Chapter12FluctuationandRegulationinSpeedofMachines1.ForcesActingonaMachine(1)WorkingresistanceWorkingresistancereferstothetypesofmachines.

(2)DrivingforceThedifferentprimemotorshavedifferentoperatingpeculiarities.Therelationshipbetweenthedrivingforceanditsspeedisoftenrepresentedbythepeculiarcurveofamachine.Fig.12-1ashowsapeculiarcurveofaninternalcombustionengine,andFig.12-1bshowsapeculiarcurveofanACelectromotor.12.1OperatingAnalysisofMachineryFig.12-1Mechanicalbehaviorcurveofprimemachines(原動(dòng)機(jī)的機(jī)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(jī))Fig.12-3Operatingprocessofmachinery(機(jī)械的運(yùn)轉(zhuǎn)過程)12.2EquivalentKineticModelofMechanismSystems1.TheMethodofResearchingRunningProcessofMachines

Fig.12-4Forceanalysisofacrankpunch

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

Weoftenselecttherotatinglinkorreciprocatinglinkasanequivalentlink.Fig.12-5showsthoseequivalentlinks.Fig.12-5Equivalentlinks(等效構(gòu)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(jī)構(gòu))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(jī)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.Ift