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2.810ManufacturingProcessesandSystemsQuiz#2

November15,2017

90minutes

Openbook,opennotes,calculators,computerswithinternetoff.Pleasepresentyourworkclearlyandstateallassumptions.

PrintName:Solutions(TA)

Problems:

1. TPS Cell Rate Increase

2. Waterjet Scheduling

3. Additive Mfg Vs Machining

4. Additive Mfg Systems

5. Readings

/30points/20points/15points/25points/10points_________

/100points

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1)(30pts)ToyotaCellProductionRateIncreaseConsidermachiningthefollowingaluminumpartinaTPScellwithaprocessplan,timesandconfigurationasshownbelow.Thepartismachinedfrombarstock2.5inX2.0in

ProcessStep

Operation Approx.vol.removed

Toolchanges Processtime(minutes)

Manualtime(minutes)

#1 ColdSawto4.5in(nofacingrequired)

(notoolchangeneeded)

2 2(includestakingmaterialfromrawstock)

#2 Mill:Largehogout

10in3 1endmill(notoolchange)

8 2

#3 Drill&Mill:Shallowdrillandradius

0.6in3 3(centerdrill,formdrill,endmill)

2 2

#4 Drill&Mill:Deepdrillandradius

2.4in3 3(centerdrill,formdrill,endmill)

4 2

#5 Mill:Smallhogout

3.6in3 1endmill(notoolchange)

3 2

#6 Inspectionanddeburr

0 2(includesdepositingfinishedpartintoadjacentbin)

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Thedrillingandmillingstepsaredepictedinthefiguresbelow.

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#1 #2 #3

#6 #5 #4

TheTPSCellthatusestheprocessplanaboveisshownbelow.TheManualTime/MachineTimeforeachprocessaregivenbelowinminutes.Thewalkingtimebetweeneachstationis1/12minute. RawMaterials FinishedPartsa)Currentlythiscellisoperatedwithoneoperatortravelingfrom#1aroundtheloopto#6andthenbackto#1.Pleasedeterminetheproductionrateforthecell(aspartsperhour)aswellastheinventoryinthecellandthetimeittakesforoneparttomovethroughthecell(hours).

Step WalkingTime ManualTime MachineTime

1 2 2

2 1/12 2 8

3 1/12 2 2

4 1/12 2 4

5 1/12 2 3

6 1/12 2 0

7 1/12

TOTAL 0.5 12 19

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(+3pts)Thefirstthingweneedtodoischeckwhetherthemanual+walkingtimeorthemanual+machinetimedictatesthecycletime.max(ManualTime+MachineTime)=2+8=10minutes(from2ndmachine)WalkingTime+ManualTime=0.5+12=12.5minutesTherefore,WalkingTime+ManualTime>max(ManualTime+MachineTime)andthewalking/manualtimedeterminesthecycletime.(+3pts)Calculatetheproductionrateofthesystem

𝜆 = 𝑝𝑎𝑟𝑡𝑠𝑡𝑖𝑚𝑒 =

1𝑝𝑎𝑟𝑡12.5𝑚𝑖𝑛 ∗

60𝑚𝑖𝑛1ℎ𝑟 = 𝟒. 𝟖

𝒑𝒂𝒓𝒕𝒔𝒉𝒓

(+3pts)Findtheaveragenumberofpartsinthesystem

𝐿 = 611212.5 + 7

12.5 − 11212.5 = 𝟔. 𝟗𝟗𝒑𝒂𝒓𝒕𝒔

(+3pts)UseLittle’sLawtocalculateaveragetimeinthesystem

𝐿 = 𝜆𝑤

𝑤 =𝐿𝜆

𝑤 =6.99𝑝𝑎𝑟𝑡𝑠4.8𝑝𝑎𝑟𝑡𝑠/ℎ𝑟 = 𝟏. 𝟒𝟔𝒉𝒐𝒖𝒓𝒔

b)Wewouldliketoincreasetheproductionrateforthiscellbyusingtwooperators.Pleaseshowthebestarrangementforthehighestproductionratebyonlyaddingasecondoperators.Add“decouplers”(additionalinventory)ifnecessary.Pleasedrawonthediagrambelowtoshowhowyouhavearrangedtheoperators.Whatistheproductionratenow?Whatlimitstheproductionrate?Pleasemakethreesuggestionsonhowtoimproveonthisproductionrate.Rankorderthemintermsonthecoststhatmightbeincurredandgivetheestimatednewimprovedproductionratewiththisimprovement.Stateallassumptionsclearly.

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(+3pts)Choosinganoperatorconfigurationthatreducestheproductionrate.Actuallymostchoiceswillworkaslongasthechoiceleavesyouwithmachine#2asthelimitingfactor.ThebestchoiceforeasiestexplanationandcalculationisforOperator#1toberesponsibleformachines1->2->6(butstopat5topickupthepartfromthedecoupler)andOperator#2toberesponsibleformachines3->4->5(butstopat2topickupthepartfromthedecoupler)(+3pts)Dependingonyouroperatorconfiguration,decouplersshouldbeaddedafterthelastmachinethateachoperatoruses.Thereneedstobeadecouplertoaccountforeachhandofforintersectionoftheoperator’spaths.Andthedefinitionofadecoupleristhatitonlyholdsoneuniquepart.Inthisconfiguration,adecouplerisplacedrightafterMachine#2(forOperator#1topickup)andMachine#5(forOperator#2topickup).Addingextradecouplersfornoreasonwasacommonmistakehere.Moredecouplerswouldincreasetheinventoryandnumberofpartsinthesystemandnotbeoptimal.Therewasalsoanissueofpartsnotbeinginthecorrectlocationfortheotherworkertopickuporonlybeingavailableatcertaintimesduringtheloop.

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Operator1:

Step WalkingTime ManualTime MachineTime

1 2 2

2 1/12 2 8

5 1/12

6 1/12 2 0

7 1/12

TOTAL 0.33 6 10

Operator2:

Step WalkingTime ManualTime MachineTime

3 1/12 2 2

4 1/12 2 4

5 1/12 2 3

2 1/12

TOTAL 0.33 6 9

(+3pts)Byinspectionofthenewtables,itisclearthatOperator#1hasthelongertimes,andsoweshouldinvestigatefurther.Asbefore,let’scomparetheWalkingTime+ManualTimetothemax(ManualTime+MachineTime).max(ManualTime+MachineTime)=2+8=10minutes(from2ndmachine)WalkingTime+ManualTime=0.33+6=6.33minutesTherefore,WalkingTime+ManualTime<max(ManualTime+MachineTime)andMachine#2limitsthecycletimebecauseitistheslowestoperationinsideOperator#1’sloop.(+3pts)CalculatetheproductionrateusingtheMachine#2limitation.

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𝜆 = 𝑝𝑎𝑟𝑡𝑠𝑡𝑖𝑚𝑒 =

1𝑝𝑎𝑟𝑡10𝑚𝑖𝑛 ∗

60𝑚𝑖𝑛1ℎ𝑟 = 𝟔

𝒑𝒂𝒓𝒕𝒔𝒉𝒓

Varioussuggestionsthatcouldberanked(+2ptsforeachofthetwosuggestionsand+2forrankingthem).

● ExtrudeorbandsawthepartratherthanmillinginMachine#2.Noticethatwearemilling10in^3andthatisalotofmaterial,whichcouldberemovedmuchfasterincross-section.ThiswouldsubstantiallyreducethetimeofMachine#2(probablytolessthanaminute).

● OffloadsomeofthemillingvolumeinMachine#2toadifferentmachinesothatthemachinetimesaremorebalanced.Makesurethismakessensewiththeprocessplanstepsandorderofoperations.

● IncreasetheMRR(orfeedrateorotherfactorsthatwouldpositivelyinfluencetheMRR)andthenaccountforamoreoftentoolchange

● BettertraintheworkersatMachine#2orhaveapre-setfixturethatreducesmanualtimetobelow0.33minutes(forthosethatcalculatedthewalkingtimeof8.33minutes)

● Addasecondmachine(veryexpensivebutwoulddropthecycletimedowntowalkingtime+manualtimeagainsincenowthemachiningstepfor#2wouldtakeonly4minutes(andthiswouldgiveamaxtimeof6includingthemanualtimewhichislessthanthewalking+manualtimeof6.33)

BecausewearealreadylimitedbytheMachine#2,addinganotherworkerwillnothelpusnomatterwheretheyareplacedinthesystem(unlesswealreadyduplicateMachine#2ormakeoneoftheseotherchangesabove).AllanswersmustbesomehowrelatedtoeitherthemanualormachinetimeassociatedwithStep#2.Betteranswersdefinitelytookintoaccounttheprocessplanonthefirstpage.

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2)(20pts)Waterjetschedulinga)Weallknowthatthewaterjetisapopularmachinein2.810.Thisproblemisconcernedwiththeefficientschedulingofthismachine.Assumingthatthe2.810teamsarescheduledtoarriveeverytwohoursatthewaterjet.Toensureatimelyprogressofeachproject,eachteamisaskedtoensurethattheirwaterjetcuttingcanbeaccomplishedin1.5hours.However,weknowthatsomeprojectsareambitiousandtheywilltakelongerthan1.5hours.Modelthisproblemasaqueuingproblemassumingtheaverageprocessingrateisoneprojectevery1.5hoursbutthereissignificantvariationintheprocessingtimesandarrivaltimes(i.e.exponentiallydistributed).Howlongdoyouthinkitwouldtaketoprocesseightprojectsbythismethod?(+2pts)

𝜆 = 𝑎𝑟𝑟𝑖𝑣𝑎𝑙𝑟𝑎𝑡𝑒 = 1𝑡𝑒𝑎𝑚2ℎ𝑜𝑢𝑟𝑠 = 0.5𝑡𝑒𝑎𝑚𝑠/ℎ𝑟

(+2pts)

𝜇 = 𝑠𝑒𝑟𝑣𝑖𝑐𝑒𝑟𝑎𝑡𝑒 = 1𝑡𝑒𝑎𝑚1.5ℎ𝑜𝑢𝑟𝑠 = 0.67𝑡𝑒𝑎𝑚𝑠/ℎ𝑟

(+2pts)MM1Queue(exponentiallydistributed)

𝐿 =𝜆

𝜇 − 𝜆 = 0.5

0.67 − 0.5 = 3.125𝑡𝑒𝑎𝑚𝑠

(+2pts)

𝑤 =𝐿𝜆 =

3.125𝑡𝑒𝑎𝑚𝑠0.5𝑡𝑒𝑎𝑚𝑠/ℎ𝑟 = 6.25ℎ𝑜𝑢𝑟𝑠

(+2pts)

𝑇𝑜𝑡𝑎𝑙𝑝𝑟𝑜𝑐𝑒𝑠𝑠𝑡𝑖𝑚𝑒 = 𝑤 ∗ 8 = 6.25ℎ𝑜𝑢𝑟𝑠 ∗ 8 = 𝟓𝟎𝒉𝒐𝒖𝒓𝒔Fullcreditwasgivenforsmallchangesduetorounding.Mostpeoplelostpointsformisinterpretingtheservicerateandarrivalrates.Creditwaspassedthroughifthoseerrorspropagatedthroughtheproblem.Otherstudentsmultipliedthenumberofprojectsincorrectlyduetoabadmisinterpretationofthewaittimeandprocesstime.

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b)Oneofthestudentsin2.810suggeststhatwecanredesignourwaterjetprojectsbyreschedulingtheteamstoarriveevery2.5hoursandpickanaverageprocessingratethatensuresthattheaveragetimeforeachprojectistwohours.Whatistheaverageprocessingratethatensuresthisoutcome?(+2pts)

𝜆 = 𝑎𝑟𝑟𝑖𝑣𝑎𝑙𝑟𝑎𝑡𝑒 = 1𝑡𝑒𝑎𝑚2.5ℎ𝑜𝑢𝑟𝑠 = 0.4𝑡𝑒𝑎𝑚𝑠/ℎ𝑟

(+2pts)

𝜇 = 𝑠𝑒𝑟𝑣𝑖𝑐𝑒𝑟𝑎𝑡𝑒 = 1𝑡𝑒𝑎𝑚𝑥 =?

(+2pts)MM1Queue(exponentiallydistributed)

𝑤 = 2ℎ𝑜𝑢𝑟𝑠(+2pts)

𝑤 = 2 =1

𝜇 − 0.4

(+2pts)

𝜇 = 𝑠𝑒𝑟𝑣𝑖𝑐𝑒𝑟𝑎𝑡𝑒 = 1 + 0.82 = 𝟎. 𝟗𝒕𝒆𝒂𝒎𝒔/𝒉𝒓

𝜇 = 𝑠𝑒𝑟𝑣𝑖𝑐𝑒𝑟𝑎𝑡𝑒 = 1𝑡𝑒𝑎𝑚𝑥 , 𝑥 = 1.1ℎ𝑜𝑢𝑟𝑠

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3)(15pts)AdditiveManufacturingVsMachininga)Figure1binthepaperonadditivemanufacturingprovidedbyProf.JohnHartshowsthecosttomakeafamilyofplanarstainlesssteelpartsofincreasingcomplexitybybothCNCmillingandselectivelasermelting(SLM).Thefiguresuggeststhatascomplexityincreasesthereisacrossoverandtheadditivemanufacturedpartsappeartobelessexpensivethanthemachinedparts.Thissuggeststhatformoderatelycomplexparts,additivemanufacturing(AM)maydisplacemachininginproductionmanufacturing.Pleasegiveyourthoughtsonthismatter.Forexample,discussotherparametersbesidescostthatmightbeimportantinpromotingthiscrossover.Inparticular,pleaseaddressqualityandrate.Morecreditisgiventoanswersthatusenumericalestimatestosupportthearguments.Usethenatureofthepartsshowninthefigureasabasisforyouranswers.Besuretomakeclearwhetheraparticularaspectofthetrade-offbetweenthetwoprocesseswouldbeinfavorofAM,oragainstit.(ThereisNONEEDtoconcernyourselfwithattemptingtousethecomplexitymetricusedinthepaper.DON’TWASTETIMEONIT!)

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(+3pts)Natureofthepart.Basedonthehintfromthepromptwiththepictureofthevariouspart,weseethatthecomplexityalludestothenatureofthepart(whatitlookslike).BecauseSLMisanadditiveprocessandmachiningisasubtractiveprocess,thenatureofthepart(whetheritishollowornearlyasolidpart)aswellasitsfunctionhasanextremelylargeimpactonalloftheparameters(cost,rate,quality,etc).(+2pts)2ptsofcreditwasgivenforanyotherinterestingcommentsgiveneitheraboutflexibility(SLMcanbemoreflexiblethanmachiningincasetheproductchangesorbecomesmorecomplex),aboutthegraphitself(thereisawidevarianceofdatabetweenthetwobureaussoitseemslikethereissomeskillinvolvedorvarioustypesoftechniqueswithinCNCandSLM),ormoredetailaboutcost(someofthesimplestpartscanbeverydifficulttomachinesuchasasphereandsomeofthesimplestpartscanbeverydifficultforSLMiftheyrequireseveralsupportstructures,etc).Rate(+3pts)Themoredetailthebetter.Ingeneral,SLMisslowerthanmachining.Butwhy?Rateinadditivemanufacturingislimitedbytheheattransferneededtomeltthematerial.Inmachining,youcanovercomesomeoftheheatconstraintsbyusingharder/strongertools,changingthematerial,andusingcoolant.(+2pts)Asaskedfor,morecreditwasgiventonumericalanswersthatmentionedaprintrateof0.01-1kg/hr(HartAMSlide17)forSLM.Quality(+3pts)Themoredetailthebetter.Ingeneral,SLMhasworseresolutionthanmachining.Forthevastmajorityofcurrentproducts,post-processing(machining)isactuallyneededtoachievetherequisitesurfacefinish.Inaddition,thereisanisotropicstrengthpropertiesdependingontheaxisofprinting.Thisfurtherslowsdowntheeffectiverateandincreasestotalcost.Meanwhile,machiningcanhaveverygoodresolutiononitsownbyusingdifferenttools,cuttingspeeds,andmillingdirections.Sinceitisasubtractiveprocess,strengthcanbemuchmoreisotropic.(+2pts)Asaskedfor,morecreditwasgiventonumericalanswersthatmentionedaresolutionof0.1mm(HartAMSlide17)forSLM.

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Print1.1

Print1.2 Wash Cure

Print1.3

4)(25pts)AdditiveManufacturingSystemPerformanceConsiderthefollowingSLMmanufacturingsystemmadeupof3sequentialsteps.Inthefirststeppartsareprinted;inthesecond,partsarewashed(toremovethesupportstructures);andinthethirdstepspartsarefullycured.Inthesystemshownbelowthereare3parallelprintingmachines.Thepartsmovingthroughthesystemhaveavolumeof50cm3.Machine Capacity(parts) RateorTimePrinter(singlemachine) 60 100cm3/hrWash 60 15minutes/batchCure 60 60minutes/batchConsidertheoperationofthesystemunderthefollowingconditions:Partsareprinted120atatime(40ineachprintmachine)thentheymovetothesubsequentsteps.Oncetheprintersfinishthe120partsanother120partsareloaded.

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a)Pleasedrawthesystemboundariesaroundtheentiresystemanddeterminetheaveragenumberofpartsinthesystem,theaveragetimeforthepartsinthesystem,andtheaverageproductionrate.(+2)Calculatetheproductionratesofeachstep(drawingthesystemboundaryaroundeachstep)todeterminethebottleneckandtheproductionrateofthetotalsystem.Printvolume=40parts*50cm^3/part=2000cm^3Printtime=(2000cm^3)/(100cm^3/hr)=20hoursPrintproductionrate=40parts/20hours=2parts/hrSincethereare3printers,totalprintproductionrate=2parts/hr*3=6parts/hrWashproductionrate=60parts/0.25hours=240parts/hrCureproductionrate=60parts/1hour=60parts/hr(+3)Thebottleneckinthesystemistheprintstations.Therefore,theproductionrateofthesystemis6parts/hr.Manystudentsconfusedhow3Dprintingworksinbatchescomparedtootheroperationsandalsohowprintvolumerelatestoprinttime.ThiswaspenalizedheavilyaswellasnotutilizingLittle’sLawforthesystem.(+2pts)Calculatetheaveragepartsinthesystem.2ptsweregivenforanon-averagedattempttosumthepartsbasedsolelyonthebatchsizesforeachstation(120+60+60forinstanceforatotalof240parts).(+3pts)Themoreexactanswerusesaweightedaverageforthenumberofpartsinthesystem.Seebelowforthedrawingofthesystemwherewetrack240partsgoingthroughthesysteminsteadystateacross40hours.Usingthisanalysis,wecanaccountforhowlongeachbatchofpartsstayinthesystemorhowmanypartsareineachlocationduringthattimeline.

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𝐿 = 120 ∗20 ∗ 6020 ∗ 60 + 60 ∗

15 + 6020 ∗ 60 + 60 ∗

15 + 60 + 6020 ∗ 60 = 𝟏𝟑𝟎. 𝟓𝒑𝒂𝒓𝒕𝒔

(+5pts)UseLittle’sLawaroundtheentiresystemtocalculatetheaveragetimeinthesystem.

𝑤 =𝐿𝜆 =

130.5𝑝𝑎𝑟𝑡𝑠6𝑝𝑎𝑟𝑡𝑠/ℎ𝑟 = 𝟐𝟏. 𝟕𝟓𝒉𝒐𝒖𝒓𝒔

ManystudentsdidnotuseLittle’sLaw,whichwascrucialforthisquestion,andendedupmakingmorethanoneaveragequantitythatultimatelydidnotabidebyLittle’sLaw.Alsothebottleneckhadtobeanalyzedfirstandsotheprintratecouldnotbecalculatedlast.b)Whatinventoryholdingspaceisrequiredinthissystem?Pleasedrawitonthefigureandgivethepartvolumesizeneeded.(+1pt)Therearetwoinventorystationsneeded,onebecauseofthebatchbottleneckandonebecauseofthebuildupofthedifferentialbetweenwashandcuretimes.(+2pts)Theinventoryneededinfrontofthewashstationis60parts(or3000cm^3ofspace)becauseoutofthe120partsthatarefinishedprinting,only60partscanenterthewashatatime.(+2pts)Theinventoryneededinfrontofthecurestationis60parts(or3000cm^3ofspace)becausethewashstationfinishesthose60partsandthenanother60partsfromtheoriginalprintbatchbeforethecurestationisreadyagain.

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Ifyoutriedtosaysomethingelse,youmusthavebeenextremelyclearwithyourassumptionsbecausethesystemexplainedabovewouldcreatethesebydefault.c)Whatistheshortesttimetoproduceonepartinthesystem?Howdoesthisproductionratecomparewiththeaverageproductionrateforthesystemoperatingwith120partsatatime?(+3pts)Ifonlyanalyzingonepart,thenweneedtoredotheprintcalculations.Printvolume=1part*50cm^3/part=50cm^3Printtime=(50cm^3)/(100cm^3/hr)=0.5hoursWashtime=0.25hoursCuretime=1hourShortesttimetoproduceonepart=0.5hr+0.25hr+1hr=1.75hours(105minutes)(+2pts)Comparethistothe120-partsystem.Thisisamuchshortertimetowaitforasinglepart.Therefore,thissystemisgoodforasmallnumberofpartsiftheleadtimeisconstrained.Otherwise,the120-partsystemproducespartsmuchfasterbutasamuchlongerleadtime.

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5)(10pts)ReadingsInterchangeablepartsplayedanoutsizedroleinthedevelopmentofmodernmanufacturing.However,itshistoricaldevelopmentappearstohavebeenlargelymisunderstood.Inyourliteraturereadings,thecurrentunderstandingofthisdevelopmentwasclearlyarticulated.Pleaseanswerthefollowingquestionsandidentifyinyourreadingwhereyoulearnedthesefacts;(+2pts)CitationsfromHounsellIntroduction(pgs.3and4)a)WhoconclusivelydemonstratedthatEliWhitneydidnotproduceproductswithinterchangeableparts?(+2pts)Woodburyconvincinglyarguedthatitwasn’tEliWhitney.EdwinBattinsonsolidlyconfirmedthispoint.StudentsthatwroteMerrittRoeSmithwereawarded1pt.b)Whothenwasidentifiedastheprimemoverofthedevelopmentofinterchangeableparts?(+2pts)TheUnitedStateOrdinanceDepartmentwastheprimemoverinthedevelopmentofinterchangeableparts.StudentsthatwroteJohnHallwereawarded1pt.c)Whatwastheproductthatdemonstratedinterchangeability?(+2pts)Smallarmsorthebreech-loadingriflewastheproductthatdemonstratedinterchangeability.Studentsthatonlywrotegunsorsomethingsimilarweregiven1ptiftheyalsoprovidedsomegreaterdetail.d)Didinterchangeabilityreducethecosttomakethisproduct?(+2pts)No,“theunitcostofSpringfieldsmallarms…wassignificantlyhigherthanthatofarmsproducedbymoretraditionalmethods”.Itwasn’tuntilmuchlaterthatinterchangeabilityreducedcostsinmanufacturing.Studentsthatdidnotexplicitlywrite“No”weregiven1ptiftheymentionedthateventuallyitreducedcost.