1、10FTM05AGMA Technical PaperComparison of theAGMA and FEACalculations of Gearsand GearboxComponents Applied inthe Environment ofSmall Gear CompanyByDr.V.Kirov,BucyrusInternational, Inc.Comparison of the AGMA and FEA Calculations of Gears andGearbox Components Applied in the Environment of SmallGear C
2、ompanyDr. Vanyo Kirov, Bucyrus International, Inc.The statements and opinions contained herein are those of the author and should not be construed as anofficial action or opinion of the American Gear Manufacturers Association.AbstractThe current AGMA standards provide a lot of information about the
3、calculations of loose gears and gearboxcomponents shafts, splines, keys, etc. These recommendations are based mostly on the “traditional”methods of mechanical engineering, found in many classical textbooks and research papers. Their accuracyand reliability have been proven in many years of gearbox d
4、esign and field tests. They are clear, concise, inmost cases easy to program and apply even by a small gear company with limited resources.However new methods for calculations of mechanical engineering components like FEA (finite elementanalysis) are becoming wide spread. Once these techniques were
5、used only by big companies because oftheir complexity and price but with the development of the computer technology they become more and moreaccessible to small gear companies which are the majority of participants in the market.In nowadays gear business even a small gear company is usually in posse
6、ssion of a modern CAD systemwhich always includes a basic or advanced FEA package. Such CAD systems are most often run by one gearengineer who makes 3D models, engineering calculations and production drawings. The level of the FEApackages is such that it allows the gear engineer to be able to do com
7、ponents calculations without deepknowledge in the FEA itself.So the question about the effectiveness of the traditional AGMA calculations and the new FEA methodsbecomes of vital importance particularly for small firms.The presented paper compares AGMA with FEA strength and deflection calculations of
8、 spur gears andgearbox components and draws conclusion and recommendations about their effectiveness in theenvironment of a small gear company.Copyright 2010American Gear Manufacturers Association500 Montgomery Street, Suite 350Alexandria, Virginia, 22314October 2010ISBN: 978-1-55589-980-63Compariso
9、n of the AGMA and FEA Calculations of Gears and GearboxComponents Applied in the Environment of Small Gear CompanyDr. Vanyo Kirov, Bucyrus International, Inc.IntroductionAGMA calculationsThe current AGMA standards 1 provide a lot ofinformation about the calculations of loose gearsand gearbox compone
10、nts shafts, splines, keys,etc. These recommendations are based mostly onthe “traditional” methods of mechanical engineer-ing, found in many classical textbooks and researchpapers. Their accuracy and reliability have beenproven during many years of gearbox design andfield tests. They are clear, conci
11、se, in most caseseasy to program and apply even by a small gearcompany with limited resources. Though theAGMA standards and information sheets areexcellent source of gear information they are notrecommended for beginners.FEA calculationsA new method Finite Element Analysis (FEA) isused nowadays exte
12、nsively for calculations of thestrength and deflections of mechanical engineeringcomponents. Before it was used only by bigcompanies because of its complexity and price, butwith the development of the computer technology itbecomes more and more accessible to small gearcompanies, which are majority o
13、f participants on themarket. Almost all FEA manuals require simplifica-tion of the parts. This approach is very dangerousfor gearbox components where the part featuresare very close to each other and every one of themusually influences the stress concentration of theother and the whole part. The pro
14、per modeling ofthe gearbox parts and assemblies requires meshrefinement which needs a lot of computingresources not always available to the small firm. It iscommon during the calculations to get a messagethat there is not enough calculation power,especially if convergence process is used. Apartfrom
15、the mesh refinement the finite elements them-selves require special attention, which usually isbeyond the scope of the gear engineer knowledge.The FEA has its own inherent errors for each of itsstages modeling, discretization and solution 4,thats why it is recommended to be only one of themethods fo
16、r engineering design.The small gear companyIn nowadays gear business even a small gearcompany is usually in possession of a modern CADsystem which always includes a basic or advancedFEA package. Such CAD systems are most oftenrun by one gear engineer who makes 3D models,engineering calculations and
17、production drawings.The level of the FEA packages is such that it allowsthe gear engineer to be able to do componentscalculations without deep knowledge in the FEAitself.So the question about the effectiveness of thetraditional AGMA calculations and the new FEAmethods becomes of vital importance par
18、ticularlyfor small firms.This paper presents comparison of calculations ofgears and gearbox components carried out accord-ing to AGMA standards and information sheets, andaccording to FEA package, which is part of com-mercially available CAD system 3.Comparison of AGMA and FEAcalculationsTable 1 sho
19、ws the direct comparison of thecapabilities of AGMA standards and informationsheets and FEA to calculate gears and gearboxcomponents. It also suggests that FEA is superiorto AGMA and should be used extensively. Howeverit is necessary to remember that FEA has itsinherent errors as mentioned above and
20、 the AGMAcalculations are empirical and proven by fieldexperiments. It is sometimes very difficult to makedirect comparison between the two methods.AGMA calculations in most cases are fatiguecalculations based on proven fatigue data. Onlyhigh level FEA software is capable of doing fatiguecalculation
21、s. This paper considers calculationswhich can be compared by both approaches gearteeth, shafts and splines. Keys and bolts4calculations are not considered due to spacelimitation.Table 1. Comparison of AGMA and FEAcapabilitiesGearboxelementCalculationtypeAGMA FEAGear teethpittingbendingdeflectionYesY
22、esLimitedYesYesYesShaftstressdeflectionYesYesYesYesSplinesstressdeflectionYesNoYesYesKeysstressdeflectionYesNoYesYesBoltsstressdeflectionYesNoYesYesHousingstressdeflectionNoNoYesYesAssemblystressdeflectionNoNoYesYesGearbox exampleTo compare the calculation done by the traditionalAGMA methods and FEA
23、, a simple gearbox isdesigned (Fig. 1) with the following parameters:one stage spur gears, power 30 KW, pinion speed 1200 rpm, pinion number of teeth 22, gear num-ber of teeth 55, module 4mm, face width 30 mm, no profile shift, carburized and groundgears.Gear calculationsThe AGMA strength calculatio
24、ns of gear teeth aregiven in ANSI/AGMA 2001-D04. This standarddetermines the pitting and bending strength of thegear teeth based on empirical formulas. Thegeometry factors used in this standard are determ-ined based in the information sheet AGMA908-B89. The proper application of this standardrequire
25、s deep knowledge of the gear misalignmentand dynamics. The bending of the gear teeth andthe load distribution factor are discussed in AGMA927-A01 and partly in ANSI/AGMA 6001-E08.There are also some other standards which give in-formation about the gear teeth strength ANSI/AGMA 6002-B93, ANSI/AGMA 6
26、032-A94 and AN-SI/AGMA/AWEA 6006-A03.Figure 1. Gearbox model5The AGMA gear rating suite 2 is based on ANSI/AGMA 2001-D04. It is used to rate the gearbox.The results for the pinion are given in Table 2.The gear geometry must be modeled properly in or-der to use FEA for the strength calculations and d
27、e-flections of the gear teeth. In the popular gear liter-ature there are examples showing how to do that5. The most difficult part is the modeling of thecontact area of the two gears. The easiest way is tocalculate the contact band 5 and present it asplanes on the gear teeth, however this calculatio
28、n isnot given in the AGMA standards. Then theseplanes can be easily mated in the CAD software andthe calculations carried out. Figure 2 shows band ofcontact equal to 0.3mm.The FEA strength calculations are shown onFigure 3 the meshing, the loading, the contactarea and the stress numbers. It seems th
29、at thecontact stresses are very high. However if we lookcarefully at the stress distribution on Figure 4, wesee that those high stresses are only in certain smallareas, close to the edges of the band of contact.Definitely this is due to errors in the model, whichrepair usually is beyond the knowledg
30、e of the gearengineer. But looking at the surrounding colors wesee that the stresses are close to those predicted bythe AGMA software (Table 2).Figure 2. Band of contact applied at thehighest point of single tooth contactTable 2. Comparison of AGMA and FEA calculationsGearbox element Calculation typ
31、e AGMA FEAGear teeth Pitting, pinionBending, pinion815 MPa137 MPaAbout 800 MPaAbout 116 MPaShaft StressDeflection (bending)Deflection (torsion)134 MPa8 mkm0.0026 radAbout 100 MPa10 mkm0.0011 radSplines Stress (shear) 27 MPa About 23 MPaFigure 3. FEA model of the gears6Figure 4. FEA contact stress of
32、 the pinionAGMA does not have a procedure for determiningthe gear deflections except for the tooth deflectionin the gap analysis of AGMA 927-D07.Having in mind that AGMA predictions allow forabout 25% scatter of the results we can concludethat both methods give close results.Figure 5 shows bending s
33、tresses of the pinionwhich are very close to the AGMA numbers(Table 2).Shaft calculationsThe shaft calculations are given in ANSI/AGMA6001-D97. They are very detailed strength anddeflection calculations. However the deflectioncalculations are simplified either for bending or tor-sion only. In AGMA 9
34、27-A01 there are detailed de-flection calculations for shafts again separated fortorsion and bending, however this time they aresummed in the approach for the gap analysis. Thisgap analysis includes also the tooth modification,the lead variation and the shaft misalignment whichis beyond the scope fo
35、r FEA modeling in this paper.Figure 5. FEA bending strength of the pinion7A calculation spreadsheet based on ANSI/AGMA6001-D97 shows the bending deflections of the in-put shaft (Figure 6). The angle of twist calculatedper this standard is 0.0026 rad. Figure 7 andFigure 8 show the deflections in the
36、same locationcalculated by FEA.The stresses in the shaft in a given critical sectionscalculated by ANSI/AGMA 6001-D97 are given inTable 2. Figure 9 shows the stresses in the samesection calculated by FEA and also presented inTable 2.SplinesAGMA does not have a separate standard forsplines. The calcu
37、lations of the splines are given inANSI/AGMA 6123-B06. The splines are rated forshear, fretting and wear and ring bursting. Theshear calculations consider the core hardness ofthe splines, while the fretting and wear the surfacehardness. The shear calculations assume that thetorque is transmitted onl
38、y through half the splines.For comparison purposes it is assumed that all theteeth are carrying the load. The results arepresented in Figure 10 and Table 2.Figure 6. AGMA bending and torsion deflections of the input shaftFigure 7. FEA torsion deflection of the input shaft8Figure 8. FEA bending defle
39、ction of the input shaftFigure 9. Input shaft stress in critical sectionConclusionsS It is not always easy to make direct comparisonbetween AGMA and FEA calculations due to thedifferent nature of both methods.S Whenever direct comparison is possible AGMAand FEA methods give similar results.S The AGM
40、A and FEA calculations givecomparable results for the contact and bendingstrength of the gears. However the bending cal-culations should be considered more reliabledue to the controversial approach of modelingthe contact between the gear teeth.S The AGMA standards and information sheetsshould be pre
41、ferred by the gear engineer for thecalculations of the gears and gearbox compon-ents because he/she has deeper knowledge inthem then in FEA.9Figure 10. Spline shear stressS FEA calculations should be preferred fordeflection calculations rather than for strength,because deflections are easier to calc
42、ulate andbesides AGMA has limited number of suchmethods.S FEA calculations should be used where AGMAdoes not have similar methods.S Whenever necessary FEA consultant should beinvolved and calculations should be done withhigher level of FEA software.S Gear engineers should be encouraged stronglyto in
43、crease their competence in FEA in order toquickly size gearbox parts for which AGMA cal-culations are not applicable and to improvedcommunication with FEA engineers.Reference1. AGMA Standards Collection 2009.2. AGMA Gear Rating Suite, Version 2.2.1, Amer-ican Gear Manufacturers Association.3. Cosmos Works Designer 2008 Training Manu-al, Copyright 1995-2007, Dassault Systems,S.A.4. Kurowski, Paul, Finite Element Analysis forDesign Engineers, SAE International, War-rendale, Pa, 2004.5. Townsend, Dennis, Dudleys Gear Handbook,McGraw-Hill, 2 Sub Edition, September 1991.
