AGMA 930-A05-2005 Calculated Bending Load Capacity of Powder Metallurgy (P M) External Spur Gears《粉末合金外啮合直齿齿轮的计算抗弯承载力》.pdf

1、AGMAINFORMATIONSHEET(This Information Sheet is NOT an AGMA Standard)AGMA930-A05AGMA 930-A05AMERICAN GEAR MANUFACTURERS ASSOCIATIONCalculated Bending Load Capacity ofPowder Metallurgy (P/M) External SpurGearsiiCalculated Bending Load Capacity of Powder Metallurgy (P/M) ExternalSpur GearsAGMA 930-A05C

2、AUTION NOTICE: AGMA technical publications are subject to constant improvement,revision or withdrawal as dictated by experience. Any person who refers to any AGMAtechnicalpublicationshouldbesurethatthepublicationisthelatestavailablefromtheAs-sociation on the subject matter.Tablesorotherself-supporti

3、ngsectionsmaybereferenced. Citationsshouldread: SeeAGMA930-A05,CalculatedBendingLoadCapacityofPowderMetallurgy(P/M)ExternalSpur Gears,published bythe AmericanGear ManufacturersAssociation,500Montgom-ery Street, Suite 350, Alexandria, Virginia 22314, http:/www.agma.org.Approved January 19, 2005ABSTRA

4、CTThis information sheet describes a procedure for calculating the load capacity of a pair of powder metallurgy(P/M)externalspurgearsbasedontoothbendingstrength. Twotypesofloadingareconsidered: 1)repeatedloadingovermanycycles;and2)occasionalpeakloading. Inaseparateannex,italsodescribesanessentiallyr

5、everse procedure for establishing an initial design from specified applied loads. As part of the load capacitycalculations, there is a detailed analysis of gear teeth geometry. These have been extended to include usefuldetails on other aspects of gear geometry such as the calculations for defining g

6、ear tooth profiles, includingvarious fillets.Published byAmerican Gear Manufacturers Association500 Montgomery Street, Suite 350, Alexandria, Virginia 22314Copyright 2005 by American Gear Manufacturers AssociationAll rights reserved.No part of this publication may be reproduced in any form, in an el

7、ectronicretrieval system or otherwise, without prior written permission of the publisher.Printed in the United States of AmericaISBN: 1-55589-845-9AmericanGearManufacturersAssociationAGMA 930-A05AMERICAN GEAR MANUFACTURERS ASSOCIATIONiii AGMA 2005 - All rights reservedContentsPageForeword iv.1 Scope

8、 1.2 Definitions and symbols 1.3 Fundamental formulas for calculated torque capacity 34 Design strength values 45 Combined adjustment factors for strength 66 Calculation diameter, dc77 Effective face width, Fe88 Geometry factor for bending strength, J 89 Combined adjustment factors for loading 9.Bib

9、liography 78.AnnexesA Calculation of spur gear geometry features 13B Calculation of spur gear factor, Y 27.C Calculation of the stress correction factor, Kf37.D Procedure for initial design 39E Calculation of inverse functions for gear geometry 44F Test for fillet interference by the tooth of the ma

10、ting gear 46G Calculation examples 50.Tables1 Symbols and definitions 2.2 Reliability factors, KR73 Manufacturing variation adjustment 11.AGMA 930-A05 AMERICAN GEAR MANUFACTURERS ASSOCIATIONiv AGMA 2005 - All rights reservedForewordThe foreword, footnotes and annexes, if any, in this document are pr

11、ovided forinformational purposes only and are not to be construed as a part of AGMA InformationSheet 930-A05, Calculated Bending Load Capacity of Powder Metallurgy (P/M) ExternalSpur Gears.ThisinformationsheetwaspreparedbytheAGMAPowderMetallurgyGearingCommitteeas an initial response to the need for

12、a design evaluation procedure for powder metallurgy(P/M) gears. The committee anticipates that, after appropriate modification andconfirmationbasedonapplicationexperience,thisprocedurewillbecomepartofastandardgearratingmethodforP/Mgears. Assuch,itwillservethesamefunctionforP/Mgearsasthe rating proce

13、dure in ANSI/AGMA 2001-C95 for wrought metal gears. Toward this end,the design evaluation procedure described here closely follows ANSI/AGMA 2001-C95,withchangesmadeforthespecialpropertiesofP/Mmaterials,gearproportions,andtypesof applications. These design considerations have made it possible to int

14、roduce somesimplifications in comparison to the above mentioned standard.The first draft of AGMA 930-A05 was made in June 1996. It was approved by the AGMATechnical Division Executive Committee in January 2005.Suggestionsforimprovementofthisdocumentwillbewelcome. TheyshouldbesenttotheAmericanGearMan

15、ufacturersAssociation,500MontgomeryStreet,Suite350,Alexandria,Virginia 22314.AGMA 930-A05AMERICAN GEAR MANUFACTURERS ASSOCIATIONv AGMA 2005 - All rights reservedPERSONNEL of the AGMA Powder Metallurgy Gearing CommitteeChairman: H. Sanderow Management and2)occasion-al peak loading. This procedure is

16、to be used onprepared gear designs which meet the customarygear geometry requirements such as adequatebacklash, contact ratio greater than 1.0, and ade-quatetopland. Anessentiallyreverseprocedureforestablishing an initial design from specified appliedloads is described in annex D.1.1.2 Strength prop

17、ertiesFatigue strength and yield strength properties usedinthesecalculationsmaybetakenfromprevioustestexperience,butmay also bederived frompublisheddata obtained from standard tests of the materials.1.1.3 ApplicationThis procedure is intended for use as an initialevaluation ofa proposed designprior

18、topreparationof test samples. Such test samples might bemachinedfromP/MblanksormadefromP/Mtoolingbased on the proposed design after it passes thisinitial evaluation. Final acceptance of the proposeddesign should be based on application testing andnot on these calculations. If samples made fromtoolin

19、g fall short in testing, it may be possible to usethe same tooling for a design adjusted for greaterface width.1.1.4 LimitationsGearsmadefromallmaterialsandbyallprocesses,including P/M gears, may fail in a variety of modesother than by tooth bending. This information sheetdoes not address design fea

20、tures to resist theseother modes of failure, such as excessive wear andother forms of tooth surface deterioration.CAUTION: The calculated load capacityfrom thispro-cedureisnottobeusedforcomparisonwithAGMArat-ings of wrought metal gears, even though there aremany similarities in the two procedures.1.

21、2 Types of gearsThiscalculationprocedureisappliedtoexternalspurgears,thetypeofgearmostcommonlyproducedbythe P/M process.1.3 Dimensional limitationsThis procedure applies to gears whose dimensionsconform to those commonly produced by the P/Mprocess for load carrying applications:- Finest pitch: 0.4 m

22、m module;- Maximum active face width: 15 module, witha65mmmaximum;- Minimum number of teeth: 7;- Maximum outside diameter: 180 mm;- Pressure angle: 14.5 to 25.1.4 Gear mesh limitationsSome of the calculations apply only to meshingconditionsexpressedasacontactratiogreaterthanone and less than two. Th

23、is translates into therequirement that there is at least one pair ofcontacting teeth transmitting load and no more thantwo pairs.2 Definitions and symbols2.1 DefinitionsThe terms used, wherever applicable, conform toANSI/AGMA 1012-F90.AGMA 930-A05 AMERICAN GEAR MANUFACTURERS ASSOCIATION2 AGMA 2005 -

24、 All rights reserved2.2 SymbolsThe symbols and terms used throughout this infor-mation sheet are in basic agreement with thesymbols and terms given in AGMA 900-G00, StyleManual for the Preparation of Standards, Informa-tionSheetsandEditorialManuals,andANSI/AGMA1012-F90,GearNomenclature,Definitionsof

25、Termswith Symbols. In all cases, the first time that eachsymbol is introduced, it is defined and discussed indetail.NOTE: The symbols and definitions used in this infor-mation sheet may differ from other AGMA documents.The user should not assume that familiar symbols canbe used without a careful stu

26、dy of their definitions.The symbols and terms, along with the clausenumberswheretheyarefirstdiscussed,arelistedinalphabetical order by symbol in table 1.Table 1 - Symbols and definitionsSymbol Terms Units ReferenceCAOperating center distance mm Eq 24d Gear pitch diameter mm Eq 37dAGOperating pitch d

27、iameter of gear mm Eq 25dAPOperating pitch diameter of pinion mm Eq 24dcCalculation diameter mm Eq 1E Modulus of elasticity N/mm2Eq 38FeEffectivefacewidth mm Eq 1FoOverlapping face width mm Eq 26FxEach face width extension, not larger than m mm Eq 27Fxe1Effective face width extension at one end mm E

28、q 26Fxe2Effective face width extension at other end mm Eq 26fqmFactor relating to axis misalignment adjustment - - Eq 36fqvFactor relating to manufacturing variations adjustment - - Eq 37htWhole depth of gear teeth mm Eq 32J Geometry factor for bending strength - - Eq 28JtGeometry factor for bending

29、 strength under repeated loading - - Eq 1JyGeometry factor for bending strength under occasional peak loading - - Eq 2KBRim thickness factor - - Eq 31KfStressconcentrationfactorusedincalculatingbendinggeometryfactor,J- - 8.2KftStress correction factor for repeated loading - - Eq 29KfyStress correcti

30、on factor for occasional overloads - - Eq 30KLLife factor - - Eq 12KLRLoad reversal factor - - Eq 12KLyLife factor at 0.5104cycles - - Eq 13KmtLoad distribution factor for repeated loading - - Eq 31KmyLoad distribution factor for occasional overloads - - Eq 40KotOverload factor for repeated loads -

31、- Eq 31KoyOverload factor for occasional overloads - - Eq 40KRReliability factor - - Eq 12KsSize factor - - Eq 12KTTemperature factor - - Eq 12KtsCombined adjustment factor for bending fatigue strength - - Eq 1KtwCombined adjustment factor for repeated tooth loading - - Eq 1KvDynamic factor - - Eq 3

32、1KyYield strength factor - - Eq 21(continued)AGMA 930-A05AMERICAN GEAR MANUFACTURERS ASSOCIATION3 AGMA 2005 - All rights reservedTable 1 (concluded)Symbol Terms Units ReferenceKysCombined adjustment factor for yield strength - - Eq 2KywCombined adjustment factor for occasional peak loading - - Eq 2k

33、utConversion factor for ultimate strength to fatigue limit - - Eq 5m Module mm Eq 1mBBackup ratio - - Eq 32mctModifying factor due to tooth compliance for repeated loading - - Eq 35mcyModifying factor due to tooth compliance for occasional overloads - - Eq 41mwModifying factor due to tooth surface w

34、ear - - Eq 35NGNumber of teeth of gear - - Eq 24NPNumber of teeth of pinion - - Eq 24n Number of tooth load cycles - - Eq 14nuNumber of units for which one failure will be tolerated - - Eq 20qmAdjustment due to axis misalignment - - Eq 35qvAdjustment due to manufacturing variations - - Eq 35SbBearin

35、g span mm Eq 36SFSafety factor for bending strength - - Eq 31stDesign fatigue strength N/mm2Eq 1stGFatigue limit, full reversal, adjusted for G-1 failure rate N/mm2Eq 3stTG-10 failure rate fatigue limit (published data) N/mm2Eq 3stTGAdjustment in fatigue limit from G-10 to G-1 N/mm2Eq 3suGUltimate t

36、ensile strength, adjusted for G-1 N/mm2Eq 9suMMinimum ultimate strength listed in MPIF Standard 35 N/mm2Eq 10suTTypical ultimate strength (published data) N/mm2Eq 5suTGReduction in ultimate strength from typical to G-1 N/mm2Eq 9syDesign yield strength N/mm2Eq 2syGYield strength, adjusted for G-1 N/m

37、m2Eq 6syMMinimum yield strength listed in MPIF Standard 35 N/mm2Eq 7syTTypical yield strength (published data) N/mm2Eq 6syTGReduction in yield strength from typical to G-1 N/mm2Eq 6TtTorque load capacity for tooth bending under repeated loading Nm Eq 1TyTorque load capacity under occasional peak loa

38、ding Nm Eq 2tRRim thickness mm Eq 32VqTTooth-to-tooth composite tolerance (or measured variation) mm Eq 39vtPitch line velocity m/s Eq 39Y Tooth form factor - - Eq 283 Fundamental formulas for calculatedtorque capacityTwo types of loading have been identified in 1.1.1.Each has its own formula for ca

39、lculated torquecapacity,reflectingthecorrespondingcriticalmateri-al properties and other factors. To find the loadcapacity of a gear under the combined types ofloading, calculate the two torque values from theformulasandusethelowercalculatedvalue. Tofindthe overall load capacity of a pair of non-ide

40、nticalgears, or of all the gears in the drive train, thecalculated load capacity torque for each gear mustbe converted to a power value. This is done bymultiplying the torque value for each gear by thecorresponding gear speed, generally expressed asradiansperunittimeinterval. Thelowestofallthesepowe

41、rvaluesbecomesthecalculatedpowercapac-ity of the complete gear pair or drive train.AGMA 930-A05 AMERICAN GEAR MANUFACTURERS ASSOCIATION4 AGMA 2005 - All rights reserved3.1 Tooth bending under repeated loadingTt=stKtsdcFeJtm2000 Ktw(1)whereTtistorqueloadcapacityfortoothbendingun-der repeated loading,

42、 Nm;stis design fatigue strength, N/mm2(see4.1.2.1);Ktsis combined adjustment factor for bendingfatigue strength (see 5.1);dcis calculation diameter, mm (see clause 6);Feiseffectivefacewidth,mm(seeclause7);Jtis geometry factor for bending strength un-der repeated loading (see clause 8);m is module,

43、mm;Ktwis combined adjustment factor for repeatedtooth loading (see clause 9).3.2 Tooth bending under occasional peakloadingTy=syKysdcFeJym2000 Kyw(2)whereTyis torque load capacity under occasionalpeak loading, Nm;syis design yield strength, N/mm2;Kysis combined adjustment factor for yieldstrength;Ky

44、wis combined adjustment factor foroccasional peak loading;Jyis geometry factor for bending strengthunder occasional peak loading.4 Design strength valuesDesign strength values depend not only on the P/Mmaterial composition, and any heat treatment, butalso on the density achieved during compaction or

45、post-sintering repressing.4.1 Fatigue strength, stThe value for design fatigue strength can beobtained from alternate sources.4.1.1 Previous test experienceIf there has been previous successful experience inthelaboratoryorfieldtestingofgearsfromthesamematerialofsimilar density and processing,it may

46、bepossible to perform reverse calculations to arrive atan acceptable design fatigue strength. The valuederivedfromthisproceduremaybeoverlyconserva-tiveunlessthetestprogramincludedarangeofloadconditionsthatbracketedthelinebetweensuccess-ful operation and failure by repeated bending.4.1.2 Derived from

47、 published dataWhen suitable gear test data is not available,published data based on standard material testingmethodscanbeused,butonlyafteradjustmentsaremade to adapt the fatigue strength values to thedesign procedures of this information sheet. Theseprocedures are based on values that correspond to

48、the following conditions:a) number of test cycles of 107;b) test failure rates projected to “less than 1 in a100”, i.e., 1 percent or “G-1” failure rate;c) loadcyclingofzero-to-maximumload(toreflecttypical gear tooth load cycling).4.1.2.1 Data published as “typical fatigue limit”Such data for P/M ma

49、terials generally meet condi-tion(a)of4.1.2,butnotconditions(b)and(c). Valuescalled “typical” generally refer to test results with50% of the specimens falling below and 50% abovethe published value. This corresponds to a “G-50”failure rate, also known as mean fatigue life.Data published by the Metal Powder IndustriesFederation (MPIF) 1 has been determined as the90% survival stress fatigue limit, using rotatingbendingfatiguetesting. Thisfatigu