Backlash Detection in CNC Machines Based on Experimental Vibration Analysis

Transcription

1 Bacah Dtctio i CNC Machi Bad o Expita Vibatio Aayi S. Ai A. Mooaia Dpatt of Mchaica Egiig K. N. Tooi Ui. of Tchoogy Tha, Ia ooaia@tu.ac.i Ebahi MohaadiA Dpatt of Maitac Mapa Tubi Maufactuig Co. (TUGA) Kaaj, Tha, Ia ohaadi@apatubi.co Abtact Expoitig bacah f chai ad gabox, th tiff of o ax i CNC achi ca b ipod. I fact, th igidity of th ax wi b icad, o that difft typ of fd-fowad coto ca b iptd. Futho, bacah f chai faciitat digig foopoof yt without chagig with th itabiity ad oia bhaio of bacah. How, ay chaica faiu ad oo cau bacah which i tu ay ad to ibatio. So, bacah dtctio ad xpoitig fficit pti aitac (PM) to pt itupt i th poductio i i of itt. I thi pap, fit a ip od fo chaica yt of a CNC o axi, ad it coto yt wi b ptd. Thi ducd od yt fo pd coto wi b dtaid. Nxt, th badwidth of ibatio fquci du to bacah i tiatd ad bhaio of a o axi with aiou bacah i iuatd. Th, to capuat th o of bacah i difft coditio, pfoac po of fi chaicay difft ax with difft o gai i aiou CNC achi a piicay itigatd. Th xpita fquci of ibatio obtaid i copty difft CNC achi (a, diu ad hay iz) a copad with tho tiatd. Siuatio ad xpita ut how that th fqucy of ibatio i a o axi with bacah i ot affctd by th au of bacah, whi th poitio coto gai dictat thi fqucy. Fiay, a xpita quatio wi b dopd that tiat thi fqucy fo aiou CNC achi. Kywod Bacah, CNC achi, Vibatio Aayi. I. INTRODUCTION Bacah cau iaccuat otio, ad xtaodiay ibatio which ipo iitatio o th quaity of coto. Thi wi daag th pow taiio tai pat, thu aiou tchiqu ha b uggtd fo bacah dtctio ad tiatio, [-]. Sip od of chaica bacah foud i th coto yt itatu igo th ipact bhaio that doiat otio at ow apitud. A a ut, uch od ca ot chaactiz th ow-apitud iit cyc ociatio that occu i cod-oop coto yt. Thfo, a o aitic od of chaica bacah houd icopoat ico-atic cotact foc btw th two a, [3]. O th oth had, fo bacah copatio, high-pfoac coto qui highquaity aut of th cut tat of th pow tai, [4-5]. Ifoatio about th iz of th bacah i ao dd. I th ca of ow bacah, a bacah copatig coto ca guaat xact output tacig. Wh th bacah chaactitic a uow, adapti aw ha b popod to updat th coto paat ad to guaat boudd iput-output tabiity, [6-7]. Itoducig a ooth i fuctio of th bacah ad uig that i th coto dig with bac tppig tchiqu, a bacah copato ha b popod, [8]. Fo th dig ad iptatio of thi coto, o owdg i aud o th uow yt paat. Bacah copato ha b ao popod uig dyaic iio by th fuzzy ogic, [9]. Th caificatio popty of fuzzy ogic yt a th a atua cadidat fo th jctio of o iducd by th bacah, which ha gio i which it bha diffty. A adaptatio agoith ca b dopd to tiat th bacah paat oi, ad ud ctai coditio a fuzzy copato with th adaptatio agoith guaat that th bacah output cog to th did tajctoy, []. Extdig th dyaic iio tchiqu to dict-ti yt by uig a fitd pdictio, ad uig a ua two fo itig th bacah oiaity i th fdfowad path, a agoith ha b popod fo bacah copatio that guaat boudd tacig o, ad ao boudd paat tiat, []. I idutia CNC achi too, to ha a accuat fiihd ufac, both xact poitioig ad ooth ot with ow cotou diatio a dadd. O th oth had, pog i poidig high pd iig ad gidig pid (with th ai of xpoitig caic/ hydotatic baig), ad ipot i cuttig atia ha faciitatd poducig high quaity fiihd ufac with high pd o axi. Bacah f chai (i doub ut cw, doub piio gabox, tc.) ha pfct ia dyaic, ad ab u to fufi a afotiod dad. How, i th ca of a bacah that i iig fo wo chaica pat, a ucotod oiaity wi ipo to th yt that ditot th dyaic bhaio of th axi ad ditub it xpctd ooth ot. I thi pap, fit a ducd od od of th chaica yt of a o axi wi b itoducd, ad a odiay CNC coto yt wi b iwd. Th po of pd ad cut coto fo th chaica /8 /$5. 8 IEEE RAM 8

2 ibatio wi b dicud. Nxt, bad o th xpita ut of fi chaicay difft ax (with difft o gai), a ip od of bacah i iutatd ad th badwidth of ibatio fqucy du to bacah i tiatd. Th, th ffct of au of bacah o a o axi i iuatd ad th xpita fquci of ibatio i aiou CNC achi too (a, diu ad hay iz) a copad with th tiatd fquci. II. AXIS MECHANICAL MODEL Bacah btw chaica pat ay ta pac du to faiu o oo, wa, tc., which ipo oiaity to th yt. Baicay, i a citica coditio bacah ad to ibatio wh did accatio i zo (pd i cotat) ad ot i ot affctd by th gaity. Th ut woud b watd ufac fiih, bo cuttig too, daagd chaica t of axi, which i tu ica bacah. Thfo, dtctio, ad coto of bacah bco igificaty tia pciay fo CNC achi too that th dfaut auptio i a bacah f chaica chai. I a CNC achi, ach axi copod of difft chaica pat i coupig, ga, ad cw, tc. that ha difft chaica popti. A of th t ca b odd a a t of pig ad dap, whi th o t w ta th o oac fquci wi xit. How, i ot ca th o axi ca b odd bad o th ow oac fqucy, ad th oth t ca b igod o aud to b igid. I Fig. a ducd od of chaica od i iutatd wh: : oad toqu d : actio of axi o oto : oto toqu : ot of itia of th oto icudig it ga o coupig : ot of itia of th oad : ocity of axi obtaid fo oto id : ocity of axi dicty obtaid : tiff of axi c : dapig of axi : atio btw oto pd ad axi pd δ : aout of bacah ω : pd of oto Equatio of otio fo thi od (without bacah) i: M ( ) = ( + M ( )).. ω () + ξ( ω ) Wh: M ( ) =, + ξ( ω ) + ( ω ) Figu. Axi od boc diaga ω = ad ξ = c ) ( III. AXIS CONTROL SYSTEM Th oftwa of th itigatd CNC achi too i Si SINUMERIC 84D that ipt a cacad coto yt icudig th ai pat: poitio coto (P), pd coto (PI) ad cut coto (PI), wh actuato i a pat agt ychoou oto (AC o oto). Fig. how th ipifid boc diaga of a o axi cod oop coto yt. Vaiou paat ad iga i thi boc diaga a dfid a: x d : ttig poitio fo itpoato x act : axi actua poitio aud by dict cod : foowig o : poitio coto gai : atio btw oto pd ad axi pd t : ttig pd of oto act : actua pd of oto aud by oto cod p : pd coto popotioa gai T i : pd coto itgato ti t : ttig toqu i t i act d : ttig cut : actua (aud) cut Ao th o axi i quippd with two cod that a ow a auig yt (oto cod), ad auig yt (dict cod). Dict cod i dicty coctd to th axi ad poid th xact poitio of th axi whth th i bacah o ot. Th au of dict auig yt i utiizd fo poitio fdbac i poitio coto. Th oth cod i ocatd iid th oto ad it i ud a a fdbac fo pd coto. How, i ot CNC achi too accodig to th iatic of th axi, th diffc btw oto cod ad dict cod houd b i a iitd toac to au a af otio. δ c ω

3 x d t p + T i t t it d-q axi PI Cut coto i act t d ω x act act Fo Dict Ecod Fo Moto Ecod Figu. Cod oop poitio coto yt i a o axi Th coto of th cacad coto a to b digd to poid high co fqucy i ach i oop with pct to it out oop. Fo tuig th o gai of th pd ad cut coto a attpt houd b do to p th apitud of pd (ao cut) coto at db o th widt fqucy badwidth. I pactic, th co fqucy of pd ad cut coto houd ach about -3HZ ad 5-HZ, pctiy, []. Th agitud of taf fuctio of pd ad cut coto i bod diaga fo th badwidth houd b ay db ( tha 3db), []. Fig.3 how th a fqucy po of cod oop pd coto fo a o axi wh th fqucy badwidth i about 8Hz. Expitay th fqucy of chaica ibatio i tha 5Hz ad i ot of th ca i tha 3HZ, o ipy fo ou tudy of chaica ibatio th agitud of pd ad cut coto ca b pacd by. Th pha of cut coto fo th fqucy of ibatio i zo, o by pacig th taf fuctio of cut coto oop with th taf fuctio fo th who yt ca b witt a: ω + pti = + T + T ( + ( p i i TiM ( ) + () ) M ( )) A =. ω o th taf fuctio btw ad ca b wit a: Ti ( + ( ) M ( )) = ( ) (3) + T + T ( + ( ) M ( )) p i i H, a tiod bfo gadig th badwidth of pd ad cut coto fo th fqucy of chaica ibatio (th fudata fqucy aud by FFT aayi of cut ad pd iga), th taf fuctio of (3) ca b popy appoxiatd a: = iφ (4a) wh φ dcib th pha of ibatio ad ca b cacuatd by (3). Fo itac, by pacig th coto paat fo CNC, th taf fuctio fo th iuoida iga with th fudata fqucy i: Figu 3. Fqucy po of cod oop pd coto Pha Apitud j Fqucy poc of cod oop pd coto Fqucy(Hz) -8 3 Fqucy(Hz) = ( + ) =.4 (4b) Accodig to (4), if th ibatio caud by bacah i ipifid a a ig iuoida iga with th fudata fqucy, ad th oth t of FFT aayi gctd, th pd of axi wi b popotioa to th tacig o; which i a ipotat fact to b ud i bacah dtctio ad aagt. A tiod bfo, o axi i CNC achi a quippd with two auig yt; yt (oto cod) ad yt (axi cod). Th ot ipotat adatag of dict auig yt i accuacy i axi poitioig i th pc of bacah. How; it i ot o ay to dtct ad au bacah with ipy copaig obtaid iga of th two auig yt duig otio. I fact, du to toio ad atic dipact i th chai of th axi, th itaig coditio, tpatu aiatio ad it ffct o th ia ca (dict auig yt), taittig accuacy of chai (i ad cw, ac ad piio, tc.) th xit a aiab diffc btw th two auig yt pciay duig accatig o dcatig otio. Thfo, i ot of th CNC achi too a accptab toac (about.5 o.5dg fo ia ad out axi, pctiy) i aowd fo th two auig yt jut fo dtctio of axi af opatio. Sic th bacah au that cau ibatio i uch tha thi aowd toac, thi diffc btw th two auig yt i jut ufu fo dtctio of axi ooad o ay iou faiu i chaica pat of axi.

4 Spd(/i) Ti(c) FFT 8 Apitud(/i) Moto cut(a) Apitud Miig achi(no.) axi oituig Fqucy(Hz): Ti ctio=[,] 5-5 Fqucy=8Hz Apitud= 65./i K=.(/i*) Figu 4. Lia axi pd oitoig Ti(c) FFT.5.5 Boig achi(no.3) tu tab oituig Fqucy(Hz): Ti ctio=[4,5] Figu 5. Rotay axi cut oitoig δ x Fqucy=5Hz Apitud=.667A K=.5*.77(p/dg) c Figu 6. Axi chaica od Figu 7. Bacah iuatio i a ip yt IV. BACKLASH MODEL x Bacah at cotat pd ay ad to ibatio that ca b obd a fuctuatio i th oto cut, accatio ad x x M otu o pd of th axi. Such ibatio, uig Fat Foui Tafoatio (FFT) ca b tafod to a i i which ach t i copod of two chaactitic au; i.. th apitud ad th fqucy. Fig. 4 ad 5 how th ut of FFT aayi of th pd ad cut fo xpita aut of two CNC achi ax; i.. CNC ad CNC3. A i th iutatio, i both of th o ax th i a fudata fqucy with ay th a apitud a th apitud of actua iga. So, with a aoab accuacy, bacah fuctuatio ca b itptd a th fudata t of FFT. I fact, a pocdu of bacah dtctio ad it uppio ca b dopd by aayzig th cut/pd fuctuatio (wh ttig accatio i zo), bad o th owdg of apitud ad ag of fudata fqucy of ibatio caud by bacah. I od to dop a ip od of th chaica yt th bhaio of a chaica t atd to th high atua fquci ca b coidd a igid. Th od a how i Fig.6 i poidd bad o th chaica pat i pow taittig i that itpt th owt atua fqucy. Equatio of otio fo thi yt ca b witt a: if ( x x > δ) Mx = c ( x x ) + ( x x ig( x ) δ) Wh M i th a itia of th axi caiag. I Lapac pac(if bacah i zo): X X + ξ( ω ) (5) = (6) + ξ( ω) + ( ω ) V. FREQUENCY BANDWIDTH ESTIMATION To tiat th badwidth of fqucy that ca happ fo a o axi, a ipifid chaica yt i coidd a how i Fig.7. I fact, otio of th ba ( x ) i cotod with th ot of th cat ( x ), wh th dcibd o coto yt i iptd. Thi yt wo bad o th ipact btw th ba (axi) ad th wa (actuato). Th a coditio of ibatio fo th pd of axi ( ) ad oto ( ) i two difft iig achi (CNC ad CNC5) ca b i Fig8. Ao i Fig.9 thotica xpctatio of bacah ad it utd ipact i poit A ad C ha b iutatd. At th ti of paatio (poit B i Fig.9) btw oto ad caiag of axi (i ay poit of chai) w xpct a cotat ad hight of pd fo th caiag (aud by dict cod) uti th xt ipact i poit C. Ipact i a y copx t ioig atia dfoatio ad coy ad hat/oud gatio (gy o), How, h a ip od of ipact with a cotat cofficit of titutio i iptd. So itad of oig (6) fo th yt of Fig.6 with a copx od of ipact th quatio of otio (piodic otio) of th ip yt how i Fig.7 i witt.

5 Spd(/i) Spd(/i) - bacah= Ti(c) Rotoy axi of Tubo i 4.7 Spd(p) Figu 8. Fuctuatio i th pd of axi du to bacah Lia(tica) axi of iig achi (with hydauic baac) V V 4.4 bacah=.dg Ti(c) Figu 9. Expctig bacah bhaio H, fo cacuatig th upp iit of fqucy, th ffct of ipu o th diig oto i gctd ad th ti of cotact (A-B i Fig. 8) i aud to b zo which yid a axiu poib fqucy. I a a coditio a how i Fig.8 atia dfoatio ad coy ta coidab ti. Auig that at t =, x =, o duig th ti bfo ipact w ha: if ( x V T dx t ) = 4 dt =.t A Ti(c) = cot Wh T i th piod of ibatio. Ipact wi happ at t = T 4, ad if i dfid a th cofficit of titutio, o: (7) = (8) + T V B C = x =.. (9) 4 D E Thfo, th atiohip btw ad th fqucy ( T ) ca b obtaid a: + f = 4 () Th cofficit of titutio fo t i about.6 ad a th gy o i th a ibatio i uch high tha th aud od (bcau of high atio of a to cotact aa, ao fictio), th th fqucy of ibatio i a o axi i dfiity iitd a: f < () Eq.() xpicity how that th fqucy of ibatio i ot affctd with th aout of bacah, ad it i popotioa to th poitio coto gai that wi b cod by th iuatio i pat VI. Thi thotica ut ao wa cofid with th xpita ut of ibatio aayi i CNC i which fo difft aout of bacah (. -.7) th copodig fudata fqucy wa uiqu(8hz). By pacig cofficit of titutio with zo (that i ctaiy tha th a coditio a how i Fig. 8) th ow iit fo th fqucy of ibatio wi b obtaid a: f > 4 () VI. SIMULATION I thi pat o of itigatd o axi with th pc of difft bacah i iuatd. Siuatio i accopihd bad o th achi data of th o axi ad couob + ico fictio i ud fo fictio odig. Ao, bad o xpita ut, axi chaica od (Fig. 6) i tud fo thi axi. Fig. how th axi pd fuctuatio(aud by oto cod) fo pd t poit of.6(/) wh au of bacah i. ad.4 (dg). Th au of bacah w aud at th d cotact poit of chai wh th iatic atio i Fig. cay how that ay ica of bacah do ot affct th fqucy of ibatio but th apitud of ibatio. VII. EXPERIMENTAL RESULLTS To gaiz () ad (), difft CNC achi with difft dyaic pcificatio, o gai ad difft bacah w xpitay itigatd. Th achi a:. Lia axi (tica) of iig achi di by ad cw quippd with hydauic baacig cyid (CNC).. Lia axi of hoizota tuig achi di with hydotatic cw chai (CNC). 3. Rout axi (Tu tab) of boig achi di by twi piio ad ga wh (CNC3).

6 4. Lia axi of boig achi di by ac ad twi piio (CNC4). 5. Rout axi of iig achi di by twi piio ad ga wh (CNC5). Fig. idicat that th fqucy of ibatio i a o axi i coy popotioa to th poitio coto gai ad iitd i th badwidth dfid by () ad (). A a cocuio, with a accptab accuacy w ca poid a xpita quatio a bow: f =. 6 (3) VIII. CONCLUSIONS Bacah i a coo toub i a o axi of CNC achi, dfiig th badwidth of fqucy of ibatio i a o axi with th pc of bacah ad tiatig th fqucy, wi b igificaty hpfu fo both digig obut o axi without icuio of oat fqucy ad bacah dtctio though th coditio oitoig (CM). Thi wa th ai focu of thi ach pap. Dopig ip od fo th chaica yt of a o axi, ad th bacah itf, it wa how that th fqucy of ibatio i a o axi with bacah i ot affctd by th au of bacah, whi th poitio coto gai dictat thi fqucy. Accopihig aiou xpit o fi difft CNC achi, iitatio fo th badwidth of th fqucy of ibatio i a o axi w dfid. Ao, a xpita quatio wa poidd that tiat thi fqucy with a accptab accuacy fo aiou CNC achi. IX. REFERENCES [] Sti,. L., ad Wag, C. H., Autoatic dtctio of caac i chaica yt: thoy ad iuatio, Pocdig of th Aica Coto Cofc, Vou 3, -3 u 995, pp [] Lagbg, A., ad Egadt, B., Bacah Etiatio With Appicatio to Autooti Pow tai, IEEE Taactio o Coto Syt Tchoogy, Vou 5, Iu 3, May 7, pp [3] Gd,.C., ad Kua, V., A ipact od of chaica bacah fo coto yt aayi, Pocdig of th Aica Coto Cofc, Vou 5, -3 u 995, pp [4] uic, T., ad Pic, N., Mod bad bacah copatio, Pocdig of Aica Coto Cofc, Vou, 5-7 u, pp [5] Capo,., Lwi, F.L., ad Sic, R., Bacah copatio with fitd pdictio i dict ti oia yt by dyaic iio uig ua two, IEEE Itatioa Cofc o Dciio ad Coto, Vou 4, -5 Dc., pp [6] Gag, T., ad Kootoic, P.V., Cotiuou-ti adapti coto of yt with uow bacah, IEEE Taactio o Autoatic Coto, Vou 4, Iu 6, u 995, pp [7] Tao, G., ad Kootoic, P.V., Adapti coto of yt with uow output bacah, IEEE Taactio o Autoatic Coto, Vou 4, Iu, Fb. 995, pp [8] ig Zhou, Chgji Zhag, ad W, C., Robut Adapti Output Coto of Uctai Noia Pat With Uow Bacah Noiaity, IEEE Taactio o Autoatic Coto, Vou 5, Iu 3, Mach 7, pp [9] Woo, K. T., Li-Xi W., Lwi, F. L., ad Li, Z. X., A fuzzy yt copato fo bacah, IEEE Itatioa Cofc o Robotic ad Autoatio, Vou, 6- May 998, pp [] u Oh ag, Pyog Gi L, H Ta Chug, ad Gi oo o, Output bacah copatio of yt uig fuzzy ogic, Pocdig of Aica Coto Cofc, Vou 3, 4-6 u 3, pp [] Sid, D.R., Sui-Lu La, Puta,.A., ad Loz, R.D., Nua two copatio of ga bacah hyti i poitio-cotod chai, IEEE Taactio o Iduty Appicatio, Vou 3, Iu 6, No.-Dc. 995, pp [] Si iodi 6 digita/sinumeric84d/8d tatup ad optiizatio. Fqucy(Hz) Spd(/) Spd Moitoig bacah i.dg bacah i.4dg Ti() Figu. Effct of au of bacah o ibatio Bad width K ad F i difft ax F=K Bt Fittig F=K/ Poitio coto gai(/) Figu. Fqucy of ibatio ad th poitio coto gai