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    A

    PROJECT

    REPORTSUBMITTEDINPARTIALFULLFILMENT

    FOR

    THEAWARDOFDEGREEOFBACHELOROFTECHNOLOGY

    IN

    MECHANICALENGINEERING

    BYCH.KRISHNACHAITANYAVARMA(07241A0309)

    PADMANABHDAS(07241A0313)

    PUNEETKUMAR.J(07241A0315)

    THERMALANDSTRUCTURALANALYSISOFVENTEDANDNORMALDISC

    DEPARMENTOFMECHANICALENGINEERING

    GOKARAJURANGARAJUINSTITUTEOFENGINEERINGANDTECHNOLOGY

    (AFFLIATEDTO

    JAWAHARLAL

    N

    EHRU

    TECHNOLOGICAL

    UNIVERSITY)

    HYDERABAD

    20072011

    BRAKEROTORS

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    ACKNOWLEDGEMENT

    Iexpressmygratitudetochairman,projectReviewCommittee,JNTUCollegeof

    Engineering,

    for

    their

    valuable

    recommendations

    and

    for

    accepting

    this

    project

    work.

    Iexpressmydeepsenseofgratitudetowardsmyableandacknowledgeguide,Mr.

    Ra t n a ki r a n ,Asst.Professor,MechanicalEngineering,GRIET,Hyderabad,t o w h o mIowe

    thecreditofbeingthemovingspiritbehindthisproject,wh o s e gu i d a n c eandconstant

    inspirationledmetowardsitscompletion.

    I

    convey

    my

    sincere

    thanks

    to

    Mr . K . G . K MU RT H Y ,

    Head

    of

    the

    Mechanical

    Engineering

    Department&Mr . P . S . V . K U RMA RA OProfessor,GOKARAJURANGARAJUINSTITUEOF

    ENGINEERINGANDTECNOLOGY,HYDERABADforhiskindcooperationi n t h ecompletionof

    theproject.

    Atthisjuncture,Ifeelthat,IamgratefultoMr.PRADEEP,ORANGETECHNOLOGIES,

    AMEERPET, HYDERABAD,forassistanceincompletionofprojectwork.

    Finally,Iextendmysenseofgratitudetoallmyfriends,teachingandnonteachingstaff,

    whodirectlyorindirectlyhelpmeinthisendeavor.

    CH,K r i s h a n a c h a i t a n y a v a r m a ( 07241A 0309)

    P a d m a n a b h D a s ( 07241A 0313)

    P u n e e t ku m a r .J(07241A0315)

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    ABSTRACT

    Safety

    aspect

    in

    automotive

    engineering

    has

    been

    considered

    as

    a n u m b e r

    onepriorityindevelopmentofnewvehicle.Eachsinglesystemhasbeenstudiedand

    developedinordertomeetsafetyrequirement.Insteadofh a vi n g a i rbag,goodsuspensionsystems,

    goodhandlingandsafecornering,thereisonemostcriticalsysteminthevehiclewhichisbrakesystems.

    Withoutbrakesysteminthevehiclewillputapassengerinunsafeposition.Therefore,itisamustforall

    vehiclestohaveproperbrakesystem.Duetocriticalsysteminthevehicle,manyofresearchershave

    conductedastudyonbrakesystemanditsentirecomponent.Inthisproject,theauthorhasconducted

    astudyonventilatedandnormaldiscbrakerotorofnormalpassengervehiclewithfullloadofcapacity.

    Thestudyismorelikelyconcernofheatandtemperaturedistributionondiscbrakerotor.

    Steady

    state

    and

    transient

    response

    has

    been

    conducted

    through

    the

    heat

    transfer

    analysiswheretopredicttheworsecasescenarioandtemperaturebehaviorsofdiscbrakerotor.

    Inthisstudy,finiteelementanalysisapproachedhasbeenconductedinorderto

    identifythetemperaturedistributionsandbehaviorsofdiscbrakerotorinsteadystateandtransient

    responses.An s y s i s h a sbeenusedasfiniteelementssoftwaretoperformthethermalanalysisonboth

    responses.Bothresultshavebeencomparedforbetterjustification.Thus,bothresultsprovidebetter

    understanding

    on

    the

    thermal

    characteristic

    of

    disc

    brake

    rotor

    and

    assist

    the

    automotive

    industry

    in

    developingoptimumandeffectivediscbrakerotor.

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    OBJECTIVEANDSCOPE

    ., :

    , ,.

    ( )

    . .

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    Partsofdiscbrake

    1.DISCCALIPERS

    ..( ,1996)..

    ,

    .

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    2.BRAKEPADS

    . ( , 1980),

    ,

    .

    750 , - 950'~

    0.25 0.5.

    ,

    . ,

    .

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    3.BRAKEDISC/DISCBRAKEROTOR

    Disc

    brake

    rotor

    is

    a

    crucial

    partinthebrakesystemwherethemainroleoftherotoristoreducetheheat

    generated

    by

    dissipates

    all

    oftheheat.Inthatcase,

    ventilateddiscbrakerotorismuchbetterthansolidrotorwhere

    more

    airflow

    from

    the

    surroundingareatodissipateproducedheat.Figure2.9,

    shows

    the

    internal

    vanesallowairtocirculatebetween

    twofrictionsurfacesoftherotors

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    MODELLINGSOFTWARE

    Therearedifferentsoftware'savailableformodelingsomeofthemare:

    Solidworks

    ProE

    Ideas

    Inventor

    Mechanical

    desktopUnigraphics

    C a t i a v 5

    CATIA

    V5

    (computer

    aided

    three

    dimensional

    interactive

    a ppl i ca ti o n)a mul tiplatformCAD/CAM/CAEisusedasthemodelingtoolinthisproject

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    CATIAV5

    CATIAV5providesthepowerofparametricdesign.With

    parametric,wedefinethemodalaccordingtothesizeand

    positionalrelationshipofitsparts

    1.INTRODUCTION

    2.PART MODELLING

    Manytechnicaldesignsconsistsofcomplexassembliesmadefromangular

    shapedparts.Thistypeofdesignworkcanbemadea s i e r b ypartand

    assemblymodelingcapabilitiesthatarewellintegrated.TheCATIAV5isa

    3

    D

    parametric

    solid

    modeler

    with

    both

    part

    and

    assembly

    modeling

    capabilities.YoucanseetheCATIAV5tomodelpiecepartsandthen

    combinethemintomorecomplexassemblies.WithCATIAV5apartis

    designedbysketchingitscomponentsshapesanddefiningtheirsizeshape

    and

    inter

    relationships.

    By

    successfully

    creating

    these

    fea t u r es y o uconstructthepartinabuildingblockfashion.SinceCATIAV5has

    parametricfeatures,youcanchangeonefeatureandallrelatedfeatures

    areautomaticallyupdatedtoreflectthechangeanditseffectsthroughout

    thepart.Itcanbeusedtocreateangularshapedpart,tow h i c h 3 Dsurface

    canbeappliedtocreatehybridpartsconsistingofmixtureofangularand

    curvedshapes.Thisprovidestheabilitytocreatemodeld esi gn s wi t h

    shapesofvaryingtypes

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    3.GENERALMODELINGPROCESSFOREACHPART

    P l a nthepart

    C r e a t e

    the

    base

    feature

    C r e a t etheremainingfeatures

    Analyze

    the

    part

    Modifythefeaturesasnecessary

    Assembly

    modeling

    FINITE ELEMENT ANALYSIS

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    FINITEELEMENT

    ANALYSIS

    Thefiniteelementmethodisnumericalanalysistechniqueforobtaining

    approximatesolutionstoawidevarietyofengineeringproblems. Becauseofits

    diversityandflexibilityasananalysistool,itisreceivingmuchattentioninalmost

    everyindustry.Inmoreandmoreengineeringsituationstoday,wefindthatitis

    necessaryto

    obtain

    approximate

    solutions

    to

    problem

    rather

    than exact

    closed

    form

    solution.

    INTRODUCTION

    PROCEDUREFOR

    ANSYS

    ANALYSIS

    Theprocedureforstaticanalysisconsistsof

    thesemainsteps

    Buildingthe

    model

    Obtainingthesolution

    Reviewingtheresults

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    BUILDTHEMODEL

    MATERIALPROPERTIES

    InthisstepwespecifythejobnameandanalysistitleusePREP7todefinetheelement

    types,

    element

    real

    constants,

    material

    properties

    and

    model

    geometry

    element

    type

    bothlinearandnon linearstructuralelementsareallowed.TheANSYSelementslibrary

    containsover80differentelementtypes.Auniquenumberandprefixidentifyeach

    elementtype.

    E.g.

    BEAM

    94,

    PLAN

    71,

    SOLID

    96

    and

    PIPE

    16E

    Y o u n g.s mo d u l u s(EX)mustbedefinedforastaticanalysis.Ifweplantoapplyinertia

    loads

    (such

    as

    gravity)

    we

    define

    mass

    properties

    such

    as

    density

    (DENS).

    Similarly

    ifweplantoapplythermalloads(temperatures)wedefinecoefficientofthermalexpansion

    SOLUTIONInthisstepwedefinetheanalysistypeandoptions,apply

    loadsandinitiatethefiniteelementsolution.Thisinvolves

    threephases:

    PreprocessorphaseSolutionphasePostprocessorphase

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    PRE

    PROCESSOR

    PHASE SOLUTION

    PHASE

    POST

    PROCESSOR

    GEOMETRYDEFINITION ELEMENTMATRIXFORMATION POSTSOLUTIONOPERATION

    MESH GENERATION OVERALLMATRIXT RIA NG ULAR IZA TIO N P OSTDATAPRINTOUTFORREPORTS

    MATERIAL WAVEFRONT POSTDATA

    DEFINITIONS SCANINGPOSTDATADISPLAY

    CONSTRAINDEFINITIONS DISPLACEMENT,STRESS,ET.,

    LOADDEFINITIONS CALCULATION

    MODELDISPLAY

    ThefollowingTable showsthebriefdescriptionofstepsfollowedineachphase

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    FINITEELEMENTGENERATIONThemaximumamountoftimeinafiniteelementanalysisisspent

    on

    generating

    elements

    and

    nodal

    data.

    Pre

    processor

    allows

    the

    usertogeneratenodesandelementsautomaticallyatthesame

    timeallowingcontroloversizeandnumberofelements.There

    arevarioustypesofelementsthatcanbemappedorgenerated

    on

    various

    geometric

    entities.

    The

    elements

    developed

    by

    variousautomaticelementgenerationcapabilitiesofpreprocessorcanbe

    checkedelementcharacteristicsthatmayneedtobeverified

    beforethefiniteelementanalysisforconnectivity,distortion

    indexetc.Generally,automaticmeshgeneratingcapabilitiesof

    preprocessorareusedratherthandefiningthenodesindividually.Ifrequirednodescanbedefinedeasilybydefiningtheallocations

    orbytranslatingtheexistingnodes.Alsoononecanplot,delete,

    orsearchnodes.

    BOUNDARYCONDITIONSANDLOADING

    Aftercompletionofthefiniteelementmodelithastoco n st r a i n a n d

    loadhastobeappliedtothemodel.Usercandefineconstraints

    and

    loads

    in

    various

    ways.

    All

    constraints

    and

    loads

    are

    assigned

    set

    ID.Thishelpstheusertokeeptrackofloadcases.

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    MODELDISPLAY

    During

    the

    construction

    and

    verification

    stages

    of

    the

    model

    it

    may

    be

    necessary

    to

    view

    itfromdifferentangles.Itisusefultorotatethemodelwithrespecttotheglobalsystem

    andviewitfromdifferentangles.Preprocessoroffersthiscapabilities.Bywindowing

    featurepreprocessorallowstheusertoenlargeaspecifica r e a o f themodelforclarity

    and

    details.

    Pre

    processor

    also

    provides

    features

    like

    smoothness,

    scaling,

    regions,

    active

    set,etcforefficientmodelviewingandediting.

    MATERIALDEFECTIONS

    Allelementsaredefinedbynodes,whichhaveonlytheirlocationdefined.Inthecase

    of

    plateandshellelementsthereisnoindicationofthickness.Thisthicknesscanbegiven

    aselementproperty.Propertytablesforaparticularpropertyset1Dhavetobeinput.

    Differenttypesofelementshavedifferentpropertiesfore.g.

    Beams:Crosssectionalarea,momentofinertiaetc

    Shell:

    Thickness

    Springs:Stiffness

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    POSTPROCESSORIt is a powerful user- friendly post- processing programusing interactive colour graphics.

    It has extensive plotting features for displaying the resultsobtained from the finite element analysis. One picture ofthe analysis results (i.e. the results in a visual form) canoften reveal in seconds what would take an engineer hourto assess from a numerical output, say in tabular form. Theengineer may also see the important aspects of the results

    that could be easily missed in a stack of numerical data.Employing state of art image enhancement techniques,facilities viewing of:

    Contours of stresses, displacements, temperatures etc.Deform geometric plots Animated deformed shapes Time-history plots Solid sectioning Hidden line plot Light source shaded plot

    Boundary line plot etc.

    The entire range of post processing options of differenttypes of analysis can be accessed through thecommand/menu mode there by giving the user addedflexibility and convenience.

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    THERMALANALYSISAthermalanalysiscalculatesthetemperature

    distributionand

    related

    thermal

    quantitiesinbrakedisk.Typicalthermal

    quantitiesare:

    1.Thetemperaturedistribution

    2.Theamountofheatlostorgained

    3.Thermalfluxes

    Typesofthermalanalysis

    1.Asteadystatethermalanalysisdeterminesthetemperature

    distributionandotherthermalquantitiesundersteadystateloading

    conditions.Asteadystateloadingconditionisasituationwhere

    heatstorageeffectsvaryingoveraperiodoftimecanbeignored.

    2.Atransientthermalanalysisdeterminesthetemperature

    distributionandotherthermalquantitiesunderconditionsthat

    varyingoveraperiodoftime.

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    PLANNINGTHEANALYSIS

    In this step a compromise between the computer time andaccuracyoftheanalysis ismade.Thevariousparametersset inanalysis

    are

    given

    below:

    Thermalmodeling

    Analysistype.thermalhmethod.

    SteadystateorTransient?Transient

    Thermalor

    Structural?

    Thermal

    Propertiesofthematerial?Isotropic

    Objectiveofanalysistofindoutthetemperaturedistributioninthebrakedisk

    whenthe

    process

    of

    braking

    is

    done.

    UnitsSI

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    Structuralanalysisisthemostcommonapplicationofthefinite element

    analysis.The

    term

    structural

    implies

    civil

    engineering

    structure

    such

    as

    bridge

    andbuilding,butalsonaval,aeronauticalandmechanicalstructuresuchasship

    hulls,aircraftbodiesandmachinehousingaswellasmechanical components

    suchaspiston,machinepartsandtools.

    STRUCTURALANALYSIS

    Typesofstructuralanalysis:

    Staticanalysis

    Modalanalysis

    Harmonicanalysis

    Transientdynamicanalysis

    Spectrumanalysis

    Buckling

    analysis Explicitdynamicanalysis

    TheseventypesofstructuralanalysesinANSYS.Onecanperform the

    followingtypes

    of

    structural

    analysis.

    Each

    of

    these

    analysis

    types

    are

    discussedasfollows:

    MODELING AND ANALYSIS

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    MODELINGANDANALYSIS

    Itisverydifficulttoexactlymodelthebrakedisk,inwhichtherearestill

    researchesare

    going

    on

    to

    find

    out

    transient

    thermo

    elastic

    behavior

    of

    disk

    brake

    duringbrakingapplications

    1.Thediskmaterialisconsideredashomogeneousandisotropic.

    2.Thedomainisconsideredasaxissymmetric.

    3.Inertia

    and

    body

    force

    effects

    are

    negligible

    during

    the

    analysis.

    4.Thediskisstressfreebeforetheapplicationofbrake.

    5.Brakesareappliedontheentirefourwheels.

    6.Theanalysisisbasedonpurethermalloadingandvibrationand thusonlystresslevel

    due

    theabove

    said

    is

    done.

    The

    analysis

    doesnotdeterminethelifeofthediskbrake.

    7.Onlyambientaircoolingistakenintoaccountandnoforced

    Convectionistaken.

    8.Thekineticenergyofthevehicleislostthroughthebrakedisksi.e.

    noheatlossbetweenthetyre andtheroadsurfaceanddeceleration

    isuniform.

    9.Thediskbrakemodelusedisofsolidtypeandnotventilated one.

    10.Thethermalconductivityofthematerialusedfortheanalysisis

    uniformthroughout.

    11.Thespecificheatofthematerialusedisconstantthroughoutand

    doesnotchangewithtemperature.

    DEFINITION OF PROBLEM DOMAIN

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    DEFINITIONOFPROBLEMDOMAINDuetotheapplicationofbrakesonthecardiskbrakerotor,heat

    generationtakesplaceduetofrictionandthisthermalfluxhas tobe

    conductedand

    dispersed

    across

    the

    disk

    rotor

    cross

    section.

    The condition

    ofbrakingisverymuchsevereandthusthethermalanalysishas tobe

    carriedout.Thethermalloadingaswellasstructureisaxissymmetric.

    Henceaxissymmetricanalysiscanbeperformed,butinthisstudywe

    performed3D

    analysis,

    which

    is

    an

    exact

    representation

    for

    this

    thermal

    analysis.Thermalanalysisiscarriedoutandwiththeaboveloadstructural

    analysisisalsoperformedforanalyzingthestabilityofthestructure.

    The3dmodelofthesolidtypebrakeisdoneinCATIAandconvertedinto

    Parasolid

    file.

    Fig.solidtypediskbrake3Dmodelisometricview

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    Fig.solidtypediskbrake3Dmodelfrontview

    Fig.

    solid

    type

    disk

    brake

    3D

    model

    wireframe

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    SOLID90isahigherorderversionofthe3Deightnodethermalelement(SOLID70).The

    elementhas20nodeswithasingledegreeof

    freedom,temperature,ateachnode.The20

    node

    elements

    have

    compatible

    temperature

    shapesandarewellsuitedtomodelcurved

    boundaries.The20nodethermalelementis

    applicabletoa3D,steadystateortransient

    thermal

    analysisThegeometry,nodelocations,andthe

    coordinatesystemforthiselementareshown

    inFigure"SOLID90Geometry".Theelementis

    definedby20nodepointsandthematerial

    properties.

    A

    prism

    shaped

    element

    may

    be

    formedbydefiningduplicateK,L,andS;Aand

    B;andO,P,andWnodenumbers.

    SOLID90ElementDescription

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    face

    1

    (J

    I

    L

    K),

    face

    2

    (I

    J

    N

    M),

    face

    3

    (J

    K

    O

    N),

    face4(KLPO),face5(LIMP),face6(MNOP)

    HG(I),HG(J),HG(K),HG(L),HG(M),HG(N),HG(O),HG(P),HG(Q),HG(R),

    HG(S),HG(T),HG(U),HG(V),HG(W),HG(X),HG(Y),HG(Z),HG(A),HG(B)

    SOLID90InputSummary

    Nodes

    I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A,B

    Degrees

    of

    Freedom

    TEMP

    MaterialProperties

    KXX,KYY,KZZ,DENS,C,ENTH

    SurfaceLoads

    C o n v e c t i o n o r

    Heat

    Flux

    (but

    not

    both)

    and

    Radiation

    (using

    Lab

    =

    RDSF)

    BodyLoads

    HeatGenerations

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    Fig.solidtypediskbrakemeshmodel Fig.solidtypediskbrakemeshmodelisometricview

    Totalnumberofelements=39800

    Totalnumberofnodes=98104

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    APPLYINGTHEBOUNDARYCONDITIONSInthermalandstructuralanalysisofdiskbrake,wehave

    to

    apply

    thermal

    and

    boundary

    conditions

    on

    3D

    disk

    modelofdiskbrake.

    THERMALBOUNDARYCONDITIONSAsshowninFig.amodelpresentsathreedimensional

    solid

    disk

    squeezed

    by

    two

    finite

    width

    friction

    material

    calledpads.Theentiresurface,S,ofthediskhasthree

    differentregionsincludingS1andS2.OnS1heatfluxis

    specifiedduetothefrictionalheatingbetweenthepads

    anddisk,andS2isdefinedfortheconvectionboundary.

    The

    rest

    of

    the

    region,

    except

    S1

    U

    S2,

    is

    either

    temperaturespecifiedorassumedtobeinsulated:the

    innerandouterrimareaofdisk.

    Fig.ThermalmodelofDiskbrake

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    Fig.Temperatureboundaryconditionof77degreesCappliedonsolidtype

    DiskbrakeFig.ConvectionboundaryconditionappliedonsolidtypeDiskbrake

    Material

    Properties

    on

    Pad

    and

    Disk

    Thermalconductivity,K( w / m k )

    Density,r (kg/m3)

    1800

    Specificheat,c(J/Kgk) 1.88

    Poissons

    ratio,

    v 0.3

    Thermalexpansion, ( 1 06/k) 0.3Elasticmodulus,E(GPa) 50.2

    Coefficientoffriction, 0.2

    Fig.TemperaturedistributiononsolidtypeDiskbrakeonthefront

    side

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    Fig.TemperaturedistributiononsolidtypeDiskbrakeontherearside

    Fig.TemperaturedistributiononsolidtypeDiskbrakealongthe

    thickness

    Fig.GraphicalrepresentationofTemperaturedistributiononsolidtypeDisk

    brake

    along

    the

    thickness

    STRUCTURALANALYSISNORMALDISCBRAKEROTOR

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    STRUCTURALBOUNDARYCONDITIONS

    Sincetheaxissymmetricmodelisconsideredallthenodesonthehubradius

    arefixed.Sothenodaldisplacementsinthehubbecomezeroi.e.inradial,

    axialandangulardirections

    Fig.StructuralboundaryconditionappliedonsolidtypeDiskbrake

    Fig.TemperaturedistributionisappliedasThermalloadsonsolidtype

    Diskbrakefromthethermalanalysis

    RESULTS

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    RESULTS

    Fig.

    Total

    deflection

    of

    solid

    type

    Disk

    brakeFig.DeflectioninXdirofsolidtypeDiskbrake

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    Fig.DeflectioninYdirofsolidtypeDiskbrake

    Fig.DeflectioninZdirofsolidtypeDiskbrake

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    Fig.

    V o n M i ses st r ess

    on

    solid

    type

    Disk

    brake

    Fig.XdirstressonsolidtypeDiskbrake

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    Fig.

    Y

    dir

    stress

    on

    solid

    type

    Disk

    brake

    Fig.ZdirstressonsolidtypeDiskbrake

    Tooptimizetheabovediskbrakeacomplicatedmodelofventilateddiskbrakeistaken

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    andtherebyforcedconvectionisconsideredintheanalysis

    Fig.Ventilatedtypediskbrake3Dmodelisometricview Fig.Ventilatedtypediskbrake3Dmodelisometricviewontherearside

    Fig.Ventilatedtypediskbrake3Dmodelfrontview Fig.Ventilatedtypediskbrake3Dmodelinwireframe

    CREATINGAFINITEELEMENTMESHFOEVENTEDROTOR

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    APPLYINGTHE

    BOUNDARY

    CONDITIONS

    Fig.Ventilatedtypediskbrakemeshmodelinisometricview Fig.Ventilatedtypediskbrake3Dmodelinshowingthevents

    Fig.Temperatureboundaryconditionof77degreesCappliedonVenttype

    Diskbrake Fig.ConvectionboundaryconditionappliedonVenttypeDiskbrake

    Results

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    Fig.TemperaturedistributiononVenttypeDiskbrakeonthefrontside Fig.TemperaturedistributiononVenttypeDiskbrakeontherearside

    Fig.TemperaturedistributiononVenttypeDiskbrakealongthethicknessFig.GraphicalrepresentationofTemperaturedistributiononventtypeDis

    brakealongthethickness

    STRUCTURALANALYSISFORVENTEDDISCBRAKEROTOR

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    Results

    Fig.StructuralboundaryconditionappliedonVenttypeDiskbrake Fi g.TemperaturedistributionisappliedasThermalloadsonVenttypeDiskbrake

    from

    the

    thermal

    analysis

    Fig.TotalDeflectiononVenttypeDiskbrake Fig.DeflectioninXdirofVenttypeDiskbrake

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    Fig.DeflectioninYdirofVenttypeDiskbrake Fig.DeflectioninZdirofVenttypeDiskbrake

    Fig.V o n M i s es s t r es sonVenttypeDiskbrake Fig.XdirstressonVenttypeDiskbrake

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    Fig.

    Y

    dir

    stress

    on

    Vent

    type

    Disk

    brake

    Fig.ZdirstressonVenttypeDiskbrake

    CO C S O S

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    SolidType VentilatedType

    TotalDeflectionin(mm) 2.35 1 0.248

    Vonmises Stress 2.26E+1 2 2.17 E+06

    CONCLUSIONSThepresentstudycanprovideausefuldesigntoolandimprovethe

    brakeperformance

    of

    disk

    brake

    system.

    From

    the

    below

    Table

    we

    cansaythatallthevaluesobtainedfromtheanalysisarelessthan

    theirallowablevalues.Hencethebrakediskdesignissafebasedon

    thestrengthandrigiditycriteria.Comparingthedifferentresults

    obtainedfrom

    analysis.

    It

    is

    concluded

    that

    ventilated

    type

    disk

    brakeisthebestpossibleforthepresentapplication.

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