带式输送机 外文翻译 外文文献 英文文献 输送带的二维动态特性.docx
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带式输送机外文翻译外文文献英文文献输送带的二维动态特性
TheTwo-DimensionalDynamicBehaviorofConveyorBelts
3.1.1NONLINEARTRUSSELEMENT
Ifonlythelongitudinaldeformationofthebeltisofinterestthenatrusselementcanbeusedtomodeltheelasticresponseofthebelt.AtrusselementasshowninFigure2hastwonodalpoints,pandq,andfourdisplacementparameterswhichdeterminethecomponentvectorx:
xT=[upvpuqvq]
(1)
Forthein-planemotionofthetrusselementtherearethreeindependentrigidbodymotionsthereforeonedeformationparameterremainswhichdescribes
Figure2:
Definitionofthedisplacementsofatrusselement
thechangeoflengthoftheaxisofthetrusselement[7]:
ε1=D1(x)=∫¹o
ds²-ds²o
dξ
(2)
2ds²o
wheredsoisthelengthoftheundeformedelement,dsthelengthofthedeformedelementandξadimensionlesslengthcoordinatealongtheaxisoftheelement.
Figure3:
Staticsagofatensionedbelt
Althoughbending,deformationsarenotincludedinthetrusselement,itispossibletotakethestaticinfluenceofsmallvaluesofthebeltsagintoaccount.Thestaticbeltsagratioisdefinedby(seeFigure3):
K1=δ/1=q1/8T (3)
whereqisthedistributedverticalloadexertedonthebeltbytheweightofthebeltandthebulkmaterial,1theidlerspaceandTthebelttension.Theeffectofthebeltsagonthelongitudinaldeformationisdeterminedby[7]:
εs=8/3K²s (4)
whichyieldsthetotallongitudinaldeformationofthenonlineartrusselement:
3.1.2BEAMELEMENT
Figure4:
Definitionofthenodalpointdisplacementsandrotationsofabeamelement.
Ifthetransversedisplacementofthebeltisbeingofinterestthenthebeltcanbemodelledbyabeamelement.Alsoforthein-planemotionofabeamelement,whichhassixdisplacementparameters,therearethreeindependentrigidbodymotions.Thereforethreedeformationparametersremain:
thelongitudinaldeformationparameter,ε1,andtwobendingdeformationparameters,ε2andε3.
Figure5:
Thebendingdeformationsofabeamelement
Thebendingdeformationparametersofthebeamelementcanbedefinedwiththecomponentvectorofthebeamelement(seeFigure4):
xT=[upvpµpuqvqµq] (5)
andthedeformedconfigurationasshowninFigure5:
ε2=D2(x)=
e2p1pq
(6)
1o
ε3=D3(x)=
-eq21pq
1o
3.2THEMOVEMENTOFTHEBELTOVERIDLERSANDPULLEYS
Themovementofabeltisconstrainedwhenitmovesoveranidlerorapulley.Inordertoaccountfortheseconstraints,constraint(boundary)conditionshavetobeaddedtothefiniteelementdescriptionofthebelt.Thiscanbedonebyusingmulti-bodydynamics.Theclassicdescriptionofthedynamicsofmulti-bodymechanismsisdevelopedforrigidbodiesorrigidlinkswhichareconnectedbyseveralconstraintconditions.Inafiniteelementdescriptionofa(deformable)conveyorbelt,wherethebeltisdiscretisedinanumberoffiniteelements,thelinksbetweentheelementsaredeformable.Thefiniteelementsareconnectedbynodalpointsandthereforesharedisplacementparameters.Todeterminethemovementofthebelt,therigidbodymodesareeliminatedfromthedeformationmodes.Ifabeltmovesoveranidlerthenthelengthcoordinateξ,whichdeterminesthepositionofthebeltontheidler,seeFigure6,isaddedtothecomponentvector,e.g.(6),thusresultinginavectorofsevendisplacementparameters.
Figure6:
Beltsupportedbyanidler.
Therearetwoindependentrigidbodymotionsforanin-planesupportedbeamelementthereforefivedeformationparametersremain.Threeofthem,ε1,ε2andε3,determinethedeformationofthebeltandarealreadygivenin3.1.Theremainingtwo,ε4andε5,determinetheinteractionbetweenthebeltandtheidler,seeFigure7.
Figure7:
FEMbeamelementwithtwoconstraintconditions.
Thesedeformationparameterscanbeimaginedasspringsofinfinitestiffness.Thisimpliesthat:
ε4=D4(x)=(rξ+uξ)e2-rid.e2=0
ε5=D5(x)=(rξ+uξ)e1-rid.e1=0 (7)
Ifduringsimulationε4>0thenthebeltisliftedofftheidlerandtheconstraintconditionsareremovedfromthefiniteelementdescriptionofthebelt.
3.3THEROLLINGRESISTANCE
Inordertoenableapplicationofamodelfortherollingresistanceinthefiniteelementmodelofthebeltconveyoranapproximateformulationforthisresistancehasbeendeveloped,[8].Componentsofthetotalrollingresistancewhichisexertedonabeltduringmotionthreepartsthataccountforthemajorpartofthedissipatedenergy,canbedistinguishedincluding:
theindentationrollingresistance,theinertiaoftheidlers(accelerationrollingresistance)andtheresistanceofthebearingstorotation(bearingresistance).Parameterswhichdeterminetherollingresistancefactorincludethediameterandmaterialoftheidlers,belt