1、11FTM12AGMA Technical PaperThe Application of theFirst InternationalCalculation Method forMicropittingBy U. Kissling, KISSsoft AGThe Application of the First International Calculation Methodfor MicropittingDr. Ulrich Kissling, KISSsoft AGThe statements and opinions contained herein are those of the
2、author and should not be construed as anofficial action or opinion of the American Gear Manufacturers Association.AbstractThe first edition of the international calculation method for micropitting, ISO TR 15144-1:2010, was justpublished last December. It is the first official international calculati
3、on method to check for the risk ofmicropitting ever published. Years ago, AGMA published a method for the calculation of the specific oil filmthickness containing some comments about micropitting, and the German FVA published a calculationmethodbasedonintensiveresearchresults. TheFVAandtheAGMAareclo
4、setotheISOTR. Howeverthecalculation of the micropitting safety factors is new.In this paper the ISO TR 15144 will be explained briefly. The technical report presents two calculation rules,method A and B. Method A needs as input the Hertzian pressure on every point of the tooth flank. This isbasedona
5、naccuratecalculationofthemeshingofthegearpairconsideringtoothandshaftdeflectionstogetthe load distribution over the flank line in every meshing position. Such a calculation is very time consumingwhenusinganFEMtool. Alternativelyspecificanalyticalprogramswhicharecommerciallyavailable(suchasLDP, RIKOR
6、, KISSsoft) may be used. In either case, the use of Method A without such an advanced tool isimpossible. Method B is much simpler; the load distribution is defined for different cases as spur or helicalgears,withandwithoutprofilemodifications. MethodBcanbeprogrammedasstandalonesoftware,maybeeveninEx
7、cel. However,arestriction,whicharoseinthelastmeetingoftheISOworkinggroupresponsibleforthistopic,limitsconsiderablytheapplicationofmethodB:Ifgearswithprofilemodificationhavetobeverified,the tip relief Camust correspond exactly to a proposed value Ceff. If not, the method for gears without anyprofile
8、modifications has to be used. As modern gear design implies profile modifications of different kinds,this is a critical limitation for the application of method B in ISO TR 15144.Copyright 2011American Gear Manufacturers Association1001 N. Fairfax Street, 5thFloorAlexandria, Virginia 22314October 20
9、11ISBN: 978-1-61481-011-73 11FTM12The Application of the First International Calculation Method for MicropittingDr. Ulrich Kissling, KISSsoft AGIntroductionThe first edition of the international calculation method for micropitting, ISO TR 15144-1:2010, was justpublishedlastDecember. Itisthefirstoffi
10、cialinternationalcalculationmethodtocheckfortheriskofmicropit-tingeverpublished. Years ago, AGMA publisheda methodfor thecalculation ofthe specificoil filmthicknesscontaining some comments about micropitting, and the German FVA published a calculation method basedon intensive research results. The F
11、VA and the AGMA are close to the ISO TR. However the calculation ofthe micropitting safety factors is new.An ISO TR is a Technical Report, which normally after3 yearswill becomean internationalStandard. Duringthe last years, micropitting has become a very important topic in gear box design, specific
12、ally for wind tur-bines. Therefore, even before the official publication, the evaluation of the risk of micropitting based on ISO15144 is requested by some authorities such as for example the Germanische Lloyd.In this paper the ISO TR 15144 will be explained briefly. The technical report presents tw
13、o calculation rules,method A and B. Method A needs as input the Hertzian pressure on every point of the tooth flank. This isbasedonanaccuratecalculationofthemeshingofthegearpairconsideringtoothandshaftdeflectionstogetthe load distribution over the flank line in every meshing position. Such a calcula
14、tion is very time consumingwhenusinganFEMtool. Alternativelyspecificanalyticalprogramswhicharecommerciallyavailable(suchasLDP, RIKOR, KISSsoft) may be used. In either case, the use of Method A without such an advanced tool isimpossible. Method B is much simpler; the load distribution is defined for
15、different cases as spur or helicalgears,withand withoutprofile modifications. MethodB canbe programmedas standalonesoftware, maybeeveninExcel. However,arestriction,whicharoseinthelastmeetingoftheISOworkinggroupresponsibleforthistopic,limitsconsiderablytheapplicationofmethodB:Ifgearswithprofilemodifi
16、cationhavetobeverified,the tip relief Camust correspond exactly to a proposed value Ceff. If not, the method for gears without anyprofile modifications has to be used. As modern gear design implies profile modifications of different kinds,this is a critical limitation for the application of method B
17、 in ISO TR 15144.The risk of micropitting is highly influenced by profile and flank line modifications. A new software tool canevaluate the risk of micropitting for gears by automatically varying different combinations of tip reliefs, otherprofilemodifications, andflanklinemodifications,incombinatio
18、nwith differenttorque levels,using methodA.The user can define the number of steps for variation of the amount of modification (for example tip relief Cafrom30to70mmin4steps,crowningvalueCform10to40mm). ThenallpossiblecombinationsCa=30(withC=10,20,30,40),Ca=40(.),etcarecheckedcombinedwithdifferentus
19、erdefinedtorquelevels. Anymodi-ficationsincludingflank twist,arc-like profilemodifications, etc.,can becombined. The resultis presentedina table, showing the safety factor against micropitting for different subsets of profile/flank modifications,depending on the torque level. Additionally peak-to-pe
20、ak-transmission-error, maximum Hertzian stress,wear etc., is documented. This is a tool to show the possibilities to reduce the micropitting risk with profilemodifications and is very helpful for designing an optimum gear modification for varying torque levels.Three different gear sets with micropit
21、ting problems, example “D” (spur gear, module 10.93 mm, Z 18:18),example“U”(helicalgear=19.578,module4.5mm,Z33:34)andexample“F”(helicalgear=9,module30 mm, Z 19:76) will be discussed.Micropitting as a phenomenonMicropittingiswellexplainedinISOTR151441. “Micropittingisaphenomenonthatoccursin Hertziant
22、ypeof rolling and sliding contact that operates in elastohydrodynamic or boundary lubrication regimes.4 11FTM12Micropitting is influenced by operating conditions such as load, speed, sliding, temperature, surfacetopography, specific lubricant film thickness and chemical composition of the lubricant.
23、 Micropitting is morecommonly observed on materials with a high surface hardness.Micropitting is the generation of numeroussurfacecracks. Thecracks growat ashallow angleto thesurfaceformingmicropits. Themicropitsaresmallrelativetothesizeofthecontactzone,typicallyoftheorder10 - 20mm deep. The micropi
24、ts can coalesce to produce a continuous fractured surface which appears as a dull,matte surface during unmagnified visual inspection. See Figure 1.Micropitting is the preferredname forthis phenomenon,but ithas alsobeen referredto asgrey staining,greyflecking, frosting and peeling. Micropitting may s
25、top but if it continues to progress, it may result in reducedgeartoothaccuracy,increaseddynamicloadsandnoise. If itdoes notstop andcontinues topropagate itcandevelop into macropitting and other modes of gear failure.”Classicpitting(alsocalledmacropitting)isacompletelydifferentphenomenon. Inthiscaset
26、hecracksstartina certain depth under the surface, where shear stress due to Hertzian pressure is highest. This effect is wellexplained in the ISO 6336-2 standard.Figure 1. Traces of micropitting at the root of the flank of the pinion (Photo: CMD, France); andcorresponding result of safety against mi
27、cropitting (Method A). Curves for left side, middle andright side of facewidth. Gear example “F” (Helical gear, mn=30 mm, =9, Z 19:76).5 11FTM12ISO Technical Report 15144The ISO Technical Report 15144-1 provides principles for the calculation of the micropitting load capacity ofcylindrical involute
28、spur and helical gears with external teeth. The basis for the calculationof themicropittingload capacity of a gear set is the model of the minimum operating specific lubricant film thickness in the con-tact zone, GF,min. For the calculation of the risk of micropitting, a safety factor Sis defined as
29、 ratio betweenGF,minand the permissible specific film thickness GFP.The permissible specific lubricant film thickness GFPis calculated from the critical specific lubricant filmthicknessGFTwhichistheresultofanystandardizedtestmethodapplicabletoevaluatethemicropittingloadcapacity of lubricants or mate
30、rials by means of defined test gears operated under specified test conditions.GFTisafunctionofthetemperature,oilviscosity,baseoilandadditivechemistryandcanbecalculatedinthecontactpointofthedefinedtestgearswheretheminimumspecificlubricantfilmthicknessisfoundandforthetest conditions where the failure
31、limit concerning micropitting in the standardized test procedure has beenreached. The most widely used test procedure is the FVA-FZG - micropitting test 2. Several oil providersalready document the micropitting load stage following the FVA test in their oil specification.The ISO TR 15144, part 1, wa
32、s published in December 2010. Part 1 contains the basic calculation method.TheISOcommitteeresponsibleforthistopiciscurrentlyworkingonpart2,whichwillcontain someexamplesof gear sets having micropitting. Part2 willbe veryhelpful tounderstand betterthe applicationof thecalcula-tion rules as described i
33、n part 1.The Technical Report presents two calculation rules, method A and B. The Technical Report stipulates, thatformethodAexperimentalinvestigationsorserviceexperiencerelatingtomicropittingonrealgearsareused.This is not very practical when designing new gears. As it will be shown in part 2 of the
34、 Technical Report, amore practical approach when using method A, is to first calculate the load distribution over the flank line inevery meshing position. Than the Hertzian pressure on every point of the tooth flank, based on an accuratecalculationofthemeshingofthegearpair,consideringtoothandshaftde
35、flections. Thisisamostcomplicatedcontact analysis problem, which could be solved using a FEM tool. However such a calculation is very timeconsumingwhenusingaFEAtool. Alternatively, specificcommerciallyavailableanalyticalprogramsmaybeused. OncethelocalHertzianpressureandtheslidingvelocityaredetermine
36、d,thelocalspecificlubricantfilmthicknessGFis calculated using the equations of the Technical Report.TheuseofmethodBismuchsimpler;theHertzianpressureisdefinedbyequationsforsuchcasesasspurorhelical gears, with and without profile modifications. The equations for the calculation of the local pressurean
37、d velocities are based on an unmodified involute tooth form. The calculation is performed for some of thecriticalpointsinthetoothmeshingcycle,whicharepointsA,AB,B,C,D,DEandE(Figure 2)1,3. Inthesepoints, the specific lubricant film thickness GFis then calculated.Research on micropitting is relatively
38、 new, therefore the Technical Report states, that “there are many influ-ence parameters, such as surface topology, contact stress level, and lubricant chemistry. Whilst thesepara-metersareknowntoeffecttheperformanceofmicropittingforagearsetitmustbestatedthatthesubjectarearemainsatopicofresearchandas
39、suchthesciencehasnotyetdevelopedtoallowthesespecificparametersto be directly included in the calculation methods. Also the correct application of tip and root relief (involutemodification) has been found to greatly influence micropitting therefore application of the suitable valuesshould be applied.
40、Surface finish is another crucial parameter and at present Ra is used but other aspects such as Rz orskewness have been observed to have significant effects which could be reflected in the finishing processapplied.”6 11FTM12Figure 2. Significant points on the path of contact, where micropitting has
41、to be checked, whenusing ISO 15144, method B. (Point A: Begin of contact, SAP; point E: End of contact, EAP.)Overview on the calculation procedureCalculation of the safety factor against micropittingFor the calculation of the risk of micropitting, a safety factor Sis defined as follows:(1)S=GF, minG
42、FP S,minGF,min=min(GF,Y) is the lowest specific film thickness over the meshing cycle;GFPis the permissible specific film thickness; it may be determined by different methods;S,minis the required safety factor, to be agreed on between supplier and purchaser of the gearbox.The lowest specific film th
43、ickness (GF,min) is defined as the minimum of all locally calculated film thicknessvalues GF,Yas per equation (2). The permissible film thickness GFPis calculated as per equation (5). Theratiobetweenthesetwovalues(GF,min/GFP)resultsinasafety factoragainst micropittingS,which thenhasto be equal or hi
44、gher than the required safety factorS,min. As the calculation method is quite new, and relat-ivelyfewknowndata pointsare available,the generalidea forthe interpretationof themicropitting safetySisto have a range between low and high risk limits:Safety S 2 Low risk of micropitting1 Safety S 2 Limited
45、 risk of micropittingSafety S25% 0.95Gas nitrided (HV 850) 1.50Induction - or flame hardened steel 0.65Through hardening steel 0.508 11FTM12Figure 3. Required specific film thickness, GFP, for mineral oil.The accurate way to get a value for the permissible specific lubricant film thickness is to use
46、 data of the oilperformancefromaFZGtestrig. Manyoilsaretestedonsuchatestrigwith gearstype FZGC-GF. In theoilspecificationyouwillthanfindthedeclaration: “Failureloadstage(SKS)formicropittingtestC-GF/8,3/90=n(n=510)”. TheSKSnumbercorrespondstoatorquelevel,atwhichthegearintherigwiththetestoilshowsmicro
47、pitting. If theSKSnumber of theoil isknown themicropitting calculationof thetest riggear isperformedwith:S Gear data as specified for the C-GF/8,3/90 test rig gear 2;S Torque and Hertzian pressure as specified by Table 2;S Oil data as viscosity, density;S Oil temperature according oilof the actual g
48、ear reducer (not the oil temperature used on the FZG testrig!). Note: It is recommended, that the FZG test should be performed with the same oil temperature asused in the gear reducer. But normally the FZG test is executed with 90C oil temperature. Thereforedata published by oil providers are valid
49、for 90C (if not otherwise declared).Table 2. Torque T1,line load Fbband corresponding Hertzian pressure on FZG test rig 2SKS number Torque T1(Nm) Line load Fbb(N/mm)Hertzian pressure at thepinion at point A (N/mm2)5 70.0 63.3 764.06 98.9 89.1 906.47 132.5 119.0 1047.68 171.6 153.7 1191.09 215.6 192.7 1333.010 265.1 236.3 1476.29 11FTM12ThecalculationofthetestgearwiththisinputdataisdoneforpointA,becausetheminimumspecificlubricantfilmthicknessfortheFZG”typeC”testgearisalwaysatpointA. Theresultingspecificlubricantfi
