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TheIntroductionofthegearsIntheforceanalysisofspurgears,theforcesareassumedtoactinasingleplane.Weshallstudygearsinwhichtheforceshavethreedimensions.Thereasonforthis,inthecaseofhelicalgears,isthattheteetharenotparalleltotheaxisofrotation.Andinthecaseofbevelgears,therotationalaxesarenotparalleltoeachother.Therearealsootherreasons,asweshalllearn.Helicalgearsareusedtotransmitmotionbetweenparallelshafts.Thehelixangleisthesameoneachgear,butonegearmusthavearight-handhelixandtheotheraleft-handhelix.Theshapeofthetoothisaninvolutehelicoid.Ifapieceofpapercutintheshapeofaparallelogramiswrappedaroundacylinder,theangularedgeofthepaperbecomesahelix.Ifweunwindthispaper,eachpointontheangularedgegeneratesaninvolutecurve.Thesurfaceobtainedwheneverypointontheedgegeneratesaninvoluteiscalledaninvolutehelicoid.Theinitialcontactofspur-gearteethisalineextendingallthewayacrossthefaceofthetooth.Theinitialcontactofhelicalgearteethisapoint,whichchangesintoalineastheteethcomeintomoreengagement.Inspurgearsthelineofcontactisparalleltotheaxisoftherotation;inhelicalgears,thelineisdiagonalacrossthefaceofthetooth.Itisthisgradualoftheteethandthesmoothtransferofloadfromonetoothtoanother,whichgivehelicalgearstheabilitytotransmitheavyloadsathighspeeds.Helicalgearssubjecttheshaftbearingstobothradialandthrustloads.Whenthethrustloadsbecomehighorareobjectionableforotherreasons,itmaybedesirabletousedoublehelicalgears.Adoublehelicalgear(herringbone)isequivalenttotwohelicalgearsofoppositehand,mountedsidebysideonthesameshaft.Theydevelopoppositethrustreactionsandthuscanceloutthethrustload.Whentwoormoresinglehelicalgearsaremountedonthesameshaft,thehandofthegearsshouldbeselectedsoastoproducetheminimumthrustload.Crossed-helical,orspiral,gearsarethoseinwhichtheshaftcenterlinesareneitherparallelnorintersecting.Theteethofcrossed-helicalfearshavepointcontactwitheachother,whichchangestolinecontactasthegearswearin.Forthisreasontheywillcarryoutverysmallloadsandaremainlyforinstrumentalapplications,andaredefinitelynot1recommendedforuseinthetransmissionofpower.Thereisondifferencebetweenacrossedhelicalgearandahelicalgearuntiltheyaremountedinmeshwitheachother.Theyaremanufacturedinthesameway.Apairofmeshedcrossedhelicalgearsusuallyhavethesamehand;thatis,aright-handdrivergoeswitharight-handdriven.Inthedesignofcrossed-helicalgears,theminimumslidingvelocityisobtainedwhenthehelixangleareequal.However,whenthehelixanglearenotequal,thegearwiththelargerhelixangleshouldbeusedasthedriverifbothgearshavethesamehand.Wormgearsaresimilartocrossedhelicalgears.Thepinionorwormhasasmallnumberofteeth,usuallyonetofour,andsincetheycompletelywraparoundthepitchcylindertheyarecalledthreads.Itsmatinggeariscalledawormgear,whichisnotatruehelicalgear.Awormandwormgearareusedtoprovideahighangular-velocityreductionbetweennonintersectingshaftswhichareusuallyatrightangle.Thewormgearisnotahelicalgearbecauseitsfaceismadeconcavetofitthecurvatureoftheworminordertoprovidelinecontactinsteadofpointcontact.However,adisadvantageofwormgearingisthehighslidingvelocitiesacrosstheteeth,thesameaswithcrossedhelicalgears.Wormgearingareeithersingleordoubleenveloping.Asingle-envelopinggearingisoneinwhichthegearwrapsaroundorpartiallyenclosestheworm.Agearinginwhicheachelementpartiallyenclosestheotheris,ofcourse,adouble-envelopingwormgearing.Theimportantdifferencebetweenthetwoisthatareacontactexistsbetweentheteethofdouble-envelopinggearswhileonlylinecontactbetweenthoseofsingle-envelopinggears.Thewormandwormgearofasethavethesamehandofhelixasforcrossedhelicalgears,butthehelixanglesareusuallyquitedifferent.Thehelixangleonthewormisgenerallyquitelarge,andthatonthegearverysmall.Becauseofthis,itisusualtospecifytheleadangleontheworm,whichisthecomplementofthewormhelixangle,andthehelixangleonthegear;thetwoanglesareequalfora90-deg.Shaftangle.Whengearsaretobeusedtotransmitmotionbetweenintersectingshaft,someofbevelgearisrequired.Althoughbevelgearareusuallymadeforashaftangleof90deg.Theymaybeproducedforalmostanyshaftangle.Theteethmaybecast,milled,orgenerated.Onlythegeneratedteethmaybeclassedasaccurate.Inatypicalbevelgearmounting,oneofthegearisoftenmountedoutboardofthebearing.Thismeansthatshaft2deflectioncanbemorepronouncedandhaveagreatereffectonthecontactofteeth.Anotherdifficulty,whichoccursinpredictingthestressinbevel-gearteeth,isthefacttheteetharetapered.Straightbevelgearsareeasytodesignandsimpletomanufactureandgiveverygoodresultsinserviceiftheyaremountedaccuratelyandpositively.Asinthecaseofsqurgears,however,theybecomenoisyathighervaluesofthepitch-linevelocity.Inthesecasesitisoftengooddesignpracticetogotothespiralbevelgear,whichisthebevelcounterpartofthehelicalgear.Asinthecaseofhelicalgears,spiralbevelgearsgiveamuchsmoothertoothactionthanstraightbevelgears,andhenceareusefulwherehighspeedareencountered.Itisfrequentlydesirable,asinthecaseofautomotivedifferentialapplications,tohavegearingsimilartobevelgearsbutwiththeshaftoffset.Suchgearsarecalledhypoidgearsbecausetheirpitchsurfacesarehyperboloidsofrevolution.Thetoothactionbetweensuchgearsisacombinationofrollingandslidingalongastraightlineandhasmuchincommonwiththatofwormgears.3齒輪簡介在直齒圓柱齒輪的受力分析中,是假定各力作用在單一平面的。我們將研究作用力具有三維坐標的齒輪。因此,在斜齒輪的情況下,其齒向是不平行于回轉軸線的。而在錐齒輪的情況中各回轉軸線互相不平行。像我們要討論的那樣,尚有其他道理需要學習,掌握。斜齒輪用于傳遞平行軸之間的運動。傾斜角度每個齒輪都一樣,但一個必須右旋斜齒,而另一個必須是左旋斜齒。齒的形狀是一濺開線螺旋面。如果一張被剪成平行四邊形(矩形)的紙張包圍在齒輪圓柱體上,紙上印出齒的角刃邊就變成斜線。如果我展開這張紙,在血角刃邊上的每一個點就發(fā)生一漸開線曲線。直齒圓柱齒輪輪齒的初始接觸處是跨過整個齒面而伸展開來的線。斜齒輪輪齒的初始接觸是一點,當齒進入更多的嚙合時,它就變成線。在直齒圓柱齒輪中,接觸是平行于回轉軸線的。在斜齒輪中,該先是跨過齒面的對角線。它是齒輪
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