IN DEGREE PROJECT TECHNOLOGY,FIRST CYCLE, 15 CREDITS
, STOCKHOLM SWEDEN 2016
Woven steel mesh for usage in bedsA case study for IKEA
KASIM AYTEKIN
SANDRA MUHR
KTH ROYAL INSTITUTE OF TECHNOLOGYSCHOOL OF INDUSTRIAL ENGINEERING AND MANAGEMENT
AbstractThisstudyexamineswhetherwovenmetalmeshisanappropriateoptionforusageinbedsandwhatmaterialthemeshshouldconsistoftobestbesuitedforthepurpose.Thewovensteelmesh’sconstructionwasbasedonareferencemodelthatconsistsofcross-linkedrodsandwires.Sincetheaimoftheprojectwastoreachaconclusionofthemesh’susabilityinbeds,differentparameterswereexaminedandtakenintoconsideration.Theseparameterswerethedurabilityofthemeshwhencarryinghumanweight,acousticpropertiestominimizechatterwhenlyingonthemeshandrollingproperties.ThedurabilitywasexaminedusingCOMSOLmultiphysics.Acousticswerestudiedthroughaliteraturereviewandrollingpropertieswerecalculatedusingmeasurementsonthereferencemodel.AmaterialinvestigationwasdoneinthedatabasesoftwareCESEduPack.Itwasfoundthatsteel,stainlesssteelandaluminumfulfilledtherequirementssetondurability.Stainlesssteelwasconsideredtooexpensiveandsteeltooheavy.Usingaluminumhalvestheweightofthemeshincomparisontosteelbutdoublestheprice,inthiscasehowevertheweightwasconsideredtobeaparameterofgreaterimportanceoverridingprice.
Tableofcontents
1.Introduction....................................................................................................................................11.1Background.............................................................................................................................................11.2Projectdescription..................................................................................................................................11.3Hypothesis...............................................................................................................................................2
2Modelingandexaminationofwovensteelmesh...........................................................................32.1Modeling.................................................................................................................................................3
2.1.1Referencemodel..............................................................................................................................32.1.2Simplification...................................................................................................................................4
2.2Computations..........................................................................................................................................42.2.1Approach..........................................................................................................................................52.2.2Assumptions.....................................................................................................................................62.2.3BoundaryConditions........................................................................................................................62.2.4Methodicconditions.........................................................................................................................72.2.5TestconditionsgivenbyIKEA...........................................................................................................8
2.3Investigationofsuitablematerials..........................................................................................................82.3.1Surfacetreatmentsandcoatings.....................................................................................................9
2.4Rollingproperties..................................................................................................................................10
3.Result............................................................................................................................................123.1Materialinvestigation...........................................................................................................................12
3.2Computations.............................................................................................................................133.2.1SolidMechanics..............................................................................................................................13
3.3Rollingproperties..................................................................................................................................19
4.Discussion.....................................................................................................................................204.1Sourceoferrors.....................................................................................................................................22
5.Conclusion.....................................................................................................................................235.1SWOT-analysis.......................................................................................................................................23
6.FutureStudies...............................................................................................................................24
7.Acknowledgments........................................................................................................................25
8.References....................................................................................................................................26
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1.IntroductionTheprojectencompassedtwostageswhereinthefirstwasawidescopesearchforametalshapeofwhichIKEAwishedacloserexamination.Thesecondstagewasanarrowingdownofthescopeandacloserexaminationoftheselectedshape.Asuitablematerialbasedontheresultsoftheexaminationwassuggested.
1.1 BackgroundIKEAhavebeentraditionallyusingthemetalpartsofthefurnituredesignsinastaticmannerwhileamoredynamic,flexibleandsoftapproachwithadjustabilityremainsrelativelyunexplored.Therefore,thecompanywishesaconductedstudyofdynamicmetalshapesinordertoenhancethecomfortofacertaintypeoffurnitureusedforrelaxationsuchasbeds,sofasandarmchairs.Materialpropertiesofmetalsuchasformability,lightweightandflexibilityshouldbeutilizedinordertocreatecomfortandfindthinner,softerandsmartersolutionsintheconstructionofthecompany’sfurniture.Specifically,thefocusshouldbeonprovidingflexibilityandusageoflessmaterial,resultinginasimilarorbettercomfortthanwhatappliestodate.Inordertofindanappropriatemethodforachievingthisgoal,designsusingdifferentmetalprofilessuchasrods,pipes,springs,wires,sheetmetal,profiles,meshandmetalslatswerepresented.Followingthepresentationoftheconcludedstudytheproposeddesignswerediscussedandanelementcoveredinthestudywasagreeduponforcloserexamination.
1.2ProjectdescriptionTheshapeselectedfromthepre-studyforcloserexaminationofitspotentialwasmetalmesh.Itwasdecidedtoexploreifametalmeshwouldbeaviableoptionforusageinbedsandwhatmaterialselectionwouldbeidealbasedonthecalculatedresults.Inordertonarrowdownthescopeoftheprojectameshreferencemodelwasselected.Thereferencemodelwastobeconsideredwhenmodelingthemetalmeshinacomputerenvironment.Basedonthemodel,durabilityofmeshdimensionswereexaminedandoptimized.Oncethematerialselectionwasmade,considerationwasgiventopotentialnoisecausedbytheuserwhenmovingaround,whichcouldhaveanimpactoncustomersatisfaction.Differentcoatingsandsurfacetreatmentswereexaminedinordertominimizesuchproblems.Thematerialselectionregardingthestiffrodswaslimitedtometal.
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Astheassemblyofthebedwaslefttotheindividualcustomer,weightofthemeshwasexaminedwithconsiderationtofactorsasstorageandtransportation.Additionallythefeatureofrollingthemetalmeshintoamoreportableandcompactrollwerestudied.Thus,flexibilityinthecontextofusageandstoragewereanalyzed.
1.3Hypothesis Theroddimensionsofthereferencemodelwillhavetobeoveraspecificminimumvalueofroddiametertopreventplasticdeformationwhensubjectedtoaperson’sweight.Thisminimumvaluecanbecalculatedusingthemeshmodelandadditionalcomputersoftware.FollowingconsultationswithIKEA,aloadingscenariowasdefined(describedinchapter2.2.5).Itisassumedthatsteelwillprovidethebestmatchingmetallicmaterialpropertiestomeettheprojectrequirementsfortherodsregardingpreventionofplasticityanddeformationoverthedefinedlimits.However,itisassumedthatametalmeshstructurewillgenerateaweightwhichistooheavyandimpracticalfortheintendedpurposeofusageinbeds.Thedimensionsoftherolledmeshwillbeoutsideareasonablerangeofmanageabledimensionsofeasypackaging.Thus,theadditionalfeatureofrollingthemeshisassumedtobeinefficientfortheaimedusage.
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2Modelingandexaminationofwovensteelmesh
2.1ModelingTheexaminationofthemetalmeshstructurewasinitiatedbymakingacomputeraideddesign(CAD)modelofthestructureinthesoftwareSolidEdgeST7[1].Sincetheexaminationincludescalculationsinsolidmechanics,investigationofsuitablematerialsandcomparisonofgeneralpropertiessuchastotalweightandtotalpricebetweendifferentmaterials,themodelwasdoneasawholesinglebedwiththegivendimensionsdescribedinchapter2.2.5[6].
2.1.1ReferencemodelInaccordancewiththeprojectdescriptionareferencemodelforfurtherexaminationwasselected.AtavisittotheMaterialLibraryatStockholminternationalfairinÄlvsjö,ametalmeshstructurewasobservedandafterconsultationwithIKEAtheproductCWTigrisbyArtMeshABwaschosentobethereferenceforthemodeling[2].Thereferencemodelconsistsofmetalrodslinkedbyatriple-setsteelwire.Therodsareevenlydistributedthroughthemeshandsoarethewiresasseeninfigure1.ThereferencedimensionsforthemetalmeshweretakendirectlyfromdatagivenbythecompanyArtMeshAB[2].
Figure1CWTigrisbyArtMeshAB
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Table1ParametersofthereferencemodelgivenbyArtMeshAB
Parameter Quantity
Roddiameter 3mm
Roddistribution 10mm
Wirediameter 3*2mm(3wireswith2mmeach)
Wiredistribution 80mm
ThedefaultmaterialusedinthereferencemodelisastainlesssteeldenotedasAISI316L.TheYoung’smodulusofAISI316Lis200GPaandotherintrinsicmaterialpropertiesasPoisson’sratioanddensityare0.28and7850kg/m3respectively[3].
2.1.2SimplificationConsultationswithprofessorBoAlfredssonfromthedepartmentofSolidMechanicsatKTHtheRoyalInstituteofTechnology,steeredthemodelingprocessinanotherpath.AccordingtoAlfredsson,thewirewillnotcontributetothemechanicaldurabilityofthemetalmeshsincetherodswillbethepartsdeformingfirst.Thus,themodelcouldbesimplifiedtoaseriesofmetalrodsdistributedinaccordancewiththereferencemodelbutlackinganylinkingwires[4].Alfredssondescribedthetaskasasimplesolidmechaniccasewhensimplified,wheretherodsaredeformedlinearly.Therefore,aftertheconsultationitwasdecidedtodealwiththeproblemasalinearsolidmechaniccase[4].
2.2ComputationsToexaminethedurabilityofthemetalmesh,thefiniteelementmethodwasapplied.Thefiniteelementmethodprovidesafundamentalunderstandingandtheabilityforforeseeingsolidmechanicbehaviorwhenengineering.Forthispurpose,thesoftwareCOMSOLMultiphysics5.1wasused.COMSOLisavirtualengineeringtoolcommonlyusedinthiskindofengineeringproblems[5].Durabilitywastestedforasetofrodradiiandthenextrapolatednumericallyforaspanbetween1.5mmand5mm.Secondgradepolynomialextrapolationwasdecidedtohavesufficientsensitivityinthismannerandthuswaschosenasdefaultmethod.
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Computationswereruninrespecttoguidelinessetinaccordancewiththeprojectdescription,andalsobasedonconsultationswithProfessorBoAlfredsson.Asanyothercomputationalproblemthisstudyrequiredtomakecertainassumptionsandsettingofboundaryandinitialconditions.Thefollowingchapterwillgiveadetailedexplanationofeach.
2.2.1ApproachSincetheproblemissimplifiedtobealinearsolidmechaniccase,itneededanappropriateapproachforthesolidmechaniccomputations.Aftersomebrainstormingitwasfoundthatthemostadequateapproachwouldbetoexpectmostdeformation,andaccordinglyhighesttensions,inthecasewhereasinglehumanfootisdirectedinthedirectionoftherodsandplacedsymmetricallyinthecenteroftherodsasillustratedinfigure2and3.Thus,thiscasewaschosentobethedimensioningapproachwhenexaminingthemesh’sdurabilityandthesuitabilityofthechosenmaterial.
Figure2VisualizationofasinglehumanfootdirectedinthedirectionoftherodsmodeledinSolidEdgeST7.
Figure3Closeupofthefoot,showingthealignmentoftheload(foot)andthesupportingstructure(rods).
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2.2.2AssumptionsSinceexactmodelingofahumanfootisextensiveandimpractical,assumptionsaremadesothattheproblemcanbesimplifiedtoamoreperceptibleloadcase.Thefootisassumedtoexposetensionsoverthemeshonanareaequivalenttoarectangularplatewiththedimensions300*100mm2asillustratedinfigure4.Thereferencemodelforthemeshissettohave10mmbetweeneachrods’centrum,whichhaveadiameterof3mmeach,whichmeansthattheplatewillcoverasetof10wholerods.Thethicknessoftheplatewillnothaveanyimpactonthetensionexposure.Henceitissettoanarbitrarysmallvalue,forthiscase1mm.
Figure4Plateequivalenttoahumanfoot,modelledinCOMSOLMultiphysics.
2.2.3BoundaryConditionsMoststeelsexhibitamodulusofelasticityofabout190-210GPa,includingstainlesssteels[3].InthisstudyitwasfoundtobemostusefultouseasteeltypewithaYoung’smodulusof200GPa.Thus,asteelwith200GPaandstandardvaluesofintrinsicpropertieswascustomizedinCOMSOL.
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2.2.4MethodicconditionsThisstudydoesnotexaminethefixingpoints.Instead,abuilt-infunctionofCOMSOLthatfixesselectedsidesofastructureisused.Therodsextendalongtheentirewidthofthebed,itisthereforemostsuitabletofixthemattheoutercircularcrosssectionsasillustratedinfigure5.Alltherodsaresetwithafixedconstraintontheselocations.
Figure5Usingthe‘fixedconstraint’functiontofixtherodsinCOMSOLMultiphysics,locationoffixationindicatedinblue.
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Tosimulatetheactualloadascloselyaspossibleaboundaryloadwasaddedontheplateasillustratedinfigure6.Thismethodexposesanevenlydistributedloadofasimplifiedvirtualfootonthedimensioning10rods.
Figure6BoundaryloadontheplateinCOMSOLMultiphysics.
2.2.5TestconditionsgivenbyIKEAIKEAspecifiedtestconditionstobeusedfortheassessmentwherethedurabilityshallallowforamaximumdeflectionof20mmatapressureof1000-1400Nandbeddimensionsof900x2000wasused[6].Sincetheworstcaseloadingscenarioisforthebiggestload,1400Nwasusedwhenperformingcalculations.
2.3InvestigationofsuitablematerialsTheparametersofhighestinterestforperformingthestudyarethosethataffectdeformationandplasticity.Therefore,Young’smodulusandyieldstrengthwerethedecidingfactorsoftheinvestigationofmaterialselection.Forthispurpose,thematerialdatabasesoftwareCESEdupackwaschosenassearchingtool[7].
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Thematerialcostisalsoofinterestbecauseithasanimpactontheaffordabilityandfeasibilityoflaunchingtheproductonthemarket.Therefore,thepriceinSwedishcrownsperkilogram(SEK/kg)wasplottedversustheyieldstrengthfordifferentmetalsusingthesamematerialdatabasesoftware.Acousticsofchatterisafactorofinterestwhenexaminingametallicmaterial’ssuitabilityforusageinbeds.Ifthemetalmeshgenerateschatterwhenmovingaroundonit,theusabilityandgeneralsatisfactionofthecustomerdecreases.Surfacetreatmentsandavailablecoatingswerethereforestudied.
2.3.1SurfacetreatmentsandcoatingsThereareactiveandpassivemethodsfordampingmechanicalvibrationsthatresultinchatter.Activemethodsrelyonsensorsandactuatorsforsuppressionofvibrationwhilepassivecontroltechniquesuseamaterial’sabilitytoabsorbvibrationalenergy.Passivemethodsarepreferableinthiscasebecauseoftheirlowcostandeasyexecution[8].Therefore,coatingsorsurfacetreatmentsthatminimizechatterbydampeningtheacousticvibrationshavebeenlookedinto.Minimizationofvibrationsisfavorablenotonlybecauseofthereductionofnoisebutalsoenhancesdurabilityagainstfatigueandimprovesstabilityandgeneralperformance[8].Awidelyusedsurfacetreatmentconsistsofviscoelasticvibrationdampingusingmaterialsexhibitingbothviscousandelasticcharacteristicssuchasmetalsandpolymers.Aparticularlywell-knownviscoelasticmaterialisrubberthatexcelsbytheeaseofapplyingitanditshighdampingcapacity.Thedownsideofviscoelasticvibrationdampinghoweveristhefactthatthedampingcapacitydependsonvibrationfrequencyandtemperature[9].Ontheotherhand,neitherhighvibrationfrequenciesnorhightemperaturesaretobeexpectedfortheapplication.AnewmethodthatiscurrentlybeinglookedintoatKTHtheRoyalInstituteofTechnologyisthedepositionofalayermadefromcarbon-basednanocomposite.Nanoscaleclustersinthecoatingmaterialprovidemechanicalpropertiesthatcanbetailoredtoreducemechanicalvibrations.Themethodissuitabletotheapplicationofthinwalledstructuresbutisatthemomentratherexpensiveasitisresearchanddevelopmentoriented[10,11].AcousticsspecialistUlfErikCarlssongavehisviewonthematterviaemailandrecommendedasurfacetreatmentoftherodsandthewirewithplasticorrubbercoatingasthesimplestsolution.However,healsoexpressedsomeconcernoverthesustainabilityofsuchacoating[12].
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2.4RollingpropertiesTherollingpropertiesweretobederivedfromthereferencemodelasseeninfigure7.Forameasuredinnerdiameter,extrapolationscanbederived.Thus,atotalrollingdiameterfortheentirestructurecanbeapproximatedasafunctionofrod-radius.
Figure7Afotofromthemateriallibraryinwhichtherolledreferencemodelcanbeseen.
Totalradiuscanbeapproximatedaccordingtocalculationsbasedontheparameterssetasillustratedinfigure8.Acompilationanddescriptionoftheparametersispresentedintable1.
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Theroll’sthicknessdependsontherods’diametersandnumberofturnstherollmakesandthenumberofturnsdependsonthetotallengthoftherollasgiveninequation1(eqn1)andequation2(eqn2)respectively.Sincetheroddiameteristheparameterofinterest,itisnecessarytoderiveanequationthatisindependentofthenumberofturns.Thereforeequation1andequation2havebeencombinedintoequation3(eqn3).
Figure8Schematicdrawingoftherolledmesh,includingparametersused.[13]
Table2Descriptionofparametersusedinthecalculationofrollingproperties.
Parameter Description!" Outerdiameter(Totalwidth)!# Innerdiameter$ Roddiameter% Gapbetweenturns& Numberofturns' = 2000 Totallengthofroll(lengthofbed)
!" = !# + 2& $ + % ,-./ ' = 0& !" + !#
2 ,-.1 23&1 5&$ 23&2 →
!" =4'($ + %)
0 + !#:(,-.;)
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3.Result
3.1MaterialinvestigationTheinvestigationofsuitablematerialswasinitiatedbyfocusingonsteel.Asmentionedearlier,steelsexhibitaYoung’smodulusinscopebetween190GPato210GPa.Infigure9theyieldstrengthsbetweenabout500to2000MPawerethereforeplottedagainstYoung’smodulusbetween190GPato210GPa.Theplotpresentsforwhatareasitismostlikelytofindsuitablesteelsthatfulfilltherequirementssetontheprohibitionofplasticdeformation.Notethattypesofstainlesssteelsdonotallowforthehighestoccurringstressesover1000MPawhilesteelsclassifiedas‘lowalloysteel’aretoleratingstressesuptocirca1500MPa.
Figure9Metalswithyieldstrengthof500-2000MPaandYoung’smodulusof190-210GPainCESEdupack.
Inthefollowingstageoftheinvestigation,economicaspectswerethemainsubject.Infigure10yieldstrengthisplottedagainstmetalpricesinSEK/kg.Forthispartoftheinvestigationitwaschosentonarrowthepricesdowntolaywithinaspanof0to100SEKandasforthespanoftheplottedyieldstrengthitwaschosentolaywithinaspanof500MPato1500MPa.Inthisplotitisnotablethataluminumalloysarewithinareasonablerangeofpriceastheyhavepricesbetweenstandardsteelandstainlesssteel.
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Figure10Metalswithyieldstrengthof500-1600MPaandapricerangeof2-100SEK/kginCESEdupack.
3.2Computations3.2.1SolidMechanicsAmateriallimitisthepointbeyondwhichthemetalcannothandletheassignedyieldstrengthi.e.therearenotypesofthemetaltobefoundmanagingvonMisesstresseshigherthanthemateriallimit.Thevaluesforthemateriallimitaretakenfromtheresultsofthematerialsinvestigationinchapter3.1.Theauthorsofthisreporthavemadetheconventiontocallcertaintypesofsteel‘standard’.Thisbecauseofthefactthatthesetypesofsteelexhibitsimilaryieldstrengthsandeconomicalaspects.Thesetypesarelowalloysteel,highcarbonsteelandmediumcarbonsteel.Therefore,theyhavebeenplottedtogetheras‘steel’.Resultsinchapter3.2arebasedonsolidmechanicandgeneralcalculationsofthemetalmesh.Theplotsarecombinedwithmateriallimits,requirementssetbyIKEAanddataachievedinchapter3.1.Pricesusedinthepresentedresultsare4SEK/kgand14SEK/kgforsteelandaluminumrespectivelyaccordingtoresultsfromchapter3.1.
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3.2.1.1SteelTheseplotsarepresentingcomputationsmadeonsteelmetalmesh.Intheupperplotinfigure11,vonMisesstressesoccurringinthemetalstructureareplottedagainstrodradius.Thestressesareplottedforradiivaryingbetween1.5mmto4mmsincethecomputationsweredonein-betweentheseradiiwithstartatthereferenceradius1.5mm,andthenextrapolated.Notethatthedimensionsofthereferencemodeldonotfulfilltherequirementssetontheprohibitionofplasticdeformationsinceitexceedsthelimitsetonsteelsat1500MPa.Inthelowerplot,therelationshipbetweendeformationandrodradiusisextrapolatedandpresented.NotethatmeshmadeofsteeldoesnotexceedthelimitfordeformationsetbyIKEAsincethebiggestdeformationoccursforarodradiusequalto1.5mmandis18mm.
Figure11VonMisesstresseswithmateriallimitsofstandardsteeltypes.Displacementdependenceinrelationtoradiusforsteel
rods.
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Resultsoftheexaminationofgeneralpropertiesastotalpriceandtotalweightarepresentedinfigure12.Intheupperplottotalweightinkgisplottedagainsttherodradius.Toavoidplasticityintherods,steelmeshislimitedtoatleast2mm(figure10),thusitisnoticedinfigure11thattheminimumtotalweightisabout20kg.Consequently,rodradiiover2mmwillgenerateatotalpriceatminimumcirca75SEKasseeninthelowerplotinfigure12.
Figure12Weightandpricerelationtoradiusforstandardsteeltypes.
3.2.1.2AluminumThissectionpresentscomputationsmadeonmetalmeshstructureofaluminum.Intheupperplotinfigure13,maximumoccurringvonMisesstressesareplottedagainstvaryingrodradiiincombinationwiththemateriallimittakenfromchapter3.1andinthelowerplotthedeformationoftherodsareplottedagainstvaryingrodradii.Generalpropertiesastotalpriceandtotalweightarepresentedinfigure14asfunctionsofvaryingrodradii.Thedeformationofthealuminumrodswithradiibelow2.75willexceedthemaximumpermissibledeformationrate.Therefore,infigure13thedeformationcurveiscombinedwiththemaximumpermissibledeformationrate.
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Figure13VonMisesstresseswithmateriallimitforaluminum.Displacementdependenceinrelationtoradiusforaluminumwith
limitformaximumpermissibledeformation.
Figure14Totalweightandtotalpricerelationstorodradiiforaluminum.
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3.2.1.3ComparisonToemphasizethedifferencesandsimilaritiesbetweenresultsfromthetwomaterialsthathavebeenpresented,resultsfromchapter3.2.1.1and3.2.1.2arecombinedwitheachotherinfigure15,16,17and18.
Figure15ComparisonofvonMisesstressesforsteelandaluminumandtheirrespectivemateriallimits.
Figure16Comparisonofdeformationinrelationtoradiusforaluminum,steelandthelimitformaximumpermissible
deformation.
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Figure17Comparisonofweightinrelationtoradiusforsteelandaluminum.
Figure18Comparisonofpriceinrelationtoradiusforstandardandstainlesssteelandaluminum.
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3.3RollingpropertiesTheapproximatedwidthofarollasafunctionofrodradiusispresentedinfigure19.Theresultsarebasedonanexperimentallymeasuredinnerdiameterof16.7mmandanapproximate2mmgapbetweentheturns.
Figure19Totalwidthoftherolledmeshasafunctionofrodradius.Calculationsmadebaseduponmeasurementsonthe
referencemodelwheretheinnerradiusoftherollwasmeasuredto16.7mmandanapproximategapbetweeneachturnwith2
mm.
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4.DiscussionThemodellinginSolidEdgeconstitutedabigpartofthestudy.EventhoughCOMSOLhasamodellingfunction,itwouldnotprovidetheabilitytomodelcomplexstructuressuchaswires.Therefore,SolidEdgewaschosentobethemodellingsoftwarefortheproblem.ThesimplificationoftheproblemtonotconsistofrodsandwiresbutonlyrodsmadetheusageofSolidEdgeyetmoreinefficientsincethemeshconsistingonlyrodscouldeasilybemodelledinCOMSOL.Hence,themodellinginSolidEdgewasnotasbeneficialasitwasintendedtobewhenperformingthecomputations.Sincetheprojectaimstoexaminewhethermeshedstructuresofmetalsaresuitableforusageinbeds,thestudyfocusedoncertainrelationshipsbetweenYoung’smodulusandyieldstrength,plottedinfigure9.Steelwasthepreferredmaterialinaccordancewiththestatedhypothesisandeventhesetmaterialselectionforthereferencemodel.Thereforefocuswassetonalltypesofsteelprimarily.Whentakingeconomicaspectsintoaccountinfigure10,itisnoticedthatsteelprovidesthecheapestmetallicalternativeforusageinmetalmesh.Eventhoughsteelgenerallyposesacheapprofile,stainlesssteelisaremarkablymuchmoreexpensivealternative.Withapricetentimesbiggerthanthatofstandardsteel,stainlesssteelisfromaneconomicperspectiveconsideredtobeanexpensivesolutionforthispurpose.Corrosionresistanceisalsoconsideredanexcessivepropertyforthesekindsofapplicationsandconsequentlythechoicewasmadetoexcludestainlesssteeltypesforusageinbedsinthisstudy.Theanalysisoftherelationshipbetweenyieldstrengthandeconomicaspects,anewmetallicoptionwasdiscovered.Asmentionedinthehypothesisoftheproject,earlieronlysolutionswithsteeltypeswereconsidered.Although,itwasobservablethataluminumismakinganalternativesolutionforaspanofyieldstrengthsuntilabout600MPa.Hence,aluminumwasincludedintoaccountinthestudywhenanalyzingsolidmechanicbehaviorofthemesh.Itisobservableinfigure11thatmetalmeshmadeofsteelfulfillstherequirementssetondisplacementandprohibitionofplasticdeformationsinceallmaximumvonMisesstressesexposedontherodsarebelow1500MPa,whichistheupperlimitforyieldstrengths’ofthemostcommonsortsofsteel.Sincestandardsteelhasanupperlimitaround1500MPaforyieldstrengths,rodswitharadiusunder2mmisnotmeetingtherequirementssetbyplasticityconditionsalthoughthedisplacementisunder20mmforsmallerradii.Thus,meshesmadeofsteelmusthavearodradiusabove2mm.Generalpropertiesastotalpriceandtotalweightforsteelareplottedandanalyzedinfigure12.Thesepropertiesareanimportantpartofthemarketabilityofaproduct.Itisconcludedthat
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rodradiimustlayabove2mm.Rodradiiover2mmgenerateatotalweightofabout20kgandthetotalpriceisconsequentlyaround75SEK.Thesevaluesarethereforetheminimumpriceandweightpropertiestobeexpectedbymeshmadeofsteel.Analogouslywiththerepresentationandanalysisofthemechanicalpropertiesofsteelmesh,resultscalculatedforaluminumwereplottedinfigure13.Asdiscussedearlier,aluminumhasanupperlimitforyieldstrengthsaround600MPa.Whentakingthisintoaccountandintegratedwiththeresultsfromsolidmechaniccalculations,itisobservedthatrodradiimustlayaboveabout2.75mm.Unlikesteel,aluminumdoesnotfulfilltherequirementssetondisplacementforallradii.Radiibeneath2mmgeneratedisplacementsover20mmasseenintheplot.Thustheplasticitypropertiesarethedecidingfactorforaluminummesh.Asforthegeneralpropertiesofaluminum,itisseeninfigure14thatforaradiusof2.75mmthemeshhasatotalweightofabout10kgandatotalpriceofabout150SEK.Analogouslywithsteelmesh,thesevaluesconstitutetheminimumlimitforameshmadeofaluminum.Thereareonly3differencesbetweensteelandaluminumwhencomputinginCOMSOL.Thesedifferencesarethevaluesofdensity,Poisson’sratioandYoung’smodulusofelasticity.Thus,itisseeninfigure16thattheseonlyaffectthedeformationcurvebyarelocationverticallyupwards.Thisstrengthensthecorrectnessoftheapproachmadeinchapter2.2.3.SmalldeviationsintheYoung’smoduluswillnotalteranyremarkabledifferencesinthedeformationbehavior,thustheapproachofselectingtheYoung’smodulusofanaverage200MPawasproventobeaccurateforthecomputations.Onlywhenthedeviationisbigenough,suchasinthecaseforthedifferencebetweenaluminumandsteel,thedeformationcurvewillbeaffected,andthisonlybyarelocationverticallyasonceagainseeninfigure16.Generally,itisconcludedfromtheresultsfromchapter3.2.1.3thatbothaluminumandsteelfulfilltherequirementswhendiscussedfordifferentspanofrodradii.Althoughtherearesomeparametersthatdistinguishapossiblematerialselectionoutofthetwo,suchasweightandprice.Steelprovidesacheapbutyetveryheavysolutionforthepurpose,whereasaluminumdoublesthepriceandhalvestheweight.Inthismatter,theauthorsofthisreportconsiderweighttobethedecidingparameterwhenselectingthemostsuitablematerial.Thisbecauseoftheindividualtransportationofthepackagecontainingthemeshandadditionalcontentsofthebedwhenbuyingtheintendedproduct.Figure19displaystheresultsofthecalculationsregardingtherollingproperties.Anapproximategapof2mmbetweeneachturnhasbeenusedwhichallowsforcertainmarginoferror.Asteelrodradiusof2mmwillgeneratearollwithawidthofabout145mmwhilethealuminumradiusof2.75mmgeneratesasomewhatthickerrollof155mm.Bothrollwidthsarereasonableforstorageandtransportationpurposesandcaneasilyfitintoapackage.Inthis
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manner,itisoncemoreimportanttonotethatarollwidthofcirca150mmmeansthatthemetalmeshwillbedeliveredinrectangularpackageswiththedimensionsofabout900*150*150mm3.Whentheweightofthemetalmeshistakenintoconsideration,itisseenthatweightistheoneparameterthatshouldbeconsideredcarefullywhendeterminingthebestsuitablematerial.
4.1Sourceoferrors
• WireThebiggestsourceoferrorsinthisprojectistheassumptionmadeinchapter2.1.2thatthewirehasnoeffectonthesolidmechanicbehaviorofthemetalmesh.ThisassumptionismadeasmentionedearlierbasedonlyonconsultationswithProfessorBoAlfredsson.ThusthecredibilityofthisassumptionlaystotallyonAlfredssons’sperceptionoftheproblem.TheproblemlayswithintheconsultationitselfsinceBohadnotenoughtimetoanalyzeandthoroughlythinkthroughbeforegivinghisadvice.Heonlycouldgiveadvicebasedonhisfirstimpressionsoftheproblemashehimselfexplained.Theabsenceofthewireisalsoaffectingtheresultsonweightandrollingpropertiesdirectly.Thepresentedtotalweightcalculationsdonotincludetheweightofthewire.Itisevenclearthatthestiffnessandthicknessdependingonthematerialselectionofthewirewillinfluencetherollingproperties.
• Distribution
Thedistributionoftherodswereonlybasedonthereferencemodelinwhichitwas10mm.Itisasourceoferrortonotstudytheoptimizationofthedistributionwhenvaryingtherodthickness.Thisbecausethethicknessoftherodscorrelatewithimprovedsolidmechanicproperties.Thus,amoresparsedistributioncouldbestudiedforthickerrodsandarelationshipbetweenminimumrequireddistributionandrodradiuscouldhavebeendesigned.WhenthedistributionislockedtothereferencemodelandtheconditionssetbyIKEA,themeshalwayscontains200rodstotally.Anoptimizationofthedistributionwoulddecreasethistotalamountofrodsandaccordinglythetotalweightaswellastotalpricecouldbereducedtominimumvalues,makingitasourceoferrorsinmannerofoptimizationforthestatedpurposeofusage.
• FixationTheexaminationoffixationpointsforarigidbodyisaspecificareainsolidmechanicswhichwouldrequireanentirestudyinitself.Thefixedconstraintusedwhenperformingthecalculationsisasimplewaytosimplifythecomplexproblemsthatfixationpointscause.Fixationisaffectingthesolidmechanicbehaviorofabodydirectlybygenerating
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nodesinthefixedpoints.Hence,thisbehaviorisnotconsideredinthisstudybecauseoftheusageofthesimple‘fixedconstraint’applicationinCOMSOL.
5.Conclusion
• Aluminumfulfillscriteriasetonplasticityanddeformation.Thussteelisnottheonlyoption.
• Itisconcludedthatweightisamoreimportantparametertoconsider.Aluminumistherecommendedmaterialofchoicebasedontheresultsdiscussed.
• Themeshisgeneratingarollofatleastcirca90mmthickness,whichisconcludedtobeareasonabledimensionforamanageablepackage.
5.1SWOT-analysisBelowfollowsaSWOT-analysismadeontheproductthathasbeenexaminedandconcludedtofitbestfortheaimedusage.Table3SWOTAnalysisofmetalmeshofaluminum
Strengths Weaknesses• Lightweight• Recyclability• Durability• Abilitytoberolled
• Expensive• Relativelythickerrodsrequired• Chatter• Fatigueofloadbearingcomponents
Opportunities Threats
• Easyproduction• Coatingand/orsurfacetreatmentto
avoidchatter.• Reusabilityofcertaincomponentor
wholemesh• Widerangeoffixationpossibilities
• Unpredictablepricefluctuationofrawmaterial
• Weakcompetitivenessagainstcurrentcheapsolutionsonthemarket
• Lowawarenessofexistenceinthefurniturebranch
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6.FutureStudiesSincethewirehadnoeffectonthesolidmechanicbehaviorofthemesh,itwasexcludedwhileperformingthecalculations.Althoughtheimpactofthewireonthesolidmechanicsisasuggestedareaoffuturestudies.Theexaminationofthemetalmeshincludingthelinkingwireswouldprovidemoreadequateandaccurateresultsforthefinalanalysisoftheproduct.Therearemanyaspectsthatcouldbeasubjectforsuggestedfuturestudiessuchasaninvestigationoffindingsuitablematerialsuggestionsforthewires,solidmechanicimpactofthewiresonthemetalmeshandalsotheacoustics.Sincethewiresareinconstantcontactwiththemetalrods,thiscontactwillgeneratechatter.Chattercanbedecreasedbyseveraltechniquesandhenceitisawideareaofpossiblefuturestudies.Inthisstudy,somesurfacetreatmentsandcoatingshavebeenbrieflypresented.Thusaparallelinvestigationofasuitablenon-metallicormetallicmaterialforthewirecouldbestudied,inwhichacousticandsolidmechanicaspectsareincluded.Asmentionedinthereport,thescienceoffixationforrigidbodiesisadeepandwideareaofsolidmechanics.Sincethisstudyhaschosentonotconsiderfixation,itissuggestedasanimportantandnaturalcontinuation.Itisalsoimportantsincethesolidmechanicbehaviorofaloadedmeshwillhaveadirectdependencyofthefixation.Furniture’scomfortdependsverymuchonitsdurabilityingeneralwhereallkindofaspectsthatwillinfluencemusthavebeenoptimizedforthecertainpurpose.Thus,fixationisoneofthemajorfuturestudyareas.
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7.AcknowledgmentsTheauthorsofthisreportwouldliketothankIKEAforgivingusfreereignandprovidingtheopportunitytodefinethescopeforaprojectthatmatchedourlineofinterest.FurthermorewethankBjoernGlaserforhishelpandguidanceregardingCOMSOLMultiphysics,BoAlfredssonforhisguidanceregardingsolidmechanicsandPerJohanssonforhelpingwithmodellinginSolidEdgeST7.TheauthorswouldlastlyliketoexpresstheirsincerethankstoPärJönssonforgettingusintocontactwithIKEAandAndersTillianderfromKTHRoyalInstituteofTechnologyatITMIndustrialEngineeringandManagementforprovidingsuchexcellentsupportandguidancethroughouttheproject'sprocess.KasimAytekinSandraMuhrStockholm,May162016
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