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1、06FTM06 An Analytical Approach to the Prediction of Micropitting on Case Carburised Gears by: D. Barnett, Renold Gears, J.P. Elderkin, MTM Precision and W. Bennett, MoD (Navy) TECHNICAL PAPER American Gear Manufacturers Association Copyright American Gear Manufacturers Association Provided by IHS un
2、der license with AGMA Licensee=Boeing Co/5910770001 Not for Resale, 07/25/2008 02:31:54 MDTNo reproduction or networking permitted without license from IHS -,-,- An Analytical Approach to the Prediction of Micropitting on Case Carburised Gears Dave Barnett, Renold Gears, John P. Elderkin, MTM Precis
3、ion and William Bennett, MoD (Navy) The statements and opinions contained herein are those of the author and should not be construed as an official action or opinion of the American Gear Manufacturers Association. Abstract Micropittingisoneareaofgearfailurethathasbecomemorepredominantoverrecentyears
4、,mainlybecause ofitseffectongearnoiseandtransmissionerror.Thispaperwilloutlineanapproachtoanalysingmicropitting bylookingatthecriticalfactorsforagivengeardesign.Apracticalcalculationprocedure,whichincorporatesa three-dimensional spring model, was used to predict the micropitting wear rate and the po
5、sition that wear would take place on test gear pairs. Case studies have been included that directly compare the predicted levels of micropitting with those actually measured. A simplified formulation suitable for manual calculations will also be discussed. Copyright 2006 American Gear Manufacturers
6、Association 500 Montgomery Street, Suite 350 Alexandria, Virginia, 22314 October, 2006 ISBN: 1-55589-888-2 Copyright American Gear Manufacturers Association Provided by IHS under license with AGMA Licensee=Boeing Co/5910770001 Not for Resale, 07/25/2008 02:31:54 MDTNo reproduction or networking perm
7、itted without license from IHS -,-,- 1 An Analytical Approach to the Prediction of Micropitting on Case Carburised Gears Dave Barnett, Renold Gears, John P. Elderkin, MTM Precision and Lt. William Bennett, MoD (Navy) Introduction Micropitting is one area of gear failure that has be- come more predom
8、inant over recent years, mainly because of its effect on generated noise and trans- mission error. It is also possible that micropitting couldbeconsideredastheprecursortootherfailure mechanisms. At the present time, practical testing is being undertaken by many organisations across the world includi
9、ng: - the British Gear Association (BGA), the AmericanGear ManufacturersAssocia- tion (AGMA), FZG and others. This work has pri- marilybeentargetedatthedeterminationoftheme- chanicsofmicropittingandhowtoreduceorprevent it. Previously, the use of sophisticated lubricants, with their appropriate addit
10、ive packages, has been the mainmethodofattemptingtocontrolthegeneration and propagation of micropitting. However, the ad- vent of superior manufacturing methods and im- provements in the quality and cleanliness of steels, has allowed the design engineer to significantly in- crease the gear tooth loa
11、ding. This factor has indi- rectlyledtothefactthatmicropittingisnowcurrently seen as a major problem in commercial gears. The primary author has been involved with gear testing over a number of years and this has enabled him to compileamathematicalmodelthatpredictsthelike- lihood of micropitting occ
12、urring. The model is flex- ible enough to allow calculation of the various pa- rameters, under specified load conditions, for a given designwith orwithout involuteand leadmodi- fications. At present, the procedures include cal- culations for lubricant viscosity and temperature, but not those for oil
13、 chemistry. Once the actual ef- fects of the additive packages are known these can be incorporated into the model. Calculations Thepracticalcalculationprocedureutilisesathree- dimension model that is based on spring theory. It was originally developed for the specific purpose of analysing bending st
14、rength and noise in high con- tact-ratiospurgears.Itwaslatermodifiedtoinclude helical gears. Specifics of the initial work were first published in 1986 and updated in 1994. The model itself functions by mathematically dividing the sur- face of the tooth into nodes, based upon the base pitch of the g
15、ear pair to be considered. Contact is assumed to take place along the line of action (LOA),althoughinpracticethisis incorrect.Howev- er, measurement of the true stresses on actual gears with tooth modifications has shown that the errors are insignificant. The analysis also checks the approach and re
16、cession of the gear mesh for any premature engagement or delayed disengage- ment. These factors have been shown to change the load distribution between meshing teeth due to deflectionunderload.Themodelcalculatesthenor- mal tooth force exerted on each tooth as it moves throughmesh.Thisisinfluencedbyt
17、hegeardesign, involute and lead modification, tooth stiffness and applied load. The calculated example (Figure 1) illustrates the magnitude of load sharing on a standard FZG C type gear (which has no involute or lead modifica- tions) as it rolls through mesh. The resultant loads shown to the left an
18、d right of the “length of theoreti- calengagement”areduetoprematureengagement and delayed disengagement. These factors effec- tively increase the profile contact ratio. Figure 1. Load Sharing - - Standard FZG Test Gear Copyright American Gear Manufacturers Association Provided by IHS under license w
19、ith AGMA Licensee=Boeing Co/5910770001 Not for Resale, 07/25/2008 02:31:54 MDTNo reproduction or networking permitted without license from IHS -,-,- 2 Using the stiffness, the selected increments along the LOA and any tooth modifications, the load intensityper mmof facewidth iscalculated overthe tot
20、al tooth surface for each node point. Figure 2 depicts the load intensity over the entire contact area. The analysis shows that premature engagement and delayed disengagement exist on this gear(as shownpreviously). Theblack zonede- pictszeroloadintensity.Theloadintensitygradually increases, as indic
21、ated by the various shades of grey until it reaches a maximum (depicted by the white band). The yellow lines mark the limits of theoretical contact and the grey areas above and below these lines show the zones of potential con- flict. Figure 2. Load Intensity - - Standard FZG Test Gear The calculati
22、on procedure considers each individu- al node point to be equivalent to a roller bearing with its own individual radius of curvature, sliding velocity, entrainment velocity and slide roll ratio. Hence, knowing the applied torque, it is possible to calculate the contact stress and the oil film thick-
23、 ness that is generated. The empirically derived analysis has been corroborated against actualgear testsanditcanbeconcludedthatmicropittingispri- marily dependent on the following factors: 1. Contact stress 2. Sliding velocity 3. Oil film thickness 4. Oil temperature 5. Slide roll ratio (SRR) 6. Sur
24、face finish (the RMS parameter Ra is used in the calculations at present, but this may re- quire modification) 7. Surface hardness 8. Number of contact cycles 9. Direction of sliding and the time that each sur- face is in contact with the corresponding gear in the pair. 10.Oil additivepackage (atpre
25、sent thisis notincor- porated in the calculations as more work is re- quired to define these parameters) Description of the Test Testing was commissioned by the MoD (Navy) and conductedatQinetiQ,aspartoftheBGAsProject6 programofworkintothe“understandingofmicropit- ting”.Thissegmentoftheworkconsisted
26、oftrialson standard FZG C type spur gears, as well as modi- fied C type spur gears. The modified gear sets were calculated to precisely defined project specifi- cations and were manufactured by FZG. Two oils were considered for the work program, one with a micropitting additive and the second withou
27、t. Simi- lar trials were also conducted (in parallel) using a PCS (3-roller type) disc-testing machine. Analysis of the Standard FZG Gears Asstatedpreviously,theanalysisdoesnotconsider theeffectsofoilchemistryatpresent.Hencethefol- lowing examples have been derived from the gear test results utilisi
28、ng a lubricant without micropitting additives. The trials were conducted with an oil sump temperature of 50C. Figure 3 graphically represents the predicted ero- sionasthegearprogressedthroughtheloadstages (LS)5to10andontotheendurancelevels.UptoLS 10, erosion of the tooth surface due to micropitting
29、can be seen in the dedendum portion of the tooth and is concentrated at the start of active profile (SAP).Duringtheendurancephasesofthetest,the maximum erosion changed to a point close to the lowestpointofsingletoothcontact. Theseobserva- tions suggest that this is due to premature engage- ment and
30、can be directly attributed to the lack of tip and root relief on the standard FZG C type gears. The tip of the mating gear would appear to contact the flank of the test gear above the SAP. This pre- matureengagementresultedinhighcontactstress, even for small loads, which could be as much as four (4)
31、 times higher than that normally anticipated. As the micropitting erosion progressed, the erosion Copyright American Gear Manufacturers Association Provided by IHS under license with AGMA Licensee=Boeing Co/5910770001 Not for Resale, 07/25/2008 02:31:54 MDTNo reproduction or networking permitted wit
32、hout license from IHS -,-,- 3 reduced the level of premature engagement. This, in turn, reduced the contact stress and could slow downtherateofmicropittingerosion,ortransferitto a different point on the tooth. LS 5 LS 6 LS 7 LS 8 LS 9 LS 10 LS 8E LS 10E Figure 3. LS 5 to LS 10 and Endurance Standard
33、 FZG Test Gear Analysis of the Modified FZG C type gears ThemodifiedCtypegearswerere-designedstan- dard FZG gears with a 0.038 mm tip relief, starting just above the highest point of single tooth contact. Theamountoftipreliefwas chosensuch thatunder a torque level of LS10,premature engagementwas jus
34、t avoided. As can be seen in Figure 4, the prediction indicated that, with tip relief, the maximum erosion due to mi- cropitting would occur just below the lowest point of single tooth contact. In the case of the standard gear, this would have been at the SAP. Similarly, on the modified gear, the ac
35、tual predicted depth of the erosion due to micropitting was also reduced when compared to the standard gear. The measured re- sults, for both depth and position, on the actual test gears gave a good correlation to the predicted values. LS 5 LS 6 LS 7 LS 8 LS 9 LS 10 LS 8E LS 10E Figure 4. LS 5 to LS
36、 10 and Endurance Modified FZG Test Gear Figure 5. Standard FZG at end of Load Stage 10 Actual / Predicted. Figure 6.Standard FZG at end of the Endurance Stages Actual / Predicted. Copyright American Gear Manufacturers Association Provided by IHS under license with AGMA Licensee=Boeing Co/5910770001
37、 Not for Resale, 07/25/2008 02:31:54 MDTNo reproduction or networking permitted without license from IHS -,-,- 4 Figure 7. Modified FZG at end of Load Stage 10 Actual / Predicted. ComparingtheresultsoftheStandardandModified FZG gears: It can be noted that, during LS 5 to 10, thelevelofmicropitting e
38、rosiondeveloped amagni- tude of root relief of a similar size to the tip relief on the modified gears. Once the level reached was approximately0.04mm,the positionof themicropit- tingerosionmovedtoapproximatelythesamepoint on the tooth as seen on the modified gears. The re- sults of these tests indic
39、ated that if the correct level ofinvolutemodificationhadbeenappliedatthegear design stage, it could have reduced and in some cases eliminated micropitting altogether. Analysis has taken place on the gears produced for AGMA, which were tested for pitting but also exhib- ited micropitting. These gears
40、 not only have profile modification,butalsoleadcrowning.Theresultsare contained in Appendix 1. Similarly, an analysis has been performed on a helical gear set. Again, an example is shown in Appendix 1. Derivation of the Calculation Procedures The following micropitting equation was empirically deriv
41、edbased onthe observationsfrom actualgear and roller testing. It was found that the level of mi- cropitting erosion was proportional to the localised contactstress,numberofcyclesandslidingvelocity (at the point of consideration). It was also found to be inversely proportional to the surface hardness
42、 and 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 effect and this was also included in the calculation proce- dure.Significantly,itwasfoundthatitwasdifficultto obtain micropitting with aslide roll
43、-ratioof lessthan approximately 40%. It was further noted that the erosion due to micropitting was more dominant in thededendumportionof thetooth ofboth thepinion and gear. It was concluded that this was possibly due to the motion of the interacting tip of the pinion as it moved across the flank of
44、its mate. As a result, a retardation factor was also included such that: Retard = 1 Z1 2 Z2(1) Where: 1=Radius of curvature of flank 1 (gear 1) Z1=Number of teeth in gear 1 2=Radius of curvature of flank 2 (gear 2) Z2=Number of teeth in gear 2 Afactorfortherateofmicropittingwasalsoincluded to allow
45、for the possible use with gear sets made from differing materials. The results of the early tests appeared to indicate that there was a contact stress threshold below which micropitting would not occur. It is also believed that micropitting will not normally occur once the lambda ratio () exceeds a
46、factor of 3.Aswitchhasbeenincludedtopreventcalculation once these conditions are met. The resulting equation for micropitting erosion is as follows: Mp:= XMPrate Cy vpnHUsRa h Us Ue 2 Retard (2) Where: MPrate= Rate of micropitting erosion per cycle Cy= No of cycles Vpn= Vickers hardness H1= Localcon
47、tactstressatpoint1(startof engagement) Hp1= Local contact stress at point 1 (for pre-engagement) US1= Sliding velocity at point 1 (m/sec) Ra= Mean surface roughness of the mat- ing surfaces h?= Oil film thickness Ue1= Entrainment velocity Retard = Theratioofslidingofonesurfaceover the other As indic
48、ated above, X is a switch (atpresent) andis dependent on the ratio. For the purposes of this paper,Xcanbe either1 or0 andis currentlyset to0 if the formulation 3 is satisfied. It is envisaged that, in the future, this could be utilised as a Copyright American Gear Manufacturers Association Provided by IHS under license with AGMA Licensee=Boeing Co/5910770001 Not for Resale, 07/25/2008 02:31:54 MDTNo reproduction or networking permitted without license from IHS -,-,- 5 modification factor dependent on the oil additive package used. Significantly more work has