Experimental evaluation of on-line discrete tile rotations in the polishing process of ceramic tiles

Experimental

evaluation

of

on-line

discrete

tile

rotations

in

the

polishing

process

of

ceramic

tiles

Fa´bio

J.P.

Sousa

a,

*

,

Jan

C.

Aurich

a

,

Rubens

Maribondo

do

Nascimento

b

,

Carlos

Alberto

Paskocimas

b

_,

_Danieli

_Tartas

c

a

FBKDepartmentofMechanicalandProcessEngineering,InstituteforManufacturingTechnologyandProductionSystems,UniversityofKaiserslautern, TU-KLPOBox3049,D-67653,Kaiserslautern,Germany

b

GraduationPrograminMaterialsScienceandEngineering,PPGCEMDepartmentofMaterialsEngineering,FederalUniversityofRioGrandedoNorte, UFRNPOBox1524,cCEP59078-900,Natal,RN,Brazil

c

DepartmentofProductionandSystemsEngineering,EPSFederalUniversityofSantaCatarina,UFSC,POBox476,CEP88040-900,Floriano´polis,SC,Brazil

Introduction

Thekinematicsadoptedinthepolishingtrainisakeyfeaturefor definingthefinalglossinesspatterntobeexpectedoverthesurface ofthepolishedtiles[1].Eachpolishingtrainoffersacontinuous spectrum of kinematic possibilities, according to the set of differentavailablemotions.Besidessomegeometricparameters, the option for a particular kinematics defines how often each regionofthetilesurfaceissubjectedtotheactionoftheabrasives duringpolishing[2].

Modern polishing trains possess a kinematicsthat basically resultsfromdifferentcomponents[3],whichare:(1)rotationW (rads1_{)oftheabrasiveblocks(fickerts)aroundthecenterofeach}

polishinghead, (2) transverseoscillationof thepolishing head, withamplitudeA (mm)and frequency f(s1_{), and (3) forward}

motionV(mms1_{)oftheconveyerbelt,whichdirectlydefinesthe}

productivityofthepolishingprocess.

Bothforwardand transverseoscillation motions are accom-plishedatthesametime,sothateachpolishingheadperformsa sinusoidal trajectory relative to the tile surface. As result, an

undesired zigzag pattern of glossiness, known as ‘‘polishing shadows’’, are sometimes observed on the polished surfaces

[1]. However, due to the fixed alignment of the tiles on the conveyer belt,thevariability ofglosstendstobe moreintense alongthepolishingdirection(definedbytheforwardmotion).In addition,thelackofabrasivesinthecenterofthepolishingheads leadstofurtherdirectionalgradients[4].

According toprevious works[6],theaforementioneddefects canbepartiallymitigatedbyprovidingaconvenientoverlappingof thosewaveliketrajectories.AspresentedinFig.1,whenadjacent tilesundergoamultipleof908-rotationinsidethepolishingtrain, severalnewalignmentsbecomepossible.Asconsequence,amore uniformdistributionofglossinessoverthepolishedsurfacecanbe expected.Suchincreasinginpolishinguniformityrepresentsnot onlyanadvantageintermsofaestheticeffects,butalsointermsof processefficiency.

Thewavelikecurvesrepresentthesinusoidaltrajectoryofthe center of thepolishing heads over the tilesurface. After being polished by the first polishing head, the tiles are ready to be convenientlyrotatedusingdiscretevaluesofangles,sothatnext polishingheadscanfinddifferentpreviouspolishingpatternsto overlap with. The term discrete is used to point out that the rotation motion can only assumed values multiples of 908. Intermediaryvaluesarenotallowedduetotheunderuseofthe

ARTICLE INFO

Articlehistory:

Availableonline18April2016 Keywords: Polishing Porcelain Grinding Simulation Opticalmaterials/properties ABSTRACT

Thisworkevaluatesanewkinematicsfortheindustrialpolishingprocessofporcelainstonewaretile.In additiontothetypicalmotionsavailableinindustrialpolishingtrains,eachceramictileundergoesa discreterotationduringthepolishingprocess,sothatmoreuniformglossdistributionscanbeobtained without radical changes in the industries facilities. The consequences of this alternative were quantitativelyanalyzed.Acustomizedcomputernumericcontrol(CNC)-machinewasusedforobtaining the corresponding experimental results. A reasonable linear correlation between theoretical and experimentalgainsinuniformitywasverified,makingviabletheuseofcomputationalsimulationsto assisttheon-linedecisionsduringthetileproduction.

ß2016CIRP.

* Correspondingauthor.

E-mailaddress:[email protected](Fa´bioJ.P.Sousa).

ContentslistsavailableatScienceDirect

CIRP

Journal

of

Manufacturing

Science

and

Technology

j o urn a l hom e pa g e : ww w . e l se v i e r. c om / l oca t e / ci r pj

http://dx.doi.org/10.1016/j.cirpj.2016.04.001 1755-5817/ß2016CIRP.

conveyerbelt,aswellastoavoidabruptre-entrancesofthefickerts onthetilesurface.

Inthisinvestigation,thetotaltimeinsecondsduringwhicha given region of thetile surface effectively remains exposed to abrasivecontactsunderthepolishingheadsisreferredastimeof effective polishing (TEP) to be distinguished from the time requiredforthepolishing process.Thelatter simplyrepresents thetimeduringwhich aparticularregionremains beingdriven alongtheconveyerbelt,whereastheformertakesintoaccount that the polishing heads cannot cover the entire tile surface incessantly, because of the transverse oscillation motion, its circularshape,andthelackofabrasivesinitscenter.Therefore,the TEPcanbeseenastheeffectivepartofthetotalpolishingtime.

Fig. 2 provides a better understanding of these two terms, including a typical gloss-gaining curve found in literature

[7]. An abrasive contact is considered to occur every time an abrasiveparticlescratchesagivenregionofthetilesurface.

Inamicroscopicpointofview,theevolutionofglossresultsfrom themultipleabrasivecontactsaccumulatedduringthe polishing time.AsseeninFig.2,theresultingevolutionofglossinesshasan asymptoticbehavior,whichisverywelldescribedandmodeledby Hutchings[8].Incontrast,therelationshipsamongpolishingtime, TEP,andnumberofabrasivecontactsarealllinear.

In quantitativeterms, significantimprovementsin polishing uniformity could be provided by such extra rotation motion, specially using rotation levels of either 908 or 2708 (or 908 clockwise). According to somesimulated results, the improve-mentsinuniformityweresupposedtovaryfrom10% uptono remarkableimprovementsatall[6],dependingonthekinematics andonthetilepositionalongthepolishingtrain.

implementation of this extra rotationmotion in new polishing trains, this evaluation is also devised to check applicability of kinematicsimulationsinestimating thefinalpolishingpatterns basedonTEPdistributions.

Theoreticalconsiderations

Atypicalwavelikepolishingpatternleftafterthepassageofa single polishing head is given in Fig. 3aa, based on simulated resultsforonlytwoadjacenttiles[6].Thescaleofcolorusedinthe graphsreferstotheTEP,whichasexplainedpreviously,isthetime in seconds during which each region over thetile surface has effectivelysufferedthepolishingprocess.ThevalueofTEPforeach singlesurfaceregionisdescribedindetailelsewhere[2].Afterthe passageof successivepolishing heads,such polishinggradients mayfadeawayorevenbeenhancedaccordingtotheoverlapping degree.AnexampleofsuchoverlappingispresentedinFig.3.

StillinFig.3,itisessentialtonoticethatthewavelengthsofthe polishingtrajectoryareonlyrarelyaperfectmultipleofthetile length. As consequence, the overlapping of polishing patterns before and after tile rotations will continuously vary between adjacenttilesandalsoalongthetime,asdetailedinFig.3dand 3e.Eachpictureelement(pixel)ofthegraphrepresentsadefined regionof55mm2_{onthetilesurface.}

The effect of such continuous variation was simulated by admittingthepolishingtrajectoriestobeshifted,pixelbypixel, and considering arbitraryorigins, along thepolishing direction (Fig.4).Theshifteddistancesweretermed

a

and

b

.Theformeris theshiftdistancerightbeforethetilerotation,whereasthelatteris thedistancerightafterit.Inotherwords,

a

and

b

aremathematical artifacts devised toenable the simulation of all possible over-lappingconditionsbetweentwoconsecutivepolishingheads.

By considering all possible combinations of

a

and

b

, a quantitative analysis of the resulting polishing patterns were carriedoutandgraphicallypresentedasafunctionofthesetwo variables. The homogeneity of each polishing pattern was quantifiedby the standard deviationof thespatial distribution ofTEP,takingintoaccounttheentireregionofthetilesurface.Such standarddeviationwasrepresentedby

s

.Theresulting3Dsurface plotispresentedinFig.5.Noteworthyisthatthescaleofcolorin graphsofFigs.3 and4representstheTEP,whereasinFig.5,it representsthedegreeofpolishinghomogeneity.Thesmalleris

s

, thehigheristhepolishinguniformity.

Duetotheperiodicityofthewavelikepolishingtrajectory,the samelevelofuniformitycanbeachievedbyperiodical combina-tionsof

a

and

b

,asobservedinthefigure.Asdescribedinthenext section,resultsfromthis3Dsurfaceplotwereusedtoidentifythe mostpromisingpolishingpatternstobeexperimentally investi-gated.

Method

Toevaluatetheimpactofintroducingadiscretetilerotation inside industrial polishing trains, the difference of uniformity betweentilesprocessedwithandwithoutthetilerotationmotion

Fig.1.Rotationofthetilesinsidethepolishingtrainandtheresultingoverlapping.

Fig.2.EvolutionofTEPandglossduringthepolishingprocess.Adaptedfrom Matsunagaetal.[7].

was considered. Such difference was determined for both simulatedandexperimental resultsseparately,accordingtothe followingequations:

Ds

Theoretical¼

s

T90

s

_T0 (1)

Ds

Experimental¼

s

E90

s

_E0 (2)

Inthoseequations,

s

E908representstheexperimental

measure-mentsofpolishinguniformitycollectedinasingletile, polished underaspecifickinematics,andadmitting908oftilerotation.For

s

E08, the same experimental procedure was performed, but

withoutrotatingthetilebeforethesecondpassageofthepolishing

head.Analogously,

s

T908and

s

T08refertoresultssimulatedwith

andwithoutconsideringtilerotation,respectively.

Asthepolishinguniformitydecreaseswiththeincreaseofthe standard deviation

s

,improvementsinuniformityareexpected wheneverthevalueof

Ds

isnegative.Moreover,theperiodicity exemplifiedinFig.5reveals theexistenceofa minimumanda maximumvalueof

s

=f(

a

,

b

),foreachpolishingpattern. Accord-ingly,themostpromisingsituationfordetectingimprovementsin polishinguniformity,exclusivelycausedbytilerotation,arethose in whichtheshifted distances

a

and

b

leadtoanoverlapwith maximumabsolutevaluesof

Ds

,i.e.,highestpositivevaluesand smallestnegativevalues.Thiswasthereforethecriterionusedfor

Fig.3.Continuousvariationofpolishingpatternbetweenadjacenttilesandalongtime.

selecting the values of

a

and

b

considered in this work. The selectionofthekinematicsisdescribedinthenextsection.

Selectionofkinematics

Six different polishing kinematics were investigated. These kinematics were carefully selected in order to cover a wide spectrumofpolishingpatterns,lyingatthesametimewithinthe feasiblerangeofmostindustrialpolishingtrains.

Accordingtoliterature[2],thepolishingpatternisratherruled bytheratiobetweentheforwardspeed(V)andthefrequencyof the transverse oscillation motion (f), than by each variable separately. Different values of V and f yielding identical ratios havethesamequalitativepolishingpattern.Thedifferenceoccurs onlyintheabsolutescaleofpolishingtime.Simultaneously,the ratioV/falsodefinesthewavelength(

l

)ofthecentraltrajectoryof thepolishinghead,asseeninFig.6aa.Therefore,thekinematics investigatedinthisworkfollowedagradualscaleof

l

,aspresented inFig.6b.

ThenominalvaluesofVandfadmittedinthisworkaregivenin

Table1,includingthecorrespondingwavelength

l

.The simula-tions and experimental activities were carrying out for each kinematics, withand withoutadmitting a discrete tilerotation motionat908.

Polishingmachine

The experimental polishing process was carried out at the InstituteforManufacturingTechnologyandProductionSystems– FBK,inGermany,usingacustomizedpolishingmachineconceived

and developed to reproduce the typical polishing condition of industrialpolishingtrains.Themachineoperateswithcomputer numericcontrol(CNC),whichenabledthepolishingheadtofollow everykinematicsinvestigated withgreat precision.A systemof toolholderwithatiltedshaftmaintainsadesiredcurvatureonto thesurfaceoftheabrasiveblock(fickert),causingalinearcontact between the abrasive blocks and tile surface. Details on the performanceofthismachineareavailableinliterature[13].The abrasiveblockswereextractedfromacommercialfickert(German companyH.W.TheobaldGmbH).Theyconsistedofsiliconcarbide (SiC) abrasive particles embedded in magnesium oxychloride cement(MOC)matrix.

TheparametersusedinallexperimentsaregiveninTable2.A commercial stoneware tile with nominal size 350350mm (Italian company Fiandre Architectural Surfaces), was used as sampleforcarryingouttheexperiments.Withineachsample,the areaofinterestwasacentralizedsquareof110mm.Thiscentral areawassettorepresentasingletile(withscale4:1)inatypical polishingtrain.

Allsamplesweretakenaspolishedtoassuretheflatnessofthe surfacetobepolished.Theoriginalglossinesswasremovedby passing the abrasive tool two times in sequence, and using abrasiveswithgrainsize#600.Thesetwopassageswerecarried outwithV=50mms1_{andusingnotransverseoscillation(i.e.,}

onlyforwardmotion). Aftersuchsurfacepreparation,thetiles werethensubjectedtotheexperimentalprocedureoutlinedin

Fig.7.

AscanbeseeninFig.8,theexperimentalprocedureconsistsof twofurtherpassagesofthepolishingheadoverthetilesurface,this

Fig.6.Spectrumofpolishingpatterns.(a)Theratiol=V/f.(b)Selectedkinematics. Fig.5.Periodicalnatureofthepolishinguniformityasafunctionoftheshifted

overlappingdistances,aandb.

Polishingparameters. Externalradius,R(mm) 57.5 Internalradius,r(mm) 27.5 Oscillationamplitude,A(mm) 15 Lubricant Water Normalload(N) 100

Rotationofabrasivetool(RPM) 1800

Tilesize(mm) 440

timeusing amuchfinerabrasivesize,#1500(Lux),in orderto promote a detectable gloss enhancement. Two samples are requiredfordeterminingeachvalueof

Ds

Experimental;onesample

providesthespatialvariabilityinglossinesswhenthetileisrotated at908beforethesecondpassage,whiletheothersampleworksas reference(notilerotation).

TheoverlappingofpolishingtrajectoriesperformedbytheCNC polishingmachineisexemplifiedinFig.8.Thecontinuousredline representsthetrajectoryofthefirstpassageofthepolishinghead, whereasthedashedlinestandsforthesecondpassage.Whenno rotation is admitted, thesecond passageoverlaps the firstone obeyingthepresetshifteddistances

a

and

b

previouslyexplained. Inbothcases,thesameamountofpolishingworkwasintroduced intothesamples.Yet,thefinalpolishingpatternsareexpectedto differprominently.Eachpassagefollowedthewavelike trajecto-riesdefinedbyitskinematics.

The spatial distribution of gloss for each polished tile was obtainedbymeasuringagridof23by23pointsdistributedover theareaofinterest,i.e.,thesquareregionof110110mmlocated

atthecenterofeachsample.Allmeasurementswerecarriedout with a precision glossmeter(Swiss Company Zehntner, model ZGM 1120), with an incident angle of 608. During each measurement,theequipmentanalyzesanellipticalarea[11]of 25mm2_{. Each grid point was measured considering two}

orthogonal alignments of the glossmeter. The gloss value for eachpoint was the average value of gloss collectedusing thesetwoalignments.Theequipmentwascalibratedbeforethe entiresequenceofmeasurementsforeachtile,usingalwaysthe samestandardblackpolishedglasswithrefractionindexof1.567, assuggestedinliterature[12].

Simulations

ThesimulatedresultsconsistofthespatialdistributionofTEP, associated to each polishingcondition. Based on thekinematic equationsassociatedwiththepolishingprocess[3],a computa-tional algorithm was developed using G language (Platform LabVIEW12014),inordertosimulateallthesetheoreticalresults. Besides,thisalgorithmwasalsousedtodeterminethetrajectories tobeperformedbytheCNCpolishingmachineforobtainingthe correspondingexperimentalresults.Thisapproachispresentedin

Fig.9.

Apartfromsomegeometricalfeatures,theinputsaretheshifted distances

a

and

b

,andthepolishingkinematicsKadoptedfromK1

toK6.Asoutputs,thealgorithmdeliversthestandarddeviationsof

thedistributionofTEP,withandwithoutconsideringtilerotations (

s

908and

s

08,respectively).Atthesametime,thealgorithmalso

provides thecorresponding trajectoriestobeperformed bythe polishing headsin theexperimental tests.Allsimulationswere carriedoutconsideringapixelsizeof55mm2_.

As mentioned before, for each kinematics the theoretical improvementinpolishinguniformity(

Ds

Theoretical)wasquantified

bythedifferencebetweenstandarddeviations

s

ofthedistribution ofTEPforrotated(

s

T908)andnon-rotated(

s

T08)tilesamples.The

pairsofshifteddistances

a

and

b

selectedforrunningthepolishing experimentsarepresentedinTable3,yieldingonepointforeach kinematics.Everyindividualvalueofboth

a

and

b

correspondsto either the minimum or the maximum level of polishing

Fig.7.ApproachfordeterminingDsExperimental.

Fig.8.OverlappingoftrajectoriesperformedbytheCNCpolishingmachine.

tiles,andquantifiedby

s

.Thesevalueswerechosensothat the widestcoverageof

Ds

Theoreticalcouldbeobtained,andwithnearly

spacedintermediaryvalues.Ascanbeobserved,therearethree points P(

a

,

b

) associated with an improvement in polishing uniformity (

Ds

<0), and three points representing worsened results(

Ds

>0).

Besides checking the technical viability of adopting such rotation motion experimentally, a direct comparison between resultsfromsimulationandexperimentswasalsoprovided.The correspondence between such theoretical and experimental resultswas evaluated considering a linear correlation of those results.Alltheevaluationsanddiscussionsaregivenindetailinthe nextsection.

Resultsanddiscussion

AllresultsregardingTEPandglosspatternsarepresentedin

Figs.10–15.Toprovidedirectcomparisons,thefirstandthesecond rowsineachFig.arereferredtothesimulateddistributionofTEP andthecorrespondingexperimentalglosspattern,respectively.In thesameway,thefirstandsecondcolumnsaccountfortheresults obtainedwith(a)andwithout(b)consideringthetilerotationat 908,respectively.

Acomparisonbetweenpolishingpatternssimulatedwithand withoutconsideringtilerotation indicates a large potentialfor changingthefinalpolishingpatternexpectedforthetilesurface afterthepolishingprocess.Nevertheless,asparticularlyrevealed inFig.11(pointP2),theuseoftilerotationdoesnotnecessarily

leadtoamoreuniformpolishingpattern.

ForthosepolishingkinematicsrepresentedbypointsP4,P3,and

P1,inthisorder,anincreasinglyimprovementinthehomogeneity

oftheeffectivepolishingtimewasobserved.Ontheotherhand,the rotationmotion of thetileforthose kinematicsrepresented by

Fig.10.SpatialdistributionsofTEP(aandb)andglossiness(candd)P1,with(aand

c)andwithout(bandd)consideringatilerotationat908.

Fig.11.SpatialdistributionsofTEP(aandb)andglossiness(candd)P2,with(aand

c)andwithout(bandd)consideringatilerotationat908.

Fig.12.SpatialdistributionsofTEP(aandb)andglossiness(candd)P3,with(aand

pointsP6,P5,andP2negativelyaffectedtheuniformityofthefinal

polishing patterns. In fact, these tendencies were already announcedbythecorrespondingvariationsinstandarddeviation (

Ds

Theoretical)previouslypresentedinTable3.Themorenegative

thevalueof

Ds

is,thebetteristheexpectedpolishinguniformity. Conversely,positivevaluesof

Ds

Theoreticalrepresentlessuniform

distributionsofTEP.

Besidesquantitativeimprovements,itmustalsobementioned thatthehigherradialsymmetryprovidedbythetilerotationoffers somerobustnessfortheposteriortilesettingoperation.Thus,as exemplifiedin Fig. 16, in a more qualitative point of view the implementationoftilerotationcouldstillbeanoptioninthose caseswherethepolishinguniformitywasonlyslightlydamaged.

Whenfocusingonexperimentalresultsonly,theimpactofusing tilerotationbecomemuchlessobvious.Contrastsbetweenadjacent regionsinsidethesamepolishingpatternaremuchsmallerthan those offered by simulated results. The corresponding standard deviationsandtheirresultingvaluesof

Ds

Experimentalarepresented

in Table 4. As before, negative and positive values indicate improvementanddegenerationofthefinalpolishinguniformity, respectively.Accordingly,theworstcaseoccurredinpointP2,in

whichtheexperimentalmeasurementsrevealedthattheuniformity becameabout34%worse(

Ds

Experimental/

s

E08=1.17/3.45).

Ascanbeseen inTable4, thevariations ofuniformitiesare muchsmallerforexperimentalvaluesofglossthanforsimulated valuesofeffectivepolishingtime.Forinstance,animprovementof 38% in uniformityof effective polishing time wasobtained for pointP3,whereasthecorrespondingimprovementregardingthe

Fig.13.SpatialdistributionsofTEP(aandb)andglossiness(candd)P4,with(aand

c)andwithout(bandd)consideringatilerotationat908.

Fig.14.SpatialdistributionsofTEP(aandb)andglossiness(candd)P5,with(aand

c)andwithout(bandd)consideringatilerotationat908.

Fig.15.SpatialdistributionsofTEP(aandb)andglossiness(candd)P6,with(aand

c)andwithout(bandd)consideringatilerotationat908.

Fig.16.Robustnessagainsterrorsduringthetilesettingoperation.Presenceofa centralmismatchingtileconsideringTEPpatterns(a)withand(b)withouttile rotation.

Table4

Quantifiedimpactofthetilerotationoverexperimentalandsimulatedresults. Point sE08(GU) sE908(GU) DsExperimental(GU) DsTheoretical(GU)

P1 6.09 5.17 0.92 0.333 P2 3.45 4.62 1.17 0.214 P3 3.83 3.20 0.63 0.582 P4 5.49 5.37 0.12 0.184 P5 4.31 5.25 0.94 0.048 P6 4.61 5.53 0.92 0.108

distributionofglossiness wasonly approx.16%. Onereasonfor explainingthis tendencywasalreadyexposedinFig.2.TheTEP increaseslinearlywiththepolishingtime,whereastheglossiness increases asymptotically toward a maximum value of gloss, definedbythematerialmicrostructure[14].

Toevaluatetheconstancyofsuchbehavior,allthesixpoints investigatedwereplottedaccordingtotheirvaluesof

Ds

Theoretical

and

Ds

Experimental.TheresultinggraphisfoundinFig.17,including

thecorrespondinglineartendency.

AreasonablecoefficientofdeterminationofR2_{=0.86wasfound}

usingalinearfittingequation(y=0.3103x–0.1917).Accordingto thisfittingequation,therateofgloss-gainingwasinaverage31%of theincrementofpolishingtime,i.e.,eachincrementofglossunit resultsfromtheworkofaboutthreesecondsofeffectivepolishing. Duetothetestspecificitiesandespeciallytotheverysmallrangeof polishingtimeinvestigated(withinafewseconds),nodirectdata forcomparisonpurposescouldbefoundintheliteraturesurveyed. However,basedonvisualanalysesoftheresultsreportedbyC.Y. Wangand X. Wei [10], a gloss-gaining ofabout 10 glossunits during the first 30sec was achieved using #600 grit size SiC abrasives.AlsofromtheresultsreportedbyHutchingsetal.[8],an increaseof5glossunitsduringthefirst15seccouldbeestimated when using a grit size of #1500. Neglecting the differences regardingabrasive size,these two ratesfound in literatureare comparabletothevalueof0.31obtained.

StillinFig.17,insidethefirstquadrantarethosepointsinwhich the tile rotation improved the spatial distribution of both simulated and experimental results. Analogously, the third quadrant contains those points exhibiting worse uniformity regarding both TEP and glossiness after the tile rotation. Such synchronized behavior between TEP and gloss was already expected, considering that the glossiness is produced by the multiplesscratchesaccumulatedduringthepolishingprocess[5]. Moreover,accordingtothereasoningabove,nopointshouldbe expectedinside the second and fourth quadrants. This was in agreement with the observed results. In the second quadrant, experimentalimprovementsinuniformitywouldbedetectedeven withadjacentregionsofthetilesurfacebeingsubjectedtomore differingpolishingtimes.Suchimprovementwouldbeagainstthe assumptionofproportionalitybetweenglossgainingandnumber ofabrasivecontacts.Analogously,apointinthefourthquadrant indicatesadecreaseinglossuniformityevenwhenthetilesurface undergoesamoreuniformdistributionofpolishingtime.Thisis alsoveryunlikelytooccur,consideringthateachregiononthetile surfaceisexpectedtorequireasimilarnumberofabrasivecontacts todevelopagivenglossincrement.

Althoughpointsinthesecondandfourthquadrantsintuitively seem to be equally unlikely to occur, the latter case becomes physicallymoreprobablethantheformerwhenoneconsidersthe heterogeneityofthe tilesurface andalso thesensitivity of the gloss-gainingcurve,previously presentedin Fig. 2. Obtaininga

TEP,eachsmallregionofthetilesurfaceisalsosubjectedtoitsown history of scratching conditions, such as scratching speed and intersection angle of subsequent scratches. Once a particular kinematicsisselected,thescratchinghistoriesfortheentiretile surface become simultaneously defined. As consequence, the gloss-gainingcurveofregionshavingthesamemicrostructureand undergoingsimilareffectivepolishingtimesstillmaydifferinview oftheirdifferentscratchingconditions.

The influence of the scratching condition may have also contributed to the differences observed among the different kinematics. The elimination of such effect would require the determinationofthescratchingconditionoccurredineverysingle abrasivecontact.Such massivetasktranscendsthefocusofthis article,which wasfocused on theevaluationof polishingtime. Besides,inamorephenomenologicalpointofview,therearestill manyotherfactorsaffectingthesurfacequalityofthepolishedtile, suchasnormal pressure,and thecharacteristicsofthegrinding wheels,suchastype,bond,andmeshsizeofabrasives[15].

Finally, in all cases the simulated results were capable of predictingthegeneraltendencyofuniformitygain.Therefore,based on thereasonable relationshipfoundbetweenexperimentaland simulatedresults,thedecisionaboutwhetheraspecifictileshould berotatedornotcanbetheoreticallyassistedbycomputational simulations, focusing on the time during which each region throughout the tile surface effectively remains under polishing. Nevertheless,althoughsignificantadvantagesinpolishing unifor-mitymayberevealedbysuchkinematicssimulations,theactual improvementisexpectedtobeaboutthreetimessmaller.

Conclusions

Theexperimentalinvestigationcarriedoutinthisstudyrevealed thatthepolishinguniformityofferedbytypicalindustrialpolishing trainscanbeimprovedbyintroducinganextradiscreterotation motion, to be individually performed by the tiles during the polishingprocess.However,thisextramotioncanalsoleadtoworse distributionsofgloss,accordingtothekinematicsadoptedandalso to the position of the tile on the conveyer belt. Based on the correlationfoundbetweenexperimentalandsimulatedresults,the decisionaboutwhetheraspecifictileshouldberotatedornotcan betheoreticallyassistedbycomputationalsimulations.Intheworst case,theuniformitybecameabout34%worse,whileinthebestcase theimprovementinuniformitywasabout16%.Inqualitativeterms, suchextrarotationmotionalsoprovidedpolishingpatternwithless directionalpolishinggradients,sothattherobustnessagainsterrors duringtheposteriortilesettingoperationisincreased.

Acknowledgments

Thisworkwascarriedoutwiththefinancialsupportreceived from the Brazilian Coordination for the Improvement of High Education Personnel – CAPES, and the Deutsche Forschungsge-meinschaft – DFG,within the scope of theBrazilian - German CollaborativeResearchInitiativeonManufacturingTechnology– BRAGECRIM.Theauthorsthanktheseentities.

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