AGMA, ISO, and B,SGear Stan'dard'sP,artI Pitting Resistance Rati,ngs

Doug Walton, Yuwen Shi, Stan Taylor,Mechanical Engineering Department

University of Birmingham, Birmingham, U.K.

Summary:A study of AGMA 218, the draft ISO standard 6336, and

5S 436: 1986 methods for rating gear tooth strength and sur-face durability for metallic spur and helical gears ispresented. A comparison of the standards mainly focuses onfundamental formulae and influence factors, such as theload distribution factor, geometry factor, and others. No at-tempt is made to qualify or judge the standards other thanto comment on the facilities or lack of them in each standardreviewed. In Part I a comparison of pitting resistance ratingsis made, and in the subsequent issue, Part IIwill deal withbending stress ratings and comparisons of designs.

IntroductionStandard spur and helical gears are usually designed to

specific standards to meet the requirements of proportions,manufacturing accuracy, and load rating. The load rating isthe most important issue discussed in AGMA (AmericanGear Manufacturers Association), ISO (International Stan-dards Organization), DIN Deutsche lndustrie Norrnen) andBSI (British Standards Institution) gear standards. The stan-dards written by these organizations are widely used for geardesign throughout the worJd and also fonn the basis of"minority" gear standards. China, for example, issues a geardesign standard based on ISO. European gear standards arenow becoming very similar. The new BS and the draft ISOstandard share much in common with DIN. This paper con-siders BS 436:1986, the draft ISO standard 6336, and AGMA218.01. Since this review was written, AGMA introducedAGMA.2001-B88, although this new standard is not con-sidered here. However, the trend toward a universal standardcontinues, with AGMA 2001 publishing rating factors, someof which are similar to the draft ISO standard.

This article is intended for designers who will appreciate areview of this complex subject ..Many designers in the USAwill still use AGMA 218 because they are familiar with it, andwill, we suspect, continue to do so for some time ..(This situa-tion also exists in the UK with respect to the old and newBritish Standards on gear ratings.) It will take the authorssome time before they have enough experience in the use ofAGMA 2001 and have been able to validate it against realdesigns and other rating standards. While there are markedsimilarities between the old and new AGMA formulas for pit-t 0 Gear Technology

ting resistance and bending strength ratings, we have main-ly excluded any reference to AGMA 2001.

Although, theoretically, any standard will produce a gearpair which is satisfactory, it is no longer enough to accept anystandard when other procedures might produce more com-petitive designs. On the other hand, if the design calls forspecial operating conditions, such as shock loads or flexibledrives, it may be advantageous for the designer to address astandard which deals more closely with these conditions, Inaddition, the customer may specify the code to be used. Aworking knowledge of more than one standard is desirable,particularly if the product is aimed atinternational markets.An understanding of the differences between gear standardsis, therefore, important. It should be pointed out, however,that in a review of gear standards it is impossible to coverevery aspect of each code. ISO 6336 Parts 1 to 4, for exam-ple, contain over 90 figures and over 20 tables.

Standards for Spur and Helical GearsThe old British Standard, BS 436:1940, (I} in use for nearly

fifty years, was a revision of the original Specification forMachine Cut Gears first issued in 1932. During its long ex-istence, the rating method remained the same with only minorrevisions. Though obsolescent, it is still used extensivelythroughout Britain and elsewhere, mainly because it is easyto use. The standard rates gears on the basis of bendingstrength and contact stresses, which are referred to as wear(meaning non-abrasive wear). The tooth root bendingstrength is based on the Lewis equation, (2) considering bothtangential and radial loads. The effect of stress concentrationsat the root is not taken into account directly, but allowancesare made in the use of the allowable bending strength of thegear material, values for which are supplied in the standard.The bending strength is also factored for running speed andlife. Contact stresses are based on a modified Hertz equationwith allowances for speed, running time, and geometry. Thelatter item is taken into consideration by a zone factor, whichaccounts for the influence on the Hertzian stress of tooth flankcurvature at the pitch point, and converts the tangential loadto a normal force. No serious attempt was made to keep thisstandard up to date on newer gear materials and processes topredict the higher performances being achieved in practice.Another serious deficiency is that no account was made forsurface finish or uneven load distribution.

NOMENCLATURECv, Helical overlap factord Operating pitch diameter of pinionF Net facewidth of the narrowest numberI Geometry factor for pitting resistancemN Load sharing rationp Pinion running speedP 1I Diarnetral pitchSac Allowable contact stress number

BS 436:1940d Pitch diameters of pinion and wheelEe Equivalent Young's modulusF Face widthk Constant in Hertz contact stress formulaK Pitch Eactorn, N Pinion and wheel running speedP DiametraJ pitchR Gear ratioRr Relative radius of curvatures Maximum contact stress set in the surface layers of

the gear cylindersSc Surface stress factorT Number of teeth on wheelXc Speed factor for contact. stressZ Zone factorat Transverse pressure angle at reference cylinderatw Transverse pressure angle at pitch cylinderI3b Base helical angle

AGMA218.01C.. Application faetar for pitting resistanceCc Curvature factor at pitch lineCI Surface condition factorCH Hardness ratio factorCL life factor for pitting resistanceem Load distribution factor for pitting resistancec;, Elastic coefficientCR Reliability factor for pitting resistanceC, Size factor for pitting resistanceCT Temperature factor for pitting resistancec,.. Dynamic factor for pitting resistanceCx Contact height factor---

Smith(3) described B5 436 as "an. average experiencemethod, wherebygear manufacturers and users collaborateto provide extremely empirical rules of thumb based onoperating experience. Permissible loads are specified for'typical' manufacturir1g accuracies of a given class with'typical.' loading cycles and corrections for speed, etc."Although the standard did not take into account factorsknown to influence bending and contact stresses, such as ap-plication conditions (i.e., the load fluctuations caused by ex-ternal sources), system dynamics and gear accuracy and thebenefits of surface hardening, the standard served its userswell.

The original AGMA standard was issued in1926, and thefirst draft of AGMA 218.01,(4) used. in this review, wasdrafted in 1973 and approved for publication in 1982. AGMA218 also rates gearson the basis of bending strength and sur-face contact stresses, (referred to as surface durability or pit-ting) but also introduces a. number of other factors in therating equations. For example, influence factors are used totake into account load distribution across the face width,quality ofthebcansmission drive, and transmission accuracyrelating to manufacture, Considerable knowledge and judg-ment is required to determine values for these factors.

Compared to the old British Standard, AGMA 218 is con-siderably mare comprehensive. Ratings for pitting resistanceare based on 'the Hertzian equation for contact pressure be-tw'een curved surfaces, which is modified for the ,effectof loadsharing between adjacent teeth. The Lewis equation has beenmadified to account far ,effects, such as stress concentrations,at the tooth root, compressive stresses resulting from the

Reference diameter of pinionApplication factorTransverse load factor for contact stressFace load factor for contact stressDynamic factorPinion running speedMinimum demanded safety factor on contact stress(BS only material quality factor for contact stress)life factor for contact stressSize factor for contact stressElasticity factor for contact stressZone factor for contact stressLubricant influence. roughness, and speed factor forpittingWork-hardening factor for contact stressContact ratio factor for contact stressHelix angle factorTransverse pressure angle at reference cylinderTransverse pressure angle at pitch cylinderBase helix angleBasic endurance limit for contact stressPermissible contact stress

85436: 1986 and ISO/DIS 6336b Face widthd1KAKHaKH,9

Kvn1

SHmmZMZNZxZEZHZL,ZR,ZV

ZwZ,Zfjat

atw

(3b'O'HlimuHP

radial. component of the gear load, load distribution due tomisalignment between meshing teeth, andload sharing. The'Critical bending stress is assumed to occur at the tooth filletbut, as in the old British Standard, the effect of blankgeometry (e.g., rimand web size and how the relative size ofthese effects stresses at thetooth root) is not considered.

The 150 standard, ISO 6336,<5) was issued in. 1980,though it is sHUa draft. The standard covers a wide range ofdesigns and applications, and is the most detailed documentamong the gear rating standards considered here. It containsa vast amount of collected knowledge and the options tocalculate factors at various levels afcomplexi ty. Itgives pro-cedures for determining gear capacity as limited by pittingand tooth breakage, as in other standards, and also considers

OR. DOUG WAlTON is a Senior Lecturer in the MechanicalEngineering DepartmMt of the University of Binningham. He ho.ldsBreck and PhD degrees in Aeomautical Engineering and is ChAir-rnan of the department's Design Group. He is a Mernber of the In-stitution of Mechanical El1,gineersand the British Gear.Association.

YUWEN SHI is a visting~esearch student from the Harbin Instituteof Technology, People's RepubUc of China. He has a BS degree inMechanical Engineering and is curren tly working in the Area of theCAD of geared drives at the U.niversi~y of Binningh.am.

DR. STAN TAYlOR is a Lecturer in the Mechanical EngineeringDepartment of the University of Binningnam. He holds a PhD inMechAnical' Engineering and is III Member of the Institution ofMechanical Engineers. He luts been ,It pioneer in the use of computersin soioing engineering problems.

NovemberjDec,ember 1990 11

AUTHORS:

scuffing ..The basic equations are modified by applying. in-fluence factors as in A:GMA. These procedures demand arealistic appraisal of all influence factors, particularly thosefor the allowable stress, the probability of failure, and the ap-propriate safety factor. ISO also offers three differentmethods for determining bending and contact stresses andtheir influence factors, depending on the application and ac-curacy required. Since the latest German standard, DIN 3990:1987, (6) is substantially similar to ISO 6336,. a detailed discus-sionof DIN is excluded.

The new British standard, BS 436:1986,(7) is similar toISO / DIS 6336 and is a complete revision of the old standard.It is, however, much more user friendly than [SO. Like theother standards, the new British standard uses modified Lewisand Hertz equations, using correction factors, such as thedynamic factor to account for load fluctuations arising frommanufacturing errors, and a load distribution factor to takeinto account the increase in local load due to non-uniformloading arising from conditions such as shaft stiffness and, inthe case of helical gears, helix error. The correction factors arethe same or are similar to those used. by ISO. Geometry fac-tors in the new BS 436 are similar to those in ISO (method B)willIe other methods in ISO use different approaches forgeometry factors ..The new British standard, however, drawson a considerable amount of previously published researchand uses additional parameters, like materia] quality factors,not allowed for by ISO or AGMA. This standard does notwork on "typical" figures for each rating factor as in the oldstandard, but uses researched data to predict load increasescaused by deflections, alignment tolerances, and helixmodifications. Throughout this review, the term.BS refers tothe new standard, except where stated.

In the stress analysis procedures of BSand ]50, bendingand contact stresses are classified into three groups: 1)Nominal or basic stresses, which <we calculated forgeometrically perfect gears meshing with perfect loaddistribution, 2) Actual stresses, calculated from the nominalstresses, but allowing for manufacturing and mounting er-rors, and 3) Permissible stresses, calculated for the gearmateria] taking into account the required life, gear finish,lubrication, and the minimum specified.factors of safety. TheBS differs significantly from ISO and DIN in the determina-tion of permissible stresses.

Literature SurveyComparisons have been made between AGMA and ISO

covering basic theories and results for applications. Thosecomparisons that were published were mainly based on oldversions of AGMA (A:GMA 215.0'1 and AGMA 225 .01) (8.9)

and the older, approved version of ISO/DP 6336. No de-tailed comparisons have been made between BS 436 and otherstandards. More recently some cornpasisons have been madebetween the latest British and German standards by Hof-mann, (10) who described the theoretical basis of the latest BSand DIN and the differences in determining permissiblestresses.

Imwalle and Labath(ll) made a design survey of differentgear sets for the purpose of comparing AGMA (AGMA 215and AGMA 225) and [SalOP 6336. The results weresummarized for a comparison of dynamic load distributionI 2 Gear Jechnol'ogy

and geometry factors and allowable stress. In the comparisonof geometry factors, aD the factors which are linked withgeartooth geometry were combined to form a "total geometry fac-tor". Comparisons showed that ISO usually gives a higherfactor of safety and higher calculated bending and contactstresses for case-hardened gears compared to AGMA, butlower values for-through-hardened examples. It may be notedthat ISO provides data on the latest and most advanced gearmaterials and treatments ..In another paper{U) by the sameauthors the concept of at basic stress was used, defined as thestress which is calculated if all the modifying factorsare setat unity. The results showed that ISO usually gives a higherbasic bending stress, but a lower basic contact stress com-pared to AGMA. Again, comparisons were made ofgeometry, dynamic load distribution factors, life fact,ors, andallowable stresses.

Mathematical means were provided by Castellani. andCastel1i(1Jf to compute the parameters for calculating thetooth form factor and the stress correction factor (allowingfor stress concentrations at the tooth fillet) which are used inAGMA and ISO. Comparisons made between these two fac-tors in the gear strength ratings gave the following twodifferences:

1) A different choice of reference points on the tooth rootprofile for the tooth fonn and stress correction factors ismade. ISO chooses the same critical point for both tooth formand stress correction factors relating to the point of the filletwhose tangent forms a 30'0 angle with the tooth axis. Thecritical point for the tooth form factor depends on the geartype (spur or helical) and its accuracy. AGMAconJ>iderstheminimum curvature radius for the stress correction factorrelaJing to the point where the .fil1etconnects to the root rude.

2) Both standardsassume that the load application side ofth • th a nk . iti _1 ith . . t t bending f il.. 12'.00. na. IS ·cn.ccu WI . respec 0 !Jcn . _. a ure,AG!V1Atakes this assumption into consider-ation by subtract-ing the radial, compressive stress component from the bend-ing stress, while ISO only considers the tangential bendingstress. ISO compensates for this by making allowances on thevalues-of the stress correction factor.

Comparison of Pitting Resistance RatingsComparing gear standards can present difficulties for the

fonowing reasons:1) There are a number of influence factors included in each

standard, but the number and the numerical values of thesefactors differ ..Taking the power rating formula for pittingresistance as an example, BS 436:1940 has four influence fac-tors, while there are twelve in AG!V1A218, compared withsixteen in both ISO and the BS. These are discussed later.

2) The determination of influence factors usually requiresa knowledge of additional parameters, some of which are notalways readily available. For example, in order to use theanalytical method to calculate the AGMA geometry factorfor pitting resistance, four additional data items (a curvaturefactor at the pitch line to determinethe radius ofcurvatarebetween the two contact surfaces; a.contact height factor toadjust the location of the height of the tooth profile where thestress is caIcuIated;a. helical factor to account for the effect orhelix angle on contact stresses; and a load sharing ratio) haveto be employed .]:0 determine these four factors more infor-

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mation is required and some, like generating the tooth layoutto give the necessary geometry data, may be difficult toobtain.

3) Each standard has its own definitions for the influencefactors, but factors bearing the same names do not necessarilyhave the same effects. This makes direct comparisons of in-fluence factors difficult. For example, although AGMA andISO both introduce a service factor, the values cannot becompared directly.

The terms used in each standwdare listed in thenomenclature .

The power rating for contact stressesgiven by BS436: 1940

XcScZFNT

126000KP

Equation 1can be rewritten as

n Fd2 R 0.8 s2____ r_Xe126000 d k Ee

For AGMA 218.01 the transmissible power based on pitting is

n Fd2e ..126000

The as 436:1986 power rating is

b d12n1 u 1

126000 u+1 ZH2 Z~1

and for ISO lOIS 6336 the power is

bdlnl U 1126000 u+I zi Z; z3

1

where

UHP = (O"H1irn ZN). z, ZR Zv Zw z, (7)SHmin

From Equations 2-7 it may be seen that for a given gearratio the transmissible power is proportional to the squareof the pinion pitch circle diameter and permissible contactstresses. Therefore, to increase gear power capacity in termsof surface durabilty, it is more effective to increase the pinionpeD or permissible surface stresses than to increase the gearpair facewidth.

The pitting resistance related factors above may begrouped into common and non-common factors. Commonfactors are those which have the same meanings in all thestandards, (not all these factors appear in the standards) andthei:r values can becompared directly. For example, thedynamic factor whichallows for internally generated geartooth loads induced by non-conjugate meshing action of thegear teeth, appears in all the standardsexcept the old BS, andvalues can be compared directly. Non-common factors,such as the geometry factor,are those which are onlyequivalent to each other in the sense of having the same eE-l'4 Gear feehnology

(1)

fects on the rating results, although specific values cannotbe compared.

Table 1classifies all the contact stress influence factors intoeither common or non-common groups where it can be seenthat the old British Standard had few parameters for com-parison with other standards. The similarity between BSandISO isalso apparent. A comparison between the infl'uencefactors given ineach standard is made in the followingparagraphs.

1) Application factors. An application factor is used inAGMA, ISO,. and BS to evaluate external influences tendingto apply a greater load to the gear teeth than that based onsteady running conditions. Typical external influences arethe drive characteristics (e..g., smoothness and load fluctua-tions) of the prime mover and of the driven machine ..Valuessuggested in ISO correspond to those for the overload fac-tor in AGMA 215. While no data appears in.AGMA 218,these factors may be found in related AGMA applicationstandards. BS gives more detailed conditions than ISO,although values are similar.

2) Dynamic factors. As discussed above, the applicationfactor is used to handle dynamic loads unrelated to tooth ac-curacy. The effect of dynamic load related gear tooth ac-curacy is then evaluated by the Inclusion of a dynamic fac-tor which accounts for effects ·of gear set mass elastic effectsand transmission errors. AGMA modified the experimentalwork of Wellauer(14l to obtain dynamic factors as a functionof transmission error. These accuracy levels can under cer-tain manufacturing conditions be the same as the gear qualitynumbers given in AGMA 390. (15)

ISO dynamic factors are based on Buckingham's incremen-talload methodU6J and work by Weber and Banaschek.(l7JISO (analytical) method B presents a calculation procedurefor the main resonance speed and divides the running speedinto three sectors. The dynamic factor corresponds to eachof these speed sectors and may help designers to adjust theoperating speed or alter the design to avoid critical speeds ..ISO method C is only applicable to gears with accuracynumbers of 3 to 10 and cannot be used for gears operating ator near the main. resonance speed. The dynamic factor in theBS is very dose to [SO method C. In the old BS, dynamic ef-£ects were not considered. The speed factor used in the old BSis not to be confused with dynamic loads, but was intendedto allow f·or load reversals and their eHed on fatigue duringthe life of the gear.

It has been customary fer AGMA to put the dynamic fac-tor in the denominator of the rating formula, whereas ISOand BS apply it to the numerator. Nevertheless, the dynamicfactor is defined as a multiplier of the transmitted load in allthe standards, although some believe that the effect shouldbe additive. (18)

3) Load distribution factors. A load distribution factor isused in the rating equations to reflect the non-uniform loaddistribution along the contact lines caused by deflections,alignment, and helix modifications (including crowning andend relief), and profile and pitch deviations ..The evaluationprocedure for this factor is rather complex, siace manyvariables are involved, and some of them, such as the com-ponent of the gear system alignment and manufacturingerrors, are difficult to determine.

(2)

(3)

TABLE 1 COMPARISON OF PITTING RESISTANCE INFLUENCE FACTORS

BS436:1940 AGMA21B BS 436:1986 150/0[56336Geometry R~·8

I u 1 u 1Factors- - -- --- --

d u + 1 Z"; Z2 u+1 Z].Z2 Z2• H , Ii

Elasticity (k~}O.5 Cp ZE ZEFactors"

Size Cs1 1

Factors" - - -Z2 Z;~Lubrication 1 ]

Film - C~·5CT ZLZVZR ZtZVZRFactors"

Application - Ca KA KAFactors]

Dynamic Cv1 1

Factors] - - -Kv Ky

Load 1 1Distribution - Cm

KHaKHIl' KH ..KHIlFactorst

WorkHardening - CH Zw ZwEactors]

Life CL ZN ZNFactorst -

Reliability - CR SHlim SHminFactors]

MaterialQuality - - ZM -Factor]

Speed Xc - - -Factor]

t denotes common and .. non-common factors'""--

In AGMA the load distributi.on factor is the product of theface and 'transverse load distnbution ~fa.ctors.The face orIongituilinaJ (as described in the ISO and BS) load distribu-tion factor accounts for the non-uniform load across the faceof the gear. while the transverse load factor reflects the effectof non-uniform distribution of load down the tooth flank dueto profile, pitch deviations. and tooth modifications.Although AGlv1Auses this factor to allow for the effect of thenon-unilorm distribution of load among the teeth.which sharethe t.otalload, no specific wonnanon is given in the standard.The AGMA standard assumes that if the gears are accuratelymanufactured, the value of the transverse load distributionfactor can be 'taken as unity. AGMA provides both empiricaland analytical methods to.determine the face load distribu-tion factor ..The empirical method is recommended for nor-ma1,relatively stiff gear .a.ssemblies,and only a minimumamount of information is required. The second method isbased. on elastic and non-elastic lead mismatch and needs in-formation about design. manufacture. and mounting and is.theoretically, suitable tor any ge.ar design ..

The ISO load distribution factor is also the product of thetransverseand longitudina] load factors. Three differentap-preaches have been made by ISO to detennine thelongitudinal load factor ..Method B is a final proof ratingcalculation method based on known manufacturingerrors.Method C is a preliminary rating method and uses assumedvalues of manufacturing errors within limits of prescribedtolerances. Method 0 is even more simplified than methodC. The transverse load factor is a function of longitudinal loadfactor, contact ratio, pitch tolerance, and mean load inten-sity. Procedures for calculating the load distribution factorsin ISO are the most complex and are still under revision . Loaddistribution factors in the BSemploy virtually the same pro-cedure as method C in 150,. except for a diffef'ence in deter-mining total misalignment. ISO gives .five approximationmethods for this. while the BS only gives one.

4) Life factors. Life factors take into. account the effects otincrements in permissible stresses if a limited number of loadcycles is demanded, Among AGMA, ISO,. and BS,.the mostdistinct diHel'ence lies in the definition. of endurance limits.

November/December 1990 1.5

AGMA 218 sets 107 load cycles as the endurance limit forhoth bending and pitting, while ISO and BS define limits of2x10P, 5x107, and l09cyc1es for contact stresses ..Althoughthere is no life factor in the old BS, a procedure to calculatevariable duty cycles by determming an equivalent runningtime was provided. BS 436:1986 also has a procedure to dealwith variable duty cycles, while this aspect of gear runningis not considered by ISO.

5) Material quality factor. Among the four standards, onlythe BS introduces material facto.rs in its bending and contactstress ratings in an attempt to allow for the higher permissi-ble stresses to be obtained from using higher quality materials.

6) Size factors ..Size factors are used in all. except 'the oldBS, to take into account the influence of tooth size on surfacefatigue strength . Values are usually taken as unity because nofurther information is provided in any of the standards.

7) Work-hardening factors. When the pinion material issubstantially harder than the wheel, the effects of cold workhardening and internal stress changes in the softer wheelmaterial may occur, in which case the surface contact stresseswill be reduced. These effects have been considered byAGMA, ISO., and BS by introducing a hardness ratio orwork-hardening factor, In AGMA, the hardness ratio factoris a function of the gear ratio and pinion and wheel hardness,but AGMA only applies this factor to the wheel rating. Aguidance diagram is given by BS for determining the work-hardening factor, based on surf ace roughness and haJdness,The ISO work-hardening factor is only related to wheelhardness ..

.8) Permissible stresses. Permissible bending and contactstresses are given in the old BS for a limited number ofmaterials listed in. the standard. It is usually agreed that thevalues are generally too pessimistic for snrface-hardenedgears. Allowable bending and contact stresses, based onlaboratory and field experience for each material and heattreatment condition, are provided inAGMA. For most of thesteels the allowable bending and contact stress numbers arefunctions only of material hardness ..

In both BS and ISO the pennissible bending / contact stress'is based. on the bending/surface fatigue endurance limit forthe material, taking into account the required life and runningconditions. According to the BS, for most gear materials thebending/contact endurance limit depends only on hardnesswithout differentiating between materials and heattreatments. In ISO,. bending/ contactendurance limit is deter-mined either based on experimental data for test gears of thesame material or on prepared, polished specimens. Values areprovided in the ISO standard for a wide range of steels andheat treatments.

For surface-hardened gears, the BS bending endurancelimit is based on residual stresses and the ultimate tensilestrength of the gear material. Detennining the residual stressesand tensile strength of surface-hardened gears is, however,difficult casting some doubt as to the ease with which thismethod can be used.

9) Factors of safety and reliability. So far there is no ac-cepted method of relating gear reliability to safety factors con-sidering the effect of material quality and gear accuracy. TheAGMA reliability factor accounts for the effect of the normalstatistical distribution of failures from the allowable stresses16 GearTechnology

and can be chosen according to the reliability required. BSand ISO leave the user to specify a value for this factor.Minimum demanded safety factors for bending strength andcontact stress are recommended by both ISO and BS to reflectthe confidence in the actual operating conditions and materialproperties, but the values for these factors are different. Thesafety factor for bending strength in the old BS is defined asthe ratio of ultimate tensile strength to the product of thespeed factor and bending stress factor.

10) Non-common geometry factors. Geometry factors ac-count for the influence of the helix angle, contact ratio, andtooth flank curvature at the pitch point on gear load capacity.Ignoring the experimental exponent of 0.8, the geometry fac-tor for the old BS can be written

R cosat cosatw

R+l 2coS~b

For the BS and ISO the geometry factor is

(·8)

1 casal smatw

2 cost3b cosatw

(9)--=

The similarity between Equations 8 and 9 is not apparentwhen expressed in the way given in the standards. (SeeGeometry Factors, Table 1.)

The AGMA geometry Iactor.T, for contact stress is

ccCxqmN

(10)

where C, is the curvature factor at the pitch line and is afunction of the gear ratio and pressure angle, <=x is a contactheight factor adjusting the location of the tooth profile whe.rethe stress is calculated. The helical factor C", accounts forthe helical effect in low contact ratio helical gears, and mN

is the load sharing ratio which depends on the transverse andface contact ratios. Similarly, ISO uses a helix angle factorto account for the helix effect on contact stresses. Both ISOand BS include a contact ratio factor to allow for the in-fluenee of transverse contact ratio and overlap ratio on con-tact stress based ratings ..

11) Non-common elasticity factors ..Elasticity factors ae-count for the influence of material mechanical properties onthe Hertzian stress. Those used in AGMA,. ISO, and BS areidentical. The only difference between the old BS and theothers is that the equation for calculating this factor has beensimplified by assuming that Poisson's ratios for the pinionand wheel are the same ..

12) Non-common lubrication HIm factors. BS and [SO ac-count for minimal. film thickness between contacting teethon surface load capacity. In their rating procedures, oilviscosity, surface hardness, and pitch line velOCity are con-sidered to be the main factors influencing film thickness.There are some differences between the calculation methodsused by BSand ISO, BS gives two diagrams: one forroughness and the other for the product of a lubricant andspeed factor ..ISO provides three equations and correspond-

I ing diagrams to determine these factors. Although AGMA

218 does not consider lubrication, it does take tooth surfaceroughness and temperature effects into account by introduc-ing a surface condition and a temperature factor. In the oldBS, lubrication was ignored aJtogether. Tooth scuffing.which is covered by ISOand DIN in separa.te parts, attemptsto predict the t'emperatuN at which scuffing will occur, Thisis not dealt with by any of the other standards and,therefore, no comparisons can be made, although scuffingdoes appear in the new AGMA standard.ReferentleS:

1. BR111SH STANDARDS INSTITUTION. "Spedlication for 'MaChine Cut Gears. A. Helical and Straight Spur." BS436;1:940. London, 1973.

2. LEWIS. W. EngineeisOubofPhiladeJ.phla. Proceedin8$ Vol.X,1893.

3. SMfJ11, ~.D. Gears and Their Vibrations. The MaanillanPress Ltd, London, 1983.

4. MLERICAN GEAR MANUFACTIJRERS ASSOClATION.-A:GMA Standard For Rating the Pitting Resistance and Bend-ing Strength of Spur and Helical Involute Gear Teeth."AG1vfA218.01, 1982.

5. ORGANIZATION FOR INTERNATIONAL STAND'AR-DIZAnON. "Calculation of Load Capacity of Spur andHelical Gears .."ISO/DlS 6336:1983, Part H, Belgium, 1983.

6. DEUTSCHE lNDUSTRlE NOR1Vl:EN. "Grundlagen fur dieTragfahigkeitsberechnung von Gerad - uad Sdtragslim-radem," DIN 3990': Part 1-5,1986.

7. BRITISH STANDARDS rNSTITUTION. "Spur and H.elicalGears. Pt. 3. Method for Calculation .of Contact and RootBending Stress limitations for Metallic Invelute Gear." B5 436:1986. London, 1986.

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As'K your GMI·FHUSA re,presentative for a Q,uotationandl copies ot our ,quality documentation.

8. M1ERICAN GEAR J\.IfANUFAcruRERS ASSOCIATION."1nfonnation Sheet for Surface Durability (Pitting) of Spur,Helical, Heningbone, and Bevel Gear Teeth." AGMA215.m,1966.

9. AMERICAN GEAR MANUFACTIJRERS ASSOCilA110N."Information Sheet .forStrength of Spur, Helica], Herringbone,and Bevel Gear Teeth." AGMA22S.01. 1967.

10, HOFMANN, D.A. 'The Imporlance .of1111 New Standards BS436 (1986) and DIN 3990 (1986) f,orGear Design in the UK."Marine Gearing and Revision of Bririsfl Standards. The ~stitute of Marine ElIgineers. Marine Management (Holdings)Ltd,1987.

11. RvlWALLE,D'.E.,O.A. LABATHandN. HUr'otINSON. ~AReview of Riec~nt Cear Ratiqg Dev lopmenl ,]501 AGMAComparison Study." ASME Paper ao.C2/DET~25. 1980.

iz. tMWAlLE, D.E., O.A. LABATH. "Differences BetweenAGMA.and[s()RatingSystem.M AG1vfAP per219.lS,l981.

13. CASTELLANI, G. and V.P. CAS:rELU. "Rating GearStrength." ASME Paper8(}Q/DET-88, 1981.

14. WiELLAUER.,E.J. "Ana1ys:isof FactorsUsecHorRaIing HelicalGears." ASME PaperS9-A-Ul, 1959.

15. GEA.R HANDBOOK. Vol 1. Gear Classification, Material,and Measuring Methods for Unassernb.led Gears. AGMA.390',Washington D.C.

16. BUCKINGHAM,E. "Dyn~ic Load on Gear 'Jeeth." ASMEResearch Publications. New York, 1931, also in AnalyticalMechanics of Gears, PI' 426-452, Dover, 1963.

17. WEBER C. and K.. BANASOfiEK."F.ormanderung und Pl'o~fiIrucknahme bel Gerad-undScheagveeaahnten." Radem,Schriftenreihe Anl:riebstechnik, No. 11, 1955.

lB. DUDLEY, D.W.. Handbook of Practical Gear Des.ign.McGraw-HiIlBook Company, New York, 1984,

AGMA 12

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