第七章 蜗杆传动

§7蜗杆传动wormgearing

（shaftangle交错轴Σ＝90°）§7－1Generalconsiderations概述§7－2ChoiceoftheparametersandgeometricalcalculationsforArchimedeanwormgearing普通圆柱蜗杆传动参数选择和几何计算§7－3Materials,typesoffailureanddesigncriteria蜗杆传动材料、失效和计算准则§7－4Forcesinwormgearing受力分析§7－5Strengthcalculations强度计算§7－6Heatbalancecalculation热平衡计算Designexample习题课Characteristicsandapplications特点和应用Typesofthewormgearing

分类§7－1Generalconsiderations概述

回总目录1、Advantages①Highspeedratio

i→Smalloverallsize（Z＝1～4）结构紧凑②

Smoothandsilentoperation平稳，噪音小（Continuousengagementbetweenwormandwormgear

蜗杆与蜗轮连续啮合）Formotiondrives

传递运动：Upto1000Forpowerdrives

传递动力：8～80一、Characteristicsandapplications特点和应用

2、

Drawbacks①

Lowefficiency效率低（Σ＝90°，Vs）UsuallyP<50KW②

Highcost成本高（

Thenecessityofusingexpensiveantifrictionmaterialsforthewormgear蜗轮轮圈用贵重有色金属青铜制造）3、Applications应用二、

Types

分类

：1、

Cylindricalwormgearing

圆柱蜗杆传动：Byshapeofthethreadsinanendsection按轴截面内螺旋线形状分：2、

Envelopingwormgearing环面蜗杆传动3、

Conewormgearing锥蜗杆传动①

Archimedeanworm阿基米德蜗杆（

Ordinary普通）②

Involuteworm渐开线蜗杆③Convoluteworm延伸渐开线蜗杆（

Straight-sidedinthesectionnormaltothethread

法向直廓）三、Meshingfeaturesoftheordinarycylindricalwormgearing普通圆柱蜗杆传动啮合特点Centralcrosssection

中间平面（主平面）：Aplanewhichisnormaltothewormgearshaftandparalleltowormshaft通过蜗杆轴线并垂直于蜗轮轴线的平面Thetoothprofileonwormisstraight-sided蜗杆齿廓：直线Thetoothprofileonwormgearisinvolute蜗轮齿廓：渐开线Meshbetweenastraight-sidedrackandaninvolutegear

为（直）齿条与渐开线齿轮啮合Specialfeatures特点：Inthecentralcrosssection中间平面内特点：中间平面内蜗杆齿廓：直线蜗轮齿廓：渐开线为（直）齿条与渐开线齿轮啮合BACK§7－2Choiceoftheparametersand

geometricalcalculationsfor

Archimedeanwormgearing

普通圆柱蜗杆传动参数选择和几何计算

Choiceoftheparameters参数选择Geometricalcalculations

几何计算回总目录1、Modules

模数m，

Profileangle

齿形角α

Inacentralcrosssection,modulesandprofileanglearestandardized

中间平面内为标准值

α＝20°m——P84表6－4

一、Choiceofparameters参数选择

2、d1，qd1——Thepitchdiameterofaworm

蜗杆中圆直径q——Thewormdiameterfactor

蜗杆直径系数①Gear齿轮d1＝mZ1IfmandZ1aredetermined，d1isdetermined.②Worm蜗杆d1＝mZ1/tgγ≠mZ1m，ifmandZ1aredetermined，d1isindeterminate.③Numberofthehobscuttingwormgearsdependsonthediameterd1

Inordertolimitnumberofthehobsandstandardize

them,severalstandarddiametersarespecified

d1多，则加工蜗轮滚刀多

为减少刀具数目，并便于实现标准化、系列化：对每一m蜗杆规定几个标准d1——P84表6－43、i、Z1、Z2①Z1thenumberofworm

蜗杆头数

1，2，4，6P83：Z1＝f（i）②i

Speedratio

传动比★Z1↓i↑η↓★Z1↑η↑i↓加工难③Z2＝i

Z1

28≤Z2≤100(32~63isoptimalforpowerdrives一般32~63)★Z2<28,Stationery则平稳性↓★Z2>100,则d2=mZ2↑Longerdistancebetweenthebearingsoftheworm→杆长↑→Rigidityofworm杆刚度↓④γThepitchhelixangleoftheworm

蜗杆导程角γ>33°ηIncreasesslightly,Difficultiesinmanufacture

η

↑缓慢,加工难γ<3.5°Self-locking自锁γ=3.5°~33°η低二、Geometricalcalculations

几何计算Application

传动功用、i→Z1（Z2＝iZ1）Strengthconditions

强度条件，qP78表4－5Geometricaldimensions

arecalculated

计算几何尺寸.BACK§7－3Materials,typesoffailureanddesigncriteria

蜗杆传动材料、失效和计算准则

Materials材料Typesoffailure失效形式Designcriteria计算准则Structureandmanufactureofthewormandwormgear蜗轮蜗杆的结构及加工方法回总目录一、Materials材料Requirements要求：NotonlyhaveenoughstrengthAndthegoodantifrictionismoreimportant

不仅要有一定强度，更重要的是要有良好的减摩性和耐磨性。（Materialpairsoflowandhighlevelsofhardness软硬相配）1、Wormmaterials蜗杆Usually：45Structurallyimprovement调质

Highvelocitiesandheavyload

高速重载：45、40Cr、20CrHardening淬火

2、Wormgearmaterials蜗轮

Highvelocitiesandheavyload高速重载Tinbronze锡青铜ZCuSn10P1ZCuSn5Pn5Zn5Betterseize-resistantlowerstrengthhighercost抗胶合能力强，机械强度低，价格高（σb<300MPa）（Vs＝12～25m/s）ZCuAl10Fe3Mn2ZCuAl8Mn13Fe3Ni2Lowerseize-resistant,Higherstrength,Lowercost抗胶合能力差，机械强度高，价格低（σb>300MPa）Usually：Aluminum－Ironbronze铸铝青铜（Vs＝2～8m/s）Lowvelocitiesandlightload低速轻载：Castiron

灰铸铁HT200HT150（Vs<2m/s）BACK二、Typesoffailure失效形式Similartotypesoffailureinthetoothedgearing：Fatiguepitting,Seizing,Abrasivewear,Plasticflowofmaterialandtoothbreakage与齿轮类似：点蚀、胶合、磨损、塑性变形、断齿Specialfeaturesasbelow特点如下：①Wormgearfailure蜗轮失效（Strengthofthewormismorethantheoneofwormgear蜗杆强度高于蜗轮）Tinbronze锡青铜：Theprincipaltypesoffailurearepitting点蚀为主（Becauseithasgoodseize-resistantability抗胶合能力强）Aluminum-ironbronzeandcastiron无锡青铜和铸铁：Theprincipaltypesoffailureareseize胶合为主

②Closeddrives闭式传动：③Opendrive开式传动：Breakageafterseverewear磨损→折断BACK三、Designcriteria计算准则

Closeddrive闭式传动①Designedaccordingtocontactfatiguestrengthofthetoothsurface按齿面接触疲劳强度设计②Checkedaccordingbendingfatiguestrengthofthetoothroot按齿根弯曲疲劳强度校核③Heatbalancecalculation热平衡计算Opendrive开式传动：

Designaccordingtobendingfatiguestrength按弯曲疲劳强度设计1、Structure

结构①Wormgear

蜗轮②Worm

蜗杆2、Manufacture

加工方法①Wormgear

蜗轮②Worm

蜗杆

四、Structureandmanufactureofthewormandwormgear

蜗轮蜗杆的结构及加工方法Wormsaremadeintegralwiththeshaftandareseldommadefabricated,thefollowingtypesofthewormdesignsareused蜗杆通常与轴做成整体，很少做成装配式,可分为：Withtoolescape有退刀槽Withouttoolescape

无退刀槽BACKRelationshipbetweenforcesactingonwormandwormgear各力间关系Magnitudeofforces力的大小Directionofforces力的方向§7－4Forcesinwormgearing

受力分析

回总目录一、

Relationshipbetweenforces

各力间关系

BACK二、Magnitudeofforces力的大小

BACK3三、Directionofforces力的方向

AsbeforeWormdrivingHelixdirection:lefthandforleft-handhelixgearandrighthandforright-handhelixgear.

Rotatingdirection:bendingdirectionoffourfingers.DirectionofFa1:ThesamedirectionofthumbingBACKContactfatiguestrengthofthetoothsurfaceonwormgear蜗轮齿面接触疲劳强度计算Bendingfatiguestrengthofthetoothrootonwormgear蜗轮齿根弯曲疲劳强度计算§7－5Strengthcalculations

强度计算

回总目录一、蜗轮齿面接触疲劳强度计算

ContactfatiguestrengthofthetoothsurfaceonwormgearInthecentralcrosssection,thetoothprofilesofthewormandwormgeararethesameasthatofinvoluteshelicalgearandrack.Hence,thestrengthcalculationsaredoneforthetoothprofilesoftheirequivalentspurgearandrack.在主平面内，蜗轮蜗杆的啮合相当于一对渐开线斜齿轮与斜齿条的啮合→取其当量直齿轮与直齿条的啮合进行强度计算。②③Lengthofthecontactline接触线长度L计入：a、多对齿啮合→×εab、齿倾斜→÷cosγc、接触线长度变化系数→χεa＝2θ＝100°χmin＝0.75Takingintoaccountthefollowingfactors：a、Morethanonepairofteethmesheachother多对齿啮合→×εab、Theteethareinclinedtotheelementsofthecylindersoftheworm齿倾斜→÷cosγc、Changefactorofthecontactlinelength

接触线长度变化系数→χεa＝2θ＝100°χmin＝0.75④Substitutingequations把式②、③、④代入intoequation①：Forchecking⑤Substitutingd1=mqandd2=mz2intoaboveequation：Fordesign①[σ]H：Tinbronze锡青铜（σb≤300MPa）：

Theprincipaltypeoffailureispitting，[σ]Hdependonthenumberofstresscycles点蚀为主,[σ]H与应力循环次数N有关；2、Notes:Aluminium-ironbronze无锡青铜（σb>300MPa）：

Principaltypeoffailureisseizure,[σ]Hisindependentofthenumberofstresscycles,butdependsonslidingvelocity.胶合为主，[σ]H与应力循环次数N无关而与相对滑动速度Vs有关。②K＝KAKVKβSteadyload→KA、KV、Kβ

SmallervaluesofKA、KV、Kβ

见P80表4－6及P80说明BACK二、Bendingfatiguestrengthoftoothrootonwormgear

蜗轮齿根弯曲疲劳强度计算Byanalogywithhelicalgearing,butstressconcentrationfactorstressconcentrationfactorYsaisnotconsidered

按斜齿轮方法计算但不计应力修正系数Ysa★①★②Theteethofwormgearsaretakenfrom20to40%strongerthanthoseofhelicalgears弯曲强度与斜齿轮相比增大约40％→Strengthincreasingfactor强度增长系数1.4Tooththicknessgrows(Theirarchedtoothshaperesultsinso-callednaturalcorrectionwhichoccursinallcrosssectionsexceptthecentralone)★③Themaximumallowablewearamountofthetoothrootthicknessis20％

允许齿根厚度最大磨损20％→补偿轮齿磨损系数1.5F★

④ForcheckingFordesignNotes说明①

YF,Formfactorforwormgearteeth,selectedaccordingtothevirtualnumberofteethZv＝Z2/cos3γ.YF齿形系数，根据Zv＝Z2/cos3γ查取P82表4－8②YβHelixanglefactor螺旋角系数BACK§4－6

Heatbalancecalculation

热平衡计算

Efficiency

效率η＝η1η2η3Heatbalancecalculation

热平衡计算回总目录一、Efficiency

效率η＝η1η2η31、η1——Efficiencyinengagement

啮合效率（Theslidingvelocitybetweentoothsurfaces

齿面间相对滑动→Powerlosses功率损失）Meshlosspowerisprincipallosspower.Itiscomputedapproximatelybyefficiencyformulaforscrews

最主要功率损失近似用螺旋面效率计算公式①

Equivalentfrictionangle

ρv当量摩擦角＝f（

Pairofmaterials材料组合、

Typesoflubricationoils润滑剂、Vs........）

Vs↑→ρv↓→η↑②Theslidingvelocity

Vs相对滑动速度2、η2——Efficiencyinsplashi