剪切与挤压课件

剪切与挤压Shearandextrusion杆件的基本变形拉伸（压缩）Stretch(compression)剪切与挤压Shearandextrusion扭转reverse弯曲bendBasicdeformationoftherod一、剪切shear二、挤压Squeeze一、剪切shear一、剪切所谓联接是指结构或机械中用螺栓、销钉、键、铆钉和焊缝等将两个或多个部件联接而成。图1销轴连接图2铆钉连接shearTheso-calledconnectionreferstotheconnectionoftwoormorecomponentsinastructureormachineryusingbolts,pins,keys,rivets,andwelds.Figure1PinshaftconnectionFigure2RivetConnection一、剪切剪切变形是杆件的基础变形之一，是指杆件受到一对垂直于杆轴的大小相等、方向相反、作用线相距很近的力作用后所引起的变形。杆件的剪切变形shearSheardeformationisoneofthebasicdeformationsofarod,whichreferstothedeformationcausedbyapairofforcesperpendiculartotherodaxisthatareofequalsize,oppositedirections,andcloselyspaced.Sheardeformationofmembers一、剪切受力特征：杆件受到两个大小相等，方向相反、作用线垂直于杆的轴线并且相互平行且相距很近的力的作用。Forcecharacteristics:Therodissubjectedtotheactionoftwoforcesofequalsize,oppositedirection,perpendiculartotheaxisoftherod,paralleltoeachother,andcloselyspaced.变形特征：杆件沿两力之间的截面发生错动，直至破坏。Thememberundergoesdisplacementalongthecross-sectionbetweenthetwoforcesuntilitfails.剪切面shearplane剪切面shearplaneshear一、剪切实用计算：假设连接件剪切面上的应力分布均等，从而算出截面上的平均剪应力，或称“名义剪应力”。

剪切面shearPracticalcalculation:Assumingthatthestressdistributionontheshearplaneoftheconnectorisequal,theaverageshearstressonthesection,alsoknownasthe"nominalshearstress",canbecalculated.shearplane一、剪切实用计算：用与受剪构件相同的材料制成试件，在试件与受剪构件受力尽可能相似的条件下进行直接剪切实验，用所得到的破坏荷载按照同样的名义应力公式算出材料的极限应力τь

，将此极限应力除以适当的安全系数即得到材料的许用剪切应力[τ]。

剪切面shearplaneshearPracticalcalculation:Usingthesamematerialastheshearcomponenttomakespecimens,directshearexperimentsareconductedunderconditionswherethestressonthespecimensisassimilaraspossibletothatontheshearcomponent.Theultimatestressofthematerialiscalculatedusingthesamenominalstressformulabasedontheobtainedfailureloadτь，Dividethisultimatestressbyanappropriatesafetyfactortoobtaintheallowableshearstressofthematerial[τ]。一、剪切请计算下图中销轴的剪应力。

FsF/2

shearPleasecalculatetheshearstressofthepinshaftinthefigurebelow.

二、挤压Squeeze二、挤压局部接触面受压的现象称为挤压，受压的局部表面称为挤压面。剪切面shearplane挤压面Extrusionsurface挤压面ExtrusionsurfaceSqueezeThephenomenonoflocalcontactsurfacecompressioniscalledcompression,andthecompressedlocalsurfaceiscalledcompressionsurface.二、挤压挤压破坏的两种形式Twoformsofcompressionfailure

钢板在孔缘压成椭圆Thesteelplateispressedintoanellipseattheholeedge

螺栓压扁BoltflatteningSqueeze二、挤压挤压时两接触面上的压力称挤压力，用Fs表示。其压强称为挤压应力，其方向垂直于挤压面。在通常情况下，挤压应力只局限于接触面的附近区域。

SqueezeThepressureonthetwocontactsurfacesduringextrusioniscalledtheextrusionforce,denotedbyFs.Itspressureiscalledcompressivestress,anditsdirectionisperpendiculartotheextrusionsurface.Undernormalcircumstances,compressivestressislimitedtotheareanearthecontactsurface.

二、挤压实用计算：假设挤压力Fs均匀地分布在挤压面Ajy上

SqueezePracticalcalculation:AssumingthattheextrusionforceFsisuniformlydistributedontheextrusionsurfaceAjy

二、挤压挤压面积的面积Ajy计算CalculatetheareaAjyoftheextrusionarea当挤压面为平面接触时，挤压面积Ajy等于实际承压面积Whentheextrusionsurfaceisinplanecontact,theextrusionareaAjyisequaltotheactualbearingarea当接触面为柱面时，挤压面积Ajy为实际面积在其直径平面上投影Whenthecontactsurfaceiscylindrical,theextrusionareaAjyistheactualareaprojectedonitsdiameterplaneSqueeze实际面积面Actualareasurface直径投影面Diameterprojectionsurface二、挤压通过实验来确定其半圆柱表面被压溃的挤压极限荷载，然后按照名义应力公式算出其在直径正投影面上的平均极限应力，再除以适当的安全系数，就得到连接件材料的许用挤压应力[σjy]。

SqueezeDeterminethecompressiveultimateloadofitssemicylindricalsurfacebeingcrushedthroughexperiments,thencalculatetheaverageultimatestressonthediameterprojectionplaneaccordingtothenominalstressformula,anddivideitbyanappropriatesafetyfactortoobtaintheallowablecompressivestressoftheconnectingmaterial[σjy].

二、挤压由于剪切和挤压同时存在，为保证连接件的强度，材料的剪切强度条件和挤压强度条件必须同时满足：Duetothesimultaneousexistenceofshearandextrusion,inordertoensurethestrengthoftheconnector,theshearstrengthconditionandextrusionstrengthconditionofthematerialmustsimultaneouslymeet:

用剪切强度设计Designwithshearstrength用挤压强度校核VerifywithextrusionstrengthSqueeze二、挤压如图传动轴，直径d=50mm，齿轮与轴用平键联接，传递的力偶矩Me=720N·m。键材料的许用切应力[τ]=100MPa，许用挤压应力[σjy]=250MPa，试选择平键，并校核强度。键key轴axle轮wheelSqueezeAsshowninthediagram,thetransmissionshafthasadiameterofd=50mm,andthegearisconnectedtotheshaftwithaflatkey.ThetransmittedtorqueisMe=720N·m.Allowableshearstressofkeymaterial[τ]=100MPa,allowableextrusionstress[σjy]=250MPa,tryselectingaflatkeyandverifythestrength.二、挤压解：取轴键组合为研究对象进行受力分析ΣM0=0F×d/2﹣Me=0F=2Me/d=28.8kN根据轴径、传递的力偶矩查设计手册，得到键的尺寸16*10*45（宽*高*长）SqueezeSolution:TaketheshaftkeycombinationastheresearchobjectforforceanalysisAccordingtothedesignmanualbasedontheshaftdiameterandtransmittedtorque,thesizeofthekeyis16*10*45(width*height*length)二、挤压键的强度校核——联接键安全

按设计规范选取的键，能正常工作，通常不需再校核其强度SqueezeVerificationofKeyStrength-ConnectionKeySafetyThekeysselect