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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Word文档下载推荐.docx
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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
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
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