Multi-objective optimization of machining parameters for drilling LM5/ZrO2 composites using grey relational analysis

Ci a ion: Jeba ose Juliyana, S.; Udaya P akash, J.; ˇ Cep, R.; Ka hik, K. Mul i-Objec i e Op imiza ion o Machining Pa ame e s o D illing LM5/Z O2Composi es Using G ey Rela ional Analysis. Ma e ials 2023, 16, 3615. h ps://doi.o g/10.3390/ ma16103615 Academic Edi o s: An onio Ri ei o and Bol Xiao Recei ed: 2 Ap il 2023 Re ised: 21 Ap il 2023 Accep ed: 7 May 2023 Published: 9 May 2023 Copy igh : © 2023 by he au ho s. Licensee MDPI, Basel, Swi ze land. This a icle is an open access a icle dis ibu ed unde he e ms and condi ions o he C ea i e Commons A ibu ion (CC BY) license (h ps:// c ea i ecommons.o g/licenses/by/ 4.0/). ma e ials A icle Mul i-Objec i e Op imiza ion o Machining Pa ame e s o D illing LM5/Z O2Composi es Using G ey Rela ional Analysis Sunde Jeba ose Juliyana 1, Jaya elu Udaya P akash 1, Robe ˇ Cep 2and K ishnasamy Ka hik 1,* 1Depa men o Mechanical Enginee ing, Vel Tech Ranga ajan D . Sagun hala R&D Ins i u e o Science and Technology, Chennai 600062, India; [email p o ec ed] (S.J.J.); [email p o ec ed] (J.U.P.) 2Depa men o Machining, Assembly and Enginee ing Me ology, Facul y o Mechanical Enginee ing, VSB-Technical Uni e si y o Os a a, 17. Lis opadu 2172/15, 708 00 Os a a, Czech Republic; [email p o ec ed] *Co espondence: [email p o ec ed] Abs ac : In oday’s wo ld, enginee ing ma e ials ha e changed d ama ically. T adi ional ma e ials a e ailing o sa is y he demands o p esen applica ions, so se e al composi es a e being used o add ess hese issues. D illing is he mos i al manu ac u ing p ocess in mos applica ions, and he d illed holes se e as maximum s ess a eas ha need o be ea ed wi h ex eme cau ion. The issue o selec ing op imal pa ame e s o d illing no el composi e ma e ials has ascina ed esea che s and p o essional enginee s o a long ime. In his wo k, LM5/Z O 2 composi es a e manu ac u ed by s i cas ing using 3, 6, and 9 w % zi conium dioxide (Z O 2 ) as ein o cemen and LM5 aluminium alloy as ma ix. Fab ica ed composi es we e d illed using he L 27 OA o de e mine he op imum machining pa ame e s by a ying he inpu pa ame e s. The pu pose o his esea ch is o ind he op imal cu ing pa ame e s while simul aneously add essing he h us o ce (TF), su ace oughness (SR), and bu heigh (BH) o d illed holes o he no el composi e LM5/Z O 2 using g ey ela ional analysis (GRA). The signi icance o machining a iables on he s anda d cha ac e is ics o he d illing as well as he con ibu ion o machining pa ame e s we e ound using GRA. Howe e , o ob ain he op imum alues, a con i ma ion expe imen was conduc ed as a las s ep. The expe imen al esul s and GRA e eal ha a eed a e (F) o 50 m/s, a spindle speed (S) o 3000 pm, Ca bide d ill ma e ial, and 6% ein o cemen a e he op imum p ocess pa ame e s o accomplishing maximum g ey ela ional g ade (GRG). Analysis o a iance (ANOVA) e eals ha d ill ma e ial (29.08%) has he highes in luence on GRG, ollowed by eed a e (24.24%) and spindle speed (19.52%). The in e ac ion o eed a e and d ill ma e ial has a mino impac on GRG; he a iable ein o cemen pe cen age and i s in e ac ions wi h all o he a iables we e pooled up o he e o e m. The p edic ed GRG is 0.824, and he expe imen al alue is 0.856. The p edic ed and expe imen al alues ma ch each o he well. The e o is 3.7%, which is e y minimal. Ma hema ical models we e also de eloped o all esponses based on he d ill bi s used. Keywo ds: composi es; d illing; g ey ela ional analysis; design o expe imen s; ANOVA 1. In oduc ion Aluminium ma ix composi es (AMCs) ha e gained he a en ion o many scien is s because he Al alloy o e comes he sho comings o e ous me als and p o ides he bes speci ied pe o mance pa ame e s. AMCs a e popula ma e ials o mee ing all o he igo ous demands in echnical applica ions ha equi e p ope ies such as low weigh , high s i ness, and medium s eng h [ 1 – 3 ]. AMCs combine he me al p ope ies o ma ix alloys wi h ce amic ein o cemen s o p oduce complex se ice empe a u e capabili ies, inc eased s eng h, and comp ession esis ance [ 4 – 6 ]. Noo ul Haq e al. (2008) p oposed a comp ehensi e wo-dimensional a ay wi h he GRA me hod o op imising p ocess pa ame e s o d illing Al/SiC composi es [ 7 ]. Ponnu el and Moo hy (2014) s udied he Ma e ials 2023,16, 3615. h ps://doi.o g/10.3390/ma16103615 h ps://www.mdpi.com/jou nal/ma e ials Ma e ials 2023,16, 3615 2 o 13 impac o d illing pa ame e s on hyb id polyme composi es (MWCNTs) [ 8 ]. Op imal cu ing pa ame e s we e disco e ed using GRA while simul aneously add essing he TF, SR, and BH o d illed holes. The g ey- uzzy me hod was applied by Rajmohan e al. (2013) o ind he bes machining pa ame e s o d illing composi es o hyb id aluminium me al ma ix. In he expe imen s, a h ee-le el OA L 27 is used [ 9 ]. Emin Salu a e al. (2019) used a ho p ess o c ea e MMC, and he e ec s o he ou pu a iables on he TF and SR o composi es we e s udied using ANOVA [ 10 ]. The e ec s o p oduc ion a iables we e in es iga ed and isualised. I is possible o de e mine he ideal alue o each ou pu ac o using he S/N a io app oach. The indings demons a ed ha he addi ional phase ma e ial p opo ion was he p ima y de e minan o he SR o he MMCs o bo h eed a es. As he eed a e inc eased du ing machining, he TF and SR alues inc eased, acco ding o he li e a u e. Howe e , when he eed a e inc eased, he TF and SR alues in his MMC sys em dec eased, making his s udy mo e no el. Palanikuma e al. (2012) employed GRA o op imise he d illing pa ame e s o GFRP composi e d illing based on SR and TF. The Taguchi L 9 3-le el OA is employed in he expe imen . Using he GRG acqui ed om he GRA, hey es ablished he p e-eminen pa ame e s o mul i-pe o mance ea u es [ 11 ]. Da im (2001) examined he consequences o p ocess pa ame e s on he su ace quali y o u ned componen s. Expe imen s based on Taguchi’s me hodologies we e planned and ca ied ou on con olled machining o wo kpieces wi h p ede e mined cu ing condi ions. Those associa ions we e disco e ed using mul iple linea eg essions. Finally, hey used con i ma ion es s o compa e he heo e ical ou comes wi h he expec ed esul s om he co ela ions [ 12 ]. Samy and Kuma an (2017) concluded he e ec s o cu ing ac o s on empe a u e, TF, and SR on AA6351/B 4 C composi e ma e ials du ing d illing ope a ions. Comple ely di e en angles o i anium ni ide-coa ed ca bide d ill bi s, such as 90 ◦ , 118 ◦ , and 135 ◦ , we e employed. Lowe spindle speeds and eed a es a e used o achie e he much lowe empe a u e. Unsui able poin angles, on he o he hand, cause ool wea and inc ease su ace oughness. Changing he machining ac o s also a ec s he p oduc ion o h us o ce. The h us o ce is mino when d illing wi h a ool wi h a 135 ◦ poin angle, bu he delamina ion is g ea e [13]. Acco ding o Jun eng Xiang e al. (2017), SiCp/Al ma ix composi e ma e ials ha e nume ous ema kable physical and mechanical p ope ies. Thei goal is o in es iga e he mechanisms ha in luence he mac o-scale wea o diamond ools when d illing SiCp/Al composi e ma e ials. Aside om ha , d illing o ces and hole eliabili y we e used o assess he machinabili y o he SiCp/Al 6063 composi e ma e ial. The indings imply ha mechan- ically gene a ed ab asi e wea and he modynamically allowed chemical g aphi ica ion a e impo an and likely wea mechanisms in SiCp/Al6063 d illing. Diamond-coa ed ca bide d ills a e chosen o composi e ma e ial because o hei longli e, low wea a e, and abili y o gene a e su icien machined e iciency wi h a g owing numbe o holes [ 14 ]. Jayagan h e al. (2018) used Taguchi’s L 9 a ay o conduc d illing es s wi h a ious cu ing speeds, eeds, and cu ing luids. Su ace oughness alues dec ease, bu machining ime inc eases as cu ing speed and eed a e inc ease. Op imal p ocess pa ame e s ha e been designed and con i med o imp o e machinabili y. A highe speeds and eeds, he coconu oil medium p o ided supe io machinabili y [ 15 ]. Mahamani (2014) explo ed he e ec s o eed, speed, poin angle, and d ill bi diame e on su ace oughness (SR) in he d illing o AA2219/TiB 2 /Z B 2 hyb id composi es. In es iga ional analysis explo es he in luence o one p ocess a iable while keeping he o he a iables cons an [ 16 ]. Ekici e al. (2017) assessed he e ec s o p ocess pa ame e s on h us o ce (TF), SR, dimensional accu acy, and bu heigh (BH) when d illing Al/10B 4 C and Al/10B 4 C/5G composi es using ca bide wis d ills a a ious le els o speeds and eed a es unde d y cu ing condi ions. ANOVA was used o e alua e he pe cen age con ibu ion o p ocess a iables o p oduc quali y. Finally, hey de eloped s a is ical equa ions o e alua e quali y a ibu es. Al/10B 4 C/5G , a second-phase ma e ial wi h 5% g aphi e, dec eased he TF and BH o he composi es, enhancing he su ace’s quali y [17]. Ma e ials 2023,16, 3615 3 o 13 Ra ind ana h e al. (2017) examined he consequences o p ocess pa ame e s du ing he d illing o Al2219/8% bo on ca bide (B 4 C) composi e and hyb id composi e Al2219/8% B 4 C/3% G . The expe imen was ca ied ou a a ious speeds and eeds; he impac o he TF and SR was examined, and he indings show ha when he FR ose, he TF and SR inc eased. Because g aphi e has good lub ica ing cha ac e is ics, hyb id composi es ha e lowe h us and a la ge su ace oughness [ 18 ]. In d illing SA182 wo k ma e ial, Sunil Ankalagi e al. (2017) s udied he ou come o d illing a iables such as F, S, and d ill poin angle on TF, SR, and ci cula i y e o . To explain he beha iou o machinabili y and hole quali y, he in es iga ions we e designed using an o hogonal a ay (OA) and esponse su ace me hodology (RSM). The easibili y o he models o he indica ed esponses was alida ed using an ANOVA. All he esponses we e ound o dec ease wi h inc easing spindle speed, while he ci cula i y e o dec eased wi h a high cu ing speed and eed, acco ding o he esponse su ace analysis. Ci cula i y e o and su ace oughness we e educed when he poin angle was inc eased [ 19 ]. This esea ch wo k’s objec i e is o conduc mul i-objec i e op imisa ion o d illing p ocess pa ame e s o achie ing minimum TF, SR, and BH o LM5/Z O 2 composi e and o in es iga e he e ec o p ocess pa ame e s on TF, BH, and SR. 2. Ma e ials and Me hods 2.1. Ma e ials Due o i s widesp ead a ailabili y, zi conia (Z O 2 ) has been chosen as he ein o cemen ma e ial and LM5 aluminium alloy as he ma ix. The alloy is used o de ices used in he p oduc ion o oods u s, culina y u ensils, and chemical indus ies, as well as o he moulding o ine polish a eas whe e qui e s ong co osion esis ance om sal wa e o ma ine a mosphe es is desi ed. They a e e y well known o hei aes he ic cas s as well as cas s u ilised in applica ions o building and deco a i e ma i ime i ings, ood handling dai y equipmen , and chemical and ma i ime plumbing i ings [ 20 ]. LM5 is examined o i s chemical composi ion by means o op ical emission spec ome y, and i is p esen ed in Table 1. Table 1. Chemical composi ion o aluminium alloy (LM5). Cu Mg Si Mn Fe Pb Zn Al 0.032 3.299 0.212 0.022 0.268 0.02 0.01 Balance Zi conium dioxide (Z O2), a c ys alline oxide o zi conium (zi conia), which is whi e in colou , is b oadly conside ed o be a ce amic elemen . Making zi conia includes he ga he ing and emo al o laid-o ing edien s and scum. Mining zi conia has many ou es, including plasma disassocia ion, chlo ine and alkali oxide disin eg a ion, and lime amalga- ma ion. Simila o many ce amics, zi conium oxide is a subs a e wi h a high ole ance o c ack p opaga ion. Z O 2 ce amics a e he mally es ablished, and o en hey a e he ma e ial o linking ce amics and s eel. Li le he mal conduc i i y and g ea s eng h a e ano he aw ul combina ion o p ope ies. 2.2. Manu ac u ing o LM5/Z O2Composi es To ab ica e he composi e, a closed u nace, which is o he C- ype, is used wi h he s i cas ing se -up. The s i e inco po a es a chuck o con enien sha in e changeabili y. I has a ou -bladed an impelle ha is made o high-ch omium s eel. Ini ially, small ingo s o LM5 alloy we e hea ed o a ound 850 ◦ C in he c ucible un il he en i e alloy was mel ed. To e adica e dampness in he ein o cemen , he Z O 2 powde is d ied o 20 min a 200 ◦ C using a mu le u nace. The s i e was p og essi ely inse ed in o he mel , c ea ing a o ex in he mol en me al. The wa med Z O 2 , wi h an a e age pa icle size o 60 o 80 µ m, was hen ca e ully and slowly mixed in o he liquid me al a a consis en a e while upholding he speed o he s i e a 600 pm. E en a e pa icle eeding, he s i ing con inued o ano he 7 min. To educe po osi y, a gon gas was added o he slu y Ma e ials 2023,16, 3615 4 o 13 o h ee minu es be o e pou ing i in o he mould. The pou ing empe a u e was ixed a 750 ◦ C. To achie e uni o m solidi ica ion, he mould was wa med o 650 ◦ C o 30 min be o e pou ing he slu y in o i . This me hod was used o c ea e h ee dis inc se s o unique composi es cons uc ed o LM5 ein o ced wi h 3, 6, and 9 weigh pe cen s o Z O 2 pa icles [21]. 2.3. Mic os uc u e o Fab ica ed Composi es Using Op ical Mic oscopy Me allog aphic examina ions p o ide a signi ican in es iga i e ool and e ec i e quali y con ol. Samples we e collec ed om e e y composi e, and each su ace was inely polished o achie e a mi o -like sheen. The p ima y goal o a mic os uc u al analysis is o alida e he uni o m dispe sion o a ma ix’s ein o cemen pa icles. The op ical mic oscope was used o in es iga e he composi e specimens. The homoge- nous sp eading o ein o cemen pa icles in he ma ix is shown in he op ical pho omic o- g aphs (Figu e 1). The dispe sion o composi e Z O 2 pa icles is seen in he mic os uc u e o me al ma ix composi es con aining 3% and 6% Z O 2 . The p ima y aluminium g ains con ain he pa icles. MgAl 2 eu ec ic pa icles ha did no dissol e a e solidi ica ion a e p ecipi a ed a he g ain bounda ies. The magni ica ion is 200 × . The main aluminium phase includes g ains ha a e 40 o 60 mic ons in size. In he 9% Z O 2 composi e, pa icle dispe sal is de ec ed and exis s as la e al bunches on he g ain bounda ies, al hough he mic og aph only displays he esol ed composi e pa icles. Ma e ials2023,16,xFORPEERREVIEW4o 13   ingcon inued o ano he 7min.To educepo osi y,a gongaswasadded o heslu y o  h eeminu esbe o epou ingi in o hemould.Thepou ing empe a u ewas ixeda  750°C.Toachie euni o msolidi ica ion, hemouldwaswa med o650°C o 30min be o epou ing heslu yin oi .Thisme hodwasused oc ea e h eedis inc se so  uniquecomposi escons uc edo LM5 ein o cedwi h3,6,and9weigh pe cen so  Z O2pa icles[21]. 2.3.Mic os uc u eo Fab ica edComposi esUsingOp icalMic oscopy Me allog aphicexamina ionsp o ideasigni ican in es iga i e oolande ec i e quali ycon ol.Sampleswe ecollec ed ome e ycomposi e,andeachsu acewas inelypolished oachie eami o ‐likesheen.Thep ima ygoalo amic os uc u al analysisis o alida e heuni o mdispe siono ama ix’s ein o cemen pa icles. Theop icalmic oscopewasused oin es iga e hecomposi especimens.Theho‐ mogenoussp eadingo  ein o cemen pa iclesin hema ixisshownin heop ical pho omic og aphs(Figu e1).Thedispe siono composi eZ O2pa iclesisseenin he mic os uc u eo me alma ixcomposi escon aining3%and6%Z O2.Thep ima y aluminiumg ainscon ain hepa icles.MgAl2eu ec icpa icles ha didno dissol ea ‐ e solidi ica iona ep ecipi a eda  heg ainbounda ies.Themagni ica ionis200×.The mainaluminiumphaseincludesg ains ha a e40 o60mic onsinsize.In he9%Z O2 composi e,pa icledispe salisde ec edandexis sasla e albuncheson heg ain bounda ies,al hough hemic og aphonlydisplays he esol edcomposi epa icles.  (a)  (b) Figu e 1. Con . Ma e ials 2023,16, 3615 5 o 13 Ma e ials2023,16,xFORPEERREVIEW5o 13    (c) Figu e1.Mic os uc u eso  ab ica edcomposi es.(a)LM5+3%Z O2;(b)LM5+6%Z O2;(c)LM5+ 9%Z O2. 2.4.D illingo LM5/Z O2Composi es TheGau a ‐BMV35T12(Model)Ve icalMachiningCen e(VMC),equippedwi h aKis le peizo‐elec icdynamome e showninFigu e2,isused o d illingholesin composi ema e ials.InFigu e3,specimen1 ep esen sLM5+3%Z O2,specimen2 ep‐ esen sLM5+6%Z O2andspecimen3 ep esen sLM5+9%Z O2.Acompu e ‐con olled da acollec ion oolcap u esands o es he esul so expe imen s.The eliabili yo  he d illedholeis hep ima yconce ndu ingd illing.Apiezo‐elec icdynamome e was used omeasu e heTFgene a eddu ingd illing,whichis hemainde e minan o  he hole’squali y.BHwas oundusing heVisionMeasu ingSys em(VMS),andSRwasde‐ e minedusing hesu ace oughness es e —su co de [22].Cu ing oolsusedin his esea chwo kwe emadeo  h eedi e en ma e ials:HSS,ca bide,and i aniumni ide (TiN)‐coa edca bide.Fo all h eed ills, hediame e is6mm, hepoin angleis118°, and hehelixangleis30°.Theexpe imen ’s ou p ima yp ocesspa ame e swe e picked.The h eele elso d illing a iablesa ep esen edinTable2.  Figu e2.Expe imen alse ‐upwi hadynamome e .  Figu e 1. Mic os uc u es o ab ica ed composi es. ( a ) LM5 + 3%Z O 2 ; ( b ) LM5 + 6%Z O 2 ; (c) LM5 + 9%Z O2. 2.4. D illing o LM5/Z O2Composi es The Gau a -BMV 35 T12 (Model) Ve ical Machining Cen e (VMC), equipped wi h a Kis le peizo-elec ic dynamome e shown in Figu e 2, is used o d illing holes in composi e ma e ials. In Figu e 3, specimen 1 ep esen s LM5 + 3%Z O 2, specimen 2 ep esen s LM5 + 6%Z O2 and specimen 3 ep esen s LM5 + 9%Z O 2. A compu e -con olled da a collec ion ool cap u es and s o es he esul s o expe imen s. The eliabili y o he d illed hole is he p ima y conce n du ing d illing. A piezo-elec ic dynamome e was used o measu e he TF gene a ed du ing d illing, which is he main de e minan o he hole’s quali y. BH was ound using he Vision Measu ing Sys em (VMS), and SR was de e mined using he su ace oughness es e —su co de [ 22 ]. Cu ing ools used in his esea ch wo k we e made o h ee di e en ma e ials: HSS, ca bide, and i anium ni ide (TiN)- coa ed ca bide. Fo all h ee d ills, he diame e is 6 mm, he poin angle is 118 ◦ , and he helix angle is 30 ◦ . The expe imen ’s ou p ima y p ocess pa ame e s we e picked. The h ee le els o d illing a iables a e p esen ed in Table 2. Ma e ials2023,16,xFORPEERREVIEW5o 13    (c) Figu e1.Mic os uc u eso  ab ica edcomposi es.(a)LM5+3%Z O2;(b)LM5+6%Z O2;(c)LM5+ 9%Z O2. 2.4.D illingo LM5/Z O2Composi es TheGau a ‐BMV35T12(Model)Ve icalMachiningCen e(VMC),equippedwi h aKis le peizo‐elec icdynamome e showninFigu e2,isused o d illingholesin composi ema e ials.InFigu e3,specimen1 ep esen sLM5+3%Z O2,specimen2 ep‐ esen sLM5+6%Z O2andspecimen3 ep esen sLM5+9%Z O2.Acompu e ‐con olled da acollec ion oolcap u esands o es he esul so expe imen s.The eliabili yo  he d illedholeis hep ima yconce ndu ingd illing.Apiezo‐elec icdynamome e was used omeasu e heTFgene a eddu ingd illing,whichis hemainde e minan o  he hole’squali y.BHwas oundusing heVisionMeasu ingSys em(VMS),andSRwasde‐ e minedusing hesu ace oughness es e —su co de [22].Cu ing oolsusedin his esea chwo kwe emadeo  h eedi e en ma e ials:HSS,ca bide,and i aniumni ide (TiN)‐coa edca bide.Fo all h eed ills, hediame e is6mm, hepoin angleis118°, and hehelixangleis30°.Theexpe imen ’s ou p ima yp ocesspa ame e swe e picked.The h eele elso d illing a iablesa ep esen edinTable2.  Figu e2.Expe imen alse ‐upwi hadynamome e .  Figu e 2. Expe imen al se -up wi h a dynamome e . Ma e ials 2023,16, 3615 6 o 13 Ma e ials2023,16,xFORPEERREVIEW6o 13   Table2.D illingp ocesspa ame e sand hei le els. Fac o Le el1Le el2Le el3 F(mm/min)50100150 S( pm)100020003000 DHSSCa bideTiNCoa ed R(%)369  Figu e3.D illedholes. 2.5.G eyRela ionalAnalysis Mul i‐pe o mancecha ac e is icsa e ough oop imiseincomplexp ocesses; hence,GRAisla gelyemployed oadd esssucha oughp oblem.Thead an ageso  g eysys em heo yha ebeencon i medincopingwi h hechallengeso incomple e, pa ial,andunclea da a.The e msblack,whi e,andg eya ede ineddi e en lying ey ela ionalanalysis.Blackdeno esasys emwi hnoin o ma ion,whi edeno esasys em wi hexac in o ma ion,andg ey ep esen s hein o ma ionbe weenblackandwhi e. This echniqueadd esses heissueo imp o ing he esponse ea u eso cu en ma‐ chiningsys ems[23,24]. Ing ey ela ionalanalysis, he i s s episda ap e‐p ocessing,whe e heTF,SR,and BHexpe imen alda aa es anda dised obein he angeo ze o oone.Da a p e‐p ocessingis ypicallynecessa ybecause he angeanduni o oneda ase di e  om heo he s.Theme hodo con e ingasequencein oone ha iscompa able o he o iginaliscalledda ap e‐p ocessing.Dependingonada ase ies’cha ac e is ics, he e a eanumbe o da ap e‐p ocessingme hodsaccessible o GRA.The“high‐ e ‐ he‐be e ”cha ac e is icappliesi  he a ge  alueisin ini e.Thesequencecanbe no malisedasshowninEqua ion(1): * i x(k)= )(min)(max )(min)( )0()0( )0()0( kxkx kxkx ii ii  (1) When heo iginalsequencehas he“lowe ‐ he‐be e ”cha ac e is ic,i shouldbe no malisedasshowninEqua ion(2): * i x(k)= )(min)(max )()(max )0()0( )0()0( kxkx kxkx ii ii  (2) whe ei=1,2,...,mandk=1,2,...,nsigni y heo iginal e e encesequenceand p e‐p ocessedda a, espec i ely.* i x(k)deno es heno malised alue,)0( i x ep esen s hein endedsequence,min)( )0( kxideno es hesequence’sminimum alue,andmax Figu e 3. D illed holes. Table 2. D illing p ocess pa ame e s and hei le els. Fac o Le el 1 Le el 2 Le el 3 F (mm/min) 50 100 150 S ( pm) 1000 2000 3000 D HSS Ca bide TiN Coa ed R (%) 3 6 9 2.5. G ey Rela ional Analysis Mul i-pe o mance cha ac e is ics a e ough o op imise in complex p ocesses; hence, GRA is la gely employed o add ess such a ough p oblem. The ad an ages o g ey sys em heo y ha e been con i med in coping wi h he challenges o incomple e, pa ial, and unclea da a. The e ms black, whi e, and g ey a e de ined di e en ly in g ey ela ional analysis. Black deno es a sys em wi h no in o ma ion, whi e deno es a sys em wi h exac in o ma ion, and g ey ep esen s he in o ma ion be ween black and whi e. This echnique add esses he issue o imp o ing he esponse ea u es o cu en machining sys ems [ 23 , 24 ]. In g ey ela ional analysis, he i s s ep is da a p e-p ocessing, whe e he TF, SR, and BH expe imen al da a a e s anda dised o be in he ange o ze o o one. Da a p e-p ocessing is ypically necessa y because he ange and uni o one da a se di e om he o he s. The me hod o con e ing a sequence in o one ha is compa able o he o iginal is called da a p e-p ocessing. Depending on a da a se ies’ cha ac e is ics, he e a e a numbe o da a p e-p ocessing me hods accessible o GRA. The “highe - he-be e ” cha ac e is ic applies i he a ge alue is in ini e. The sequence can be no malised as shown in Equa ion (1): x∗ i(k)= x(0) i(k)−minx(0) i(k) maxx(0) i(k)−minx(0) i(k)(1) When he o iginal sequence has he“lowe - he-be e ” cha ac e is ic, i shouldbe no - malised as shown in Equa ion (2): x∗ i(k)= maxx(0) i(k)−x(0) i(k) maxx(0) i(k)−minx(0) i(k)(2) whe e i= 1, 2, . . . , m and k = 1, 2, . . . , n signi y he o iginal e e ence sequence and p e-p ocessed da a, espec i ely. x∗ i ( k ) deno es he no malised alue, x(0) i ep esen s he in ended sequence, min x(0) i(k) deno es he sequence’s minimum alue, and max x(0) i(k) ep esen s he sequence’s maximum alue. The o al numbe o obse a ions is n, whe eas he e a e m expe imen s. Ma e ials 2023,16, 3615 7 o 13 2.6. G ey Rela ional Coe icien (GRC) A me ic used in GRA o judge he applicabili y o wo sys ems o sequences is he GRC. Equa ion (3) illus a es he GRC, which is used in GRA o show how closely ela ed he sequences o x0(k) and xi(k) a e o one ano he . γx0(k),x∗ i=∆min +ζ∆max ∆0i(k) + ζ∆max (3) whe e ∆0i (k) is also ecognised as he de ia ion sequence and eplica es he change be ween x0(k) and x∗ i(k). ∆0i(k) = x0(k)−x∗ i(k), ∆min is he smalles alue o ∆0i(k), ∆max is he la ges alue o ∆0i(k), and ζis he dis inguishing coe icien . In mos cases, he ζ alue is smalle and he dis inc abili y is la ge , so ζ = 0.5 is employed. 2.7. G ey Rela ional G ade (GRG) By calcula ing he GRC, he GRG is usually calcula ed using he a e age alue o he GRC. GRG is used o e alua e mul i- esponse cha ac e is ics. Equa ion (4) shows how i is exp essed: τi=1 n n ∑ i=1 (γ(x0(k),x∗ i(k))(4) whe e nis he numbe o p ocess esponses and τi is he GRG. The g ea e GRG shows ha he associa ed expe imen al esul is close o he ideal no malised alue. 2.8. P edic ing he Op imal Responses The op imal le els o each ac o a e used o p edic he bes answe s using he bes le els o each elemen in he Taguchi design o expe imen s, ollowed by con i ma ion ials. Depending on whe he he expe imen ’s objec i e is o minimise o maximise he esponse, he bes condi ion is selec ed [ 25 , 26 ]. When he e a e h ee le els, 1, 2, and 3, wi h le el 1 being he ideal si ua ion, and he e a e h ee componen s, A, B, and C, Equa ion (5) p o ides he p edic ed op imal esponse. µp ed =A1+B1+C1−2Y(5) whe e Yis he o e all mean esponse, and A1,B1,C1a e he a e age esponses a le el 1 o hese ac o s. 3. Resul s and Discussions 3.1. Expe imen al Resul s U ilising GRA, mul i-objec i e op imisa ion was pe o med wi h he in en ion o p oducing he minimum TF, SR, and BH simul aneously. Table 3lis s he ial ou comes and hei GRC, GRG, and anks. 3.2. Analysis and Discussion o Resul s The expe imen s a e anked acco ding o he GRG alues. Figu e 4e iden ly displays ha GRG is high o he i s le el o F, he hi d le el o SS, and he second le els o D and R% A1B3C2D2. Ma e ials 2023,16, 3615 8 o 13 Table 3. Resul s o a g ey ela ional analysis (LM5/Z O2). Sl No Feed (mm/min) Speed ( pm) D ill Ma e ial Rein o cemen (w %) GRC o TF GRC o SR GRC o BH GRG Rank 1 50 1000 HSS 3 0.655 0.654 0.678 0.662 11 2 50 1000 Ca bide 6 0.615 0.744 0.695 0.685 10 3 50 1000 TiN Coa ed 9 0.612 0.499 0.781 0.631 13 4 50 2000 HSS 6 0.7 0.434 0.648 0.594 17 5 50 2000 Ca bide 9 0.84 0.744 0.496 0.693 9 6 50 2000 TiN Coa ed 3 0.904 0.433 0.76 0.699 8 7 50 3000 HSS 9 0.716 0.418 0.695 0.610 16 8 50 3000 Ca bide 3 0.969 0.702 0.678 0.783 2 9 50 3000 TiN Coa ed 6 1 0.747 1 0.916 1 10 100 1000 HSS 3 0.481 0.436 0.678 0.532 24 11 100 1000 Ca bide 6 0.421 1 0.864 0.762 3 12 100 1000 TiN Coa ed 9 0.454 0.583 0.695 0.577 19 13 100 2000 HSS 6 0.704 0.462 0.333 0.500 27 14 100 2000 Ca bide 9 0.625 0.758 0.741 0.708 5 15 100 2000 TiN Coa ed 3 0.7 0.392 0.509 0.534 23 16 100 3000 HSS 9 0.652 0.468 0.760 0.627 14 17 100 3000 Ca bide 3 0.846 0.581 0.678 0.702 7 18 100 3000 TiN Coa ed 6 0.762 0.487 0.935 0.728 4 19 150 1000 HSS 3 0.358 0.595 0.581 0.511 26 20 150 1000 Ca bide 6 0.348 0.414 0.891 0.551 20 21 150 1000 TiN Coa ed 9 0.333 0.559 0.85 0.581 18 22 150 2000 HSS 6 0.53 0.411 0.634 0.525 25 23 150 2000 Ca bide 9 0.497 0.522 0.634 0.551 21 24 150 2000 TiN Coa ed 3 0.577 0.516 0.77 0.621 15 25 150 3000 HSS 9 0.673 0.333 0.62 0.542 22 26 150 3000 Ca bide 3 0.747 0.522 0.85 0.706 6 27 150 3000 TiN Coa ed 6 0.704 0.581 0.695 0.66 12 Ma e ials2023,16,xFORPEERREVIEW9o 13    Figu e4.Responseg aphs o GRG. Themean esponse alues o each ac o le ela eshowninTable4.The ankshows ha  heDhasmo esigni icanceon heGRG, ollowedby heF,S,andR%.Theac ual expe imen als a egywase alua edwi ha95%le elo con idence.The indingso  he GRGANOVAa elis edinTable5.Theob ainedR 2  alue o GRGis80.47%.Fo F,SS, andD, hep‐ alueisless han0.05,indica ing ha  heyha easigni ican impac on he GRG. Table4.Response able o GRG(LM5/Z O 2 ). Le elFeedRa e(F)SpindleSpeed(S)D illMa e ial(D)Rein o cemen %(R) 10.6970 0.6102 0.5670 0.6389 20.6300 0.6028 0.6823 0.6579 30.5831 0.6971 0.6608 0.6133 Del a0.1139 0.0943 0.1153 0.0446 Rank23 1 4 Table5.ANOVA o GRG(LM5/Z O 2 ). Sou ceo Va ia ionDOFSSMSFpC% FeedRa e210.574 5.28719.93 0.002 24.24 SpindleSpeed28.516 4.25828.00 0.004 19.52 D illMa e ial212.688 6.344211.92 0.001 29.08 Feed a e*D illMa e ial43.326 0.83151.56 0.232 7.62 PooledE o 168.519 0.5324    19.53 To al2643.624   100.00 The abula edF‐ alueisF 0.05,2,16 =3.63.I isob ious omTable5 ha  heF‐ es ed alues o F,S,andDa eg ea e  han heF‐ abled alue,andhence heyha easigni i‐ can impac onGRG.TheF es  alueo R%andin e ac ionso Fwi ho he  a iablesa e less han he abula ed alue.I isno ed ha D(29.08%)has hemaximumin luenceon heGRG, ollowedbyF(24.24%)andS(19.52%).The esponse a iableR%and hein‐ e ac ionso Fwi he e yo he  a iablewe epooledup o hee o  e masi doesno  ha eamajo impac onGRG[27,28]. Figu e 4. Response g aphs o GRG. Ma e ials 2023,16, 3615 9 o 13 The mean esponse alues o each ac o le el a e shown in Table 4. The ank shows ha he D has mo e signi icance on he GRG, ollowed by he F, S, and R%. The ac ual expe imen al s a egy was e alua ed wi h a 95% le el o con idence. The indings o he GRG ANOVA a e lis ed in Table 5. The ob ained R 2 alue o GRG is 80.47%. Fo F, SS, and D, he p- alue is less han 0.05, indica ing ha hey ha e a signi ican impac on he GRG. Table 4. Response able o GRG (LM5/Z O2). Le el Feed Ra e (F) Spindle Speed (S) D ill Ma e ial (D) Rein o cemen % (R) 1 0.6970 0.6102 0.5670 0.6389 2 0.6300 0.6028 0.6823 0.6579 3 0.5831 0.6971 0.6608 0.6133 Del a 0.1139 0.0943 0.1153 0.0446 Rank 2 3 1 4 Table 5. ANOVA o GRG (LM5/Z O2). Sou ce o Va ia ion DOF SS MS F pC% Feed Ra e 2 10.574 5.2871 9.93 0.002 24.24 Spindle Speed 2 8.516 4.2582 8.00 0.004 19.52 D ill Ma e ial 2 12.688 6.3442 11.92 0.001 29.08 Feed a e*D ill Ma e ial 4 3.326 0.8315 1.56 0.232 7.62 Pooled E o 16 8.519 0.5324 19.53 To al 26 43.624 100.00 The abula ed F- alue is F 0.05, 2, 16 = 3.63. I is ob ious om Table 5 ha he F- es ed alues o F, S, and D a e g ea e han he F- abled alue, and hence hey ha e a signi ican impac on GRG.The F es alue o R% and in e ac ions o F wi h o he a iables a e less han he abula ed alue. I is no ed ha D (29.08%) has he maximum in luence on he GRG, ollowed by F (24.24%) and S (19.52%). The esponse a iable R% and he in e ac ions o F wi h e e y o he a iable we e pooled up o he e o e m as i does no ha e a majo impac on GRG [27,28]. 3.3. Con i ma ion Expe imen s The esul s o he con i ma ion expe imen s show ha he p edic ed GRG is 0.824 and he expe imen al alue is 0.856. A good ag eemen is ound be ween he p edic ed and in es iga ional alues, and he e o is 3.7%. 3.4. In luence o Inpu Va iables on GRG The TF, SR, and BH esponses we e included in he GRG as a high-quali y depic ion o all he esponses. Figu e 5displays he impac o he ac o s on he GRG. The GRG esponse g aph’s g ea es alue indica es ha d illing ac o s had a highe in luence on machin- abili y a ibu es [ 29 , 30 ]. The bes p ocess pa ame e s o d illing we e F = 50 mm/min, S = 3000 pm, D = Ca bide, and R = 6 w %, which led o he maximal alue o he GRG. The maximum GRG was ound a he lowes F and highes S, sugges ing ha he esponse TF, SR, and BH we e a hei lowes le els a he lowes F and highes S. This is due o a lowe TF esul ing om a dec ease in he amoun o ic ion be ween he d ill bi and he specimen [ 31 , 32 ]. A lowe F indica es a lowe d illing empe a u e, which enhances he quali y o he su ace. A lowe F was ound o esul in a lowe TF, which p o ided a sa is ac o y su ace inish a a smalle F. The wo kpiece so ens and pene a es smoo hly as a esul o he quick hea ise caused by ic ion a highe spindle speeds, which esul s in a smalle TF. Be e GRG alues a e p oduced by inc easing spindle speed because sho e