科技论文 机械Word格式.docx

科技论文 机械Word格式.docx

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cGearR&

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

Received22February2005;

revised6May2005;

accepted17May2005. 

Availableonline25January2006.

Abstract

Transmissionerrorsareconsideredasthemainsourceofvibrationandnoiseof

geardrives.

Theimpactoftwomainfunctionsoftransmissionerrorsonnoiseisinvestigated:

（i）

a

linearone,causedbyerrorsofalignment,and（ii）

predesignedparabolicfunctionoftransmissionerrors,appliedforreductionofnoise.Itisshownthat

linearfunctionoftransmissionerrorsisaccompaniedwithedgecontact,andtheninsidethecycleofmeshing,themeshingbecomes

mixedone:

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

predesignedparabolicfunctionoftransmissionerrorsenablestoabsorbthelinearfunctionsoftransmissionerrorscausedbyerrorsofalignment,reducenoise,andavoidedgecontact.Theinfluenceoftheloadonthefunctionoftransmissionerrorsisinvestigated.Elasticdeformationsofteethenabletoreducethemaximaltransmissionerrorsinloaded

Computerizedsimulationofmeshingandcontactisdevelopedforloadedandunloaded

Numericalexamplesforillustrationofthedevelopedtheoryareprovided.

Keywords:

Geardrives

;

Transmissionerrors;

Toothcontactanalysis（TCA）;

Finiteelementanalysis;

Reductionofnoise

ArticleOutline

1.Introduction

2.Modificationoftoothsurfaces

2.1.Helicalgeardrives

2.2.Spiralbevelgears

2.3.Wormgeardriveswithcylindricalworm

3.Typesofmeshingandbasicfunctionsoftransmissionerrors

4.Transmissionerrorsofaloadedgeardrive

4.1.Preliminaryconsiderations

4.2.Applicationoffiniteelementanalysisfordeterminationoffunctionoftransmissionerrorsofaloadedgeardrive

5.Numericalexamples

6.Comparisonofthepowerofnoisefortwofunctionsoftransmissionerrors

6.1.Conceptualconsiderationofappliedapproach

6.2.Interpolationbyapiecewiselinearfunction

7.Conclusion

Acknowledgements

References

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].

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].Transmission