Measuring simultaneously translational and angular acceleration with the new translational-angular-piezobeam (TAP) system

282

Sensors and Actuators, A21 -A23 ( 1990) 282-284

Measuring Simultaneously Translational and Angular Acceleration with the New Translational-Angular-Piezobeam (TAP) System B BILL

Kstler Inst-nte

AG, Eulachstrasse22, CH-8408 Wntterthur (Swrtserland)

A L WICKS

Vugma Polytechmc lnstltute and State Umversrty,Blacksburg, VA 24061 (U S A )

Abstract

The new translational/angular accelerometer presented m this paper consists of a pair of identical piezoelectnc cantilever beams mslde a metal housmg Integrated hybnd charge amplifiers convert the plezoelectnc charge signals to high level, low impedance voltages The sensor 1s easily mounted on the surface of the structure under test by fixing it with wax or glue It allows the simultaneous measurement of translational and angular acceleration An example of an estimation of the frequency response function of a free-free beam 1spresented 1. Introduction In the past, when rotational data on structures was desired, either the translational data was curvefitted and differentiated or a transducer conslstmg of two translational accelerometers separated by a known distance was used Both of these methods have obvious disadvantages The use of fitted translational data for all but the most basic of structures has not yielded quality results The pseudo-rotational transducer has the disadvantages of averaging the measurement over the spatial point of Interest In addition, transducers have to be light-weight, mmlmlzmg the effects of mass-loadmg Furthermore, high sensltlvlty 1sdesired, which Increases the mass of the transducer, when using normal selsmlc accelerometers The void of adequate transducers 1s now filled by the new TAP system by Klstler It allows the simultaneous measurement of one translational and one rotational degree of freedom

consists of a pair of identical plezoelectnc cantilever beams Hrlth a common ams and arranged symmetncally about a mam axis z, normal to the beam axis The beams are attached at their inner ends, thus allowing free osclllatlon of the beams, which may be caused by an acceleration acting on the sensor Each beam consists of a bllammar piezoceramic flexure element, as shown m Fig 2 Each of these elements consists of two plezoceramlc layers wth the polanzatlon direction normal to the beam axis These two layers are connected electncally m senes Bending the beam yelds an electnc charge, which 1s picked up at the upper and lower surfaces of the element Using the equations of the elastic beam [l] and the plezoelectnc equations [2] it can be shown that the resultmg charge results to Q =OSdp&

(1)

where d,, = 4, = - 190 x lo-” C/N is the piezoelectnc coefficient for the sensor matenal, m 1s the mass, 1the length and a the thickness of the beam These charge signals are detected by hybnd charge amplifiers, whch are integrated mto the sensor These amplifiers convert the plezoelectnc charge signals to high level, low impedance voltage signals By appropnate choice of the polanzatlon dlrectlon of the plezoelectnc elements,

2. Sensor Design The basic design of the new translational/angular accelerometer IS shown m Fig 1 The sensor 09244247/90/$3 50

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1 Basic design of TAP sensor

Elsevler Sequora/Prmted m The Netherlands

283

3. Application

Rg

2 Prmclple of bdammar

pwoceraauc

element

addition of the charge signals yields an electrical value proportional to the acting translational acceleration m the z-direction as shown m Fig 3 Subtractmg the charge signals yields an electrical value proportional to the acting angular acceleration around the y-axIs, as shown m Fig 4 Using the circuit shown m Fig 5, translational and angular acceleration signals are measured simultaneously A drawmg of the transducer IS presented m Fig 6 The sensor waghs 10 g, and the sensittvitles are 1000 mV/g for translational acceleration and up to 50 mV/rad/s2 for rotational acceleration

my

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3 2 Results The fundamental purpose of this expenment was to evaluate the effectiveness of the rotational measurements as cornbared to the standard translatlonal measuremenk m the context of expenmental modal analysis Table 1 presents a comparison of the e&mated mean values and

s;;

1

3 Lmear acceleratron

3 I Descrlptlon A senes of measurements were made on a slender steel beam supported such that free-free boundary condltlons were simulated The frequency response functions (FRFs) for both the translational and the rotatlonal measurements were estimated Using the method of the ‘rovmg accelerometer’ over 12 measunng points were used and a frequency-domain parameter estlmatlon techmque [3] was applied on each FRF T’he natural frequency, damping raho and residue were extracted at each measurmg point for the first seven beam bendmg modes These local properties of the beam, specifically the residues, are compared to the Euler beam theory [4,5], that was chosen for this comparison because of its relative simplicity

actmg on the sensor

TABLE 1 E&mated natural freqwncy dewatlon for the measured modes Mode @ a4 Fig 4 Rotational

A

acceleration

u-+a;

Fig 5 Cmxut for measunng rotatlonal acceleration

Rg

1 2 3 4 5 6 7

actmg on the sensor

6 TAP sensor

simultaneously

translatlonal

and

(Hz) and standard

Translatton Nat freq f Std dev

Rotatton Nat freq &Std

17 575 + 0 0243 48299?00613 94591 f0 1186 156409zO 184 233669kO 144 326 5!Jl f 0 276 434946*0343

17571+00290 48299:00637 94586+01179 156409zO 1848 233 671 f 0 145 326 580 f 0 272 434947+0342

TABLE 2 Eshmated modal dampmg and standard for the measured modes

dev

devlatlon

Mode

Translation %Cnt damp fStd dev

Rotation %Cnt damp fStd dev

1 2 3 4

3462+0056 1274100246 06878&00422 04011&-00213 02904kOO443 0 1927 f 0 0106 01123~01141

3 476 f 0 0755 1272 IO 0335 0 6737 f 0 0314 0 4070 f 0 0172 02905*00449 0 1928kOOlO8 0 1453*00069

i 7

284

IO

0

20 BEAM

30 LENGTH

40

50

C 1 n>

Fig 7 Mode 5 hsplacement data and rotational data

TABLE 3 Comparison of the correlation between the measured results and theory Mode

Translation Correlation with theory

Rotabon Correlation with theory

1 2 3 4 5 6 7

09998 09999 09998 09997 0 9997 0 9995 0 9995

0 9936 0 9954 0 9968 0 9982 0 9987 0 9981 0 9983

measured data are supernnposed to demonstrate the quality of the rotational values 4. Conclusions The new TAP system offers the registration of degrees of freedom of a structure m a simple manner Compared with analytical data, the hghtweight, highly sensltlve sensor yields good results

6n

References 1 R J Roark and W C Young, Formula~for StressamiStram,

standard devlatlon of the natural frequencies It can be Seen that the estimated mean for the rotational measurements are w&m the estnnatlon range of the translational measurements Table 2 presents the modal damping, whereas Table 3 shows the comparison of the correlation between the measured results and the theory Figure 7 shows, as an example, the fifth bendmg mode of the beam The analytical mode shapes are plotted as solid lines for displacement and rotation The

McGraw-HI& London, 1976, pp 96-101 2 J Tlchy and G Gautsclu, Paezoelektraxhe Messtechnrk, Sprmgcr, Berhn, 1980 3 R E Cobb and L D M&hell, A method for the unbmsed estimate of system FRFs m the presence of multiple conelated mputs, Proc 4th Int Mod01Analysis Conf, Kmmmee, FL, USA, Feb l-4, 1988 4 L Mnrovltch, Analytical Methd m Vabratlons,Macnullan, London, 1967, pp 126-154 5 R A Romr, A L Wicks and J Wdhams, Angular acceleratlon measurements of a free-free beam, Proc 7thInt MoaW AnalysrrConf, LuaVegas, NV, U S A , Jan 30-Feb 3,198Y