《機械原理（英漢雙語）（第2版）》 課件Chapter 12、13 Fluctuation and Regulation in Speed of Machines；Balance of Machinery

Chapter12FluctuationandRegulationinSpeedofMachines1.ForcesActingonaMachine(1)WorkingresistanceWorkingresistancereferstothetypesofmachines.

(2)DrivingforceThedifferentprimemotorshavedifferentoperatingpeculiarities.Therelationshipbetweenthedrivingforceanditsspeedisoftenrepresentedbythepeculiarcurveofamachine.Fig.12-1ashowsapeculiarcurveofaninternalcombustionengine,andFig.12-1bshowsapeculiarcurveofanACelectromotor.12.1OperatingAnalysisofMachineryFig.12-1Mechanicalbehaviorcurveofprimemachines(原動機的機械特性曲線圖)2.OperatingProcessofMachines(1)StartupperiodTherunningspeedofamachineisfromzerotoworkrunningspeedinthisperiod,andtheworkdonebythedrivingforceisgreaterthantheworkdonebytheresistance.

(2)SteadyrunningperiodInthesteadyrunningperiod,theworkdonebythedrivingforceisequaltotheworkdonebytheresistanceinaperiod.Theincrementofthekineticenergyiszero.

(3)StoppingperiodInthestoppingperiod,thedrivingforcewillceasetowork,thusWd=0.Themotioncontinuesforacertaintimeowingtotheinertiakineticenergyofthemachine.Fig.12-2Crankpunch(曲柄壓力機)Fig.12-3Operatingprocessofmachinery(機械的運轉過程)12.2EquivalentKineticModelofMechanismSystems1.TheMethodofResearchingRunningProcessofMachines

Fig.12-4Forceanalysisofacrankpunch

(曲柄壓力機的受力分析)InordertofindtheactualmotionofamechanismshowninFig.12-4,wemustsolvethedrivingtorqueactingonthelink1andtheangularvelocity.Thedynamicforceanalysisoftheslidercrankmechanismhasalargenumberofunknownstosolve.

Weoftenselecttherotatinglinkorreciprocatinglinkasanequivalentlink.Fig.12-5showsthoseequivalentlinks.Fig.12-5Equivalentlinks(等效構件)(1)RotatingequivalentlinkWhentheequivalentlinkisrotatingaboutanaxiswithaconstantangularvelocity,thekineticenergyisasfollows：2.TheParameterofTheEquivalentLink

Iftheequivalentlinkperformsarotatingmotion,theinstantpowerisasfollows:

Theinstantpowergeneratedbytheequivalentlinkisequaltotheonesgeneratedbythewholemachine,sowehave：(2)Reciprocatingequivalentlink

Allthedrivingforcesormomentsactingonthemachinearereplacedbyoneforceormomentappliedtotheequivalentlink,thisiscalledtheequivalentdrivingforceordrivingmoment.Alltheresistancesactingonthemachinearereplacedbyoneforceormomentappliedtotheequivalentlink,thisiscalledtheequivalentresistantforceorresistantmoment.Obviously,wecanwritethemasfollows：Example12-1Fig.12-6showsaplanetarygeartrain.Thenumbersofteethofgearsarez1、z2、z3respectively.Themasscentersofthesegearsarecoefficientwiththeirrotatingcenters,andthemomentsofinertiaofgears1,2andthearmabouttheircentersareJ1、J2、JH.Themassoftheplanetarygearism2.Weassumethegear1tobetheequivalentlink.Determinetheequivalentmomentofinertia.

Fig.12-6Planetarygeartrain(行星輪系)Example12-2Fig12-7showsaScotchyokemechanism.Thecrankhasalengthofl1,andthemomentofinertiaaboutitsrotatingcenterAisJ1.Thelink2and3havemassesofm2、m3.Theresistanceactingonthelink3isF3.Determinetheequivalentmomentofinertia,whenthecrankistheequivalentlink,andequivalentresistanceactingonthecrank.Fig.12-7Scotch-yoke

mechanism(正弦機構)1.KineticEquationsoftheEquivalentLink12.3KineticEquationsofMechanismSystemsRearrangingtheaboveequations，wehave：consideringtheborderconditions,weobtain:consideringtheborderconditions,weobtain:2.SolutionoftheKineticEquation(1)TheequivalentmomentofinertiaandequivalentmomentareconstantsThisissuitableformachineswithconstantratioandconstantforceormoment,suchasagearhoist.

(2)TheequivalentmomentofinertiaandequivalentmomentarefunctionsofpositionWhentheequivalentmomentofinertiaandequivalentmomentareanalyticalforms,wecanusetheintegratingequationtosolvethisproblem.Example12-3Fig.12-8showsamechanismsysteminwhichtheelectricmotorrotatesat1440r/min,andtheratioofthegearreducerisi=2.5.TheshaftBisselectedasanequivalentlink,anditsequivalentmomentofinertiaJe=0.5kg·m2.IftheshaftBhasbeenbraked,thehoistmustbestoppedwithinthreeseconds.DeterminethebrakingmomentsuppliedtotheshaftB.Fig.12-8Simplemechanical

system(簡單的機械系統(tǒng))1.WorkandEnergyinaSteadyRunningPeriodFig.12-9Equivalentmomentdiagram

(等效力矩線圖)12.4PeriodicSpeedFluctuationandRegulationinaMachineFig.12-9showsadiagramofequivalentdrivingmomentMdandequivalentresistantmomentMr.WhenMd＞Mr,thekineticenergyofthemachineincreases,andtheangularvelocityincreasestoo.WhenMd＜Mr,thekineticenergyofthemachinedecreases,andtheangularvelocitydecreasestoo.2.FluctuationofSpeed

Whenaflywheelismountedinamachinespindle,thetotalkineticenergyisthesumofthekineticenergyoftheflywheelandthekineticenergyofthemachine.Sowehave:SupposethemomentofinertiaoftheflywheelisJf,themaximumkineticenergyEfmaxandtheminimumkineticenergyEfminoftheflywheelareasfollows：Asweknow,themomentofinertiaconsistsoftwoportions：oneportionisconstantandtheotherisvarious.Thekineticenergyoftheequivalentlinkcanbewrittenas：Becausewhenthekineticenergyismaximumthespeedismaximum,andwhenthekineticenergyisminimumthespeedisminimum.Rearrangingtheseequations，wehave：

Themomentofinertiaoftheflywheelisbasedonthattheflywheelismountedtotheequivalentlink.Iftheflywheelisfixedtotheotherlink,suchasxlink,ratherthantheequivalentlink,itsmomentofinertiaJxcanbedeterminedaccordingtothesameenergysuppliedbytheflywheel.Thiscanbewrittenas:Fig.12-10Dimensionsofflywheels(飛輪尺寸)3.DimensionsofFlywheels

Therearetwoshapesofflywheels：theoneisdisk,andtheotherisdiskwithweb.Fig12-10showstheseflywheels.Theinertiaofaflywheelisprovidedbythehub,webandtherim.However,theinertiaduetothehubandthewebisverysmall,usuallyitisignored.Example12-4Theequivalentlinkisselectedasthecrankshaftofashaper,anditsaveragespeedis60r/min.Theoperatingperiodofsteadymotionis2π.Theallowablecoefficientofspeedfluctuationδ=0.1.ThediagramoftheequivalentresistantmomentMrversusangleφisshownasFig12-11,andtheequivalentdrivingmomentMdisaconstant.Ifthemomentofinertiaofthemachinehasbeenignored,determinethemomentofinertiaoftheflywheel.

Fig.12-11ThediagramofEquivalentmomentoftheshaper(刨床等效力矩圖)12.5AperiodicSpeedFluctuationandRegulationinaMachine

Fig12-12showsadiagramofagovernor.Thegovernorshaft1isrotatedbytheengineW1andasleeve2carriedontheshaftispositionedbytheballcranklever.Whentherotatingspeedoftheshaftincreases,thecentrifugalforcesactingonthetwoballsincreasetoo,thesleevewillmoveup.Theoilsupplywillbereduced,andtheelectricpowergeneratedwillbereducedduetothereductionoftherotatingspeed.Fig.12-12Centrifugalgovernor(離心調速器)

1—shaft(主軸)2—sleeve(套筒)3、5、7—Rod(桿件)

4—ball(重球)6—spring(彈簧)Chapter13BalanceofMachinery1.BalancePurposes13.1Introduction

Arotatingshaftorrotorwillexperiencecentrifugalforcesifitscenterofmassdoesnotlieexactlyontherotatingcenterline.Thecentrifugalforceexertedontheframebymovingmachinememberwillbetimevaryingandimpartvibratorymotiontotheframe.Thisvibrationandaccompanyingnoisecanproducehumandiscomfort,alterthedesiredmachineperformanceormaycausefailureoftherotororthesupport.Thepurposeofbalanceistoreduceunbalancetoanacceptablelevelandpossiblytoeliminateitentirely.(1)BalanceofrigidrotorsWhenarotorisrotatingaboutitsowncenterlineofrotationatanangularvelocity,thedeformationoftherotorissmallandcanbenegligible,anditissaidtobetherigidrotor,otherwise,itisaflexiblerotor.Fig13-1showsarigidrotorataconstantangularvelocity.Fig.13-1Centrifugalforcesof

therotor(轉子的慣性力)2.ClassificationofBalance(2)BalanceofflexiblerotorsWhenarotorisrotatingaboutitsowncenterlineofrotationatanangularvelocity,thedeformationoftherotorcannotbenegligible,itissaidtobeaflexiblerotor.(3)BalanceoflinkagesTherotatinglinksofalinkage,suchascrankandrockers,canbeindividuallybalancedbytherotatingbalancemethods.Thecouplerisincomplexmotionandhasnofixedpivot,thusitsmasscenterisalwaysinmotion,andtheinertiaforceofthelinkhasvariablemagnitudeandsense.Wecannotattachamasstothelinkforbalancingit.Theglobalmasscenterofthelinkagenormallywillchangepositionasthelinkagemoves.Sobalanceofalinkageismoredifficultthanbalanceofrotors.Ifwecansomehowforcethisglobalmasscentertobestationaryintheframe,wewillhaveastateofbalancefortheoveralllinkage.1.StaticBalanceofRigidRotors13.2BalanceDesignofRigidRotors

Theunbalancedforcesofarigidrotorareduetotheaccelerationofmassesintherotor.Therequirementforstaticbalanceisthatthesumofallforcesintherotatingrotormustbezero.Fig13-2showsarigidrotorrotatingwithaconstantangularvelocityofω

.Anumberofmasses,suchasthree,aredepictedbypointmassesatdifferentradiiinthesametransverseplane.Fig.13-2Staticbalanceofrigid

rotor(剛性轉子的靜平衡)2.DynamicBalanceofRigidRotors

ThemostgeneralcaseofdistributionofmassesonarigidrotoristhatinwhichthemasseslieinvarioustransverseplanesasshowninFig13-3.Therotorrevolveswithauniformangularvelocityω,andm1,m2,m3arethemassesattachedtotherotorinplanes1,2,3respectivelyandatradiir1,r2,r3.

Fig.13-3Dynamicbalanceofrigidrotors(轉子的動平衡)1.StaticBalanceTest13.3BalanceTestofRigidRotorsIfthedistancebofarotorissmall,usuallyb/d≤0.2,theinertiamomentcausingabendingoftheshaftcanbeneglected.Staticbalancemachinesareusedforrotorsofsmallaxialdimensionssuchasfans,gears,beltwheelsandimpellers,etc.Fig.13-4showsarigidrotor1withtheshaftlaidonthehorizontalparallelways2.BygravityG,therotorwillrolluntilthecenteroftherotorgravityliesonthelowestposition.Fig.13-4Staticbalancetest(靜平衡實驗)2.DynamicBalanceTestFig.13-5Dynamicbalancemachineinindustry(工業(yè)動平衡機)

1—Base(底座)2—Powerbox(動力箱)3—Computersystem(計算機系統(tǒng))

4—Spindle(主軸)5—Rotor(轉子)6—Carriage(支承架)

Fordynamicbalanceofarotor,twobalanceofcountermassesarerequiredtobeusedinanytwocorrectplanes.Dynamicbalanceisachievedbyaddingorremovingmassesinthesetwoplanes.Thisrequiresadynamicbalancemachine.Fig.13-5showsacommontypeofdynamicbalancemachine,whichisusedinindustry.3.BalancePrecisionAfterarigidrotorhasbeenbalancedbyusingabalancemachine,thecenterlineofmassoftherotorwillbecoincidentwiththecenterlineofrotationoftherotortheoretically,butinpractice,theycannotbecoincidentcompletely.Anoffsetbetweenthecenterlineofmassandthecenterlineofrotationoftherotoralwaysexists.Toassurethebalanceprecision,theactualunbalancemustbelessorequaltotheallowableunbalance.Therearetwotypesoftheallowableunbalance.Theyareallowablemassradiusproductandallowableoffset.Therelationshipbetweenthe［mr］andthe［e］isasfollows:Fig.13-6Distributionofthe

allowedmass-radiusproduct

(許用質徑積的分配)13.4BalanceofPlanarM