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MIT2.810Fall2016 Homework2

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MIT2.810ManufacturingProcessesandSystemsHomework2

Machining

September27,2016Problems1&2arebasedontheflashlightprojectfromlab.PleaserefertoyourlabbookletortoFigures1&2fordimensions.Problem1.DrillingConsiderthedrillingofFeature3(ThruHole)ontheflashlighthead(Figure1).Assumethefeedofthedrillingoperation(i.e.,thedistancethedrillpenetratesperunitrevolution)isf=0.01in/rev.Note:DrillingiscoveredinSection23.5ofKalpakjian,7thed.a) Calculatethematerialremovalrate(inin3/sormm3/s).

b) UsetheTaylorToolLifeequationtoestimatethetoollife(inminutes)forthisoperation.UseTable1

topickappropriatevaluesofCandn(theflashlightmaterialisaluminumandthetoolsarehigh-speedsteel).Howmanysuchholeswouldyoubeabletodrillbeforethetoolneedstobereplaced?

Table1.RepresentativevaluesofnandCintheTaylortoollifeequationforselectedtoolmaterials

(fromM.P.Groover,FundamentalsofModernManufacturing,5thed.)c) Estimatethepower(inhporW)requiredforthisoperation.Thespecificenergyrequirementsin

cuttingoperations(Table21.2inKalpakjian,7thed.)canbeappliedtodrillingprocesses.d) Estimatetheriseintemperatureatthetool-chipinterfaceduringthedrilling(inFor°C).Howclose

isittothemeltingpointoftheworkpiecematerial?Howcloseistheadiabatictemperaturerisetothemeltingpoint?

e) IfyouwerefabricatingtheflashlightfromStainlessSteelinsteadofAluminum,whatwouldbe(1)

thetoollife,(2)thepowerrequirement,and(3)thetemperaturerise?

MIT2.810Fall2016 Homework2

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Recommendedtool:Vdrillbit.Recommendedspeed:1200RPM.

Figure1.ThruholestepforProblem1

Figure2.TurningstepforProblem2

1.0”

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Problem2.TurningConsiderStep2(TurnShoulder)inmachiningtheflashlighthandle(Figure2).Assumeyouareusingafeedf=0.015in/revandaspindlespeedΩ =900RPM.a) Calculate the cutting time (in s) and the material removal rate (in in3/s or mm3/s) for this cut,

assumingyouremoveallofthematerialwithonepass(i.e.,depthofcutd=(1”-0.6”)/2=0.2”).Approximatelyhowlongdidittakeyoutomakethiscutinthelab?

b) Estimatethepower(hporW)requiredforthisturningoperation.Whatchangescouldyoumaketo

theprocessifyouneededtodecreasethepowerrequirement?c) Assumethelatheisequippedwitha5-hpelectricmotorandhasamechanicalefficiencyof80%.

Estimatethemaximumfeedthatcanbeusedbeforethelathebeginstostall.d) EstimatethecuttingforceFc(inNorlb)duringthecut.e) Weare interested inpossibledeflectionscausedby thecutting forcesactingon therod.Estimate

theelastictwistanglewhenthetoolengagesattheverytipofthecantileveredworkpiece(assume2inchesoftheworkpieceextendsoutsidethecollet).TheshearmodulusofAluminumisG=3.77x106psi(=26GPa).(Hint:Youwillneedtofindthetorqueandthepolarmomentofinertiafortherod.)

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Problem3.AnglesandForcesinCuttinga) Fororthogonalcutting,pleaseverifythatthefollowingexpressionforshearstressholds:

𝜏 =𝐹! 𝑠𝑖𝑛 𝜙 𝑐𝑜𝑠 𝜙 − 𝐹! 𝑠𝑖𝑛!𝜙

𝑡!𝑤

wheretheanglesandforcesareillustratedbelow,𝑡!isthedepthofcutandwisthewidthofthecut.

Figure 3. Orthogonal cutting model.

b) Assumingthattheshearangleadjuststominimizethecuttingforce,derivethefollowingexpression:

𝜙 = 45° +𝛼2−𝛽2

c) CuttingforcesweremeasuredduringthemachiningofasteelbarandfoundtobeFc=520NandFt

=189N.Therakeangleonthetoolis10º.Basedonthisinformation,calculate:(1)thecoefficientoffrictionatthetool-chipinterface,(2)theshearangle.

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Problem4.VariablesinMillingYouareworkinginamachineshopandwanttouseamillingmachinetoremovematerialfromapieceofAluminum.

a. BothBillandGerryareonlunchbreakatthemoment,soyou’reonyourowntochooseatoolandsetupthemachine(NOTarealscenario).Whatarethetoolandoperationvariablesforwhichyouneedtoestablishvaluesbeforeyoucanstartcutting?(hint:wecounted7,2forthetooland5fortheoperation).

b. Usingthemachininglectureslides,whatequationsdowehavethatrelatethesevariablestoeachother?

c. Table24.2inKalpakjianprovidesrecommendedvaluesfortwooftheunknowns.Usingthis

table,areyouabletodetermineallofthevariablesyouneedtoperformyourcut?Ifnot,whatvariableswillyouneedBillandGerry’sexpertisetoestablish?