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第六章机械的平衡Chapter6.BalancingofMachinery1.Purposes§6-1IntroductionDynamicpressinkinematicpairFrictionandinnerstressinlinkefficiencyandlife-spanInertiaforce(torque)CompelledoscillationThepurposeofmechanicalbalancingistoclearupordecreasethebadeffectbybalancingthecomponent’sunbalancedinertia.ThebalanceofcomponentrotatingaboutafixedaxisRotor(转子):Partsconstrainedtorotateaboutafixedaxis.2.Contents(1)Balancingofrigidrotor刚性转子的平衡staticbalancing(静平衡)dynamicbalancing(动平衡)(2)Balancingofflexiblerotor绕性转子的平衡Balancingofmechanismsrigidrotorflexiblerotormechanism(avi)1.Phenomenaofstaticimbalance§6-2CalculationforstaticbalancingofarigidrotorIfmasscenterofrotordoesn’tcoincidewiththeaxisofrotation,theireccentricmasswillleadtocentrifugalinertiaforce(离心力)whenrotating,andcausesanadditionaldynamicpress(附加动压力)inthelinkage.2.GeometricconditionB/D≤1/5BDm3m1m2m3m1m23.TheoryofstaticbalancingF1F2F3m1m2m3r2r1r3centrifugalforces(离心力)oftheunbalancedmasses(偏心质量):F1=m1r1w2F2=m2r2w2F3=m3r3w2If,F1+F2+F3≠0FPmPThen,imbalanceF1F2F3m1m2m3r2r1r3F1+F2+F3+FP=0FPmPSomecounterweight质量点(mp)canbeaddedtotherotortobalanceitscentrifugalforce.Tobalance:Fp=mprpw2m1r1w2+m2r2w2+m3r3w2+mPrPw2=0m1r1+m2r2+m3r3+mPrP=0miri----mass-radiusproduct(质径积)Conclusion:Requirementforstaticbalance:∑m1r1=0AddRemoveConclusion:Abalancecanbeachievedbyaddingorremovingabalancemassinthesameplane.resolution:A.GraphicalmethodF1F2F3m1m2m3r2r1r3FPmPWPW1W2W3Scale(比例尺):W=(kgm/mm)miriWiWi=mirim1r1w2+m2r2w2+m3r3w2+mPrPw2=0B.Analyticalmethodmx1rx1+mx2rx2+mx3rx3+mxPrxP=0my1ry1+my2ry2+my3ry3+myPryP=0F1F2F3m1m2m3r2r1r3FPmPEXAMPLEGiven:ThesystemshowninFIGhasthefollowingdata:m1=1.2kgR1=1.135mθ1=113.4°m2=1.8kgR2=0.822mθ2=48.8°Find:Themass-radiusproductionanditsangularlocationneededtostaticallybalancethesystem.Solution:1.Resolvethepositionvectorsintoxycomponents:R1=1.135mθ1=113.4°;R1x=-0.451,R1y=-1.042R2=0.822mθ2=48.8°;R2x=+0.541,R2y=0.6182.SolveequationsmbRbx=-m1R1x-m2R2x=-(1.2)(-0.451)-(1.8)(0.541)=-0.433mbRby=-m1R1y-m2R2y=-(1.21.042)-(1.8)(0.618-2.3633.SolveequationsSolution:4.Themass-radiusproductcanbeobtainedwithavarietyofshapes.WhenRb=0.806matrequiredangleof259.6°,themassforthiscounterweightdesignisthen:mb=2.042kg.m/0.806m=2.980kgatthechosenradiusofRb=0.806m§6-3Calculationforthedynamicbalancingofarigidrotor刚性回转体的动平衡1.geometricconditionB/D1/5Massmaybeunevenlydistributedbothrotationallyaroundtheiraxisandalsolongitudinallyalongtheiraxis.F1F2F3r1m1m2r2m3r32.Force-balance-condition∑Fi=0centrifugalforces∑Mi=0centrifugalmomentFFⅠFⅡ3.CorrectionplanesTocorrectdynamicimbalancerequireseitheraddingorremovingtherightamountofmassattheproperangularlocationsintwocorrectionplanesseperatedbysomedistancealongtheshaft.l1l2l3lF1F2F3r1m1m2r2m3r3F'3F3F'1F1F'2F2ⅡⅠ平衡基面平衡基面4.TheoryL1L2L3LF1F2F3r1m1m2r2m3r3ⅡⅠF2ⅠF1ⅠF3ⅠF2F1F3ⅡⅡⅡConverteachcentrifugalforcestothecorrectionplaneⅠandⅡ.ThatisF1,F2andF3canbereplacedbyF1Ⅰ,F2Ⅰ,F3ⅠandF1Ⅱ,F2Ⅱ,F3Ⅱspatialforcesystem2planarforcesystems平衡原理:将集中质量点所产生的离心力F向两个平衡基面上分解,得到两个分力F1和F2;合力F对系统的影响可以完全有两分力F1、F2对系统的影响所代替;F-F'-FL1L2LⅠⅡF2F1在平衡基面上分别对两个分力F1、F2进行平衡,得平衡力F'和F,从而完成对集中质量点的平衡。FF'F将力F平行分解到两个平衡基面上,得F1和F2:L1L2LⅠⅡF2=FL1L(4)F1=FL2L(3)F2F1F=F1+F2(1)F1L1=F2L2(2)l1l2l3lF1F2F3r1m1m2r2m3r3F'3F3F'1F1F'2F2ⅡⅠ平衡基面平衡基面L1L2L3LF1F2F3r1m1m2r2m3r3F'2F'1F'3F3F1F2ⅡⅠF'1=F1L-L1LF1=F1L1LF'2=F2L-L2LF2=F2L2LLF'3=F3L-L3LF3=F3L3m'r'F'F'1+F'2+F'3+F'=0F1+F2+F3+F=0从而求得m'r'和mr。mFrL1L2L3LF1F2F3r1m1m2r2m3r3ⅡⅠF2ⅠF1ⅠF3ⅠF2F1F3ⅡⅡⅡ步骤:(1)分别将各回转平面上集中质量点mi所产生的惯性力Fi(或质径积、重径积)向两个平衡基面上分解,得到F'i和Fi。(2)分别在两个平衡基面上用静平衡的方法求解平衡质量点的质径积miri(或重径积)。1.StaticBalancingExperiment静平衡实验§6-4Balancingexperimentofrigidrotor静平衡试验台2.DynamicBalancingExperiment动平衡实验3.On-spotbalancing现场平衡§6-5BalancingofplanarmechanismsConditionforbalancingofmechanisms:Thetotalinertiaforceandinertiatorqueactingonthecenterofmassarezero.机构平衡的条件作用于机构质心的总惯性力和总惯性力偶矩应分别为零。1.Entirebalancingofmechanism(1)makeuseofsymmetricalstructuretobalance(2)makeuseofbalancingmasstobalance2.Partialbalancingofmechanism(1)makeuseofbalancingmechanismtobalance(2)makeuseofbalancingmasstobalance(3)makeuseofspringtobalance.本章结束
本文标题:机械原理第六章动平衡
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