Investigation of dynamics of the mechatronical comparator

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1 Invesgon of dnms of e meon ompo A. evčus V. Vees. Svnss A. sps d Depmen of nes Engneeng Vnus Gedmns Ten Unves J. Bsnvčus S. LT- Vnus Lun E-m: evus@gm.om; E-m: vees@me.vgu.; E-m: ss.svnss@me.vgu.; d E-m:.sps@sp.; As Invesgon of e nfuene of dnm popees of e g peson ne ses on ompo o s u s ned n e ppe. Teefoe mu- od dnm nd mem modes of e ompo wee poposed. Te owed o evue es soues of eons nd posses of sng undese osons nfuenng e u of e ompo opeon. Cued mpude-feuen esponses nd modes of osons esonne feuenes ow o deemne dngeous feuenes. e wods: ompo dnm mode dnm uons ge osons ne se. Inoduon Wen desgnng pese mnes w s e en ss of g enooges e essene pope soug of e new ssem s s peson. A pd pogess of enooges fs of mo- nd nnoenooges ses ge nd ge euemens o u poduv nd oe feues of pese meon ssems. A e sme me smues o desgn mnes of new u nd o mpove esng mnes nd deves. Te suve of ppes [ ] sows opeon pnpes nd e pe of e pese eng mesuemen ompo ge dves used nd s desgn d nfuenes e mesuemen u. Ts f s eed w e dnm mp on e edng u euse wen so eng s mesued vons e sgnfn fo nfuenng e edng u. Te peson eng mesuemen ompo eng desgned [ ] s e mos ue eng mesuemen men n Lun. Dung nss of dnm eos s neess o now von mpude vues of e ge w e pupose o evue e nfuene of ge dves nd dmpes used on e ge von v nd e sme me on e mesuemen u. Te von v of e ge nd s nfuene on e mesuemen u s ned n e pesened wo. Oje of nvesgon oden ne guges e podued of vous oss seon spes nd eng sng fom seve momees seve mees ( mm n Lun []) usng fo e poduon su mes s see gss gss ems nd su nowes me s e gss-ems Zeodu vng n espe sm epnson oeffen. Addon e dsne eween nes n e vous fom μm n espe pese mnes seve mmees nd moe. Dung on of ne guges e dsnes eween ne enes e mesued oveve n pu ses e e mesued eween e edges of pofes of e nes []. Dg mesung mosopes ene o pefom e pese posonng of e ne guge on ssems nd o esme e u of e nes nd u of e ne poson. Te ompo ws nsed no sndd ondoned pemses. Te pese ne guge on ompo unde e nvesgon onsss of nne mn ps: se pe nefeomee guge fo mesuemen of envonmen pmees mosope w CCD me dve ssem onoe d geng nd poessng ompue oeon ssem gne gude ws e ge ssem onssng of e foe ge nd e pese ge. A ps e neeed nd snoned. Te se p of e ompo s e mssve fne suue gne fme of e m eng w gude ws w n e oon pne s ped on fou pneum suppos w dmpes g feuen osons. Te ge ssem moves ong e fme gude ws. Te eve of osons of e gne gude ws dung mesuemens n e es se dd no eeed μm H nd μm oe nges of oe oson feuenes []. Afe suppng e pessue no eos engs of ges e ges sde e ep of ese eos engs ong s g u gudes. Te ene eween pnes of engs nd gude sufes does no eeed μm. Te fow e s ve sm. Te ge ssem s desgned n su w e ges e oed on sff mouned eos suppos w e peoded e ep of suppos mouned n e oppose sde w e mouned w poss o spng. I enes o djus eued sm enes n e eos suppos nd o nese e gd. Te ge ssem s pued ong e snd e ep of e fon dve onoed pogm. Te ge nd e dve ssem onsuon enes emne e nfuene of e dve on e u of e

2 ongudn moon. Fo s m e ge ssem s omposed fom e foe ge nd e pese one. Te dve s onneed o e fs p nd mesung ssems w e used o mesue of ge moons nd o dee nes of e se eng ed o e seond one. Te foe ge nd e pese ge e neonneed e eemen w s e foe nsmng men. Ts eemen s desgned of su onsuon e deon of e foe nsmed ondes w e deon of moon of ges on e gudes (foes n e nsvese deon do no ). I s mpon so e f e eemen onneed e foe nd e pese ges s mouned n su poson e deon of e foe nsmed m goes oug e pese ge mss ene. Ts emnes wsng momens w n gve se e negve mp o e u of e on. Te dnm mode nd meodoog of devng of moon euons Te peson eng ompo s omped meon ssem fo g evuon of w dnm nvesgon soud e pefomed. Dung desgn of su ssems odng o e don meodoog sed on e seng e [] e poeon of e ssem fom sm (of e ode of momees o ens of nnomees) oweve undese nfuene of oson of e em fousng pon sng s esu of e ommon esen osons of e onsuon s neess. Tese d peded osons n se due o sesm eon of e onsuon oug no ofen e eson of e sng n e peues of e mne opeon e.g. e dve ssem dung opeon n se sm osons w e nsmed e onsuon n dependene of s geome spe nd dmensons nd onsuon pues w nfuene e gd popees nd mss dsuon. Ve mpon s onsuon of gudes nd s gd dmpng popees n onneons vng enes e. Even sm nges n empeue n nfuene e pu oosng n onneons nd n gudes o use em defomons w fn s nfuene n e se em umned pon poson. Tese defomons nd dspemens e of nson nue so e n no e emned usu ompensng mens. Euons of moon we w deve dvdng e ompo mode no ee sussems (Fg. ): e gne fme sussem O omposes e gne gude ws w von nsuon suppos wou eons w e ge ssem; e foe ge ssem O w ns eed w e gne fme; e pese ge ssem O w ns eed w e gne fme nd e foe ge. Te onneon of sussems no e unnmous ssem s evued e ep of u ns w e epessed e ep of u oodnes. Fg.. Dnm mode of e pese eng mesung ompo: - e wev n e pne - e wev n e pne - e wev n e pne

3 Epnons of noons used n Fg. : O O O e ognes of oodne ssems of sepe sussems of e mode e onde w e mss enes of oespondng ps; m m m e e mss enes; I j I j I j e e momens of ne wee j oesponds o e wsng nges ; n e e oeffens of gd odng o ne es of moon (n... ); n e e oeffens of gd odng o e ngu moon oodnes (n... ); n e dmpng oeffens odng o e ne es of moon (n... ); n e dmpng oeffens fo ngu moon (n... ); η epesses e nem eon funon (osons of e foundon). Te oodnes ( ) we w e s e mn oodnes e f ne nd ngu moons of e mss enes of sussems n e oodne ssems. Te oodnes e supus (u) oodnes. Tee e mn oodnes nd u oodnes. Te ne ses on ompo s omped dnm ssem vng mn degees of feedom w esen dsspve nd oes eons. To deve dffeen euons of s epedene o use e Lgnge euon of e seond ode: d d dt dt d d () wee T e e ne nd poen eneges nd e dspve funon of e ssem {}{}{} e e veos of dspemens veoes nd eeons nd s e veo of een eon foes. ne nd poen eneges of ndvdu sussems w e e foowng: ( ) ) (wen I I I m T () () () ( ) ( ) ( ) ( ) () wee e e mpudes of nem eons ng of e foundon odng o e oespondng oodnes. Epessons of dspve funons w ve e foowng fom: () () ( ) ( ) ( ) ( ). () Te mem mode of e o ssem w ompose e ssem of dffeen euons of e seond ode nd ge onsn euons: ) e ssem of dffeen euons [ ] [ ] [ ]{}. C B A () ) onsn euons:. ; ; ; ; ; ; ; ; ; ; ; () Hee [A] [B] [C] e e mes of ne dmpng nd gd; e e veos of dspemens veoes nd eeons s e veo of een foes nudng foes due o nem eon ( ) ( ) ( ) een.. Te mes [A] [B] [C] e veos {} nd e veo of foes ( ) ve foowng omposons: [ ] ; A () [ ] ; B () [ ] ; C () {} ; {} ; {} ; () ; ()

4 Te d eued fo modeng e sffness of eos suppos gd of eos engs of e ges gd of e dve ssem onneng e foe ge w e fme nd e gd of e eemen onneng e foe ge w e pese ge dmpng oeffens mpudes of nem eon of e fme sng due o osons of e foundon wee deemned epemen. Fo s m osons eed mme mp e es pons of o ges wee ned so osons of e sesm nue e fme suppos wee mesued nd ned. On e se of eped mem mode oeffens wee eed espe dmpng oeffens. Te dmpng oeffens we evue s esu of e vsous fon fo e ene mode. Addon fo e onneon of e foe nd pese ges we oo e suu fon evuon w ses e fon foe s popoon o e dspemen nd s evued n mos ses n men onneons. I gves ompe oeffens n e sffness m of e mem mode. Te foowng mn eons w e eed o dnms nd m ve nfuene on e ompo on u e found n e ompo opeon envonmen: e sesm osons of e foundon nd eon foes sng dung e dve ssem opeon. Te fs soue ws evued mesung sesm osons of e foundon nd fe s spe nss mpudes nd feuenes wee deemned. I gves e nem eon. Te seond soue ws evued s e eon foe dded o e foe ge n e deon s deon onde w e ng foe deon nd s e mos mpon deon eed w e on u. esuemens wee pefomed usng e mesuemen eupmen sown n Fg.. Fg.. Eupmen used fo mp eon ("Büe jæ"): ) e mp mme w e foe nsdue ) e mpfe ) e poe mesuemen esus poessng son ne Dgnoss Tooo Tpe ("Büe jæ") Tp empe of mesuemen d usng s eupmen s gven n Fg.. Cuon esus Cuon of mpude feuen esponses ws ed ou usng e eed dnm mode of e Fg. Tp d eng mesued ompo. n oodnes w e mos eed w e ompo u e oodnes. Jus s deon ondes w e mesung deon dung on. T s w we ne osons ong oodnes. Te uon esus e sown n Fgs. -. Te ssem esponse o e mos mpon eon e foe dded o e foe ge s sown n Fg.. Tee e mpude-feuen esponses of e foe ge () e pese ge () nd e fme () e sown. Ampude-feuen esponses of e foe ge w espe o e pese one () nd of osons of e fme w espe o e pese ge e sown n Fg.. Tee e seen wo esonne s ones on e feuen uves: e one of - H nd e one of - H. Te eo depends on e u eon foe mpude. Tee s en s e un foe. odes of osons fng no ese ones e sown n Fg.. I s seen osons ong e oodnes nd ese feuenes e of oppose pses. Te nvesgon of e sesm osons sows e speum of sesm osons poess s mn feuenes of - H oug ddves of ge feuen n e - H (Fg. ). Te deon of e sesm eon mn ondes w deon nd n e se of e smme on of fou eos suppos nd evenness of gd of em w use osons of ges so n nd deons w e no so mpon o e ompo on. A wose se s wen eons ng suppos e one end of e ompo dffe fom eons ng suppos e seond end of e ompo. Tese use osons odng o oodne of e oon moon w gve ddves ong e es. Tese feuenes n f no e fs esonne one. We ued e mpudefeuen esponse o s eon (Fg. ) en s

5 mpude sm o w ws mesued fom e speum so e esu oned s ose o e u one. Fg.. Ampude-feuen esponse o e eon dded o e foe ge n e deon: of e pese ge ong e oodne () of e foe ge ong e oodne () e fme ong e oodne () Fg.. Ampude-feuen esponse o e eon dded o e foe ge n e deon: of e foe ge n espe o e pese ge - () of e pese ge n espe o e fme - () Fg.. odes of osons of e ssem e feuen H () nd e feuen H ()

6 Fg.. Sgn of e von dspemen () nd s speum (): ve deon ongudn deon nsvese deon Fg.. Ampude-feuen esponse o e eon foes dded o e fme n e nd deons: ) mpudes of e esponses of e foe ge ong e oodne ; () mpudes of esponses of e pese ge ong e oodne () mpudes of e esponses of e fme ong e oodne ; ) mpude of e esponses of e foe ge w espe o e pese ge - () nd e pese ge w espe o e fme - () As s seen fom Fg. mpude of e mos mpon osons e foe ge w espe o e pese ge - s n enoug ow eve w does no nges sgnfn n e woe nge of e ow feuenes. Aoug osons odng oodne w espe o e fme - s e esonne w sgnfn nesed mpude (Fg. uve ). Conusons. Te eed dnm mode of e ompo ssem ows o ne s es dnm osons nd e nfuene on e ompo u.. I ws found osons eed e sesm nem eon w e essng foundon movemen mpudes e sm nd do no ve sgnfn nfuene on e ompo u.. Osons used e dve ssem n sgnfn nfuene e ompo opeon u nd e oespondng enon soud e pd dung seeon of e dve ssem. Refeenes. Swe. ed F. Ymo Y. Smomu T. Su Y. uo T. S H..nd Aog S. A new vuum nefeome ompo fo ng e fne ne enodes nd ses Peson Engneeng. Ju. Vo.. Issue. P. -.. Tmnn R. A new g peson eng mesung mne. Pogess n peson engneeng nd nnoenoog. Poeedngs of e -IPES/UE. Bunsweg Gemn.. Vo.. P.-.. Demes F. C. Hg-esouon g-speed ow d ge unen eeodne dspemen mesung nefeomee eeons. es. S. Teno.. No.. P. -.. Bees J. S. nd Penes W. B. Te NIST eng se nefeomee. J. Res. N. Ins. Snd. Teno.. Vo.. P... Nno: D gngs WGD-: Pemn ompson on nnomeoog odng o e ues of CCL e ompsons Fn epo. Df B Wen.. Noveme. P... sps A. Vees V. evus A. A Von soue n ompo. Seven Inenon Confeene on Von esuemens Lse Tenues: Advnes nd Appons Anon I.. Vo.. ISBN -X/.. evčus A. Vees V. Vons Soues Ang e Compo Snd. Poeedngs of e nenon onfeene. uns. en..

7 . evčus A. Vees V. Dgnos esng of e ompo ge vons. Ugss.. N. (). P.-.. Vees V. evčus A. Rese of vons ng e meon ompo. Zon. smpojum s medunodnm učeščem OD Zon Rdov Poeedngs. Pč.. Svnss. nevčus A. H. Esmon of suu dmpng n e mu degee of fedom dnm ssem. en.. N. (). A. evčus V. Vees. Svnss A. sps Dnmn meonno ompous m Reumė T peno go mvmo ompous dnmnų svų į jo sumu. Tm uvo suu ompous dugeo svės psnų dnmns memns mode edžns įven ūdngojo ždnmo šnus nepgedujmų vpesų dnčų įą ompous vemo sumu mo gmes. Apsčuoos džnnės mpudės esos pusnčos nuo eų ompous do meu vsnčų ždnmų p p vpesų fomos s edo nus ompous du pvojngus džnus. Do eu šngnė peos švdos. Reeved:..