraction. For a 53% piezocomposite, it is noticeable that the losses are about twice smaller than those of the massive transducer. Similar results are observed for Navy III composite transducers (P189). Hence, despite a lower TVR, piezocomposites with low to medium PZT volume fractions have to be preferred for high electrical input because of higher efficiencies. For the different transducers, the efficiencies measured at 10 W/cm2 of input power density have been summarized in Table 2. The best configurations for short burst measurements are the P189 based piezocomposites with 53% and 20% PZT volume fraction where efficiencies reach up the 92–95% range. They are closely followed by the 31% P762 based, with an efficiency of 91%.
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Fig. 3. Losses in the same conditions as in Fig. 2 for composite transducers with various PZT P762 volume fractions: 100% (––), 53% ( ) and 31% ( ).
Table 2 1.3 composite transducer efficiencies PZT volume fraction (%)
PZT Type P762 (Navy I)
P188 (Navy II)
P189 (Navy III)
100 53 31 20
71% 84% 91% –
67% 67% – –
80% 92–95% – 92%
Fig. 4. Theoretical piezocomposite mechanical loss angle (thin lines) and efficiencies (thick lines) as a function of the PZT volume fraction for various PZT types. Losses are computed with a simple homogeneization model and efficiency is obtained with a KLM model with losses.
tions are greater when the loss angle of the PZT is important showing that the PZT material losses can be largely comparable to the polymer ones. So there is a trade-off between these effects, which is favorable to the low to medium volume fraction composites made with hard PZT materials.
5. High level––long burst 4.2. Interpretation 5.1. Measurements Fig. 4 shows the composite theoretical mechanical loss angles (thin lines) and the efficiencies (thick lines) versus the PZT volume fraction for P189, P188 and P762. The transducer efficiencies have been computed using the KLM model. The input parameters including the loss angles have been obtained with a classic homogenization approach in which losses were introduced with imaginary parts on the stiffness and permittivity matrixes of both the PZT and the polymer. PZT losses introduced in the model are measured on rods using usual methods and are inaccurate to predict losses of massive disk shaped transducers. The higher volume fraction (above 80%) results shown in Fig. 4 are then not truly representative. The polymer losses are measured with the method described in Section 5. Despite the steady rise of the loss angle while decreasing the PZT volume fraction, the efficiency of piezocomposites presents a maximum for a 10–30% PZT volume fraction. As the PZT volume fraction decreases, the rise of the loss angle is compensated by a better acoustic impedance matching to water. Fig. 4 points out that this second effect is preponderant as long as the global losses are small enough. The global losses varia-
The instantaneous input power is in this case set at 250 W and the total input power is increased by increasing the burst length, while the burst rate is kept constant (100 Hz). The axial radiated pressure and the peripheral transducer temperature are measured when the thermal equilibrium is reached (a few minutes after the power step). The duty cycle is then increased and this process is repeated until the transducer destruction is reached, which looks like a thermal avalanche process (Fig. 5). Fig. 6 shows the equilibrium temperature of the transducer versus the duty cycle. These plots are nearly straight with a slope representative of the losses. The curves are interrupted by the transducer destruction figured with a square marker. For all of them, the destruction begins in the 50–65 °C temperature range. The axial pressure is rather steady up to the failure and then drops suddenly. The principal mode of destruction is the debonding of the electrode layer as a consequence of the generated heat. Among piezocomposites, the P189/epoxy type presents the best performances, since 50% duty cycle is reached without significant damages.
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fraction, allowing higher duty cycle operation. Now, even if the 31% P762 piezocomposite presents an efficiency close to the P189 53% composite, as the area of ceramic in contact with the water is smaller, thermal exchanges are lower, this raises the temperature and precipitates the transducer failure. For this reason, bulk transducers can work under higher duty cycle (about 70%) and higher temperatures than piezocomposites. 5.2. Epoxy phase characterization
Fig. 5. Variation of the composite temperature with time during the high-level long burst evaluation of a 50% P189/epoxy piezocomposite (D7A). Instantaneous input power is 250 W and the duty cycle is increased by 5% steps.
Fig. 6. Piezocomposite transducer working temperature as a function of the burst duty cycle. The instantaneous power is 250 W. The squares represent the last steady regime prior breakdown. The dashed temperature area is the beginning of the polymer glass–rubber transition zone.
The temperature of the transducers, which causes their destruction, is in fact determined both by the losses and by the thermal exchange with the water. These exchanges are dependent both on the thermal conductivity of the materials (about 2 W/m2 °C for the PZT and 0.2 W/m2 °C for the polymer) and their respective areas in contact with the water. For piezocomposites of the same volume fraction, exchange areas or the thermal resistance are nearly the same. So, only the losses in the materials will differentiate them. Therefore, for a given duty cycle, the P189 based piezocomposite, which presents lower losses, has a temperature lower than the other piezocomposites with the same PZT volume
The increase of the polymer losses near the glassy transition zone is responsible for the transducer failures. To have a representation of it, the polymer mechanical losses have been evaluated as a function of the temperature. A parallelepipedic 25% P189/epoxy piezocomposite sample has been made. The sample is 3 mm wide, 14.6 mm long and 3.9 mm thick with the rods oriented along the thickness. Its first lateral resonance mode (approximately 60 kHz) quality factor has been monitored at low signal level as a function of the temperature. Because of the composite anisotropy and of the low PZT volume fraction and losses (tan d ffi 0:08%), mechanical losses on this mode are mainly due to the polymer (mechanically in series connection with the PZT) and the PZT contribution is ignored, therefore a direct measurement of the polymer losses is obtained. This assumption has been checked at room temperature by a measurement of the polymer losses with an ultrasonic method [7] which gave a value of 3.9% at 25 °C, instead of the 3.1% obtained by the composite resonance way. Fig. 7 shows the evolution of the loss angle of different polymers as a function of temperature. As expected for the Ciba Specialties Resin D used in the previous experiments, the loss angle which rises steadily below 60 °C, increases drastically above this temperature
Fig. 7. Mechanical losses (tan d) of various polymer resins as a function of temperature (measured at 60 kHz).
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when reaching the glass–rubber transition zone. If in the low increase rate region, the piezocomposite temperature always reaches an equilibrium, when the loss increase is steep, the heating of the polymer increases even more the losses of the transducer up to its destruction. In order to make composite transducers for higher power rates, a better stability of the passive materials is needed and especially to shift up the thermal avalanche zone, resins with a higher transition temperature are required. Also plotted on Fig. 7 are the losses for two polymer candidates (Resins 1 and 2) evaluated in the same way and which are also interesting since they exhibit a low viscosity and rather low curing temperatures. As shown in Fig. 7, the failure temperature can be moved higher than 130 °C, making them promising materials for power piezocomposite design.
6. Thermal analysis The thermal behavior of bulk and composite transducers in the permanent regime, has been simulated using finite element modeling [7,8]. The transducer model is constituted of a bulk or composite disk, surrounded by epoxy and polyurethane rings as in the experimental case. Five PZT volume fractions have been studied: 100%, 53%, 31%, 25% and 9%. Due to symmetry considerations, only one eighth of the structure was meshed. Boundary conditions outcome from the experimental set-up. The water is considered as an purely diffusive infinite medium and we assume that no thermal convection take place which is reasonable for low temperatures. Consequently, the temperature is constant on the radiating face. The good thermal conductivity of the metallic housing surrounding the structure and which is in contact to water allows also to assume a constant temperature on the peripheral face. Finally, no thermal exchanges between the rear transducer face and air are considered, therefore, the heat flow through this face is null. The heat sources are the PZT rods and the polymer matrix losses that can be obtained through the transducer efficiency and input or radiated power. It was shown that as the thermal diffusion scale is large compared to the composite pitch, the results are quite independent on the distribution of the losses between the PZT and the matrix. This was shown by the isothermal plots which were found to be parallel to the transducer front face, and the thermal gradients due to the PZT rods or the polymer strips were very weak, showing a piezocomposite as a rather homogeneous medium from a thermal point of view. For computations, the global losses were consequently equally distributed between both phases. Fig. 8 represents the computed temperature increase of P762 and P189 based piezocomposites as a function
Fig. 8. Theoretical temperature elevation (obtained with thermal FEM modeling) of a piezocomposite disk radiating a 20 W acoustic power in water as a function of the PZT volume fraction for P762 and P189 materials.
of the PZT volume fraction for a constant radiated power of 20 W (i.e. 200 W with a 10% duty cycle). Both curves show a minimum, one near 50% for P189 based piezocomposites, the other near 30% for P762 based piezocomposites. Because a higher heating means an early destruction when increasing the duty cycle, Fig. 9 shows that among piezocomposites, the best suited configuration is close to 50% P189/epoxy, as experimentally observed. The minimum heating shown in Fig. 8 is representative of a trade-off between the thermal exchange resistance which decreases and the total losses which increases in the same time with the PZT volume fraction.
7. Conclusion 1.3 piezocomposites made with different PZT type and various PZT volume fractions have been tested under high driving signals. The measurements for high instantaneous input power (up to 40 W/cm2 ) and low duty cycle have shown that 1.3 piezocomposites are more adapted to high power applications than bulk transducers because of their higher efficiencies. This results from the better impedance matching to water. The efficiency is governed by a trade-off between the loss angle and the characteristic impedance of the composite, which is to some extend favorable to low to medium PZT volume fractions. Losses in piezocomposites are strongly dependent on the PZT material type and hard PZT are optimal compositions even for piezocomposite transducers.
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At low duty cycle (1%), the best configurations were obtained with a 53% and a 20% P189/epoxy piezocomposite vibrating at 350 and 365 kHz respectively with a total efficiency of 92–95%. Output power densities of 30 W/cm2 have been achieved. It is shown that the glass rubber transition of the polymer induces a strong limitation especially for low PZT volume fractions in long burst applications. Then using polymers with higher transition temperatures could bring great improvements in the composite transducers performances. Finally, it is pointed out that a power piezocomposite design is governed by a second trade-off between efficiency and thermal exchanges. Numerical modeling have shown that 50% P189 based piezocomposite is the best suited configuration for high power applications.
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