论文翻译轨道方面Word文档下载推荐.docx
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论文翻译轨道方面Word文档下载推荐.docx
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Slipstickvibrationsareoneoftheformsofselfexcitedvibrations.Whenavehiclerunsonasharplycurvedtrack,thewheelsarelikelytoslipduringrollingontherailsincethedifferenceofrollingradiusbetweentheoutsideandinsidewheelisnotenoughforthewheelsettonegotiatethecurve.Astheaxlesofawheelsetareelasticbodies,undersomeconditions,forexample,thecreepcurvewithafallingcharacteristicinthesaturatedpart,slip-stickvibrationsmaybecausedbythetorsionorbendingvibrationofwheelsetorthecombinedeffectofthem[1,2].Theslip-stickvibrationisgenerallythoughttoinducerailcorrugationsoncurvedtracks[3].Butmuchoftheformationmechanismofrailcorrugationshasnotbeensuccessfullyexplained,fortheresearchabouttheslip-stickvibrationsisratherinsufficient.Therearetwomainshortcomingsintheexistinganalyses.First,thesimulatingmodelsareoversimplifiedinwhichonlythetorsionorbendingvibrationofwheelsetisconsidered,butothervibrationsinthewheel/railsystemareallomitted.Second,ithasnotbeeninvestigatedhowtheslip-stickvibrationsbehavewhenthemasses,stiffnessanddampinginthesystemvaryoverwideranges.Infact,theslip-stickvibrationsmayshowgreatdifferences.Therailcorrugationsarealsolikelytohavevariousfeatures.Obviously,itisnecessarytofurtherinvestigatetheslip-stickvibrationsandrailcorrugations.
1DynamicModel
ThedynamicmodeldevelopedinthispaperbasedonRef.[4]isaverticallateral,spacecoupling,nonlinearandtimedependentmodelforsimulatingthewheel/railsystemvibrationsaswellasthetorsionandbendingvibrationsofwheelsets.
1.1Tracksinthemodel
Thelongitudinalvibrationoftrackscanbeneglectedascomparedwiththeverticalandlateralvibrationsaccordingtoafieldtest(tobepublished).Theballast,subgradeandfasteningsaresimplifiedasaseriesoftwo-dimensionallinearspringsanddampers.Thesleepersareregardedasstiffblocks,fortheirbendingdeformationscanbeneglectedincontrasttotheballastsettlement.Eachsleeperhas3degreesoffreedom,theverticalandlateraldisplacementsandtherollingangle.
Thetworailsaresimplifiedasdouble-directionalflexibleEulerbeamswithverticalandlateralflexures,ZrandYr.Alengthoftrackisselectedasthecalculatedsegment,whichcontainsN-1sleeperspans,whereNisgenerally30.Eachspanisafiniteelementwith8degreesoffreedom.Thetrackinthemodelhas11Ndegreesoffreedomintotal.
1.2Vehicleinthemodel
Themodelinvolveshalfavehicle,i.e,onebogieandhalfacar-body.Thecar-bodyhas2degreesoffreedom,i.e,theverticalandlateraldisplacement.Betweenthecar-bodyandbogieframe,therearesecondarysuspensions,whicharesimplifiedasthree-dimensionallyfixedspringsanddampers.Thebogieframehas5degreesoffreedom,ie,theverticalandlateraldisplacements,rollingangle,yawingangleandpitchingangle.Betweenthebogieframeandwheelsets,thereareprimarysuspensions,whicharealsosimplifiedasthree-dimensionallyfixedspringsanddampers.Eachwheelsethas8degreesoffreedom.Asastiffblock,awheelsethas4degreesoffreedom,thatis,theverticalandlateraldisplacementsZwandYw,rollingangleΨw,andyawingangleφw,Whenanaxleisconsideredasaelasticbody,awheelsethasanother4degreesoffreedom,i.e.,twotorsionanglesθjandtwobendinganglesβjThesubscriptj(j=1to4foratwo-axlebogie)istheserialnumberofwheels,1and3beingonthehighrail,2and4beingonthelowrail.Wheel1istheleadingwheel.Theoperationofsubscriptsbelongstointegerdomain.Thetotaldegreesoffreedomforthevehicleare23.Onceawheelflangeiscontactingwiththerailhead,thecorrespondingflangeforceFjandthecooperativeconditionsofthewheel/raillateraldisplacementsareaddedintothevibrationequations.
1.3Nonlinearcreepforces
Equs.
(1)to(3)expressthelongitudinal,lateralandspincreepages.Thecoordinatesaredefinedas:
Xforward,Ytowardthecurvaturecenterofcurvedtrack,Zdownward,andalltheangulardisplacementsareobedienttotheright-handrule.
InEqus.
(1)to(3),γjistimedependentrollingradiusofthej-thwheel,γ0isnominalrollingradiusofthewheel,bishalfofthetrackgauge,Risradiusofthecurvedtrack,λisconicity
ofthe
ofthewheeltread,Visspeedofthevehicle,ηHjisamplitudeofthelateralirregularitiesoftrackunderj-thwheel,and,
ThecreepforcesT1jandTT2jandmomentM3jcanbeobtainedwithKalkermethod[5]anditeratedbythecubicsaturationlawofVermeulenandJohnsonshowninEqu.(5a)
saturation,oriteratedbyacreepcurvewithnegativeslopeinEqu.(5b)aftersaturation.AccordingtothevirtualworkinEqu.(6),thecreepforcescanbeaddedintotheloadvectorstepbystep.Thewearindex(wearwork)betweenwheelandrail,bywhichthewearonrailsurfacesisqualitativelydescribed,canbecomputedbyEqu.(7).
InEqus.(5)to(7),μ2isfrictioncoefficientbetweenthewheeltreadandrail,μdisdynamicfrictioncoefficientbetweenthewheeltreadandrail,Pjiscontactforcesbetweenthej-thwheelandrail,TRJandT′RJiscombinedcreepforcesbetweenthej-thwheelandrail.
1.4Nonlinearcontactforces
Wheel/railcontactsareregardedasnonlinearsprings.Thedeformationenergiesofcontactspringsaretobeaddedintothetotalpotentialenergyofthesystem.Theoneordervariationofthe
deformationenergyisexpressedaswhereKcjisthetimedependentstiffnessofthej-thcontactspring,and
InEqu.(9),ρjisthecompressionofthej-thcontactspring,
whereηvjstandsfortheamplitudeofverticalirregularityoftrackunderthej-thwheel.EveryterminEqu.(8)shouldbeaddedintotheglobalstiffnessmatrixandtheloadvectorstepbystep.
1.5Flangeforces
Itshouldbedeterminedineverystepduringcomputationwhetherawheelflangeis
contactingwiththerailhead.Thecriteriaisgivenby
whereδ0ishalfthenormalplaybetweenthewheelflangeandrailhead.WhenІj>
0,thejthflangeiscontactingwiththerail,andwhenІj<
0,itisnot.Whenthej-thflangeiscontactingwiththerail,Іj=0playsasacooperativeequationofthewheel/raillateraldisplacements.TheflangeforcesandflangefrictionforcescanbeaddedintotheglobalstiffnessmatrixaccordingtothevirtualworkinEqu.(12).
whereμ1isthefrictioncoefficientbetweentheflangeandrail.Otherwise,thepivotelementrelatedwithFjintheglobalstiffnessmatrixshouldbegivenavaluelargeenough.
1.6Assemblyandsolutionofvibrationequations
ThevibrationequationscanbederivedinthelightofHamiltonvariationprincipal.Firstly,theone-ordervariationoftotalkineticenergyandtotalpotentialenergyofthewholesystemarederived,soarederivedthevirtualworkofdampingforces,creepforces,wheel/railcontactforces,flangeforcesandflangefrictionalforces,unbalancedcentrifugalforces,weightforces,andsoon.Then,thevibrationequations,intheformofEqu.(13),areautomaticallyformedintheprogramme.
Thevibrationequationsaresolvedbythedirectintegrationmethod.TheWilsonmethodischoseninthefirsttwosteps.FromthethirdsteptheParkmethodisutilized.Itisdemonstratedthroughdatumexperimentthatiftheanalysisfrequencyislowerthan200Hz,thetimestepshouldbelessthan0.5ms.Thecomputerprogrammeisofafour-loopstructure.Theouterloopistofindthebogielocation.Thesecondloopistodetermineflangecontacts.Thethirdloopistoiteratenonlinearcreepforcesinwhichtheaccuracyofcombinedcreepforcesisgiventobe1%.Theinnerloopistoiteratenonlinearcontactforcesinwhichtherelativeerrorofcontactforcesissetto0.1%.Theoutputsoftheprogrammearevariousvibrationquantitiesintimedomain.ThefastFouriertransformalgorithm(FFT)canalsoobtainthefrequencyfeatures.Theprogrammeisdemonstratedtobemuchefficientinsimulatingwheel/railspacecouplingvibrationswhenvehiclesorlocomotivesmoveoverthestraightandcurvedtrackwithanykindsofirregularities.
2Slip-StickVibrationsofWheelsets
Itisverifiedthroughlargequantityofcomputationsthatundercertainconditionsthethreeformsofvibrationscanformacirculativeselfexcitedvibrationsysteminviewofcrossingexcitationorselfexcitation.Itisdiscoveredforthefirsttimethattheslipstickvibrationsmayoccurinmorethanoneforms,foroneoranotherofthethreevibrationsisexcitedmoreseverelywhentheparametersofwheel/railsystemvaryoverwiderages.Sometypicalexamplesareenumeratedanddescribedasfollowing.
2.1Thefirstkindofslip-stickvibrations
Thefirstkindofslip-stickvibrationsismainlycausedbythetorsionvibrationofwheelsetundertheconditionofexcessivelateralstiffnessofsharplycurvedtrackwherethecreepforcesreachorapproachsaturationstates.Forexample,whenafreightvehiclewithrunsonthecurvedtrackof300minradiuswithalateralballaststiffnessof2.0*105kN/m,thevibrationoftheleadingwheelbehavesasthefirstkindofslip-stickvibration.ThewearindexoftheleadingwheelfromEqu.(7)isshowninFig.1.Intheslipzones,thevaluesofwearindex(W)arelargeandalmostkeepconstant.Inthestickzones,thevaluesaresmallerandvaryalittle.Thewearindexintimedomainexperiencesaseriesofnegativepulsesandthiscoursecontinuessteadily.Theconversionratesofcreepforces
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