_-----------GEAR FUND.AMENITAlS _

Metallurgical Aspectsto be Considered in

Gear and Shaft Design

IntroducUoDIn his Handbook qf Gear Design

(Ref. 1). Dudley tates (or understates);"The best gear people around ll1eworldare now coming to realize that metallur-gical qualiryis just a . important as gee-metric quality." Geometric accuracywithout metallurgical integnt.yin anyhighly , tre ed gear Oil' shaft would onlyres 11II in wasted effort for all con-cerned-the gear designer. the manufac-turer, and the customer-as the compo-nern' life cycle would be prematurelycut hart. A carburized automotive gearor shaft with the wrong . urface hard-ness, case depth all' core hardne s may1'101 even complete it ha ic warrantyperiod before failing 'I.orally at can ider-able expense and loss 'of prestige for theproducer and the eu tornez The unex-pected early failure of a lar~e industrialgear or shaft ina coal mine or mill couldresult in lost production and incomewhile the machine i down sincereplacement components may not bereadily available. - ortunately, this sce-nario j not common. Most reputablegear and shaft. manufacturers around theworld would never neglect. the metallur-gical quality of their product.

Additionally.thereexi t today awide range of sophisticated and reliablecontrol equipment available to the geari'ndustry to ensure that all of the metal-lurgical processes in gear making areadequately quality a ured,

New Oppo.rtunlti forManufacturers

In the automotive indu try, cus-tamer' have always demanded lighter,

M. G.,Cnnyngham

cheaper and quielerhigher loads at increasing speeds. Wtisonly through an increa ed knowledgeand understanding of 'the metallurgicala peel of gear and shaft design thatthe. e demands can beati fied.

For many y,ear , indu trial gear man-ufacturers have followed me \arger auto-motive gear companies in introduclngproces es . uch as gas carburizing '~ortheir small to medium siz'edgear .Surface hardening techniques such asflame hardening and contour inductionbardening are frequently used [0

improve the endurance or load carryinga:bil'ity. allowing reduced weight andco 1. Gears and shafts manufactured formining machines. for example. havebeen surfa e hardened using techniquesthat. include go. earburizing, nitriding,induction hardening and shot peening.In all of these cases, cu torner demandscan be fuUy mel by an intimate knowl-edge of the metallurgical change occur-ring before, during and! after manufac-turing, Thi includes material selection,machining, heal. treatment processing,shot peening. grinding. chemical treat-ment and ubseqnent lubrication.

Desigp Engineer's RoleThe de ign engineer has overall.

respen ibmty of the engineering specdl-cations of new gears and shafts used totransmit torque, change rotationalspeeds or drive machinery. This respon-sibility includes calculating the geomet-ric or dimensional specification andensuring that the .Ioad can be transmit-ted moothly and safely without. break-age or seizure, The designer mak:es u e

and computer software (0 aid in this,process. He will utilize table and chartsin these references '10 obtai:nthe loadcarry:ing properties of variou materialor, more likely. to compare the urfaceload and bending endurance limits ofth available material . The mo I com-monly tabulated metal!lugical propertyshown in these tables ami graphs isBrinen hardne s, which is directly relat-.dm ultimate tensile strength, as are .allindentation hardne S 'tests (Ref. 2).

The e chart apply to n rmalized orhardened. and tempered ueel gears up toa maximum. of about 400 Brinell hard-ness. MetallUll'gi.cal factors such a ur-

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50 GEAR TECHNOLOGV

GEAR:FUNDAMENTALS •• _face microstructure, grain size and steelcleanliness can have a major influenceall. gear and shaft endurance limits. butthey are typically ignored. Such factorare not easily expressed numerically andare difficult for the design engineer touse directly in his calculations. It isprobable that the designer may consulttabtesgiving the full mechanical andphysical properties of specific materialsand rate them on performance in areasuch as impact strength, ducrility,

:fatigue life, or surface load and bendingendurance limits if these figure areavailable. In reality. it is implied that thevast majority of vital metallurgical fac-tors must be correctly dealt with by thematerial supplier or process provider.who must ensure that metallurgicalintegrity and the optimum balancebetween trength and toughne s proper-tie .are achieved ill the final product.

Materials Engineer's Roleht larger gear and shaft companies, it

is the responsibility of the materialsengineer to ensure the metallurgicalintegrity of the final product. Thisineludes selecting the correct materialsandthermal processing, as well as qual-ity assurance of all the vital productionprocesses that could change the proper-ties of the final gear or shaft. Manymetallic and nornmetaUic materials havebeen successfuUy used to manufacturegears (Ref. 6). A wide variety of steels.cast irons, nonferrous alloys, phenolicresin • thermoplastic and sintered ironare available. but by far the greatestnumber of highly stressed gears andshafts are made from steels because oftheir high strength to weight ratio andrelatively low cost. Additionally. fer·reus materials gain their wide accep-tance from the fact that their structuralproperties can be modified by Ileattreatment, and their surface chemistrycan. be changed by diffusing carbon ornitrogen into their surfaces. It has beenestimated. for example, that reelsaccount for about ninety percent of allgears and shafts produced in Australia.There are also, a wide range of surfacehardening options to select from, sospecia.list knowledge and material te t

equipment is required. [t is in this ailea

_------------IGEARIFUN!DAIMENTALS., _For the most. highly loaded gears andshafts, this uncertainty may affect thefinal fa tor of afety in the de ign calcu-laLions. The gear design standards may'mention certain metallurgical factors tobe con idered, but '!Jileymay not giveprecise answer regarding what can betolerated, Finally, confusion may existbetween !Jiledifferent standards regard-ing how they hould be applied. I

These problems are of major concern

dun most materials engineer receivellIeir training.

Mechanical and materials engineerswork together in, their differing roles toarrive at the correct design and manu-facturing route to make better andcheaper gear, and Rafts that will notfai,1 prematurely.

Materials and, Preeess SeI~ecUonIn general. the de ign engineer will I

con lilt, with the materials engineer to !discus all of the available optionsbefore selectingthe final materials andheat treatment processes that satisfy thedesign requirements for a particular gear ior ' han 11 well as :fulfill.the economic i

requirem.ents of lhe tmsi,ness in anincreasingly competitive environment.In Australialhere are a limited Dumber i

of steels and prece options available ;(Ref. 6), .0 the right deci ion at thede igl'l tage i .e ential. For example, anautomottseuansmissloa shan may be !made from a low carbon alloy teel and icarburizedl and quenched, Of it could beatl factorily made from a cheaper plain

carbon steel and induction hardened.The final decision wiU depend on theconfiguration and type of gear or shaftbeing considered as well as the location,magnitude and duration of stresses thatare l:ikel.yto be present Abo vital are thecnpabil,i.l)" reliability and cost of the met-aJiurgi.cal proce es available at the time.

At this stage, ihe materials engineermust consider metallurgical problemssuch as distortion duri~g heal treatmentprocessing, the lLlrely impact and fatigueload that may be encountered duringservice, and the added cost related toensuring metallurgical ,quality. The twoengineer must be able to apply theoryand experience 10 the particular applica-tion in question so as to' arrive al thedesired resu·lt-a precision product at acompetitive price to satisfy the customer.

Con iderable experience and knowl-edge of existing successfal designs isnormally required. Discussion of theprecise application needs and require-ments may reveal, !.bat special problernsexist with lubrication or overheating.Impact loads are llonnaUy impossible toe timate accurately and some melallurgi-cal factors may not be known precisely.

to smaller gear eompaaies thaI cannotafford an in-house araterials engineerand do not. pos ess ln-hou e heal trear-rnent racHitie .

,G r Tooth iLou.dio,gAny discussion of the metallasgical

aspects of gear de ign mu t begin bylooking at ba ic gear tooth loading.Regardle s of the gear type, whetherpur, bevel, helical. hypoid or worm, in

highJy loaded mechanicali gear trains, the

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_------------GEAR FUN!DAMENTAlS _forces acting on the mating gear teethwhen they engage to transmi; power willproduce high mace contact stresses onthe loaded flanks of the mating teelh andhigh bending stresses at OJ near the rootof those teeth. Differences exist in themagnitude and depth of the shear stress aswell as in the thrust direction and amountof sliding that OCCIUS in the different geartypes, bUI these differences will not beconsidered at this point.

Su.rface stresses. Surface fatigue is afrequent cause of gear failure. Althoughwear and scoring can be related to poorlubrication or surface roughness, pimngfatigue and subsequent breakage 'can berelated to metallurgical factors.

The surface and near surface stress-es developed between two steel sur-faces under load have been studied bythe 19th century German engineerHertz, who developed formulae to aid

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CIRCLE 111652 GEAR TECHNOLOGY

in rating pitting resistance. However,these Hertzian ,equatjolls are correctonly for static load on i otropic homo-geneous materials. Because of the com-plex stress patterns existing in modem.gears, where sliding and rolling takeplace above and below the pitch line,more recent]y developed relationshipsare available. However, these too are oflimited value as the effect of lubricantswas notconsidered (Ref. 4),

Initial wear or "wearing in" may benormal, and unles cracks develop inthe tooth surface, it willI generally notlead to pitting. However, pitting fatigueis progressive and leads to the destruc-tion of the loath profile.

A combination of rolling and slidingtakes place both above and below thepitch line. The sliding motion plus the.coefficient of friction tend to causeadditional. surface and sub urface stress-es. Compressive stres es are present justahead of the contact zone in the directionof sliding .. Just behind this zone, thereare tensile stre ses. Beneath the contactzone are shear stresses. The depth oflllepoint of maximum shear stress is aboutone third the width of the contact bane!.For any given load. 'the magnitude ofthese stresses is dependent. on the lengthof the contact band and the action ohhelubricant present.

As already mentioned, gear designtables and standard make use of thetrong relation hip that exists between

indentation hardnes , olrimate tensilestrengthcthe surface stress factor (Sc)and the bending stres factor (Sb) forstatic loads ..But as th majority of gearsand shafts fail by fatigue at loads welJbelow the ultimate tensile strength,thensuch tables are only \I eful in detennin-ing the steel's behavior under staticloads. They are of little help in predict-ing the material's behavior under cycli-cal loading. It is at this point that theinfluence of residual stresses on fatiguemust be discussed.

It has been well documented thatprocesses introducing residual tensilestresses into the surface of a cycl:icallyloaded specimen decrease its fatigue life,Processesthat introduce residual com-pressive stresses i.nto the surface of a

• -.GEA:R.FUNDAME~NTAJ.S - •

pecimen increase il fatigue life (Ref.3). Because indentation hardness doesnot indicate the ign or magnitude ofresidual I1e e exi ting at or below thesurface, load table . ba ed onhardnessare of little help in designing fatiguere istant, higlit.lyloaded gear and shafts.It ha also been well documented that tilepre enee of surface abnormalities in litemicro true lure. orinelu ion in the basematerial. can initiate. fatigue cracks thateventually lead to failure. 10 addition,cracks can initiate at the urface of highhardnes .gears and shafts if high impactload. are present. Therefore, in order [0

know more about improving the fatiguelife of gears and shafts, and 0 be able tobuild lighter and cheaper gears andshafts that give longer service, we mustconcentrate Oil knowing more about;I. processes that introduce high r~sidualcompressive tresses into the surfaces ofgears and shafts where fatigue failure islikely.2. the metallurgical factors controllingimpact toughnes •3. the factors affecting the cleanliness ofthe reel.

ResiduaJ' Compressive Stresses.High urface contact loads can produceunfavorable tensile stresses in the toothurface. These stresses eventually pro-

duce cracks. thai lead '10 failure of thesurface by pitting and breakage. Theintroduction of re idual compressivestresses into the tooth urfaee opposethe tensile tres e and prevent the ini-tiation of :fati.gue cracks. It is well doc-umented 'that manufacturing processessuch a carburizing. carbnnirriding,nitriding, induction hardening and shotpeening considerably increase there idual compressive tress level at theurface of ferrou components. Also,

thermal, mechanical and chemicalprocesse can be used together as in thecase of automotive planetary gearswhich are carburized, acidueated andshot peened with hardened steel shot.(This process produce the most fatigueresistant gear that the author is awareof.) It is extremely importanttbat allsuch processe be preci ely controlledif maximum residuall compressive streslevels are to be con i tently achieved,

TltermalProcessing ofGears and Shafts

Carburizing;. Case hardening processeshave been known to impart high residualcompressive stresses at the surface of a gearor shaft It is these beneficial internal stress- !

e thal give the gear or shaft the improvedendurance properties that allIow the compo-nellis Lacarry higher loads withem failing.

Carburizing ha . been used for many I'Year to ca e harden gears and hafts to i

improve wear resistanc _ and load carry-ing ability. The process ba .come. longway from the early years of pack IlI'Id altbath hardening to modem controlledatmosphere furnace that us sophisti-cated gas. measuring devices and corn-puten . The process, when correctly car-ried out. produces very high residunlcompre sive . tresse l Ihe mace IlI'Idunderlying cased region. This results jn

improvedurt'aee endUranceand wear resis-

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_-----------GlAR FUNDAMiE,NTALS, _lance, as well as improved bending fatiguelife and impact resistance, The metallurgicalrequirements (in the tooth, contact. zone) toachieve these benefits can be slated brieflybelowas:1. surface carbon level 'to achieve theeotectoid composition for the particularsteel used:2. absence of excessive retained austen-ite after quenching:3. absence of cementite networks (car-bides) at or near the contact. face:4. absence of sub-surface oxides:5. absence of intermediate transforma-lion products. 100% martensite or mix-tures of martensite and lower bainitebeing the aim (no pearlitic or upperbainuic skins):6. fine grain size throughout the case.

The above requirements can only beachieved by preci e control overI. furnace temperature and carbonpotential of the furnace atmosphere atthe desired level:2. use 'of the optimum quenehant andquench conditions (oil type. agitation,and oil temperature):3. fine grain steel of the correct harden-ability to ensure the gear or shaft meetsthe requirements for surface hardness,effective case depth. and core hardness:4. optimum heat treatment cycle to pro-duce the required case depth (carbon gra-dient) and micmstructure.

The above requirements become diffi-cult to achieve if the carburizing furnaceload contains gears or shafts made fromcarburizing steel!s of different composi-tion, or the furnace is overloaded to theextent of reducing either gas circulationor subsequent quench oil circulation, Forexample, ,a plain carbon manganese car-burizing steel such as YK1320H wi11.require a higher carbon potential than ahigb nickel carburiziog steel such asX3312H.

Residual surface stresses must now beconsidered in relation to the commonlyavailable gear heat treatment operations.By far the greatest quantity of highlystre sed gears are carburized. The e gearsare made from low calibon.low alloysteels which, in and of themselves. lacksurface durability. However, after raisingthe urface carbon of these gears to about54 GEAR 'TECHNOLOGY

0.8-0.'9% carbon, they exhibit the mostdesirable combination of surface en-durance, bending endurance and tough-ness. Extremely precise control of all vari-ables is required during earburizing andsub equern quenc.l:ring to achieve the hJgh-est qua:lity. lowest distortion gears.

Whether the gear designer requestsdirect quenching or reheat quenchingafter carbarizing will depend. on theknown applications of the gear . Directquenching has been used for manyyears with automotive gears whereextremely fine grained. autemctivequality steels are specified. However,the reheat method for more precisegears such as turbine gears bas beensaid to produce better metallurgicalstructures and more assurance that thegears can run satisfactorily for a muchhigher number of cycles.

In.duction hardening. Induction hard-ening has long been used to hardenplaincarbon automotive axle shafts. Surfacehardening shafts using induction tech-niques also develops residualcompres-sive stresses at the surface and in thehardened zone (Ref. 7). The exact panernof these stresses depends on the process.conditions and the composition of thematerial being hardened.

Apart from delaying the initiation ofratigue cracking in service. these residualcompressive stresses are known to delaythe process of stress corrosion cracking.Gear can also be induction hardenedusing different inductors and fixtures.The method best suited to' large gears,where the pro me and root area can behardened without embrittling the tip ofthe tooth, involves using an jnductarshaped to fit between the teeth. Modemtechni'ques use dual frequencies .in order1.0 achieve the deeper ca e depthsrequired by larger gears. Shaft areinduction hardened using a scanning-typemachine. which progressively moves thehaft through the inductor, heating and

then quenching a small moving zone. Thedepth of the induced currents that heat thesteel shaft. or gear are related to the fre-quency ofthe induction hardening unit.Ca e depths lor small hafts require high-er frequencies (RF), while larger shaftsrequire low frequencies (AF).

Automotive axle shafts are hardened[Ising motor alternator units with a fre-quency between 3 and to Khz. The result-ing hardened depth, measured to 40 KRC,is approximately 2.5 mm. Smaller olid

state units operating at radio 'frequency450KHz can harden small shafts withinseconds to a depth of 0.7 mm.

Mecbani.cal ProcessingShot Peening. The automotive industry

uses dynamometers. driven by either elec-tric molDISor gasoline engines, to clUl)' outprecise life tests on finished transmissionassemblies. The e tests have proven thatcatburized automotive gears and shafts canachieve significantly improved fatigue lifeafter peening with hardened steel hoL, pre-cisely earned oui, The shot peening processis expensive but has allowed automotivecompanie (0 upgrade the rating of auto-matic and manual transmis ions without'the need 'to make expensive dirnen ionalchanges 10 their gear trains. The peeningoperation induces beneficial residual com~pressive stresses LIJithe flank and root areaof the teeth under strictly controlled condi-tions. Compressive "tress prevents or limitsfailure in gearing due to fatigue failure atthe fiUet and pilting failure at the pitch line.

Rolling ..In some applications, work. bard-ening of a component surface by rolling caninduce residual compressive surface tressesand improve the smfaee futiSh. bu.t care mustbe taken not to prodooe tine mface cracksthat may inriliate fatigue.

Common FaUure Modes ofGears and Shafts

Fatigue Considerations. In regard [0

surface stresses, the limiting load for weardepends upon the urface endurance limitsof !he material, which in turn depend ongeometric as well as melallurgica:i factors.Surface endurance limi'l values appear tobe related consistenijyto a Brinell. hard-ness number up to approximately 400BrineU hardness (Ref. 2). Wilen the Brinellhardness is over 400. the steel does not

TABLE 1Spur and helical Gears IRel. 2t

Brinall HardnessHB200

Surface EnduranceLimit (psil

70,000110,000150,00

300400 I

_ ••••••••••• -IGIEARIFUINIDAMENTALSIII _

TABLE 2---for steels over 400HB IRe •..2)

Brinell Hardness

HB450500'55(1

600

~urlacBendurance limit [psi)11 X U)Ii 2 X lao 5 XI OS 107188000 1170000 147000 132000210000 190000 165000 148000233000 210000 182000 163000255000 230000 200000 179000

Wnen tile Brine" hardness is over 400

appeal!" to hav a definite endurance

limit. Values for the surfa e endurance

limit for steel over 400 Brinen are

given in the table above.

The focus up until. now has been onuniform loading, but ill reality many gear

systems experience fluctuaring loads rang-ing from moderate 10 heavy shock. Thesensitivity of !be gear or shafl material to

notches or s.barp comers is a major con-sideration. Wn addition, rno l gears: andshafts fail by fatigu at loads well below

their yield strength, Although Tables I. and2 above are comparatively useful to design

engineers in calculating load carrying

capacity. they do not impart any informa-tion about the toughne or impact proper-ties of the material. nor can they shed anylight on the materials' fatigue sliellgth.

The onen quoted "rule af'thumb" !hal the

fatigue strength i.about 50% of the yieldstrength is probably very conservative.

More infonnatioDBbout the metallurgicalfactors that influence toughness and

fatigue life is needed 0 that the engineercal'lconfidenlJy reduce !he weight andhence the cost of a drive sy em. Researchwork 10 dale points clearly at factors uchas steel cIeanliness.a11'oy combinations

present. heal treatmenr condition. grainsize and gram flow and the nature ofmicro-constituents prescnt at or near ·Iheurtaee, Of critical impenance is the steel-

making practice and the proce ing routeused to make ihe components. Two steel

with the . arne Brinell bardn could vary(lramatically in impact and f,uig~e proper-

tie, particularly in the presence of smallstress concentrators such a machine tool

marksor ub uri ce defects.

lmpad PropertiesThe selection of the correct material

and heal. treatment proce for: teel mustbe considered [0' be a comproml ebetween strength and ductility. Although

through hardened gears with a surface

hardness over 400 Brinell can giveexcellent wear properties, they may lack

the toughne s for many applications.

Tempering will reduce the hardness andwear re istance but will increase thetoughne s, The balance betweenstrengjh and toughness, developed afterquenching and tempering, is a eritieal \'Consideration for the materials engineer.

The only processes where both strength ,.and toughne increase together are those Iinvolving grain refinement. This is Iachieved by making micro-alloy additions I

,!10 teel and thenno mechanical process-ing. Heal. treatment processes involving

the diffusion of carbon, or carbon andnitrogen combinations, into the surface 0:1"

I

Ii

D! low or medium carbon steel can re ult .inth _ production of wear resistant gears andshaft that axe also tough, The resulting

lrigh hardness is at the surface of the case

wh reit can improve wear and fatigustrength. while the core is softer and moreductile, giv.ing .rughtouglmess propertie .The core, however, must not be too soft asthe case needs adequate support to prevent

case crushing (Ref. 4),Importance of Flow Line

The impact propertie of steel cast-

ings, plates, and forgings are not uniformin all directians, but. are related to the

now line direction.: harpy tests indicatemal. the impact strength acro s the Howlines can be up to 50% lower than te t

where the test piece is parallel with theflow lines. Since any incluionsandmicro egregation will follow these flowlines, they must not be parallel with thebase of the gear teeth in highly stressedgears ,(Ref". 4).

~mpol"fanc,e of Composition

During the eigilt ies, re earth wascompleted on the impact propertie ofalloy steels with higher mol.ybdenum

eontem using instrumented Charpy

testers. Although the early re ults indi-cared that molybdenum steels were

tougher than nickel steel • it w laterhewn that. cenain combination of the

two alloys gave the best results. The.in trumented Charpy re Is gave theresearchers valuable inform lion re-garding the initiation of the propagationof cracking that could :nOl be obtainedotherwise.

ConclusiolL'lMany workers have g nerated a wealth

of meLallurgicalk-nowledge and informa-·lion about the surface fatigu re istanceand impact resistance of vnsiou materi-als. There is also con idera:ble Informationabout the metall.urgical :fact affectingthose thermal and mechani aI proce. sesused to improve. the life of highly sltessed

gears and haft . Much of lhh informationi available for the de igner to c nsideJand apply in order to a hieve metallurgi-

cal and geometric quality and meet ell -lamer demands for precision gears and

shafts at minimum costs, 0

REFERENCESI. Dudley, D.W. Handbook of Pro tical Gi'al"Design, McGraw-Hili Book Company, NewYon., ]984.2. Sloke • A. Gear Handbf:KJk. SAE Intern-ational, Oxford; Boston: Buuerwenh-Heinemann. 1992.3. Cavanaugh. AX "Gear and Shalt Design,The Metallurgical Engineering Approach:'Ausiralian Institute of Mellils Seminar, Mel-bourne,1979,4 . Beale, R.F. "The Mechanical Engineers'Approach to Design, SpecUicationand 'i[;!;slinof Gears;' Australian Instiune ,of MelalsSeminar. Melbourne, 1979.5. Killey. J.M. and M.G. Conyngham, "Mctal-Iurgical Contribution to the Produ tiun ofAutomotive and Lighl Industrial 'Gear ,"Australian Institute of Metal Seminar, Mel-bourn ,1979.6. ConYllgnam, M.G, "Gear M terials," Trans-

I action of Mechanical Engineering, Vol. ME15, No.1, 1989.7. Semiatin .. S.L.and D.E. Slutz .. lnductiQ/1Heal Treatment of Slut, ASM. 1986.

This paper wasfirse presented ,aerha,Gearand Shaft Technol'ogy: seminar orOloiledb,WLhe Institute lof Mat,erialls EnginsarinAustralasia.

Tel' Us ... v.. TIIiIIk .••If you found tillS arliele of interest and/oruseful, please Circle 215.

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