54883《机械原理（英语）（第2版）》基本课件Chapter 4 Force Analysis of Planar Mechanisms

Chapter4ForceAnalysisofPlanarMechanism1.ContentsofForceAnalysis1)Knowingtheexternalappliedloads,calculatetheconstraintforceswhichoccurinpairs.Constraintforcescanbeusedtodesignkinematicpairs.2)Knowingtheresistanceactingondrivenlink,calculatetheforcesactingondrivinglink,orknowingthedrivingforce,calculatetheresistanceactingondrivenlink.3)Theforceanalysisisthetheoreticalfoundationtocalculatetheefficiency.4)Makeuseoftheforceanalysis,wecandesignsomeselflockingmechanism.4.1Introduction2.MethodsofForceAnalysis

Therearetwogeneralmethodsofperformingacompleteforceanalysis：Graphicalforceanalysis&Analyticalforceanalysis.1.InertiaForcesFig.4-1Inertiaforceandinertiatorqueintoresultantforce(连杆的惯性力与惯性力矩的合成)4.2ForceAnalysisIncludingInertiaForcesinMechanisms

Fig4-1ashowsaslidercrankmechanism.Becauseoftheconstrainedmotionofthemechanism,accelerations,suchasas2,α2oftheindividuallink2andaC3oftheslider3,maybedeterminedfirst,thentheinertiaforcesFi2andtorqueMs2actingonthelink2canbecalculatedrespectively.2.KinetostaticAnalysisofPlanarMechanism(1)Kinetostaticanalysisofplanarmechanismbygraphicalmethod

Example4-1Fig4-2ashowsaconventionalshapermechanisminwhichtheangularvelocityofthecrankandalldimensionsoflinksareknown.SupposetheweightoftheramisG5,resistanceactingontheramisFr,andinertiaforceactingontheramisFi5.Theotherweightsandinertiaforcesneednottobeconsidered.DeterminetheinputtorqueMbactingonthedrivinglinkandtheconstraintforcesinpairs.Fig.4-2Graphicalforceanalysisofsharper(牛头刨床的动态静力分析)Fig.4-3Analyticalforceanalysis(动态静力分析的解析法)

Example4-2Fig4-3showsaslidercrankmechanismusedinalotofmachines,suchasinternalcombustionengineandreciprocatingcompressors.Allthedimensionsoflinks,angularpositionofthecrankandangularvelocityofthecrankareknown.Thekinematicanalysisisfirstperformedalso.

(2)Kinetostaticanalysisofplanarmechanismbyanalyticalmethod1.FrictioninKinematicPairs(1)FrictioninslidingpairsThefrictioninslidingpairscanbedividedintoplanesurfacefrictionandVsurfacefriction.

4.3ForceAnalysisIncludingFrictioninMechanismsFig.4-4Frictionontheplane

surface(平面中的摩擦)1)Frictiononplanesurface.Aslider1isrestonasmoothplanesurface2whichishorizontal.Supposethattheslider1isslidingrelativetothesurface2totherightataconstantvelocityv12actedbyadrivingforceFwhichisinclinedatanangleαtothenormal,asshowninFig4-4.2)Frictiononinclinedplanesurface.AblockofweightGrestingonaplaneinclinedatanangleαtothehorizontalisactedonbyahorizontalforceFdwhichtendstomovethebodyuptheplanewithauniformvelocityv12.ThisisshowninFig4-5a.Fig.4-5Frictionontheinclinedplanesurface(斜面摩擦)3)FrictiononVplanesurface.IftheblockshowninFig4-6aischangedintoaVblockwithaincludedangle2θshowninFig4-6b,anditsweightisG,therearetwonormalreactionforcesN21,andfromFig4-6c,Fig.4-6FrictiononV-planesurface(槽面摩擦)(2)FrictioninturningpairsThebearingsareusedextensivelyastuningpairsinmachinery,andtheycanbedividedintojournalbearingandthrustbearing.1)Frictioninjournalbearing.Whenashaftrestsinthebearing,theverticalloadGactsthroughtheaxisoftheshaft.ThenormalreactionN21ofthebearingactsinlinewithGintheverticallyupwarddirectionshowninFig4-7a.

Fig.4-7Frictioninajournalbearing(径向轴承中的摩擦)2)Frictioninthrustbearing.Whenarotatingshaftissubjectedtoanaxialload,thethrustistakenbyacollarbearing,orthrustbearing.Fig4-8ashowsathrustbearingactedbyanaxialloadG.Fig.4-8Frictioninathrustbearing(推力轴承的摩擦)（3）FrictioninhelicalpairsAccordingtothetoothshape,thescrewcanbedividedintosquarethreadsandVthreads.Asquarethreadscrewisusedtotransmitpower,andVthreadedscrewisusedtofastenanelementtoanother.Fig.4-9Frictioninsquarethread(矩形螺纹的摩擦)Fig4-9ashowsasquarethreadedscrew;itmaybethoughtofsimplyasaninclinedplaneorwedgewrappedaroundacylinder.Fig.4-10FrictioninV-thread(三角形螺纹的摩擦)Fig4-10ashowsaVthread;itsthreadangleis2β,andtheanglebetweentheVfacesofthethreadis2θ.Fig4-10bshowsatrianglewhichisthedevelopmentofahelixofdiameterdandleadl.2.ForceAnalysisIncludingFrictionExample4-3Fig4-11showsaslidercrankmechanisminwhichresistantforceFrisappliedtothepiston4.Thecrank1isrotatingintheclockwisedirection;thedimensionsoflinksandthefrictionalcoefficientofpairsareknown.Determinetheconstraintforcesinpairsandtheinputtorque.

Fig.4-11Forceanalysisconsideringthefrictioninaslider-cranklinkage

(考虑摩擦的曲柄滑块机构力分析)Example4-4Fig4-12ashowsacammechanismwithanoscillatingfollowerinwhichresistantforceFrisappliedtothefolloweratpointF.Thecam1isrotatinginthecounterclockwisedirection;thedimensionsofthemechanismandthefrictionalcoefficientofpairsareknown.Determinetheconstraintforcesinpairsandtheinputtorque.

Fig.4-12Forceanalysisconsideringthefrictioninacammechanism

(考虑摩擦的凸轮机构的力分析)1.SelflockinginKinematicPairs4.4FrictionandDesignofSelflockingMechanismsTherearetwoforcesinakinematicpairwhichisusedtoconnecttwolinks;theoneisdrivingforceandtheotherisfrictionforcewhichresiststhemotionofthelink.Ifthedrivingforceactinginapairisinfinite,andthelinkisnotmovable,itiscalledasselflockingofapair.Foraslidingpair,appliedresultantforceactswithinthefrictionalangleofabody,theselflockingwilloccurintheslidingpair.Forarotatingpair,appliedresultantforceactswithinthefrictionalcircleofabody,theselflockingwilloccurintheturningpair.2.SelflockingMechanisms(1)Travelofamechanism

1)Positivetravelofamechanism.AdrivingforceactsonthedriverAshowninFig4-13;theworkisdonebytheresistantforceactingonthedrivenlinkB.Thistravelispositivetravel.Fig.4-13Travelofmechanism

(机构的行程)(2)SelflockingmechanismIfthenegativetravelofamechanismisinselflocking,itiscalledasselflockingmechanism.Selflockingmechanismcanbeusedwidelyinmechanicalengineering.2)Negativetravelofamechanism.IftaketheresistantasadrivingforceanditactsonthelinkB,andtheoriginaldrivinglink,suchasA,becomesadrivenlink,thistravelisnegativetravel.3.DesignofSelflockingMechanisms