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TheMechanics ofThreadedFasteners andBoltedJoints forEngineering andDesign ToshimichiFukuoka
ProfessorEmeritusatKobeUniversity, Kobe,Japan
Elsevier
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ISBN:978-0-323-95357-3
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2Fundamentalsofthreadedfasteners23
4.3Stressdistributionalongthreadroot
4.4Fatiguefailureofscrewthreads
4.5Evaluationmethodoffatiguestrengthofthreadedfasteners
4.6SeparationphenomenaofplateInterfaceandstress amplitude
4.7Stressamplitudealongthreadroot
4.8Improvementmeasuresoffatiguestrengthofthreaded fasteners
5Boltedjointsunderthermalload217
5.1Fundamentalsofthermalandmechanicalbehaviorsofbolted joints
5.2Evaluationmethodofamountofheattransferredthrough contactsurface
5.3Evaluationmethodofamountofheattransferredthrough asmallgap
5.4Thermalcontactcoefficientandapparentthermalcontact coefficientinboltedjoints
5.5Analysisofthermalandmechanicalbehaviorsofbolted jointsbyFEM
5.6Seizureofthreadedfasteners
6Looseningofthreadedfasteners247
6.1Rotationlooseningandnonrotationloosening
6.2Whyboltedjointsareeasytoloosen
6.3Boltforcereductionduetorotationloosening
6.4Boltforcereductionduetononrotationloosening
6.5Inspectionofbolttighteningstatebytorquemeasurement
7Thermalandmechanicalbehaviorsofpipeflangeconnections277
7.1Thermalandmechanicalbehaviorsinherenttopipeflange connections
7.2Gasketcompressioncharacteristicsandflangerotation
7.3Temperaturedependencyofgasketcompression
7.4Analysisofthermalandmechanicalbehaviorsinrunning conditionandduringshutdownoperation
7.5Thermalandmechanicalbehaviorsofpipeflangeconnections forlowtemperaturefluids
8Learningfromproblemsandaccidentswiththreaded fasteners291
8.1Introduction
8.2Fatiguefailureofwheelboltsforlargevehiclesspecified
8.3Fatiguefailureofthreadedportionofrollercoasteraxle
8.5Strengthandloadcapacityofreamerboltsusedforrigid flangedshaftcouplings
8.6Tighteningprocessofreamerboltbycooledfitting
8.7Sealingperformanceofoilsealplugsusedforhydraulic
8.8Modeanalysisofboltedjoints
Preface Threadedfasteners,typifiedbyboltsandnuts,arethemostwidelyandcommonly usedmachineelements,hence,theirexistenceisoftenforgotten.However,onceafailureorlooseningoccursinthreadedfasteners,thefunctionofmachinesandstructures clampedbythemmaybecompletelylost.Itcanbesaid,therefore,thattheprimary taskimposedontheengineersengagedinjobsrelatedtothreadedfastenersisthe designandassemblyofboltedjoints,sothattheyarenotbrokenorloosenedinthe tighteningprocessorinserviceconditions.
Thisbookintendstoprovidethewidevarietyofknowledgeandinformation requiredforengineersinchargeofthreadedfastenersandboltedjointstoattainsecure tightening,sufficientstrength,andnoloosening;andthesethreemajorissuesare explainedinaneasy-to-understandmannerforpracticaluse.Atthesametime,to maintainmechanicalstringency,corechaptersandsectionsarewrittenlargelybased onreliableresearchresultspublishedbyprominentacademicsocietiesasjournal papersorconferenceproceedings.
Thecontentsofthisbookcoveravarietyofjoblevels,rangingfromthebasic designofboltedjoints,suchasthedeterminationofthejointassemblyprocedure, tothesophisticateddesignandstrengthevaluationofboltedjointsbyuseofadvanced CAEtechnologies.Theproblemsthatthisbookiswrittentosolveforreadersareas follows:
l Selectionofanappropriatetighteningmethodandestablishmentofareliabletightening procedure.
l Understandingwhatthestaticandfatiguestrengthsofboltedjointsareandhowtheybehave.
l Evaluationmethodsofstaticandfatiguestrengthsofboltedjointsbysolidmechanics andFEM.
l EstablishmentofpreventionmethodsoffatiguefailuresbysolidmechanicsandFEM.
l Effectofhighandlowtemperaturethermalloadsonthestrengthofboltedjointsbytaking accountofthermalcontactresistanceattheinterface.
l Understandingthelooseningmechanismofthreadedfastenersbyclassifyingintorotation looseningandnonrotationloosening.
l Establishmentofthemethodtopreventormitigatethelooseningofthreadedfasteners.
l HowtoapplyadvancedCAEtechnologiestodesignboltedjointswithhighsafetyandevaluatetheirthermalandmechanicalbehaviors.
In Chapter1,abriefhistoryofscrewthreadsandtheprogressintherelevantresearch areasareintroduced,andthebasicsofthreadedfastenersandboltedjointsare explainedfromthegeometricalandmechanicalpointsofview.Theideaofthepressureconeisdiscussedindetail,becausethecontactpressuredistributionattheinterfacesignificantlyaffectstheinterfaceseparationthatleadstothefatiguefailureof boltedjoints.Thelastsectionprovidesanoutlineofthestrengthandthethermal
andmechanicalpropertiesoffastenermaterials,wherevariouspropertiesofengineeringmaterialscommonlyusedforthreadedfastenersaretabulatedwiththeirtemperaturedependency.
In Chapter2,inordertounderstandthefundamentalsofthreadedfasteners,the essentialcharacteristicsoftheirstrengthandstiffnessarediscussedindetail.Itis shownhowthetrueprofileofthecrosssectionofscrewthreadscanbeexpressed bymathematicalformulas,bywhichfiniteelementmodelsofboltedjointswithperfectgeometrycanbeconstructedinordertoperformnumericalanalysiswithhigh accuracy.Inaddition,asummaryoftheinterfacestiffnessandthermalcontactresistance,bothofwhichareprimarilyduetothemicroprojectionsexistingoncontactsurfaces,isgiventoconductfiniteelementanalysisbytakingaccountoftheconditionsof contactsurfacesexistinginboltedjoints.
In Chapter3,thetighteningmethodsofthreadedfastenersarediscussed—which representsthefirstproblemofboltedjoints.Thefourcommonlyusedmethods, i.e.,torquecontrolmethod,elasticanglecontrolmethod,directtensionmethod, andthermalexpansionmethod,areexplainedingreatdetailfromthepracticalpoint ofview.Thechapteralsocoversthetighteningprinciple,applicationrange,andtighteningguidelinesofeachmethod.Anewtighteningmethodthatcombinestorquecontrolmethodwithelasticanglecontrolmethodisproposed.Thiscanevaluatenut factor,whichrelatestighteningtorquetoboltforce,duringthetighteningoperation withhighaccuracy.Theproblemofelasticinteraction,whichoccursinthecaseof tighteningmultipleboltsonebyone,issolvedwithhelpofFEM,anditisshown howtoestimatetheboltforcescatterandobtaintheoptimaltighteningsequence.
In Chapter4,thestaticandfatiguestrengthsinherenttothreadedfastenersandboltedjointsaredealtwith—whichisthesecondproblemofboltedjoints.ThedistributionsofstressandstressamplitudealongthethreadrootareevaluatedbyFEanalysis usinghelicalthreadmodels.Itispointedoutthatboltedjointdiagrams,whichhave widelybeenusedforboltedjointdesign,havesomeessentialdefectsandareeffective onlyinlimitedconditions.Anotherimportantpointisthatthefatiguefailureofbolted jointsisgreatlyaffectedbytheinterfaceseparationbetweenfastenedplates.The fatiguestrengthcanprimarilybeimprovedbyraisingtheboltforce,whichissubstantiatedbycomprehensiveFEanalysis.Inaddition,variouspracticalmeasuresareintroducedtoenhancethefatiguestrengthofthreadedfastenersandboltedjoints.
In Chapter5,thermalandmechanicalbehaviorsofboltedjointsaredescribed basedonthetheoryofthermalstressandtheresultsofFEanalysis.Highandlowtemperaturethermalloadsoftencausethefailureorlooseningofthreadedfastenersand boltedjoints.Inordertoanalyzethephenomenawithhighaccuracy,itisexplained howtotakeaccountoftheeffectoftheheattransferredthroughcontactsurfacesand smallgapsusingthethermalcontactcoefficientandapparentthermalcontactcoefficient.Themechanismofseizureoccurrenceinthreadedfasteners,whichisanasty problemsometimesencounteredduringthetighteningoperation,isclarifiedbyusing thetheoryofheatconduction,anditspreventionmethodsareexplainedfromthetheoreticalpointofview.
In Chapter6,looseningofthreadedfasteners,whichisthethirdproblemofbolted joints,isdiscussedbyclassifyingthelooseningmechanismintorotationlooseningand
nonrotationloosening.Asfortheformer,thelooseningmechanismisanalyzedin detailbyfiniteelementsimulation.Hence,itisshownthattheslipoccurrenceon thenut-orbolthead-bearingsurfaceisadecisivefactor.Incontrast,nonrotationlooseninginevitablyoccurstosomeextent.Therefore,itisexplainedhowtoestimatethe boltforcereductionbyuseofaboltedjointdiagram.Inaddition,practicalcountermeasuresareintroducedthatareeffectiveinpreventingrotationlooseningandmitigatingnonrotationlooseningforvarioustypesofboltedjoints.Inthelastsection, theinspectionmethodsofboltedjointintegritybytorquemeasurementarediscussed.
In Chapter7,thermalandmechanicalbehaviorsofpipeflangeconnectionsare expoundedbyconductingexperimentsandfiniteelementanalysis,aimingat preventingtheleakageofcontainedfluidsathighorlowtemperature.NumericalanalysisbyFEMandexperimentsquantitativelyclarifyhowmuchboltforceisreducedin therunningconditionandduringtheshutdownoperationofpipelines.Itisshownthat themechanicalbehaviorofgaskets,thestiffnessofwhichismuchlowerthanthatof metalgaskets,istheprimaryinfluencingfactoronleakage.Oneofthemostimportant issuesstatedhereisthatthestiffnessofsheetgasketsandspiralwoundgasketsissignificantlyreducedatelevatedtemperatureandthiscausesboltforcereductionleading totheleakageofcontainedfluids.
In Chapter8,aimingatprovidingeffectivehintstosolvevariouson-siteproblems concerningthreadedfastenersandboltedjoints,severalproblemsandaccidentsthat actuallyhappenedinthepastarediscussedbasedonrigorousresearchresults.This coverswheelfalling-offaccidentsoflargevehicles,theruptureofthethreadedportion ofarollercoasteraxle,fatiguefailuresofreamerboltsusedforrigidflangedshaft couplings,etc.Alsotreatedishowmuchthenaturalfrequenciesofboltedjoints areincreasedwithincreasingboltforce.Inthelastsection,inordertoperformfinite elementanalysiseffectively,someconcretemeshpatternsandsimplifiedmodelsof engagedthreadportionsareshown,andafewpracticalstrategiestoimprovethecomputationalefficiencyarepresentedbyutilizingthegeometricsymmetryofbolted joints.
Theauthorwouldliketoexpresshissincereappreciationtothreedistinguished professors,i.e.,thelateProf.MinoruHamada,Prof.HiroshiKitagawa,andProf. NoboruKikuchi.Prof.Hamadaenthusiasticallysupervisedtheauthor’sPhDthesis onthemechanicalbehaviorofboltedjointsandProf.Kitagawaledtheauthorto theworldofnumericalanalysisatOsakaUniversity.Prof.Kikuchimotivatedthe authortoapplythelatesttheoriesofcomputationalmechanicstoboltedjointsat TheUniversityofMichigan.Theauthorwouldalsoliketoexpressspecialthanks tohismanyex-studentsfortheircooperationinachievingtheresearchresultsforming thebasisofthisbook.Finally,theauthorwouldliketogivethedeepestappreciationto hiswifeNorikoforherprovidingacomfortableenvironmentover40yearstosupport hisresearchactivity.
ToshimichiFukuoka
Listofsymbols A boltcylindricalarea,othercross-sectionalareas
A1, A2, A3 truecross-sectionalareasofscrewthread
AI, AII cross-sectionalareasofstraightbar
Aap, Are apparentcontactareaandrealcontactarea
Acn contactarea
Ae truecross-sectionalareaofmalethread
Aex, Ain cross-sectionalareasofmaleandfemalethreads
Af cross-sectionalareaoffastenedplates
Afk contactareaonthreadsurface
Ains truecross-sectionalareainsidefemalethread
An nut-bearingsurfacearea
Ar cross-sectionalareaatthreadroot
As stressareaofscrewthread
a, b innerandouterradiiofhollowbolt,hollowcylinderandhollowshaft
a1, a2 constantsforrepresentingloaddistributions
ap radiusofcontactareaofmicroprojection
B meandiameterofhexagonboltheadorhexagonnut
Bp diameterofboltpitchcircle
b1, b2 constantsfordeterminingapproachofinterface
C1–C5, C1n, C2n constantsforrepresentingtruecross-sectionalareas
c, c1, c2, c3 constants
co, mo constantsintheOstrovskyequation
csp specificheat
D, D1, D2 major,minor,andpitchdiametersoffemalethread
Do outerdiameteroffastenedplates
d nominaldiameter,majordiameterofmalethread,diameterofroundbar
d1, d2 minorandpitchdiametersofmalethread
dbt equivalentdiameterofbottomingtorque
dc diameterofprojectionpartofbottomingstud de truepitchdiameter
dh boltholediameter
dhd equivalentfrictiondiameterofbolthead-bearingsurface
dnu equivalentfrictiondiameterofnut-bearingsurface
dr threadrootdiameter
drm diameterofreamerbolt
ds diameterofstressarea
E, EI, EII Young’smodulus
Eb, Ef Young’smoduliofbolt-nutandfastenedplates
Eex, Ein Young’smoduliofmaleandfemalethreads
e widthacrosscornerofhexagon
F axialforceactingalongboltaxis
F02 boltforcecorrespondingto0.2%proofstress
Fb axialboltforce,boltpreload
Fb0 axialboltforceforthecasewithoutinclinationatbearingsurface
Fb1, Fb2, Fb3
axialboltforcesofmultiboltedjoints
Fbi initialboltforce
Fbt compressionforcegeneratedbybottomingtorque
Fc reductionofcompressionforceinfastenedplatesduetoexternalforce
Fcn compressionforceactingonbottomsurfaceofbolthole
Ff objectiveboltforceintighteningoperationbyhydraulictensioner
Fi initialboltforceofbolt i,normalforceactingonbolt i
FiN, Fiμ bearingforceandfrictionforcesustainedbybolt i
Finn Fout boltforcesgeneratedininner-wheelandouter-wheeltighteningprocesses
Fn normalforceactingoncontactsurface
Fnu, Fhd, Fpl frictionforcesactingonjointcontactsurfaces
Fo, f1, f2 axialforcesgeneratedwhentighteningouternut
Frm1, Frm2 normalforcesactingonreamersurface
Fs shearforce,shearload
Fslp criticalshearloadcorrespondingtowholeslip
Ft initialtensionappliedbyhydraulictensioner
Fth axialforcegeneratedinengagedthreadsofbottomingstud
Fz boltforcereductionduetoembedment
f naturalfrequencyofbendingvibration
H heightoffundamentaltriangle
H1 threadoverlap
Hnu thicknessofnut
HV, HV1, HV2 Vickershardness
h platethickness,beamheight
hc thermalcontactcoefficient
hcv coefficientofconvectionheattransfer
he apparentthermalcontactcoefficient
hr coefficientofradiationheattransfer
I secondmomentofarea
i numberofthreads,boltnumber,orderofvibrationmode
K nutfactor
K restraintcoefficient
[K],[M] stiffnessmatrixandmassmatrix
Kcn, Kth, Knu, springconstantsrepresentinginterfacestiffness
Khd, Kf
Kinn, Kout nutfactorsininner-wheelandouter-wheeltighteningprocesses
Ktru truenutfactor
k springconstant,springconstantofstraightbar
kA, kB springconstantsofplateandthinhollowcylinder
kb springconstantofbolt-nutconnection
kbm, kplc, kple springconstantsofjointedcomponentsundershearload
kcyl springconstantofboltcylindricalportion
kex, kin springconstantsperoneridgeofmalethreadandfemalethread
kf, kf∗ springconstantsoffastenedplates
kn, kt springconstantsrepresentinginterfacestiffness
ks springconstantofunengagedthreads
kpt springconstantoffastenedplatesundertension
kth springconstantofengagedthreads
ktotal springconstantofentireboltedjoint
L leadofscrewthread,lengthofstraightbar
L1, L2, La lengthsofjointedpartsundereccentricexternalforce
Lcyl lengthofboltcylindricalportion
Lex lengthofprotrusionaddedtojointendportion
Lf griplength
Lfk lengthofhelix
Lhd equivalentlengthofbolthead
Ls lengthofunengagedthreads
Lth equivalentlengthofengagedthreads
m parallelrownumberofmultiboltedjoint
mh, nh constantsinequationforevaluatingthermalcontactcoefficient
N numberofrepeatedexternalforce,numberofmicroprojections
Nu Nusseltnumber
n numberofbolts,perpendicularrownumberofmultiboltedjoint,matingnode numbersatinterface
np divisionnumberofone-pitchhelicalmodelinaxialdirection
P threadpitch
pm plasticflowstressofmaterial
pn contactpressureatinterface
pnu contactpressureonnut-bearingsurface
Pr Prandtlnumber
pt stressintangentialdirection
Qth, Qshk, amountsofheatflowingthrougheachpartofboltedjoint
Qhd, Qf
Qtotal totalamountofheatflowingthroughboltedjoint
q heatflux
R, S constantsinBach’sequation
{R} loadvector
Ra1, Ra2 arithmeticmeanroughnessofmatingsurfaces
Rat sumofarithmeticmeanroughnessofmatingsurfaces
Rcn thermalcontactresistance
Re Reynoldsnumber
Ri shearload-bearingratioofbolt i
RiN, Riμ shearload-bearingratiosbybearingforceandfrictionforce
Rrm, Rμ shearforcetransferratiosbyreamersurfaceandfrictionforce
Rz, Rz1, Rz2 maximumheightroughness
Rzt sumofmaximumheightroughnessofmatingsurfaces
r, r1, r2 radialcoordinates
ri radialcoordinateofnode
s widthacrossflatofhexagon
T temperature,torque
T1, T2 threadtorqueandnut-bearingtorque
Tb, Tf bolttemperatureandtemperatureoffastenedplates
Tbt bottomingtorque
Te temperaturedifferencebetweenmatingsurfaces
Tinn, Tout tighteningtorquesofinnernutandouternut
Tl looseningtorque
Tl1, Tlbt looseningtorquesofbottomingstud
Trt re-tighteningtorque
Tsng snugtorqueinelasticanglecontrolmethod
Tst secondtighteningtorque
Tt tighteningtorque
U strainenergy
Uf circumferentialforceactingonthreadsurface
u displacement,axialdisplacementofstraightbar
u fg, u fg displacementvector,accelerationvector
u uniformdisplacementappliedtoboltcylindricalportion
uhd , unu meandisplacementsunderbolthead-andnut-bearingsurfaces
ui nodaldisplacement
uslp criticaldisplacementcorrespondingtowholeslip
uup , udw uniformdisplacementsappliedtoboltcylindricalportion
V amountofvolumepushedawaybynut-bearingsurface
v slidingspeed
W externalforce
Wtrq, Wth, Wnu tighteningenergy
wfk contactwidthbetweenmaleandfemalethreads
Z embedmentfactor
z axialcoordinate
α threadangle,stressconcentrationfactor
α1 flankangle
α1 0 flankangleintheplaneperpendiculartohelix
αΙ –αIV stressconcentrationfactorsofplateswithsemicircularnotch
αb, αf coefficientsoflinearexpansionofbolt-nutandfastenedplates
αex, αexI, αexII coefficientsoflinearexpansion
β leadangle,notchfactor
γ effectivetensilecoefficient
γ c contactratio
ΔFb variationofboltforce
Δri averagewidthbetweennodes
ΔT, ΔTI, ΔTII temperaturechangeortemperaturedifference
ΔTb, ΔTf temperaturechangesofboltandfastenedplates
ΔTe temperaturedifferencebetweenmatingsurfaces
ΔTm meantemperatureincreaseofmicroprojection
Δσ b variationofaxialboltstress
Δσ f variationofcompressionstressoffastenedplates
Δσ rm boltstressreductionperunittemperaturedifference
Δϕ returnrotationangleofnut
δ boltelongation,amountofthermalexpansionorshrinkage
δair gapsizeofairlayer
δb elongationofbolt-nutconnection
δc fitofreamerbolt
δf shrinkageoffastenedplates
δpl clearanceatbearingsurfaceofoilsealplug
δz amountofembedment
εp plasticstrain
ζ approachofinterface
ζ max maximumvalueofapproachofinterface
ζ t displacementintangentialdirectionduetointerfacestiffness
ζ th, ζ nu, ζ hd, ζ f approachesofinterfaceateachjointinterface
η boltforcegeneratedperunitnutrotationangle,notchsensitivityfactor
η3, η4 efficienciesoftriangularandsquarescrewthreads
θ angle,circumferentialcoordinate
θ1–θ6 anglesspecifyingthreadgeometry
θcn pressureconeangle
θhd inclinationangleofbolthead-bearingsurface
θnu, θtp inclinationangleofnut-bearingsurface
λ, λ1, λ2 thermalconductivity
λair thermalconductivityofair
λi Eigenvalueof ithmode
μ, μr, μθ coefficientoffriction
μhd coefficientoffrictiononbolthead-bearingsurface
μith, μinu coefficientsoffrictionininner-wheeltighteningprocess
μoth, μonu coefficientsoffrictioninouter-wheeltighteningprocess
μth, μnu coefficientsoffrictiononthread-andnut-bearingsurfaces
ν Poisson’sratio
ρ rootradius,threadrootradius
ρdn density
ρmax, ρnmax upperlimitsof ρ and ρn
ρn radiusoffemalethreadroot
ρth, ρth 0 frictionanglesofthreadsurfaceforsquareandtriangularthreads
σ stress,truestress,thermalstress,standarddeviation
σ vonMisesstress
σ 1, σ 2, σ 3 threecomponentsofprincipalstress
σ I, σ II thermalstressesgeneratedinbarIandbarII
σ a stressamplitude
σ B tensilestrength
σ b axialboltstress
σ bi initialboltstress
σ bnd bendingstressgeneratedinbolt
σ IN, σ OUT axialstressesonboltcylindricalsurfaceinradialdirection
σ L, σ R axialstressesonboltcylindricalsurfaceincircumferentialdirection
σ max maximumstressoccurringatnotchroot
σ max maximumvonMisesstress
σ n meanstressatnotchedcrosssection
σ r meanstressatthreadroot
σ th tensilestressofboltthreadedportion
σ Y yieldstress
σ w fatiguelimit
σ wo fatiguelimitofsmoothedtestspecimen
σ z axialstress
τ shearstress
τth shearstressofboltthreadedportionduetothreadtorque
τw fatiguelimitofshearstress
ϕ nutrotationangle
ϕu loadfactor
Threadstandardsandforms 1.1Briefhistoryofscrewthreadsandrelevant researchactivities Itissometimessuggestedthattheoriginofscrewthreadstracesbacktothe“screw pump”inventedbyAristotlebeforetheCommonEra,afterwhich,large-sizedwooden powerscrews,suchasthescrew-typemechanicalpress,cametobeused.Then,metal screwsappearedinthe16thcentury.Itwasin1543thatscrewthreadswerefirstintroducedintoJapanalongwiththearrivalofguns.Ithasbeenreportedthatgunsmithsof thedaystruggledtoprocessthescrewthreadsofthetailplugs.
IntheIndustrialRevolutionerainthe19thcentury,MaudslayintheUnitedKingdomsucceededinthemanufacturingofscrewthreadswithamodernprocessing methodusinglathes.Clement,whoworkedinMaudslay’sfactory,devisedatapthat couldformfemalethreadsbyacuttingoperation.Whitworth,whowasoncean apprenticeofMaudslay,iscalledthefatherofmodernscrewthreadsbecauseheproposedascrewstandardforthefirsttimein1841,theearlystageoftheIndustrialRevolution.Threadcuttinglathes,inventedinthosedays,hadalmostthesamestructureas thepresentones,whichenabledthemassproductionofpowerscrewsandfastening screws.Athreadrollingdevicewasdesignedin1851byBroomannintheUnited Kingdom,andthenthePWCorporationinGermanymanufacturedthreadrolling machinesin1938thathadasimilarstructuretothepresentones.Detailedhistory onscrewthreadsisavailablein [1,2],forinstance.
Theprimarypurposeofthisbookistoexplainthemechanicsofthreadedfasteners assimplyaspossible,aimingattheprovisionofanefficientdesignmethodforbolted jointswithahighlevelofsafety.Inthefollowing,abriefreviewismadeofhow researchonscrewthreadsprogressed,whichbuiltthefoundationofthecurrent designmethod.
Themaincauseofthefailureofscrewthreadsismetalfatigue.Thestudyofmetal fatiguewasstartedaround1860byWohler,whoisfamousfordevelopingtheS-N curve.ResearchonthefatiguestrengthoffasteningscrewswasbegunbyThumin the1930s.Theideaofaboltedjointdiagram,whichiswidelyusedtodaytoevaluate thefatiguestrengthofthreadedfasteners,firstappearedinthebookwrittenbyRotcher [3].Heproposedtheideaofapressureconewithrespecttotheareaattheinterface composedofclampedplates,overwhichcontactpressureisexertedduetoboltforce. Goodier,whoisthecoauthorofthehistoricalmasterpiecethe“TheoryofElasticity” writtenbyTimoshenko,evaluatedtheparticularloaddistributionpatternalongthe engagedthreadsofabolt-nutconnection.Hesucceededintheevaluationbyapplying thetheoryofelasticitytothedisplacementsmeasuredontheoutersurfaceofthenut [4].Sopwithfurtherdevelopedthestudyofscrewthreadsbymeansofthetheoryof elasticity,andheproposednutshapesthatcouldimprovetheloaddistributionpattern alongtheengagedthreads [5].
TheMechanicsofThreadedFastenersandBoltedJointsforEngineeringandDesign. https://doi.org/10.1016/B978-0-323-95357-3.00002-2 Copyright © 2023ElsevierInc.Allrightsreserved.
2TheMechanicsofThreadedFastenersandBoltedJointsforEngineeringandDesign
InJapan,somenoteworthystudieswerepublishedinthe1970s.Sawaetal.clarified variousmechanicalbehaviorsofboltedjoints,suchastheamountsofequivalentlengths ofengagedthreadsandboltheadthatrepresentthestiffnessofabolt-nutconnection,by applyingthethree-dimensionaltheoryofelasticityinasophisticatedmanner [6].Using complexstressfunctions,Otakianalyzedhowgeometricfactors,suchasnominaldiameterandthreadpitch,affectthestressconcentrationatthethreadroot [7] andthefatigue strength [8].Asapioneeringstudybynumericalanalysis,Maruyamaevaluatedthe stressconcentrationfactoratthethreadroot [9],inwhichapoint-matchingmethod wasincorporatedintotheFEM(finiteelementmethod)whenmodelingthegeometry ofengagedthreads.Bretletal.calculatedtheloaddistributionalongengagedthreadsby replacingtheengagedthreadswithastackoflayeredfiniteelements [10].Milleretal. proposedasimplemethodusingspringelements,whicharediscussedlaterinthisbook, forcalculatingtheloaddistributionalongengagedthreads [11].Tanakaetal.proposeda finiteelementapproachthatcouldsolvecontactproblemsandanalyzedvarious mechanicalpropertiesofboltedjoints [12],andtheyalsocalculatedtheloaddistributionalongengagedthreadsinaningeniouswaybymeansofspringelements [13].
Asforexperimentalstudiesthatevaluatedthestressdistributioninaboltedjoint,a seriesofresearchesbyHetenyithroughphoto-elasticexperiments [14] areworthyof specialmention,inwhichtheresearcherrevealedthespecificloaddistributionsalong engagedthreadsinspecialnutswithvariousconfigurations.Itcanbesaidthathis researchachievementswerethestartingpointofalotofcontrivancesfoundthereafter invarious-shapednuts,aimingatsmoothingtheloaddistributionalongengaged threadsandmitigatingthestressconcentrationatthethreadroot.Stressconcentrations atthethreadrootofactualbolt-nutconnectionsweresuccessfullymeasuredbythe copperplatingmethod.MaruyamacomparedthemeasuredresultstothestressconcentrationfactorsobtainedbyFEM [9,15].Seikaetal.obtainedthemagnitudeand locationofthemaximumstress [16] usingthesameexperimentalmethod.Theyconcludedthatitoccurredatthemalethreadroot2/3pitchapartfromthenut-bearing surface.
Thejointedportionsfastenedbyuseofscrewthreadsaregenerallycalledabolted joint.Inthisbook,therefore,thecomponentsclampedbyvariouskindsofthreaded fastenersarereferredtoasboltedjoints.Basicformsandtheusagesofscrewthreads havebeenfundamentallyunchangedsincetheIndustrialRevolution.Nevertheless, threadedfastenersandboltedjointshavecontinuouslybeenimportantresearch objectsinthemechanicalengineeringfield.Thebiggestreasonisthattheexternal loadsexertedonboltedjointsarecontinuouslybeingincreased!
1.2Geometryandapplicationpurposesofscrewthreads Screwthreadsareroughlyclassifiedintotwotypes,whichareusedforclampingand movementtransmission,respectively.Mostthreadedfastenerssuchasboltsandnuts arebasicallyusedforclampinganumberofpartscomposingmachinesandstructures. Ontheotherhand,screwthreadsusedformovementtransmissiondelivervarious movementsbyutilizingtheirhelicalshape.Theyarefurthercategorizedintotwo
types.Oneisusedforgeneratinglargeforcesbymakinguseoftheactionofthethread asaninclinedplane,e.g.,ajackforliftingheavyparts;theotherfacilitatestheconversionbetweenlinearandrotationalmotions,e.g.,feedscrewsbuiltintomachine tools.Asasimilarexample,amicrometerprovidesadimensionalaccuracyof 10 μm,inwhichalargerotationangleisconvertedintoasmalllinearmovement.A certaintypeofmicrometerequippedwithadigitaldisplaydeviceprovideshigheraccuracyof1 μm.
Fig.1.1 showsscrewthreadsofvariousforms.Triangularscrewthreadsarethe mostcommonlyusedwhenclampingmultipleparts.Ontheotherhand,trapezoidal screwthreadsareusedformotionandpowertransmission.Thesetypesofscrew threadsareoftencalledpowerscrews [17].Therelationshipbetweenthreadform andapplicationpurposeisexplainedindetailinsection3.2.4.Toexplainitbriefly fornow,triangularscrewthreadsareprimarilyusedforclampingbecauseoftheirhigh antilooseningperformance.Trapezoidalandsquarescrewthreadsareemployedfor motionandpowertransmissionduetohighthreadefficiency.Pipethreadsareclassifiedintoparallelpipethreadsandtaperpipethreads.Theformerisusedformechanicaljoiningofstructureswithhollowcylindricalshapes.Thelatterisappliedto connectingpipelinesthatrequireleakagepreventionperformancetocontainfluids. Taperpipethreadsareprocessedonthetargetsurfacealongone-sixteenthoftaper. Thematingthreadsurfacescomeintoclosecontactasmalethreadsareprogressively screwedintofemalethreads.Thethreadangleoftriangularscrewthreadsis60 degrees,whiletheangleofpipethreadsis55degrees.
Besidestheaforementionedtypesofscrewthreads,squarethreads,roundthreads, andbuttressthreadsaresometimesused.Thethreadefficiencyofsquarethreadsis
Fig.1.1 Threadridgeformsofvarioustypesofscrewthreads.
higherthanthatoftrapezoidalscrewthreads;however,duetotheprocessingdifficulty,thethreadsurfaceisoftenmanufacturedtohaveaninclinedangleofabout5 degrees [17].Roundthreadscanberegardedastrapezoidalscrewthreadstowhich largeradiiareaddedtothecrestandthreadroot.Althoughthestressconcentration atthethreadrootislowered,roundthreadshaveanessentialdrawbackofsmallthread overlap.Buttressthreadsareshapedlikeasawwithasymmetricgeometrytosupport largeforcesactingfromonedefiniteside.Thebuttressthread’ssurfaceoftenhasan inclinedangleofabout7degrees [17] forthesamereasonasinthecaseofsquare threads.
Powerscrews,suchasacmethreads,whoseshapeissimilartotrapezoidalscrew threads,andbuttressthreadsarestandardizedbyANSI(AmericanNationalStandards Institute).Thetappingscrew,althoughnotshownin Fig.1.1,isakindoftriangularshapedscrewthreadusedforclampingparts.Itisamalethreadscrewedintothemain body,thusproducingafemalethreadhole.Thepartstobeclampedarecommonlythin metalplatesorwoodenplates,wherefemalethreadsareeasilyprocessedandhigh workingefficiencyisrequired.Thetighteningprocessoftappingscrewscanbeevaluatedintermsofthreetorques,i.e.,tappingtorquerequiredforprocessingfemale threads,tighteningtorqueforseatingthescrewheadandgeneratingclampingforce, andbreakagetorquecausingtheruptureofthetappingscrew [18].Fromthepointof viewofthetighteningoperation,itisnecessarythatthebreakagetorquebelargerthan thetighteningtorque,totheextentthattheruptureofscrewthreadsdoesnotoccur evenifbeingsomewhatover-tightened.
Inthisbook,thefocusisplacedonboltsandnutswithtriangularthreadgeometry, whicharemostwidelyusedforclampingallkindsofparts.
1.3Standardsofscrewthreads 1.3.1Standardspecificationsofscrewthreads InJapan,forinstance,standardspecificationsofscrewthreadsarespecifiedindetail inJIS(JapaneseIndustrialStandards).Sincescrewthreadsarecommonlyusedforall sortsofmachines,structures,electricdevices,etc.,thehighestlevelofinternational consistencyisrequiredinthestandardspecifications.Accordingly,thestandardson screwthreadsspecifiedinJISalmostcompletelyagreewithISO(InternationalOrganizationforStandardization)standards,aswellasthenationalstandardsestablishedin manycountries.However,perfectconsistencybetweenJISandISOispractically impossible.Tocopewiththosecases,therefore,thedegreeofinconsistencybetween ISOandJISisexplainedforeachspecificationinJIS.Asaresultofconsideringthe abovesituation,thescrewsandthreadedfastenerstreatedinthisbookarebasically standardizedinJIS.ThecorrespondencebetweenJISandISO,describedinthisbook, ispresentedin Table1.1,inwhichthestandardsspecifictoJISareshownseparately. Accordingtotheunitoflength,screwthreadsareclassifiedintometricthreadand inchthread.Themostcommonlyusedscrewthreadsaremetric.Pipethreads employedinpipingsystemsareinchthreads.Unifiedthreads,whichareanothertype 4TheMechanicsofThreadedFastenersandBoltedJointsforEngineeringandDesign
Table1.1 CorrespondencebetweenJISandISOinorderofappearance.
JISB0206B0208B0205B0209-1B0216B0202B0203 ISO26326368-1, 261, 262 965-12901, 2902, 2904 228-17-1
JISB1180B1181B1001B1052B1051B1083B1056
ISO4014–4018, 8676,8765 4032–4036, 8673–8675 273898-2, 898-6 898-116,0472320
JIS specific B1082B1173B2238B2251B1089B1090B1451
ofinchthread,areextensivelyusedinaircraft,andarespecifiedinJISB0206andJIS B0208.
1.3.2Basicprofileofscrewthreads Fig.1.2 representsthebasicprofileofmetrictriangularscrewthreadsforgeneraluse, specifiedinJISB0205.Theexternalor“male”threadisprocessedontheoutersurfaceofcylindersorcones,whiletheinternalor“female”threadisprocessedonthe innersurfaceofhollowcylindersorhollowcones.Majordiameterofexternalthread d isequaltomajordiameterofinternalthread D.Thetwomajordiametersarethe basicdimensionsrepresentingthesizeofscrewthreadsandthreadedfasteners,which aredenotedasnominaldiameter.Thepitchdiametersofmaleandfemalethreads, d2 and D2,arevirtualdiameters,atwhichthewidthofthethreadridgeisequaltothat ofthethreadgroove.Theyareusedwhenevaluatingthreadstrengthandcalculating thehelixangleofthescrewthread,termedtheleadangle.Minordiameterofexternal thread d1 isequaltominordiameterofinternalthread D1.Thedimensionsofeachpart
Fig.1.2 Basicprofileofmetrictriangularscrewthread.
6TheMechanicsofThreadedFastenersandBoltedJointsforEngineeringandDesign
oftriangularscrewthreadsareexpressedasfollows,bymeansofnominaldiameter d, threadpitch P andfundamentaltriangleheight H:
Threadpitch P isthedistancebetweenthecorrespondingpointsonneighboring ridges. H1 denotesbasicthreadoverlap,whichistheengagedlengthofmaleand femalethreadsintheradialdirection.However,itisdifficulttoderivearigorous equationthatcanpreciselyevaluatethestrengthofscrewthreadstakingintoaccount thecomplexhelicalthreadgeometry.InJISB1082,therefore,aconceptofstressarea As proposedtoevaluatethestressandstiffnessofhigh-strengthbolts,inwhichthe threadedportionisreplacedbyacylinderofcross-sectionalarea As:
InEq. (1.5), d3 correspondstothediameteratthreadrootwhenrootradiusisequalto H/6. ds isanimportantdimensionforstrengthevaluationanddesignatesthediameter ofstressarea.Theamountof ds canbecalculatedintermsofnominaldiameter d and threadpitch P:
ComparingEq. (1.6) toEqs. (1.2)and(1.3),itisfoundthat ds islocatedbetweenminor diameter d1 andpitchdiameter d2,asshownin Fig.1.2. Highstressconcentrationoccursatthethreadrootduetoitsnotchedshape.To lowerthestressconcentration,therefore,anappropriatesizeofradiusisprocessed there.Asfortherootradius ρ ofthemalethread,itisrecommendedinJISB2091that ρ shouldbelargerthan0.125P forboltsofstrengthclassificationof8.8and higher.Thedefinitionofstrengthclassificationisexplainedin Section1.6.1.
ρ 0 125P (1.7)
Fig.1.3 showsthebasicprofileofmetrictrapezoidalscrewthreads,asspecifiedin JISB0216.Thethreadangleis30degrees,whichishalfthatoftriangularscrew threads. Fig.1.4 depictsthebasicprofilesofparallelandtaperpipethreads,specified
Fig.1.3 Basicprofileofmetric trapezoidalscrewthread.
Fig.1.4 Basicprofilesofparallelandtaperpipethreads.(A)Parallelpipethreadand(B)taper pipethread.
