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CHARACTERIZATION OF HIGH POWER PIEZOELECTRIC CERAMICS UNDER HIGH
MECHANICAL DRIVING LEVELS
P. Champ, P. Gonnard
To cite this version:
P. Champ, P. Gonnard. CHARACTERIZATION OF HIGH POWER PIEZOELECTRIC CERAMICS
UNDER HIGH MECHANICAL DRIVING LEVELS. Journal de Physique Colloques, 1990, 51 (C2),
pp.C2-621-C2-624. �10.1051/jphyscol:19902146�. �jpa-00230442�
1er Congrès Français d'Acoustique 1990
CHARACTERIZATION OF HIGH POWER PIEZOELECTRIC CERAMICS UNDER HIGH MECHANICAL DRIVING LEVELS
P. CHAMP and P. GONNARD*
Groupe d'Etudes Sous-Marine de l'Atlantique. VCAN Brest, F-29240 Brest
*'Laboratoire
6'de Génie Electrique et Férroélectrlclté, INSR Lyon, Bat.
504, 20 Avenue A. Einstein, F-69621 Villeurbanne, France
Résumé : U n e nouvelle méthode d e caractérisation des pertes mécaniques des céramiques piézoélectriques pour émission de puissance est développée à partir du modèle de Mason. La méthode de caractérisation sous hauts niveaux de sollicitations mécaniques utilise une excitation harmonique non permanente autour de la fréquence de résonance, dans l'air.
Les résultats concernant les meilleures céramiques de puissance industrielles et de laboratoire sont proposés. Une attention particulière a été donnée à la validation de la méthode, que ce sort par des mesures optiques, thermiques ou acoustiques.
A b s t r a c t : A new method for characterizing high power piezoceramics mechanical losses is developed on Mason's model.
T h e method corresponds to a high mechanical driving level context, since samples are tested under pulsed harmonic excitation, at a resonance frequency, in the air. T h e results of the best high power industrial and laboratory ceramics are given. A special care was taken to check the method by optical, thermal and acoustic measurements.
1. I n t r o d u c t i o n
High power transducers require high mechanical or electrical driving levels. A s a result, there is a n o n - l i - near behavior of the active parts of transducers, that is t h e piezoceramics. Internal losses increase faster than t h e acoustic emission, creating excessive overheating which can cause for worse a depolarization of the ceramics or at least a reduction of the efficiency. Such phenomena implie new characterization methods of the physical properties of the piezoelectric materials.
2. T h e o r y
W a consider the longitudinal mode of cylindrical bars (cross section A = nr2, length I » r) loaded at the two end faces.
2.1. Mason's equivalent circuit with losses
The well-known Mason's equivalent circuit e n - ables the use of analogies between electrical and m e c h a - nical quantities /1,21.
Around the resonance frequency, the mechanical impedances from the secondary are reflected into the pri- mary of a n electromechanical transformer (Fig. 1) with a transformation ratio N given by :
A d3 3 A - _ I electric current 1 »E33 1 * u face velocity with 1I33 : piezoelectric coefficient
sC33 : elastic cooplianca at constant electric field E /133 l" I'M* e33T\"
Mo -I --—1 -I 1 figure of merit t >E33l 1 »33 I
1*33 : longitudinal coupling factor
«33T : permittivity at constant stress T
a ) Electric circuit M Mechanical circuit Pfc. 1 : Lossy Transducer w i t h low loading at series resonance.
The dielectric losses result in a leakage resis- tance Ro while t h e mechanical losses result in a resis- tance Rm (Zm in the mechanical circuit) in series with the load impedance. With a low acoustic load, Ro can be n e - glected.
T h e non-linear behavior of mechanical losses should be illustrated by t h e important variations of Rm versus I or Zm versus u.
. 1 Mo A
u - — , I ( 1 ) Zm - Rm ( 2 ) A U M o l1
At the resonance frequency, using the relation :
E - - ( 2 2m * 2 a ) /^ _ _ ( 3 ) 1 y"2 Mo
w e obtain the acoustic emitted intensity / 3 / :
u „ > Bo IE j =
P - Z a . L _ i - n> ( 4 ) 2 Z a 2
uitn i - z a / 2— transducer efficiency (51
Zm * 2 a / 2
T h e measure of the impedance of mechanical loss Zm versus the face velocity allows to predict the ef- ficiency for given acoustic load and electrical excitation field.
2.2. Approach from propagation equations 13/
(The acoustic load being indentical on the two fanes, the study can be reduced to that of a half bar of
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19902146
COLLOQUE DE PHYSIQUE
length E, with a permanent vibration node at the abs- cissa X = 0).
If we call U the particle displacement, the New- ton's law is written :
with the piezoelectric equation
we obtain the propagation equation :
which solution is the superposition of an incident wave and of a reflected wave.
writing that In x
-
o u ( 0 )-
o (vibration node)we obtain the analytical expressions of stress and velocity.
depending on the electric field e = Eo e j(w +
v)
which is the excitation term.~ne'veloolry is : d
-
2u uo sin 2 jnt ( 9 )"0
The displacement amplitude and the velocity are
maximat In X
- L
whereas the stress is maximal in X = o.One can find the emitted power density
X. 110 eoz
POP the reaonance in - one finds P
-
- .-
in2 ZLI 2
accordance wlth (4) when q = 1 (the model is lossless).
The maximum dynamic Stress at the vibration node is : TM (0) =
\I-
Uy(112) ( l l ) , giving the maximum face velocity that the ceramic is able to stand.The acoustic intensity is then :
the maximum of wlch is obtained for Za = Zo.
According to Hook's law, the strain presents the same re- partition as the stress inside the vibrator.
LBt'S Eonlide~ the .train veloslty ;
-
bS and calculate 6fthe average value along the vibrator :
The current density J can be written :
On the same way, one can find 131 that: T = m 0 E(16) The new electromechanical transfomlation ratio is with a new equivalent circuit (Fig. 2) :
The mechanical impedance Zm becomes a me- chanical resistivity pm = Zm. 1 (17) rsresenting the me-.
chanical losses. The new variables
8
and pm are of in- terest because they are not linked with the dimensions of the sample.3. Flectrical p
-anifaI levels
It is based on electrical measurements performed at series resonance. In the air, the sample is unloaded ; high levels of vibration are obtained with low electrical ex- citation field (E < 10 Vlmrn) 141.
The sample is excited by a sweeping generator (to avoid heating effects) through a power amplifier. The electrical admittance and the current are measured with a vectorial analyser. Thegechanical loss resistivity pm, the average strain velocity $ are then computed using the re- lations (2), (14) and (17).
3.2. l o w l eveln-
The knowledge of the figure of merit MO is ne- cessary for the calculations of losses and strain veiocity.
Low level characteristics are determined using standard procedures /5,6/.
t a b l e I : ceramics d l e l e c l r i c a l , e l a s t l c a l and s l e c r r o n s c h a n l c a l p l o p e r t i e . .
All the sample tested here are "hard ceramics suitable for high power applications. The laboratory ceramics are multi-substitued compositions.
The behavior of the different materials is pre- sented figure 3. The non-linearities of mechanical losses are well illustrated, since the mechanical loss resistivity is not constant versus strain velocity. Most of the ceramics have a linear range for S 5 1 W S-1, where losses move slowly, but show a large evolution for higher strains.
M19, EDO EC69 and VS133 have nearly the same losses until
3
= 140 S-? which correspond to a theoretical acoustic intensity of 90 Wlcm2 in water for the sample geometry used IFor a better understanding of those results, an emission in water has been simulated with the equations (3) and (4). (the sample is directly loaded at the two end faces) in order to obtain the acoustic intensity and the mechanical losses versus the electrical field (Fig. 4 et 5).
pc/N
275 0.66 240 0 . 6 5 225 0.61 230 0 . 6 4 225 0 . 6 0 280 0 . 6 2 258 0 . 6 285 0.66 P762 Q e t S l l i c e
P119 Q et S i l l c m X5105 PONS PC69 ~ d e P218 Varnirron VS133 LGEF
193 *011d pro=.
LG200 w e t Proc.
Mechantcal loses resistlvlfy versus average svain velxiv
305 310 290 320 275 420 410 410 l 2 7 0 0 . 4
l l G 0 0 . 2 1200 0 . 4 1130 0 . 2 l 1 8 0 0 . 7 1670 0 . 8 1634 0 . 9 1500 0 . 8
kg/&
7.55 7 . 6 6 7.44 7 . 6 3 7 . 5 2 7 , 6 3 7.61 7 . 6 3
2 : u i s 3 ; E W 80 4 : P275
-
5 : X 5 l O d 8 : L 0 1 0 0-
7 : 1 0 3-
8 : VSfll-
0.- I I I I
0 1 0 2 0 3 0 40 5 0 60
W Acoustlc Inlmrify emined E (V'MM' 'lersus elenrk excilallon tlsld
9 15.8
7 . 6 1 3 . 2 8 . 3 13.2
8 13.6
8 . 8 1 3 . 6 8 . 3 1 3 . 6 7 . 3 1 2 . 3 7 . 7 1 3 . 6
A Michelson homodyne interferometer is able to detect displacements superior to 0,2 nm in the range of a few kHz to 50 MHz 171. The system, has been modified to permit the measure of large displacements (until several ),laser) with a harmonic excitation of the sample.
The validity of the equatlon (l), that is to say of the definition of an ideal transformer ratio beetwen elec- trical current and face velocity b(l) =
8
has been studied with differents compositions. The displacement Um is given by the interferometer. Simultaneously at resonance frequency, - the current is measured, permitting the calculation of the velocity Oc and then of the displacement Uc.-
At low level, a good agreement is always found beetwen Um and Uc, since the differences are lower than 5 %.-When the vibration level increases, the agree- ment is illustrated by Figure 6. The tolerance of the last points is explained by the heating of the sample during continuous excitation, a phenomena which causes the shift of the resonance frequency : a simuttaneous measure of current and displacement is difficult at an unstable re- sonance.
Such results show that the figure of merit does not significantly move with the mechanical level of vibra- tion, in comparison with the non-linearities of losses.
4 1
"
Uc (pm)
1.8
Laboratory ceramic
0
~~~
0 0.4 0.8 1.2 1.6 (pm) EQWbkl CalCUIatOd dbpwsmmlveow malsursd dirpllvsmen 1
-
0
E i g u r ~ L Mechanical losses E (Vlmm) versus elecltic excitation field
The best performances are reached by LGEF's ceramics which have high figure of merit. Nearly 30 pourcent higher emission is obtained for the same elec- trical field, keeping identical or lower mechanical losses.
The use of a figure of merit obtained at low level, during high level characterization, must be discussed : does this factor stay constant when mechanical excitation increases ? This point has been studied with an optical measurement.
4 : P I T 5 5 : XdlO.
8 : L 0 1 0 0
7 : 1 9 3 7 1 5
8 : VS133
6
COLLOQUE
DE
PHYSIQUEn ('cl
vanataon. of the figurn of ment wth tempralun
- -
Overheating Venus face veloc~ty of cylindrical samples.
In all, at reronance frequency, constant current Pm (Wlcm2) harmonic Permanent excitation. (W,c m 3 )
6 7 . 5
1
6 LGZOO
::::"
8 V S 1 3 3
0 0
0 5 0 -. I 0 0
EiOUlllk: Mechanical bsses /w1cm2) versus acoustic intensity
5. E-tudv of the thermal
Under continuous excitation, the losses lead to a sample heating. According to the hypothesis that eiastical losses depend on strain velocity, the sample heating should have the same repartition along the abscissa, as the strain S.
Heating repartition has been investigated with a radiation pymmeter on a resonant vibrating sample in air.
The pymmeter permits a nor-contact measure on a very small surface (a few mm2) by focalization. Here too, a good accordance was found beetwen experimental results and theoretical prediction based on the modeliza- tion of § 2.2 and on the precedent hypothesis 181.
An interesting way for the comparaison of ce- ramics performances consists in determinating the heating of different compositions for a same face velocity, that means a same acoustic emission. The Figure 7 presents experimental heating versus the face velocity, calculated with (l), taking or not into account the dependence of the figure of merit on temperature
/W.
Such experimental results are to be compared with curves of Figure 8 built from Figures 4 and 5.
The classification of ceramics performances re- mains the same both in electrical or thermal characte- rization.
6.
P -
The Rrst results obtained with an air backed transducer having the front face of ceramic directly in contact with water, illustrate the superiority of new cera- mics (Fig. 9)
The origins of the tolerances are :
-
first the differences between the samples of a same batch ;-
then the discrepancies between the successive mountings ;- at last the imprecision of the acoustic mea- surements.
CoItIpPriSm in water lank of emittlng performances P (PS rmS) of hlph poww pburceramla
EklYlbe;.Pressum IWd obtained 1 m lar fmm the cadiata. v e m l VoltaQe excitaIIMI
7. Conclusion
A new method to characterize high power piezo- ceramics is pmposed : the samples are tested under high levels of mechanical strain : elastical losses are depending on the strain inside the sample. This simple method high- lights the non-linear behavlor of the mechanical losses and allows to plan the efficiency of piezoelectric materials for a given acoustic load.
The results ace confirmed by optical measure- ments of the face velocity of samples.
The thermal study of vibrators of different com- positions is in good agreement with the theoretical predic- tions.
Finally, sound level measurements in water tank demonstrate an improvement of about 30 % of the acous- tic emission of the laboratory pmducts in comparison with standards ceramics.
Acknowledoments
This work was supported by the Direction des Constructions et Armes Navaies de Brest. FRANCE.
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-
Ultrasonic transducer materials-
N.Y.LONDON : Plenum Press, 1971.
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A paraitre dans Entropie
