A PRIMARY ANGULAR ACCELERATION CALIBRATION STANDARD

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1 XVIII IMEKO WORLD CONGRESS Metrology or Sutinble Development September, 17, 006, Rio de Jneiro, rzil A PRIMARY ANGULAR ACCELERAION CALIRAION SANDARD Li ZHANG 1, Jun PENG 1 Chngcheng Intitute o Metrology & Meurement (CIMM), eijing ,Chin. zhngli@bj163.com Chngcheng Intitute o Metrology & Meurement (CIMM), eijing ,Chin. peng-jun@vip.in.com Abtrct: Primry ngulr ccelertion clibrtion tndrd i developed by CIMM to generte tndrd rottionl ngle, ngulr velocity nd ngulr ccelertion, which re trceble to the Interntionl Sytem o Unit (SI). It cn be ued to clibrte ngulr trnducer, i.e. ngulr ccelerometer, ngulr velocity trnducer, nd rottionl ngle trnducer to obtin mplitude enitivity nd phe hit by inuoidl vibrtion. hi pper will introduce the mechnic ytem, control ytem nd meurement ytem o the tndrd. Clibrtion reult o ngulr trnducer uing the tndrd lo introduced. It how tht the tndrd cn be ued in ngulr movement clibrtion in the requency rnge rom 0.1Hz to 00Hz with mplitude uncertinty better thn 1% nd phe uncertinty o 1 degree. clibrted, n rbitrry wveorm genertor i ued to control the ngulr exciter t the me time. he otwre nlye dt nd clculte the complex enitivity o the trnducer. he PXI bu intrument i tnd-long ytem in the primry ngulr ccelertion clibrtion ytem, which i ued to mple dt rom opticl-electricl detector o grting (in the ce o low rottion rte), intererometer nd trnducer, control ngulr exciter nd proce dt. It h n embedded computer, everl dt cquiition crd, n rbitrry wveorm genertor crd nd digitl multimeter crd. he embedded computer i highperormnce PXI/CompctPCI-comptible ytem controller; it i lo generl computer. Keyword: ngulr exciter, ngulr ccelertion, tndrd, grting, ler intererometer. 1. INRODUCION Primry ngulr ccelertion clibrtion tndrd i ued to generte tndrd rottionl ngle, ngulr velocity nd ngulr ccelertion, which re trceble to the Interntionl Sytem o Unit (SI), nd it cn be ued to clibrte ngulr trnducer, i.e. ngulr ccelerometer, ngulr velocity trnducer (tchometer, gyro, etc), nd rottionl ngle trnducer to obtin mplitude enitivity nd phe hit by inuoidl vibrtion. ISO Method or the clibrtion o vibrtion nd hock trnducer-prt15: Primry ngulr vibrtion clibrtion by ler intererometry i on the tge o drt t preent nd Germny h etblihed ngulr ccelertion clibrtion tndrd everl yer beore [1]. he primry ngulr ccelertion clibrtion tndrd introduced in thi pper i developed by CIMM. It include three ytem, i.e. mechnicl ytem, control ytem nd meuring ytem. he ngulr exciter i hown in Fig.1. A hown in Fig., ngulr ccelertion relized by the ervo motor driving the ir bering ytem, the trnducer i mounted on the top o ngulr exciter tble urce. A dirction column grting nd two ler intererometer re ued to meure the ngulr ccelertion, nd the tble urce i ued to mount trnducer to be clibrted. he computer in PXI bu ytem control ADC module to mple the dt rom the intererometer nd the trnducer to be Fig.1. Photo o ngulr ccelertion exciter

2 PXI u Sytem Control Crd rnducer ble Grting Signl Conditioner 4it 100kHz 8CH ADC Crd 7½ Digitl Multimeter Crd PXI US Intererometer nd ignl preproceing 1it 10MHz 4CH ADC Crd Power Ampliier nd Controller Arbitrry Wveorm Genertor Crd Fig. Lyout o the tndrd. INVESIGAION OF HE SYSEM.. he control ytem.1. he mechnicl ytem he mechnicl ytem ue ervomotor driving n irbering ytem. Shown in Fig.3, tble, which i mde o mrble, i ued to mount trnducer to be clibrted. wo grting re ixed on the hit. Grting 1 i dirction column grting, which collborte with two ler intererometer to meure ngulr movement. Grting i ued ngle poition meurement component to provide eedbck ignl or the control ytem. A bruhle DC ervomotor i ued to drive ir-bering ytem. he riction i reduced to gret extend becue the ue o bruhle motor nd the ir bering ytem. ble Surce Grting 1 Grting Sht Primry ngulr ccelertion clibrtion tndrd mechnicl eqution cn be expreed by J & θ + C & θ = M (1) where J i moment o inerti o the whole rotting ytem, C i riction coeicient, i torque generted by the θ & M & θ motor. i ngulr peed nd i ngulr ccelertion. he electromgnetic torque generted by the ervomotor i = M Ki () where i torque coeicient o the motor nd i i current. K he electric eqution cn be expreed by di u E = L + Ri (3) dt where u i input voltge o the motor, E i induced voltge, L i inductnce o the motor, nd R i the reitnce o the motor. Fig.3.he mechnicl ytem Air bering Motor he induced voltge cn be expreed by K b θ & E = (4) where K b From (1) to (4) i coeicient relted with the motor. i di dt J & θ + C & θ = (5) K J & θ && + C & θ = (6) K

3 Velocity Accelertion Poition + Poition Velocity Accelertion PWM Power Ampliier Angulr Accelertion rnducer M Angulr Velocity Grting Angulr Poition Fig.4. lock digrm o the controller Finlly, the dierentil eqution o the ytem i L J) & && θ + ( L C + R J) && θ + ( R C + K K ) & θ = K u ( (7) he Lplce trnorm o the ytem unction (7) i K Θ( ) L J G( ) = = U( ) ( LC + R J) ( RC + KbK ) (8) [ + + ] L J L J he controller i hown in Fig.4. riple loop re ued to control the ytem, nd prmeter o ll triple loop cn be djuted digitlly by computer commnd. he rbitrry wveorm genertor bed on PXI bu ytem i ued to generte control voltge ignl to the controller. Grting i ued or poition eedbck nd the dierentil reult o ngle poition i ued or ngulr velocity eedbck. An ngulr ccelerometer i ued or ngulr ccelertion eed bck. he control ytem work in dierent mode depend on dierent ppliction. High mplitude tbility nd low hrmonic ditortion i very importnt or ngulr movement clibrtion. When clibrting rottionl ngle trnducer, the control ytem work in poition control mode to generte tndrd rottionl ngle movement. In thi mode, three loop work t the me time; the prmeter o ll three loop mut be djuted to obtin high qulity rottionl ngle movement. Angulr velocity loop nd ngulr ccelertion loop re ued to compente the chrcteritic o poition loop nd incree the reponibility. When clibrte ngulr velocity trnducer, the control ytem work in three loop or two loop mode, which depend on dierent clibrtion requency. In clibrting ngulr ccelerometer, the control ytem work in only one loop mode; only ngulr ccelertion loop work in thi mode. b.3. Principle o uing ler intererometer nd column grting meuring ngulr movement A column dirction grting i locted under the irborne meuring tble o the ngulr vibrtion exciter, concentriclly to the xi o rottion, nd trnducer() re mounted on the urce o the tble. he object light bem o the intererometer trike the grting t the ngle, which the irt-order bem dircted by relection. he dircted bem return into the direction o the incident bem. When the grting rotted, the phe o dircted bem chnge, which i proportionl to the rottion ngle o the grting. he ngle o dircted bem i in ccordnce with the dirction ormul kλ = in α + in β d where k i the order o dircted bem, λ i wvelength o ler, d i grting ditnce contnt, α i incidence ngle, β i dirction ngle. o reduce the error due to eccentricity mounting o the grting nd other error ource, two ler intererometer re ued in the meurement t the me time. he ngulr movement vlue i clculted uing two intererometer ignl eprtely, nd then uing the verge vlue the meurement reult. he heterodyne intererometer nd ignl proceing ytem re hown in Fig.5. It modiied Mch-Zehnder intererometer uing helium neon ler with wvelength o 0.638μm, nd the requency reltive tbility o the ler i in the order o A rgg Cell with reltive requency tbility better thn 10-8 i ued in the ytem. he rgg cell generte requency hit (5 MHz) in the reerence rm o the intererometer, which i ued to determine the ign o the ngulr movement. he intererence ignl o the (9)

4 Ler rgg cell Qurtz ocilltor Photo detector Signl genertor Lowp ilter Lowp ilter U m U re A D C.4. Clculting the ngulr ccelertion he rottion ngle o the inuoidl ngulr vibrtion in (11) cn be expreed by Φ[ n Δt] = Φˆ co( ω nδt + ) Φ + C (1) where Φˆ i the mplitude o rottion, Φ i the phe o rottion ngle, Δt i the mple intervl o ADC,ω i the vibrtion rdin requency, ω = π, C i contnt, n = 0, 1,, Fig.5. Intererometer nd ignl proceing ytem object bem nd the reerence bem i converted into n electricl ignl in the photo detector. When the grting rotted, it will generte requency modulted crrier ignl in the RF region, whoe centre requency i identicl to tht o the couto-opticl modultor drive ignl (5 MHz). he directionlly enitive Doppler inormtion i thu contined in the RF crrier. he igned object velocity o grting determine ign nd mount o requency devition with repect to the centre requency ± Δ. he intererometer output ignl nd then ± Δ mixed with ignl genertor output ignl, ter mixing nd low-p iltering the output ignl turn to nmed U ± Δ m nd nmed Ure. I i 6MHz, then the output ignl requency ter mixing i rom round 5MHz down to round 1MHz, thereore, they cn be mpled by ADC crd nd needn t uing very high mple requency []. he mpled dt then decoded by the PXI bu intrument nd qudrture ignl U 1 nd U re obtined imilr to homodyne intererometer with qudrture output [3] [4]. he dicrete-time ignl U 1 nd U cn be expreed U 1 [ n ] nd U [ n ]. he erie o modultion phe mod[ n ] rom the movement o grting cn be clculted by rctn clcultion nd phe unwrpping procedure 1 U [ n] [ n ] = tn + kπ U [ n] mod (10) where n i imple eril number, nd k = 0, 1,, 3, Chooe n integer number k o tht dicontinutie o mod[ n ] re viod or the vlue k π. From the reult o modultion phe veru time erie mod[ n ], the rottionl ngle cn be clculted by g Φ [ n] = mod[ ] π n (11) where g i grting ngle contnt in rdin, which depend on the mnucture with ccurcy in the order o erverl rc econd. 1 For the inuoidl ngulr movement, the mplitude nd phe o ngulr velocity nd ngulr ccelertion cn be clculted by: Ωˆ = π Φˆ, Ω = Φ π / (13) ˆ α = (π ) Φˆ, = Φ π (14) α i the requency o ngulr vibrtion, Ωˆ nd Ω where i the mplitude nd phe o ngulr velocity, αˆ nd i the mplitude nd phe o ngulr ccelertion. α he output voltge o the trnducer i mpled by the ADC nd cn be expreed in the me wy (1). U [ nδ t] = Uˆ co( ω nδt + u ) + C u (15) where Uˆ i the mplitude o trnducer output voltge, u i the phe o trnducer output voltge, C u i contnt. In (1) nd (15) the mplitude nd phe o rottion ngle nd trnducer output voltge Φ ˆ, Φ, U ˆ, u cn be clculted uing two method. One method i inepproximtion [5], which ue let qure method clculting the mplitude nd the phe o the rottionl ngle. Another method i DF, which ue the dicrete-time Fourier trnorm method clculting the mplitude nd the phe ccording to the clibrtion requency. Digitl imultion nd experiment howed tht the irt method could obtin good reult i the vibrtion in low hrmonic ditortion nd high ignl-noie rtio; otherwie, DF method cn obtin better reult [6]. 3. CALIRAING ANGULAR RANSDUCERS Dierent kind o ngulr trnducer, including rottionl ngle trnducer, ngulr velocity trnducer nd ngulr ccelerometer, re clibrted uing the primry ngulr ccelertion clibrtion tndrd. It how the tndrd i tble nd repetbility o the clibrtion reult i very good.

5 Fig.6. Clibrtion reult o n ngulr velocity trnducer Fig.7. Clibrtion reult o n ngulr ccelerometer Fig.6 i clibrtion o n ngulr velocity trnducer; the clibrtion requency rnge i rom 0.5Hz to 30Hz. Fig.7 i clibrtion reult o n ngulr ccelerometer; the tndrd work in contnt ngulr ccelertion mode in the clibrtion proce nd the requency rnge i rom 0.5Hz to 100Hz. 4. DISCUSSION he ngulr ccelertion tndrd introduced in thi pper uing ler intererometer nd grting meuring ngulr movement, nd P ue imilr method [1]. he ccurcy o thi tndrd cn be increed in the uture. ecue there i no limit o rottion ngle nd the uing o ir bering ytem, thi device how high perormnce in low requency ngulr movement clibrtion. For the requency bove 00Hz, nother device h been developed nd will be introduced in the uture. 5. CONCLUSIONS he primry ngulr ccelertion clibrtion tndrd h developed. It ue the bruhle motor nd the ir bering ytem to generte ngulr movement. riple loop re ued in the controller nd grting nd ngulr ccelerometer re ued in the eedbck ytem. he tndrd cn work in contnt ngle, velocity or ccelertion control mode with no limittion o rottion ngle. wo ler intererometer nd one dierentil column grting re ued in the meurement o ngulr movement. he tndrd how low hrmonic ditortion nd high tbility in generting ngulr movement. It cn be ued in clibrting complex enitivity o ngulr trnducer in the requency rnge rom 0.1Hz to 00Hz with mplitude uncertinty better thn 1% nd phe uncertinty o 1 degree. REFERENCES [1] H.-J.v.Mrten, A.äubner, W. Wbinki, A. Link, H.-J. Schlk, rcebility o vibrtion nd hock meurement by ler intererometry, Meurement, 8 (000), pp.3-0. [] W. Wbinki, H.-J.v.Mrten, ime intervl nlyi o intererometer ignl or meuring mplitude nd phe o vibrtion, Proceeding nd Interntionl Conerence on Vibrtion Meurement by Ler echnique, Ancon, Itly, 1996, pp [3] Li Zhng, Jun Peng, Primry ccelertion clibrtion by heterodyne intererometer nd PXI ytem,proceeding o SPIE Vol.5503,004 [4] Li Zhng, Rol Kumme, Invetigtion o homodyne nd Heterodyne Ler Intererometer or Dynmic Force Meurement,Proceeding o SPIE Vol.5503,004 [5] Interntionl Stndrd ISO , Method or the clibrtion o vibrtion nd hock trnducer- prt11: Primry vibrtion clibrtion by ler intererometry, [6] Li Zhng, Rol Kumme, Invetigtion o intererometric method or dynmic orce meurement, XVII IMEKO World Congre, Metrology in the 3rd Millennium, 003, pp