考虑转速的船舶推进轴系建模和冲击响应分析

第17卷第12期2013年12月

ArticleID：1007-7294（2013）12-1473-08

船舶力学

JournalofShipMechanics

Vol.17No.12Dec.2013

ModelingandShockResponseAnalysisofRotatingPropulsionShaftingofShip

JIChang-lu,JIANGFeng

(SchoolofAerospaceEngineeringandAppliedMechanics,TongjiUniversity,Shanghai200092,China)

Abstract:Asthepresentfiniteelementsoftwaresfailtosimulatepropulsionshaftingofshipwhenitrotates,anaccuratemodelwhichtookaccountofbothrotationspeedandbendingrigiditywasbuiltbymulti-bodieddynamicsmethod.Therotatingshafting’sdisplacementandstressresponsesunderimpactwereobtained.Whentheshaftingdidnotrotate,theresponsecouldalsobecalculatedbythismethodandthenwascomparedwiththeresultoffiniteelementsoftware.Thecomparisonprovedthecorrectnessofthemodel.Finally,thedisplacementandstressresponsesindifferentrotationspeedwerecompared.Theresultshowsthattheeffectrotationhadonshockresponsecouldnotbeignored.Also,thecalculationofstressprovidesanewwayofthinkingtofurtherresearch.

Keywords:propulsionshaftingofship;multi-bodieddynamicsmethod;bendingrigidity;

displacement;stress

CLCnumber:U664.3

Documentcode:A

doi:10.3969/j.issn.1007-7294.2013.12.011

1Introduction

Propulsionshaftingisacorecomponentofship’spowerplantanditsshockresistanta鄄bilityisembodimentofvitalityofship.Atpresentthecommercialfiniteelementsoftwareisunabletosimulatethepropulsionshaftingwhenitrotates,howrotationaffectstheshockre鄄sponseofshaftinghasagreattheoreticalsignificance.Manyresearchershavemadeplentyofresearchinthisfield.Finiteelementmethod[1]andmulti-bodieddynamicsmethod[2]onmodel鄄ingofpropulsionshaftingofshipareusedtosolvethecouplingproblemoftransversevibra鄄tionandrotation.Butallthesemethodsfailtoshowhowbendingrigidityaffectstheresponseofshafting,neithercanshockresponsebecalculated.Onthebasisofmulti-bodieddynamicsmodelingmethod,thispaperbuildsamoreaccuratemodelinwhichbothrotatingandbendingrigidityareconsidered:theforceonelementoftheshaftingisanalyzedandshafting’sbendingrigidityistakenaccountof.Thentheexactnaturalfrequencyandmodeofvibrationareob鄄tainedandtheorthogonalityofmodeundersuchconditionsisdiscussed.Theaccuratemodeanditsorthogonalityareusedtodecouplethekineticequation.Bydispersingthedecoupledkineticequation,thedisplacementandstressresponsesofpropulsionshaftingarecalculated.

Receiveddate:2013-08-26

Biography:JIChang-lu(1990-),male,masterstudentofTongjiUniversity,E-mail:theone900909@http://doc.guandang.net;

JIANGFeng(1966-),male,Ph.D.seniorengineer.

1474船舶力学第17卷第12期

2Themodelingofpropulsionshafting

Toanalyzetheresponseoftherotatingshafting,somesimplificationmustbedonetotheshaftingtogetthefinalmechanicalandmathmodel.Theshaftingissimplifiedtorotatingsteppedbeamwhichiscontinuous,elasticandsymmetrical.Thebeamsectionwillkeepononeflatsurfacewhendeformingandthedeformationandstressofthematerialhavealinearcor鄄relationwiththespeedofdeformation.Thesupportissimplifiedtospring-damperandpro鄄pellertolumpedmassoncenterofmassofthesectionofbeam.Theboundingconditionoftheendclosetothepropelleristreatedasfreewhileanotherendconnectedtohostistreatedasanelasticsupport.

Whendeducingthekineticequation,thefollowingthreecoordinatesystemsareused:theinertialcoordinatesystemo-Ix1y1z,wherethez-axiscoincideswiththeinitialaxisofthero鄄tatingshafting,istheglobalcoordinatesystem;therotatingcoordinatesystemo-RxRyRz.Itdescribestherotationoftheshafting;thelocalcoordinatesystemo′-ExEyEz.Itdescribesthelocationofthepoint.

Fig.1Coordinatesystemsoftheelement

Usetheoremofmomentumontheelement,andtransformwhatisobtainedintotherotat鄄ingcoordinatesystem[2],wecanget:

R

觶+棕軒dPRIRRdP-Rdf=0

(1)

軒iswhereRdPisthetotalmomentumoftheelementintherotatingcoordinatesystemR;R棕IRvectoroftheangularspeed,itreflectstheinfluencebyrotating;Rdfistheexternalforceontheelement.

Theremaybelumpedmasses,so

R

觶+棕軒觶軒dPRIRRdP=RVs+R棕IRRV

軒z-z軒dm+m啄軒軒軒軒

j

j

(2)

TheforcediagramoftheelementisshowninFig.2.Fromthediagram,wecanknow:

軒F+F+F軒坠Fsdz

Rdf=RkRcRadz-(3)

第12期JIChang-luetal:ModelingandShockResponseAnalysisof…1475

Treatanypointontherightsectionascentroidto

deducethetorquebalanceequationoftheelement[3].Ashigh-speedlargeoverallmotiondoesnotexistinthismodel,wecantakethezeroorderapproximatemethod[4].Also,thesecondderivativeoftherigidbodydisplacementtoziszero,wecanget:

Fs=坠M,M=EIz坠z

r坠R軃

2

(4)

Fig.2Forceontheelement

Thekineticequationcanbeobtainedbysubstituting

Eq.(2),Eq.(3)andEq.(4)inEq.(1).

軃軃咬軃觶-棕2r軃軃-棕2r-棕r觶軃-2棕rr軃rx軃xyxxy軃軃軃軃軃軃

軃r軃2z-zj z-zj dm+mj啄 +軃2+kj啄 +軃軃軃軃咬軃軃軃觶觶y軃軃r+2棕r-棕r-棕r+棕rxy軃軃yx軃軃軃y軃軃0軃00軃軃軃軃軃軃

軃觶軃r-棕r軃ax軃2軃2軃rxxy軃軃坠坠軃a軃z-zj z-zj dm+mj啄 -軃+軃EIcj啄 z軃ry軃軃觶軃y軃軃軃軃r+棕rx軃軃y坠z軃0軃0軃坠z軃0軃軃

軃軃

軃軃dz=0軃軃軃軃

(5)

3Thesolutionofdisplacementandstressresponse

Takethemodesuperpositionmethodtogettheresponse.Asrx,ryhavethesamebound鄄arycondition,rx,rycanbeexpressedas:

rx=移准i zqui t,ry=移准i zqvi t

i=1

i=1

∞

∞

(6)

where准i zistheorthogonalmodalshapefunctionofthesteppedbeam.

Wecanusethefollowingmethodtogetthevibrationmodeoftheshaft:thetransferma鄄

trixoftheboundaryconditionofbothendsisobtainedandthenextendedtotheconditionthattheshaftinghaslumpedmassedandelasticsupportsonit[5].Thenewrecurrencerelationisshownasfollows:

Ln 軃軃准n 0 軃軃准1 軃軃軃准′ L 0 軃****1軃准n′n軃軃軃軃軃軃浊n軃浊n-1軃浊2軃……軃=Kn軃(7)軃軃Kn-1軃K2軃K1軃 准″Ln 軃軃0軃准n″ 軃軃軃1軃軃軃 准苁0 L准苁1軃軃n軃n軃

Substitutetheboundaryconditionswhichare4oftheeightunknownsinEq.(7).Thenat鄄areobtainedbecausetheboundaryconditionscannoturalfrequencyandtransfermatrix軃Kn軃

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