齿轮翻译.docx

齿轮翻译.docx

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齿轮翻译

Symbol:

Identifier:

PowerTransmission.Transmissions.Gear

Version:

3.5

File:

PowerTransmission.cat

Connectors:

ConnectorsforGear1:

MechanicalConnector（linear）

ctrT1x

radial（tangential）supportgear1,x-component;

connectabletoelementsoftheLinearMechanicslibrary

MechanicalConnector（linear）

ctrT1y

radialsupportgear1,y-component;

connectabletoelementsoftheLinearMechanicslibrary

MechanicalConnector（linear）

ctrT1z

axialsupportgear1,z-component;

connectabletoelementsoftheLinearMechanicslibrary

MechanicalConnector（rotational）

ctrR1

element forgear1canbeconnectedhere（rotationaroundz）;

connectabletoelementsoftheRotationalMechanicslibrary

ConnectorsforGear2:

MechanicalConnector（linear）

ctrT2x

radialsupportgear2,x-component;

connectabletoelementsoftheLinearMechanicslibrary

MechanicalConnector（linear）

ctrT2y

radialsupportgear2,y-component;

connectabletoelementsoftheLinearMechanicslibrary

MechanicalConnector（linear）

ctrT2z

axialsupportgear2,z-component;

connectabletoelementsoftheLinearMechanicslibrary

MechanicalConnector（rotational）

ctrR2

element forgear2canbeconnectedhere（rotationaroundz）;

connectabletoelementsoftheRotationalMechanicslibrary

ParametersandResults:

seeTableofParametersandResultQuantitiesbelow

Description:

ThemodeltypeGearstagecanbeusedfortheconversionofrotationalspeedandtorqueduringthetransmissionprocess.Itmodelsthemeshingofthegears,takingthetoothstiffnessandrotarybacklashintoaccount.Itissuitableformodelingspurandhelicalgears.Ifrequired,thegearcontactcanbemodeledasrigid.

Theradialandaxialsupportbehaviorcanbemodeledexternallyandthuscanberigidorelastic.Force,spring,andpre-loadmodelsarepossible.

Figure1:

CoordinatesystemsoftheGearstagemodel

Thegearelementtransformsdisplacements,velocities,accelerations,andforces（torques）betweentheredconnectorcoordinatesystemsandthegreeninnercoordinatesystematthetoothcontact（indicatedbyI）.ThetoothcontactmodelisdescribedinthechapterToothContact.

Furthermore,theelementisabletorepresentlosses.Thelossescanbeconsideredinthetoothcontactand/orinthegearsupports（attherotationalconnectors）.

Parameters:

Geometry

Itispossibletouseonlyconstructionaldatafortheparameterizationofthegear（seeFigure1）.Theseareinparticular:

∙theNormalModulus,

∙theToothWidth,

∙theNumberofTeethz1andz2forthetwogears,

∙theHelixAngle （measuredwithrespecttogear1,seeFigure1）,

∙thePressureAngle,

∙andtheRotaryBacklashjt.

Allthemechanicalparameters（stiffness,damping,overlap）canbecalculatedinternally,ifnothingelseisspecified.Inadditioneachparameter（ifknown）canbealteredmanuallyinfurtherparametergroupsinordertopreciselyadjustthemodeltothesituationtobesimulated. 

ToothContact

Thetoothcontactcanbemodeledasrigid（seebelow）orelastic.Ifnovaluesaregiven,SimulationXcomputesthetoothstiffnessbyaninternalapproach.Otherwiseyoucanchoosebetweenanelasticorarigidtoothcontactmodel.Furtherinformationforparameterization,calculationandresultsofthetoothcontactcanbefoundinchapterToothContact.

TheprincipalmodelofthegearstageisdefinedbytheRigidcheckbox.Itcanbehaveas

∙Spring-Damper-Backlash:

TheRigidcheckboxisdeselected.Thebehaviorisdefinedbythegivenorcomputedstiffness,damping,andbacklashparameters.Withinthebacklashthestiffnessanddampingarealwayszero.

∙RigidEndStop:

IftheRigidcheckboxisselected,themodelbehavesasrigid.I.e.,itconsistsofanidealtransformationwithrigidconnectionbetweenallconnectors（kindR=="withoutBacklash"）oranidealtransformationcombinedwitharigidendstop.ThekindofimpactcanbespecifiedbytheuserviatheToothContactparameter-inthesamewayasfortherigidendstopintheLinearMechanicslibrary.Ifabacklashispresent,itissetviatheRotaryBacklashparameter.

∙IfthecheckboxRigidisselectedandiftheContactenumerationkindRisswitchedto"withoutBacklash",thegearstageasatransformer（transmission）.Inthiscase,forceswillonlybetransferredviatherighttoothflanks,nomatterinwhichdirectionthepoweristransmitted.So,therighttoothflankstransfertensileandcompressiveforces（tensileforceshaveanegativesign）.Inthiscase,theresultvariablesfortheforcesofthelefttoothflanksFbnlandFtlaredeactivated.

∙IfConsiderationofStiffnessChangeisselected（onlypossibleifRigidisdeselected）theelementcomputesavariabletoothingstiffnessbyaninternalapproach（seechapterToothContact）.

StiffnessofToothingandDampingofToothing

∙IfRigidisdeselected,thepropertiesdialogpageFreeDefinition1providesparameterstodefinetheelastictoothcontactmodel.ReadmoreabouttheparametersandthecalculationinthechapterToothContact.

ModifiedProfile/ContactRatio

Thisgroupprovidesfurthergeometryparametersofthegear.IfConsiderationofModifiedProfileisselected,itispossibletoenter

∙profileoffsetfactorsx1andx2foreverygear.BasedonthistheeffectiveradiifortheforceandmotionquantitytransformationbetweenToothContactandconnectorcoordinatesystemswillbecomputed.

∙thecenterdistanceaofthegears.Togetherwiththetoothnumbers,theeffectivetransformationradiicanbecomputed.

∙Furthermore,theInputofanAddendumModificationispossible.TheAddendumModificationkmnintheelementGearisanabsolutevalue.Ifonlyanrelativevaluekmn,relisgiven,theabsolutevaluecanbecomputedusingthenormalmodulusmnby:

∙FinallytheTotalContactRatiocanbespecified.Bydefaultitiscomputedinternally,

butitispossibletoenteraconstantvalueforepsilon（,seechapterToothContact）inordertoconsiderdifferentkindsofmodifiedprofiles.Thetotalcontactratioisusedforthecomputationofthetotalstiffnessbythespecificstiffnessofonepairofteeth（seealsochapterToothContact）.Thus,thisparameterisredundantifSummatedMeshingSpringStiffnessisselectedforkindSonpageFreeDefinition1.Ifyoudecidetoenteravalueforthetotalcontactratio,theaddendummodificationisobsolete,becausethismodificationisalwaysconsideredwithinthetotalcontactratiovalue.

Losses（pageLoses1andpageLosses2）

Therearethreelocationsfortheconsiderationoflosses:

∙thetoothcontact,

∙thegearbearingatgear1（ctrR1）,and

∙thegearbearingatgear2（ctrR2）.

Eachlosslocationcanbeparameterizedseparately.Alllossescanbeconsideredseparatelyorincombination.

Ifreliabledataisonlyavailableforthewholegearstage,e.g.,theoverallefficiency,onlytheparametersintheboxToothing/GearStageonthedialogpageLosses1havetobeenteredandwilldeterminetheoverallefficiency.

AdetaileddescriptionofthelossmodelsingearstageelementscabefoundinthechapterLossesinGearStages.

Results:

∙Thegearmodelprovidesthenormalforces,thetangential,radial,andaxialforces,deformationsandvelocitydifferencesofthetoothcontactfortheleftandtherightflank（seechapterToothContact）.

Thetangential,radial,andaxialforcesareactingaspressureforcesw.r.t.thegreencoordinatesysteminFigure1ongear2.So,anegativeradialforcewillmovethegearsappart.

∙FurthermoretheTotalMeshingSpringStiffnessiscomputedduringsimulationandcanbeobservedintheresultvariablekbt.

∙Ifaspring-damper-backlashmodel（non-rigidmodel）ofthetoothcontactisselected,theChangeofPotentialEnergy（thepowerflowintothespringinthecontact）andthePowerLoss（powerdissipatedinthedamper）canbeexaminedtoo.

∙Ifthereisachangeofthecontactsurface,thereisalsoachangeintheplaceanddirectionwherethespringstiffness,damping,andthenormalforceact.

∙IfRigidisselectedandkindR=="withoutbacklash",thetoothcontactforcesFbnlandFtlaredeactivated（seesectionToothContactinthischapter）.

PeriodicSteadyStateSimulation:

TherelativedampingandLehr'sdampingfactorDaswellasthespectralpowersoftheleftandtherightflankPSpeclandPSpecr,resp.,areonlytakenintoaccountinthePeriodicSteadyStateSimulation.TheseparametersaredescribedinsomedetailinsectionsPeriodicSteadyStateSimulation（Parameters）andPeriodicSteadyStateSimulation（Results）ofthechapterToothContact.

Remarks:

Thegearelementonlycalculatesthedeformationforcesinthetoothengagement.Theinertiaproperties,i.e.themomentsofrotaryinertiainthegears,havetobeassignedtoexternallyconnectedobjects.

Thelinear（translatory）connectorsctrT1x,ctrT1y,ctrT1z,ctrT2x,ctrT2y,andctrT2zcanbeusedtomodelsupportproperties,aswellasforexamplepreloads,whichareappliedtothegearstage.SomeexamplesonhowtomodelsuchsituationsaregiveninthesubsectionLinearconnectionsoftheGear.

TableofParametersandResultQuantities:

Parameters:

Geometry:

NormalModulus

mn

ToothWidth

bw

HelixAngle

beta

RotaryBacklash

jt

notvisibleforRigidmodelandkindR=="WithoutBacklash"

No.ofTeeth,Gear1

z1

No.ofTeeth,Gear2

z2

PressureAngle

alphan

ToothContact:

Rigid

rigid

Selectsrigid（endstop）behaviorinsteadofelasticbehaviorin

toothcontact

ToothContact

kindR

Onlyvisible,ifRigidisselected;

Possiblesettings:

"withoutBacklash","RigidPlastic","RigidElastic",and"CoefficientofRestitution"