Bolt Preload-White Paper

Bolt Preload Theory and ApplicationBoltPreloadTheoryandApplication

withFemap andNXNastran

1 /152011 AllRightsReserved

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

2011 AllRightsReserved 22011 AllRightsReserved


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.



SettinguptheModelforBoltPreloading

Acommonapplicationofboltpreloadingistheconnectionofflangegeometries.Intheexamplebelow,asymmetricflangeisboltedtogetherwithfourbolts.Theboltsaremodeledusingbeamelementsandtheirendnodesareconnectedtothesolidmeshmodelusingrigidlinks.Thisidealizationisquitecommon.AllmodelsassociatedwiththiswhitepapercanbedownloadedfromthePredictiveEngineeringwebsite.

Contactisenforcedbetweenthetwopartsandaboltpreloadisappliedtothebeamelements.Ifthereaderisunfamiliarwiththistypeofmodeling,theyshouldtakealookatthePredictiveEngineeringwebsiteunderSeminarsandreviewourseminaronContactModeling.



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.



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.



ContactRegions

Forboltpreloadtowork,linearcontactmustbeenabled.Foradetailedexplanationofhowtodothis,seeourwebinarandwhitepaperonLinearContactAnalysis.

Shownbelowishowlinearcontactwassetupforthisexample.



ClassicBoltPreloadExample:Tension

Shownbelowarecontactpressureandboltaxialforceresultsfromthecurrentexampleundertensileloadingof100,000lbfwith aboltpreloadof50,000lbfperbolt.Thecontactpressureshowsthattheboltsarepullingtheflangestogethersincethetensileloadispullingthecenterofthestructureapart.Theboltsaxialforcesrangefrom62,827to62,837lbf orapproximately62,800lbf.Iftheboltpreloadis50,000lbf,isitcorrecttosaythatthisanalysisisaccurate?Beforeweanswerthisquestion,letslook atanotherload case using this modelloadcaseusingthismodel.



ClassicBoltPreloadExample:Bending

Abendingloadisappliedtothemodelandonesideofthecontactfaceisundercompressionwhiletheopposingsideseparates.Thesameboltpreloadof50,000lbfperboltwasapplied.Undertheseconditions,theboltaxialforceis50,113lbfonthesideundercompressionand84,410lbfonthesideundertension.Arethesereasonableresults?Theonlywaytoknowwhetherornotthesearelogicalresultsistounderstandabitofthetheoryunderlyingboltpreloadanalysis.



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.



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.



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.



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.



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.



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

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