386. LINE SCALE COMPARATOR CARRIAGE VIBRATIONS DURING DYNAMIC CALIBRATION

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1 86. LINE SCALE COPARATOR CARRIAGE VIBRATIONS DURING DYNAIC CALIBRATION A. Kasparats, V. Vekters, A. Klkevchus,, Vlnus Gemnas Techncal Unversty, Basanavcaus str. 8, Vlnus, Lthuana E-mal: (Receve 8 arch 008, accepte 0 ay 008) Abstract. Oscllatons of the comparator, whch s use for the ynamc calbraton of long optcal lne scales, are analyze n the paper. The accuracy of etermnaton of the poston of optcal lnes on the scale epens on the velocty of the carrage, whch transports the mcroscope wth a CCD camera n relaton to the lne scale. Oscllatons nfluence the velocty equablty, ts value, an at the same tme the error compo measurng. The base part of the comparator s acte upon by external exctatons whch come through the founaton an supports, also ue to natural frequences of the comparator set. It s shown n the work that vbraton surrounngs actng on the comparator have a ranom character an correspon to the crtera of the normal (Gauss) strbuton. It s prove expermentally that preachng ampltues of measure components of vertcal an horzontal oscllatons nfluence the stablty of the carrage movement whch causes the error of measurng. Keywors: comparator, ynamc calbraton, vbraton, carrage, measurng, calbrate scale. Introucton Lne gauges are mportant components n the length lnk chan. They are use n the measurng evces (systems) an technologcal equpment, etc. The worl practce wtnesses ncrease focusng on the mprovement of lne gauge technologes an applcaton thereof n length measurement an precse controlle moton systems. oern precson scale proucton technologes enable to create small-step splacement transucers wth measurng possbltes that come close to those of optcal nterferometers. Currently, lne gauges wth 0.5 nm (,5 Å) resoluton are use n precson evces [,, ]. A rap avance of technologes, prmarly mcro- an nanotechnologes as well as mcro-electro-mechancal system (ES) technologes rases hgher an hgher precson requrements, measurng spee requrements an other requrements thus stmulatng creaton of new precson length calbraton systems. Reactng to these challenges the natonal metrology nsttutes (NI) an manufacturng companes create new lnear scale comparators whereof calbraton uncertanty s a value of the nanometer range. A lne gauge efnes one or several length values whch are etermne by the shortest stance between the centers of two lnes of the peroc structure (scale). Lne gauges are calbrate by means of optcal nterference comparators wth a slng mcroscope for vewng scale lnes an wth a slng measurng scale [4, 5, 6]. Interferometrc measurng systems are use for precse measurement of the splacement of these slng parts. Generally, the sources of nterferometer stablze frequency raaton are ouble-frequency He-Ne lasers. A calbrate scale s precsely expose uner the mcroscope. Splt-fel photoelectrc mcroscopes, pont projecton mcroscopes, confocal mcroscopes an photoelectrc mcroscopes wth CCD camera are use for the ntal postonng an the postonng of the centers of lnes of the measurng scale. The type of the mcroscope use etermnes n essence the measurement sgnal processng algorthm an the calbraton precson an rate. Further etals about lne (ege) etecton mcroscopes are presente n [4, 6]. Beses many evce characterstcs whereon scannng of lne gauges of the comparator s epenent, external factors affect the precson of the evce as well. One of the utmost effects s prouce by vbratons. Lengthwse vbratons affect the carrage spee ynamcs whch rectly affects the scannng precson. The length of the calbrate en gauge an the poston of lne centers are precsely etermne (calculate) by processng of the measurement ata, by estmatng the correctons of the envronment contons on the bass of pressure, humty, temperature an CO content measurement results. The lengths of the scale ntervals obtane from the measurng system are recalculate for the 0 C temperature. The lne gauge calbraton proceures are etermne by ocuments [7, 8]. 47

2 ost angerous are the vbratons that occur n the recton of the carrage moton (x axs) an torsonal vbratons that occur on the carrage axs z (on x, y plane) whch s perpencular to the recton of moton x. Vbratons that occur n the recton of the length of the carrage,.e. the carrage velocty an ts ynamcs etermne the precson of scannng of the lne gauge poston. Precson s efne by means of a photoelectrc mcroscope wth a CCD camera. Object of research. An nterference comparator wth ar refracton coeffcent compensaton meets the techncal an economc crtera by estmatng the refracton coeffcent from Elen formula accorng to the results of measurement of the envronment parameters or by means of a refractometer. The structural agram of the equpment s shown n Fg.. It s base on a lne gauge calbraton comparator wth a slng mcroscope an a statonary scale. The comparator s frame s mae from grante an s mounte on vbraton-proof supports, the mcroscope holer moves on ar gues. The carrage s rven by means of motor, worm reucton gear an frcton gear. The laser measurng system comprses laser, nterferometer an retroreflector. Fg.. A structural agram of the comparator: - vbraton nsulaton supports; sprngy aerostatc bearng; electromotor wth reucer; 4 belt rve; 5 grante gueway; 6 frcton gear; 7 jont member of two carrage; 8 frame of force carrage; 9 frame of the precson carrage; 0 mcroscope wth camera an flash; retroreflektor; calbrate scale; laser hea; 4 lnear nterferometer; 5 tght bult aerostatc bearng Dynamcal moel of the comparator 48

3 Fg.. Dynamcal moel of the comparator There O, O center of masses; m, m are masses of assembly unts; I j, I j, nerta moments, where j conces wth angles α, β, γ; Stffness coeffcents k n s of lnear moton; c n s of angular rotaton moton (n=,..., 6). Dampng coeffcents r n s of lnear moton; h n s of angular rotaton moton (n=,...,6). For equaton formng smplfcaton the ynamc moel at a comparator we are vng nto two subsystems: the st subsystem conssts of vbraton nsulaton supports wthout connecton wth a carrage; the n subsystem conssts of carrage wth tes connectng t wth the be of grante. The man coornates of two subsystem are x, y, z, α, β, γ (=, ) whch fx lnear an angular motons of mass centers n coornate systems wth ntal poston n ponts O an O. All members of coornates are man ones an 6 atonal: x, y, z, α, β, γ. To research vbraton of egree of freeom systems s mostly compact at usng matrces. A vbraton of the system s mostly convenent to escrbe by matrx: [ A ]{ q& } + [ B]{ q& } + [ D]{ q} = { Q( t) } & () There [A], [B], [D] are generalze nerta, ampng an stffness coeffcents of matrces; { q }, { q& }, { q& } are generalze coornates of splacement, velocty an acceleraton one columns matrces; { Q ( t) } external generalze force column actng n accorance wth force: [ A] [ B] [ D] a a = a b = b b = q q q q&& q&& q&& b a a b a b K a K a { q} = ;{ q& } K b K a K b K b K K K { q&& } = ;{ Q( t) } q& q& = ; q& Q Q = Q ( t) ( t) ( ) t () () 49

4 Expresson at knetc an potental energy an sspatve functon t s possble to wrte as a prouct of row matrx an one columns matrx: T = Π= Φ= T { q& } [ A]{ q& }; T { q} [ D]{ q} ; T { q& } [ B]{ q& }; There [A], [B], [D] are generalze nerta, ampng an stffness coeffcents square members matrx; q, q& are one columns matrces an ther fferental; { } { } { q } T { q& } T, are one row matrces of generalze coornates an ther fferental. T = m Π Π = k ( x& + y& + z& ) = k (4) When a ynamc moel s obtane (Fg. ) a mathematcal moel of the teste system s create (vbraton equaton). To ths en Lagrange s equaton of the secon type s use [9]: t T q & T q Φ Π + + q& q = Q ( t) (5) There T, Π are the system's knetc an potental energy; Φ sspaton functon; q -th generalze coornate; Q (t) generalze force actng n accorance wth coornate q. At formng of equaton lat we use expressons of T an П (=, ) presente n formula 6. ( x x0) + k( y y0) + k( z z0) + c( α α 0) + c( β β 0) + c( γ γ 0) ( x x ) + k ( y y ) + k ( z z ) + c ( α α ) + c ( β β ) + c ( γ γ ) 4 + I 5 & α + I α & β + I β 6 & γ ; γ (=, ) (6) There x 0, y 0, z 0, α 0, β 0, γ 0 are exctatons of a be wth consequent coornates. Vew at sspaton functon (Φ ) s receve from Π, after changng stffness coeffcents to ampng coeffcents. Connectng equatons are expresse: x x l β l γ =0; y y l α l γ =0; z z l α +l β =0; α α =0; β β =0; γ γ =0; After performng moelng by means of atlab 6. an Orgn 6. software packages we obtan the results presente n Fg.. Fg.. Spectrum of the vbraton velocty (urng ynamc calbraton) Expermental tests Expermental tests were conucte n measurement pont shown n Fg.. To ths en a measurng system (Fg. 4) was nstalle comprsng an accelerometer 806, vbrometer 5, sgnal nput an control boar Ebol Comlab SeTech an personal computer IB 50 [0,,, ]. The obtane results are presente n Fgs

5 Fg. 4. Flow chart of agnostc measurements The measurement pont wth the precson carrage beng n a statc poston (wthout ar supplyng). Fg. 5. The sgnal of the vbraton velocty an ts hstogram Table Statstcal parameters of the vbraton velocty measurement sgnal Statstcal parameter Arthmetcal mean, Root mean square evoton nmum value, axmum value, Scatter, Value -.E Fg. 6. The spectrum of the vbraton velocty sgnal (wthout ar supplyng) The measurement pont wth the precson carrage beng n a statc poston (wth ar supplyng). 5

6 Fg. 7. The sgnal of the vbraton velocty an ts hstogram Table Statstcal parameters of the vbraton velocty measurement sgnal Statstcal Arthmetcal Root mean square nmum value, axmum value, Scatter, parameter mean, evoton Value.88E Fg. 8. The spectrum of the vbraton velocty sgnal (wth ar supplyng) The measurement pont urng ynamc calbraton Fg. 9. The sgnal of vbraton velocty an ts hstogram Table. Statstcal parameters of the vbraton velocty measurement sgnal 5

7 Statstcal Arthmetcal Root mean square nmum value, axmum value, Scatter, parameter mean, evoton Value.88E Fg. 0. The spectrum of the vbraton velocty sgnal (urng ynamc calbraton) Dscusson of the results easurements were carre out n horzontal rectons. Supply of ar to the comparator s frame supports an the carrage s aerostatc bearngs was controlle. The llustratons show the measurement pont at whch vbraton velocty ampltues reach maxmum values at the respectve frequences. The obtane expermental results show that the ampltues of vbraton velocty level at 0, 0,4 mm/s (wthout ar supplyng) ecrease at 0,05 0,5 mm/s. The vbraton veloctes urng ynamc calbraton fluctuate from 0, to 0,4 mm/s. The obtane expermental results show that the spectral ampltues of vbraton velocty (wthout ar supplyng) at 0 0 Hz frequences fluctuate from 0,5 0 - to,4 0 - mm/s, whereas at other frequences vbraton velocty ampltues are nconserable. The spectral ampltues of vbraton velocty (wth ar supplyng) at 6 Hz frequences fluctuate from 0, 0 - to, mm/s, whereas at other frequences vbraton velocty ampltues are nconserable. The spectral ampltues of vbraton velocty urng ynamc calbraton at 8 0 Hz frequences fluctuate from 0,05 to 0,040 mm/s. Results obtane n theoretcal tests are markely expresse at 0 Hz frequences only, where ampltues reach up to 0,040 mm/s. Ths s relate to naccurate settng of parameters of fferental equatons. Hence, result relablty problems arse n the course of etermnng the vbraton level of such accurate calbraton evces by calculatng methos. Therefore, to fn out possble sources of uncertantes an errors n the course of creatng tools of such hgh-en technologes one shoul be gue by expermental tests espte the fact of ther expensve costs. Conclusons Such expermental results are receve on the groun of ynamc mathematcal moels:. Where the comparator s calbraton uncertanty s 0, µm/m the obtane values of vbraton veloctys may affect the accuracy of reang.. The spectra of ranom vbraton veloctys obtane wthn the low-frequency range ( 0 Hz) efne the preparaton requrements of the vbraton-proof supports.. These vbraton veloctes are actng an must be measure settng the accuracy of raster ncaton. REFERENCES [] Thalmann R. A new Hgh Precson Length easurng achne, Progress n Precson Engneerng an Nanotechnology (Proceengs of the 9-IPES/UE4, Braunschweg, Germany, 997, Vol., pp. -5). [] Demarest F. C. Hgh-resoluton, hgh-spee, low ata age uncertanty, heteroyne splacement measurng nterferometer electroncs (eas. Sc. Technol. 9 (998), P ). [] Beers J. S., Penzes W. B. The NIST Length Scale Interferometer (J. Res. Natl. Inst. Stan. Technol. 04, 5 (999)). [4] NANO : Lne Scale Stanars, WGD-7, Prelmnary comparson on nanometrology accorng to the rules of CCL 5

8 key comparsons (FINAL REPORT, Braunschweg, August 9, 00, p. 9). [5] Nano4: D gratngs, WGD-7: Prelmnary comparson on nanometrology accorng to the rules of CCL key comparsons (Fnal report, Draft B, Wabern, 0. November 000, p. 4). [6] Creaton an Research nto Precson Length Calbraton Systems (00 Report on the VSF Research Program Reg. No B-0008, Kaunas 00, p. 8). [7] EUROET Guelnes on Conuctng Comparsons EUROET (Gue No Issue: Revse: /Sa Verson: 0.7b, p.6). [8] EUROET Guelnes on Conuctng Comparsons [9] Vbratons n engneerng. //Reference book n 6 volumes. Vol. / Ete by V.V. Bolotn,.: achne-bulng, 978, 5 p. [0] Klkevčus A., Vekters V. Vbratons Sources Actng the Comparator Stan (echanka 006 Proceengs of the th nternatonal conference. Kaunas 006). [] Klkevčus A., Vekters V. Dagnostc testng of the comparator carrage vbratons (Ultragarsas Nr. (59). 006). [] Vekters V., Klkevčus A. Research of vbratons actng the mechatroncal comparator (Zbornk 4. smpozjuma sa meunaronm učeščem KOD 006 Zbornk Raova Proceengs. Palč 006). [] Kasparats A., Vekters V., Klkevčus A. A Vbraton Source n Comparator (Seventh Internatonal Conference on Vbraton easurements by Laser Technques: Avances an Applcatons Vol.645. Ancona, Italy, 006). 54