1、06FTM06An Analytical Approach to the Prediction ofMicropitting on Case Carburised Gearsby: D. Barnett, Renold Gears, J.P. Elderkin, MTM Precisionand W. Bennett, MoD (Navy)TECHNICAL PAPERAmerican Gear Manufacturers AssociationAn Analytical Approach to the Prediction ofMicropitting on Case Carburised
2、GearsDave Barnett, Renold Gears, John P. Elderkin, MTM Precisionand William Bennett, MoD (Navy)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.AbstractMicropittingisonearea
3、ofgearfailurethathasbecomemorepredominantoverrecentyears,mainlybecauseofitseffectongearnoiseandtransmissionerror.Thispaperwilloutlineanapproachtoanalysingmicropittingbylookingatthecriticalfactorsforagivengeardesign.Apracticalcalculationprocedure,whichincorporatesathree-dimensional spring model, was
4、used to predict the micropitting wear rate and the position that wearwould take place on test gear pairs. Case studies have been included that directly compare the predictedlevels of micropitting with those actually measured. A simplified formulation suitable for manual calculationswill also be disc
5、ussed.Copyright 2006American Gear Manufacturers Association500 Montgomery Street, Suite 350Alexandria, Virginia, 22314October, 2006ISBN: 1-55589-888-21An Analytical Approach to the Prediction of Micropitting on Case CarburisedGearsDave Barnett, Renold Gears, John P. Elderkin, MTM Precisionand Lt. Wi
6、lliam Bennett, MoD (Navy)IntroductionMicropitting is one area of gear failure that has be-come more predominant over recent years, mainlybecause of its effect on generated noise and trans-mission error. It is also possible that micropittingcouldbeconsideredastheprecursortootherfailuremechanisms. At
7、the present time, practical testingis being undertaken by many organisations acrossthe world including: - the British Gear Association(BGA), the AmericanGear ManufacturersAssocia-tion (AGMA), FZG and others. This work has pri-marilybeentargetedatthedeterminationoftheme-chanicsofmicropittingandhowtor
8、educeorpreventit.Previously, the use of sophisticated lubricants, withtheir appropriate additive packages, has been themainmethodofattemptingtocontrolthegenerationand propagation of micropitting. However, the ad-vent of superior manufacturing methods and im-provements in the quality and cleanliness
9、of steels,has allowed the design engineer to significantly in-crease the gear tooth loading. This factor has indi-rectlyledtothefactthatmicropittingisnowcurrentlyseen as a major problem in commercial gears. Theprimary author has been involved with gear testingover a number of years and this has enab
10、led him tocompileamathematicalmodelthatpredictsthelike-lihood of micropitting occurring. The model is flex-ible enough to allow calculation of the various pa-rameters, under specified load conditions, for agiven designwith orwithout involuteand leadmodi-fications. At present, the procedures include
11、cal-culations for lubricant viscosity and temperature,but not those for oil chemistry. Once the actual ef-fects of the additive packages are known these canbe incorporated into the model.CalculationsThepracticalcalculationprocedureutilisesathree-dimension model that is based on spring theory. Itwas
12、originally developed for the specific purpose ofanalysing bending strength and noise in high con-tact-ratiospurgears.Itwaslatermodifiedtoincludehelical gears. Specifics of the initial work were firstpublished in 1986 and updated in 1994. The modelitself functions by mathematically dividing the sur-f
13、ace of the tooth into nodes, based upon the basepitch of the gear pair to be considered. Contact isassumedtotakeplacealongthelineofaction(LOA),althoughinpracticethisis incorrect.Howev-er, measurement of the true stresses on actualgears with tooth modifications has shown that theerrors are insignific
14、ant. The analysis also checksthe approach and recession of the gear mesh forany premature engagement or delayed disengage-ment. These factors have been shown to changethe load distribution between meshing teeth due todeflectionunderload.Themodelcalculatesthenor-mal tooth force exerted on each tooth
15、as it movesthroughmesh.Thisisinfluencedbythegeardesign,involute and lead modification, tooth stiffness andapplied load.The calculated example (Figure 1) illustrates themagnitude of load sharing on a standard FZG Ctype gear (which has no involute or lead modifica-tions) as it rolls through mesh. The
16、resultant loadsshown to the left and right of the “length of theoreti-calengagement”areduetoprematureengagementand delayed disengagement. These factors effec-tively increase the profile contact ratio.Figure 1. Load Sharing - Standard FZG TestGear2Using the stiffness, the selected increments alongthe
17、 LOA and any tooth modifications, the loadintensityper mmof facewidth iscalculated overthetotal tooth surface for each node point.Figure 2 depicts the load intensity over the entirecontact area. The analysis shows that prematureengagement and delayed disengagement exist onthis gear(as shownpreviousl
18、y). Theblack zonede-pictszeroloadintensity.Theloadintensitygraduallyincreases, as indicated by the various shades ofgrey until it reaches a maximum (depicted by thewhite band). The yellow lines mark the limits oftheoretical contact and the grey areas above andbelow these lines show the zones of pote
19、ntial con-flict.Figure 2. Load Intensity - Standard FZG TestGearThe calculation procedure considers each individu-al node point to be equivalent to a roller bearingwith its own individual radius of curvature, slidingvelocity, entrainment velocity and slide roll ratio.Hence, knowing the applied torqu
20、e, it is possible tocalculate the contact stress and the oil film thick-ness that is generated. The empirically derivedanalysis has been corroborated against actualgeartestsanditcanbeconcludedthatmicropittingispri-marily dependent on the following factors:1. Contact stress2. Sliding velocity3. Oil f
21、ilm thickness4. Oil temperature5. Slide roll ratio (SRR)6. Surface finish (the RMS parameter Ra is usedin the calculations at present, but this may re-quire modification)7. Surface hardness8. Number of contact cycles9. Direction of sliding and the time that each sur-face is in contact with the corre
22、sponding gear inthe pair.10.Oil additivepackage (atpresent thisis notincor-porated in the calculations as more work is re-quired to define these parameters)Description of the TestTesting was commissioned by the MoD (Navy) andconductedatQinetiQ,aspartoftheBGAsProject6programofworkintothe“understandin
23、gofmicropit-ting”.Thissegmentoftheworkconsistedoftrialsonstandard FZG C type spur gears, as well as modi-fied C type spur gears. The modified gear setswere calculated to precisely defined project specifi-cations and were manufactured by FZG. Two oilswere considered for the work program, one with ami
24、cropitting additive and the second without. Simi-lar trials were also conducted (in parallel) using aPCS (3-roller type) disc-testing machine.Analysis of the Standard FZG GearsAsstatedpreviously,theanalysisdoesnotconsidertheeffectsofoilchemistryatpresent.Hencethefol-lowing examples have been derived
25、 from the geartest results utilising a lubricant without micropittingadditives. The trials were conducted with an oilsump temperature of 50C.Figure 3 graphically represents the predicted ero-sionasthegearprogressedthroughtheloadstages(LS)5to10andontotheendurancelevels.UptoLS10, erosion of the tooth
26、surface due to micropittingcan be seen in the dedendum portion of the toothand is concentrated at the start of active profile(SAP).Duringtheendurancephasesofthetest,themaximum erosion changed to a point close to thelowestpointofsingletoothcontact. Theseobserva-tions suggest that this is due to prema
27、ture engage-ment and can be directly attributed to the lack of tipand root relief on the standard FZG C type gears.The tip of the mating gear would appear to contactthe flank of the test gear above the SAP. This pre-matureengagementresultedinhighcontactstress,even for small loads, which could be as
28、much asfour (4) times higher than that normally anticipated.As the micropitting erosion progressed, the erosion3reduced the level of premature engagement. This,in turn, reduced the contact stress and could slowdowntherateofmicropittingerosion,ortransferittoa different point on the tooth.LS 5LS 6LS 7
29、LS 8LS 9LS 10LS 8ELS 10EFigure 3. LS 5 to LS 10 and EnduranceStandard FZG Test GearAnalysis of the Modified FZG C typegearsThemodifiedCtypegearswerere-designedstan-dard FZG gears with a 0.038 mm tip relief, startingjust above the highest point of single tooth contact.Theamountoftipreliefwas chosensu
30、ch thatundera torque level of LS10,premature engagementwasjust avoided.As can be seen in Figure 4, the prediction indicatedthat, with tip relief, the maximum erosion due to mi-cropitting would occur just below the lowest point ofsingle tooth contact. In the case of the standardgear, this would have
31、been at the SAP. Similarly, onthe modified gear, the actual predicted depth of theerosion due to micropitting was also reduced whencompared to the standard gear. The measured re-sults, for both depth and position, on the actual testgears gave a good correlation to the predictedvalues.LS 5LS 6LS 7LS
32、8LS 9LS 10LS 8ELS 10EFigure 4. LS 5 to LS 10 and EnduranceModified FZG Test GearFigure 5. Standard FZG at end of Load Stage10 Actual / Predicted.Figure 6.Standard FZG at end of theEndurance Stages Actual / Predicted.4Figure 7. Modified FZG at end of Load Stage10 Actual / Predicted.Comparingtheresult
33、softheStandardandModifiedFZG gears: It can be noted that, during LS 5 to 10,thelevelofmicropitting erosiondeveloped amagni-tude of root relief of a similar size to the tip relief onthe modified gears. Once the level reached wasapproximately0.04mm,the positionof themicropit-tingerosionmovedtoapproxim
34、atelythesamepointon the tooth as seen on the modified gears. The re-sults of these tests indicated that if the correct levelofinvolutemodificationhadbeenappliedatthegeardesign stage, it could have reduced and in somecases eliminated micropitting altogether.Analysis has taken place on the gears produ
35、ced forAGMA, which were tested for pitting but also exhib-ited micropitting. These gears not only have profilemodification,butalsoleadcrowning.Theresultsarecontained in Appendix 1.Similarly, an analysis has been performed on ahelical gear set. Again, an example is shown inAppendix 1.Derivation of th
36、e Calculation ProceduresThe following micropitting equation was empiricallyderivedbased onthe observationsfrom actualgearand roller testing. It was found that the level of mi-cropitting erosion was proportional to the localisedcontactstress,numberofcyclesandslidingvelocity(at the point of considerat
37、ion). It was also found tobe inversely proportional to the surface hardnessand lambda ratio (oil film thickness/surface rough-ness). The actual tests on gears and rollers indi-cated that the slide roll-ratio had a significant effectand this was also included in the calculation proce-dure.Significant
38、ly,itwasfoundthatitwasdifficulttoobtain micropitting with aslide roll-ratioof lessthanapproximately 40%. It was further noted that theerosion due to micropitting was more dominant inthededendumportionof thetooth ofboth thepinionand gear. It was concluded that this was possiblydue to the motion of th
39、e interacting tip of the pinionas it moved across the flank of its mate. As a result,a retardation factor was also included such that:Retard =1 Z12 Z2 (1)Where:1 = Radius of curvature of flank 1 (gear 1)Z1 = Number of teeth in gear 12 = Radius of curvature of flank 2 (gear 2)Z2 = Number of teeth in
40、gear 2Afactorfortherateofmicropittingwasalsoincludedto allow for the possible use with gear sets madefrom differing materials.The results of the early tests appeared to indicatethat there was a contact stress threshold belowwhich micropitting would not occur.It is also believed that micropitting wil
41、l not normallyoccur once the lambda ratio () exceeds a factor of3.Aswitchhasbeenincludedtopreventcalculationonce these conditions are met.The resulting equation for micropitting erosion is asfollows:Mp:= XMPrateCyvpnHUsRahUsUe2Retard(2)Where:MPrate= Rate of micropitting erosion per cycleCy = No of c
42、yclesVpn = Vickers hardnessH1= Localcontactstressatpoint1(startofengagement)Hp1= Local contact stress at point 1 (forpre-engagement)US1= Sliding velocity at point 1 (m/sec)Ra = Mean surface roughness of the mat-ing surfacesh?= Oil film thicknessUe1= Entrainment velocityRetard = Theratioofslidingofon
43、esurfaceoverthe otherAs indicated above, X is a switch (atpresent) andisdependent on the ratio. For the purposes of thispaper,Xcanbe either1 or0 andis currentlyset to0if the formulation 3 is satisfied. It is envisagedthat, in the future, this could be utilised as a5modification factor dependent on t
44、he oil additivepackage used.Significantly more work has still tobe undertakentodetermine the exact relationship between micropit-ting and contact stress, hardness, sliding velocity,viscosity etc. However, this can only realistically beaccomplished with practical testing on disc/ rollertest rigs. To
45、date, many different spur and helicalgear sets have been analysed (from physical testsand field failures), with good correlation to the cal-culation procedures described in this paper.It is pertinent to point out that when calculating themicropitting erosion of the gear surface it is neces-sary to a
46、dd the erosion from premature engage-menttothatofthenormalgearoperation.Toquan-tify if premature engagement exists, the obviouspoints to check are the start of contact, lowest pointof single tooth contact, highest point of single toothcontact and end of contact as shown in appendix 2.However, these
47、may not be the points of maximumerosion. The proposed simplified analysis can beadapted for use with helical gears and gears withleadcrowning.Althoughtheactualmeshstiffnessatthe point of consideration has been used, it is pos-sibletoperformthe calculationsassuming thetoothhas constant stiffness.Micr
48、opitting on the Pinion at the start ofengagement, when premature engagement existsMp11:= XMPrateCyVpnHp1Us1Rahp1Us1Ue12(3)Micropitting on the Pinion at the start of engage-ment: Retard + Mp11Mp11:= XMPrateCyvpnH1Us1Rah1Us1Ue12(4)MicropittingontheGearat thestart ofengagement:Mp12:=XMPrateCyvpnH1Us1Ra
49、h1Us1Ue121Retard(5)Further ExamplesAppendix2includesasimplifiedcopyofthecalcula-tionroutine,todemonstrate howthis procedurecanbe used to manually access the gear pair for micro-pitting damage at the design stage. The actual stiff-ness values have used at the mesh points. Howev-er, it is possible to assume that the tooth stiffness isconstant,inordertosimplifythecalculations,togiveanapproximateindicationofthepossibilityofmicro-pitting occurring. In the case where premature en-gagement exists, the top
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