Parameter Study in Plastic Injection Molding Process using Statistical Methods and IWO Algorithm

Transcription

1 Itratoal Joural of Modlg ad Optmzato, Vol. 1, No., Ju 011 Paramtr Study Plastc Ijcto Moldg Procss usg Statstcal Mthods ad IWO Algorthm Alrza Akbarzadh ad Mohammad Sadgh Abstract Dmsoal chags bcaus of shrkag s o of th most mportaroblms producto of plastc parts usg jcto moldg. I ths study, ffct of jcto moldg paramtrs o th shrkag polypropyl (PP) ad polystyr (PS) s vstgatd. h rlatoshp btw put ad output of th procss s studd usg rgrsso mthod ad Aalyss of Varac (ANOVA) tchqu. o do ths, xstg data s usd. h slctd puaramtrs ar mltg tmpratur, jcto, packg ad packg tm. Effct of ths paramtrs o th shrkag of abov mtod matrals s studd usg mathmatcal modlg. For modlg th procss, dffrt typs of rgrsso quatos cludg lar polyomal, Quadratc polyomal ad logarthmc fucto, ar usd to trpolat xprmt data. Nxt, usg stp backward lmato ad 9% cofdc lvl (CL), sgfcaaramtrs ar lmatd from modl. o chck valdty of th PP modl, corrlato coffct of ach modl s calculatd ad th bst modl s slctd. h sam procdur s rpatd for th PS modl. Fally, optmum lvls of th puaramtrs that mmz shrkag, for both matrals ar dtrmd. Ivasv Wd Optmzato (IWO) algorthm s appld o th dvlopd mathmatcal modls. h optmzato rsults show that th proposd modls ad algorthm ar ffctv solvg th mtod problms. Idx rms IWO algorthm, Optmzato, Plastc jcto moldg, Rgrsso, shrkag. I. INRODUCION Nowadays, compttv markt rqurs producrs to produc hgh qualty parts, wth lowr prc th last possbl tm. Ijcto moldg s kow as a ffctv procss for mass producto of plastc parts wth complcatd forms ad hgh dmsoal prcso. I ths mthod, hgh flud polymr s jctd to th cavty wth dsrd form. Nxt, udr hgh, flud soldfs. Durg th procss, plastc matrals ar udr hgh ad tmpratur. Matrals ar coold to gt dsrd form. Ijcto moldg procss ca b dvdd to four stags: Plastczato, jcto, packg ad coolg. Although moldg procss may sm smpl, th moldd polymrs ar ffctd by may mach paramtrs ad procss codto [1-]. Mauscrpt rcvd March 31, 011; rvsd May 4, 011. Alrza Akbarzadh s wth th Dpartmt of Mchacal Egrg, Frdows Uvrsty of Mashhad, Mashhad, Ira.l/Fax: ; E-mal: Al_Akbarzadh_@ yahoo.com. Mohammad Sadgh s wth th Dpartmt of Mchacal Egrg, Frdows Uvrsty of Mashhad, Mashhad, Ira.E-mal: H.Sadgh@ymal.com. Icorrct puaramtrs sttgs wll caus bad qualty of surfac roughss,dcrass dmsoal prcso, Warpag, uaccptabl wasts, crass lad tm ad cost [3].hrfor, fdg th optmzd paramtrs s hghly dsrabl. I past sctsts usd trals ad rror to fd good procss codtos but ths mthod s tm ad cost cosumg. I addto, wh thr ar a larg umbr of puaramtrs, ths mthods ca t b usd. Nowadays, th modl of th procss ad optmal codto ar dvlopd usg aalytc mthods ad hurstc algorthms [4-8]. I prvous studs, crtcal paramtrs that affct th qualty of th parts ar vstgatd. Hag t al. [4] cosdrd sx puaramtrs as; mold tmpratur, mltg tmpratur, packg, packg tm ad jcto tm. hy studd ffcts of ths paramtrs o surfac qualty of th th moldd parts. L yag t al. [] vstgatd ffct of th sam paramtrs wth th addto of jcto spd, jcto acclrato o wdth of th sgrgato l. Chag t al. [6] studd ffcts of mltg tmpratur, jcto tmpratur, packg tm ad packg o th surfac qualty of th producd parts usg fuzzy logc. Su t al. [7] usd Artfcal Nural Ntwork (ANN) ad SA algorthm to optmzd surfac qualty of producd parts. Sh t al. [8] usd umrcal smulato ad Gtc Algorthm (GA) to achv bst shar strss. Warpag plastc parts du to at-symmtrc shrkag s o of th most mportat dfcts causd by rsdual strss. hs strsss ar usually du to th o drctoal at-symmtrc shrkag. As th shrkag dcrass, shrkag 3 drctos dcras ad thrfor warpag dcrass [9]. Prdcto of shrkag s vry dffcult bcaus of th umbr of paramtrs ad complxts of th procss. Dspt hug studs o modlg ad optmzg of jcto moldg procss, a fw rsarchs dal wth PP ad PS producd parts. Alta [] utlzd aguch mthod to optmz shrkag of plastc, PP ad PS, jcto moldg parts. H also appld ural twork to modl th procss ad was abl to achv 0.937% ad 1.4% shrkag PP ad PS, rspctvly. I ths papr, w xtd th Dsg of Exprmt (DOE) study prformd by Alta [] by dvlopg a rgrsso modl ad applyg IWO algorthm to obta th optmum lvls. W show that our mthod rsults slght mprovmt lowrg shrkag. hs papr s orgazd as follows. Frst xprmtal data ad slctd matral s troducd. Rgrsso aalyss s prformd ad 1 st ad d ordrs as wll as logarthmc modls ar dvlopd. ANOVA s usd to dtrm sgfcat modl paramtrs. Fally, IWO algorthm s usd to optmz puaramtrs to achv dsrd output, mmum shrkag. 141

2 Itratoal Joural of Modlg ad Optmzato, Vol. 1, No., Ju 011 II. EXPERIMENAL MEHOD Exstg xprmtal data s usd []. h data s basd o a modfd orthogoal array aguch mthod. h slctd puaramtrs clud, mltg tmpratur, packg, packg tm ad jcto. Shrkag, whch s o of th most mportat crtra, s slctd as output. Slctd matrals ar PP ad PS. Grad of th PP MH-418 wth mltg dx of 4.g/m ad grad of th PS s LGH-6 wth mltg dx of 7.g/m. Lvl of puaramtrs ach xprmt ad th masurd rsults ar show abl 1. ABLE 3.P-VALUE RESULS FOR POLYSYRENE MODEL Prdctor P-valu Costat p p P * 0.07 * III. MODELING HE PROCESS Rgrsso modlg s usd to dtrm th rlato btw put ad output varabls of th jcto moldg procss. For modlg th procss dffrt mathmatcal fuctos cludg lar polyomal, Quadratc polyomal ad logarthmc ar usd. hs modls ar modfd usg stp backward lmato mthod wth 9% CL Mtab softwar. rms wth CL of hghr tha 9% (P-valu lss tha 0.0) ar slctd. hs trms wth thr corrspodg P-valus ar rportd abls ad 3. O crtro for choosg th modl s corrlato coffct [11]. hrfor, corrlato coffcts (R valu) of th quatos for shrkag ar calculatd. As show abl 4, basd o thr R tst, quadratc polyomal modls ar bst fttd for both outputs. h R valus dcat that th prdctors xpla 90.1% ad 9.7% of th PP ad PS varacs, rspctvly. Furthrmor, to chck th valdty of th modls ormal probablty plot of rsduals, Fg. 1 ad Fg. ar vstgatd. Basd o Fg. 1 ad Fg., both modls ar ormally dstrbutd. Low dsprso of th pots from th rfrc l dcats hgh qualty of th modls. h slctd modls ar show abl. hs two modls wll latr b usd by th IWO algorthm to obta th optmum put varabl sttgs. Paramtr s Ut Symbol Mltg tmpratur C ABLE 1.EXPERIMENAL RESULS [] Ijcto Mpa P prssur Mpa Pack g tm Sc Polypropyl shrkag (%) - PP Polystyr shrkag (%) - PS ABLE 4. R ES FOR REGRESSION MODELS Fucto typ paramtr Lar Quadratc polyomal polyomal Logarthmc Polypropyl Polystyr Fgur 1. Normal tst for Polypropyl shrkag rsults Fgur.Normal tst for Polystyr shrkag rsults A graphcal rprstato dpctg th ffct of th crtcal paramtrs o output s also xplord. I th prst Paramtr Polypropyl Polystyr ABLE.REGRESSION MODELS Fttd Fucto PP= PP P p PP P PS= P PP P tp P PP 14

3 Itratoal Joural of Modlg ad Optmzato, Vol. 1, No., Ju 011 Study, thr ar four ma puaramtrs. Howvr, th smultaous ffct of all four paramtrs o output caot b dsplayd graphcally. hrfor a lar ANOVA study, cosdrg oly th four ma puaramtrs for ach matral s prformd. F-tst s usd by ANOVA to dtfy th mportat varabls. For valus of y ad th ma valu y, w ca wrt, SS = ( y y) (1) = 1 whr SS s sum of squard dvatos from th ma. s ma of squars ad dfd as, SS = () DF whr DF for =1,,4 dots dgr of frdom whch s th umbr of lvls for ach factor mus 1. DF s th umbr of xprmts mus 1. Mawhl, DF s DF mus sum of DF for =1,,4. F valu s th rato btw th ma of squars ffct ad th ma of squars rror. F = (3) F-tst dtrms th sgfcac of ach factor o th rspos varabl. ANOVA rsults ar show abls 6 ad 7. Accordg to ths two abls, jcto both matrals has th last ffct o shrkag. At 90% CL, accordg to ts F-valu, show abl 7, jcto has o sgfcat ffct o output for PS. h ANOVA rsults ca also b usd to dtrm th cotrbuto prctag of ach output by, SS DF ρ (%) = ( ) 0 (4) SS Rsults ar tabulatd Fg. 3. As show ths Fgur, packg ad mltg tmpratur ar th most mportaaramtrs affctg th shrkag of th PP ad PS, rspctvly Upo dtfyg th two most mportat puaramtrs, th quadratc polyomal rgrsso modls, abl, ar usd to plot th par-ws ffcts 3D charts. o do ths, th two most mportat ma paramtrs, dtfd by cotrbuto prctags, ar vard whl th othr two ma paramtrs ar hld costat at thr md-lvls. Fg. 4 shows th smultaous ffct of packg ad packg tm o shrkag of PP ad Fg. shows th ffct of mltg tmpratur ad packg o shrkag of PS. Sourc ABLE 6.ANOVA RESULS FOR POLYPROPYLENE Dgr of Frdom (DF ) Sum of (SS ) Ma ( ) P Error otal F valu 90% C.I s.63, * Sgfcat factor F Valu P valu * * * * Sourc ABLE 7.ANOVA RESULS FOR POLYSYRENE Dgr of Frdom (DF ) Sum of (SS ) Ma ( ) F Valu P valu * P * * Error otal F valu 90% C.I s.63, * Sgfcat factor Fgur 3.Cotrbuto prctag for paramtrs As Fg. 4 shows by crasg packg ad dcrasg packg tm, shrkag s mmzd. As Fg. shows by crasg mltg tmpratur ad dcrasg packg, shrkag rachs ts mmum. As statd arlr, ffct of o mor tha two puts ca b dsplayd graphcally. If th output spac s ot too complcatd, t may b possbl to us such graphs to dtfy th sttgs rsultg optmum output. Howvr, as th prst study, th umbr of puts s four ad graphcal tchqus ar o logr ffctv. hs s why IWO algorthm s usd to dtfy th optmum lvls. IV. OPIMIZAION MEHOD Ivasv Wd Optmzato (IWO) s a probablstc sarch algorthm sprd by th bhavor of vasv wds colozg opportuty spacs thr atural habtats. Bascally, wds ar plats whos vgorous, vasv habts of growth pos a srous thrat to cultvatd plats, makg thm a hazard to agrcultur. Wds hav show to b vry robust ad adaptv to th chags of vromt. h algorthm starts wth a tal populato of wds dsprsd radomly o th solutos spac. h ftss of Each wd s th dtrmd by valuatg t agast th objct fucto. o smulat th atural survval procss, ay gv wd th coloy producs sds basd o thr crtra: ts ftss, th coloy's lowst ftss ad th hghst ftss. h sds ar radomly dstrbutd wth a lmtd dstac aroud thr parlat. Usually as th coloy gts dsr th dsprsos of sds bcom closr. All wds th coloy, cludg w offsprg, ar th valuatd. I ths stag, f th populato has rachd ts maxmum allowabl umbr, th lssr fttd os ar lmatd. hs compttv xcluso rsults voluto of th coloy 143

4 Itratoal Joural of Modlg ad Optmzato, Vol. 1, No., Ju 011 coscutv gratos. 9, ths valus rprst 3.7% ad.7% mprovmts shrkag of PP ad PS parts, rspctvly. Fgur 4.Estmat Polypropyl shrkag rgard to packg ad packg tm. V. CONCLUSIONS Warpag s o of th ma dfcts jcto moldg procss whch appars du to at-symmtrc shrkag. I ths study, mathmatcal modls for dtrmg ffcts of ky procss put varabls o shrkag for PP ad PS matrals ar vstgatd. Svral rgrsso modls ar vstgatd. Stp backward lmato mthod, at 9% CL, s usd to lmat sgfcat trms from th modls. R ad P-valu statstcs ar usd to dtfy th bst modls. Rsults dcat that quadratc polyomal s bttr tha th othr modls. Nxt, ANOVA s usd to dtrm th most ffctv paramtrs for th slctd modl. Basd o ANOVA, for Packg s th most ffctv whl jcto s th last mportat. h othr two varabls, mltg tmpratur ad packg tm ar sgfcat ad hav approxmatly th sam ffct. Aga, basd o ANOVA, for PS, mltg tmpratur s th most flutal varabl whl packg ad packg tm ar xt th flutal paramtrs. Fgur.Estmat Polystyr shrkag rgard to mltg tmpratur ad packg. IWO attmpts to mak us of th robustss, adaptato ad radomss of colozg wds. Usg such proprts, th algorthm s abl to covrg towards optmal soluto. I IWO, a wd rprsts a soluto to th problm; our cas a rspos for ach rgrsso modl a spcal paramtr sttg. A st of radom lvl of paramtrs crats th tal populato of sds. Sc th goal s mmzg shrkag th a wd havg lssr shrkag has mor ftss. A w sd s producd by xchagg th lvl of two paramtrs wth th all paramtrs th rgrsso modl. At ach tratos, th trasposto rag (th dstac) btw two lvls must b lss tha th stadard dvato (SD) of sds dstrbuto gv by followg quato: ( tr tr) σ = σ σ + σ () max tr [ ] ( tal fal ) fal trmax I ths formula, σ tr s th currt trato SD, tr max s th maxmum umbr of tratos, tr s th currt trato umbr ad σ tal ad σ fal ar th tal ad fal valu of SD. h ma stps of IWO algorthm s schmatcally llustratd Fg. 6. h dtals of ths tchqu ad ts varous applcatos ar wll documtd ltratur [1-14]. I ths study, proposd algorthm s codd Matlab 7.1 softwar ad s usd to optmz th problm. Optmzd paramtrs sttgs ad prdctd output ar show abl 8. As show ths abl, by sttgs th put paramtrs at th statd valus, shrkag prctag of lss tha 1% for both matrals s achvd. As dcatd abl Fgur 6.Sd producto procdur a coloy of wds ABLE 8.OPIMIZAION RESULS Optmum lvls of ach paramtr % Shrkag Mltg tmpratur Ijcto tm PP PS C Mpa Mpa Sc % %0.9 paramtr Polypropyl Polystyr ABLE 9.COMPARISON RESULS Ital Mach sttgs % 1.37 % 1.8 Aftr Optmzato % 0.88 % 0.9 Improvmt % 3.7 %.7 Addtoally, jcto s ot statstcally sgfcat. Fally, IWO optmzato mthod s appld to dtrm optmum put lvls to mmz shrkag. Rsults dcat that shrkag s rducd to blow 1% whch s slghtly bttr tha th prvous study []. hrfor, th prst study dmostrats th ffctvss of modls ad proposd optmzato mthod. 144

5 Itratoal Joural of Modlg ad Optmzato, Vol. 1, No., Ju 011 Abbrvato ANN ANOVA CL GA IWO PP PS RSM SD Notato DF F tr max Ms P ρ SS SS Ybar Y σ tal σ fal σ tr APPENDIX artfcal ural twork aalyss of varac Cofdc lvl gtc algorthm vasv wd optmzato polypropyl polystyr rspos surfac mthodology stadard dvato dgr of frdom f-valu maxmum umbr of tratos ma squar of rror ma squar jcto packg prctag cotrbuto sum of squar total sum of squar mltg tm packg tm ma of outputs output tal valu of stadard dvato fal valu of stadard dvato currt trato of stadard dvato [] J.M. Lag ad P.J. Wag, Mult-objctv optmzato schm for qualty cotrol jcto moldg, J. Ijct. Mold. ch. Carr ad chcal Educato, vol. 64, 00, pp [6] K.. Chag ad F.P. Chag, Applcato of gry-fuzzy logc o th optmal procss dsg of a jcto-moldd part wth a th shll fatur, Itratoal Commucatos Hat ad Mass rasfr, Aprl 006, pp [7] C.. Su ad H.H. Chag, Optmzato o f paramtr dsg: a tllgt approach usg ural twork ad smulatd aalg, It. J. Systms Scc, vol. 31, 000, pp [8] F. Sh, Z.L. Lou, J.G. Lu ad Y.Q. Zhag, Optmzato of plastc jcto moldg procss wth soft computg, It. J. Adv. Mauf. ch. vol. 1, 003, pp [9] R.A. Malloy, Plastc part dsg for jcto moldg, Much: Hasr Publshrs, [] M. Alta, Rducg Shrkag Ijcto Moldgs va th aguch, ANOVA ad Nural Ntwork Mthods, j. Mat. & Dsg, vol. 31, 0, pp [11] D.C. Motgomry, Dsg ad aalyss of xprmts 7th d., Nw York: Joh Wly & Sos, 008. [1] A.R. Mhraba ad C. Locas, A ovl umrcal optmzato algorthm sprd from wd colozato, Ecologcal Iformatcs, vol. 1, 006, [13] A.R.Mhraba, Aghl Yousf-Koma, optmal postog of pzolctrc actuators o a smart f usg bo-sprd algorthms, Arospac Scc ad tchology, vol. 11, 007, [14] H. Sphr-Rad ad C. Lucas, A rcommdr systm basd o vasv wd optmzato algorthm, Proc. IEEE Cogrss o Evolutoary Computato, 007, pp Alrza Akbarzadh was bor July of 19 Mashhad, Ira. H rcvd hs PhD Mchacal Egrg 1997 from Uvrsty of Nw Mxco USA. H workd at Motorola USA for 1 yars whr h ld R&D as wll as Automato tams. H jod Frdows Uvrsty of Mashhad 00 ad s currtly assocat profssor of M.E. Dpartmt. H has ovr 18 Joural publcatos ad ovr cofrc paprs. Hs aras of rsarch clud Robotcs (Paralll Robots, Bologcally sprd Robots, Bpd), Dyamcs, Kmatcs, Automato, Optmzato, Dsg ad Aalyss of Exprmts. REFERENCES [1] G. Pötsch ad W. Mchal, Ijcto moldg: A troducto, Much: Hasr Publshrs, 199. [] J.A. Brydso, Plastc matrals, Buttrworth-Hma: Oxford, 199. [3] D.V. Rosato, M.G. Rosato, Ijcto moldg hadbook Massachustts: Kluwr Acadmc Publshrs, 000. [4] M.C. Huag ad C.C. a, h ffctv factors th warpag problm of a jcto-moldd part wth a th shll fatur, J. Mat. Proc. ch., vol. 1, 001, pp Mohammad Sadgh was bor Sptmbr of 1984 Mashhad, Ira. H rcvd hs B.Sc. dgr Maufacturg Egrg from Brjad Uvrsty, Ira 008. H s currtly a M.S.c studt at th Dpartmt of Mchacal Egrg, Frdows Uvrsty of Mashhad Ira. 14