DETERMINATION OF THE COEFFICIENT INDICATING

THE EFFECT OF STRAIN ON PIEZOELECTRIC

MEASURING TRANSDUCERS OF ACCELERATION

Sh. A. Nemsadze and G. ~. Dolaberidze UDC 531.768.088.2

According to [1, 2] high-quality piezoelectric measuring transducers (MT) of acceleration are highly sensitive to the strain in the surface of the object under investigation. This is due to the small strain of their seining element under the operatingconditions concerned and to the presence in the piezoelement matrix of components generating a signal at the MT output resulting from the piezoelement strain. To eliminate or to take into account the corre- sponding component errors of the measurement results, data on the strain of the object surface and on the coefficient of the effect of strain on the MT of acceleration is needed.

The process of strain transfer from the object surface to the piezoelement is affected by a number of factors: contact rigidity, the tightening torque and the rigidity of the threaded joint or adhesive bond of the MT and the object, the orientation of strain in the plane normal to the MT sensitivity axis, and the height of the MT base. For this reason it is not at present possible to calculate this coefficient analytically.

Devices are known [2, 3] which are intended for experimental determination of the effect of strain on the readings of MT of acceleration. A typical feature of devices of this type is that the piezoelement of the MT is subjected to a simultaneous action of acceleration and strain.

Figure 1 gives a schematic diagram of the apparatus which makes possible the determination of the coefficient of the effect of strain for some types of piezoelectric MT of acceleration in which the MT is practically not af- fected by the action of aeoeleration. Here the MT of acceleration 3 is mounted on the central part of rectangular cross-section beam 5 which rests on two-sided supports applied to this section; the free ends of the beam perform synchronous cophasal vibrations excited by two two-tact electromagnetic vibrators 1 magnetized by dc.

The electromagnetic vibrators are powered by ae amplifier TU-50M (10) excited by GZ-34 audio generator 9, and by de from rectifier 4. The apparatus is tuned to resonance by varying the audio generator frequency.

The output signal of the acceleration measuring transducer is measured by oscilioseope 2 . The bending strain generating this signal is measured, indirectly, by an optical method. For this purpose lamp 6, mirror 7, and measuring microscope 8 (MPB-2) are provided for measuring the deflection of the free end of the beam.

The apparatus is supplied with a set of beams suitable for securing the MT of acceleration (IS-312, IS-313, IC-318, PI 93-1, and others) which are mounted on M2, M4, and M5 screws or by adhesive bonding.

Hg. 1

For each beam supplied with the apparatus the coefficient of the correlation factor of the strain in the beam center to the deflection of the free beam end has been determined. The strain in the beam center was measured by means of PKB-5 wire resistance strain gauges, a TA-5 amplifier, and anN107 light-beam oscil- loscope.

The apparatus produces in the plane in which the MT

of the acceleration is fixed, a bending strain, ranging from 0 to 0.1%; the variation of strainin timeis harmonic.

Translated from Izmeritel'naya Tekhnika, No. 5, pp. 29-30, May, 1974.

�9 1974 Consultants Bureau, a division of Plenum Publishing Corporation, 227 West 17th Street, New York, N. Y. 10011. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, me- chonical, photocopying, microfilming, recording or otherwise, without written permission of the publisher. A copy of this article is available from the publisher for $15.00.

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TABLE I

Specif icat ion of MT

Natural frequency of mounted MT, kHz Range, m/sec z

Conversion factor for stress, mV �9 secZ/m Nominal moment of bonding, N �9 m Relat ive coeff ic ient of the effect of strain,

m/see z

Relative coefficient of the effect of strain, ~

IS-312

Type of MT

IS-318

21 8. lO s

0.15 30

0 1 7 �9 1 0 -6

2.1 "10 "9

14 8" I0 s

0.53

(0.038-0.094). i0 "6

(0.48-1.2) �9 10 -9

PI 93-1

77 5. I0 4

0.49 0.9

0.69" I0 "6 1.4" 10 .9

Um, mV

tO(] /

o Is h2i2 ~f 0,r 0,6 g6' e. I0 -J

Fig. 2

ks, m/see z �9 I0 6

] , 2 - - -

0,~

0,4

0

The peak value of acce le ra t ion act ing in a ver t i ca l (working) direct ion on the MT of acce lera t ion exceeds 1 m / s e c z.

Using this apparatus the following coefficients of the effect of strain on p iezoe lec t r i c MT of acce lera t ion (types I8-312, IS-318, and PI 93-1) were de- termined for the strain range 0-0.1%.

Figure 2 shows the relationship U m = f ( s ) plot ted for the above MT types secured on the corresponding beams using the nominal t ightening torque.

This information was used to determine the re la t ive c o d f i e i e n t of the ef- fect of strain K s and the re la t ive coeff ic ient of the effect of strain Ksr.

Um 1 1 Ks K s = - �9 �9 - - .100, e Su 10_T , K sr = amax

where is the output signal generated by strain, mV; s is the bending strain U m of the beam; S U is the conversion factor of the MT stress, mV �9 secZ/m; and

~max is the measurement range of the MT for accelera t ion.

The former coeff ic ient shows which of the input signals (accelerat ions)

I / corresponds to the vol tage at the MT output in the case of a strain of 10 4 . This coeff ic ient can be convenient ly used in determining the absolute value of the

0,J 06 0,9 1,2 m, N �9 m corresponding error in the measurement result. The second coefficient produces

Fig. 3 the relative error directly in 070 for a strain of I0 -6, provided that the acceleration

corresponds to the measurement range of the MT. These coefficients are given

in Table 1 together with some characteristics of the MT.

The curves of Fig. 2 represent the s ta t is t ical ly processed results of repeated measurements. For example , for the PI 93-1 transducer the re la t ive coeff icient of the effect of strain is Ks=0.69" 10 "s m/ see z for a confidence range of A = (--0.02 to 0.12) �9 10 .6 m/sec z with a probabil i ty of p = 0.973. For the IS-312 transducer K s = 0.17 �9 10 -6 m/secZ; A= ( -0 .009 to 0.01) �9 10 -6 m / s e c 2 , p = 0.99. For the IS-318transducer the coeff ic ient of the effect of strain depends

on strain and is measured over the range (0.04 to 0.09)" 10 "6 m / s e e z.

The experiments produced the relationship between the coeff ic ient of the effect of strain and the torque of

fastening the MT for the transducer PI 93-1. The curve representing this re la t ion is given in Fig. 3.

We also invest igated the effect of vibration frequency of the beam on the coeff ic ient of the effect of strain of MT on the MT accelera t ion . In the frequency range 100-160 Hz it was found to be insignificant .

An analysis of results leads to the following conclusion: for p iezoe lec t r i c MT of acce le ra t ion of types PI 93-1 and IS-312 the re la t ion Urn(e) is p rac t i ca l ly l inear . The coeff ic ient of the effect of strain is strongly dependent on

the torque appl ied in t ightening the joint . For example , for PI 93-1 an increase in the torque from 0.25 to 1.5 N. m changes the coeff ic ient from 0.16.10 .6 m/ see 2 to 1 .4 .10 -6 m/see 2.

The MT IS-312 and IS-318, whose natural frequencies are re la t ive ly low, are charac ter ized by a r e la t ive ly

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low coefficient of the effect of strain, whereas the high-frequency MT PI 93-1 has a higher coeff ic ient of this effect. However, i f transducers are used in measuring accelerat ions close to the l imi t of their ampl i tude range, the errors of the three invest igated MT are comparable and reach only a few % for a strain of 0.1%.

LITERATURE CITED

I. I.B. Sinani, "Accelerometers for measuring accelerations during the collision of solid bodies," in: Vibrome- ters [in Russian], No. I, MDNTP, Moscow (1965).

2. N. Heymann and G. Kleinmichel, Messen-Steuem-Regeln, No. I0, (1990). 3. V.S. Golubev and M. D. Genkin, "Sensitivity of piezoelectric sensors to mechanical stresses," in: Vibration

Technology [in Russian], No. I, MDNTP, Moscow (196'/).

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