Artificial Neural Network to the Control of the Parameters of the Heat Treatment Process of Casting

Transcription

1 A R C H I V E S o f F O U N D R Y E N G I N E E R I N G Publishd quartrly as th organ of th Foundry Commission of th Polish Acadmy of Scincs ISSN ( ) Volum 15 Issu 1/ /1 Artificial Nural Ntwork to th Control of th Paramtrs of th Hat Tratmnt Procss of Casting J. Wróbl *, A. ulawik, A. Bokota Institut of Computr and Information Scincs, Czstochowa Univrsity of Tchnology, Dąbrowskigo 73, Częstochowa, Poland *Corrsponding author. addrss: oanna.wrobl@icis.pcz.pl Rcivd ; accptd in rvisd form Abstract In th papr th us of th artificial nural ntwork to th control of th work of hat trating quipmnt for th long axisymmtric stl lmnts with variabl diamtrs is prsntd. It is assumd that th vlocity of th hat sourc is modifid in th procss and is in ral tim updatd according to th currnt diamtr. Th masurmnt of th diamtr is prformd at a constant distanc from th hat sourc (z = 0). Th main task of th modl is control th assumd valus of tmpratur at constant paramtrs of th hat sourc such as radius and powr. Thrfor th paramtr of th procss controlld by th artificial nural ntwork is th vlocity of th hat sourc. Th input data of th ntwork ar th valus of tmpratur and th radius of th hatd lmnt. Th larning, tsting and validation sts wr dtrmind by using th quation of stady hat transfr procss with a convctiv trm. To vrify th possibilitis of th prsntd algorithm, basd on th solv of th unstady hat conduction with finit lmnt mthod, a numrical simulation is prformd. Th calculations confirm th ffctivnss of us of th prsntd solution, in ordr to obtain for xampl th constant dpth of th hat affctd zon for th gomtrically variabl hardnd axisymmtric obcts. ywords: Hat tratmnt, Moving hat sourc, Artificial nural ntwork, Numrical modlling, Systm of th control of th hating procss 1. Introduction Modrn control systms of th quipmnts usd in th hat tratmnt procss allows for th significant automation in th production procss. Using th tmpratur or thicknss snsors givs th possibility to prform th hat tratmnt procss for th small sris production. Th dvics quippd with masuring systms significantly rducs th costs associatd with th us of th production lin. Th possibility of th suprvision of th procss in th modrn quipmnts significantly improv th quality of th hat tratmnt [1]. Th work station with movabl hat sourc which moving not only along th path but also having th possibility to dtrmin th distanc and angl to th hating surfac ar quit oftn usd. Using ths typ of quipmnts in th hat tratmnt for th axisymmtric lmnts with variabl radius facilitats th production lin srvic and rducs th numbr of tratmnts rquird from th usr [2]. Th control lmnts in such quipmnt ar th systm dscribd by th analytical functions connctd with conditional statmnt. Dtrmination th cofficints for ths mpirical functions rquir larg financial outlays. A significant disadvantags of such solutions is th lack of systm control raction for th cass which th systm dsignr didn't provid. A R C H I V E S o f F O U N D R Y E N G I N E E R I N G V o l u m 1 5, I s s u 1 / ,

2 Most of th drawbacks can avoid by using a control systm with artificial intllignc. Th on of th bst, spcially in th trms of spd, ar artificial nural ntworks (ANN). Th important advantag is that nural ntworks can ract corrctly on th situation clos to th larning pattrns [3, 4]. 2. Fundamntal assumptions of th modl In th papr th artificial nural ntwork to th control th vlocity of th hat sourc in th hat tratmnt procss for th axisymmtric lmnts with variabl valus of radius is usd. It was assumd that hating stl lmnts rotat to provid uniform distribution of th tmpratur on th primtr of th lmnt. This typ of th approach is rquird by usd th suprficial hat sourc. It allows for th constant distanc to th hating lmnt in th cas of th parts with variabl diamtrs. Th dsign of control systm which basd on th artificial nural ntwork rquir prform th following stps: dtrmin th larning and tsting sts on th basis of data from numrical simulations, dfin th numbr of th ntwork layrs and nurons in ths layrs, slct th appropriat larning algorithm and spcify th wights of th intrnural connctions, validation of th ANN. Th numrical modls of th stady and unstady hat transfr ar usd to dtrmin th larning and tsting st or to vrify th ANN. 3. Th numrical modls of th hating procss In th papr th two hat transfr modls ar usd. To dtrmin th larning and tsting sts, th application to calculat th tmpratur filds is dvlopd. This valus on th basis of solution of th hat transfr quation with convction trm in th axisymmtric coordinats (stationary task) ar obtaind T r r T T r r z z CV z T z 0 whr: T [] tmpratur, λ= λ(t) [W/m] th thrmal conductivity cofficint, ρ [kg/m3] th dnsity, C [J/kg] th thrmal capacity, V z [m/s] th vlocity of th hat sourc, r is a distanc from th symmtry axis. Th quation (1) is complmntd by th appropriat boundary conditions. To solv this quation th finit lmnt mthod in Ptrov-Galrkin formulation is usd. Finit lmnt mthod in th PG formulation allows to obtain th corrct solutions for th cass whr Péclt numbr is gratr than 2 [5]. Systm of quation aftr aggrgation is in th form T B q (2) (1) whr lmnt matrix: conductivity ( ), boundary condition (B ) ar dscribd as [6] B Q rw i,, i, k k rw d i drdz C rw V drdz whr: w i ar th wight functions, ar th shap functions. Th scond numrical modl is usd to vrify th traind artificial nural ntwork. In ordr to th numrical modl of unstady hat transfr for axially symmtric spac is applid T r r T T r r z z T C t 0 whr: t [s] - tim. Th abov quation by finit lmnt mthod in Bubnov- Galrkin formulation is solvd. For this task and for diffrnt tim schm th solution tak th following form s 1 M T M 1 B q * s1 * s 1 B q s T whr lmnt matrix: conductivity ( ), hat capacity (M ), boundary condition (B ) ar dscribd by th intgrals M B C t Q r r d i i,, drdz r drdz i In th prsntd modl which vrifying th control systm built on th basis of artificial nural ntwork, is assumd that th location of th hat sourc is incrmntally changing according to th vlocity calculatd by ANN. Th suprficial hat sourc (Numann boundary condition) in th simulation of th hating procss is dtrmind by th function [5] q Q z z xp 2 2R 2R whr: Q [W] powr of th hat sourc, R [m] radius of th hat sourc, z 0 [m] is th coordinat of th cntr of th hat sourc. (3) (4) (5) (6) (7) 120 A R C H I V E S o f F O U N D R Y E N G I N E E R I N G V o l u m 1 5, I s s u 1 / ,

3 4. Calculation xampl To dtrmination of th input and output data to th larning procss of th artificial nural ntwork th 2000 numrical simulation wr prformd. This data wr obtaind for th stl lmnts with constant diamtrs (Fig. 1). Th appropriat boundary conditions wr assumd: th vlocity of th hat sourc was takn th random valu from 0,005 to 0,03 m/s, th radius of th stl lmnt was slctd randomly in th rang 0,006 0,014 m, Dirichlt condition on boundary D with T = 293, th powr of th hat sourc Q was qual 500 W, th radius of th hat sourc R = 0,0015 m. Th matrial proprtis wr assumd lik for th mdium carbon stl [9]. From th obtaind rsults th valus of tmpratur for th 25 snsors locatd on th boundary of considrd lmnt (Fig. 1) and th radius of lmnt wr slctd. This valus wr th input data to th ANN. Th output paramtr of th ntwork was th vlocity of th hat sourc. Th ANN rquirs to th larning procss th right numbr of divrsifid data in th larning st (Fig. 2 and 3) Fig. 2. Th numbr of considrd radius for th stl lmnts (r = 0,0009 m) and maximum valu of th tmpratur (T = 133 ) in th larning st, input data Fig. 3. Th numbr of vlocitis of th hat sourc (V z = 0,001 m/s) in th larning st, output data Th rangs of th valus of vlocity and radius of th lmnts allowd for obtain th appropriat maximum valu of th tmpratur for hat tratmnt procss (Fig. 2 and 4). Fig. 1. Th gomtry of th prsntd stl lmnt with th snsors A R C H I V E S o f F O U N D R Y E N G I N E E R I N G V o l u m 1 5, I s s u 1 / ,

4 (RMSE) and prcntag rror (Fig. 6) for th tsting st. Th numbr of lmnts in th larning and tsting sts for ach pochs was Fig. 4. Th xampl of th distribution of th tmpratur for r = 0.01 m, V z = m/s For th abov assumptions th artificial nural ntwork was dsignd. Th on way multilayr prcptron with sigmoidal nurons was usd. Th ntwork was crat using a on input layr (26 nurons), two hiddn layrs (20 and 10 nurons) and on output layr (1 nuron). Fig. 6. Th valus of RMSE and prcntag rrors in th larning procss for th tsting st 5. Th tsting of th artificial nural ntwork To vrify th corrctnss of th implmntd algorithm a numrical tst was conductd. Th tst was prformd for axisymmtric lmnt with variabl diamtr (Fig. 8). Th rquird distribution of tmpratur on th boundary of th lmnt was assumd. On th basis of th distribution of tmpratur th valus of vlocity of th hat sourc was computd by th artificial nural ntwork (Fig. 7). Th initial position of th hat sourc was situatd blow th hatd lmnt and th start vlocity was qual 0,02 m/s. Fig. 5. Th diagram of th applid multi-layr nural ntwork To train th ntwork th backpropagation algorithm was usd. To incras th spd of th larning nural ntwork th backpropagation with momntum was applid [3]. Th momntum cofficint was qual α = 0,7, and th larning cofficint was η = 0,03. During th larning procss mad an analysis dpnding th numbr of pochs on th valu of root man squar rror Fig. 7. Th input data for th nural ntwork - th rquird distribution of th tmpratur 122 A R C H I V E S o f F O U N D R Y E N G I N E E R I N G V o l u m 1 5, I s s u 1 / ,

5 Fig. 10. Th changs of tmpratur for th constant vlocity of th hat sourc (Vz = 0,148 m/s) a) b) Fig. 8. Th gomtry of th considrd xampl tst Th rsponsibl snsor for th rad th currnt radius of th lmnt was locatd on th sam coordinats (z) as th hat sourc. Th initial valu of tmpratur of th stl lmnt th was qual T 0 = 293. On th basis of tmporary valu of radius th nural ntwork updating th vlocity of th hat sourc, what causd th changs of tmpratur (Fig. 9). In th figurs 9 and 10 th valu of tmpratur for th masuring point of th radius was prsntd. To dtrmin th ffctivnss of usd ANN th tst was prformd. This tst was consistd in th vrification th distribution of th valu of tmpratur in cas whn artificial nural ntwork wasn't work and th vlocity of th hat sourc is constant (Fig. 10). Th siz of th hat affctd zon was dtrmind by A C3 curv on th lvl 1058 (Fig. 11). Fig. 11. Th comparison of th hat affctd zon for: a) constant vlocity of th hat sourc, b) vlocity of th hat sourc controlld by ANN 6. Conclusions Fig. 9. Th changs of th tmpratur in th cas of variabl vlocity of th hat sourc dtrmind by artificial nural ntwork Using th artificial nural ntwork in th control lmnts of th quipmnt in th hat tratmnt allows for ffctiv control th paramtrs of ths procss. In th papr this paramtr was th vlocity of th hat sourc. Th ffcts of changs of th vlocity of th hat sourc was th maintnanc of th stablishd maximum tmpratur on th surfac of hatd lmnt. Th artificial nural ntwork corrctly ractd on th changs of th radius of th stl lmnt. Th prsntd mthod of string of paramtr for th A R C H I V E S o f F O U N D R Y E N G I N E E R I N G V o l u m 1 5, I s s u 1 / ,

6 hating procss can b also using to control th dpth of th hat affctd zon. Th instability of th maximum tmpratur on th boundary of aras with diffrnt radius wr th rsult from assumd position of th radius snsor. Th maximum valu of th tmpratur wasn't xcd th mlt tmpratur. Rfrncs [1] Canal, L.C.F., Msquita, R.A., Tottn, G.E. (2008). Failur Analysis of Hat Tratd Stl Componnts. Unitd Stats of Amrica: ASM Intrnational. [2] Tottn, G.E. (2006). Stl Hat Tratmnt: Equipmnt and Procss Dsign. Unitd Stats of Amrica: CRC Prss. [3] Rutkowski, L. (2005). Computational Intllignc: Mthods and Tchniqus. Brlin: Springr. [4] Ygnanarayana, B. (2006). Artificial nural ntworks. Nw Dlhi: Prntic-Hall of India Larning. [5] Bokota, A. (2012). Modlling of hardning tool stls. Thrmal phnomna, phas transformations, mchanical phnomna. Częstochowa: Wydawnictwo Politchniki Czstochowski. [6] Wait, R., Mitchll, A.R. (1985). Finit Elmnt Analysis and Applications. Chichstr: John Wily & Sons. [7] Zinkiwicz, O.C., Taylor, R.L. (2000). Th finit lmnt mthod. Buttrworth-Hinmann: Oxword. [8] Mochnacki, B., Nowak, A., Pocica, A. (2002). Numrical modl of suprficial layr hat tratmnt using th TIG mthod. In. Świątkowski (Eds.), Polska mtalurgia w latach , Tom 2 (pp ). raków: WN Akapit. [9] ulawik, A. (2012). Modling of thrmomchnical phnomna of wlding procss of stl pip. Archivs of Mtallurgy and Matrials. 57(4), A R C H I V E S o f F O U N D R Y E N G I N E E R I N G V o l u m 1 5, I s s u 1 / ,