REALIZATION OF SINUSOIDAL FORCES AT CEM

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1 IMEKO nd TC3, 1 th TC5 nd 3 rd TC Interntonl Conferences 3 to 5 Februry, 14, Cpe Town, Republc of South Afrc REALIZATION OF SINUSOIDAL FORCES AT CEM M. N. Medn 1, J.L. Robles nd J. de Vcente 3 1 Centro Espñol de Metrologí (CEM, Tres Cntos, Spn, mnmedn@cem.mnetur.es Centro Espñol de Metrologí (CEM, Tres Cntos, Spn, jlrobles@cem.mnetur.es 3 Escuel Poltécnc Seror de Ingeneros Industrles, UPM, Mdrd, Spn, jvo@ets.m.es Abstrct: Ths pper descrbes the procedure mplemented t CEM for dynmc force clbrton usng snusodl excttons of force trnsducers. The method s bsed on snusodl exctton of force trnsducers eqped wth n ddtonl top mss excted wth n electrodynmc shker system. The ccelerton s mesured by mens of lser vbrometer. nd ts correct mplementton s crucl for the optml functonng of the whole system. Keywords: Dynmc force, snusodl exctton, lser vbrometer, hrmonc dstorton, rockng moton. 1. INTRODUCTION Sttc clbrton of force trnsducers hs well estblshed procedure, but most pplctons of force trnsducers re n dynmc condtons. Tht s the reson why dynmc clbrton s essentl for proper chrcterzton of force trnsducer. Ths lso hppens wth other qunttes so tht more nd more reserch s beng performed n metrology for dynmc condtons. Ths work s prt of project clled Trceble dynmc mesurement of mechncl qunttes fnnced by the Europen Unon under the Europen Reserch Metrology Progrm. The m of the project s to provde trceblty for pressure, torque nd force n dynmc condtons [1]. The relzton t CEM s focused on the development of prmry stndrd for snusodl forces. Ths stndrd s bsed on the drect defnton of force s mss tmes ccelerton. The trnsducer s loded wth dfferent clbrted msses nd dfferent ccelertons re generted by vbrton shker system. The ccelerton s mesured by lser vbrometer trceble to the unt of length (lser wvelength. The trnsducer s chrctersed by ts dynmc senstvty, whch s the rto of ts electrcl output sgnl of the force trnsducer nd the ctng dynmc force. Beng fully dynmc mesurement t requres multchnnel dt cquston system n rel tme. Ths system wll cqure electrcl sgnls from the lser vbrometer, sensor under clbrton nd other uxlry ccelerometers n rel tme. Ths system s very mportnt, Fg 1: Overew of the system. DESCRIPTION A specl tble for plcng the lser vbrometer (Polytec CLV 34 over the shker (LDS 76 wth power mplfer PA, whch cn work to 4 Hz hs been desgned (Fg. 1. The lser vbrometer s modfed Mch-Zehnder nterferometer nd t ncorprtes Brgg cell (optocoustc modultor. The sgnl from the photodetector s mxed wth two phse-shfted π / sgnls wth the Brgg cell frequency n seprte brnches. When they pss through ther correspondng low pss flters, two sgnls n qudrture re obtned tht contn the nformton of dsplcement gnst tme. Such nformton s obtned by the rc tngent method wth specl lgorthm bsed on the estblsment of the functon contnuty for π multples. As result voltge output proportonl to the velocty of the snusodl movement under mesurement s obtned from the lser vbrometer. As n uxlry sensor B&K 835 ccelerometer wth ts sgnl condtoner B&K s used. The requred msses for genertng the forces on the trnducers hve been mnufctured nd clbrted to

2 determne ther mss nd ther correspondng uncertnty. The msses hve nomnl vlues 347 g, 1 kg, kg, 7.3 kg nd 1.3 kg. The three smller msses re connected drectly to the sensor under clbrton, the bgger ones re connected by mens of specl dptor. These mses defne the mxmum force the sstem cn generte, but further studes wth lrger msses re plnned to be mplemented n the future. Dependng on the sensor to be clbrted specl dptors my be requred n order to ttch the msses to the sensor or the sensor to the shker. Specl cre hs to be tken to ensure tht the contct between peces s mde by mens of flt surfces. The torque whch s ppled to connect the dfferent prts s lso under creful control. the output of the lser vbrometer s velocty nto ccelerton s strght forwrd. Hrmonc dstorton nd nose were very mportnt dsturbng fctors. As frst step some flterng technques were mplemented n Lbvew to mnmze ts effects such s choosng just the fundmentl frequency components or elmnte the nose. These technques were mplemented through Lbvew functons. In the end the sne pproxmton method, lso mplemented wth Lbvew functons n rel tme, ws the chosen opton. Accordng to ths method every sgnl (t s ftted ccordng to: ( t = Acos( πft B sn( πft C (1 = 1 N nd N the totl number of mesurements consdered for the fttng. Ths genertes n overdetermned system of equtons n whch A, B nd C cn be found. Ampltude ˆ nd phse, ϕ, cn then be determned s â = A B ϕ A = tn B ( In our cse ths method hs been mplemented consderng lso hrmoncs s follows Fg : Vew of the msses nd the dptor used for tht purpose lso connected to sensor. As frst dt cquston system the Aglent Infnum osclloscope DSO864A (6 MHz, 4GS/s of four chnnels ws used. Ths osclloscope cqured electrcl sgnls drectly s functon of tme nd t llowed to export the dt for subsequent mthemtcl processng by mens of the sne pproxmton method. Its problem ws tht sgnls vlues were not ccurte enough, so more ccurte system hd to be mplemented. The current dt cquston system s NI PXI 133 module wth 446 crd (4 bts, 4.8 ks/s, whch s progrmmed n Lbvew. In the frst verson of the softwre the dt cquston system ws only used to cqure the sgnls s functons of tme nd export them nto fle. After dfferent versons the current one drectly clcultes the trnsducer senstvty (modulus nd phse n rel tme both wth the lser vbrometer s the reference stndrd nd wth B&K 835 ccelerometer wth ts sgnl condtoner B&K s the reference stndrd. As frst check of the relblty of the softwre the ccelerometer ws locted n the centre on the top of one mss nd ccelerton mesurements were performed wth both, the ccelerometer nd the lser vbrometer, wth greement wthn mesurement uncertnty. The mplemented softwre smples the sgnls seprtely wth speed of 4 ks/s. The exctton frequency s drectly detected by the softwre, so tht the converson of ( t ( ( = A cos πft B sn πft A cos( 4πft B sn( 4πft 1 1 A cos( ft ( 6π B sn 6πft A cos( 8πft B sn( 8πft 3 3 C For senstvty determnton only the fundmentl frequency components re consdered â = ϕ ( A ( B A = rctn B Ths lest squres pproxmton s performed by mens of the sngulr vlue decomposton method. 3. MEASUREMENT MODEL AND INFLUENCE FACTORS The prmeter tht chrcterses the force trnsducer s the senstvty S, whch the rto of the electrcl output sgnl of the trnsducer to the ctng dynmc force. Its modulus cn be determned s ( m m (3 (4 U S = V (5

3 where U s the output of the condtonng mplfer, V s the mplfcton fctor of the condtonng mplfer, m s the mss for lodng the trnsducer, m s the nternl mss of the trnsducer tht constrbutes s lod nd s the ccelerton mesured by the lser vbrometer. The senstvty phse s determned s the phse dfference between the sensor output nd the lser vbrometer output. The system behves s mechncl resontor, ths s lodng mss m connected to the sensor by sprng of stffness k nd velocty-proportonl dmper of dmpng fctor b, ccordng to equton (6 ( x x b ( x& x& m & x = k (6 down down Accelerton rto Fg 4: Accelerton rto modulus for Kstler 9175 B trnsducer nd 1.3 kg lodng mss. In order to study ths behvour the ccelertons of the top of the mss & nd the top surfce of the shker x& & x& down hve to be mesured (see fgure 3. Ths s performed by the lser vbrometer t the top of the mss nd n ccelerometer wth the sgnl condtoner t the top surfce of the shker. The cquston system s lso used to perform these mesurements. & x& & x&down Mss Lser bem Sensor Shker Auxlry ccelerometer Fg 3:Smplfed dgrm tht shows the mesurement confgurton.. The rto of these two ccelertons follows k bω = k bω mω down where m s the lodng mss, ω s the ngulr frequency, k s the stffness nd b s the dmpng fctor. Fgures 4 nd 5 qulttvely show ths behvour. There re mny nfluences n ths system whch re potentl sources of uncertnty. Among the potentl sources of type B uncertnty the ones cused for externl trceblty re ncluded n Tble 1. The lbortory condtons re stble enough so tht temperture nfluence on the trnsducer cn be consdered neglgble for most trnsducers. (7 Accelerton rto phse / º Fg 5: Acclerton rto phse for Kstler 9175 B trnsducer nd 1.3 kg lodng mss. Uncertnty contrbuton Contrbuton to the senstvty modulus Contrbuton to the senstvty phse Dt cquston system.5 % 1-5 º/frequency Lser vbrometer.1 %. º Condtonng mplfer.5 %. º Lodng mss.1% - Tble 1: Sources of type B uncertnty derved from externl trceblty. The most mportnt contrbutons re the sources of type A uncertnty, especlly for the senstvty modulus, but not so much for the senstvty phse. They lso depend strongly on the exctton frequency for the senstvty modulus, but not for the senstvty phse. One source of type A uncertnty s the the fttng men squre error of the sne pproxmton. Ths source of uncertnty quntfes the hrmonc dstorton nd the nose. The softwre performs fttng per 4 ks, so f the hrmonc dstorton nd the nose re smll, the contrbuton mybe neglgble. Another mportnt effect s rockng moton. Ths effect hs been brodly studed for ccelerometers []. In other to study ths effect we used the lser vbrometer to mesure the

4 velocty of severl dots n crcle round the centre on the top of the mss. Ths effect hs been found to be very mportnt, especlly for hgh frequences. Fgures 6, 7 nd 8 show n exmple of ths effect. Normlsed senstvty modulus 1,5 1,3 1,1,99,97, Orentton /º Fg 6: Ech lne represents the normlsed senstvty modulus to the men vlue for ech mesurement frequency for the pezoelectrc trnsducer Krstler 9175 B when t s loded wth the 7.3 kg mss. The lser vbrometer bem hs been focused on the dptor severl dots round crcle centered on the mss top surfce wth rdus 1 cm. In the x xs the orentton of ech dot n degrees s presented. 31, 56, 6, the mss top surfce wth rdus 1,7 cm. In the x xs the orentton of ech dot n degrees s presented. Fgures 9 nd 1 show ths effect for fxed frequency s functon of the poston of the lser bem on the top of the mss. It cn be concluded then tht the best dot to mesure the ccelerton by mens of the lser vbrometer s the center of the lodng mss. The uncertnty contrbuton s usully less thn.1% for frequences wthout trnsverse resonnces. Trnsverse ccelerton cn be n mportnt nfluence. In prctce, f the trnsverse ccelerton s n mportnt nfluence for certn frequency, ths frequency s not consdered. The reson for ts mportnce my be the exstence of trnsverse resonnce for ths frequency. As n exmple of the effect of trnsverse ccelerton the lne for 16 Hz shows some dstorton n 7 nd the mpltude of ths lne s much bgger thn others n fgure 8. Normlsed senstvty modulus 1,15 1,1 1,5 1,95,9,85,8 1 3 Orentton/º 31, 56, 6, Fg 9:Contour plot of the normlsed senstvty modulus for 15Hz s functon of the poston of the lser bem on the top of the mss. Fg 7: Ech lne represents the normlsed senstvty modulus to the men vlue for ech mesurement frequency for the pezoelectrc trnsducer Krstler 9175 B when t s loded wth the kg mss. The lser vbrometer bem hs been focused on the mss severl dots round crcle centered on the mss top surfce wth rdus 1,7 cm. In the x xs the orentton of ech dot n degrees s presented. Normlsed senstvty phse Orentton /º Fg 8: Ech lne represents the normlsed senstvty phse to the men vlue for ech mesurement frequency for the pezoelectrc trnsducer Krstler 9175 B when t s loded wth the kg mss. The lser vbrometer bem hs been focused on the mss severl dots round crcle centered on 31, 56, 6, Fg 1: 3D plot of the normlsed senstvty modulus for 15Hz s functon of the poston of the lser bem on the top of the mss. Most tmes the lodng mss of the trnsducer s not known, so t hs to be determned from the mesurement results. The de s to mesure the senstvty for dferent msses nd fnd the lodng mss of the sensor tkng nto ccount tht the senstvty for sttc condtons (zero frequency hs to be ndependent from the lodng mss. It s cler tht the uncertnty of the lodng mss of the sensor

5 wll ffect more the senstvty modulus the smller the lodng mss s, but t s very useful to use smll msses for senstvty determnton n order to be ble to obtn n ccurte lodng mss of the sensor. One most mportnt nfluence s the reproducblty of the mountng. Cre should be tken n usng n dequte nd reproducble mountng torque for ll the components of the system: mss, sensor, shker nd dptors. Fgure 11 shows the dfferences n the sytem resonnt behvour when mountng torque s not dequte. Further studes hve to be performed n order to get more nformton of the mountng torque nfluence. Accelerton rto modulus Fg 11: Accelerton rto modulus for the sme system n dfferent test when the mountng torque s not fxed. 4. CONCLUSIONS Ths pper descrbes the procedure mplemented t CEM for dynmc force clbrton usng snusodl excttons of force trnsducers. It s contrbuton to the EMRP project Trceble dynmc mesurement of mechncl qunttes. The mnmum clbrton expnded uncertnty tht cn be obtned s round.5 % for the senstvty modulus nd 1º for the sensblty phse. Ths uncertnty my ncrese dependng on the exctton frequency. Acknowledgement The EMRP s jontly funded by the EMRP prtcptng countres wthn EURAMET nd the Europen Unon. 5. REFERENCES [1] C. Brtol, M. F. Beug, T.s Bruns, C. Elster, T. Eswrd, L. Klus, A. Knott, M. Kobusch, S. Sxholm, C. Schlegel Trceble dynmc mesurement of mechncl qunttes: objectves nd frst results of ths Europen project, Proceedngs of XX IMEKO World Congress, 1. [] A. Cbrl, I. Godnho, V. Olver, J. M. Rebordão, M. C. Nunes Prmry lser vbrton metrology: evluton of the rockng moton mpct n the ccurcy of ccelerton mesurements Proc. of SPIE Vol Z-3