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Hunting Phenomenon Study of Railway Conventional View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Directory of Open Access Journals JournalofEngineeringScienceandTechnology Vol.6,No.2(2011)146-160 ©SchoolofEngineering,Taylor’sUniversity HUNTINGPHENOMENONSTUDYOFRAILWAY CONVENTIONALTRUCKONTANGENTTRACKSDUETO CHANGEINRAILWHEELGEOMETRY KARIMH.ALIABOOD*,R.A.KHAN DepartmentofMechanicalEngineering,CollegeofEngineering&Technology JamiaMilliaIslamiaNewDelhi-110025,India *CorrespondingAuthor:[email protected] Abstract A mathematical dynamic model of railway conventional truck is presented with 12 degrees of freedom equations of motion. The presented dynamic systemconsistsofconventionaltruckattachedwithtwosinglewheelsetsin which equipped with lateral, longitudinal and vertical linear stiffness and damping primary and secondary suspensions. This investigated model governslateraldisplacement,verticaldisplacement,rollyawanglesofeach ofwheelsetandthelateraldisplacement,verticaldisplacement,rollandyaw angle of conventional truck. Kalker's linear theory has been adopted to evaluate the creep forces which are introduced on rail wheels due to rail wheel contact. The railway truck mathematical equations of motion are solvedusingfourthorderRung-Kuttamethodwhichrequiresthatdifferential equationstobetransformedintoasetoffirstorderdifferentialequations.The transformed state space equations are simulated with computer aided simulationtorepresentthedynamicbehaviorandtimesolutionofdynamics ofconventionaltruckmovingontangenttracks.Influencesofthegeometric parametersoftherailwheelsuchaswheelconicityandnominalrollingradius onthedynamicstabilityofthesystemareinvestigated.Itisconcludedthat the geometric parameters of the rail wheel have different effects on the huntinginstabilityandonthechangeofthecriticalhuntingvelocityofthe system. In addition critical hunting velocity of rail trucks is proportional inversely with the square roots of wheel conicity but high critical hunting velocityobtainedbyincreasingthenominalrollingradiusoftherailwheel. Keywords:Railwheel,Conventionaltruck,Criticalhuntingvelocity,Tangent tracks,Lateralresponse,Yawresponse. 146 HuntingPhenomenonStudyofRailwayConventionalTruck 147 Nomenclatures a Halfoftrackgage,m b2 Halfdistancebetweenlongitudinalsecondarysuspensions,m Cpx Viscousdampingconstantoflongitudinalprimarysuspension,N.s/m Cpy Viscousdampingconstantoflateralprimarysuspension,N.s/m Cpz Viscousdampingconstantofverticalprimarysuspension,N.s/m Crail Lateralraildampingcoefficient,N.s/m Csx Viscousdampingconstantoflongitudinalsecondarysuspension,N.s/m Csy Viscousdampingconstantoflateralsecondarysuspension,N.s/m dp Halfdistancesbetweenprimarylongitudinalsuspensions,m Fciw Creepforcesinrail-wheelcontact(i=right,left),N Fniw Normalforcesinrail-wheelcontact(i=right,left),N Fraili Forceproducedbyrail(flangecontactforce),(i=right,left),N Fsyt Lateraltrucksuspensionforce,N Fsywi Lateralwheelsetsuspensionforce,(i=front,rear),N Fszwi Verticalwheelsetsuspensionforce,(i=front,rear),N f11 Lateralcreepcoefficient,N f12 Lateral/spincreepcoefficient,N.m 2 f22 Spincreepcoefficient,N.m f33 Forwardcreepcoefficient,N hT Verticaldistancefromwheelsetcentretothelateralsecondary suspension,m 2 Itx Truckmassmomentofinertiaabout X-axis,kg.m 2 Itz Truckmassmomentofinertiaabout Z-axis,kg.m 2 Iwx Wheelsetmassmomentofinertiaabout X-axis,kg.m 2 Iwy Wheelsetmassmomentofinertiaabout Y-axis,kg.m 2 Iwz Wheelsetmassmomentofinertiaabout Z-axis,kg.m Kpx Springstiffnessoflongitudinalprimarysuspension,N/m Kpy Springstiffnessoflateralprimarysuspension,N/m Kpz Springstiffnessofverticalprimarysuspension,N/m Krail Lateralrailstiffness,N/m Ksx Springstiffnessoflongitudinalsecondary,N/m Ksy Springstiffnessoflateralsecondary,N/m Lb Halfdistancebetweentwowheelsetsofthetruck,m Lcs Verticaldistancebetweenlateralsecondarysuspension and centre ofthecarbody,m Ls Horizontal distance between vertical secondary suspension and centreofthecarbody,m Msxwi Longitudinalwheelsetsuspensionmoment,( i=front,rear),N.m Mszt Verticaltrucksuspensionmoment,N.m Mszwi Verticalwheelsetsuspensionmoment,( i=front,rear),N.m mt Massoftruck,kg mw Massofwheelset,kg ro Centredrollingradiusofwheel,m V Railwayforwardvelocity,m/s W Axleload,N Yt Trucklateraldisplacement,m Yw Wheelsetlateraldisplacement,m Zt Truckverticaldisplacement,m JournalofEngineeringScienceandTechnology April2011,Vol.6(2) 148 K.H.A.AboodandR.A.Khan Zw Wheelsetverticaldisplacement,m GreekSymbols δ Flangeclearancebetweenwheelandrail,m λ Wheelconicity φt Truckrollangle,rad. φw Wheelsetrollangle,rad. ψt Truckyawangle,rad. ψw Wheelsetyawangle,rad. 1.Introduction Rail vehicles are considered as the most important transportation systems in the modernsocietyduetoitsabilitytomovemanypersonsandheavyloadsfast,safely andwithlowimpactontheenvironment.Theimportantfactortothepassengersto use appropriate rail vehicles is ride comfort in addition to safety. Railway transportation system safety requires that derailment or the wheel flange climb duringrailvehiclerunningisneverbeallowedwhileridecomfortrequiresaself excitedlateralrailwayoscillationorwhatcalledhuntingphenomenoniseliminated. Theclassicalhuntingoscillationisaswayingmotionofrailvehiclecausedby theforwardspeedofthevehicleandbywheel-railinteractiveforcesduetowheel- railcontactgeometryandfrictioncreepcharacteristics. Huntingisinstabilityappearsathigherspeedsasanoscillationinthewheelset and other vehicle components such as trucks and carbody. These higher rail vehiclespeedsknownasthecriticalvelocitiesinwhichtherailvehiclestartsto huntorstartstobeinstableequilibrium.Belowacertaincriticalspeed,themotion isdampedoutandabovethecriticalspeedthemotioncanbeviolent,damaging trackandwheels,andpotentiallycausingderailment. Wheelsetisthebasiccomponentoftherailvehicleresponsibleforsafeand comfortabletransportationanditisthemostcomponentinrailvehicleplayingan important role in this undesirable derailment and hunting phenomenon which causedduetoproducedforcesbetweenthewheelandtracks.Mostoftheseforces whicharecalledthecreepforcesintroducedaccordingtofrictionpropertiesofthe wheel rail contact geometry. It is well known that the undesirable hunting instabilities of wheelset transform to the trucks and car body in which can be eliminatedbyincreasingthecriticalvelocitiesoftherailwayvehicle. There are two types of trucks in the rail vehicle conventional and uncon- ventionaltrucks.Inwhichtherailwheelsareattachedtogetherwithasolidaxlein conventionaltruckssotherailwheelsaredependentlyrotatingandmovingwhile thewheelsareindependentlyrotatingandmovingintheunconventionaltrucks.The importantparametersintherailwheelgeometryarethewheelconicityandnominal rollingradius.Influencesofthesewheelparametersofgeometryonthestabilityof thetrucksareinvestigatedinthisresearch. Many researches have been presented to study the dynamic behaviour and stability of rail vehicle components due to wheel rail contact creep forces at the criticalhuntingvelocitywhiletheparametersoftherailwheelgeometryhavetaken intoconsideration.AnearlystudyonthissubjectwaspresentedbyWickens[1,2] JournalofEngineeringScienceandTechnology April2011,Vol.6(2) HuntingPhenomenonStudyofRailwayConventionalTruck 149 in which the dynamic stability of railway vehicle wheelsets and bogies having profiledwheelsisinvestigated.Itwasshownthatthedynamicinstabilityofrailway vehiclebogiesandwheelsetsiscausedbythecombinedactionoftheconicityofthe wheelsandthecreepforcesactingbetweenthewheelsandtherails. In the study presented by Suda et al. [3] the hunting stability and curving performance of high speed rail vehicles is represented considering non-linear creep force and flange contact. In addition, the lateral force of front wheel on outer rail and critical speed of wheelset are calculated and the influence of linkagesbetweenwheelsetandtruckframewereexamined. Conventional and unconventional wheelset were used into the research investigatedbyJawaharetal.[4]inwhichnonlinearmathematicalmodelusedto evaluate the wheel-rail contact forces. In addition the results showed that unconventional system improves the dynamic features positively than the conventional system but at the same time the unconventional system shows a tendencyforaconstantlateraldisplacementofawheelsetfromthecentre. Matsumotoetal.[5]reportedthatthemeasuredcreepcharacteristicsinwheel- railcontactagreewellwiththecalculatedvaluesbasedonKalker'slineartheory [6]andshowedthatasmallchangeinwheelsetlateraldisplacementmayleadto agreatchangeincreepcharacteristics. TheresearchesinwhichdonebyAhmadianandYang[7-9]investigatedthe Hopfbifurcationandhuntingbehaviourinarailwheelsetwithflangecontactand studied the effects of nonlinear longitudinal yaw damping on hunting critical speeds showing that large increasing in yaw damping can increase the hunting critical speeds and improve the hunting behaviour while Dukkipati and Swamy [10-11] considered modified railway passenger truck designs to improve the compatibilitybetweenthedynamicstabilityandtheabilityofthevehicletosteer aroundcurvesalsotheeffectsofsuspensionandwheelconicitywereconsidered toevaluatethetrade-offbetweendynamicstabilityandcurvingperformance. Nathetal.[12]studiedthenon-lineardynamicsonrailwaywheelsetmoving on a tangent track and the governing equations of motion are derived using Lagrangianapproach.Itwasshownintheirresearchthattheresultspresentedare helpfultounderstandthecomplicatedbutimportantbehaviourofwheelsetandits dependenceonaxialvelocityandyawstiffness. An important study is presented by Mohan [13] used controllable
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