RacingWheelEngineering101
ByDavidSchardtandJimSchardt
OnethingistrueofeverycarthatcompetesinSCCA;theyallrideonwheels.
Whetherit’sanoriginalMorrisMinirollingon10-inchstampedsteelwheels,ora
Porsche911GT3RSwithcenter-lockcarbonfiber21s,weallusewheelsandwe
alltendtotakethemforgranted.Butjustasmuchengineeringgoesintoagood
setofracingwheelsasintoanyotherpartofthecar.
Racingwheelsmustmeetcertainbasicrequirements,andonlyafewoftheseare
well-understoodbytheaverageracer.First,aracingwheelmusthavethecorrect
rimwidth,offset,centerbore,lugboltpattern,andbrakeclearance.Thatmuch
weallknow.Butaracingwheelmustalsobedesignedtoperformforatleast3
raceseasonsor10,000racemileswithoutastructuralfailure.
Additionally,racingwheelsshouldalsomeetsomeextrarequirements,including
lightweight,highstiffness,resistancetocorrosion,cleanability,repairability,and
impactresistance.Ontopofallthat,we’dlikethemtobegood-lookingonthe
car,too.That’salottoask,butmostlywejustexpectittohappen.
TheLifeofaRacingWheel
Manyfactorscanaffectaracingwheel’sfunctionallife.Theaverageracingwheel
goesthroughfarmoresetsoftiresthanitsstreet-goingcousins,anditoperates
undermuchharsherconditions.Wheellifefactorsincludethebasematerialthe
wheelismadefrom,thetypeoftiresused,theweightofthecar,downforce
exertedonthewheels,andanydamagethatthewheelmaysuffer.Youalsohave
toallowfortheoccasionalmanufacturingormaterialsdefect.We’lllookateach
ofthesefactorsinorder.
BaseMaterial
Materialscurrentlyusedinracingwheelsincludecastaluminum,forged
aluminum,magnesium,andcarbonfiber.Ofcoursesteelisstillinuse,too,but
exceptinclasseslikeFormulaVee,steelhaslargelybeenreplacedwithalloysin
SCCAracing.
Wheelmaterialsareselectedforseveralimportantfactors:
• Strength–mustbestrongenoughtowithstandrequiredforces
• Elongation–highelongationallowsbendinginsteadofbreaking
• Fatigueresistance–mustwithstandmanycyclesathighstress
• Specificgravity–lowerdensityprovideslowerweightpervolume
• Rawmaterialcost–addstofinalprice
• Easeofmanufacturing–difficultmanufacturingaddstoprice
Figure1detailsthetradeoffsinherentindifferingwheelmaterials.Predictably,
wheelswithhighratingsinsomeareashavelessattractiveratingsinothers–
usuallyintheformofahighpriceformaterialslikecarbonfiber,forged
aluminum,ormagnesium.
Illustration1WheelMaterialComparison
Tensile Yield
Elongation Endurance Specific Cost
Strength Strength
limit*
gravity
psi
psi
%
6061ForgedAl
45,000 40,000
A356castAl/Flowform 29,000 24,000
AZ91T6castmag
40,000 22,000
Carbonfiber
200,000 200,000
Steel1015
60,000 40,000
psi
15
4
6
0
35
14,000
10,000
13,000
150,000
30,000
lbs/cuin $/lb
0.100
1.80
0.100
1.00
0.066
1.70
0.050 15.00
0.280
0.30
*Endurancelimit-materialwillnotfailupto100,000,000cyclesatthisstress
Easeof
manufacture
Easy=1
Difficult=10
6
3
4
10
3
Wheel
price
range
$
800-1500
100-500
1000+
2000-3000
25-75
Figure1WheelMaterialsComparison
ThematerialslistedinFigure1are6061forgedaluminum,A356castaluminum,
AZ91castmagnesium,carbonfiber,and1015steel.Tensileandyieldstrength
respectivelyrepresentthestressesinpoundspersquareinch(psi)thatwould
causebreakageorstarttodeformthematerial.Elongationdemonstratesthe
percentageofstretchthematerialwouldendurebeforebreaking.Anyofthese
materialswouldmakeasatisfactorywheel.However,certainmaterialswould
allowastronger,lighterwheel,butatahigherpricepoint.
Anadditionalwayoflookingatwheelmaterialsistodeterminewhenthematerial
willbreakatvariousstresses.Figure2andGraph2showtheexpectedlifecycles
ofvariousmaterialsatdifferentstresses.
LIFE
CYCLES
100,000,000
10,000,000
1,000,000
100,000
10,000
6061
Aluminum
STRESS
PSI
14000
17000
22000
29000
39000
356A
Cast
Aluminum
STRESS
PSI
10000
12000
15000
19000
24000
AZ91
Cast
Magnesium
STRESS
PSI
13,000
14000
16000
18500
21,000
Figure2LifeCyclesvsStress
50000
40000
30000
STRESSPSI
20000
10000
0
LOGSCALE
6061 LIFECYCLES356
AZ91
Graph2LifeCyclesvsStress
ThedataisobtainedbyusinganRRMoorerotatingbeamtestmachine,shownin
Figure3.Amaterialspecimenismachinedtoastandardsizeandplacedinthe
machinewherespecificstressesareapplied,andthenthepartisrotateduntilit
breaks.Thenumberofcyclescanthenbeplottedagainstthespecificstress
imposed.
Figure3–RRMooreRotatingBeamTest
TireStresses
Wheellifeisdirectlyrelatedtothestressoccurringfromsideforcesgeneratedby
tirefriction.Tirescanbeconsideredtofallintothreedifferentclassifications:
streettires,DOTracetires,andracingslicks.
Streettirescanhaveafrictioncoefficientfrom0.7to1.0dependingonthe
treadwearrating.Inthe1970sthetirefrictioncoefficientwasgenerallyinthe
rangeof0.7-0.8.However,today’shighperformancetirescanhaveamuchhigher
coefficientoffriction.TireRackperformedastudybetween2002and2010to
showthecurrentrelationshipbetweentreadwearandtirefrictioncoefficient.The
resultsaresummarizedinGraph4.
Graph4TireFrictionCoefficientandTreadwear
DOTracetiresareanotherstepupfromhighperformancetiresandhavea
coefficientoffrictioninthe1.2range.Raceslickscanhaveafrictioncoefficientof
1.5ormoredependingonconstruction,compound,carweight,andcarspeed.
Also,notethateventhoughthecoefficientmaybespecifiedasonly1.5bythe
manufacturer,carswithdownforcewillhaveanapparentcoefficientwellabove
1.5.
CarWeightandDownforceStresses
Loadsonthewheelcansignificantlyreducethelifeofawheel.Therearetwo
majorloadstoconsider:Staticloadmeasuredwiththecaratrestanddownforce
loadfromwingsorbodyshape.
Thestaticloadonawheelisnormally1/2theaxleweightattheheaviestendof
thecar.Ontheotherhand,downforceloadmustbemeasuredwithonboard
sensorsorusingmanufacturer’sdatabecausedownforceiscreatedonlywhen
thecarismoving.
Staticanddownforceloadswillhavethegreatestinfluenceonwheellifebecause
bothloadscombinewiththetirefrictiontoproducethetotalsideforce.Thething
torememberisthatadding10%moreloadonthewheelwillcutthewheellifeby
50%.
WheelDefectsandDamage
Anydefectinthewheelmaterialcancreateapointofcrackpropagation.Porosity
inthematerialassmallas0.010inchcancreateanearlyfatiguecrackifitis
locatedinahighstressarea.Adentof.040inchinacriticalareacancutthe
fatiguelifeinhalf.Awell-manufacturedwheelattemptstoreducetheseeffects
byusinglowporositymaterials,removingsharpedges,andbyapplyingan
additionalsafetyfactorindesign.
Obviously,problemscanoccurifthewheelissubjectedtomanyhighforcecurb
orspeedbumpimpacts.Eventhoughthewheelmanynotsustainvisibledamage,
thehigherthannormalstressfromafewhundredimpactswillreducethewheel
life.
DeterminingtheLoadRatingofaWheel
Thestandardprocedurefordeterminingtheloadratingofawheelistousethe
SocietyofAutomotiveEngineers(SAE)formulafromspecificationJ2530.
AlternateproceduresusedaretheJapaneseJWLandGermanTUV,butallof
theseusethesameformula.
First,thefollowingformulaisusedtocalculatethesideforcesthatwillbeseenon
thewheel:
S=L[(R*u)+d]/12
Inthisformula,Sisthenumberoffoot-poundsofforceontheaxle.
Listhetotalloadonwheelincludingstaticanddownforceinpounds.
Ristheradiusofthetireininches.
uisthecoefficientoffriction.
distheoffsetofthewheelininches.
Ifawheelistobeexpectedtohavealifeof10millioncyclesunderhard
cornering,thenthestressatanypointinthewheelcannotexceedthestress
showninFigure3for10millioncycles.Inthecaseofforged6061,thiswouldbe
17,000psi.
Finiteelementanalysiscanbeusedonthewheeldesigntodetermineifthestress
wouldexceedthelimit.AtypicalfiniteelementanalysisisshowninFigure4.
Figure4FiniteElementAnalysis
Buttoverifytheresult,thewheelmustundergoanactualfatiguetesttoconfirm
thatthewheelwillnotfail.
ThisanalysisisperformedwiththeRotaryorCorneringfatiguetestanditismost
importantsincethehigheststressesoccurduringcornering.Inthistest,thewheel
isrotatedathighspeedwhileanappropriatestressloadisappliedtotheaxle.But
sinceitisnotfeasibletorunatestfor10millioncycles,anacceleratedtestis
used.Using356aluminumasanexample,inGraph2itcanbeseenthatifa
materiallasts10millioncyclesat12,000psi,itonlylasts100,000cyclesat19,200
psi.So19200/12000=1.6andthefatiguetestisrunapplying1.6timesthestress
(S).Ifthewheelpasses100,000cycles,thenitwouldlast10millioncyclesat
stressduringuse.
Twoadditionaltestsarecommonlyruntoverifyotherstructuralcapabilities.
IntheRadialfatiguetestawheel,withatiremounted,issubjectedtotwicethe
normalstraightrollingloadforoveramillioncycles.Thistestwillgenerallycreate
cracksinthetirebeadseatareaifinadequatelydesigned.
TheImpacttest,withtiremounted,isperformedbydroppingaweightonthe
edgeoftherim.Thewheelshouldnotdeformorcracktothepointofairloss.In
thecaseofawheelratedfor1300pounds,aweightof535poundswouldbe
droppedfrom9inches.
EffectofRacingTiresandDownforceonLoadRatings
Sofar,ourdiscussionondeterminingloadratingshasusedtheformulaforwheels
asusedonthestreet.Tireswithalowcoefficientoffrictionandnodownforce
havebeenassumed.
AllloadratingsplacedonOEMoraftermarketwheelsusetheSAEformulawitha
coefficientof0.7andnodownforce.TheSAEformulaisdesignedforstreet
wheelsandwasdevelopedover50yearsagowhentirefrictionwascloserto0.7.
However,formodernandracingtirestheformulashouldbeadjustedforhigher
frictionandaddedweightfromdownforce.Ifthesearenotconsidered,thestress
actuallyplacedonawheelcangreatlyexceedthedesignstress.
ItshouldbenotedthatGraph2showsthatinthecaseofaluminum,increasing
theload(stress)by10-12%willdecreasewheellifeby50%.WhenstressonA356
aluminumisincreasedfrom15,000psito16,500psi,wheellifedropsfrom
1,000,000to500,000cycles.For6061Aluminumthestresschangefrom22,000
psito24,500psialsocutswheellifeinhalf.
Foranexample,considerawheelthathasa1,300-poundloadrating,whichis
verycommononaftermarketwheels.Theallowabledesignstressofthewheel
canbecalculatedusingtheSAEformula,30-inchODtire,and2-inchoffset.
S=1300[(15)*(0.7)+2]/12=1354foot-pounds
Thisisthemaximumstressthiswheelcouldendureformanycyclesat0.7G.
Toseehowtiresaffecttheloadrating,considerchangingthetirestoracetires.
Thenewfrictioncoefficientof1.5substitutedintheequationyieldsanadjusted
loadrating.
1354=W[(15)*(1.5)+2]/12W=663pounds
Similarcalculationsareusedtodevelopthetablebelowshowingtheeffecton
loadratingofawheelratedfor1300pounds,30-inchODtire,and2-inchoffset.
Fora1300poundload-ratedwheel
G
Application
force
psi
u
Stress Adjustedloadrating
withoutdownforce
SAESTREETRATINGatWearrating550+
0.7 1354
1300
AUTOCROSSatWearrating100-200
1 1842
956
DOTRACETIRES
1.2 2167
812
GTRACETIRES
1.5 2654
663
PROTOTYPESandhighdownforce
2.5 4279
411
Illustration5WheelLoadRatingAdjustmentsduetoApplication
Adjustedloadrating
with100pounds
downforce
1200
856
712
563
NA
Notethatatthehigherfriction,thestressonthewheelincreasesdramatically
andtheloadcarryingcapacityisdiminished.Usingracingslickswoulddropthe
loadratingonawheelby50%.Ifthewheelwasusedona3,000-poundcarwith
50/50weightdistributionandDOTracetires,the1,300-poundratingwouldbe
sufficient.However,thesamewheelwithracingslickswouldnotbeacceptable
becausetheloadratingwouldbereducedto663pounds.
Additionally,shouldthesamewheelbeusedonacargenerating100poundsof
downforceperwheel,another100poundswouldneedtobedeductedfromthe
loadrating.
Adjustingtheloadratingofwheelsshouldbeahighpriorityforanyoneusinghigh
performancetiresforautocross,racing,ortrackevents.
Toassistcustomersinselectingtheproperwheelandtirecombination,ForgeLine
adoptedaprogramin2007tolabeleachwheelwithmultipleloadratingsthat
dependonthetypetireused.Figure6showstypicalloadratinglabelsforfour
differenttypesofwheelswithloadratingsdependentondesignanduse.
Figure6LoadRatingTags
Althoughthestreetratingonthelabelisshownineachcase,therealloadrating
thatdependsontypeoftirebeingusedisalsolisted.ForgeLinewheelsaremade
instreetratingsfrom1,300upto2,100poundsinordertoprovidearangeof
wheelstoprovidethenecessarywheellifeforlightcarsuptoheavycars.Inthe
caseofhighdownforce,evenhigherloadratedwheelsaremade.
ApparentCoefficientofFrictionduetoDownforce
Whendownforceisaddedtotheequation,theapparentcoefficientoffriction
andsideforceonthewheelincreasesdramatically.
Forvehiclesgeneratingveryhighdownforce,thetirefrictionisstillintherangeof
1.5.However,onboarddataacquisitionwillrecordmuchhigherreadings.
ThereasonforthiscanbeseenbyrunningtheSAEformulawiththedownforce
addedtothestaticweightonthewheel.Undertheseconditions,thestress(S)is:
S=(W+D)*u
Foranexampleusinga3,000-poundcar,50/50weightdistribution,2,000pounds
ofdownforce,anduof1.5,thecalculationis:
S=(750+500)*1.5=1875foot-pounds
Toobtaintheapparentcoefficientoffriction,thestressisequaltothestatic
weighttimesthefrictionso:
1875=750*U
whereUistheapparentcoefficientoffriction.Theequationworksoutlikethis:
U=1875/750=2.5
Inactualconditions,ifdataacquisitionisusedtofindlateralGforces,thatforce
shouldbeusedalongwiththestaticweighttocalculatethesideforcestresson
thewheel.
WhatDoesThisAllMeantoYou?
Thisarticlehasprobablydeliveredmoremaththanyoueverexpectedtothink
aboutwithrespecttoyourracingwheels.Thebigtakeawayisthatwhenyouare
consideringanewsetofwheels,theweightofthewheelisnottheonlyfactor
youwanttoconsider.Ataminimum,youmusttakeintoaccounttheweightof
yourvehicle,thetypeoftiresbeingusedtomakesuretheloadratinglistedon
thewheelistrulyaccurateforyourneeds.Andifyouarerunningasubstantial
amountofdownforceyoumaywanttotakethatintoconsiderationaswell.Ifyou
alreadyhaveinvestedinwheels,youneedkeeptrackofhowoldyourwheelsare,
andhavetheminspectedeverytirechangeforsignsofwearandfatigue.Thecost
ofareplacementwheel,orevenawholesetofwheels,isfarlessthanthe
potentialcostofawheelbreakingontrack.
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