Accurate Calibration of VibrationTransducers from 0.25H2 to 11,500 Hz

Cofttlinn.. ta Dttrnatiottnl qulitlt stnndords tlSO 90(t0) hos h.i[htttud n.rd/tn.s. nl.nlibtdhon and tra. l,ilitvThi t .n tphosis hns fa.ust i l n tar . o t te, t t io t t o , t t tu f ie lds of t t . t ro losu otd . r l ibrnt i t )n , ca\ t t i f tg hoth '1 !a ' .ar . tn ls atdopport r i i t i .s l t t thos. in1\nud h a l l n . ryct . . o f t ( t a t td t tun;wctr . r i d . i i r i t ies nt l tu l ing f ibrot tun t ran! l ! t . r !sudl as a.ct l . rorr tcrc in . l u loct tv p ickups. I rddi t io i tn a g. t . r r l or rdn,r .ss oFt le,cei l rd .d l ibrot . a . . t l . ra t t . t . r .n d Rlacitv ti(ktLt1s, ther. is d gron'nr,{ stt.nrl trr.lest itt ulv tou' fr.qR c! dnd ltrsh frqkicv .alib tions. MBDlndtn i .s has dt | t lopen a s ls ten1 that o l loa 's occutdt . cd l ibrut io t of I ibrct ion t ru isr l tc t l t f ror t A 25 l l : to11,004 Hz usin[ a rcf.r.,t.. a..tl.raNtet, a 'nore alfordrbk altunntiir to lds.r..

iLhere. g= acceler.tion (gp( nk), f= frequ€ncv ( Hz), d = d isplac.mcnl (inchcs pk pk)

Acceleraiion gcts snallc! at. frequenc! sqlared rate ifyou hold a constant displac.mcnt and go to l(nter ind

Edward L. Peterson, P.E.Directoa Appli.ations Engineernrg

MB Dynimics

IntroduationHistorically, calibrations of vibration transdu.crs have

bc.n b.tivc.n a loi'frcqucncy oI5 Hz to 10 Hz nnd ahigh frequencv of 4000 Hz to 5000 Hz. In recent years,increasirg demand has bccn nndc to cnlibrnt. bchwI H7, in $me cases as kN as 0.25 Hz, and at higher frequcncics lo 8,000 Hz, 10,000 Hz or cv.n 11,000 Hz

In concert hith this ne€d to cilibrit€ to lorler and higherfrequencies is the nlost important {a.tor oi good calib.a'iions dsstri,r!' n rsorrbl. d..!rn.v. Thc chnllcngc hns bccnfor der€lop€rs to providc solutions that are economicallvfeasible Some labs have taken the approach ofusing lasers, ivhi.hhavc somestlong technical attributes. but arec\trcmcly .xpcnsiv.. UsinS a pre.ision calibrated rcfeFence accelerometer (REF) is a much more affordable apprcach. Historicallv howevea the Rl[approach hns runInro l imira l ron, a l low f re, {Jen.rc, anJ h iBh requen. ,e. .The challenge for this projccl, thcrcIorc, rvas to push thclimits of traditional REF technologv to see hoN accurateit could be at both low and high frcqucncics.

Signal Level Challenges of Ultra-LowFrequency Accelerometer Calibration

Am.jor problem at ulfa lo( frequencies is that ac.eleration vil!es becomc rxtremely small ns thc lollolingcquat'on deDronstrates:

t = 00511 f rd

Mark McElroySoltrvar. & Il(]'bised Svstens Development

MB Dynnmi.s

Jet f Campbel l moni to ls MB Dynamics Win4T5 Vrbfaton

No\rMBrR . DELIMBR l99i 30

This effed is shown graphically inFigure L For example:

' Al l0 H2,0.5 inches pk-pk of dis-placenent ptoduc6 2.s5 g'! pk of

. At I Hz, 0-s inches pk-pk of dis-placeme.t produc€s only 0.0256g's pk of a.celeratio$ andAl 0.25 Hz, 0.5 inches pk-pk ofdieplacement prduccs onty o.ml60g's pk of accclcntion.

Itwill bc shown later that 7 mV (or7 pC) is a g()od tarSet level (or thcnonamplified output of a transducerThis lcvel of outpui ftom the trans-ducer is necessary to achieve suffi-cient accuracy. Thegraphin figure Ishows thal a l0 nV/g (or 10 pclg)accclenrmeter pnn!.es over 25 nvpkofoulput above t0 Hz, which is si8-nificantly higher than the targeted 7rnvPk of oulput, and therefon en-

However at I Hz, 0.5 inch€s pk-pkof displ.cernent produ.s only 0.25nvpk wh€n a 10 mV /g a(€leruneteris us€d. This is far short oftheTmvpklarget. In fa.t, even a 100 nv/g ac-celerometer does not prDduc enough

output .t I Hz with a displaementof 0-5 inch6 pk-pk. To accurately cali-brate a 100 mv/g devicc at 1 Hz requires approximalely 1.4 inch6 pk-pk of displac€ment to produ.e the tar-B€{ 7 mv /8 (or 7 pC) pk of output.

Sinc€ 0.25 Hz is four tim6 lowcr inh€quency than I Hz, the low acc€l-eration level p.oblems are sixteentimes worse (the s4!o/e of the fre-quency raho). A lm mV/B accl€r-ometer would need to be vibr.tedwith an amplitud€ of approximately22 inches pk-pk to produce the taEet7mVlSofoutput. Clearlythis is notpractical. However acc€l€romclcrsdsiSncd to measur€ vibration at lowtEquencies always have hiSh outputsfor the very rEasons established in thepPceding discussion. A 5oo mv/8acc€lemmetq c& produce sufficientoutput when vibratcd with an ampli-tude of 4.4 irch6 pk-pl ofdisplace-m.nt (which is practical).

Thc olher challenge faced by thcpractitioner doing low fr€quency ac-celeromcter calibrations is lhc frc-quency r€sPoM of the slandad orEf.renceaccelerometer. llistoricauy,low irnpedanceorhigh imp€dancepi,ezmlectric t'?€ acceleromelers havc

been us€d for ac(€lNm€ter calibra-lion systehs. These devic€g can bemade to respond at low frcquenciesif car€ is taken to assure the time .on-stant of the sign.l conditioning isfrkhed lo the r€quirEd ft€quency FsPons€ of the m€as'ltment and m€a-surement s€nsitivity is high (2 500mV/8). Additionalty,thcaccelerom'eter lincadt, measurement noisc,and hysteresis husl b€ low €noughto assnrc thal the signal acquired bythe device provids adcqu.te head,room against these combined nois€

Oth€r types of .ccl€roneters thatexhibit god low fnquency r€sponsearp capacilive. piezoresistivc, andseno accelemmetes. Thes€ devicescan Pr0duce high outPuts down toDC and s€nsitivitie of 500 mv/g ot

Getting the Best Resultsfrom Diff icullMeasut€drents

Th€ problems that o(orr with ul-tra low frequency signal levels can bemediated by using a device that pcvides lar8e displa.enents, high out,Put *Bitiviti6, and gffd frquencyrEsF nse. The d6ign elements usedby the MB DynamiG developmentteam to ensur€ thes€ charactcristics

1. A krw noi* signal conditionerto minamize noisc onsisiing of lhefollowing:

' Low noisc amplifiers,' Hi pass filters s€t below 0.1 tlz;low pass filters above I l 5 kHz;Massiv€ ground planes to assurecommon signal ruference thrcugh

' bw nois€ power ruppl],,.Signal conditioning of both *!,soE by one paclaged unit usingon. power supply and ground

'Noi !€noo.beloE l0gV

$.b rna -OrM. rn[ oot &!b|'rrt

Figu.e 1. Displac€rhsnt and Acceleration

3 l NdrMBEr . DKNIE|I 1995

AccLr^TE C^rruR^ro\ o| vrBLAnoN TRA\sDLcLb r Ro\r 0.25 Hz n, u,500 H7f,ohrRo 1.. P.r.ra,N. Zf.. Mai( M.ELR.\

2. Gains set to optimtze systcm rcsolurion. The daraacquisit'on is pcrfomed using a 12 bit A/D converrcr.Sincc maximum .ccuracy is deired, it is necessary toad iust the gain. The siSnal conditioner and the A/ D boa rdgains should be set antomaticall! b), $ftware. The MBDyna nics system sets the followinS gainri: 0.5, 1 , 2, 5, 10,20, 50, 100, 200, 500, 1000, and 2000. This allows inputvoltaSe Fak-to-pcak ranges from 2.5 mV to r0 V Thegain setting is indep€ndent for each channel, alloh.inthigh seNitivitv references simultaneously withlow sen-sitiviiy i.st rccclerometers. Cain levels arc set pnor todrivc signal output based on esiimatcd peak voltag€s.When the *l(ted vibration l€vel is nach(d, thegain forcach (hannel is reevaluated and adjusted accordingly.This is detemincil bv the matimufr aain *$in8rhar do6not Prqluce clipping.

3. oveMmplint to ensure gftrd spectral line spacin8in the frequencv domin and a high confidcnce tei el. Areach test level and frequency poinr, dara tullection isstarted aftervibration frequcncy and levels are confirmcdand gain is sct The data is colle.ted in ens€mblB of 2(X8Points at 6tl timcs the drivcn frEquency. Each en*mbtecontaini:]2 cvcl6 of data.

The .ollstion of data at many timcs rhe dnven fre-quency is called over-$npling. Oversmplingalhws thesyslem to be moretolerantof harmonic distortion at lowfrcquencies and using more data points gives thesyst€mb€tter sp(tral resolution. In this sysrem ir is pGsible roset the numb€r of ensemblE us€d per rneas!.€ment ro 2,4 or8. The morc ensembles taken, the more averaSes andhigher degrees of fpedon. Howeve., taking mor€ €n-sernblE requirFr more time. The +enscmble *tting isKommended since it 8iv6 sufficient accuracv whilcminimizing acquisition time. ln thc frequency domain,the spectral line spacing isdetemined by the emple rateand the number ofpoints in the ens€mble

Frequency lntePal(6)

Jr=----;-

whep, n is the number 01 polnts in an ensemble. Forexamplc, if the sample rate is 64 times rhe driven fre-

If. = 204a,then fi = 1.670 of f.

4. Data is windowed for more accurate dimre levelmeasurements. The Hanning window function is usedb€tause of its excellent pcak resolution in the hequency

t l i r = Rr r ' r05- Fr r ! r05r .o \ : : : - - -\ 4 )

5. Pril€sing is pcrfomed in thc fRtuen.v domnrnThc frequency domain prGess is morc accurateand nois.tolerant. Additionallv, it has lheadded benefit ofsign i-canlly reducing anv crcrs due to sine uavc disb.tnlncaused bv the shaker. T}le pnxcss bcgins $ith the indi-vidua I specha lor thc REF and the DUT. Th(' Au to Pos erSpectrumA(o) is calculated forcach chann€I.

Auto Power Spertrum;

5, , = FFT (X)Ft1 tX)

Scaled Magnitude SpNtrun:ls- r.rl

The fequencv and peak power arc measured for eachchannel. This is accomplishetl by a p€ak tcarch and in-

I I ,4 ( . / r r ' t ) j''f

eut

NAt- t 22

I' = co.rection for bandwidth spread €aus€d byttaming window = 1.5

The *arch region is *t to 1 /32 of the spectrum oi I /6,1of the number of points in an ensemble. This means thcsp€.trum 1 32 sp€.tral lines is included in the Fak parchWith n=204{l and 64 times over,samplin& the s€aKh re-gion includes 1 5l .2q of the d nven f'€quency.

The frcquencies of the REF and DUT are cornpared.They must be the sarne since both are e)(fr€riencing theeme vibration. Any diftpancy is reported to the u*rTh€ power values aR us€d to compute a transfer tun.-tion and DUT sensitivity is calculated from the avern8etransfer ove. the ensembl6 collected-

DUTl.rzl IDW\.tu = =::::i-----' REFs.nte . --t.tKAL

NovEMB[l . DECTMBEi ]995 32

S€lrcAL = lhe s€lf calibration transfer tunc-ti(rn of the signal conditioner orthc linear intetPolated transfer;

REFscnse = the NIST t aceablc sensinviry orth€ lin. intcrpolated *Nitiviw;

DuTlovcl/REFlerel = thcnlerage fransfer function.

channels are not elactly mat hed This diffqence is typi-cally less than 0.25 percent over the ll.5 kHz bandwidth.However, il is a consiste.l prcpcrty of the measurementsystcm and therEfore is measured and applied as a cor-(rtion factor in the calibration cquation.

Coherence is mcasured to determine thequalitv of thcsiSnalsand is us€d to mark suspe.t data. The coheienceof thc calibration should be ideally LtXx,) ar all frequen-ci$ used in lh. cnlibration. lf thr coherence is less than0950, thcn that frequcncy should be flagged asqu6tion-able. cohcFnce lK ) is defined as tullot{s:Detection and Correction of Errors in the

Test Systemwheneler possibl. thc tost sv5tem should dctecl emrs

it i!.nusing and if possiblt', correct them. To insure accu-racy in. sin8le st.p tcst, the rystem m.kcs conechons torthc nirmdtching ofthc REFand DUTchanncle in the signal.onditioner (figure 2). This js d one through sellcali'

When signal levcls out of thc sen$s are 7 mVI'k orlarger the overall systcm is able to produce elcellent r(-sults. Therefore it was d{ided to flag any frequcncres rna calibration that had lss than 7 mvpk (7 FC for highimpedance transducers.)

Ref erence or Standard Accelerometers

It is importantkr ke€pin mind that no acc.lcrometer isperfect. That is, anv accelerometcr will ha ve dif{crcnt sen-sitivities at each hequencv in the sp€rtrum. Therefore itis cru.ial that th. .alibration svstcm b€ gilen thc ini(r-mation on the trequency rcsponse charadcnshcs oi therctcrunce accele.omoter and that the tcst svstem corroclfor those known deviations in sensitivity ;i various fre-qucndes. Using this approach makcs il acceptable to usea r€f€rcnce accelerometer that rulls off at low or hish fre'qucncis - rs lonS ar it i\ srdblc (reFatable, and Js hhtas it produces al least Tmvpk ofoutput.

The b€st way to obtain sensitivitv da ta o. the referenc(accelercmeter is to have it calibrated at n pnmiry stan-dards laboratory MB Dynami.s usos ihe National lnsti-tute of Standards and Tcchnologv (N IST) in GaitheEburg,Maryland. This assu6 the b€st Fssible a.oracy andtraccability for calibrating accelcromctcrs and velocity

Keep in mind that the tumaround time fo. sendin8 areferen.e accelcrometer off premises ca. be problcmaiic.It is the.efore good pra€ticeto ke€plwo referEn.e acccler-orneteE on hand, one to u* in thc svstem and the otherlo bc sent back to NIST for penodic recalibranon.

The data is colected and ptrGsed at discrele fnquen-cies and levels sFcificd by the us€r in a sine test profile.The sine swepcan b€ steppcd to spe€d the t6r pMess,ir. the test can ramp up, collect data, and ramp down ateach specified frequ€ncy and level in the profile

Acceleration, velftitv, and displacement limits can beimDosed on the test to Drotect shakcrs or s€nsoE used in

Fi9u16 2. Closed-Wire Channelto-Chann6l Sysl6m SellCalibration

Thc svstem *ls up an accelercmet.r calibration of acloied R,lrc on the REF and DUT channels. The REF ddDLT cha nnels both mcasurcthesamesignal and the transler tun.tnrn should be 1.00 at all frqucncics.

V * =V p H nn and V, , , , =V,n H n, ,

The REF to DUT trander lunction is:

etta AL = !!lL

Uwc assutne thrt: HNb =l

thctl. V* =V,,

vfc\l,= HN =:-2!L

Thc actual transfer tunction will differ where th€ two

33 NOVEMBII{'DICEMBEN .O" ffiEAE

\ , , r F \ r F C \ r r u R ' n , \ , ' , \ . , , ( \ , , ' \ T R ' \ . . r . F N - f r , , ! L r l i r l l r , I l . i ( \ l H /E : , . , r r . , 1 / ' , r r \ l . . . r 1 . I . .

ic \ ( rnA l l rFUrc l ) The l ' rohle ( in bf\ f t . i t i fd rn A \ . r iPc. . rnd lh . rPe. ' -r r rd |1 ! ! t \ . r re p lot ted on rhc t r .Phind l r \ l t { In th. t ib le Thepn)t r le t .ub. . i ! r . l l \ r '1 led in o.Lr \ ' r . or r r i r -l r j f . l ( \ l i re . t rp\ or the REF t i re-nbl . t ( \ l ! .n . \ ponts can be u\ r lTh. l r r ( lu .n. i f ! n t $ h i .h the RFF hn\been ! r l t t . r r t .d tv NIST arc th. Dr \ ti . r for i r r l l f \ t i rc !urnr ie\ beQu{thr ! n( drncth t raccablc to \ lS lT l \ i \ i \ Inr f . r tnnt be.n! re thc rc \u l t! rA . . l i t r r , r t r ( {1 ot the DLT i i d i r . . lht r . r (crb l t , to lh . REF.. l ibr i t ron . . r .

The 7 rnv Ru le

1hr r r \ t runrent i t ion l ied i r r th . \ .i r lL l ,nr t rL, r \ rnL l rL lc e\ t renre l ! hrNh! tur l i i \ r . r fhrrer \ l l Lr i t A l )a\ rn( llL is r i { f \ . i f \ t ruDrcnt . r t i .n thr( t r rEhL , u i l l t \ \ ( \ f ' . i l \ i ! J f l d . l n r . lih r t r rqh lh . . ( t r r r ! f o t the le ' t ' th . r l\ l i ( , , l l , . n t ! r r . . l \ r t F u t t n r r l l r ! r. , . . f 1 , n l n f r r ! r i l l . l . ! l f \ : n r \ f l , , l

.rtpr,\,hatelr i m\ lt\ls. rhr (\nll\o , lhc R&ls lLn l t t f s i \ l r . . th t ( \ 'eml l\\ (em a.r!ra.! l()!..1jr tr.(.!ne un

Thr bi$ nr thri fu,lr F ,, jgn.rlt , ) fo i r . i \ !ue \ \ h r lc th r n . ,F r r l ( \ r r. l the nren tu funr rn t \ \ \ t .n r hn ! nminrmun l$ r lo t l t r \ : th f n i r { t l l r r r0 r th . l fn { t r b m! .h h ,Shf r . \11 r .n '\o r \ h r !e e i ther i r . soh l ! t r r ! f ( \ rh. i ln f o r a s iBna l - tGno i \ r \ f r . l f l . . ' -l i (n r The re !u l t i \ lh . r l (h r \ .n .o r i l$ . r \ \ ou tPuts n rm. no i \ r n \e l \ . \

c .h rn i .a l a . .e1er . t i ( r \ \ i r : r i l th i t l \ln i l l cnough b i t fn r .h th i l rL r . .l r \ c l h i l l nn t t r r tu \ , j \ .d l ' \ t l r . ' en-. ( ) r Thr . rc lo re lhc i rFn . r l l ( \ r l n ru i l. ,1$ . r r ' be abo\ e l1 [ r . , \ '

. \ \ . r n i le , r t i . d ln in l r lh . r ( f f t . rb l (to h . r ! ! nn { rder o l l r iAnr l ! J r th . r t r \N j rc \gnn l thnn t ro i \ . r , l r r ( l l J ( , rr r rn in rnnr ! i !n .n i ! . r rF . r , \ l !P .nL\ r l r rnhon t ranrduL. r lL r . r \ . r \ r i r \ ih. rn . l n . r \ , i I , \ t r th r i n , lu rn* i : m if ( r l i s n i l l h f ; n r \ n l t l L i n f r r tL . l h ( . ( ' f r t i . d { r l r n l l . r l r i , f n f df L , r . . h L i ' i t i o n . \ . t f n , L , r " r , ) r r L , n

Spec ia l P rob lemsEncoun te red a t H i ghFrequenc ies

At 'o !1 . rL r t )L r I l l l l r , f r . , ! t rh .n ! r rs. !n i ron t !d \ r (h . r J rJh nr r t \ , t L j i . h r ll !nFe i T$1, n r , t t , r l r r ( rn i 1 , i .n r r t r rca t ta .hnrent L i r lh , . ) r ( f [ i ,u r te r : r ,the nr . r l t r ind n , , , . \ l ( , , i J r f r A th ,CI iiRquende\ ih t J i ' l .h ( . . r fn t ' L in 1 . .. ( im! c \ i tun t r . l \ {n , r l l R . . rdn{ i r :lh r .qu i t ron l tu \ l r l .d i l th f h r : rn

J = g i L r i l l r. l = . l r , . t r f rh r r , rn ih . : f l f l

t = h r l l u r n 1 \ l l / rg i .n l f i , r 'L i " rL I r l I

F . r r . \ in r f l ( J l i L )L r r i I I / , r l \ f i . i lI t \ ' r l i l l r r ! l ) l n \ r ' l l . r r l f r ( th r fI L r r rL r l r f .h . . f r f r L , r J r . f l i . rn r fn r

i r . , r t h . J , . f l . , . , f r ( n r . . , r . r \t . r n \ . 1 \ . . , . , 1 : r r r . 1 , , , \ r . , 1 t l , . , l r f !n r r t r r r . r r r r ( 1 . l i l . l , . r i r . r n J . n r , \ , l l ll l r : i l ' , f , 1 , ' . . , , \ r , , l , r h r l \ l L r l . f i i t !t l k . n ) . ' r ' r ' i . ' r r r . r \ . \ . r f r ' ,e r r jn t r !r . r n . l r i L , . r i l . r ! l r l h l l l I f . \ i !€r nJ . r l . , l l ) t | . r r r L i . r f \ I \ l u . n ! r , .\ t r I r \ l l L i n r L r r f l r , l l r r . r 1 1 , l h . s h i l t i, r r L , r l r i , , l l i r , ' 1 r , , \ , n ! r l l , r L f .i l i o \ r f , ! t r i L l L L n . , f t , l \ r L r ' ' t , !l l l l r f l r l r , . l ) L | 1 . , i L r r 1 , , i - - r ,j , \ \ t r : r . r l r i r . r L , f r ! - I r ' r ' ! . ] . : '. . , 1 . 1 , . , r ( r . l t : , 1 , , \ - , r ' - - . : . i . : . .5 \ t h ! f , , ' r r ' r l r i i r ' , : r , . . : : rJ r . , J l . r - - r , . , : i \ f : , _ i i r , . . r 'i \ J i r r \ { r l l r l

T l , c , . . , f t L ' . 1 . : . , r r \ , , l : r . i - 1 , 1R E F . . , , , l , t , r i : , , r r f r { . l \. 1 L , u b L I i , l . . L l i l I - . 1 , , t r r 1 ! r l l j l

r L g h l r r l l r i . r i i t , ' l l i L . . i r d L i l l . l lj ! i t t . , L h . ! 1 1 , j i h ( . r , 1 , , r . , l ' l ( . , n J r l , ,D L T r : r l i r , i i l l i , l l r l l , l l r ! l , T ' L , i r l lI i E F l r l l , , . , , f , r L . : L , . , 1 r f . 1 l ) r f r !i r . r e J * I . i l L \ L 1 r , . , , r r l i i i J I r , , I L\ . , 1 , J n i , \ , f \ t i . , r r : , , , . , , l r L L \ r , : l :, i r { r . r f r . l ) l l . r r , r : h r f : l ! - -

, o r n ! r f , r h , , , , r l i i t . n - L r l . r 1 i \ r r r l l rr r l . . r i \ l l i , i l I t , , h . i \ r J , r r ! J . r ' :\en \ r t r \ r i t r \ In .L t { \ I L i I f l l l l rL - . r

f -rt]@ r@aF

t_t l r@

itc- -aE-,1acf

HEEHffi- t rEi ]@_t- -H@EN I

F l lu re 3 MB Dynam cs W f ,1 /5 sc feen o i s ne les1 pro l e

f-If-

C\ i-I ;T \, 1 ,, ,r . r,L , r rul i l

neously. Each of the.hannels has its own charadendi.error term, R for the r€f€ren.e chamel and D for the Dtn

lr1+* r"p rcorrD______{

- Hl- **.^"-{41-F-]I

Fiqure 4. Relerence (REF) acceleromets. sstups.

ror is minimal (t]?i.ally less than 0.25%). However atfrcquencies h lhe q.000 - ll.0O0 H/ r.nge. th6€ errors InREF sensitivitiescan get extremety large. For.xanple, ifa double-ended REFrcB Model30lA04is us(d withouta DUT (i.e., th. REF is used inside a shaker's armafur€and the DIJT attached to the top of theamature) the er-rc. can be more than 107. at 10,000 Hz. Obvioudv thispanicular confiSuration should be avoidedl

The Redstone Check

In order to evaluatc thc cffNtivencss ofthe signal proc.ssinS technjques, data manipulafion routines, and anvd€fici€n€ies of the shaker subsystem, it e'as ne.essary loperform some type oI lerification. OneofMBDynamic sfiBt generation calib.alion systems had been certificd bythe metrclogy lab at Redstone Arsenal. MB's develop-ment team was impressed with the simplicity and effe.'tivenes of R€dstone s v.rification m.thod and has since

The Redstone Check uses two accelerometers, B (bot-tom) and T (top). It work equally well for eith.r of thetivo basic configurations (figure4). ANlSTtraccable ref-erence ac.eleremeter {ac.eleromete. B) is used as a .om-panson standard to calibrate accelerometer f Thesensi-tivity data is collected on ac(elerometerT to rEdefine it asa reference accelerometer and use this data 1o calibrate

Theoreti.ally, the sensitivities obtained for accelercmeterB should beexactty whatwas started with. Ary dif-ferences in sensitivilies bell'een whal was startcd withfor nccclerometer B and what was rctumed at the encl otthe second step ar€ du€ to enors in the calibration system

The derivation shown in figure 5 defines the relatron-ship of the total measured ercr to the overall system accuracy ((XA) fo.one direction. The selup in figure 5 as-sumes that a noncriti.al voltage ofa magnitude V,. is applied to both thc Ef.rcn.. and DUT channels smulta'

Figure 5. Overall systsm accuracy d€rivalion

The voltage reported by the syslem for that measuredin the reference channel is therefore:

v*, = v^[1+t*l

Simil.rl],, the voltage reported by the system for the DUT

v",- = v,t l+tol

Th€ DUT rensitivily is calolated as a ratio of theseterms, as modified by th. known teferen€e sensitivity. Ifwc assume a reference sensilivity of 100 mV/9, then theDUT s.nsitivjty may be cal.ulated as follows:

ouT SENS = vorq/lvur/REFERENCE SENSI

DUT SENS = v-(1+:D)/tv(l+>F)/100 mv/gl

DUr SENS = 100 nV/C t(1+:J/(1+:-)l

The valuc of DUT SENS in the Redstone verificationprccess now beones by substitution the value used forthe reference sensitivity. The process ofcalolating a newDUT SENS is then conductcd in identical fashion to that

DUT SENS = v,,1,, /lvmr/REFERENCE sENsl

Agnn, hv stbslihnion:DUr sENs = v-(1+:J/lv{1+I*)/100 mv/C(l+tJ/(1+I*)l

DUT SENS = l(1+Ltl(1+tR):ll00mv/g

Thus, thedata provided by the Redstone Check rcsultsin the second test, which is the square of the a.tual errorterm in question. The net tcsult is that a second test error

3 5 "Flll-.NoVEMBER . DTCEMBER lqcq &-A.L.. ..._L A lt

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A.cLMrr Car rBuro\ or VBRAno\ TR^\snu.rrc .rort 0.25 H7 ro ll.500 H7E.)M{! I Prr.rnr\. ?E.. M.1ff M.EiRo)

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Figure 6. Scall€r rosulls tor l€st range 0.25 Hz lo 40 Hzwith a 5 inch Strok€ Limil

tem of +0-5ci reflects in fact an overall svstem accuracvemr oi (l +0.005)r I or 0.2497':i.

Typical Results

Actual calibrntioN werc prformed using a shakerca-pable of prdl ucinS s ' pk'pk of d ispla.ement and usin8 a54'o accelcrometer as the referencc having a nominal 500nv/g output TlE de\ice under t6t (DUl sas a *noacceletumetcr $ith a nominal sensitiutv of 500 mV/8.TheRedstone Chskwas pcrfc,med several timcs todcfinethe amount of $atter in thedata, and the test wasrun frctn 0.25 Hz to 40 Hz. The results ar. shoB n in fig-ore 6. lt can br Fn that in thc ranSe of 0.2 to 0.{ Hz themaximum crror is 0.9o., $ hereas in the ranAc 0.5 to 1.0Hz thc marimum error is less lhan 0.25%.

High hlquency calibrations wen p€rfom.d using a 0.5inch strckc limit, a 100 mV/g refcren.eaccelemmeter anda 100 dv/g DLiT This test {as performed in the 10 Hzto U,500 H, ranSe and the Redst(ne Checl was perfomedseleral iimcs to de6ne theolerall svstem a.aracv. Fi8'w 7 sho$s the results.

Van' commeNiall) alailable shakers have a I inchstroke linit. Typicaly, shakers in this.at.Sory have flex-uEs so it is advisable to usea bit l6s than fullstKrke whenpossible (this increases the lite ofthe flexuns and redu.esthe amount of sine wave distortion). It is also wonh not-ing that $he l-inch strokc shalers can be driven up to10,0q) Hz. This configurattun providG d uncommonlvbroad frcquency range on one shaker. It was, therefore,decided to define the minimum frcquency thal could beexpected if0.8 in.h pk-pk ofdisplacement w.re availablefrom the shakcr Figu.e 8 shows theRsults of 3 separatel1s $.ilh lhis configuration. The dala suSgest that 2 Hzis a r€asonable los-fEquenc-r limit for such a shaker

Figure 7. Resl]lls lor tssl range 10 Hz lo 1 1,500 Hz with a0.5 inch Sl.oke Limit.

Conclusion

It is not n(eisary kt usea laser to do dcL'urate calibrn-tions bek\r I Hz. A kaditional reie.ence ac..le.omete'can bc used b obtah f i OSA do$n to 0.25 Hz and 0.251OSA down to 0.5 Hz. FiSure 9 outlincs the OSA limitsfor the 0.?5 Hz ht ll,50O H7 bands'idrh.

Tha orthnft a,ish hr tlckn,Ji|l.ds. rr,dsl i d'i'idunls &,/'.I'tot'rl.d somd tech"ical crt'?/tisc anLt .Etit1tflctlt: BiltRrst,l, P E , Dit..to/ of Prodri.r & Svsl.ars lrSirc.rt,.qlot MB Dviamtcs u,as inst tum.nta l in th( . l .s i ( i o ' td.isi,rh/v dr r.sr f!{s !s.,i and is r.stoi\iblt fot d.titns!h. OSA ftr'f,alottoi d.scribtti in th. R..istofl. C,r..tilar rv l r i lhr Sv.rc4 ' l ' r t .Xrdr 'or t rMB D!n" ' r i , . . ,n .

t " "I:]I;;--I",---

-e."3+r*trlF igur€ 8 . Resul ts lo , lss l range 2 Hz to 100 Hz wth a 0.8inch Slroke Limil

ol idr.hr. l|!l rd rin' lo 'n h ri !! d&

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No,rEvBcr . DlcwBER 1995 35

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Mark McElrc! rs in \1U Dlnami.ssofhlarc cngineer rnd ( dtrecllv re-sponsiblc kir u.h o, lhe derelopment and ter t iDB ( i rncncr l o l \18 'sl ! , r .1 i r i Windo\ \ -b i \ed UbrdtnrnTrnnsdu(er Cr l ibnr t rD Slst€m. I Ic$ i l l s , r )n conr f l . l ( h i t tsSLl nt C.sel\'estern Rrscn I U.n ersii!:

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