MIT 2.810 Fall 2016 Homework 2web.mit.edu/2.810/www/files/homeworks/2016_home... · MIT 2.810 Fall...
Transcript of MIT 2.810 Fall 2016 Homework 2web.mit.edu/2.810/www/files/homeworks/2016_home... · MIT 2.810 Fall...
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?
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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?