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ORIGINALARTICLEOPTIMALMACHINETOOLSPINDLEDRIVEGEARBOXDESIGNDRSALGADOFJALONSORECEIVED4AUGUST2006/ACCEPTED23MARCH2007/PUBLISHEDONLINE4MAY2007SPRINGERVERLAGLONDONLIMITED2007ABSTRACTMANYMACHINETOOLSAREEQUIPPEDWITHAMOTORGEARBOXTOEXTENDTHECONSTANTPOWERRANGEOFTHEMACHINETOOLSPINDLEDRIVEMOTORATLOWSPEEDSCURRENTLY,INTHELATESTSPINDLEDRIVEMOTORTECHNOLOGY,THEGEARBOXESAREINTEGRATEDINLINEBETWEENTHEWATERCOOLEDMOTORANDTHESPINDLEINSIDETHEMACHINETOOL’SRAMTHEFUNCTIONALITYOFASPINDLEGEARBOXDEPENDSDIRECTLYUPONITSCONSTRUCTIONALSOLUTION,ANDONTHEKINETICENERGYCORRESPONDINGTOTHISSOLUTIONINTHISWORK,SPINDLEGEARBOXESAREOPTIMIZEDTAKINGTHISDESIGNFACTORINTOACCOUNTINTHEAUTHORS’OPINION,THERESULTSCOULDBEOFGREATINTERESTFORSPINDLEDRIVEGEARBOXMANUFACTURERSKEYWORDSSPINDLEGEARBOXDESIGNOPTIMALDESIGNMINIMUMKINETICENERGYOPTIMIZATIONNOMENCLATUREΣHHERTZCONTACTSTRESSΣFBENDINGSTRESSΣHPALLOWABLEHERTZCONTACTSTRESSΣFPALLOWABLEBENDINGSTRESSΣHONOMINALHERTZCONTACTSTRESSΣFONOMINALBENDINGSTRESSΣHLIMMAXIMUMALLOWEDHERTZCONTACTSTRESSΣFLIMMAXIMUMALLOWEDBENDINGSTRESSΑPRESSUREANGLEFTTANGENTIALGEARFORCEBFACEWIDTHΒHELIXANGLEDPITCHDIAMETERMMODULEKAAPPLICATIONFACTORKHATRANSLOADSHARINGFACTORFORPITTINGRESISTANCEKHBLONGLOADSHARINGFACTORFORPITTINGRESISTANCEKFATRANSLOADSHARINGFACTORFORBENDINGSTRENGTHKFBLONGLOADSHARINGFACTORFORBENDINGSTRENGTHYFAFORMFACTORFORBENDINGSTRENGTHYNTLIFEFACTORFORBENDINGSTRENGTHYRRELTRELATIVERUGOSITYFACTORYSASTRESSCONCENTRATIONFACTORYSTSTRESSCONCENTRATIONFACTORYXSIZEFACTORFORBENDINGSTRENGTHYDRELTNOTCHRELATIVESENSITIVITYFACTORYCONTACTRATIOFACTORFORBENDINGSTRENGTHYBHELIXANGLEFACTORFORBENDINGSTRENGTHZEMATERIALFACTORZHGEOMETRYFACTORFORPITTINGRESISTANCEZLVISCOSITYFACTORZNLIFEFACTORFORPITTINGRESISTANCEZRRUGOSITYFACTORFORPITTINGRESISTANCEZVVELOCITYFACTORZWHARDNESSRATIOFACTORZXSIZEFACTORFORPITTINGRESISTANCEZBHELIXANGLEFACTORFORPITTINGRESISTANCEZCONTACTRATIOFACTORFORPITTINGRESISTANCEKVDYNAMICFACTORNPNUMBEROFPLANETGEARSKEKINETICENERGYOFPLANETARYSYSTEMΩIANGULARSPEEDOFGEARIINTJADVMANUFTECHNOL200837851–860DOI101007/S0017000710286DRSALGADODEPARTMENTOFELECTRONICSANDELECTROMECHANICALENGINEERING,UNIVERSITYOFEXTREMADURA,STATERESADEJORNET38,06800MRIDA,SPAINEMAILDRSUNEXESFJALONSODEPARTMENTOFELECTRONICSANDELECTROMECHANICALENGINEERING,UNIVERSITYOFEXTREMADURA,AVDAELVASS/N,06071BADAJOZ,SPAINV4SPEEDOFTHEPLANETGEARMIMASSOFGEARIIIMOMENTOFINERTIAOFGEARIZINUMBEROFTEETHONGEARZNLTOOTHRATIOOFTHEGEARPAIRFORMEDBYLINKSNANDLΗEFFICIENCYOFPLANETARYGEARTRAINSPINDLESPEEDERΗOORDINARYORSTATIONARYEFFICIENCYOFTHEGEARPAIR1INTRODUCTIONTHESPINDLEISONEOFTHEMAINMECHANICALCOMPONENTSINMACHININGCENTERS,SINCEITSDESIGNDIRECTLYAFFECTSTHEFINISHEDQUALITYOFWORKPIECESANDMACHININGPRODUCTIVITYCONSEQUENTLY,SPINDLEDESIGNHASBEENSTUDIEDINDEPTHINSEVERALWORKS1–4MACHINETOOLSCANNOTPROVIDEHIGHTORQUESOVERTHEIRENTIRESPEEDRANGEUNLESSTHEMOTORISOVERSIZEDNEVERTHELESS,THEREQUIREMENTSOFSUCHANOVERSIZEDMOTORTOPROVIDECONSISTENTTORQUEACROSSTHEMACHINETOOL’SSPEEDRANGEINCREASENOTONLYTHECOSTOFTHEMOTORBUTALSOTHEOPERATINGCOSTSDUETOHIGHERPOWERCONSUMPTIONADDITIONALLY,THEMOTOR’SWEIGHTWOULDEXCEEDTHEWEIGHTOFAMOTORGEARBOXCOMBINATIONFORTHESEREASONS,SPINDLEDRIVEGEARBOXESAREUSEDTHEUSEOFMACHINETOOLSPINDLEDRIVEGEARBOXESALLOWSONETOEXTENDTHECONSTANTPOWERRANGEOFTHEMACHINETOOLSPINDLEDRIVEMOTORSTHISRANGEEXTENSIONOFPOWERANDTORQUEISILLUSTRATEDINFIG1,INWHICHTHEDASHEDLINEREPRESENTSTHERANGEEXTENSIONWHENTHEREDUCERGEARBOXISINTRODUCEDBETWEENTHEMOTORANDTHETOOLAXISFIGURE1AREPRESENTSTHEPOWEREXTENSIONANDFIG1BTHETORQUEEXTENSIONVERSUSTHEOUTPUTSPEEDDATAFROMANINDUSTRIALMACHINETOOLINSUM,THEUSEOFTHEREDUCERGEARBOXINCREASESTHEFLEXIBILITYOFMANUFACTURING,ENABLINGMACHINETOOLSTOOPERATEAT–HIGHTORQUEFORHOGGINGOUTSTEELORCASTIRONREDUCERSPEEDRATIOR1,R1–HIGHSPEEDFORFINISHINGCUTSDIRECTSPEEDRATIO11TRADITIONALLY,THESEGEARBOXESAREUSEDINCONVENTIONALAPPLICATIONSWHERETHEMOTORANDGEARBOXAREMOUNTEDOUTSIDETHEHEADSTOCK,ANDTHESPINDLEISDRIVENBYBELTS,CHAINS,ORGEARSNOWADAYS,THEGEARBOXESAREINTEGRATEDINLINEBETWEENTHEWATERCOOLEDMOTORANDTHESPINDLEINSIDETHEMACHINETOOL’SRAMTHISINTEGRATIONENABLESTHEUNITTOFITINTOTHEBOREOFTHEMACHINETOOLRAMANDSHAREINTHECOOLANTSYSTEMTHISCOMPACT,LIGHTWEIGHTCONFIGURATIONMAXIMIZESEFFICIENCYWHILEMINIMIZINGVIBRATIONSANDNOISEITISTHEDESIGNOFTHISCONFIGURATIONTHATISSTUDIEDINTHEPRESENTWORKNOTETHATINTHEINLINEGEARBOXINTEGRATEDDESIGN,THEOPTIMALDESIGNDEPENDSMAINLYONTHEDESIGNOFTHETRANSMISSIONFORTHEREQUIREDSPEEDRATIOANDPOWERHENCE,ANDFORTHESAMEREASONSMENTIONEDABOVEFORTHESPINDLEDESIGN,SPINDLEDRIVEGEARBOXESALSONEEDTOBESTUDIEDINDEPTHFORTHEIRDESIGNTOBEOPTIMIZEDINTHISCONTEXT,THEMOSTIMPORTANTDESIGNFACTORFORSPINDLEDRIVEGEARBOXESISTHATTHEKINETICENERGYOFTHETRANSMISSIONISMINIMAL,FORANOPTIMALFUNCTIONALITYDURINGMACHININGANDENSURINGALONGWORKINGLIFEPLANETARYGEARTRAINSPGTSAREUSEDFORTHEGEARBOXDESIGNSINCETHEYOFFERAVERYCOMPACTREDUCEDWEIGHTANDSIZEANDEFFICIENTSOLUTIONHIGHSPEEDRATIOSANDHIGHEFFICIENCYINCOMPARISONTOORDINARYGEARTRAINSTHEOBJECTIVEOFTHISPAPERISTOGIVEASETOFOPTIMALDESIGNSOFSPINDLEGEARBOXESFORDIFFERENTPOWERSANDSPEED101001000100000200400600800100012001400OUTPUTSPEEDRPMTORQUENM1010010001000001020304050OUTPUTSPE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