1. Nomenclature d31 piezo electro-mechanical coefficient (7) piezo dielectric permittivity at constant stress.
FM14 - 1:35 Sensor Effectiveness Coefficients for
Piezoelectric Materials B. R. Patnaikt G. R. Hepplert W. J. Wilsont Systems Design Eng. Elec. & Comp. Eng. Systems Design Eng. University of Waterloo University of Waterloo University of Waterloo Keywords: Piezoelectric Sensor, Active Control, Flexible Structure Abstract
been a growing number of various piezoelectric materials now available in the market. In order to choose a particular material for a specific application, it is desirable to have some quantitative measure of the transducer effectiveness.
Two piezoelectric sensor effectiveness coefficients that provide a quantitative measure of effectiveness for piezoelectric materials which are being used for sensing strain (voltage sensor), or strain-rate (current sensor) are introduced. The use of these coefficients for selecting sensor materials is illustrated through a numerical example.
In the case of piezoelectric actuators, an effectiveness measure known as the strain-actuatoreffectiveness(SAE) coefficient has already been defined by Crawley et al. [l]. Strangely enough, similar coefficients for piezo-sensors have not been defined. In this paper we introduce two such sensor effectiveness coefficients.
1. Nomenclature d31
piezo electro-mechanical coefficient ( 7 ) piezo dielectric permittivity at constant stress
First, we briefly describe two generic piezoelectric sensor circuits which can measure structural strain and strain-rate. Then from the governing sensor equations we derive the strain-sensor-effectiveness (SSE)and strain-rate-sensor-effectiveness(SRSE) coefficients. Finally we present a numerical example.
- W’(%-l,
Table 1: Effectiveness parameters of typical Piezo Materials
t>l
same order of magnitude as for the PZT’s, whereas the SRSE coefficient for PZT’s is much higher. This implies for strain-rate measurement purposes the ceramics are more appropriate. This is an interesting observation which goes contrary to the generdy assumed belief that PVDF h are invariably better suited as sensors [4]. For a specified strain, the amount of charge generated in the case of PVDF films is less than what is obtained using ceramics. The reason the PVDF films are able to provide voltage measurements of comparable magnitude is due to their lower electrical capacitance.
and
4. Sensor Effectiveness CO
For a piezoelectric material to be more effective as a sensor we would like to have higher values for the measured voltages V,,,or Kcper unit strain. For the given circuit configuration, the material parameters that influence the above two electrical measures can be grouped together to arrive at the following sensor effectiveness coefficients:
6. Conclusion
The two sensor effectiveness measures: SSE and SRSE can be used to select an appropriate piezoelectric material.
References [l] Edward F.Crawley and Javier de Luis. “Use of piezoelectric actuators as elements of intelligent structures.” AIAA Journal, 14(10), pp. 1373-1385, Oct 1987. [2] S. Hanagud, M. W. Obal, and A. J. Calise. “Optimal vibration control by the use of piezoceramic sensors and actuators.’’ In 27th AIAA/ASME/ASCE/AHS Structures, Structural Dynamics and Materials Conference, pp. 177185, April 1986.
(4) If we further assume that geometry of the structure is independent of the sensor material, the coefficients defined in (3)-(4) are further simplified to:
SRSE =
d31 c -
sFl m2’
5. An Illustrative Example
[3] €3. R.Patnaik. Control of a tip-impacted flexible a n n and piezoelectric vibration suppression. M. A. Sc. thesis, University of Waterloo, 1994.
Let us consider a sensor configuration where the piezoelectric material thickness ( t a ) , substructure thickness ( t 8 ) and length of the sensor segment (L;) are 0.254 mm, 2.032 mm and 40.0 mm respectively.
[4] Anthony Faria Vaz. Modelling piezoelectric behaviour for actuator and sensor applications. Technical Report, Applied Computing Enterprises, February 1991. 3802
