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Copyright©2007JohnWiley&Sons,Ltd.RelativefatiguelifeestimationofcylindricalhollowrollersingeneralpurerollingcontactWisamM.AbuJadayil1,*,†1DepartmentofIndustrialEngineering,TheHashemiteUniversity,POBox330127,Zarqa,Jordan13115Solidandhollowcylindricalrollersinpurerollingcontacthavebeenmod-elled.Thetworollersaresubjectedtoacombinednormalandtangentialloading.Thetangentialloadingisone-thirdofthenormalloadingvalue.Thefiniteelementpackage,ABAQUS,isusedtostudythestressdistributionandtheresultingdeformationsinthebodiesoftherollers.ThentheIoannides–HarrisfatiguelifemodelforrollingbearingsisappliedontheABAQUSnumericalresultstoinvestigatethefatiguelifeofthesolidandhollowrollers.Usingthefatiguelifeofthesolidrollersasthereferencefatiguelife,therelativefatiguelivesofhollowrollersaredetermined.Fourmaindifferenthollownesspercentagesarebeenstudied:20,40,60and80%.Thehollownesspercentageistheratioofthediameteroftheholetotheouterdiameterofthecylinder.Foreachofthosehollownesspercentages,twocasesarestudied–whenthetworollersincontactarehollowandwhenonehollowrollerisincontactwithasolidroller.Thisstudyincludestwomainmodels:Model1,wherethetwocylindricalrollersincontactareofthesamesize,andModel2,wherethetworollersincontactarenotofthesamesize.Theestimatedrelativefatiguelivesofhollowrollersshowedagreatimprovementofthefatiguelifecomparedwithsolidrollersunderthesameloadingconditions.Thiswasaresultoftheredistributionofstressesinthecontactzoneinthecaseofhollowrollers.Redistributionofstressesoveralargervolumeoftherollerbodydecreasedthepeakstressandreducedthevolumeunderrisk.Increasingthehollownesspercentagefrom20to60%increasedtheflexibil-ityoftheroller,andbetterstressdistributionwasachieved,whichresultedinimprovingthefatiguelife.Although80%ofhollownessrollershavemoreflexibilitythan60%ofhollownessrollers,thebendingstresses(sb)ontheinnersurfaceoftherollerstendtodecreasethefatiguelife.Copyright©2007JohnWiley&Sons,Ltd.TRIBOTESTTribotest2008;14:27–42PublishedonlineinWileyInterScience()DOI:10.1002/tt.51*Correspondenceto:WisamM.AbuJadayil,DepartmentofIndustrialEngineering,TheHashemiteUniversity,POBox330127,Zarqa,Jordan13115.†E-mail:abujadayil@hotmail.com28W.M.AbuJadayilCopyright©2007JohnWiley&Sons,Ltd.Tribotest2008;14:27–42DOI:10.1002/ttINTRODUCTIONTodate,thereisnoperfectinvestigationofthedamageinrollingcontacts.Itisjustknownthatrepeatedstressingofthemachineelementscausesirreversiblechangesinthem,whichresultsintheformationofcracks.Thesecracksoccurafteranumberofloadcyclesbasedonthestressdistributioninsidethemachineelement.Asignofcrackpropagationistheformationofdamageinthecontactsurfaceknownaspittingorspalling.1Asthestressdistributionwithinthemachineelementisamainfactorindeterminingfatiguelife,designchangesshouldbemadetoredistributethecontactstressesoftherollingelements.Usinghollowrollersintherollerbearingshastheinterestofmanydesignersbecauseoftheiradvantagesoversolidrollers.Hollowrollerbearingsaresingleordoublerowradialbearingswithaninnerring,outerringandholloworthinwallrollers.Thethinwallintherollersallowsthesebearingstobepreloaded,asopposedtocylindricalrollerbearingswithsolidrollers.Thisincreasesradialstiffnessandreducesradialvibrationandradialrunout.Forthesereasons,hollowrollersareusedintheserollerbearings,butnotyetinfrictiondrives.Intractiondrives,twoormoresetsofrollersareusedincontactbetweentheinnerraceandtheouterring.Agoodexampleofthetractiondrivesusingcylindricalrollerbearingsistheself-actuatingtractiondrivedesignedbyFlugradandQamhiyah.2Thistractiondriveisusedasabasisforthiswork.Evenso,theresultscanbegeneralisedforcylindricalrollersusedinrollerbearingsandothertractiondrives.Inspiteofthemanyadvantagesofusingtractiondrivesovergears,suchaslessnoise,easeofmanufacture,andeasyandcheapmaintenance,therearesomedisadvantages.Oneofthemaindis-advantagesisweight.Forthesameloadapplication,therequiredtractiondriveisheavierthantherequiredgearsystem.Thus,themainobjectiveofthisresearchistoresolvethelimitationsofusingthecylindricalrollers,theirfatiguelifeandtheirheavyweight.Asolutiontoboththeseproblemscanbefoundbyusinghollowrollersinsteadofsolidrollers.Usingthehollowrollersmeanslessweight,sotheproblemsarepartiallysolved.Ontheotherhand,thefatiguelifeshouldbeinvestigated.Thispaperpresentsresultsfromanumericalsimulationoftworollersincontactunderpurerollingtostudythefatiguelifeofhollowrollersandcompareitwiththatofsolidrollers.LITERATUREREVIEWFormorethanacentury,thecontactproblembetweentwoelasticbodieshashadtheattentionofmanyresearchers.Hertz3firstinvestigatedtheproblemoftwoelasticbodiessubjectedtopurenormalloading.HeusedtheNewtonianpotentialfunctiontostudythedistributionofthestressesinthecontactbodyandtostudythedistributionoftheloadoverthecontactarea.Heverifiedhissolutionbyexperimentalresults.Goodresultsforthestressesinthecontactregion,calledHertzianstresses,wereobtained.SmithandLiu4assumedtheHertziandistributionofthenormalandtangentialloadsovertheareaofcontact.Theresultingstressesofapplyingthenormalandtangentialloadswererepresentedinaclosedform