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Material Selection and Heat Treatmentby

National Broach & MachineMt, Clemens, Michigan

Tablel-AGMA Standards Useful inSelecting Gear Materials

Nom.nel.tuN110.03 Gear-Tooth Wear and Failure (USAS

86.12-1964) Jan. 1962DunblJity21S.JI Information Sheet for Surface Durability

(Pitting) of Spur, Helical. Herringboneand Bevel Gear Teeth Sept. 1966

217.01 lntcrrnancn Sheet·Gear Scoring DesignGUide for Aerospace Spur and HelicalPower Gears Oct. 1965

Strentth225.Q1 Information Sheet for Strength of Spur.

Helical, Hernngbone and Bevel GearTeeth Dec. 1967

IntplDtIan230.01 AGMA Standard· Surface Temper ln-

spectlon ProcessM.Wfals241.02

March 1968

Specificanon for General Industrial GearMaterials-Steel (Drawn. Rolled andForged)Cast Iron Blanks

245.01 Speehcatren for Cast Steel Gear Materials246.01 Recommended Procedure for Carbunzed

Industrial Gearing.247.01 Recommended Procedure for Nitridmg.

Materials and Process248.01 Recommended Procedure for mducnon

Hardened Gears and Pinions249.01 Recommended Procedure for Flame

Hardening.

242.02244.02 Nodular Iron Gear Matenals

Gear materials are selected to providethe optimum combination of properties,at the lowest possible cost consistent withsatisfying other requirements. Some ofthe important physical properties ofgears are abrasion or wear resistance,toughness, static compression strength,shear strength, fatigue strength, andstrength at elevated temperatures.

Because of widely varying require-ments, gears are produced from a widevariety of materials ..These materials in-clude plastics such as nylon, powdered

40 Gear Technol'ogy

Jan. 1965Sept. 1946July 1965Jan. 1964

Jan. 1965

Jan. 1%5

Jan. 1964

. . Jan. 1964

metals, brasses, bronzes, cast or ductileirons, and steels. Many types of steels,including stainless steel and tool steel, areused. Each of the materials mentionedwill best satisfy some specific require-ment such as corrosion resistance, ex-trerne wear resistance, special dampingqualities, ability to operate withoutlubrication, low cost, or producibility.

The majority of gears for automotive,aircraft, farm rnachineryvoff-the-roadequipment, and machine tool applica-tions are produced from hardenable car-

bon or low-alloy steels or cast iron.Therefore, this article will cover only fer-rous materials.

The choice of a gear material dependson four factors:

I. Mechanical propertiesZ. Metallurgical characteristics3. Blank-forming method4. Manufacturing processEach of these factors must be eval-

uated w.ith an eye to its effect on thethree major performance criteria - dura-bility, strength, and wear.

Mecllankal Properties *Before the optimum mechanical' prop-

erties can be selected, the working stressmust be determined, based on recom-mended allowable stresses.

This article discusses durability andstrength formulas adopted by theAmerican Gear Manufacturers Associa-tion and widely used throughout theworld, Table 1. There is a fundamentalrelationship among most formulas, sothat working and allowable stressesdetermined by different formulas can beused or compared .

Workmg stress is usually based on thefatigue or yield strength of the material.Less frequently, impact resistance, ten-sile strength, or brittle-Iracturecharacteristics of the material must beconsidered.

For most gear trains, the limitingdesign consideration is profile durability(pitting resistance), gear-tooth strength(resistance to fracture), or wear ..Norm-ally, durability is the limiting consid-eration; but sometimes an three are ofnearly equal importance.

A number of other possible modes offailure may also limit gear performance,such as scoring associated with high

•Abstracted from Machine Design, Gear MaterialsDesign Guide. June 20, 1968.

speed and heavy loads, case crushing incarburized and hardened gearing, andmicro-pitting. However, these are lesslikely to occur.

The AGMA gear-rating formulas forboth strength and durability are basicallythe same for spur, helical, herringbone,and bevel gear 'teeth. Terms in both for-mulas are divided into four major group-ings, associated with load, size, stressdistribution, and stress.

The surface-durability or pitting-resistance formula - AGMA 215..01,Sept. 1966, "Iniormation Sheet far Sur-face Durability (Pitting) of Spur, Helical,Herringbone and Bevel Gear Teeth" - is

where

The "stress" term, Equation 2, is the mostimportant consideration in selecting agear material, Table 2 lists all symbolsused in the strength and durability for-mulas. Allowable fatigue (contact)stresses, Sac are shown in Table 3.

The mechanical properties for gearmaterials are almost always specified interms of Brinell hardness rather thanultimate strength or test-bar properties.Location (normally the toothed portion)and number of hardness tests shouJd alsobe specified ..Maximum hardness is alsospecified in the interests of machinabilityand sometimes to insure a hardness dif-ference between the mating gears; sucha difference can increase wear resistance.Typical combinations are shown in Table4.

Values of Sac are based on 107 cycles,since most gear materials generally showthe typical "knee" at or below this value.Hence, these values can be consideredf.atigue-strength stresses. If a gearset mustoperate for only a finite number ofcycles, the Sac values can be increased bylife factor Cl, Fig. 1.

Pitt Lng of gear teeth is considered afatigue phenomenon. There are twokinds of pitting - initialand progressive(destructive), Corrective and non-pro-gressive initial pitting is not consideredserious and is normally to' be expecteduntil imperfections,. such as high spots,3[1e worn m.

The stresses in Table 3 are satisfactory

(2)

2 ,I

-r----,

I

,

I

.-JU

o~u,

s.-J

0.5104 105 1Q6 107

ReqUired Life In CycleslOS 1()9

Fig. I-life factor for durability rating of gears.

III

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Table 2-GeM Rating lFador

IFaetor Strength IBl!r.bUlty

Transmitted loadDynamic factorOverload factor

Pinion pitch diameterNet face widthTransverse diametral pitchSize' factor"

iWt

C~C..

SizedF

c.Load-distribution factorGeometry factorSurtace-cenditicn factorSize factor'

Calculated: stressAllowable stressElastic coefficientHaruness-ratlc factorLife factorTemperatu.re factorSafety factor

K",J

CmIC,

·Sue tector IS placed !litller In tile $UI:' or $tf,e,J$'dl$trJbuIIOll

(JfOUP"'Q, dependrtlg UPOll the Importance 01 'tile' effect,

Table 3-Allowable Contact Stress(Durability)

SteelThroug h-ha rdened

case-carburuec

Fl'ame or mductien-hardened

Cast IronAGMA Grade 20AGMA Grade 30AGMA Grade 40

Nodula'f Iron

Minim,l!mSurfaee

IHardn,ess

Con,tactStr.u. 'S.c(1ooo'llIsj,)

180 Shn,2401Shn3001Shin360 Shn440 Shn

55 Rc60 IRe

85·95I05·US120·135145·160]70·190]80·200200·225

50 IRe 170·190

50·60175 Bhn 65·75200 Shin 75·85

]65·300 Shn 10% less thanfor steel with

samehardness

Table 4- Typical GeM/Pinion HardnessCombinations

42 Gear Technol'ogy

M~lmum IHardness,(Bhn'J"G 180 210 225255 270'285 300 335 350 315 55Rc 58Rc!PiniIn, 2:10245 265 295 310 325340' 375 390 415 55Rc 58Rc

·M'U!ll1um hardn.ss ,i! U!U11I13510,40 Bhn higher.

Tab Ie 5 - Rec:om-'IRended SafetyFactol's in Pitting

Reqllired ReUabl'lity Factor C",

!Highfewer 'Ihan 1 failure in 100.IFewe'f than 1 f·allure in 3

1.25+1.0001.80·

"At 11l" "ltlue', plasl'lc proWfJ' deforma:!ion mia'ht occur befotepilling.

Ta:ble6 - ADowable Stress (Strength)'

IMawiII MILburn AI' _ I.S I"Hlfllnlll sir (1000 pSI)

Spur, HIIIeII ••MImII\IbI.. Bullu

SteelNormalized 140 Bhn 19,25Quenched & temp, 180 Bhn 25-33Quenched & temp, 300 Bbo 36,47Quenched & temp, 450 Bhn 44,59Case' esrb, 55Rc 55,65Case carb, 60Rc 60·10lnd, or flamethrough,hardened 54 Bhn 45,55'"Ind, or 'flamethrough·hardened 54 Bhn 22N!tnded AI SI 4140 53Ret 37·42-

Cast. IronAGMI\ 'Grade 20 5AGMA Grade 30 115 Bhn 8,5AGMA. Grade 40 200 Dhn 13

Nodular IronASTM 'Grs.de 60,40,18 Annealed 15ASl'M Grade 80,55-06 20ASTM Grade 100-70,03 Normalized: 26ASTM Grade 120·90,02 Quenthed& 30

temp"

Table ,.-Safety Factors for Fatigueand. Yield Strength -

Reliability

fatigue!High

Fewer than 1 failure in ]00Fewer than 1 tailure in 3

Yi:eld'HighNorma,l

1.50+LOO0.70

3,00+1.33

II1419'2527,530

13.520

V4,67

8II1418,5

for gears with smooth profiles operatingwith adequate lubrication. Some "as-hobbed" or shaped gears, or those withrough-textured profiles, should use moreconservative stresses. In this case, specialatt~ntion should be given to' the lubri-cant. Procedures for inducing favorablesurface stresses for increased profiledurability are not yet generally used.

Except for heavily loaded gears orthose subjected to unusual environments,no substantial difference in allowablecontact stress existsamong the normalqualities of available commercial steels.Free-machining steels may be used to ob-tain improved machinability or a bettersurface finish.

Because pitting is a fatigue phenom-enon, it displays a scatter which must beallowed for by a safety factor to ensurereliability. If this factor is not includedin the bask design calculations, Table 5can be used as a guide and the Sac valuesadjusted accordingly. It shouJd beremembered that "failure" does notnecessarily mean an. immediate' 'failureunder applied load, but rather shorter lifethan expected.

If one of the mating gear elements isconsiderably harder than the other, theallowable stress of the softer dement canbe increased under certain conditions.Normally, the gear ratio must be high-over 8:1- and the gears large before anyappreciable improvement is obtained.Typical of gears for which such a cor-rection is normally made are those forlarge kilns, or for ball mills. The ap-propriate AGMA standards containrecommended values of the CH factorused Ito rate gearsets having large dif-ferenees in hardness.

Generally, temperature factor CT = 1when gears operate with oil or with gear-blanktemperatures not exceeding 250F.In some instances, it is necessary to useCT> 1for carburized gears operating atoil temperatures above 180F. Tests haveindicated a drop of several points .1\:hardness for carburized steels subjectedto 200F for 10,000 hr, as weB as a 6 to8% reduction in fatigue strength.

When gears are proportioned on thebasis of alJowable surface fatigue stress,surface yielding is seldom a problem.This is partially because the contact stressonly increases as the square root of thetransmitted load. Allowable overloads of100 % above the surface-fatigue rating

are commonly specified. Greateramounts of overload are often success-fully carried. However, repeated over-loading can cause plastic How, which rip-ples or grooves the profile or extrudes a"wire edge" at the tip of the tooth. Thisextruded material. can affect lubrication.Excessive plastic flow of the profile caninduce abrasive wear because of therough surface texture developed.

Surface yieldjng does not cause im-mediate or catastrophic failur and theuse of heavier viscosities or extreme-pressure lubricants along with reducedloading can alleviat a troublesome situa-tion when it is encountered.

The effect of impact or brittle-fractureproperties of gear mat rials on surfacestresses need not be considered, exceptfor the peak stresses developed byim-

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pulse or impact loading.

Tooth StrengthThe tooth-strength raring formula-

AGMA 225.01. Dec. 1967. "In/onnatiol1Sheet for Strength of Spur. Helical, Her-ringbone and Bevel Gear Teeth" - is

where

s, : s., "K:~T)(Sir.,,)

Again. allowable stress is the most im-portant term in selecting a material.

The fatigue and yield resistancenecessary 10 prevent the fracture of agear tooth depend on more complex rela-tionships between materials propertiesthan those for profile durability. This istrue primarily because the root-radiusstress varies directly with the load. For-tunately. the root stress can be calculatedfairly accurately by applying standardbeam or plate theories.

Some allowable fatigue stresses Sal.

used with the AGMA formula are listedin Table 6.

Allowable stress or fatigue strength isnormally determined for 107 cycles,with adjustments for shorter fmite lifemade by using 'the Kl factor given inFig. .2. Unlike Cl• Kl depends on fatiguenotch-sensitivity, which is somewhatproportional to hardness: hence thenecessity for several curves for variousgear hardnesses.

Experience suggests that a dearlydefined knee is not always present in thegear fatigue stress I cycle plot. Thisphenomenon might be an inherent prop-erty, as it is with non-ferrous materials.But it is more likely a. result of wear orother service-developed changes whichaffect either the dynamic loading. loaddistribution. or stress system. Fo.r con-servative design, sometimes. Sill is re-duced by the Kl factor determined fromcurve B in Fig. 2.

Normally the stress at the root of thetooth varies from zero to the m ximumworking tensile stress. If a tuHy reversedstress is present. as it is wi.th reversingloads or with idler gears. the allowablestress should be 70% of the values shownin Table 6.

Th quality of the material has a pro-nounced effect on the strength 'of gear

stress patterns. Mechanical PI' cessing,such as hot peening, to indue favorableroot stre es is used successfully.

The fatigu strength of gear teethfollows a statistical, pattern, 0 thai asafety fa tor should be used. Some rec-ommend d Ifactors are u ted in Table 7.

It is imp rtant to, remember that atooth fracture, unlike profile pitting. iscatastrophic and cannot be rep ired oralleviated by reducing load or changinglubricant. Impac] loads in geared y t mare commonly two or m re times therated load. Because gears have backlashand ate loosely coupled, both the elec-trical rorqu and inertial energy of anelectric motor can be released imultane-ously. so that peak torques of two 10four times the nameplate ratinzar n 't

uncommon. For this reason an ad qua tesafety factor. KR• and life 'factor. Kt. areimportant.

YieM: L ads which dev lop a ro t

stress above the yield strength of thematerial cause the gear to rh to bend·permanently. Since gear-tooth dimen-sions are held to 0.001 or less, nly a.slight permanent bend or distortion canaffect th geometric dimensi n uftici nl

to cause interference on high dynamicloads. This will quickly result ina fatiguefracture.

The allowable yield stre fo·r reelrecommend d for use with th AGMArating formula is shown in .Fig. 3. Thealloy composition. heat-treatment H (-tiveness, and section size aff ct the yieldstrength at any ultimate strength or hard-ness. so that more accurate yield- trength

(4)

teeth. mol' so than in the ·C3S of pittingresistance. The values shown in Table 6are for commercially availabl steels. Inthe absence of a dear understanding ofthe criteria for judging quality. th lowervalues should be used. These are suitablefor steels with a deanliness typical ofresulphurized or leaded steels.

The upp r values in Table 6 would re-quire steels produced under good meltingand pouring conditions. Cast steels re-quire adequate directional and pro-gressive solidification. Rolled and forg-ed. steels will probably require vacuumtreatment, with special instructions toprevent excessive reduction during roil-ing or forging; this procedure will pro-vide a desirable direction of fiber flowlines with lit excessive reduction intransverse properties. finally, h al treat-ment hould be under rigid supervisionin accurately controlled Iurnaees, fol-lowed by careful hardness and m tallo-graphic inspection. For high-speed gears,or for drives requiring maximum relia-bility,additional inspection, for examplemagnetic and ultrasonic insp ction, is anecessity.

Fatigue: The fatigue strength of a geartooth is significantly aHected by size. sur-face finish. and residual stresses at theroot radii. Residual stresses in a favorabledirection can be developed by metallur-gical proc ssing such as case carburizingor nitriding. Under certain circum-stances, flame or induction hardening,which do nol develop iii uniform hard-ness pattern on the profile or in the rootarea, can induce significant unfavorable

Fig. 3- Allowable yield stress recommended for use with AGMA formulas.

data can be used if it is available.As a.general. rule, when peak loads ex-

ceed 200% of the allowable endurancestress (100% overload), it is necessary toconsider yield in both the design calcula-tions and material selection. Table 7 listsappropriate safety factors for use whenselecting materials for yield strength.

Operating temperatures can aJfect theallowable stress. According to AGMAStandards, when gears operate at oil orgear-blank temperatures not exceeding250F ternperature factor, generally Kr= 1. For case-carburized gears attemperatures above 160F, KT may befound from

460 + TF

620

where TF = peak operating oil 'tempera-ture, deg F.

Fatigue failure initiated by a bent toothcaused by loads above the yield strengthis not uncommon and should not be dis-regarded even for surface-hardenedgears. This is particularly true when thedesign is based on allowable fatiguestresses which have been increased byfavorable induced surface stresses.

Impact: Although impact is not signifi-

46 Gear Techno'iogy

(5)

cant in evaluating a material for surfacedurability. it can be important in tooth-strength considerations.

The first step is to determine whetheror not destructive impact can be deve-loped in the gear system. Normally, if thetime to develop the peak stress is asignifk.ant proportion of the natural.period of vibration, the stress can becalculated from loads deduced from theoscillatory characteristics of the masselastic system. The material must then beselected on the basis of yield strength or,if suffi.cientcycles are involved, fatiguestrength.

In some specific applications - mostlydetermin d by field experience - impactproperties should be considered as a mat-ter of course. One example is service atlow temperatures, which 3.1'e known toreduce impact strengths. Here steels con-taining nickel and those having fullyquenched and tempered metallographicstructures ar desirable. lower hardnessand sometimes lower carbon content arebeneficial, although these must be con-sidered with an eye to the required sizeof gearing and costs, Obviously thedirection of grain flow, transverse prop-erties, and area reduction during forgingmust be controlled.

Brittle fractures of gear teeth occuronly occasionally. Effort to correlatematerial properties with brittle-fractureanalysis have not yet produced results ofvalue to the designer, although someprogress is being mad.

WearThe wear in contacting teeth varies

from an unmeasurable amount with fullyhydrodynamic lubrication. through in-termediate and boundary stages, to drymetal-to-metal contact. Hydrodynamiclubrication is present when the ratio ofhim thickness to surface finish exceedsapproximately 1.4; boundary lubricationwhen the ratio is between 0.05 'to '0.2:and dry lubrication when the ratio is lessthan 0.01. These are approximate guidesbased on tests with straight mineral oils.

Normally, wear is encountered onlywhen surface finishes are rough, speedsare very low, or loads, and velocities arehigh. There are four types of wear: ad-hesive, abrasive, corrosive, and fatigue.

'Generally, when f'errous metals areused for gears, the wear rate decreaseswithincreasing hardness. Under certainconditions, softer gears will polish to afine surface finish and a good load dis-tribution; this provides improved lubri-cation. In some cases, the profile will beworn to 3. non-involute shape; once this·w aring-in" has occurred, little wear willfollow. [f this beneficial wear does notoccur, high hardness, obtained byquenching or by a surface-hardeningsourc such as induction or flamehardening, carburizing, or some form ofnitriding must be used.

It is not uncommon for changes tooc-cur in the dedendum of heavily loadedgears, particularly at slow speeds. A con-cave surface is developed which scanstabilizes and in no way affects the load-carrying capability of the gears, Thisphenomenon is due to a number ofreasons, one of them being the fact thatthe rolling and sliding are in oppositedirections on the dedendum.

In some carburized and hardened gears3. frosted appearance develops. Thisultimately results in surface spa lling,which in turn can initiate a tooth frac-ture. This frosting is probably due tomicroscopic pitting. Better surface finish

(continued OM page 38)

fig. A.l- Value of Nb

where frc (X) denotes the fraction of X. The function Nb isshown in Fig. A 1, The dimensionless value A in equation(5)can be calculated by using Nb

(A.3)

In the case that the face contact ratio mF ( = E,gJ in AGMA218.01 is greater than unity, the load sharing ratio mN isdefined by mN = F / Lmin• Therefore, A is expressed asfollows:

COS{3hA=--

m,(AA)

Appendix .2The matrix [Hk] for gear k(k = 1, 2) is defined by wk.li'

which is the deflection at node f on the contact line due toa unH normal load applied to node i.

(AS)

)T = transposed matrix

The deflection wlt.ii is calculated by FEM. When a pair ofteeth are in mesh, the distributed load {P} along the contactline is related to the sum of the deflection of the teeth and

38 Gear Technology

the relative approach due to elastic contact.

[H] {P} = {w} (A6)

The elements of matrices [HJ and {w} are

(A.7)lVt = "'1.J + \1.'~.1 + •.Ij'I~.1

where Wp, is the relative approach at node i and Gil isKronecke;'s delta. When some pairs of teeth I, U, ... arein mesh matrices [HIL [HilL .. ' . are separately obtained. Ifthe load on a pair of teeth is assumed to have littleeffect onthe deflection of other pair of teeth, the matrix IHI inequa-tion (A.6) is diagonally constructed as follows:

__ [IHd 0 ][H] = 0 (HII J (A.S)

.The equation (A.6) is solved under the followingconditions:

r;,P,=P"s,

w,+ WOO =(r/oIOI +r/j202)Cos{3I,

P, =0

(A.9)(node in conracr)

(node not in contact)

where s. [ttmlis the spacing at node j caused by the effec-rive alignment error, rb is the radius of base cylinder and e(rad) is the rotating angle of gear.

This article was contributed by the Power Transmission and Gearing Com-mittee for presentation at the Design Engineering Technical Conference. Or-tober, 1984 of TIle American Society of Mechcmical Engineers. Paper No.84-DET-68.

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MATERIAL SHECTION. __(continued from page 46)

and accuracy, and improved lubrication- rather than changesin material- are required to solve this problem.

ScoringIn some heavily loaded or high-speed gearing, scoring may

occur under boundary HIm conditions. This is believed tobe caused by frictional heat which reduces the lubricant pro-tection sufficiently to allow welding and tearing of the profile.

Materials selection alone will not prevent scoring; properlubricants and design geometry are required. This difficultyis seldom encountered in the conventional industrial geardrive. AGMA 217.0'1, Oct. 1967, "AGMA InjormationSheet - Gear Scoring Design Guide for Aerospace Spur andHelical Power Gears" provides helpful recommendations foravoiding scoring.(This article will be continued in the September/October 1985 issue of GEARTECHNOLOGY. J

Reprinted from Modem Methods of Gear Man"fachm? 4th Edition, PublishedNationo! Broaclland Mac/rine Division of LEar Siegler. lnc., 17500 TwentyThree Mile Rd .• MI. Clemens. MI 48044

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