§7蝸桿傳動wormgearing

（shaftangle交錯軸Σ＝90°）§7－1Generalconsiderations概述§7－2ChoiceoftheparametersandgeometricalcalculationsforArchimedeanwormgearing普通圓柱蝸桿傳動參數選擇和幾何計算§7－3Materials,typesoffailureanddesigncriteria蝸桿傳動材料、失效和計算準則§7－4Forcesinwormgearing受力分析§7－5Strengthcalculations強度計算§7－6Heatbalancecalculation熱平衡計算Designexample習題課Characteristicsandapplications特點和應用Typesofthewormgearing

分類§7－1Generalconsiderations概述

回總目錄1、Advantages①Highspeedratio

i→Smalloverallsize（Z＝1～4）結構緊湊②

Smoothandsilentoperation平穩，噪音小（Continuousengagementbetweenwormandwormgear

蝸桿與蝸輪連續嚙合）Formotiondrives

傳遞運動：Upto1000Forpowerdrives

傳遞動力：8～80一、Characteristicsandapplications特點和應用

2、

Drawbacks①

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

Highcost成本高（

Thenecessityofusingexpensiveantifrictionmaterialsforthewormgear蝸輪輪圈用貴重有色金屬青銅制造）3、Applications應用二、

Types

分類

：1、

Cylindricalwormgearing

圓柱蝸桿傳動：Byshapeofthethreadsinanendsection按軸截面內螺旋線形狀分：2、

Envelopingwormgearing環面蝸桿傳動3、

Conewormgearing錐蝸桿傳動①

Archimedeanworm阿基米德蝸桿（

Ordinary普通）②

Involuteworm漸開線蝸桿③Convoluteworm延伸漸開線蝸桿（

Straight-sidedinthesectionnormaltothethread

法向直廓）三、Meshingfeaturesoftheordinarycylindricalwormgearing普通圓柱蝸桿傳動嚙合特點Centralcrosssection

中間平面（主平面）：Aplanewhichisnormaltothewormgearshaftandparalleltowormshaft通過蝸桿軸線并垂直于蝸輪軸線的平面Thetoothprofileonwormisstraight-sided蝸桿齒廓：直線Thetoothprofileonwormgearisinvolute蝸輪齒廓：漸開線Meshbetweenastraight-sidedrackandaninvolutegear

為（直）齒條與漸開線齒輪嚙合Specialfeatures特點：Inthecentralcrosssection中間平面內特點：中間平面內蝸桿齒廓：直線蝸輪齒廓：漸開線為（直）齒條與漸開線齒輪嚙合BACK§7－2Choiceoftheparametersand

geometricalcalculationsfor

Archimedeanwormgearing

普通圓柱蝸桿傳動參數選擇和幾何計算

Choiceoftheparameters參數選擇Geometricalcalculations

幾何計算回總目錄1、Modules

模數m，

Profileangle

齒形角α

Inacentralcrosssection,modulesandprofileanglearestandardized

中間平面內為標準值

α＝20°m——P84表6－4

一、Choiceofparameters參數選擇

2、d1，qd1——Thepitchdiameterofaworm

蝸桿中圓直徑q——Thewormdiameterfactor

蝸桿直徑系數①Gear齒輪d1＝mZ1IfmandZ1aredetermined，d1isdetermined.②Worm蝸桿d1＝mZ1/tgγ≠mZ1m，ifmandZ1aredetermined，d1isindeterminate.③Numberofthehobscuttingwormgearsdependsonthediameterd1

Inordertolimitnumberofthehobsandstandardize

them,severalstandarddiametersarespecified

d1多，則加工蝸輪滾刀多

為減少刀具數目，并便于實現標準化、系列化：對每一m蝸桿規定幾個標準d1——P84表6－43、i、Z1、Z2①Z1thenumberofworm

蝸桿頭數

1，2，4，6P83：Z1＝f（i）②i

Speedratio

傳動比★Z1↓i↑η↓★Z1↑η↑i↓加工難③Z2＝i

Z1

28≤Z2≤100(32~63isoptimalforpowerdrives一般32~63)★Z2<28,Stationery則平穩性↓★Z2>100,則d2=mZ2↑Longerdistancebetweenthebearingsoftheworm→桿長↑→Rigidityofworm桿剛度↓④γThepitchhelixangleoftheworm

蝸桿導程角γ>33°ηIncreasesslightly,Difficultiesinmanufacture

η

↑緩慢,加工難γ<3.5°Self-locking自鎖γ=3.5°~33°η低二、Geometricalcalculations

幾何計算Application

傳動功用、i→Z1（Z2＝iZ1）Strengthconditions

強度條件，qP78表4－5Geometricaldimensions

arecalculated

計算幾何尺寸.BACK§7－3Materials,typesoffailureanddesigncriteria

蝸桿傳動材料、失效和計算準則

Materials材料Typesoffailure失效形式Designcriteria計算準則Structureandmanufactureofthewormandwormgear蝸輪蝸桿的結構及加工方法回總目錄一、Materials材料Requirements要求：NotonlyhaveenoughstrengthAndthegoodantifrictionismoreimportant

不僅要有一定強度，更重要的是要有良好的減摩性和耐磨性。（Materialpairsoflowandhighlevelsofhardness軟硬相配）1、Wormmaterials蝸桿Usually：45Structurallyimprovement調質

Highvelocitiesandheavyload

高速重載：45、40Cr、20CrHardening淬火

2、Wormgearmaterials蝸輪

Highvelocitiesandheavyload高速重載Tinbronze錫青銅ZCuSn10P1ZCuSn5Pn5Zn5Betterseize-resistantlowerstrengthhighercost抗膠合能力強，機械強度低，價格高（σb<300MPa）（Vs＝12～25m/s）ZCuAl10Fe3Mn2ZCuAl8Mn13Fe3Ni2Lowerseize-resistant,Higherstrength,Lowercost抗膠合能力差，機械強度高，價格低（σb>300MPa）Usually：Aluminum－Ironbronze鑄鋁青銅（Vs＝2～8m/s）Lowvelocitiesandlightload低速輕載：Castiron

灰鑄鐵HT200HT150（Vs<2m/s）BACK二、Typesoffailure失效形式Similartotypesoffailureinthetoothedgearing：Fatiguepitting,Seizing,Abrasivewear,Plasticflowofmaterialandtoothbreakage與齒輪類似：點蝕、膠合、磨損、塑性變形、斷齒Specialfeaturesasbelow特點如下：①Wormgearfailure蝸輪失效（Strengthofthewormismorethantheoneofwormgear蝸桿強度高于蝸輪）Tinbronze錫青銅：Theprincipaltypesoffailurearepitting點蝕為主（Becauseithasgoodseize-resistantability抗膠合能力強）Aluminum-ironbronzeandcastiron無錫青銅和鑄鐵：Theprincipaltypesoffailureareseize膠合為主

②Closeddrives閉式傳動：③Opendrive開式傳動：Breakageafterseverewear磨損→折斷BACK三、Designcriteria計算準則

Closeddrive閉式傳動①Designedaccordingtocontactfatiguestrengthofthetoothsurface按齒面接觸疲勞強度設計②Checkedaccordingbendingfatiguestrengthofthetoothroot按齒根彎曲疲勞強度校核③Heatbalancecalculation熱平衡計算Opendrive開式傳動：

Designaccordingtobendingfatiguestrength按彎曲疲勞強度設計1、Structure

結構①Wormgear

蝸輪②Worm

蝸桿2、Manufacture

加工方法①Wormgear

蝸輪②Worm

蝸桿

四、Structureandmanufactureofthewormandwormgear

蝸輪蝸桿的結構及加工方法Wormsaremadeintegralwiththeshaftandareseldommadefabricated,thefollowingtypesofthewormdesignsareused蝸桿通常與軸做成整體，很少做成裝配式,可分為：Withtoolescape有退刀槽Withouttoolescape

無退刀槽BACKRelationshipbetweenforcesactingonwormandwormgear各力間關系Magnitudeofforces力的大小Directionofforces力的方向§7－4Forcesinwormgearing

受力分析

回總目錄一、

Relationshipbetweenforces

各力間關系

BACK二、Magnitudeofforces力的大小

BACK3三、Directionofforces力的方向

AsbeforeWormdrivingHelixdirection:lefthandforleft-handhelixgearandrighthandforright-handhelixgear.

Rotatingdirection:bendingdirectionoffourfingers.DirectionofFa1:ThesamedirectionofthumbingBACKContactfatiguestrengthofthetoothsurfaceonwormgear蝸輪齒面接觸疲勞強度計算Bendingfatiguestrengthofthetoothrootonwormgear蝸輪齒根彎曲疲勞強度計算§7－5Strengthcalculations

強度計算

回總目錄一、蝸輪齒面接觸疲勞強度計算

ContactfatiguestrengthofthetoothsurfaceonwormgearInthecentralcrosssection,thetoothprofilesofthewormandwormgeararethesameasthatofinvoluteshelicalgearandrack.Hence,thestrengthcalculationsaredoneforthetoothprofilesoftheirequivalentspurgearandrack.在主平面內，蝸輪蝸桿的嚙合相當于一對漸開線斜齒輪與斜齒條的嚙合→取其當量直齒輪與直齒條的嚙合進行強度計算。②③Lengthofthecontactline接觸線長度L計入：a、多對齒嚙合→×εab、齒傾斜→÷cosγc、接觸線長度變化系數→χεa＝2θ＝100°χmin＝0.75Takingintoaccountthefollowingfactors：a、Morethanonepairofteethmesheachother多對齒嚙合→×εab、Theteethareinclinedtotheelementsofthecylindersoftheworm齒傾斜→÷cosγc、Changefactorofthecontactlinelength

接觸線長度變化系數→χεa＝2θ＝100°χmin＝0.75④Substitutingequations把式②、③、④代入intoequation①：Forchecking⑤Substitutingd1=mqandd2=mz2intoaboveequation：Fordesign①[σ]H：Tinbronze錫青銅（σb≤300MPa）：

Theprincipaltypeoffailureispitting，[σ]Hdependonthenumberofstresscycles點蝕為主,[σ]H與應力循環次數N有關；2、Notes:Aluminium-ironbronze無錫青銅（σb>300MPa）：

Principaltypeoffailureisseizure,[σ]Hisindependentofthenumberofstresscycles,butdependsonslidingvelocity.膠合為主，[σ]H與應力循環次數N無關而與相對滑動速度Vs有關。②K＝KAKVKβSteadyload→KA、KV、Kβ

SmallervaluesofKA、KV、Kβ

見P80表4－6及P80說明BACK二、Bendingfatiguestrengthoftoothrootonwormgear

蝸輪齒根彎曲疲勞強度計算Byanalogywithhelicalgearing,butstressconcentrationfactorstressconcentrationfactorYsaisnotconsidered

按斜齒輪方法計算但不計應力修正系數Ysa★①★②Theteethofwormgearsaretakenfrom20to40%strongerthanthoseofhelicalgears彎曲強度與斜齒輪相比增大約40％→Strengthincreasingfactor強度增長系數1.4Tooththicknessgrows(Theirarchedtoothshaperesultsinso-callednaturalcorrectionwhichoccursinallcrosssectionsexceptthecentralone)★③Themaximumallowablewearamountofthetoothrootthicknessis20％

允許齒根厚度最大磨損20％→補償輪齒磨損系數1.5F★

④ForcheckingFordesignNotes說明①

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

Heatbalancecalculation

熱平衡計算

Efficiency

效率η＝η1η2η3Heatbalancecalculation

熱平衡計算回總目錄一、Efficiency

效率η＝η1η2η31、η1——Efficiencyinengagement

嚙合效率（Theslidingvelocitybetweentoothsurfaces

齒面間相對滑動→Powerlosses功率損失）Meshlosspowerisprincipallosspower.Itiscomputedapproximatelybyefficiencyformulaforscrews

最主要功率損失近似用螺旋面效率計算公式①

Equivalentfrictionangle

ρv當量摩擦角＝f（

Pairofmaterials材料組合、

Typesoflubricationoils潤滑劑、Vs........）

Vs↑→ρv↓→η↑②Theslidingvelocity

Vs相對滑動速度2、η2——Efficiencyinsplashi