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GearsLessonOneChapterOneMechanicsComponentsSpurandhelicalgears.Agearhavingtoothelementsthatarestraightandparalleltoitsaxisisknownasaspurgear.Aspurpaircanbeusedtoconnectparallelshaftsonly.Parallelshafts,however,canalsobeconnectedbygearsofanothertype,andaspurgearcanbematedwithagearofadifferenttype(Fig.1-1).Fig1-1SpurgearsAddendumcircle齿顶圆Dedendumcircle齿根圆Pitchcircle节圆Basecircle基圆RootcircleFlank齿侧Chordalpitch弦间距splitgearTopreventjammingasaresultofthermalexpansion,toaidlubrication,andtocompensateforunavoidableinaccuraciesinmanufacture,allpower-transmittinggearsmusthavebacklash.Thismeansthatonthepitchcirclesofamatingpair,thespacewidthonthepinionmustbeslightlygreaterthanthetooththicknessonthegear,andviceversa.Oninstrumentgears,backlashcanbeeliminatedbyusingagearsplitdownitsmiddle,onehalfbeingrotatablerelativetotheother.Aspringforcesthesplitgearteethtooccupythefullwidthofthepinionspace.Helicalgearshavecertainadvantages;forexample,whenconnectingparallelshaftstheyhaveahigherloadcarryingcapacitythanspurgearswiththesametoothnumbersandcutwiththesamecutter.Becauseoftheoverlappingactionoftheteeth,theyaresmootherinactionandcanoperateathigherpitch-linevelocitiesthanspurgears.Thepitch-linevelocityisthevelocityofthepitchcircle.Sincetheteethareinclinedtotheaxisofrotation,helicalgearscreateanaxialthrust.Ifusedsingly,thisthrustmustbeabsorbedintheshaftbearings.Thethrustproblemcanbeovercomebycuttingtwosetsofopposedhelicalteethonthesameblank.Dependingonthemethodofmanufacture,thegearmaybeofthecontinuous-toothherringbonevarietyoradouble-helicalgearwithaspacebetweenthetwohalvestopermitthecuttingtooltorunout.Double-helicalgearsarewellsuitedfortheefficienttransmissionofpowerathighspeeds.Helicalgearscanalsobeusedtoconnectnonparallel,non-intersectingshaftsatanyangletooneanother.Ninetydegreesisthecommonestangleatwhichsuchgearsareused.Inordertoachievelinecontactandimprovetheload-carryingcapacityofthecrossed-axishelicalgears,thegearcanbemadetocurvepartiallyaroundthepinion,insomewhatthesamewaythatanutenvelopsascrew.Theresultwouldbeacylindricalwormandgear.Wormgearsprovidethesimplestmeansofobtaininglargeratiosinasinglepair.Theyareusuallylessefficientthanparallel-shaftgears,however,becauseofanadditionalslidingmovementalongtheteeth.Becauseoftheirsimilarity,theefficiencyofawormandgeardependsonthesamefactorsastheefficiencyofascrew.Wormandbevelgears.Single-threadwormsoflargediameterhavesmallleadanglesandlowefficiencies.Multiple-threadwormshavelargerleadanglesandhigherefficiencies(Fig.1-2).Fig1-2wormgearsetTheprofilesoftheteethonbevelgearsarenotinvolutes;theyareofsuchashapethatthetoolsforcuttingtheteethareeasiertomakeandmaintainthaninvolutescuttingtools.Sincebevelgearscomeinpairs,aslongastheyareconjugatetooneanothertheyneednotbeconjugatetoothergearswithdifferenttoothnumbers.Fortransmittingrotarymotionandtorquearoundcorners,bevelgearsarecommonlyused.Theconnectedshafts,whoseaxeswouldintersectifextended,areusuallybutnotnecessarilyatrightanglestooneanother.Whenadaptedforshaftsthatdonotintersect,spiralbevelgearsarecalledhypoidgears.Thepitchsurfacesofthesegearsarenotrollingcones,andtheratiooftheirmeandiametersisnotequaltothespeedratio.Consequently,thepinionmayhavefewteethandbemadeaslargeasnecessarytocarrytheload.WordsandExpressions1.spurgearn直齿轮2.thermalexpansionn热膨胀3.lubricationn润滑4backlashn侧向间隙5thepitchcirclesn节圆6.spacewidthn间隙宽度7.instrumentgearn仪表齿轮8.thesplitgearn拼合齿轮9.helicalgearn斜齿轮10.pitch-linevelocitiesn节线速度11.anaxialthrustn轴向椎力12.blankn坯件13.double-helicalgearsn人字齿轮14.non-intersectingn不相交的15.wormgearsn蜗轮蜗杆16.bevelgearsn伞齿轮17.crossed-axisn交叉轴18.nutn螺母19.screwn丝杠，螺钉20.largeratiosn大速比21.parallel-shaftgearsn平行轴齿轮22.single-threadwormsn单线蜗杆23.leadanglesn导角24,multiple-threadwormsn多线蜗杆25.hypoidgearn偏轴伞齿轮26.rollingConesn滚锥27.involutesn渐开线ExercisesGeartrainsThemaximumgearratioobtainablewithasingleofgearsvarieswiththetypeofgearandtheapplication.Thefollowingareapproximatemaximaforthevarioustypesforaverageloadconditions:spur,8;parallel-shafthelical,10;straightbevel,6;spiralbevel,8;hypoid,12;andworm,80.Forlightlyloaded,instrument,andpositioninggears,theseratioscanbeexceeded.Ratiosashighas400orhighercanbeobtainedwithgearsthatresembletaperedwormsmeshingwithhypoidgears.Forheavilyloadedgears,thegivenratiosmaybesohighthatareasonablegearsizeprecludesasatisfactorypinion.Sincetheratioinasinglepairofgearsisthequotient（商）ofthetoothnumbers,andsincethereusuallyarelimitationsonboththeminimumantimaximumnumbersofteethontheavailablegears,itfollowsthatthenumberofratiosobtainableinasinglepairislimited.Toenlargethecoverageitisnecessarytousemultiplepairs,ortrainsTheoverallspeedratioinatrainistheproduct（乘积）oftheratiosineachpair.Incertaincasesanexactratiocannotbeobtainedwithgears,butbyusingtwoormorepairs,thedesiredratiocanbeapproximatedtoanydegreeofprecision.RollingGuidesandBearingsLessontwochapterOneMechanicsComponentsRollinglinearguidesandguidewaysarewidelyusedinpractice，alongsideplainlinearguides.Thefollowingadvantagesareobtainedwhencomparedwithplainguides：lightrunningforcesduetor