机械毕业设计英文外文翻译对降低齿轮传动装载和卸载时因误差引起的噪音的研.docx

机械毕业设计英文外文翻译对降低齿轮传动装载和卸载时因误差引起的噪音的研.docx

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机械毕业设计英文外文翻译对降低齿轮传动装载和卸载时因误差引起的噪音的研

外文翻译

Reductionofnoiseofloadedandunloadedmisalignedgeardrives

FaydorL.Litvina,DanieleVecchiatoa,KenjiYukishimaa,AlfonsoFuentesb,IgnacioGonzalez-PerezbandKenichiHayasakac

aGearResearchCenter,DepartmentofMechanicalandIndustrialEngineering,UniversityofIllinoisatChicago,842W.TaylorSt.,Chicago,IL60607-7022,USA

bDepartmentofMechanicalEngineering,PolytechnicUniversityofCartagena,C/DoctorFleming,s/n,30202,Cartagena,Murcia,Spain

cGearR&DGroup,ResearchandDevelopmentCenter,YamahaMotorCo.,Ltd.,2500Shingai,Iwata,Shizuoka438-8501,Japan

Received22February2005; revised6May2005; accepted17May2005. Availableonline25January2006.

Abstract

Transmissionerrorsareconsideredasthemainsourceofvibrationandnoiseof

geardrives.

Theimpactoftwomainfunctionsoftransmissionerrorsonnoiseisinvestigated:

（i）

a

linearone,causedbyerrorsofalignment,and（ii）

a

predesignedparabolicfunctionoftransmissionerrors,appliedforreductionofnoise.Itisshownthat

a

linearfunctionoftransmissionerrorsisaccompaniedwithedgecontact,andtheninsidethecycleofmeshing,themeshingbecomes

a

mixedone:

（i）assurface-to-surfacetangency,and（ii）surface-to-curvemeshingwhenedgecontactstarts.Applicationof

a

predesignedparabolicfunctionoftransmissionerrorsenablestoabsorbthelinearfunctionsoftransmissionerrorscausedbyerrorsofalignment,reducenoise,andavoidedgecontact.Theinfluenceoftheloadonthefunctionoftransmissionerrorsisinvestigated.Elasticdeformationsofteethenabletoreducethemaximaltransmissionerrorsinloaded

geardrives.

Computerizedsimulationofmeshingandcontactisdevelopedforloadedandunloaded

geardrives.

Numericalexamplesforillustrationofthedevelopedtheoryareprovided.

Keywords:

Geardrives

;Transmissionerrors;Toothcontactanalysis（TCA）;Finiteelementanalysis;Reductionofnoise

1.Introduction

Simulationofmeshingofgeardrivesperformedbyapplicationoftoothcontactanalysis（TCA）andtestofgeardriveshaveconfirmedthattransmissionerrorsarethemainsourceofvibrationsofthegearboxandsuchvibrationscausethenoiseofgeardrive[1],[2],[4],[5],[6],[7],[10]and[11].Theshapeoffunctionsoftransmissionerrorsdependsonthetypeoferrorsofalignmentandonthewayofmodificationofgeartoothsurfacesperformedforimprovementofthedrive（seeSection2）.

Thereductionofnoiseproposedbytheauthorsisachievedasfollows:

（1）Thebearingcontactoftoothsurfacesislocalized.

（2）Aparabolicfunctionoftransmissionerrorsisprovided.Thisallowstoabsorblinearfunctionsoftransmissionerrorscausedbymisalignment[7].

（3）Oneofthepairofmatingsurfacesismodifiedbydouble-crowning（seeSection2）.Thisallowsusuallytoavoidedgecontact（seeSection5）.

TheauthorshavecomparedtheresultsofapplicationofTCAforloadedandunloadedgeardrives.Itisshownthattransmissionerrorsofaloadedgeardrivearereduced.Thedevelopedapproachisillustratedwithnumericalexamples（seeSection5）.

2.Modificationoftoothsurfaces

Reductionofnoiseofageardriverequiresmodificationofoneofthepairofcontactingsurfaces.Thesurfacemodificationisillustratedforthreetypesofgeardrives:

helicalgears,spiralbevelgears,andwormgeardrives.

2.1.Helicalgeardrives

Profilecrowningofhelicalgearsmaybeillustratedconsideringthatthematingsurfacesaregeneratedbytworack-cutterswithmismatchedprofiles[5]and[7].

Profilecrowningallowstolocalizethebearingcontact.Double-crowningincomparisonwithprofilecrowningallowsto:

（i）avoidedgecontact（causedbyerrorsofcrossingangleanddifferenthelixanglesofmatinggears）,and（ii）provideaparabolicfunctionoftransmissionerrors.Double-crowningisperformedbyplungingofthediskthatgeneratesthepinion（seedetailsinChapter15ofRef.[7]）.

2.2.Spiralbevelgears

Localizationofcontactofgeneratedspiralbevelgearsisprovidedbyapplicationoftwomismatchedhead-cuttersΣpandΣgusedforgenerationofthepinionandthegear,respectively[7].Twohead-cuttersΣpandΣghaveacommonlineCofgeneratingtoothsurfaces（inthecasewhenprofilecrowningisprovided）.Inthecaseofdouble-crowning,themismatchedgeneratingsurfacesΣpandΣgofthehead-cuttershaveonlyacommonsinglepointoftangency,butnotalineoftangency.Double-crowningofageneratedgearmaybeachievedbytiltingofoneofthepairofgeneratinghead-cutters,orbyproperinstallmentofoneofthehead-cutters.Itisverypopularforthemoderntechnologythatduringthegenerationofoneofthematinggears,usuallyofthepinion,modifiedrollisprovided[7].

2.3.Wormgeardriveswithcylindricalworm

Veryoftenthetechnologyofmanufacturingofaworm-gearisbasedonthefollowingapproach.Thegenerationoftheworm-gearisperformedbyahobthatisidenticaltothewormofthegeardrive.Theappliedmachine-toolsettingssimulatethemeshingofthewormandworm-gearofthedrive.However,manufacturewithobservationoftheseconditionscausesanunfavorablebearingcontact,andhighleveloftransmissionerrors.Minimizationofsuchdisadvantagesmaybeachievedbyvariousways:

（i）bylong-timelappingoftheproducedgeardriveintheboxofthedrive;

（ii）byrunningofthegeardriveundergraduallyincreasedload,uptothemaximalload;

（iii）byshavingoftheworm-gearintheboxofthedrivebyusingashaverwithminimizeddeviationsoftheworm-member,etc.

Theauthors’approachisbasedonlocalizationofbearingcontactbyapplicationof:

（a）anoversizedhob,and（b）modificationofgeometry（seebelow）.

Therearevarioustypesofgeometryofwormgeardrives[7],butthepreferableoneisthedrivewithKlingelnberg’stypeofworm.Suchawormisgeneratedbyadiskwithprofilesofacircularcone[7].Therelativemotionofthewormwithrespecttothegeneratingdiskisascrewone（intheprocessofgeneration）.

Veryoftenlocalizationofbearingcontactinawormgeardriveisachievedbyapplicationofahobthatisoversizedincomparisonwiththewormofthedrive.

3.Typesofmeshingandbasicfunctionsoftransmissionerrors

Itisassumedthatthetoothsurfacesareatanyinstantinpointtangencyduetothelocalizationofcontact.Henceforth,wewillconsidertwotypesofmeshing:

（i）surface-to-surface,and（ii）surface-to-curve.Surface-to-surfacetangencyisprovidedbytheobservationofequalityofpositionvectorsandsurfaceunitnormals[7].Surface-to-curvemeshingistheresultofexistenceofedgecontact[7].

ThealgorithmofTCAforsurface-to-surfacetangencyisbasedonthefollowingvectorequations[7]:

（1）

（2）

thatrepresentinfixedcoordinatesystemSfpositionvectors

andsurfaceunitnormals

.Here,（ui,θi）arethesurfaceparametersand（

1, 

2）determinetheangularpositionsofsurfaces.

Thealgorithmforsurface-to-curvetangencyisrepresentedinSfbyequations[7]

（3）

（4）

Here,

representsthesurfacethatisinmeshwithcurve

isthetangenttothecurveoftheedge.

ApplicationofTCAallowstodiscoverbothtypesofmeshing,surface-to-surfaceandsurface-to-curve.Computerizedsimulationofmeshingisaniterativeprocessbasedonnumericalsolutionofnonlinearequations[8].

Byapplyingdouble-crowningtooneofthematingsurfaces,itbecomespossibleto:

（i）avoidedgecontact,and（ii）obtainapredesignedparabolicfunction[7]（Fig.1）.Applicationofapredesignedparabolicfunctionisthepreconditionofreductionofnoise.

（17K）

Fig.1. Illustrationof:

（a）transmissionfunctions1ofamisalignedgeardriveandlinearfunction2ofanidealgeardrivewithoutmisalignment;（b）periodicfunctionsΔ

2（

1）oftransmissionerrorsformedbyparabolas.

Applicationofdouble-crowningallowstoassignaheadthatfunctionoftransmissionerrorsisaparabolicone,andallowstoassignaswellthemaximalvalueoftransmissionerrorsasof6–8″.Theexpectedmagnitudeofthepredesignparabolicfunctionoftransmissionerrorsandthemagnitudeoftheparabolicplungeofthegeneratingtoolhavetobecorrelated.Fig.2showsthecasewhereinduetoalargemagnitudeoferrorofmisalignment,thefunctionoftransmissionerrorsisformedbytwobranches:

ofsurface-to-surfacecontactand

ofsurface-to-curvecontact.

（31K）

Fig.2. ResultsofTCAofacaseofdouble-crownedhelicalgeardrivewithalargeerrorΔγ = 10′:

（a）functionoftransmissionerrorswherein

correspondstosurface-to-surfacetangencyandcorrespondtosurface-to-curvetangency;（b）pathofcontactonpiniontoothsurface;（c）pathofcontactongeartoothsurface.

4.Transmissionerrorsofaloadedgeardrive

ThecontentsofthissectioncovertheprocedureofdeterminationoftransmissionerrorsofaloadedgeardrivebyapplicationofageneralpurposeFEMcomputerprogram[3].TransmissionerrorsofanunloadedgeardrivearedirectlydeterminedbyapplicationofTCA.ComparisonoftransmissionerrorsforunloadedandloadedgeardrivesisrepresentedinSection5.

4.1.Preliminaryconsiderations

（i）Duetotheeffectofloadingofthegeardrive,themaximaltransmissionerrorsarereducedandthecontactratioisincreased

（ii）Theauthors’approachallowstoreducethetimeofpreparationofthemodelbytheautomaticgenerationofthefiniteelementmodel[1]foreachconfigurationofthesetofappliedconfigurations.

（iii）Fig.3illustratesaconfigurationthatisinvestigatedundertheload.TCAallowstodeterminepointMoftangencyoftoothsurfacesΣ1an