INTERNET BASED ROUNDNESS & CYLINDRICITY ANALYSIS

Transcription

1 INTERNET BASED ROUNDNESS & CYLINDRICITY ANALYSIS S. Fu d J. Rj Ceter of Precso Egeerg Deprtmet of Mechcl Egeerg d Egeerg Scece Uversty of North Crol t Chrlotte, NC 83, USA Abstrct: Ths pper presets Iteret Bsed Roudess d Cyldrcty Alyss System, whch pples Jv d Iteret techology to egeerg metrology. The pcge cludes most of the stdrded d dvced lyss tools for roudess d cyldrcty. The most dstct feture of ths pcge s tht t c ru o the Iteret, whch ebles pltform depedet d remote lyss of roudess d cyldrcty dt. Keywords: Roudess, Cyldrcty INTRODUCTION The softwre systems for roudess d cyldrcty lyss curretly vlble re locl to strumets tht re bult by dfferet strumet compes. There re lwys some dffereces lgorthms used ll the exstg pcges. Moreover, s lrge corportos outsource mufcturg, the eed for remote ccess of dt d process troubleshootg s stedly cresg. So there s growg eed to hve commo pltform wth stdrded tools to lye rw dt depedetly. Wth the evoluto of the Iteret d the ehced power of computers, t s possble to buld softwre pcge tht c be ru o the Iteret. SOFTWARE DESIGN AND IMPLEMENTATION The requremet of the softwre s to buld o-le tool for mesuremet dt lyss. A object oreted desg cocept s ppled to the softwre desg of the pcge []. For better modelg, the softwre developmet process uses the Ufed Modelg Lguge (UML, lguge tht produces drwgs comprble ther tet to the blueprts log used other techcl dscples. The process mes t prctcl to bse much of the developmet o reusble compoets. I developg the softwre, cremetl pproch ws te towrds gtherg requremets, desgg the softwre, d mplemetg d testg t. Ths pproch ws te so tht the requremets could be modfed to crese the scope fter terto of the developmet cycle. Ths pproch ws lso essetl to dd dfferet fetures to softwre ccordg to dfferet customer requremets. The m compoets of the system re the user terfce clsses d the bcgroud processg clsses. All the clsses of the system hve bee developed usg pure Jv (JDK.. The plottg clsses use specl Jv D grph pcge, whch ws covered by the GNU Geerl Publc Lcese []. A frot ed s bsed o Jv AWT pcge to esure proper rug d dsplyg o curret vlble web browsers. The m tools used durg the course of ths project were JDK., Jv D Grph Pcge by GNU, Rtol Softwre for UML (Ufed Modelg Lguge, HTML 3. (Hyper Text Mrup lguge. 3 ROUNDNESS ANALYSIS The softwre offers uque pproch to lye roudess d cyldrcty over the Iteret. It tegrtes curretly vlble tools o dfferet mesuremet mches, d troduces some specl purpose lyss tools. 3. Flterg Techques A totl of fve dfferet flters re cluded the softwre for roudess d cyldrcty lyss. TwoCR Flter wth 75% trsmsso. Guss Flter wth 5% trsmsso. Sple Flter wth 5% trsmsso. FFT (Fst Fouror Trsform Flter. FFT Bdpss Flter.

2 3.. RC flter RC low pss flterg s bsed o the mpltude trsmsso fucto gve Fgure. The cutoff frequecy udultos per reolvuto(upr s defed s the frequecy t whch the trsmsso s 75%. RC Log Pss Trsmsso Chrcterstcs.5 Trsmsso UPR Fgure. Trsmsso chrcterstc for the low-pss (log-pss RC flter hvg cut-off frequeces, f c = 5, 5 d 5 upr. 3.. Guss flter The Guss flter trsmts wves from upr d tteutes profle udultos progressvely the udulto rego roud the chrcterstc cut-off upr umber. The cutoff frequecy ( UPR s defed s the frequecy t whch the trsmsso s 5%. The tteuto fucto (trsmsso chrcterstc s gve by: αf π c = f e d α= l( π Where: = mpltude of se wve udulto before flterg = mpltude of gve se wve of frequecy, f, fter flterg. f = cut-off frequecy ( upr of the low pss flter c f = frequecy of gve se wve ( upr Log Pss Trsmsso Chrcterstcs. Trsmsso UPR Fgure. Trsmsso chrcterstc for the low-pss (log-pss Guss flter hvg cut-off frequeces, f c = 5; 5; 5; 5; 5 upr.

3 3..3 Sple flter The mplemetto of sple flterg s bsed o the lgorthm developed by Mchel Kryste [3], whch yelds good pproxmto to the trsfer fucto of the phse-correct flter, but vods the dsdvtges of ths flter type Fourer flter All frequeces up to d cludg the cut-off upr re trsmtted %. All frequeces hgher th the cut-off re completely suppressed. 3. Fttg Algorthms Most spdle bsed roudess mesurg mches use precso spdle to crete reltve moto betwee the prt beg mesured d the dsplcemet trsducer rdlly mouted perpedculr to the xs of rotto. The output of the trsducer s the combed formto of the out-of-roudess of the prt d the reltve eccetrcty of the prt xs wth respect to the spdle xs. The output of the trsducer s rdus suppressed eccetrc crcle. Sce the eccetrcty s usully smll compred to the rdus of the prt, the hgh order terms re omtted ledg to lmco s pproxmto. Four fttg lgorthms for roudess d oe fttg lgorthm for cyldrcty re cluded ths pcge: Lest Squre Referece Mmum Zoe Referece Mxmum Iscrbed Referece Mmum Crcumscrbed Referece Lest Squre Cylder Referece 3.. Lest Squre Referece For lest squres best ftg, we strt off wth the bsc ler equto of eccetrc crcle: ( = R + b s r + For set of mesured dt pots, (R,, b re obted by r = R =, ( r, = b ( r s = where r represets the dvdul mesured dt pots wth dex, s the gle of dt pots, d s the umber of dt pots. 3.. Mmum Zoe Referece (MZ The mmum oe lmco c be vsuled by replcg two cocetrc fgures geertg oe by the equvlet form of sgle fgure d oe wdth h refered to tht fgure. The sgle referece lmco wll be defed wth symmetrclly plced oe ± h. The MZ problems the becomes tht of mmg h subject to the costrts: R + + b s + h r d R + + b s h r for dt pots polr form ( r set of roudess dt.,, =,,...,. Fgure 3 shows the mmum oe fttg result for

4 Fgure 3. Mmum oe fttg 3..3 Mmum Crcumscrbed Referece (MC The MC ft requres fdg lmco of mmum rdus such tht the lmco les completely outsde the dt represetg the oml crcle beg mesured. The mthemtcl represetto of the bove defto bsed o the equto of lmco would be R + + b s r for dt pots polr form ( r,, =, Mxmum Iscrbed Referece (MI The MI ft s oe whch ll dt pots le outsde the referece lmco. Ths c be vewed s exteso of the MC ft descrbed bove, where the sgs re reversed the bsc lmco equto. The formulto for the MI lmco wll be R + + b s r whch s essetlly the sme s ( R + + b s r cos for ll. Algorthms proposed by D.G. Chetwyd were used for the dfferet lmco fts descrbed bove [] Lest Squre Cylder Referece A smplfed equto for cylder s gve below [6] (, = ( + + ( b + b s R R + The procedure for lest-squres fttg of cylder s s follows: Cosderg the equto: r (, = ( + + ( b + b s R + where =...36, d =,, s the umber of dt pots. Thus we hve ler equtos d fve uows (, b,, b, R c be wrtte mtrx form s d = AP: for ech dt trce. The equto

5 r r.. =.... r s s s 3 s s s b b R where = m*, m s umber of trces, s umber of pots per trces. Usg sgulr vlue decomposto, we c solve out ths mtrx equto d get vector soluto cotg the prmeters (, b,, b, R. 3.3 Prmeters Four prmeters for roudess mely, RoT: Mxmum pe to vlley devto. RoP, Mxmum pe to referece devto, RoV: Mxmum referece to vlley devto, RoQ: RMS of the profle to referece devto re computed. For cyldrcty, OOC: Mxmum pe to vlley devto s computed. 4 SPECIAL TOOLS 4. Mult-cutoff Flterg For better uderstdg of dfferet frequecy compoets of the profle, t s ecessry to loo t the prmeter vrto fter flterg wth dfferet cutoffs. The lyss pcge offers feture to flter usg four dfferet cutoff vlues. Fgure 4 shows the mult-cutoff flterg results for roudess profle. Fgure 4. Mult-cutoff flterg 4. Mult-flter Flterg Ths tool permts the comprso of dfferet flters mplemeted the softwre. Ths tool lso s useful to evlute the effect of flters. 4.3 Reversl Techque for Error Seprto I some mesuremet stutos requrg hgh precso, the out-of-roudess of the spdle moto hs to be te to ccout. Ths method s bsed o the wor doe by Doldso, whch essetlly uses reversl techque for error seprto [4]. Processg two profles mesured from two setups (dex probe to &8. I set-up, T ( = P( + S(

6 whle set-up 8, f the probe s orml prorty, ( = P( S( T p ( = P( S( otherwse, T s + where P ( -- prt error, S ( -- spdle error. I ech cse, the spdle error d worpece profle c be seprted. A procedure to seprte usg mesured dt T, T ( or T ( hs bee mplemeted. ( p s 4.4 Mult-step Method for Error Seprto The mult-step method eeds profles from mesuremets obted by dexg the prt every 3 o. It s more precse method to seprte prt error d spdle error [5]. A procedure to seprte spdle d prt error hs bee mplemeted for dt obted from 3 dexg. 5 SOFTWARE TESTING All lgorthms of the pcge were tested usg theoretcl dt. Also comprsos hve bee doe betwee the lyss result of the pcge d of softwre o commercl system. The pcge wll be feld tested dustry. 6 LIMITATION AND FUTURE WORK We pl to buld dtbse d l t wth the pcge, whch c llow globl users to sert mesured dt, query for specfc dtsets, d select specfc dtsets for lyss. A dtbse lso c provde repostory for profles from dfferet mufcturg d mesuremet process, whch s vluble for comprehesve study of processes. To llow multple users to ccess lyss pcge d dtbse t the sme tme d crese the computg cpcty of pcge, we pl to move to three-ter rchtecture tht s wdely used most eterprse computg softwre. 7 CONCLUSION Iteret bsed Roudess & Cyldrcty lyss offers uque wy of lyg crculr form dt over the Iteret. It troduces dstrbuted computg to metrology d permts globl ccess through Iteret. It lso offers set of uque fetures, whch re ot vlble most curret commercl softwre s sgle collecto. ACKNOWLEDGEMENTS The uthors wsh to th Rjesh Subrm, Kurt Stedl, Vjoy Gopl d So Bu for ther help d suggesto. REFERENCES: [] Vjoy Gopl, A Iteret bsed surfce texture lyss system, Msters thess, UNC- Chrlotte, 999. [] D.G. Chetwyd d P.H. Phllpso, A vestgto of referece crtr used roudess mesuremet, Phys E: Sc. Istrum., Vol.3, 98. [3] Mchel Kryste, Dscrete L-sple flterg roudess mesuremets, Mesuremet Vol. 8, No., pp. 9-38, 996. [4] R.R. Doldso, A smple Method for Seprtg Spdle Error From Test Bll Roudess Error, CIRP Als, Vol, 97. [5] Chrles P. Reeve, The Clbrto of Roudess Stdrd, Ntol Egeerg Lbortory, Ntol Bureu of Stdrds, 979. [6] Rjesh Subrm, A Study Of Algorthms to Assess Roudess d Cyldrcty Dt Obted From Dfferet Meuremet Techques, Msters thess, UNC-Chrlotte, 998. AUTHORS: Shegyu FU d Jy RAJA, Ceter of Precso Egeerg, Deprtmet of Mechcl Egeerg d Egeerg Scece, Uversty of North Crol t Chrlotte, NC 83, USA