The Analysis of Radial/Axial Error Motion on a Precision Rotation Stage

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1 Vol:, No:5, 007 The Analss of Radal/Aal Eo Moon on a Pecson Roaon Sage Jnho Km, Dongk Shn, Deokwon Yun, and Changsoo Han Inenaonal Scence Inde, Mechancal and Mechaoncs Engneeng Vol:, No:5, 007 wase.og/publcaon/4 Absac Roang sages n semconduco, dspla ndus and man ohe felds eque challengng accuac o pefom he funcons popel. Especall, As of oaon eo on oa ssem s sgnfcan; such as he spndle eo moon of he algne, we bonde and nspeco machne whch esul n he poo sae of manufacued goods. To evaluae and mpove he pefomance of such pecson oa sage, unessenal movemens on he ohe 5 degees of feedom of he oa sage mus be measued and analzed. In hs pape, we have measued he hee anslaons and wo l moons of a oang sage wh hgh pecson capacve sensos. To oban he adal eo moon fom T.I.R (Toal Indcaed Readng) of adal decon, we have used Donaldson s evesal echnque. And he aal componens of he spndle l eo moon can be obaned accuael fom he aal decon oupus of sensos b Esle face moon evesal echnque. Fuhe moe we have defned and measued he sensv of posonng eo o he fve eo moons. Kewods Donaldson s evesal mehods, Esle face moon evesal mehod, Eo moon, sensv, T.I.R (Toal Indcaed Readng). I. INTRODUCTION N man hgh-pecson machnes, nsumens of I semconduco manufacung and dspla ndus eque challengng accuac o pefom he funcons popel. Especall, As of oaon eo on oa ssem s sgnfcan; such as he spndle eo moon of he algne, we bonde, and nspeco machne whch esul n he poo sae of manufacued goods. To evaluae and mpove he pefomance of such pecson oa sage, unessenal movemens on he ohe 5 degees of feedom (3-Tanslaon, -Tl) of he oa sage mus be measued and analzed. Unessenal movemens ae pcall measued b dsplacemen measung sensos o a hgh pecson sphee o clnde. Oupu daa of sensos nclude pofle eo, ceneng eo, and eo moon. Ove he eas, seveal sepaaon echnques have been developed fo he accuae measuemen of pofle eo o eo moon, such as he Donaldson s evesal mehod [,], he mul-sep mehod [3], and he mul-pobe mehod [4, 5]. Revew of hese echnques s gven n [6]. And he Esle face moon evesal mehod s noduced ha allows he sepaaon of l and aal eo moons fom he ccula flaness of a efeence pa [7]. Auhos ae wh he Mechancal Engneeng Depamen, Hanang Unves, Sa- dong, Sangok-gu, Ansan-s, Gungg-do, 46-79, Koea (he coespondng auho o povde phone: 8(0) ; fa: 8(0) ; e-mal: jopunch@gmal.com, e-mals of ohe auhos: sdongk@gmal.com, enoch@hanang.ac.k, cshan@hanang.ac.k). ANSI/ASME specfed he eo moon of an as of oaon and measuemen mehod n 986 and evsed n 995 [8]. Ths specfcaon was fueled manl b ndus of machne ools, coodnae machnes, and so on. In hs pape, we have measued he hee anslaons and wo l moons of a oang sage wh hgh pecson capacve sensos. Fuhe moe we have defned and measued he sensv of posonng eo o he fve eo moons. II. THEORETICAL ANALYSIS When a pobe measues he movemen of a oang age, he aw measuemen daa s defned as he oal dsplacemen measued b an nsumen sensng agans a movng suface o moved wh espec o a fed suface. n ANSI/ASME[8]. And s called he unou o T.I.R (Toal Indcaed Readng). In conas, adal eo moon s posonng eo of he changes n poson, elave o he efeence coodnae aes. Radal unou wll be dencal o adal eo moon onl f boh of oundness eo and ceneng eo ae emoved. I s adonall llusaed as a funcon of he spndle s angula poson usng a pola plo. Fo eample, Fg. shows pola plo of he snchonous and asnchonous componens of adal eo moon fom 00 evoluons wh 00 pm of a es module ssem. Fg. Snchonous and Asnchonous adal eo moon of spndle dven b PZT To oban eo moon values, a compue-based measuemen ssem allows he anals o:. Elmnae he once-pe-evoluon componen fom adal measuemens. Inenaonal Scholal and Scenfc Reseach & Innovaon (5) schola.wase.og/ /4

2 Vol:, No:5, 007 Inenaonal Scence Inde, Mechancal and Mechaoncs Engneeng Vol:, No:5, 007 wase.og/publcaon/4. Elmnae ve low fequenc vaaons o compensae fo hemal df. 3. Pefom an eo sepaaon echnque o dsngush he pofle eo fom he spndle eo moon. A. RRO (Repeaable RunOu) vs. NRRO (Non-Repeaable RunOu) The sgnal obaned fom he capacance senso n popoonal o he adal dsplacemen of he spndles. Ths sgnal called oal ndcaed eadng (T.I.R), s he sum of a pofle eo, eccenc, eo moon componens, and a non-epeaable componens. Non-epeaable value eflecs he nfluence of he spndle plus envonmenal dsubances, sucual vbaon, and eleccal nose so ha T.I.R can be wen as follows. T.. I R() = RRO() + NRRO() () The RRO (Repeaable RunOu) s compued b akng aveage of he T.I.R (sgnal daa) fom N evoluons of he spndle a each of he angula measuemen locaons. n RRO() = TIR() () n Subsung () no (), NRRO can be obaned b subacng RRO,.e. he aveage of T.I.R, fom T.I.R. NRRO() = RRO() TIR() (3) Dsplacemen [m] Dsplacemen [m] Tme [mn] (a) Df componen daa Tme [mn] (b) Elmnaon of df componen B. Elmnaon of Once-Pe-Revoluon Componen An off-cene n mechancal mounng and se-up eo add an unwaned componen o he spndle moon eo. Those eos ae a once-pe-evoluon snusodal wave n eclnea coodnaes and mus be elmnaed n measuemen daa, even hough hese eos ae ve small. In hs pape, he FFT (Fas Foue Tansfom) and IFFT (Invese Fas Foue Tansfom) algohms ae used fo elmnang fundamenal componen. C. Elmnaon of Df Componen Low fequenc vaaons, lke hemal df and sucual moon, whch have peods eceedng he ecodng me of he spndle measuemens, should be fleed fom he measuemens daa. These low fequenc vaaons do no necessal have equal values a he begnnng and end of he ecoded daa. Fg. (a) shows he low-vaaon df elave o he Z efeence as and a bes f, low ode polnomal s emoved fom he daa o educe he nfluence of ve low fequenc dsubances n Fg. (b). D. Donaldson Revesal Mehod The Donaldson evesal mehod, whch s he oaonal equvalen of he well-known saghedge evesal, s shown schemacall n Fg. 3. The ecoded value of M ( ) θ s he sum of he oundness pofle P( θ ) and adal eo moon S ( θ ). M ( θ ) = P( + S( (4) Second ecoded value of M ( ) θ s ecoded, wh he sage and ndcao oenaon oaed b 80 beween measuemens. M ( θ ) = P( S( (5) Ths changes he sgn of he sage s pofle eo whn he wo measuemens, enablng he compuaon of he pa pofle P( θ ) and spndle eo moon S ( θ ) usng he smple elaons n (4), and (5). Sage M( θ ) + M ( θ ) P( θ ) = (6) M( θ ) M ( θ ) S ( θ ) = (7) M( ) M() θ θ Fg. Df componen daa and s elmnaon Sao Inal Poson Revesed Poson Fg. 3 Schemac of he Donaldson evesal mehod Inenaonal Scholal and Scenfc Reseach & Innovaon (5) schola.wase.og/ /4

3 Vol:, No:5, 007 Inenaonal Scence Inde, Mechancal and Mechaoncs Engneeng Vol:, No:5, 007 wase.og/publcaon/4 E. Esle Face Revesal Technque The Esle face evesal descbed n [7] uses wo measuemen seups smla o Donaldson evesal mehod as shown n Fg. 4. The fs seup s he nal poson measuemen whch value s he sum of he ccula flaness F ( θ ), aal eo moon A( θ ) and l eo moon T ( θ ). I ( θ ) = F( + T( + A( (8) In he second sep, he evesal poson, he measued sage and ndcao ae oaed 80 abou he as of oaon and elave o he fs seup. I ( θ ) = F( T( + A( (9) The on-as ndcao n he second seup I ( ) 4 θ s oponal. I ( θ ) = I ( = A( (0) 3 4 Fom (8) ~ (0), aal and l eo moon esuls n: I ( θ ) + I ( θ ) A( θ ) I( - I ( I3( θ ) + I4( θ ) T ( θ ) = - And ccula flaness s: 3 4 = () () I( + I ( I3( θ ) + I4( θ ) F ( θ ) = (3) Fuhemoe, he on-as measuemen s no decl nvolved wh he evesal pa of hs echnque bu s sll equed fo he analss. Ths measuemen, heefoe, does no necessal need o be done a he same me o on he same measued pa as he nomal and evesal measuemens. Ths feaue of he Sao Senso Jg Capacve senso (Y-as) I( ) θ 3 I( θ ) I() 4 θ I() θ Inal Poson Revesed Poson Fg. 4 Schemac of he Esle face moon evesal mehod Esle face evesal dffes fo ohe common evesals, such as saghedge and Donaldson evesal, and pesens some oppounes when educng he echnque. III. ERROR MOTIONS AND POSITION ERROR The eo moons ae dsplacemens of as. A pefec spndle povdes DOF oaonal moon abou a fed as, wheeas he acual spndle canno go whou addonal 5-DOF dsplacemens of s as of oaon: oaon angle θ Z, l eo moon X, and Y, adal eo moon X and Y and aal eo moon Z. Wh aachmen of a coodnae ssem, he posons of deal and acual spndles can be epesened b homogeneous ansfom ma. Tdeal = o( θ Z ) (4) T = an(,, ) o( ) o( ) o( θ ) (5) acual X Y Z X Z Noe ha he eo moons ae funcons of he oaon angle. The posonng eo of an aba pon on he spndle whose epesenaon n spndle coodnae ssem s (6) can be defned as (7). Uppe clnde Unde clnde Locang pn Refeence Clnde Capacve senso (X-as) (a) (b) Fg.5 (a) Pecson Sage and measuemen ssem confguaon, (b) The sepaaed efeence clnde fo evesal mehod Inenaonal Scholal and Scenfc Reseach & Innovaon (5) schola.wase.og/ /4

4 Vol:, No:5, 007 p = ( cos φ, sn φ, z,) (6) e T p T p (7) acual deal Applng small angle appomaon fo l eos, zy + X e z X + Y YC( θz + φ) + XS( θz + φ) + Z (8) (a) Radal eo moon (-as) Sensves of posonng eo e o he eo moons X, Y, Z, X, and Y ae defned as Inenaonal Scence Inde, Mechancal and Mechaoncs Engneeng Vol:, No:5, 007 wase.og/publcaon/4 s de d = e e e IV. EXPERIMENTAL SETUP (9) Dsplacemen s measued b hee capacve sensos wh 0.083mV-ms Nose (ADE Technologes wh 805-pobes). Each of he non-conac capacance sensos can moun on he senso mounng machne a 90 deg o each ohe and ae pcall algned wh he X, Y and Z aes of he machne n Fg. 5. These pobes have a measung ange of ±00μm and esoluon nfeo o 0nm. And nose levels ae 0.83 nm. Dsplacemen measuemens wee ecoded dung 0 evoluons of he oo whle oang a a fed speed of 0.7 pm. A oa encode was aached o he spndle oo and a eadng fom he dsplacemen sgnal was ggeed wh each pulse fom he oa encode, povdng 36,000,000 couns pe evoluon. The analog oupu fom he sensos s sampled b a 6 b daa acquson boad (dspace). We have desgned senso mounng and afac o easl eecue he evesals (Fg. 5). The afac s sepaable no base clnde and uppe clnde and he ae maed wh pn fo accuac n he evesed confguaon. The oang sage s dven b wom gea n he angenal decon of he sage (b) Radal eo moon (-as) - - (c) Tl eo moon (-as) (d) Tl eo moon (-as) μm Fg. 6 Epemenal Seup (e) Aal eo moon Fg. 7 Resuls of 5-DOF Snchonous and Asnchonous eo moon pola plos Inenaonal Scholal and Scenfc Reseach & Innovaon (5) schola.wase.og/ /4

5 Vol:, No:5, 007 TABLE I MEASURED ERROR MOTION AND PROFILE ERROR Snchonous E.M * Asnchonous E.M Pofle eo Radal Radal Aal Face Face Tl Tl * E.M : Eo Moon Un of Radal, Aal, Face eo moon, and Pofle eo: μm Un of Tl eo moon: μad [4] Gejda, R.D., Use and Calbaon of Ulapecson Aes of Roaon Wh Nanomee Level Meolog, n Mechancal Engneeng. 00, The Pennslvana Sae Unves, p.35. [5] Whehouse DJ. Some Theoecal Aspecs of Eo Sepaaon Technques n Suface Meolog, J. of Phs. E:Sc.Ins., Vol. 9, pp , 976. [6] Mash E., Coue J., and Vallance R., Nanomee Leve Compason of Thee Spndle Eo Moon Sepaaon Technques. [7] James G.Salsbu., Implemenaon of he Esle face moon evesal echnque., Pecson Engneeng., Vol.7, pp.89-94, 003. [8] ANSI B89.3.4, Aes of Roaon: Mehods fo Specfng and Tesng Sandad, ANSI/ASME, 004. Inenaonal Scence Inde, Mechancal and Mechaoncs Engneeng Vol:, No:5, 007 wase.og/publcaon/4 TABLE II MEASURED SENSITIVITY Sensv Posonng eo Eo moon Snc. Asnc. e e z e z Snc.: Snchonous componen Asnc. Asnchonous componen V. EXPERIMENTAL RESULT Table I and Fg. 7 show he measued eo moon values and fom eos. The face moons a adus 65mm caused b l eo ae gven o nuve compason of l eo o dsplacemen eo. Table II epesens sensves of posonng eo of he pon p= (65mm, 0 ad, 7mm) wh espec o he measued eo moon. These values ae aveaged ove ene evoluon. We can conclude he -decon eo (pependcula o he decon of moo dve) s elavel eas o educe, mpovemen should be focused on he educon of Y and X. VI. CONCLUSION We denfed he eo moons of an as of oaon and modeled he posonng eo of a oang sage wh hese eo moons. We have measued he unou of he sage and eac he eo moon fo he oang as wh seveal algohms. Fnall we analzed he sensv of he age ssem REFERENCES [] Donaldson, R.R., "A Smple Mehod fo Sepaang Spndle Eo fom Tes Ball Roundness Eo.", CIRP-Annals., Vol., No., pp.5~6., 97. [] Evans, C. J., Hocken, R. J., Esle, W. T, Self- calbaon: evesal, edundanc, eo sepaaon, and absolue esng. CIRP Annals, Vol. 45, No., pp , 996. [3] Spagg, R., and Whehouse, D., pocedues of he Insue of Mechancal Engnees, 8, 968. Inenaonal Scholal and Scenfc Reseach & Innovaon (5) schola.wase.og/ /4

Chapter 3: Vectors and Two-Dimensional Motion

Chapter 3: Vectors and Two-Dimensional Motion Chape 3: Vecos and Two-Dmensonal Moon Vecos: magnude and decon Negae o a eco: eese s decon Mulplng o ddng a eco b a scala Vecos n he same decon (eaed lke numbes) Geneal Veco Addon: Tangle mehod o addon