LNPGuidePlasticGearing——齿轮设计指导书.doc

LNPGuidePlasticGearing齿轮设计指导书 A GEPlastics CompanyAGuide toPlasticGearingGearsGearsGearslastic gearshave positionedthemselves asseri?ous alternativesto traditionalmetal gearsin a wide varietyof applications.The use of plastic gears hasexpandedfrom lowpower,precision motiontransmission intomoredemanding powertransmission applications.As designerspush the limitsof aeptableplasticgear applications,more islearned aboutthe behaviorof plasticsin gearingandhow totake advantageof theirunique characteristics.Plastic gearsprovide anumber of advantages overmetalgears.They haveless weight,lower inertia,and runmuchquieter thantheir metalcounterparts.Plastic gearsoftenrequire nolubrication orcan bepounded withinternallubricants suchas PTFEor silicone.Plastic gearsusuallyhave alower unitcost thanmetal gears,and can bedesigned toincorporate otherfeatures neededin theassembly(part consolidation).These gears are alsoresistant to manycorrosive environments.The firstuseof thermoplastic gearsundoubtedly consistedofneat nylon and acetalgears carryinglow loadsat lowspeeds.As theadvantages of using thermoplastic gearsbecame clearerand new,higher performancematerialsbecame available,designers beganusing plastic gears inmoredemanding applications.The useof reinforcementsandinternal lubricantspounded into these materialshasexpanded their use evenmore.The useof thermoplasticmaterials for gears ishamperedby alack ofestablished load carrying andwear perfor?mance data,at leastwhen pared to thereams ofeasily aessiblegear/material performancedata thathasbeen puttogether for metals.The datafor metalshasbeen collectedand confirmedthrough numeroussuess?ful applicationsand iswell understoodby mostgeardesigners.Thermoplasticslate arrivalas a gear materialhasnot providedenough timefor thepilation ofextensiveload ratingdata,and theunique mechanicalandthermal behaviorof thermoplasticshas frustratedthosewho wouldattempt tointerpolate thesevalues frommorereadily availableinformation.Noheless,there arecertain guidelinesavailable forestimating thetechnical feasibilityofusingthermoplasticmaterials ingears.Most of these techniqueshave evolvedfromequations originallyworked outformetals,and thereforedo nottake into aount some of theuniquebehavior foundin thermoplasticmaterials.This brochurewill attemptto revealsome of the importantpointsthat must be consideredwhen usingthese equationsandtechniques toevaluate thermoplastic gears.The focuswill be onspur gears;however the basic pointscoveredcan beextended toother types of gears.PFigure11GBevel gears are conicalin shape,and the teeth aretapered inboththe tooth thickness andin thetoothheight.At oneend thetooth is large,and at theother it is small.Whilethe toothdimensionsare listedbased onthelarge endof thetooth,strength calcula?tions arebased on thecentral sectionof the gear tooth.The simplesttype ofbevel gear is thestraightbevel gear(Figure5).These gears aremonly used on intersecting90shafts,but theycan operate at almostanyangle.These gears impose boththrustand radialloads,and mustbeprecisely mountedto operatecor?rectly.While plasticbevel gears arenot very mon,designers arebeginningto investigatetheiruse.Othertypes ofbevel gears are thespiral andZerolbevel gears.Face gearsare a special typeofgear withteeth cutinto theface ofthe gear(Figure6).Inface gearsthe teethpointin the samedirection as the gearsaxis.The facegear willmatewith a spur orhelical gear.Like bevelgears,the axis ofthe two gears mustintersect and theshaft angleis usually90.There arethree typesof gearsthat aremonlyreferred to as worm gears.Worm gears can bemount?ed onnonintersecting,nonparallel axes;however,themost mon arrangement isnonintersecting,90axis.Worm gearsare characterizedby onemember havingascrew thread.This memberis referred to asthe worm(Figure7).The gearit mateswithis referredto astheworm gear.There aremany differenttypesof gears,and theycan bemosteasily categorizedby theway the gear axis intersect.If the gears mustoperate onparallel axes,then spurorhelical gearsare required.If theaxes are intersecting andatright angles,then beveland worm gearsareusuallyused.If theaxes areboth nonintersectingand nonparallel,then crossed?helical,worm gears,hypoid andspiroidgears are used.The mostmon plasticgearsarespur,helical andworm gears,but the other typescould beusedif required.A singlegear cando nowork,so gearsare used in pairs.When theteeth oftwogearsare meshed,the rotationofone gearwill causetheothergear torotate also.If thetwogears havedifferent diameters,the smallerone(called thepinion)will turnfaster andwith lessrotational forcethanthe largerone(called the gear).Spur gearsare cylindricalin shape,with theflank of thegear toothparallel to the gearaxis.If theteeth of the gearpointaway from the axis,the gear is anexternal spurgear(Figure1).If theteeth pointtoward theaxis,thegear isan internalspur gear(Figure2).Spur gearsarerelatively simplein designand easyto manu?facture.Spur gearsimpose onlyradialloads on their bearingsand willoperateon avariety ofcenterdistances,making themrela?tively simple to mount.Mostdesigners usea20pressureangle,but221/2and25arealso mon.Pressure anglesabove20give higherload capacitybutdo notrun assmoothly orquietly.A helical gearissimilar to aspurgear,but the toothflank isnow atan angleto theaxisof the gear(Figure3).In fact,a helical gear with a helixangle ofzero isa spurgear.Helical gearsare usedwhen bothhigh speedsandhigh loadsare involved.Single helical gearsimposebothradial and thrust loads,and aretherefore notassimpletomount,but theydo tendtorun quieterand smootherthanspur gears.Helical gearswith oppo?site handsare oftenmountedon the same shaftto canceloutthe thrustload.These arereferredtoasdouble helicalgears(Figure4).E A R TYPE SA NDA RR ANG EM ENTSFigure2Figure6Figure7Figure5Figure4Figure32Gear T3ypes andArrangements,continuedG E A RA CTIONIt isverymonin plasticgearing tomate ametal(oroasionally plastic)worm witha plastichelical gear.Thisarrangement isactually callednon?enveloping worm gearsor crossed?helical gears.Crossed?helical gearsare mount?edonaxes which do notintersect andthat areat anangle(usually90)to each other.Crossed?helical gearsgenerateboth radialandthrustloads on their bearings.Crossed?helicalgear sets areable tostand smallchangesin center distance andshaft anglewithout impairmentinthe auracyof the gear.This makesit one of theeasiestgears tomount.Unfortunately,crossed?helicalgearshaveonly pointcontact and,therefore,do notcarry veryhighloads.However,if the gearscanwear infor sometimewithout failure,the pointcontact beesline contact,which ismore similartoasingle enveloping wormgear,and the load carryingcapacity increases.This isone ofthereasons metalworms aremated with plastic helicalgears.The helicalgear wearsfirst,and bees,for allintentsand purposes,a wormgear.The otherreasonmetal wormsareusedwithplasticworm gearsor helicalgearsis that they helpeliminate thelarge amountsof heatthatcan begenerated withwormgearsets.It is notunmon tosee plasticwormgearsfail due to heatrelatedmechanisms.True wormgearsetsare describedas single?envelopingor double?enveloping wormgears.In singleenvelopingworm gearingthewormgear has a throatedprofile whichwraps around theworm likea nutwrapsarounda thread(Figure8).This givesgreater contactandincreases theload carryingcapabilityby a factor of2?3over asimilarhelicalgear.In double?envelopingwormgears boththeworm(Figure9)and theworm geararethroated andwrap aroundeach other.It isvery difficult tomold athroated wormor wormgear,and forthat reasona wormandhelical gear(crossed?helicals)bination isused mostoften.Before wecan beginto analyzethe stressesin plasticgears,it isimportant tounderstand gearaction.Eachtooth is,in effect,a cantileverbeam supportedon oneend.The contacttries to bend thebeam andto shearthebeam fromthe bulkof the material.Therefore,a gearmaterialneeds tohave highflexural strengthand stiffness.The nexteffect isprimarily asurface effect.Stress isgenerated on the surface of thetooth byfrictional forcesandby pointor linecontact(Hertzian ContactStress).During gearmovement the gear teethroll oneach otherandslide pasteach otherat the same time.As theteethe intomesh,there isan initialcontact loading.Therolling actionof the gears pushesthe contact stress(which isaspecialpressive stress)just aheadof thepoint of contact.At thesame time,sliding isourringbecause thecontact lengthon the parts of the gear toothin meshare notthesame.This causesfrictional forcesthatdevelop aregion oftensile stressjust behindthe pointof contact.The arrowsin Figure10marked Rshow thedirection of rollingand thearrows markedS showthedirectionofsliding.In theareas wherethese twomotionsare inopposite directionsthe resultingforces causethemost problems.In Figure10a,the gearshave juste intocontact.Atpoint1onthe driving gearthe materialis underpres?sion fromthe rollingaction toward the pitch point,andunder tensiondue tofrictional resistanceto the slidingmotion awayfromthe pitch point.This binationofforces cancause surfacecracking,surface fatigueandheat buildup.All of these factors can lead to considerablewear.Figure9Figure8PITCH LINEDRIVENGEARPITCH LINEDRIVINGGEARR1XX23SSR1XFigure10aBE GINNING OF C ONTA C TAtpoint2onthedriven gear,the rollingand slidingarein4G EARDE SIGN STRE SSA NALY SISAPPLIE DTO PLASTIC GEAR Sthesame direction,towardthe pitch point.This putsthematerial atpoint2under pression(from rolling)andpoint3under tension(from sliding).This conditionis notassevere asthat onthedriving gear.In Figure10b,we seethe endof contactbetween thetwogears.The rollingmotion isstill in thesamedirection butthesliding motionhas changeddirection.Now thebase ofthedriven gearis the most highlyloaded,since point4isloaded inboth pression(due torolling)and tension(duetosliding).The tipof thedrivinggearis underlesssevere stresssince point5is underpressive stressandpoint6is intensile stress.At the pitchpointtheslidingforce changesdirection and anull pointfor slidingis created(pure rolling).One mightassumethis sectionof the gear showsthe leastsurfacefailure;however,the pitchpoint isoneof the firstareaswhere seriousfailures our.Although the pitch pointdoesnot seepound stresses,it doessee highunitloading.During initialgear contactor atthe endofcon?tact,the previous tooth pairor thenext toothpair shouldbearsomeof theload,and theunit loadingis reduced.The highestpoint loadingours when the gearsare contactingat orslightly abovethepitch line.At thatpoint,one toothpair willusually becarrying allor mostof theload.This canleadtofatigue failure,severe heatbuild?upand surfacedeterioration.The most important part of agearis the gear teeth.Without theteeth,the gearis simplya wheeland isof littleuse intransmitting motionor power.The basicmeasurement of agears abilityto carrya givenload is toestimate the gearstoothstrength.Although prototypingofa gearis alwaysremended,it can be expensiveandtime consuming,so somemethod ofdetermining agearsfeasibility isrequired.Bending StressThebending stressonageartoothof astandard toothformloaded atthepitchline canbe calculatedusing theLewisEquation:FP dS b=_fY (1)where:Sb=bending stressF=tangential toothloading atthepitchlineP d=diametral pitchf=face widthY=Lewis formfactor forplasticgears,loaded atthepitchpointTests haveshown that the mostsevere toothloadingours whenthegeartoothisloaded tangentiallyat thepitchline and the number of pairsof teethin contactapproachesone.Another usefulapproach,if thehorse?power requiredby thesystem isknown,istouse theequation:HP126050P dSb=_f YD w (2)where:HP=horsepowerD=pitch diameterw=speed,rpmAnother variationof theLewis equationincorporates thepitchline velocityand aservice factor:HP55(600+V)P dC sSb=_f yV (3)where:y=Lewis formfactor atthetoothtipV=pitchlinevelocity(fpm)C s=service factorDRIVINGGEARDRIVEN GEARPITCHLINER5XX4SSRPITCH LINE6Figure10bE NDOFCONTACTTypical servicefactors,which describe the qualityof theinputtorque andthe dutycycle of thegearare:TABLE1Service FactorsTypeof248-10Intermittent OasionalLoadhrs/day hrs/day3hrs/day1/2hrs/daySteady1.251.000.800.50Light shock1.501.251.000.80Med.Shock1.751.501.251.00Heavy Shock2.001.751.501.25With anystress equation,allowable stress,Sall,can beinputfor Sb inorder tosolve forother variables.The safeor allowable stress is not a typicaldata sheetstress level,but anallowable stressdetermined fromactual testingofa materialas agear withstandard toothform.An allowablestressalready has a materialsafety factorincorporatedinto thevalue.For anygiven materialthe allowablestresslevel isvery dependentonalarge number of factors.These include:?Lifetime cycles?Operating environment?Pitch linevelocity?Counterface?LubricationFactor ofSafetySince allowablestressisequal toa strengthvalue dividedbya materialsafety factor(Sall=S/n),this isa goodpointto talkabout factorsof safety forgears.Safety referstothe abilityof apart toperform itsproper functionfor itsservice life withoutfailure.Function,servicelifeand partfailuremustbe defined foran applicationbefore afactor ofsafety canbechosen.Factors?of?safety may bedefinedin manyways;however,they basicallyrelate what is permissibleorallowabletowhat willcause failure.A factor?of?safety canbe appliedinthree basicways.The entire factor canbe appliedto amaterial property suchas strength;or theentirefactorcanbe appliedto theloading;or separatefactorscanbe usedforeach loadand amaterialproperty.The lattercase isoften the most usefulbecause eachloadcan beinvestigated and then afactor?of?safety appliedtodetermine theabsolute maximumload.Each maximumloadis thenused in the stressanalysis suchthat thegeometryand boundaryconditions producean allowablestress.The allowablestress limit is determined by applyingastrength factor?of?safety to the materialstrength atend?use conditions.The loadfactor?of?safety canbe determinedin thetradi?tional manner.The strengthfactors?of?safetyforplasticmaterials,however,are oftendifficulttodetermine.This isbecause the strengthof aplastic isnotaconstant,but astatisticaldistribution ofstrength underend?use condi?tions.Consequently,design engineersneed tounderstandthe enduse conditions,for example,temperature,strainrate,and loadduration.Fabrication knowledge is neededtounderstand weldlinesituations,anisotropic effects,residual stresses,and processvariants.Material knowl?edgeismostimportantbecausethebetter amaterialbehavior isunderstood underend?use conditions,themore auratelyafactor?of?safety canbe established,resulting in a optimumpart geometry.The poorerthe defi?nition andthe greaterthe numberof unknowns,the largerthefactor?of?safety required.A minimumfactor?of?safetyof twois remended,even whenan applicationhasbeen carefullyanalyzed.If pre?calculated allowablestress dataisnotavailable,andfor plastics,it usuallyisnt,then thegear designer must beextremelycareful toconsider allofthefactors outlinedearlier,so thata properfactor ofsafetycanbe determinedandS allcanbecalculated.Whether similarexperienceexists ornot,itisessential thata prototypemold bebuiltand thatthegearbe testedattheexpected applicationconditions.Two materialswhichdohave pre?calculatedallowable stressvalues areNylon6/6and acetal.Thesematerials havebeen widelyused ingearapplications,andthe majorsuppliers ofthese materialshave takenthe timetogenerate thesevalues.Examples canbe seeninFigures11and12.10987654321012468102050100xx00100032PITCH20PITCHBending Stress(x1000psi)Cycle Life(Millions)Figure11MAXIMUM BENDINGSTRESSESfor Gear Teeth ofDELRIN?Delrin?is registeredtrademark ofE.I.DuPont DeNemours,Co.510987654321012468102050100xx00100048PITCH20PITCHBending Stress(x1000psi)Cycle Life(Millions)32PITCH16PITCHContact StressTheequations wehave lookedat sofar havebeen exam?ining theforces tryingto bendthegearteeth andshearthem fromthe bulkofthe material.These forceslead tofailuresby toothbreakage dueto staticloading orfatigueaction.The otherforces wesaw inour examinationofgear actiongenerated surface stresses bycontact of thegear teethand theirrelative motionto eachother.Thesestresses leadto failurein the surfaceofthegearteeth,orwear.To assurea satisfactorylife,the gearsmust bedesignedso thatthe dynamicsurfacestressesare withinthesurface endurance limit ofthematerial.The followingequation wasderived fromthe Hertztheoryof contactstress betweentwo cylinders,and modifiedtoemploy notationusedingearing:W t11S H=_fD p (4)where:S H=surface contactstress(Hertzian stress)W t=transmitted loadDp=pitch diameter,pinion?=Poissons ratioE=Modulus ofElasticity?=pressure anglem=speed ratio,N g/N pN=numberof teethThe subscriptsp andg refertothepinion andgear,respectively.The surfacecontactstressis calculatedfor agearandthenparedtothesurfaceendurancelimitofthe material.However,for plastics,this datais seldomavailable.Once again,the bestway todetermine thistypeof datais throughactual testingsets ofgears runningunderservice conditions.This calculation,however,cangive the designer someidea ofhow stressedthe surfaceofthegearwill berelative tothe purepressivestrength ofthematerial,which isreadily available.GearTooth DesignHobsused tocut teethin metalgearsareavailableoff?the?shelf,and foreconomic reasons,designers ofmerciallycut gearsseldom useany othertooth forms.Injection moldedgearsarenot constrainedto usingthesestandard hobssince specialtooling mustbe usedwhencutting themold topensate forshrinkage.If ahobTOTAL PLASTICGEAR DESIGN6Elimination ofUndercut:7The teethofgearshaving asmallnumberofteeth willoften beundercut atthe rootofthe gear.This willweaken thegear tremendouslyandshould beavoided inplasticgears.(Figure13).Balanced CircularTooth Thickness:If twogearteeth in mesh aredesignedas standard,then thegear withthesmaller numberofteeth(pinion)will haveteeththat arethinner attheroot thantheteethofthegear(Figure14).The pin?ion willnot beable totransmit as muchpoweras thegear couldcarryand will betheweak linkinthedesign.In ordertooptimize theloadcarry?ing capabilityofthegearset,the circulartooththickness ofthe