1、93FTMS1- Spur Gear BendingStrength Geometry Factors:A Comparison of AGMA and ISO Methodsby: E. R. teRaa, StudentUniversity of Waterloo, CanadaAmerican Gear Manufacturers AssociationTECHNICAL PAPERSpur Gear Bending Strength GeometryFactors:A Comparisonof AGMAand ISOMethodsE. R. teRaa, University of W
2、aterloo, Ontario, CanadaThestatementsand opinionscontainedherein are thoseof the authorandshouldnotbe construed as an officialactionoropinion of the American Gear Manufacturers Association.ABSTRACT:With the developmentof the ISO spur and helical gear rating standard (ISO/DIS 6336) it has become nece
3、ssary tocompare theISOpowerrating standardtothe correspondingAGIvIAstandard. The purpose of thepaper is tocomparethebehavior of the bending geometry factor (J factor) for spur gears. Computer software was used to compare J-factorvaluesfor 135gear meshes. Results arecompared from thematrix of gearset
4、swhich variespressure angle, tooltip radiusof curvature and tooth numbers. Of particular interest is the effect of profile-shift (also know as addendummodification).Theresultsclearly show thatthere is significant differencebetween the standards,inboth thegeometryfactor values andtheeffects of profil
5、e shift. The strength increasewhen using profile shiftin theISO method is muchlessthan is shown inthe AGMA method. The ISO methods low sensitivity to profile shift might cause the designer to abandon strengthoptimization byprofile shiftbecause the benefits are onlymarginal. The question nowremains,
6、“Which methodis morecorrect?“ Further study is required to evaluate the causes of the discrepancies andpossible remedies.Copyright 1993American GearManufacturersAssociation1500 King Street, Suite 201Alexandria, Vkginia, 22314October, 1993ISBN: 1-55589-626-XSpur Gear Bending Strength Geometry Factors
7、:_ A Comparisonof AGMAandISOMethods1“- E.R. teRaa, Graduate Student(Supervisor: G. C. Andrews, Professor)Department of Mechanical EngineeringUniversity of WaterlooWaterloo, Ontario, CanadaNomenclature Nomenclature defined in this paper:.AGMA nomenclature: J1 - pinion geomelry factor for bending stre
8、ngthCv - helicaloverlapfactor J2 - geargeometryfactorforbendingstrengthF - netfacewidth Kx - profile-shiftfactorJ - geometry factor for bending strengthKf - stresscorrectionfactor Acronyms:Ka - application factor for bending strength AGMA - American Gear Manufacturers AssociationKv - dynamic factor
9、for bending strength ISO - InternationalStandardsOrganizationKs - size factor for bending strength I-IPSTC - highest point of single tooth contactKm - load distribution factor for bending strengthKs - rim thicknessfactor 1. Introductionm - transverse modulemG -gear ratio The International Standards
10、Organization (ISO) hasmN - load sharing ratio neared completion of the strength rating standard for spur andN1 - number of teeth on pinion helical gears. The final draft of the ISO spur and helical gearN2 - number of teeth on gear strength rating standard (ISO/I)IS 6336) 1 is expected to best - tens
11、ilestress approvedand publishedsometimein 1993. The equivalentx1 - pinion addendum modification coefficient AGMA standards are AGMA 2001-B88 2 and AGMA 908-x2 - gear addendum modification coefficient B89 3. Both ISO and AGMA show agreement that the ratingY -tooth form factor procedure must consider
12、both the pitting resistance and theWt -tangential transverse load at operating pitch diameter tooth root bending strength, but the formulae often producesignificantly different power ratings.ISO nomenclature: The ISO/DIS 6336 draft standard offers a variety ofb - facewidth calculationmethodsformosts
13、tepsintheratingprocedure.Thed1 - pinion reference (standard) pitch diameter methods are named Method A, B, C, D, with each methoddwl - pinion operating pitch diameter having differentformulaefor each factor. MethodA is definedFt - tangential transverse load at reference cylinder as the experimental
14、data method, to be used when the engineerFwt - tangential transverse load at operating pitch diameter has sufficientdata and/or experience toevaluate the factors withKA -application factor greater certainty than the standards empirical equations canKv - dynamicfactor provide. MethodB is themostaccur
15、ateanddetailedapproachKF_ - face load distribution factor for root stress available in the standard, based on analytical and empiricalKFc_ - transverse load distribution factor for root stress results. Methods C and D are usually a less-sophisticatedran - normal module version of Method B, where res
16、ults are easier to compute butnat - transversemodule are also more conservative(to accountfor lowerprecision).x1 - pinion addendum modification coefficient This structure is much different from the AGMA procedurex2 - gear addendum modification coefficient where generally there is only one method of
17、computation (loadYF - toothformfactor distributionfactorbeinganexception).For thepurposesof thisYs - stresscorrectionfactor paperthe “ISOmethod“refersto the MethodB set of rulesandYI3 - helixanglefactor equations.-reference (standard)helixangle The developmentof the ISO gear rating standardOF - tens
18、ilestress producessomeimportantissuesforengineerswhocurrentlyusethe AGMA standards. Although the fundamental concepts in strength of gear sets are determined in three possible failurethe standards are the same, the procedures and calculation modes:methodsval-y significantlyin many aspects. Many of t
19、he a) Toothpitting fatiguefactors were developed empirically, so there is no complete b) Tooth root bending fatigueanalytical comparison between the methods, c) Low cycle tooth root bending failureThe inability to make a direct comparison creates some The factor of safety must be adequate in each fa
20、ilure mode inuncertainty. However, the most important question is: “How do order to ensure a safe design.the standards perform as a design tool? “In particular, how do Although the AGMA standards are primarily based onthe equations react to the modification of parameters in order the imperial system
21、 of units, the metric formulae are used into optimize the strength?“ The desired behaviour of a rating this paper to simplify the comparison of numerical data. Themethod is to ensure that the actual strength increases can be symbols used are specific to the standards; there are very fewobtained by t
22、he optimization of design parameters, symbols which are common to both standards.Within the topic of spur gear strength optimization, The AGMA and ISO descriptions of the stress deratingthere are many important aspects. Of particular interest to this factors: application, dynamic and load distributi
23、on are identical.paper is the effect of profile-shift (also known as addendum These stress derating factors are set to 1.0 for the purposes ofmodification) on the strength analysis. Profile-shift is a the stress formulae comparisons. Also, the pitting resistancetechnique which is used to create non-
24、standard gear sets with geometry factor (I) is not examined in this paper although thereincreased strength. This is usually accomplished by shifting the are discrepancies between the AGMA and ISO formulations.pinion and gear profiles to produce a stronger pinion and a These discrepancies are a resul
25、t of ISO/DIS 6336 applyingweaker gear resulting in an optimized gear set (ie. balanced single pair mesh factors (ZB and ZD) and the contact ratiostrength of components). Profile-shift is particularly useful for factor (Ze) in the stress formulae. The proposed Ze value ofthe redesign of failed gear b
26、oxes. The gear set can be made 1.0 for spur gears 7 will resolve the major difference betweenstronger, within the existing centre distance and face width, contact stress values; therefore surface pitting is not discussedwith only a marginal (or no) increase in manufacturing cost. further in this pap
27、er.In this paper, the bending strength geometry factors (J-factors) in the standards are compared. The ISO does not 3. Bending Stress Formulaedefine a single geometry factor, so the author has defined anequivalent ISO J-factor by isolating the effects of tooth Bending failure is the initiation and g
28、rowth of a fatiguegeometry in the stress equation. These geometry factors are crack at the tooth root fillet. The risk of failure in both low-then comparable; but since other aspects (eg. allowable stress, cycle and high-cycle fatigue cases were analyzed in a similarstress derating) of the standards
29、 are not analyzed, the manner, since the J-factor is the same for both failure parison is not exhaustive, but this paper shows general The governing stress is the maximum stress at the tensile roottrends, t-filetasfollows.Dr.-Ing. Theodor HOsel 4 compared several aspects a) The AGMA formula for tens
30、ile stress is:of the AGMA and ISO (and other) standards for a gear meshwith a 21 tooth pinion and a 66 tooth gear. The investigation Wt Ka 1.0 Ks K,n KBincluded the effects of profile-shift and many other parameters s t= _ (1)Kv Fm Jin the gear ratings. The purpose of this paper is to extendaspects
31、of his work, by comparing the J-factors using a matrix b) The ISO formula for tensile stress is:of 15 standard gear meshes, thus providing a wider basis fordiscussion. The strength of each mesh was analyzed for the Ftresponse to profile-shift; both long-and-short-addendum system OF= b m n YF YS Yf_K
32、A KV KI_ KFa (2)and the extended centre distance system 5, up to a pinionaddendum modification coefficient of 0.50.The J-factors were computed using gear analysis The AGMA J-factor incorporates the effect of toothsoftware developed at the University of Waterloo. The AGMA geometry on the tensile stre
33、ss into a single non-dimensionalprogram was written by J. D. Argent 6 and was verified with factor, a larger J-factor indicates an increase in gear strengththe AGMA 908-B89 3 tables and with commercially available because the stress decreases. The ISO stress formula does notsoftware. The ISO program
34、 was written by the author use a geometry factor, so the author has developed anaccording to ISO/DIS 6336 and has been verified with manual equivalent ISO J-factor for the purposes of comparison. Notecalculations, that the AGMAstress formulais basedon the tangentialload(Wt) at the operating pitch ci
35、rcle while the ISO formula uses2. Strength Analysis Procedures the tangentialload (Ft) at the standardpitch circle. Also, notethat the J-factors in the tensile stress equationsare computedAccording to both AGMA and ISO standards, the separately for the pinion and gear.The AGMA J-factor is defined 3
36、as: the effect of pressure angle and tool edge radius as listed inTable 1, and 5 sets of tooth numbers were selected to show theY CV CV = mN - 1.0 for spur gear (3) effect of different tooth numbers as listed in Table 2. ThisAGMA J- Kf-“_ “ matrix of 15 gear sets was chosen in order to examine a bro
37、adrange of practical situations. Series A and B were based on theThe equivalent ISO geometry factor for bending AGMA 908-B89 tables, while Series C is a full fillet rootstrength is developed as follows: profile using the standard tool tip radius given in ISO 53 8.The tooth numbers were chosen consid
38、ering the common rangeF t d 1 = 2 Pinion Torque - Fwt dwl (4) ofpiniontoothnumbersandrangeoftypical gearratios. Thesestandard meshes are all free of undercutting and pointed teeth.Table 1 - Definition of Sample Gear Mesh Seriesd1 cos_ISO J - dwl YF YS YI3 “ YI3 = cosl3 - 1.0 for spur gear(5) SeriesA
39、 SeriesB SerieSCTherefore, the converted form of the ISO tensile stressequationis: Addendumratio 1.0 1.0 1.0Dedendumratio 1.25 1.35 1.427F_ KA KV Klff3 KFa (6) Tool edge radius ratio 0.25 0.27 0.38_F - b m t (ISO J) Reference pressure angle 20* 25 20*which has the identical form of the AGMA tensile
40、stress Helix angle 0* 0 0*equation. Tooth thinning for backlash 0.024 0.024 0.024The J-factors involve two aspects of geometry: thecoefficient (AGMA Ash)critical position of the tooth during rotation and the criticalpoint on the tensile root fillet, at this position. Both standardsagree that the cri
41、tical rotational position is the highest point ofsingle tooth contact (HPSTC) for spur gears with contact ratios Table 2 - Definition of Tooth Number Setsless than 2.0.The nominal stress at the critical point is calculated Set # N I N2 mGusing a “tooth form factor“, and the “stress correction factor
42、“ Gear Ratioaccounts for the stress concentrationcaused by the geometry # 1 21 21 1.000change at the fillet. Both factors are discussed below.The AGMA methodcalculatesthe form factorbased # 2 21 35 1.667on the Lewis parabola, which determines the critical point on # 3 21 135 6.429the root to be the
43、tangent point to the parabola whose vertex isat the intersection of the tooth centerline and the load line in # 4 26 35 1.346the critical gear position. The slress correction correlation is # 5 26 55 2.115based on the smallest radius of curvature on the root filletwhich occurs at the root circle. Th
44、e correlation was determinedfrom photoelastic experiments by Dolan and Broghamer,publishedin 1942 3. The effect of profile-shiftwas examined simply byThe ISO method determines the form factor based on modifying the standard meshes defined above. The J-factora 30 tangent (measured from the tooth cent
45、erline) to the root was computed for pinion addendum modification coefficientsfillet. The stress correction correlation is based on the radius (Xl) from 0.0 to 0.50 in steps of 0.125. Both the long-and-of curvature at the critical point on the root fillet. The method short-addendum system and the ex
46、tended-center-distance systemwas developed using finite element results, were considered. Obviously, for the long-and-short-addendumAs shown, the two methods are similar in structure, system, the gear addendum modification coefficient (x 2) rangedbut are not identical. The differences may explain th
47、e variation from 0.0 to -0.50. The author chose zero gear offset (x2=0.0)in results shown later in this paper, for the extended-center-distance system. This range of profile-shift was applied to all 15 standard meshes, for simplicity; the4. Definition of Sample Gear Meshes application of a profile s
48、hift to Set #1 (NI=N2=21) is generallyimpractical and does cause gear undercutting in Series C atFifteen standard gear meshes were chosen to make the xl=-x2=0.50. This array of design parameters defines 135comparison. Three series of tooth forms were selected to show sample gear meshes (3 series lim
49、es 5 tooth number sets times39 profile-shift settings) which provided a substantial amount of 6. Non-standard J-Factor Comparisondata.The term “increasing profde-shift“ is defmed as The purpose of considering non-standard gear meshesprofile-shift which increases the pinion offset (xl) and/or is to isolate the effect of profde-shift, rather than to comparedecreases the gear offset (x2). Increasing profile-shift is the actual J-factor values. A “profile-shift factor“ (Kx) 9 isusual optimization direction since the pinion is strengthene
