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1、Chapter10BalancingofMachinery10JPurposesandMethodsofBalancing10・l・lPurposesThecentreofmassofsomemachineelements,e.g.cams,maynotcoincidewiththeirrotatingcentresbecauseoftheasymmetryofthestructure・Evenforsymmetricalmachineelements,thecentreofmassmaysti
2、llbeeccentricbecauseofunevendistributionofmaterials,errorsinmachiningandalsoincastingandforging.Othererrorsmaybecausedbyimproperboring,bykeysandbyassembly.Fig.10-1ShowninFig」0-1isadiskthemasscentreofwhichisdisplacedbyaneccentricityefromitsrotatingcen
3、tre.Whenthediskrunsatconstantangularspeedco,thecentrifugalforceFcreatedbythemassmisF=mea)2directedradiallyoutwards.SincethemagnitudeofthecentrifugalforceFisproportionaltothesquareofangularspeed©themagnitudeofcentrifugalforceFofhighspeedpartsmayreachq
4、uitehighlevelsevenforasmalleccentricitye.Forexample,theweightWofaroundplanecutterisW=500Nandtherotatingspeedn=2000rpm.Althoughtheeccentricityeisonly1mm,thecentrifugalinertiaforceFcreatedisF=mectf=(W/^)e=2238N,whichismuchlargerthanitsweight.Furthermor
5、e,thedirectionofthecentrifugalforceFexertedontheframeistime-varying,anditwillthereforeimpartvibrationtotheframe.Thisvibrationcanadverselyaffectthestructuralintegrityofthemachinefoundation.Italsodecreasesthemachiningprecisionandefficiency,increasesthe
6、stressincomponents,causeswearandsubjectsbearingstorepeatedloadswhichcausepartstofailprematurelybyfatigue・Iftherotatingfrequencyofapartisneartoitsresonantfrequency,theamplitudesofvibrationmayreachdangerouslevels.Therefore,weshouldtrytoeliminatetheunwa
7、ntedcentrifugalforcesinmachines,especiallyinhigh-speedmachineryandprecisionmachinery.However,somemachines,e.g・vibrators,shockdrillersetc.doworkbyvibration.10.1.2MethodsTheprocessofdesigningormodifyingmachineryinordertoreduceunwantedvibrationtoanaccep
8、tablelevel,andpossiblytoeliminateitentirely,iscalledbalancing・Thebalancingofmachinerycanbedividedintobalancingofrotorsandbalancingofmechanisms.(1)BalancingofrotorsPartsconstrainedtorotateaboutafixedaxisarecalledrotors・Suchrotorscanbedividedfurtherint
