Bolt Preload-White Paper
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Bolt Preload Theory and ApplicationBoltPreloadTheoryandApplication
withFemap andNXNastran
1 /152011 AllRightsReserved
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BoltPreloadTheoryandApplication
TableofContents
1. Introduction 3
2. SettinguptheModel 4
3. BoltRegions 5
4. DefiningaBoltPreload 6
5. ContactRegions 7
6 Classic Example of Bolt Preload 86. ClassicExampleofBoltPreload. 8
7. IdealizationofBoltPreloads... 10
8. BoltPreloadswithPlateModels.. 12
9. BoltPreloadsinSolidModels. 13
10. Summary.. 14
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BoltPreloadTheoryandApplication
Introduction
Whatisboltpreload?Boltpreloadisusedtoclamptogethertwoplatesortwostructuresandcreateafrictionallockbetweenthemembersandreducep p g ptheeffectsofcyclingloadingonthebolt.Withrespecttothelatter(i.e.,boltfatigue),boltpreloadcanmakeallthedifferencebetweenasafe,longlastingstructureorcatastrophicfailure.
Wheretouseboltpreload?Boltpreloadisnotafreelunch.ToeffectivelyuseboltpreloadonFEAconnectionsrequiresmanyadditionalstepsanditconvertsl l h l l l h ( ) h b l l d l d d h ( )alinearrunintoanonlinearrunthatrequirestwosequentialnonlinearanalysiswhere(i)theboltpreloadisappliedandthen (ii)
theexternalstructureloadisapplied.
Whatiscoveredinthiswhitepaper?Thiswhitepaperwillcoverathebasicsofsettingupyoumodelforboltpreload,theoreticalfoundation,examplesofitsuseandabolt fatigue primerboltfatigueprimer.
EngineeringComment:Boltpreloadaddsquiteabitofcomplexitytoanymodelsincetheanalysisprocedureisnonlinear(geometricallynonlinear)andthattwosequentialnonlinearrunsarerequiredtoarriveatthefinalboltpreloadsolution.Theutilityofthisapproachliesinitsabilitytoquantitativelycalculatetheboltaxialandshearforcesforanytypeofboltedconnection.Additionally,ifboltfatigueisimportant,thenaboltpreloadapproachisinvaluable.
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BoltPreloadTheoryandApplication
SettinguptheModelforBoltPreloading
Acommonapplicationofboltpreloadingistheconnectionofflangegeometries.Intheexamplebelow,asymmetricflangeisboltedtogetherwithfourbolts.Theboltsaremodeledusingbeamelementsandtheirendnodesareconnectedtothesolidmeshmodelusingrigidlinks.Thisidealizationisquitecommon.AllmodelsassociatedwiththiswhitepapercanbedownloadedfromthePredictiveEngineeringwebsite.
Contactisenforcedbetweenthetwopartsandaboltpreloadisappliedtothebeamelements.Ifthereaderisunfamiliarwiththistypeofmodeling,theyshouldtakealookatthePredictiveEngineeringwebsiteunderSeminarsandreviewourseminaronContactModeling.
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BoltPreloadTheoryandApplication
BoltRegions
BoltRegionsareuser definedregionsthatcanbedefinedusingeitherbarorbeamelements.DefiningBoltRegionsbeforeusingtheboltpreloadcommandisslower,butallowsyoutomoreeasilyname/labeleachregion,allowingyoutokeepyourmodelmoreorganized.CreatingBoltRegionsisalsousedforthespecialcaseswheneachofyourboltsaremadeupofmultiplebeam orbarelementsinseries.
DefiningaBoltRegion
TobegindefiningaBoltRegion,usetheBoltRegion command,foundeitherontheModelTreeunderConnections>Regions>BoltRegion orunderthefilemenuConnect>BoltRegion.ThiscommandbringsuptheBoltRegiondialoguebox.Sincewewillbedefining the Bolt Regions using FE mesh rather than geometry select the Element radio button under Defined By box If the boltdefiningtheBoltRegionsusingFEmeshratherthangeometry,selecttheElementradiobuttonunderDefinedBybox.Iftheboltconsistsofonlyoneelement,youcanselectthedesiredelementandclickOK.Iftheboltconsistsofmorethanoneelement, clicktheMultiple button;thisbringsupthestandardselectdialoguebox.PickalloftheelementsthatareapartofthebolttobeincludedintheBoltRegionandclickOK.Remember,eachBoltRegionshouldconsistofonlyonebolt.RepeatforeverydesiredBoltRegion.
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BoltPreloadTheoryandApplication
DefiningaBoltPreload
Itisnotneccessary tocreateaBoltRegionpriortoBoltPreloadapplication,butitisrecommendedformodelorganization.TheboltpreloadcommandcanbeaccessedbygoingtoModel>Load>Bolt Preload,orbyusingtheModelTree.ThisbringsuptheCreateBoltPreloaddialoguebox.Note:thevalueofthepreloadistheloadperbolt,notthetotalload.IftherearepreviouslydefinedBoltRegions,bothoptionswillbeavailableintheApplyTo box,ifBoltRegionshavenotbeendefined,onlytheElement(s)option will be availableoptionwillbeavailable.
IftheBoltRegion(s)radiobuttonisselectedintheApplyTo box,theEntitySelection SelectRegion(s) dialogueboxwillappear.PickeachoftheBoltRegionstheboltpreloadistobeappliedtodirectlyorusethemenutoselecttheregions.ClickOKwhendone.
IftheElement(s)optionisselected,theSelectElementsdialogueboxwillappear.Handpickeachofthebarorbeamelementstheboltpreloadistobeappliedto.ClickOKwhendone.Foreachelementselected,acorrespondingBoltRegionwillbeautomaticallycreated.
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BoltPreloadTheoryandApplication
ContactRegions
Forboltpreloadtowork,linearcontactmustbeenabled.Foradetailedexplanationofhowtodothis,seeourwebinarandwhitepaperonLinearContactAnalysis.
Shownbelowishowlinearcontactwassetupforthisexample.
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BoltPreloadTheoryandApplication
ClassicBoltPreloadExample:Tension
Shownbelowarecontactpressureandboltaxialforceresultsfromthecurrentexampleundertensileloadingof100,000lbfwith aboltpreloadof50,000lbfperbolt.Thecontactpressureshowsthattheboltsarepullingtheflangestogethersincethetensileloadispullingthecenterofthestructureapart.Theboltsaxialforcesrangefrom62,827to62,837lbf orapproximately62,800lbf.Iftheboltpreloadis50,000lbf,isitcorrecttosaythatthisanalysisisaccurate?Beforeweanswerthisquestion,letslook atanotherload case using this modelloadcaseusingthismodel.
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BoltPreloadTheoryandApplication
ClassicBoltPreloadExample:Bending
Abendingloadisappliedtothemodelandonesideofthecontactfaceisundercompressionwhiletheopposingsideseparates.Thesameboltpreloadof50,000lbfperboltwasapplied.Undertheseconditions,theboltaxialforceis50,113lbfonthesideundercompressionand84,410lbfonthesideundertension.Arethesereasonableresults?Theonlywaytoknowwhetherornotthesearelogicalresultsistounderstandabitofthetheoryunderlyingboltpreloadanalysis.
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BoltPreloadTheoryandApplication
IdealizationofBoltPreloads
Boltpreloadcanbeidealizedas:(MechanicalEngineeringDesign,Shigley,3rd Ed,1977)
l db lFb lfi llF
FkkPkF isb
bb ++=
*
stiffnessstructurekstiffnessboltkloadappliedexternallyPpreloadboltFboltonforceaxialtotalF
sb
ib
=====
Thisidealizationisonedimensionalandassumesuniformloadapplicationofbolt preload (Fi) and the applied load (P) The bolt stiffness is kb and theboltpreload(Fi)andtheappliedload(P).Theboltstiffnessiskbandthestiffnessoftheconnectedmembersisks.Toillustratethisequation,asimplebrickmodelwascreatedwithunitdimensions.Aboltwascreatedatthecenterwitha1unitcrosssectionalarea.ThematerialwasaluminumwithanE=1e7psi.Rigidlinksattheendsofthebeamkeepthetopandbottomsurfacesflat.Thismodelingidealizationwherethetopandbottomsurfacesmovetogetherwiththebeamends,satisfiesthedisplacementcontinuityasrequiredbytheaboveequation(seeShigley fordetails).
Giventhissimpleidealization,theboltstiffness(kb)isequaltoA*E/Lor1*1e7/2=5e6andthestructurestiffness(ks)isequalto1*1e7/2=5e6.Withab lt l d (Fi) 1 000 lbf d t ll li d l d (P) f 500 lbf thboltpreload(Fi)=1,000lbf andanexternallyappliedload(P)of500lbf,theequationwouldpredictatotalaxialforceonbolt(Fb)=*500+1,000=1,250lbf.Asshownontheright,thetotalaxialforceontheboltis1,250lbf.
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BoltPreloadTheoryandApplication
IdealizationofBoltPreloads
Thepriorequationisvalidaslongascompressionexistsbetweenthepreloadedparts.Iftheexternalloadcausesthepreloadedpartstoseparate,thenthetotalexternalloadiscarriedonlybythebolt.ThistippingpointcanbecalculatedusingthefollowingequationfromShigley:
partspreloadedbetweenforceFFkkPkF siss =+
=*
Iftheboltpreload(Fi)is1,000lbf,thentheclampedpartswouldseparatewhenFs=0.0.Theaboveequationcanthenberearrangedandtheexternalloadtonegatethepreloadwouldbe:
kk sb +
000,22000,1 ==+= PkkFP sbi
Ingeneralterms,ifyourboltpreloadisequalorgreaterthantheexternallyappliedload,thenthepreloadedpartswillstayclampedandfacilitatethejointstayinglocked.
000,22000,1Pk
FPs
i
j y g
Fromafatigueviewpoint,theimportanceofapreloadedjointcannotbeoverstatedduetoloweralternatingstressesintheboltandthatthejointstayslocked.Afatiguediscussionisgivenattheendofthiswhitepaper.
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BoltPreloadTheoryandApplication
BoltPreloadswithPlatemodels
Plateelementshavenothroughthicknessstiffness.Assuch,kmdoesnotexistandtheappliedloadhasnoeffectuptotheboltpreload.
Intheexampleshownbelow,ahalfsymmetricaltubeispreloadedthroughaboltatitscenter.Theboltismodeledwithabeamelement and two rigid links The bolt is given a preload of 1 000 lbf An external tensile load is given to our structure at 50 100elementandtworigidlinks.Theboltisgivenapreloadof1,000lbf.Anexternaltensileloadisgiventoourstructureat50,100,and150%oftheboltpreload.Theboltsaxialforceisthen1,000,1,000and1,500lbf,respectively.Theseresultsarecorrectalthoughonanengineeringbasis,areillogicalsinceweknowthatallstructureshavesomestiffness.
Akeypointofthisanalysisisthatwhenusingboltpreloadonplatestructures,thefinalboltloadwillalwaysbeunderestimatedornonconservative.
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BoltPreloadTheoryandApplication
BoltPreloadsinSolidModels
A3Dmodelwasconstructedusingbrickelements.Inthisexample,alltherelevantboltloadphysicsarecaptured.
Thesameexampleformatisfollowedwiththeexternallyappliedloadat50,100and150%oftheboltpreload.
The key point is that the bolt axial stiffness will always be a bit more than your preload and it should scale in a reasonableThekeypoint,isthattheboltaxialstiffnesswillalwaysbeabitmorethanyourpreload,anditshouldscaleinareasonablemanner. Inthiscase,theboltsaxialforceis1,038,1,285and1,542lbf.Withoutadirectcalculationofkbandks,areasonablemannerisopentointerpretation.Thisiswheregoodengineeringjudgmentmustbeapplied.
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BoltPreloadTheoryandApplication
SummaryofBoltPreloadTheory,ApplicationandFatigue
Boltpreloadtheorystates:
isb
bb Fkk
PkF ++
=*
Andassumesthattheboltpreloadandtheexternalloadactonthesamesectionofsolidmaterial.Thefinalaxialforceonapreloadedbolt(Fb)willbetheboltpreloadandthensomefractionoftheexternallyappliedload.
In plate models ks is infinite (it really doesnt exist since it is a plate). Hence, the applied load does not increase the bolt load
sb
Inplatemodelsks isinfinite(itreallydoesn texistsinceitisaplate).Hence,theappliedloaddoesnotincreasetheboltload(Fb)untilPexceedsFi.Thisunderpredictstheactualboltloadsinceallboltedstructureshavesomeboltedjointstiffness(km).
Inasolidmodel,boltpreloadfunctionsasonewouldexpectandthetotalboltaxialforcefollowsbolttheoryingeneralterms.However,careshouldbetakeninhowtheboltheadandnutaremodeledwithrigidlinkssincetheboltpreloadmechanismrequiresthatthestructuralmembersbecompressedunderneaththeboltheadornutforboltpreloadtofunctionasdesired.
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BoltPreloadTheoryandApplication
SummaryofBoltPreloadTheory,ApplicationandFatigue
Oneofthemainreasonsforapplyingboltpreloadistoavoidfatigueofthebolt.Thismaynotseemimmediatelyobviousafterthepriordiscussionsinceitwasshownthatthefinalboltloadisalwayshigherthantheinitialboltpreload.Thatis,the boltstressisalinearcombinationoftheboltpreloadandsomefractionoftheexternallyappliedload.But,theboltsalternatingstressisgreatlyreduced.Thisisthedominantadvantageofboltpreload.
LetsconsidertwofatiguecasesandevaluateboltlifeusingtheSoderberg equationforsimplicitywhere:
StressMeanStresseAlternativSyS
ma
m
e
a
==
=+
1
Inthisexample,wellassumethatanyexternalloadincreasestheboltpreloadby20%(seetheorysection).Herearetheparameters:BoltArea=1sqinBoltPreload=80,000lbfAlternatingStress(ExternallyAppliedLoad=100,000lbf thatcyclesfrom0.0).BoltStressEndurance(Se)=70,000psiBoltYieldStress(Sy)=140,000psi
Thequestionthatisposedisdoesboltpreloadhelporhurt?NoBoltPreload:
F il01071000,50000,50 >+
WithBoltPreload:
Fails0.107.1000,140,
000,70,
>=+
Passes
FF bb
01790000,90000,10000,100000,80000,100*2.0