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)