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Manufacturing2.810 JohnLewandowski
MachiningQuizReviewSheetOverviewThemostfundamentalequationsaboutmachiningarenotdifficult.Iwouldnotgetoverlycaughtupinthegeometryeither.Rather,understandhowandwhyoneparameteraffectsanotherbothintheformulaaswellasthephysicalsystem.Thenunderstandwherethesemajorformulasarecomingfrom.KeyFormulasShearstrainShearstraincanbecalculatedby:
𝛾 = cot 𝜙 + tan(𝜙 − 𝛼)
𝜙 = 𝑠ℎ𝑒𝑎𝑟𝑎𝑛𝑔𝑙𝑒
𝛼 = 𝑟𝑎𝑘𝑒𝑎𝑛𝑔𝑙𝑒Rememberwhatthecotangentgraphlookslike.Itdecreaseswithincreasingangles.Mostlikelyyouarenotgoingtobecalculatingtheshearstrain,sothemoreimportantrelationshipisunderstandingthefollowing:
• Whenshearangleincreases,shearstraindecreaseso Thematerial“turns”thecornerlessandsothereislessshearstrain(alsoless
shearstress)• Whenrakeangleincreases,shearstraindecreases
o Thematerial“turns”thecornerlessandsothereislessshearstrain(alsolessshearstress)
Similarly,myfeelingisthatthemostimportantpartofMerchant’sequationishowitassistswiththerelationshipbetweentheangles,notthegeometryitself.
𝜙 =𝜋4 −
𝛽2 +
𝛼2
• Whenrakeangleincreases,shearangleincreases
o Thematerial“turns”thecornerlessandsothereislessshearstrain(alsomoreshearstress)
MaterialRemovalRateDon’tmemorizetheMRRformula,insteadthinkabouthowtheformulaisconstructedforeachsystem.
Manufacturing2.810 JohnLewandowski
Turning
Milling
Theseseemsuperobvious!However,thatisbecausethegeometryissimple.ImagineifeachofyourtoolshadadifferenttypeorprofileoryouwerecalculatingtheaverageMRRacrossmultipledifferenttypesofcuts.Therefore,youcan’tjustmemorizetheequation,youmustgobacktothefundamentalgeometry(eitherheight,width,lengthorareaandlength).PowerAnotherimportantconceptistakingthematerialinteractionanddevelopingnumbersthatrelatetothesystemasawhole.Thiscanbedonewithpower.Weknowthatpowerisforcetimesvelocity.
𝑃 = 𝐹 ∗ 𝑉MRRcanalsoberepresentedby
𝑀𝑅𝑅 =𝑑(𝑣𝑜𝑙)𝑑𝑡 = 𝐴 ∗
𝑑𝑥𝑑𝑡 = 𝐴 ∗ 𝑉
Manufacturing2.810 JohnLewandowski
Thenthinkaboutwhatspecificenergymeans.
𝑢I =𝐸𝑛𝑒𝑟𝑔𝑦𝑣𝑜𝑙𝑢𝑚𝑒 =
𝑃𝑜𝑤𝑒𝑟 ∗ 𝑡𝑖𝑚𝑒𝑣𝑜𝑙𝑢𝑚𝑒 = 𝑃𝑜𝑤𝑒𝑟 ∗
1𝑀𝑅𝑅 =
𝑃𝑜𝑤𝑒𝑟𝑀𝑅𝑅
Seethereisnothingtomemorizehere!It’sjustbasicfundamentalrelationshipsbetweengeometry,force,power,andenergy.Wecansimplifytoourmainequation.
𝑃 = 𝑢I𝑀𝑅𝑅Specificenergymeanstotalpower.Let’sthinkaboutwhatworkisbeingdone:plasticdeformationandfriction.Thesearethetwomaincomponentsofthetotalpowercalculationinthesystem.Youcouldfindeithertheshearingpowerorthefrictionpowerifyouneededto(alsoforcetimesvelocity).MRRcanalsoberepresentedby
𝑀𝑅𝑅 =𝑑(𝑣𝑜𝑙)𝑑𝑡 = 𝐴 ∗
𝑑𝑥𝑑𝑡 = 𝐴 ∗ 𝑉
Thismakessense!MRRisjusttheareatimesthevelocity.Lastly,let’ssetourtwopowerequationsequalandsubstitutethatin.
𝑃 = 𝑢I𝑀𝑅𝑅 = 𝐹 ∗ 𝑉
𝑢I 𝐴 ∗ 𝑉 = 𝐹 ∗ 𝑉
𝑢I𝐴 = 𝐹Andweknowthat
𝐴 = 𝑓𝑒𝑒𝑑 ∗ 𝑑𝑒𝑝𝑡ℎ𝑜𝑓𝑐𝑢𝑡
𝐹S = 𝑓𝑒𝑒𝑑 ∗ 𝑑𝑒𝑝𝑡ℎ𝑜𝑓𝑐𝑢𝑡 ∗ 𝑢IYoujustderivedallthekeyequationsinthebookwithoutknowinganythingbutthegeometryofthesystemandbasicrelationships.OtherBriefPoints/RelationshipsToollife:Ascuttingspeedincreases,toollifedecreasesAscuttingspeedincreases,MRRincreases
Manufacturing2.810 JohnLewandowski
Astemperatureincreases,hardnessdecreasesAscuttingspeedincreases,hardnessdecreasesAscuttingspeedincreases,temperatureincreasesAsthetoolwears,cuttingforceincreases(areaofcutincreases!)KeyPagesintheBookTBDKeyReadingsBoothroydetal,"DesignRulesforMachining"(onlytwopages)