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THEINTRODUCTIONOFTHEGEARSINTHEFORCEANALYSISOFSPURGEARS,THEFORCESAREASSUMEDTOACTINASINGLEPLANEWESHALLSTUDYGEARSINWHICHTHEFORCESHAVETHREEDIMENSIONSTHEREASONFORTHIS,INTHECASEOFHELICALGEARS,ISTHATTHETEETHARENOTPARALLELTOTHEAXISOFROTATIONANDINTHECASEOFBEVELGEARS,THEROTATIONALAXESARENOTPARALLELTOEACHOTHERTHEREAREALSOOTHERREASONS,ASWESHALLLEARNHELICALGEARSAREUSEDTOTRANSMITMOTIONBETWEENPARALLELSHAFTSTHEHELIXANGLEISTHESAMEONEACHGEAR,BUTONEGEARMUSTHAVEARIGHTHANDHELIXANDTHEOTHERALEFTHANDHELIXTHESHAPEOFTHETOOTHISANINVOLUTEHELICOIDIFAPIECEOFPAPERCUTINTHESHAPEOFAPARALLELOGRAMISWRAPPEDAROUNDACYLINDER,THEANGULAREDGEOFTHEPAPERBECOMESAHELIXIFWEUNWINDTHISPAPER,EACHPOINTONTHEANGULAREDGEGENERATESANINVOLUTECURVETHESURFACEOBTAINEDWHENEVERYPOINTONTHEEDGEGENERATESANINVOLUTEISCALLEDANINVOLUTEHELICOIDTHEINITIALCONTACTOFSPURGEARTEETHISALINEEXTENDINGALLTHEWAYACROSSTHEFACEOFTHETOOTHTHEINITIALCONTACTOFHELICALGEARTEETHISAPOINT,WHICHCHANGESINTOALINEASTHETEETHCOMEINTOMOREENGAGEMENTINSPURGEARSTHELINEOFCONTACTISPARALLELTOTHEAXISOFTHEROTATION;INHELICALGEARS,THELINEISDIAGONALACROSSTHEFACEOFTHETOOTHITISTHISGRADUALOFTHETEETHANDTHESMOOTHTRANSFEROFLOADFROMONETOOTHTOANOTHER,WHICHGIVEHELICALGEARSTHEABILITYTOTRANSMITHEAVYLOADSATHIGHSPEEDSHELICALGEARSSUBJECTTHESHAFTBEARINGSTOBOTHRADIALANDTHRUSTLOADSWHENTHETHRUSTLOADSBECOMEHIGHORAREOBJECTIONABLEFOROTHERREASONS,ITMAYBEDESIRABLETOUSEDOUBLEHELICALGEARSADOUBLEHELICALGEARHERRINGBONEISEQUIVALENTTOTWOHELICALGEARSOFOPPOSITEHAND,MOUNTEDSIDEBYSIDEONTHESAMESHAFTTHEYDEVELOPOPPOSITETHRUSTREACTIONSANDTHUSCANCELOUTTHETHRUSTLOADWHENTWOORMORESINGLEHELICALGEARSAREMOUNTEDONTHESAMESHAFT,THEHANDOFTHEGEARSSHOULDBESELECTEDSOASTOPRODUCETHEMINIMUMTHRUSTLOADCROSSEDHELICAL,ORSPIRAL,GEARSARETHOSEINWHICHTHESHAFTCENTERLINESARENEITHERPARALLELNORINTERSECTINGTHETEETHOFCROSSEDHELICALFEARSHAVEPOINTCONTACTWITHEACHOTHER,WHICHCHANGESTOLINECONTACTASTHEGEARSWEARINFORTHISREASONTHEYWILLCARRYOUTVERYSMALLLOADSANDAREMAINLYFORINSTRUMENTALAPPLICATIONS,ANDAREDEFINITELYNOT1RECOMMENDEDFORUSEINTHETRANSMISSIONOFPOWERTHEREISONDIFFERENCEBETWEENACROSSEDHELICALGEARANDAHELICALGEARUNTILTHEYAREMOUNTEDINMESHWITHEACHOTHERTHEYAREMANUFACTUREDINTHESAMEWAYAPAIROFMESHEDCROSSEDHELICALGEARSUSUALLYHAVETHESAMEHAND;THATIS,ARIGHTHANDDRIVERGOESWITHARIGHTHANDDRIVENINTHEDESIGNOFCROSSEDHELICALGEARS,THEMINIMUMSLIDINGVELOCITYISOBTAINEDWHENTHEHELIXANGLEAREEQUALHOWEVER,WHENTHEHELIXANGLEARENOTEQUAL,THEGEARWITHTHELARGERHELIXANGLESHOULDBEUSEDASTHEDRIVERIFBOTHGEARSHAVETHESAMEHANDWORMGEARSARESIMILARTOCROSSEDHELICALGEARSTHEPINIONORWORMHASASMALLNUMBEROFTEETH,USUALLYONETOFOUR,ANDSINCETHEYCOMPLETELYWRAPAROUNDTHEPITCHCYLINDERTHEYARECALLEDTHREADSITSMATINGGEARISCALLEDAWORMGEAR,WHICHISNOTATRUEHELICALGEARAWORMANDWORMGEARAREUSEDTOPROVIDEAHIGHANGULARVELOCITYREDUCTIONBETWEENNONINTERSECTINGSHAFTSWHICHAREUSUALLYATRIGHTANGLETHEWORMGEARISNOTAHELICALGEARBECAUSEITSFACEISMADECONCAVETOFITTHECURVATUREOFTHEWORMINORDERTOPROVIDELINECONTACTINSTEADOFPOINTCONTACTHOWEVER,ADISADVANTAGEOFWORMGEARINGISTHEHIGHSLIDINGVELOCITIESACROSSTHETEETH,THESAMEASWITHCROSSEDHELICALGEARSWORMGEARINGAREEITHERSINGLEORDOUBLEENVELOPINGASINGLEENVELOPINGGEARINGISONEINWHICHTHEGEARWRAPSAROUNDORPARTIALLYENCLOSESTHEWORMAGEARINGINWHICHEACHELEMENTPARTIALLYENCLOSESTHEOTHERIS,OFCOURSE,ADOUBLEENVELOPINGWORMGEARINGTHEIMPORTANTDIFFERENCEBETWEENTHETWOISTHATAREACONTACTEXISTSBETWEENTHETEETHOFDOUBLEENVELOPINGGEARSWHILEONLYLINECONTACTBETWEENTHOSEOFSINGLEENVELOPINGGEARSTHEWORMANDWORMGEAROFASETHAVETHESAMEHANDOFHELIXASFORCROSSEDHELICALGEARS,BUTTHEHELIXANGLESAREUSUALLYQUITEDIFFERENTTHEHELIXANGLEONTHEWORMISGENERALLYQUITELARGE,ANDTHATONTHEGEARVERYSMALLBECAUSEOFTHIS,ITISUSUALTOSPECIFYTHELEADANGLEONTHEWORM,WHICHISTHECOMPLEMENTOFTHEWORMHELIXANGLE,ANDTHEHELIXANGLEONTHEGEAR;THETWOANGLESAREEQUALFORA90DEGSHAFTANGLEWHENGEARSARETOBEUSEDTOTRANSMITMOTIONBETWEENINTERSECTINGSHAFT,SOMEOFBEVELGEARISREQUIREDALTHOUGHBEVELGEARAREUSUALLYMADEFORASHAFTANGLEOF90DEGTHEYMAYBEPRODUCEDFORALMOSTANYSHAFTANGLETHETEETHMAYBECAST,MILLED,ORGENERATEDONLYTHEGENERATEDTEETHMAYBECLASSEDASACCURATEINATYPICALBEVELGEARMOUNTING,ONEOFTHEGEARISOFTENMOUNTEDOUTBOARDOFTHEBEARINGTHISMEANSTHATSHAFT2DEFLECTIONCANBEMOREPRONOUNCEDANDHAVEAGREATEREFFECTONTHECONTACTOFTEETHANOTHERDIFFICULTY,WHICHOCCURSINPREDICTINGTHESTRESSINBEVELGEARTEETH,ISTHEFACTTHETEETHARETAPEREDSTRAIGHTBEVELGEARSAREEASYTODESIGNANDSIMPLETOMANUFACTUREANDGIVEVERYGOODRESULTSINSERVICEIFTHEYAREMOUNTEDACCURATELYANDPOSITIVELYASINTHECASEOFSQURGEARS,HOWEVER,THEYBECOMENOISYATHIGHERVALUESOFTHEPITCHLINEVELOCITYINTHESECASESITISOFTENGOODDESIGNPRACTICETOGOTOTHESPIRALBEVELGEAR,WHICHISTHEBEVELCOUNTERPARTOFTHEHELICALGEARASINTHECASEOFHELICALGEARS,SPIRALBEVELGEARSGIVEAMUCHSMOOTHERTOOTHACTIONTHANSTRAIGHTBEVELGEARS,ANDHENCEAREUSEFULWHEREHIGHSPEEDAREENCOUNTEREDITISFREQUENTLYDESIRABLE,ASINTHECASEOFAUTOMOTIVEDIFFERENTIALAPPLICATIONS,TOHAVEGEARINGSIMILARTOBEVELGEARSBUTWITHTHESHAFTOFFSETSUCHGEARSARECALLEDHYPOIDGEARSBECAUSETHEIRPITCHSURFACESAREHYPERBOLOIDSOFREVOLUTIONTHETOOTHACTIONBETWEENSUCHGEARSISACOMBINATIONOFROLLINGANDSLIDINGALONGASTRAIGHTLINEANDHASMUCHINCOMMONWITHTHATOFWORMGEARS3齿轮简介在直齿圆柱齿轮的受力分析中,是假定各力作用在单一平面的。我们将研究作用力具有三维坐标的齿轮。因此,在斜齿轮的情况下,其齿向是不平行于回转轴线的。而在锥齿轮的情况中各回转轴线互相不平行。像我们要讨论的那样,尚有其他道理需要学习,掌握。斜齿轮用于传递平行轴之间的运动。倾斜角度每个齿轮都一样,但一个必须右旋斜齿,而另一个必须是左旋斜齿。齿的形状是一溅开线螺旋面。如果一张被剪成平行四边形(矩形)的纸张包围在齿轮圆柱体上,纸上印出齿的角刃边就变成斜线。如果我展开这张纸,在血角刃边上的每一个点就发生一渐开线曲线。直齿圆柱齿轮轮齿的初始接触处是跨过整个齿面而伸展开来的线。斜齿轮轮齿的初始接触是一点,当齿进入更多的啮合时,它就变成线。在直齿圆柱齿轮中,接触是平行于回转轴线的。在斜齿轮中,该先是跨过齿面的对角线。它是齿轮逐渐进行啮合并平稳的从一个齿到另一个齿传递运动,那样就使斜齿轮具有高速重载下平稳传递运动的能力。斜齿轮使轴的轴承承受径向和轴向力。当轴向推力变的大了或由于别的原因而产生某些影响时,那就可以使用人字齿轮。双斜齿轮(人字齿轮)是与反向的并排地装在同一轴上的两个斜齿轮等效。他们产生相反的轴向推力作用,这样就消除了轴向推力。当两个或更多个单向齿斜齿轮被在同一轴上时,齿轮的齿向应作选择,以便产生最小的轴向推力。交错轴斜齿轮或螺旋齿轮,他们是轴中心线既不相交也不平行。交错轴斜齿轮的齿彼此之间发生点接触,它随着齿轮的磨合而变成线接触。因此他们只能传递小的载荷和主要用于仪器设备中,而且肯定不能推荐在动力传动中使用。交错轴斜齿轮与斜齿轮之间在被安装后互相捏合之前是没有任何区别的。它们是以同样的方法进行制造。一对相啮合的交错轴斜齿轮通常具有同样的齿向,即左旋主动齿轮跟右旋从动齿轮相啮合。在交错轴斜齿设计中,当该齿的斜角相等时所产生滑移速度最小。然而当该齿的斜角不相等时,如果两个齿轮具有相同齿向的话,大斜角齿轮应用作主动齿轮。蜗轮与交错轴斜齿轮相似。小齿轮即蜗杆具有较小的齿数,通常是一到四齿,由于它们完全缠绕在节圆柱上,因此它们被称为螺纹齿。与其相配的齿轮叫做蜗轮,蜗轮不是真正的斜齿轮。蜗杆和蜗轮通常是用于向垂直相交轴之间的传动提供大的角速度减速比。蜗轮不是斜齿轮,因为其齿顶面做成中凹形状以适配蜗杆曲率,目的是要
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