Latest Transmission Technologies In Passenger Cars- A Review
Metallurgy Project
1. Automatic Transmission Gear
Material Selection
By
Dominick Carluccio
William Holden
Tahjee Seymour
Date: 4/28/15
Instructor: Professor Samardzic
ME438-102 : METALLURGY
SPRING 2015
3. Abstract
Helical gearsare usedinautomatictransmissionstoallow the gearteethtoengage more
graduallythenspurgearteethcausingthemto run smootherandquieter.Whenselectingthe material
for helical gears,itisveryimportanttotake the correct mechanical propertiesintoaccount.Some of the
mostimportantmechanical propertiestoconsiderare,yieldstrength,hardness,cost,modulusof
elasticityanddensity.The mainobjective of thisreportistoinvestigate possible candidatesandperform
a material selectionanalysistochoose anappropriate material andprocedure forahelical gearinside a
BMW M4 sportscar poweredbya six cylinder3.0literturbochargedengine coupledtoaGetrag
7DCI700 Powershift7-SpeedDual-ClutchTransmission.
4. Introduction
The firstattemptat an AutomaticTransmission(usinghydraulicfluid) wasintroducedbythe
companyGeneral Motors in1937. The transmissionwassemi-automaticandpromotedasthe
AutomaticSafetyTransmission(AST).Itwasimplementedinhopesof becomingthe new standardfor
vehicles,boastinghighincreasesinfueleconomy,greaterefficiency,andthe new featureof clutch-less
driving.Unfortunatelythe ASTwasquicklydubbedafailure due tounreliability,highinstallationcosts,
and lowconsumerdemand.Intwoyearstime the ASTceasedmanufacture.Howeverin1940 GM
designedanewversionof the transmissioncalledthe Hydra-Matic,the firstfullyautomatictransmission
evercreated.Witha noticeable dropininstallationcostamongotherfeatures, the Hydra-Maticbecame
the firstmass producedandcommerciallyusedautotransmission.In1948 the firstautotransmission
usinga torque converterwasintroducedbyBuick(calledthe Dynaflow).Soonafter,companiessuchas
Packard andChevroletquickly followedsuite.Atthistime vehicle transmissionswereonlytwospeed.
Notuntil the early1950’s didthe firstthree speedautotransmissionappear(equippedwithtorque
converter) createdbyBorgWarner, an Americanautomotiveindustryandpartssupplier.Three speed
auto transmissionswithtorque convertersremainedthe topsellerfor30 yearsuntil the automatic
transmissionwithoverdrivewasintroducedtothe market,providingfourormore gears,improvedfuel
economy,andincreasedefficiency.Since the inceptionof the overdrive the mostnotable improvements
on the automatictransmissionhave beenthe increasednumberof forwardgearsandthe cross overto
electronicallycontrolledtransmissionfrommechanicallycontrolledoperations.
The major componentsof the automatictransmissionare the compoundplanetarygearset,
torque converter,bands,clutches,hydraulicsystem, valves,modulators,andthe ElectronicControl
Module.Notall componentswill be discussed.The primaryfunctionof the automatictransmissionisto
5. transmitengine powertothe drive wheels(rear,front,orall wheels).Poweristransmittedinthe
transmissionthroughthe use of gearsconnectedatvariousratios.Withouta transmissioncarswouldbe
limitedtoone gearratiowhich ultimatelyresultsinthe sacrifice of eitheraccelerationortopspeed.
While amanual transmissiondoesindeedcompletethe same task,the automatictransmissiondiffersby
usingthe same setof gearsto produce multiple ratiosratherthanlockingand unlockingdifferentgears
to the outputshaftvia a manual clutch.The numerousgearsusedtoaccomplishpowertransmissionis
calleda compoundplanetarygearset.Fora four speedautomatictransmissionthe compoundplanetary
gear setincludestwosungears,twoplanetcarriers,andan outerringthat is responsible forthe output
of the transmission.Generallyinatransmissionthe 3rd
speed(gear) issetat a 1:1 (readone to one) ratio
withthe outerring,gear ratiossmallerthan1:1 put the transmissionintooverdrive.Overdriveisany
ratiothat leadsto the ringgear (output) rotatingfasterthanthe driveninputgear(example beinga.8:1
gear ratio).
All automatictransmissionscome withthe shiftingpositionsPark,Reverse,Neutral,andDrive,
withsome vehiclescomingwithadditional optionssuchasmanuallylockingat3rd
, 2nd
, and 1st
gear.The
shiftintoParkpositionsaParkingPawl (asteel pin) intothe rotationpathof the outputgear, effectively
impedingthe shaftfromrotating.The ParkingPawl’sprimarypurposeistokeepthe enginespowerfrom
reachingthe drive wheels.Movingthe shiftertothe Reverse positiontriggersasolenoidthatcausesan
additional geartoengage,thusreversingthe rotationof the outputshaft.Neutral disengagesall gears
disconnectingthe transmissionfromthe drivenwheels.Drive allowsthe automatictransmissionto
engage all gearratiosas needed.Ratiosare controlledbyanonboard computercalledthe Engine
Control Unit(ECU). The ECU monitorsa large networkof sensorswithinthe carto ensure conditionsare
innormal operatingranges.If available,shiftingintothe 3rd
,2nd
, or 1st
positionlocksthe transmissionin
saidgear,disallowingupshiftswhile enablinganylowergearratiostoengage if needed.
6. Under considerationisthe 7speedtransmissionforthe BMW M4 for the purpose of creatinga
componentof itsgearbox. The M4 usesan automatictransmissiontype calledaDual Clutch
TransmissionorDCT. The layoutof a DCT isessentiallythe combinationof twomanual gearboxesinone,
howeverall gearshiftsare conductedautomaticallywithelectronicandhydraulicscontrols.Insteadof
usinga compoundplanetarygearset,the DCT usesall external gearsandtwoshaftsconnectedtoeach
of the clutches.Made possible withahollow outershaftanda solidinnerone,the DCTcan holda
relativelylarge numberof gearsbyplacingsaidgearson differentshafts.Toclarify,ona6 speed
transmissionthe firstof twoclutchesisresponsibleforthe oddgears(1, 3, 5 in additiontoreverse) laid
on the innershaftandthe secondclutchcontrolsthe evengears(2,4, and6) laidonthe outershaft.
Withtwo clutchesoperatingalternatinggearsthe shifttime dropstoa mere eightmillisecondswhile the
bestautomatictransmissionshifttimeshoveraround100 milliseconds.A decrease inshifttime
significantlyincreasesfuel economydue tothe shortenedtime the engine powerisdisconnectedfrom
the gears.Also,a short shifttime decreasesthe severityof aphenomenonknownas“ShiftShock”which
isthe jerkingmotionone issusceptible towhenthe transmissionchangesgears.ShiftShockismore
prevalentinmanual transmissionvehiclesespeciallywithanunskilleddriver. The componentbeing
analyzedin the DCT isthe connectionbetweenthe drivingpinionandone of itscorrespondinggears. For
the creationof the gears,five chosenmaterialswillbe thoroughlyanalyzedinordertofindthe best
combinationof density,strength,cost,andhardness.
7. Theory
The transmissionunderconsiderationisthe PowerShift7DCI700 7-SpeedMDouble Clutchwith
Drive Logicand Launch Control manufacturedbyGetrag and foundinBMW’s M4, but alsoavailable in
the M3 andM5. BMW has playedalarge part inthe developmentof recentautomatictransmissionsand
was the firstcompanyto release afullyautomatedmanual gearboxinaproductioncar in1996. Since
thenthey have workedwithGetragto developevenmore efficientautomatictransmissionsthatare
now able to evenoutperformmanual
transmissions.Likemostautomotive
technology,the doubleclutchautomatic
transmissionswereaderivativeof 80’s and
90’s Formula1 sequential gearboxesand
BMW playedtheirpartinpast yearsof
Formula1 so theyhad accessto this
technologywhenitwasmostvaluable.
Dual clutch transmissionsare the forefrontof future automatictransmissionsandare growingin
popularityamongstautomotive manufacturerseveryyear.A dual clutchtransmissioniscomparable to
twomanual transmissions;itutilizestwowetclutcheswithgears1,3, 5, and 7 onthe firstclutchand
gears2, 4, and 6 on the secondclutch.Like mosttransmissionsthough,the dual clutchtransmissions
utilize helical gearstominimize vibrations.Theiruse of wetclutcheseliminatesthe needof atorque
converter;itusesa seriesof wetpadsto reduce frictionina pressurizedcylindertotransferpower,the
clutchis disengagedbyreducingthe pressure of the cylinder.Dual clutchtransmissionswill typically
outperformmanual transmissionsbecause itutilizesthe twoclutchestominimizethe time inbetween
Figure 1: The 2015 BMW M4
8. gear shiftsandmaximizingthe qualityof the meshincreasingthe comfortlevel aswell.While one clutch
isengagedonone shaft the nextgearcan be setup forthe secondclutch,the secondclutchthen
engageswhile the firstdisengages
reducesthe time betweenshiftsto
milliseconds.The mannerof upshifting
and downshiftingare almostidentical
and are controlledbythe electronic
control module (ECM);hard
accelerationwill tell the transmissionto
shiftup,and hard brakingwill tell the
transmissiontoshiftdown. Moderndaydual clutchtransmissionshave beenputtothe testand the
worldfastestdragracers withmanual transmissionscan’tshiftasfastas these dual clutchtransmissions.
BMW has developedDrivelogicwhichistheirsoftware thatcontrolsthe transmissionsand
ultimatelytellsithowtoact. The smoothgear changesthat thistransmissionispossibleof achievingare
largelyaresultof Drivelogictellingthe transmissionsexactlywhentomeshgearsandengage clutches.
NotonlydoesDrivelogiccoupledtothistransmissionresultinamore comfortable ride thana typical
automatictransmission,butitalsoresultsinabetterperformingride.Drivelogicisprogramedtoonly
shiftradicallywhenthe caris goingstraighttopreventa largerchange in force to the real wheelswhich
wouldresultina lossof traction,whichisverydangerousaroundturns.Drive logicisalsoresponsiblefor
synchronizingdownshiftsandengagingthe clutchinasmootherfashionduringdownshiftssothatsame
large change in force doesn’tresultintolarge of a change inforce to the rearwheelswhichcouldcause
a suddenlossof traction.Drivelogicalsorecognizesthe driver’sunique drivingmannerandpreferences
and triestoaccommodate and adapt to those preferences.
Figure 2: BMW’s Dual ClutchTransmission
9. The dual clutchtransmissionhas3 differentdrivingmodesDrive mode,Sportmode,and
SequentialManual mode.Drive mode isfullyautomaticanddesignedtoprovide the mostcomfortable
and efficientcharacteristicsof the transmissionsandissimilartothe drive selectionintypical automatic
transmissions.Sportmode isalsofullyautomaticbutitsprogrammingisslightlydifferent.Since
turbochargedenginesperformbestwhenthe turboisalreadyspooledup,Sportmode keepsthe engine
at the mostoptimal highrevvingrange where the turbocanstayspooledupwhichwill providethe user
instanttorque similartoa naturallyaspiratedengine.Sequential Manual mode providesthe userthe
abilitytomanuallyselectgearlike inaclutch lesssequential gearbox.
Thisgearbox alsoprovidesthe unique abilityof launchcontrol.Since aspooledupturbo
performsbetterthanone thatstill hasto be spooledup,thistransmissionallowsthe usertorevthe
motor at a complete stopandspool upthe turbowhile the brake isheld.Thenthe clutchisengaged
while the engineisrevvingallowingalaunchfroma stop withthe maximumamountof torque possible.
BMW has developedaunique coolingsystemforthistransmissionthatincorporatesthe cooling
cycle of the engine intothe coolingsystemof the transmission.Thisnotonlykeepsthe oil ata perfectly
maintainedtemperature range,butitalsoheatsup
the oil to withinthisrange fasterprovidingquicker
warm upswhichreduce the amountof time that
the transmissionhastoovercome largerthan
normal frictional forcesfromthe oil inthe
transmission.Thiswill provide betterefficiency
duringstartupsand betterperformance under
heavyuse whenthe transmissionwill producea
large amountof heatfromfriction.
Figure 3: BMW’s 3.0 litersix cylinder
turbochargedengine
10. BMW has coupleda3.0 literturbocharged6 cylinder(S55B30) coupledtotheir dual clutch
transmission.The S55B30 utilizestwotwinmono-scroll turbochargersandproduces425 horsepowerat
5500 RPMand 406 lb·ftof torque.The transmissiontransmitspowertothe rearwheel andismounted
to the car withthe engine longitudinally.Inthe sevenspeedgearbox,the twogearswiththe highest
stresswouldbe the meshingof the piniontofirstgearwhichhasa gearratio of 4.81:1. The othergears
wouldexperience lowerstressvaluessostressanalysisof the firstgearmeshwiththe givenmaterials
will suffice forthe dataneededformaterial selection.
Whenchoosinga material foruse ina
transmissionthere are certaincharacteristicsand
attributesof the material thatare necessary.Gears
are verysensitivetogeometrictolerance
differencessoanychange inthe geometryof the
gear mayresultinchatter,vibrations,oreven
ultimate failureof the gearas seeninfigure ().The
causesof gearfailure come inthe formof bendingfatigue of the teeth,wearorcontact fatigue onthe
surfaces,andscuffingwhichtransfersmaterialfromone gearontothe other.A highyieldstressisthe
firstand mostimportantcharacteristic.Whencoupledtomostmoderndayautomotive engines,gear
teethinthe transmissionwillexperience large forcesandresultingstressthatthe material mustbe
strongenoughto withstand.A highyieldstresswill preventthe gearfromfailingdue tobendingfatigue.
A highhardnessisthe secondmostimportantcharacteristic,itisnecessarytopreventanychanges in
the geometryof the gear sothat the transmissionremainsassmoothaspossible.Anyscuffing,wear,or
contact fatigue onthe surfaceswill resultinchatterorvibrationsandwill ultimatelyweakenthe gear
and create stressconcentrations.
Figure 4: Failure of helical gearsdue to high
contact stresses
11. The third characteristictotake intoconsiderationiscost.Like mostengineeringapplications
choosinga material withalowcost isusuallya limitingfactor.Costof the raw material shouldbe
investigatedaswell asthe machiningandtreatmentcosts.Sometimes shippingcostswill be anissue as
well because some materialsare exclusive tocertainlocationsof the world.The fourthpropertyto
considerformaterial selectionisalowYoung’sModulus,orhighvibrationabsorptionability.If avery
hard and stiff material waschosenforthe whole gearthe meshwouldresultinhighvibrations.To
preventthistypicallyamore ductile material ischosenforthe innerportionof the gearand thenitis
case hardenedtoincrease the hardnessjustonthe outersurfaces.Bychoosinga material withalow
Young’sModulus,butalsowiththe abilitytowithstandwearandcontact surface abrasion,thiswill
resultina very“smooth”transmission.The fifthmostimportantpropertyisalow density.The weightof
the car, and evenmore importantly,the weightof the drive trainplayalarge role on fuel economyand
performance.Bydecreasingthe weightof the drive train,the momentof inertiaisalsodecreased;this
allowsthe motorto transmitpowertothe wheelsquickerorwithlessforce.
12. Proposed Materials
The followingfive materialswerechosenbythe designteamtobe analyzedforselectionasthe
material fora single internal gearforthe automaticgeartransmission:
SAE 950X
SAE 4340H
SAE 4720H
XM023
CFRP (CarbonFiberReinforcedPolymer)
SAE 950X
SAE 950X iscategorizedasa High-StrengthLow-AlloySteel (HSLA)thismeansthatthe carbon
contentof the steel isusuallylessthan0.3 percent.SAE950X containstrace amountsof alloyingmetals
to enhance desiredmechanical propertiesandsometimesresistancetoatmosphericcorrosion.The
HSLA steelstypicallyachieve thesepropertieswithoutadditional heattreatment.
Table 1: Chemical Composition of SAE 950X Steel
SAE 950X Chemical Composition
C Fe Mn P Si S
<= 0.23% 97.43 – 100% <=1.35% <=0.04% <=0.90% <=0.05%
13. Figure 5: Stress Strain Diagram for Plain Carbon Steel and SAE 950X
Table 1 shows thatthe chemical compositionof SAE950X can range between100% pure iron to
97.43% iron withmixedalloys.Figure1showsa comparisonbetweenplaincarbonsteel SAE1010 with
SAE 950X. It isclearlyseenthatthe area underthe SAE950X curve,infigure 5, ismuch largerthan the
area underthe SAE 1010 curve whichmeansthatthe increasedtoughnessisclearlyseen.SAE950X is
typicallyusedwhere agoodstrength-to-weightratioisrequiredasHSLA steel crosssectionsare usually
20 to 30% lighterthancarbonsteel withthe same strength.
SAE 950X Mechanical Properties
Ultimate Tensile
Strength
YieldTensile Strength Brinell Hardness Modulus of Elasticity
63,500 psi 49,200 psi 120-124 29,900 ksi
Table 2: SAE 950X Mechanical Properties
Table 2 shows a summaryof the mechanical propertiesforSAE950X. SAE 950X isavailable from
suppliersinChinaandJapanas well aslimitedquantityinthe UnitedStates.
SAE 4340H
SAE 4340H isa seriesof steel withmainalloysof nickel,molybdenumandchromium.Eachthree
of these alloyshasaneffectof increase inhardenability.SAE4340H has a favorable responsetoheat
treatmentwhenquenchedinoil followedbytempering.WhentemperedSAE4340H displaysagood
14. arrangementof strengthandductilityandhasa wide varietyof usesinbearings,pistonpins,ordinance,
gears,dies,andpressure vessels.4340H can be machinedbyall conventional methodsandcanbe bent
or formedbyspinningorpressinginthe annealedstate.Heattreatmentforstrengtheningisdone at
approximately1525 degreesFthenfollowedbyanoil quench.
SAE 4340H Chemical Composition
C Cr Fe Mn Mo Ni P Si S
0.37-
0.44%
0.65-
0.95%
95.04 –
96.53%
0.55-
0.90%
0.2-
0.3%
1.55-
2.0%
<0.04% 0.15-
0.30%
<=0.04%
Table 3: Chemical Composition of SAE 4340H Steel
Figure 6: Microstructure of SAE 4340H
SAE 4340H Mechanical Properties
Ultimate Tensile
Strength
YieldTensile Strength Brinell Hardness Modulus of Elasticity
186,000 psi 125,000 psi 363 29,000 ksi
Table 4: SAE 4340H Mechanical Properties
15. Figure 6 showsthe microstructure of SAE 4340H at 25 micrometers.The blackparticlesare
Bainite andthe white orlightgreyparticlesare Martensite. SAE4340H isavailable from78 distributors
inNorth Americaandproducedby41 large mills.
SAE 4720H
SAE 4720H isclassifiedinthe same seriesasSAE4340H andis composedof the alloys
molybdenum,chromiumandnickel anddesignedforgoodstrength,wearresistance andtoughness
properties.SAE4720H isconsideredamoderatelylow carbonsteel withapproximately0.17-0.20%
carbon. The H variant of SAE 4720 isa special compositionthathasa goodcase hardeningability.SAE
4720H is rarelyannealedasitimpedesmachinabilitybutisusuallynormalizedpriortocase hardening.
The austenitizingtemperature forSAE4720 before quenchingis1500-1550 degreesFfollowedby
quenchinginwateroroil. SAE 4720H is manufacturedmainlyinChinaandIndia
SAE 4720H Chemical Composition
C Cr Fe Mn Mo Ni P Si S
0.17-
0.23%
0.30-
0.60%
96.55 –
97.93%
0.45-
0.75%
0.15-
0.25%
0.85-
1.25%
<0.035% 0.15-
0.30%
<=0.04%
Table 5: Chemical Composition of SAE 4720H
SAE 4720H Mechanical Properties
Ultimate Tensile
Strength
YieldTensile Strength Brinell Hardness Modulus of Elasticity
95,000-128,000 psi 50,100-80,000 psi 187-229 29,700 ksi
Table 6: SAE 4720H Mechanical Properties
16. Figure 7: SAE 4720H Alloy Steel Round Bar
Table 5 showsthe chemical compositionforSAE4720H steel.The alloyingcompositionof 4720H
isfairlysimilarto4340H but withminordifferencesinquantityforeachalloyingelement.Table 6shows
the summaryof mechanical properties
Figure 7 showsan example of SAE4720H roundbar stock fromthe manufacturer.Forgear
manufacturing,the gearmaterial wouldtypicallybe cutfromanendof the round bar stockthenfurther
machinedona lathe and toothcuttingmachine.
XM023
XM023 isa steel alloydesignedandmanufacturedbyXTRAC.XTRACisa worldwideleaderinthe
designandmanufacture of transmissionsystemscoveringmotorsports,defenseandmarine.XM023
steel alloywasdevelopedspecificallyforthe use inFormulaOne race transmissionsandwasusedto
secure the championshipsfor2005 and 2006. XM023 wasdevelopedtoimprove uponthe bending
fatigue andbearingproperties.The temperingtemperature forXM023 isapproximately390-480
degreesF.XM023 is usedas a varietyof gearbox internalsincludinggears,mainshaft,layshaft,hubsand
17. selectorforks.UnfortunatelyXM023 steel alloyisaproprietarymaterial andnomechanical properties
are available tothe public.
Carbon Fiber Reinforced Polymer (CFRP)
CarbonfiberreinforcedplasticorCFRPis a composite of strongcarbon fibersboundwithina
matrix polymer.The specificcompositechosenforthisprojectisQuantumCompositesLytex 4149.
Oftenthe polymerisathermosetresinsuchasepoxybutvinyl,polyesterandnylonare sometimesused.
CFRPexhibitsaverylarge strengthtoweightratioandis commonlyusedwhere strength,rigidityand
weightare the mostimportantfactors.The composite ismade upof two majorparts, a matrix and
reinforcement.Forthisprojectthe reinforcementisthe carbonfiberthatprovidesthe hightensile
strengthandthe matrix isepoxyresin.The Mechanical propertiesdependonthe characteristicsof the
twocomponentsof the composite aswell asthe orientationof the fiberswithinthe matrix.Typicallythe
reinforcementgivesthe composite itsstrengthandrigidity.AlthoughCFRPhasahighstrengthto weight
ratio,a major designlimitationisthe lackof a definablefatigueendurancelimit.Thisisextremely
importantforgear material selectionasthe gearwill constantlybe experiencingcyclicloadingandwill
resultinfatigue.Itisextremelydifficulttodocumentthe mechanical propertiesforcarbonfiber
compositesasthe manufacturingprocess,matrix materials,fiberorientationandatmospheric
environmentall have aneffectonthe mechanical properties.
Lytex 4149 iscomposedof 55% carbonfibersand45% resinepoxymatrix.
Lytex 4149 CFRP Mechanical Properties
Ultimate Tensile
Strength
YieldTensile Strength Brinell Hardness Modulus of Elasticity
Not defined 41,900 psi 32-54 65,000 ksi
Table 7: Lytex 4149 CFRP Mechanical Properties
Table 7 showsthe mechanical propertiesforthe CFRP.Notice thatthe ultimate tensile strength
isnot definedasitdependson the orientationof the carbonfibers.The hardnessisdeterminedfrom
the propertiesof the matrix.Inthiscase the hardnessisfairlylow comparedtothe otherresearched
materialsbecause itisa functionof the resinepoxy.
18. Figures 8 and 9 : Microstructure of Carbon Fiber Reinforced Polymer
Figures8 and 9 above showsthe microstructure of CFRPin side view (LEFT) andendview
(RIGHT).The individual carbonfiberscaneasilybe seen.
Summary
Mechanical Properties
Material Ultimate
Tensile
Strength
Yield Tensile
Strength
Brinell
Hardness
Modulus of
Elasticity
Comments
SAE 950X 63,500 psi 49,200 psi 120-124 29,900 ksi
SAE 4340H 186,000 psi 125,000 psi 363 29,000 ksi ExcellentHardenability
SAE 4720H 95,000-
128,000 psi
50,100-
80,000 psi
187-229 29,700 ksi Good Hardenability
XM023 N/A N/A N/A N/A Proprietary Material
CFRP Not defined 42,000 psi 32-54 65,000 ksi Unknown Yield,
Undefined Fatigue
Endurance
Table 8: Comparisonof characteristics
betweenmaterials
19. Material Analysis
Heat Treatment
Heat treatmentforgearsisusuallyfavorable asitallowsthe abilitytoimprove strengthand
hardnesstothe surfacesof the gear teethtopreventwearandfailure overtime. The twobasicstepsin
hardeningsteel istoheatthe steel to some temperature above itstransformationpointsothatit
becomesentirelyausteniticinstructure,thentoquenchthe steel atsome rate fasterthan the critical
rate to produce a martensiticstructure. Althoughnotall of the materialsconsideredinthisreportare
able to be heattreated,twoof the materialsbenefitfromanadditionalheattreatment. Carburizationis
alsonot takenintoaccount as none of the proposedmaterialsundergotreatment.
SAE 4340H can be heattreatedbyheatingthe material toapproximately1525 degreesFthen
quenchinginoil.ItisimportanttoquenchSAE 4340H inonlyoil as it wouldleadtocorrosionif itwere to
be quenchedinwater.
SAE 4720H can alsobenefitfromheattreatment.SAE4720H can be case hardenedor
carburizedbutisrarelyannealedasitimpedesmachinability. The austenizingtemperature forSAE
4720H is 1500-1550 degreesFthenquenchedusingwateroroil.
Cost
Cost isa major considerationwhenselectingamaterial forlarge scale manufacturing. To
estimate the costto have the helical gearmade itisimportantto take the raw material costinto
account. The cost perunitvolume forthe raw material was calculated,the resultscanbe seenbelowin
Table 9.
Table 9: Cost Per Cubic Inch By Material
Cost Per Cubic Inch
SAE 950X * SAE 4340H SAE 4720H * XM023 CFRP *
$0.17* $0.65 $0.18* N/A $1.71*
20. It isimportantto note that the cost percubic inchmarkedwith(*) are rough estimationsbased
on varyinggeometryanddonot include shippingfromoriginof manufacture.The costestimationfor
SAE 4340H isbasedoff of a quote for 5” diameterroundbarby 12 feetlongfroma distributorlocated
inNorth America.BothSAE950X and4720H couldnotbe sourcedwithinNorthAmericaandwouldneed
to be imported fromChina.BMW GmbH doesowntheirowncarbon fibermanufacturingplantssothe
cost analysisonCFRPwas basedonan average assumingthatBMW doesn'tpaymore than the average
price for theircarbonfiberproduction.The CFRPcostestimationonlyincludesthe raw materialsand
doesnotinclude anycost pertainingtocasts,moldsor instrumentsrequiredtocure the matrix.
Stress and Pitting Analysis
For the dual clutch transmissionunder
investigation,the meshof the piniontofirstgear
has the higheststressloadsandalsothe location
of the minimumfactorof safety;soa bending
stressand pittinganalysisonthe meshof the
pinionandfirstgearwill be sufficienttodetermine
the maximumstressesinthe transmission.This
meshresultsina gearratio of 4.81:1. The equation
usedto determine bendingstressandpittingis
fromthe AGMA designequationsfromAGMA Standard2001-C95. The bendingstressequationissimilar
to the one usedfor spurgears butwitha slightmodificationforhelical gears.The mode of stress
applicationforpittingfailure iscontactstressandthe contact stressequationisalsosimilartothe one
for spurgears butwith a slightmodificationaswell.
A factor of safetyof 2 wasusedfor the designof the gearsand pinions.All the gearsandpinions
had the same geometrical designexceptfortheirface width.The shaftswere designedusingthe max
shearstressformulaandthe geometrical preferenceswere researchedandborrowedfromprevious
designersbutalsomodifiedtoaccommodate the five proposedmaterials.The motorthatwas appliedto
the transmissionproduced425 hpat 5500 RPMand 406 lb-ftof torque.Thistranslatesto232 lbsof
force on the gear teethwithapitch line velocityof 2522. The overloadfactorforthe transmissionwas
assumedtobe 1.3 (lightshock) consideringthe qualityof modernbearingsandvibrationabsorption
material usedindesigntoday.
Figure 10: Pinionand1st
Gear Mesh for Analysis
21. Afterthe analysiswasinvestigated,the contactstressendedupbeingthe more sensitive
portionof the stressesonthe gears. The teethparticularlytookthe highestamountof stressasseenin
figures11 and 12. The piniontookthe highestloadandthe original geometricdesignhadto be modified
for use withthe twomaterialsSAE950x and CFRPbecause the factorof safetywasnot highenough.
Theirwidthhadto be increasedfrom2inchesto 3 inches.
Figure 12: X Y plane view of stresslocationsFigure 11: Isometricview of stresslocations
30. Material Selection
Withthe exceptionof the steel alloyXM023,the materialshave beenrankedbasedonafive
attribute meritanalysis.The attributesconsistof Density,Cost,Elasticity,YieldStress,andHardness.The
attribute of Machinability,thoughimportant,isan aspectof a material’sproductionwhichcanbe
factoredintothe Cost attribute.OtherattributessuchasWearResistance andDuctilityare also
importanthowever,similarlytoMachinability,WearResistance isabyproductof Hardnesswhile
Ductilityisgenerallydeterminedwithamaterial’sModulusof Elasticity.Importantattributesthatcould
not make the listsuchas Fatigue life are simplytoodifficulttoascertain.Eachof the five attributes
chosenforthe meritanalysiswere givenarankrangingfrom the mostimportant(5) to the least
important(1).The rankingfrom mostto leastimportantisas follows,YieldStress,Hardness,Cost,
Elasticity,andDensity.Thisinformationcanbe foundin table 10. The analysisyieldedthe highestvalue
for the steel alloy4340H at 73.76 percent,trailedby4720H at 35.89 percent.The pure steel alloy950X
came thirdwitha meritpercentat30.76 withCFRPfollowingata low 20 percent.Steel alloy4340H is
the clear material selectionwithitsprevailingBrinell Hardnessreaching363, a magnitude difference of
176 overitsnearestcontender,4720H. Withthe highestyieldstrengthat125 ksi,the 4340H material is
inferioronlyinthe ElasticityandCostwhichdue totheirrankingsdidn’taffect4340H’s outcome of being
the bestmaterial forthe gear set.It shouldbe notedhoweverthatthisoutcome mayhave changedif
the attributesof the steel alloyXM023 had beenmade available.
31. Conclusion
Thisreportdemonstratesanunderstandingof mechanical propertiesrequiredtoadequately
selectanappropriate material forthe BMW M4 sportscar poweredbya Getrag 7DCI700 Powershift7-
SpeedDual-ClutchTransmission.UsingTheoryfrommachine design,the designlimitsforhardnessand
yieldstrengthwere defined bythe equationsfortoothbendingandpittinginhelical gears.The results
fromthe meritanalysisconcluded thatSAE4340H has the correct combinationof propertiesrequiredto
preventthe gearfromfailing.Overallthisdesignreportwassuccessful inselectinganappropriate
material fora helical gearandallowedthe studentsanopportunitytouse the course material inareal-
worldscenario.
32. Nomenclature
Torque [ft·lbs] T
Horsepower hp
RotationsperMinute RPM, N
Rotational Velocity[rad/s] ω
InnerDiameter [in] di
OuterDiameter[in] do
InnerRadius[in] ri
OuterRadius[in] ro
Pressure Angle [degrees] φ
Helix Angle [degrees] ψ
Diametral Pitch [teeth/in] Pd
Face Width[in] F
TransmittedLoad[lbs] Wt
PitchLine Velocity[ft/min] vl
Factor of Safety Sf
OverloadFactor Ko
QualityClassof Gear Set Qv
Size Factor Ks
RimThicknessFactor KB
StressCycle Factor YN
Temperature factor KT
ReliabilityFactor KR
AllowableStress[psi] Sal
GeometryFactor J, I
PitchDiameter[in] d
DynamicFactor Kv
Load DistributionFactor Km
Stress[psi] σ
PoisonsRatio υ, μ
Young’sModulus[psi] E
ElasticCoefficient[(lb/in2
)0.5
] Cp
HardnessRatioFactor CH
Axial ContactRatio mF
Carbon C
Iron Fe
Manganese Mn
Phosphorus P
Silicone Si
Sulfur S
Chromium Cr
Molybdenum Mb
Nickel Ni
CarbonFiberReinforcedPlastic CFRP
