AGMA-90FTM6-1990.pdf
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1、90 FTM 6 I Dynamic Responses of AircraftGears by: KayaalpBuyukataman,GeneralElectricAircraftEnginesDivision ,IIIII I + ,I AmericanGear ManufacturersAssociation IIIIIIII TECHNICALPAPER Copyright American Gear Manufacturers Association Provided by IHS under license with AGMA Licensee=IHS Employees/111
2、1111001, User=Wing, Bernie Not for Resale, 04/18/2007 11:02:18 MDTNo reproduction or networking permitted without license from IHS -,-,- DynamicResponsesof AircraftGears KayaalpBuyukataman, GeneralElectricAircraftEnginesDivision The Statementsand opinionscontainedhereinare those of the authorand sho
3、uldnot be construedas an officialactionor opinionof the AmericanGearManufacturersAssociation. ABSTRACT: Rapidand destructivefailuresof high quality,high speed,lightweightand highlyloadedaircraftgears are indicationof thevibrationalenergy(associatedwithneutralfrequencymodes)exceedingthefatigue endura
4、ncelimit of advancegearmaterials. This paperreviews: A) Experimentalandanalyticalmethodsto identifyanddefineresonantmode. B) Affectsof geardesignand manufacturingvariablesto the generationand dampingof vibrational energy. AUTHORS DEDICATION: This paperhas beendedicatedto Mr. JosephS. Alford.Mr. Alfo
5、rdis with the GE Companyas engineer since1934.Mr.Alfordsteachingshada majorimpacton the traditionsof GE AircraftEngines communityand thevalueswe have today. Copyright 1990 AmericanGearManufacturersAssociation 1500 King Street,Suite201 Alexandria,Virginia,22314 October,1990 ISBN:1-55589-558-1 Copyrig
6、ht American Gear Manufacturers Association Provided by IHS under license with AGMA Licensee=IHS Employees/1111111001, User=Wing, Bernie Not for Resale, 04/18/2007 11:02:18 MDTNo reproduction or networking permitted without license from IHS -,-,- DYNAMIC RESPONSES OF AIRCRAFT GEARS KAYAALPBUYUKATAMAN
7、 GE AIRCRAFTENGINESDIVISION CINCINNATI,OHIO INTRODUCTIONOne of the earliestsuccessful effortsto apply theelementaryequationstoresonancephenomenaof Thestudyofnaturalfrequenciesisathreedimensional solids were developed byLove. well-developedbranchofengineering.ManyThetreatmenttakesintoaccounttheinerti
8、a of publicationshavebeenreleasedon thesubject oflateralcontraction.TheLovesassumptionare theapplicationforpracticalengineeringretainedthatplanesectionsremainplaneand analysis,suchas;TheoryofElasticitybylongitudinal vibrationsorstressesover across TimeshenkoandGoodier(1),MathematicalTheory ofsection
9、 is uniform. ElasticitybySokolnikoff(2),Mechanical VibrationsbyDenHortog(3), ATreatiseontheTheaircraft gears, in concern, generally consists MathematicalTheoryofElasticity byLove (4), orof twogeometricalshapes, the diskand the ring. publicationsofPeterson(5), Afford(6), DragoExitingfrequencyofsolidp
10、inionsareusually (7),Tuplin(8), and AGMA (9).beyond therange oftheir operation. 3owever, bevelandbeveloidgearswhichare basicallydisks Thegoverningequationsof naturalFrequency, asand the bull orinternal gears which are basically usedingearresonanceanalysis,datesbacktoringorfinitecylindercoupledwithth
11、in disks definitionofconceptsofelasticityandstressareoftenbeingexited,atfrequenciescloseto wavepropagationbyPythagoreanandAristotlean.oneoftheirresonantfrequenciesandduringthe Equationsand theorieslater onrefined by Galileooperation 163B,RobeFtHooke167B,Isac Newton16B6,Thomas Young 1807,Cauchy1822,
12、Novier 1821, Green 1827,Wemustbealert,duringexaminationofhigh Lord Rayleigh1877.frequencywaves, it is importantto distinguish betweenthehigherorderharmonicsofthesimple Asthe20thCenturyapproached,theoriesofmodesandlower orderharmonics of higher modes. vibrationsbegantoadvancerapidlyand separatedBothc
13、onsistsofhighfrequencyvibrations,but fromthedynamicsofelasticmaterials,theresultantmotionsarephysicallyvery Basically,theequationswenowuseandcall thedifferent. edgeof technologyweremathematicallyderivedand verifiedbylarge scale tests atthe beginning ofWithrespecttotheunderstandingofthehigher thiscen
14、tury,modes ofvibration, we can examinethenodal planespassingthroughtheaxisofthecylinder. Acircularcylindervibratingin the nth modemay beconsideredasconsistingofnpairsof BACKGROUNDdiametrically oppositesectors of a circle.The n pairsof sectorsmaybe chosenin two ways, either Resonancephenomenaingearsi
15、scomplexinboundedbynodal planes of radial motion or nodal understanding.However,elementaryequationsplanesofangularmotion.Theseplanesare whichguidethedesignofhighpowerdensityseparatedbyanangle(_/2n).Fig.(1) aerospacegearing can be derived directly from theillustratesschematicallythemotion acrosscross
16、 equationsofmotionandbyusingcertainsectionsofcylindersvibratinginthemodesn = simplifying assumptions.O,O,l,2,and3(the fundamental is considered Copyright American Gear Manufacturers Association Provided by IHS under license with AGMA Licensee=IHS Employees/1111111001, User=Wing, Bernie Not for Resal
17、e, 04/18/2007 11:02:18 MDTNo reproduction or networking permitted without license from IHS -,-,- for each mode).It is noted that n = O, O, and lIt is interesting to note that when the gear blank are;special,“i.e.,thecylindervibratesasaiseffected ata frequency sufficiently close to whole, andthesemod
18、esdonotconvenientlylendone ofitsresonant frequencies.Deflections and themselves togeneralizations; they areincludedstresses canincrease tolevels where failure can for completeness,occur withinaveryshort time.Fig.(2)shows variation of stress levels during investigation of Withrespect to theunderstand
19、ing ofthehigherabevelgear.Straingagesinthiscase were harmonics of vibration, we examine thenumber oflocated on the flange of the gear. amplitude nodal cylinders concentric with the axis ofthecylinder.Thefirstharmonicisthe_RESS_I:_Pslii_i_i_i_.-T“_-_-_-:_:-_._:i_i_._;_;_.ii _ simplestvibrationforwhic
20、hreflectionoccurs,PP_J-“_“-“ _:_ a-;_i :_-_- _ ; the reflected waves combining to produce one nodal30,000_=_.:_J cylinder.Higher harmonics would be of increasing complexities,thewavescombiningtogivetwo, three, etc., nodal cylinders.20,000. Inadditionto theinfinity ofroots of a givenzO,ooO dispersion
21、relationforrealpropagation constants, there also exists an infinite number ofo rootsforcomplexpropagationconstants.These2 ,ooo_35,_ complexdispersion curvesare extensions of theRPM higherorderharmonics belowtheircut-OffFigure2 frequencies.VariationofStress Levels with _Change in Speed at Constant To
22、rque. 1.GEARDISK VIBRATIONS,(RADIAL) Naturalfrequencyofgeardiskswereso_ved AnalyticalbyKirchoffin1850andsincethen (a)“_-_/(b)basicequationsremainedsame.Duringearly 1900sPetersonexpressedKirchoffequationsin e_j_e=_“r_=_the following format. o., o,. o. = neutralax;s in _rT “_Stm;ned“neutm_ax_s _ ;n_._
23、,_H_=_-f p is frequency X 2_ _./P-C,fl.,yEis Youngs modulus M is half-thickness ,“_-_(=)a is radius a_._Noa=I_I_o_eI_-“_ is numerical coefficient depending on mode of vibration and on Poisons ratio. ._|,_;,_r_o._“_L_y is density _%/_,_X_J-._/_/A/_._/_The modeofvibration having the lowest frequency h
24、astwonodaldiameters,forwhich_=ID.61 whenavalue of 0,3isused forPoisons ratio. Using avalue of30X 106lb. per sq. in. for E andadensityof490lb.percu.ft.,the followingformulawillgive thelowest frequency (_t_/_,_o,_o_=(.)of a thin steel disk: Figure If = 208,400 h/d2(2) Motionacrosscrosssectionsofcylind
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