AGMA-92FTM7-1992.pdf
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1、92 FTM 7 Differencein the Local Stress of the GearToothRoot Based On HobbingCuttersand PinionCutters by: H. Linkeand J. B_Smer Dresden Universityof Technology,Germany AmericanGearManufacturersAssociation TECHNICALPAPER Copyright American Gear Manufacturers Association Provided by IHS under license w
2、ith AGMA Licensee=IHS Employees/1111111001, User=Wing, Bernie Not for Resale, 04/18/2007 11:59:45 MDTNo reproduction or networking permitted without license from IHS -,-,- Differencein the Local Stress of the Gear Tooth Root Based on HobbingCutters and Pinion Cutters H. Linke and J. BiSrner Dresden
3、University of Technology The statements and opinions contained herein are those of the author and should notbe construed as an official action or opinionof the AmericanGear ManufacturersAssociation. ABSTRACT: Differences of the tooth root geometry are caused if a pinion shaped cutter is used in the
4、gear production instead of ahob. These differencesalso lead to a different stress concentrationin the tooth root.The tooth root stresses are exactly calculated with the Singularity Method (variant of Boundary-Element-Method)for both production methods and their differences are discussed.The approxim
5、ate calculation of stress concentration with the stress parameter 2pF n / sFn (on 30 - tangent) is proved to be applicable. Copyright 1992 AmericanGear ManufacturersAssociation 1500 King Street, Suite 201 Alexandria,Virginia,22314 October,1992 ISBN:1-55589-587-5 Copyright American Gear Manufacturers
6、 Association Provided by IHS under license with AGMA Licensee=IHS Employees/1111111001, User=Wing, Bernie Not for Resale, 04/18/2007 11:59:45 MDTNo reproduction or networking permitted without license from IHS -,-,- Differencein theLocalStressof theGearToothRoot Basedon HobbingCuttersand PinionCutte
7、rs H. Linke; J. BSrner Dresden Universityof Technology,Germany _ thereforearepeatedinvestigationoftheseX=rwl. sin_-(_h/sin_+_a0).cos82) problemsappearstobeworthwhile. TheperpendiculardistanceYfromtheroot cross-section,givenbythetangentangle i.FundamentalKnowledge8,tothegearcentre,is I.I,.ToothRootG_
8、ometryY=rwlCS_-(Ah/sin_+_a0).sine(3) ToothRootThickness Firstofallaneasymethodforthecalcu-Theequations(2and(3)canbeiterative- lationofthetoothrootgeometrybyuseoflysolvedwiththeaidoftherelations anytypeofcuttersistobeexplainedbygivenintable1.Itprovedtobesuitable wayofintroduction.Withthismethodthetoc
9、hangetherollingangleinsmallsteps geometryiscomputableforgivenandgene-A_foragiventangentangleO_starting rallyvariabletangentangles8tothe toothrootfillet.Thederivationforex-from_min=n/Zl-z0/zl“ Aa(4) ternalgearingsiscarriedout.Internal gearingsaredeterminedbynegativenumbersto_max=_/Zl+z0/zl“(aM- ha(5)
10、 ofteethforboththemanufacturedgearand-arccos(rb0/rw0) thepinioncutter.Forverylargenumbers ofteethof thepinioncutter(z0 -_)theuntilthepertinenttangentanglee(_) toothrootthicknessaswellastheradiiagreedwiththeratedqUantity_*(within ofcurvatureoftherootfilletcurvepermissiblesmalldeviations). asymptotica
11、llypassintothepairingof, Table1containsindividualspecification gearedrack-cylindricalgear.quantitiesforeqUations(2)to(5).Index ThetoothrootthicknessSFsisdetermi-0andindex1designatethepinioncutter nedaccordingtofig.I.Adlfferentkind(tool)andthegeartobemade(gear ofpresentationwasgivenby,e.g.,blank),res
12、pectively.Figures2and3ex- Hirschmann/5/.Forthefirsttimetheplainotherquantities.Thedesignations toothrootthicknessforatangenttothehavebeenchoseninaccordancewithDIN rootfilletwasderivedbyHofer/6/.3960,DIN3990orISO701. FigureI:Generationofthefilletcurveby meansofapinioncutter-Deri- vationofthetoothroot
13、geometry Copyright American Gear Manufacturers Association Provided by IHS under license with AGMA Licensee=IHS Employees/1111111001, User=Wing, Bernie Not for Resale, 04/18/2007 11:59:45 MDTNo reproduction or networking permitted without license from IHS -,-,- TheshowngeometrycalculationatthebasisT
14、ablei:Auxiliaryquantitiesforthecal- ofincreasing_isalsosuitabletocreateculationofrootthicknessSFnand equidistantpointsattoothrootfillettoothrootfilletradius8Fn curveforSingularityMethodusedinstress calculations.Averyefficientiteration withNewtonsMethodisalsopossibleforDesignationEquation aswasdonein
15、/7/(_=_nin/7/). Pitchcircles= a0 / (I + Zo/ZI radius rwo, rwlrwl rwo = rwl. zO/zI lentre distancea0 =Zl+ZO)-ml2.cosaOlcosawO I ,f generating _airinga0inVUw0(Xl+X0).2.tans0 =+ inva0 zl+z0 _-_Differenceof620= YM = rMcs_a the tip radius XM YMrM = ra0 - _a0 aa =Sb0/2- _a0+Spr /rb0-inv_M tossM = rb0/rM 0
16、0Auxiliaryangle _=arctan-rw0-Sin designationsaccord, to DIN3960, DIN3990,ISOT01. Sr RadiiofCurvatureoftheFilletCurve Theradiiofcurvaturearetobecalculated onthebasisoftheEuler-Savaryequation, whichresultsaccordingtofigure4from thefollowingdeliberation: pitchcircle2rollonpitchcircleI. Let Letthestraig
17、htline_becloselycon- nectedwithcircle2. _.Theradiusofcurvature8 Moftherela- 0_“Xtirepathresultingduringtherollingof circle2oncircle1isto becalculated. Fromtheratiooftherelativerotation Figure3:Dataonthepinionshaperwith_tothepolevelocityu protuberance-Tooththicknessat basecircleandpressureangle_/u=i/
18、rwl+I/rw2(6) 3 Copyright American Gear Manufacturers Association Provided by IHS under license with AGMA Licensee=IHS Employees/1111111001, User=Wing, Bernie Not for Resale, 04/18/2007 11:59:45 MDTNo reproduction or networking permitted without license from IHS -,-,- with_Maccordingtoequ.(8). In tab
19、leI, equationsaregivenforAh_rwlandrw0“ Equations(8) and(9) applyalsotointer- nalgears,ifanegativenumberofteethis usedforthem.Forthemanufacturingwith hobsandrackcuttersaverylargenumber _,ofteethcanbeusedforthetool,e.g.zQ =10,000,sothatasufficientdegreeoZ approximationwillbeobtained. 1.2.StressConcent
20、ration Investigationsofthestressconcentration effectwerecarriedoutonacomputational basisattheDresdenUniversityofTechno- logy/3/4/.TheSingularityMethodchosen forthispurpose(BEMvariant)hasproved tobeverygood.Shortcomputingtimesand acomparativelylowexpenditureforthe preparationofthenumericalinvestigati
21、ons constituted essential properties. Accuracy wastestedwiththesolutionbyNeuber/2/ foratooth-likeprojection.Deviations lowerthan2 %resulted. Fig.5showsstresscurves,whichwere calculatedwiththemethodmentioned.From Ithesecalculationsandotherinvestigations 627+followsthatthestressmaximumoccursin uFwltw2
22、therangeof, 25_8_50 incaseofhob- bingwitha0a0.25.mandbytheuseof pinionshapedcutterswith_a0z0.1-m 0_(inelasticgear bodies being assumed). Theresultsofthecalculationsperformed forthenumbersofteethandaddendummodi- ficationfactorsoccurringintherangeof Figure4:Radiusofcurvature_Moftheusualgearinggeometri
23、eswereappliedin relativepathofthecentreMoftheformerstandardTGL10545(newdraft). thetooltipradius-DerivationIncomparisonwithDIN3990andISODIS oftheEuler-Savaryequation(M-P6336/03,thesevaluesaremostly10%to15% rigidlyconnectedwithgear2,lower;agreeing,however,withnewerre- rollingon geari)sultsofotherresea
24、rchinstitutions,too. Insummary,thefollowingcouldbestated: oneobtaintheEuler-Savaryequationina* Thestressmaximummostlyliesattan- general formgent anglestothe root fillet curve greaterthan30(usually8= 30. (i/i I1/12).cos_=i/rwl+17rw2(7)50).Theuseofthenominalstressat the30-tangenttorelatethemaximum the
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