Chapter11WormGears

11.1WormGearsandWorms;Nomenclature,Materials11.2MainParametersandGeometricalCalculations11.3ForceAnalysis11.4StressAnalysisandDesign

11.5StructuralDesignofWormandGears11.6LubricationandHeatDissipationChapter11WormGears1

11.1WormGearsandWorms;Nomenclature,

MaterialsWormgearingisoftenusedinsituationsrequiringlargereductionratiosortransmissionbetween90°nonintersectingshafts,andofteninlow-powersituationssincethatfrictionlossescanbehighduetoslidingbetweenwormthreadsandthegearteeth.Commonreductionratiosofwormgearingrangefrom4to100.Wormgearsetscanbeproducedtoprovideratiosrangingfrom1to360.Ingeartrainsofdividingmechanismsreductionratioreaches600-1,000.11.1WormGearsandWorms;No2Sketchofwormgeararrangementforcylindrical(single-enveloping)worm,givingstandardnomenclature.

Shownfordoublethreadedworm.Sketchofwormgeararrangemen3十二指腸鉤口線蟲和美洲板口4十二指腸鉤口線蟲和美洲板口511.2MainParametersandGeometricalCalculationsTheplanepassingthroughtheaxisofthewormandperpendiculartotheaxisofthewheeliscalledthemainplane.Inthesectionofthemainplane,anArchimedeanwormgivesacontactbetweenaninvolutewheelandastraight-sidedrack.11.2MainParametersandGeome6Abasicrequirementofaproperlydesignedwormgearsetisthattheaxialpitchofthewormmustbeequaltothecircularpitch

ofthegear.ThematingelementsintheaxialsectionofanArchimedeanwormareidenticaltoarackofrectilinearcontourwithanangleof.Forthemoduleofawormgearmwetakethewormaxialmoduleequaltothecircumferentialmoduleofthewheel.Abasicrequirementofaprope7Toinsurepropercontactbetweenthewormandthegearteeth,thegearhobtypicallyhasthesamebasiccuttershapeusedfortheworm.Wormsmaybemanufacturedwithasinglethreadorwithmultiplethreads.Thenumberofthreadsonthewormisoftenreferredtoasthenumberofstarts.Thepitchdiameterofawormisnotafunctionofitsnumberofthreads.Thereductionratioofawormgear-setisnotequaltotheratioofgearandwormpitchdiameters,butequaltotheratioofthenumberofstarsonthewormandteethnumberonthegear.Toinsurepropercontactbetwe8Thelead,theaxialadvanceofanypointonthewormthreadforonerevolutionoftheworm,isThemeanwormleadangle

Fortheusualcase,wherethewormshaftis90?tothegearshaft,theleadangleofthewormisequaltothehelixangleofthewormgear:Table11.1givesformulaefordeterminingthemaingeometricalproportionsofawormgearwithanArchimedeanwormThelead,theaxialadvanceo9

CorrectionofthewormgearInawormgearonlythewheeliscorrectedwhilethesizeofthewormremainsthesame.Thecorrectionofthegearchangesonlythediameterofthewormpitchcylinderwhilethediameterofthewheelpitchcylinderdoesnotchange.Correctionofthe10SlidingvelocityvsatpitchpointC,isSlidingvelocityvsatpitchp1111.3ForceAnalysis

Thedesignloadisusedincalculatingthestrengthofthegear.

11.3ForceAnalysisThedesi1211.4StressAnalysisandDesignAcommonempiricaldesignapproachistoassumethattoothbendingfatigueislessseriousthansurfacedurabilitywhendefininganacceptabledesign.Further,thesurfacedurabilitycriteriontypicallyemployedinpracticeisassumedtoembodybothsurfacefatigueandadhesive/abrasivewearparameters.Wetaketheformula(10-4)astheinitialrelationforcalculatingtheactiveprofilesinthesamewayasthatforgears.

11.4StressAnalysisandDesig13

Stressanalysis

Thedesigncalculations:

StressanalysisThede14Allowablesurfacestressesareassignedforthematerialofthewheelrimdependingonthematerialofthewormrunningwithit.WhenthewheelsaremadefromcastironorbronzewithultimatestrengthMPathemainfailuremodeonthegearsurfaceisseizure.Therefore,allowablestressesareassigneddependingonthecombinationofcontactingmaterialsandthevelocityofsliding.Table11.3givesexperimentalvaluesof[σ]Hforthoroughlyrun-inandliberallylubricatedgears.Inothergearsthetabulatedvaluesshouldbedecreasedapproximatelyby30%.AllowablesurfacestressesAllowablesurfacestressesare15IfthewheelaremadeofbronzewithultimatestrengthσB<300MPatheload-carryingcapacityofthegearislimitedbycontactfatigue.ThevaluesofforsomematerialsofwheelsrunningwithsteelwormsaregiveninTable11.4.Ifthewheelaremadeofbronz16Wormsareusuallymadeintegralwiththeshaft.TypicaldesignsofwormareshowninFig.11.6.Wormgearsaremadesolid(Fig.11.7,a)orcomposite(Fig.11.7,b,c)withabronzerim.Therimofawormwheelisfittedontothewheelcenterwithinterference(Fig.11.7,b)Anothermethodoffasteningtherimofawormwheeltoitscenterbymeansofflangesisemployedifthewheelislargeindiameter(Fig.11.7,c).11.5StructuralDesignofWormandGearsWormsareusuallymadeintegra17Fig.11.7TypicalstructureofwormgearsFig.11.7Typicalstructureof181)Efficiencyofwormset

11.6LubricationandHeatDissipationForapproximatecalculationsthefullefficiencyofwormgearscanbedeterminedfromTable11.5.ThemagnitudeofatdifferentconditionscanbeobtainedfromTable11.6.1)Efficiencyofwormset11.6L19Ifthewormgearcannothack-drivetheworm,thewormsetissaidtobeself-locking.

2)Self-lockingconditionThelowleadanglesrequiredforeffectiveself-lockingimplytheuseofasingle-threadwormandproducelowefficiencies.Self-lockingconditionIfthewormgearcannothack-d20Thelubricationandcoolingissuesbecomemoreimportantforwormgearsetswithhighfrictionheating.Variousmeansofcoolingthehousin