54883《机械原理（英语）（第2版）》基本课件Chapter 13 Balance of Machinery

Chapter13BalanceofMachinery1.BalancePurposes13.1Introduction

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

therotor(转子的惯性力)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(刚性转子的静平衡)2.DynamicBalanceofRigidRotors

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

Fig.13-3Dynamicbalanceofrigidrotors(转子的动平衡)1.StaticBalanceTest13.3BalanceTestofRigidRotorsIfthedistancebofarotorissmall,usuallyb/d≤0.2,theinertiamomentcausingabendingoftheshaftcanbeneglected.Staticbalancemachinesareusedforrotorsofsmallaxialdimensionssuchasfans,gears,beltwheelsandimpellers,etc.Fig.13-4showsarigidrotor1withtheshaftlaidonthehorizontalparallelways2.BygravityG,therotorwillrolluntilthecenteroftherotorgravityliesonthelowestposition.Fig.13-4Staticbalancetest(静平衡实验)2.DynamicBalanceTestFig.13-5Dynamicbalancemachineinindustry(工业动平衡机)

1—Base(底座)2—Powerbox(动力箱)3—Computersystem(计算机系统)

4—Spindle(主轴)5—Rotor(转子)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

(许用质径积的分配)13.4BalanceofPlanarMechanismsWehaveknownthatalltheinertiaforcesactingonthemovinglinksinamechanismcanbereplacedbyasingletotalinertiaforceandasingletotalmomentofinertiawhichactontheframeofthemechanism.Iftheresultantofalltheinertiaforcesandtheresultantofalltheinertiacouplesactingontheframearezero,therearenoshakingforcesandshakingcouples.Themechanismrunssmoothly.Wewilldiscoverthatinmostmechanisms,byaddingappropriatebalancemasses,theshakingforcesandtheshakingcouplescanbereduced.

Thereciprocatingunbalanceiscausedbytheinertiaforcesassociatedwithtranslatingmass.Itseffectsareveryevidentinmachinessuchaspistonenginesandcompressors.Balanceofreciprocatemachinesismoredifficultthanbalanceofrotors.Fig.13-7Balanceoflinkages(机构的平衡)

Fig13-7ashowsasliderrankmechanism.Thecountermassm22ismountedattheextensionlineoftheconnectingrod,sothatthemasscenteroftherodandthesliderislocatedatthepivotB.