1、10FTM11AGMA Technical PaperPoint-Surface-Origin,PSO, MacropittingCaused by GeometricStress Concentration,GSCBy R.L. Errichello, GEARTECH,C. Hewette, Afton ChemicalCorporation and R. Eckert,Northwest Laboratories, Inc.Point-Surface-Origin, PSO, Macropitting Caused byGeometric Stress Concentration, GS
2、CRobert L. Errichello, GEARTECH, Charles Hewette, Afton Chemical Corporationand Rainer Eckert, Northwest Laboratories, 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.A
3、bstractPoint-Surface-Origin, PSO, macropitting occurs at sites of Geometric Stress Concentration, GSC, such asdiscontinuities in the gear tooth profile caused by micropitting, cusps at the intersection of the involute profileand the trochoidal root fillet, and at edges of prior tooth damage such as
4、tip-to-root interference. When theprofile modifications in the form of tip relief, root relief, or both are inadequate to compensate for deflection ofthe gear mesh, tip-to-root interference occurs. The interference can occur at either end of the path of contact,but the damage is usually more severe
5、near the start-of-active-profile, SAP, of the driving gear.An FZG-C gearset (with no profile modifications) was tested at load stage 9 and three pinion teeth failed byPSO macropitting. It is shown that the root cause of the PSO macropitting was GSC created by tip-to-rootinterference.Copyright 2010Am
6、erican Gear Manufacturers Association1001 N. Fairfax Street, Suite 500Alexandria, Virginia, 22314October 2010ISBN: 978-1-55589-986-83Point- Surface- Origin, PSO, Macropitting Caused by GeometricStress Concentration, GSCRobert L. Errichello, GEARTECH, Charles Hewette, Afton Chemical Corporation,and R
7、ainer Eckert, Northwest Laboratories, Inc.IntroductionStewart Way 1 first described what later becameknown as point-surface-origin, PSO, macropitting.The macropits are relatively shallow but large inarea. The fatigue crack grows from a surface originin a fan-shaped manner until thin flakes of materi
8、albreak out and form a triangular crater. The arrow-head-shaped crater points opposite to the directionof rolling (direction of load approach). Crackpropagation can extend over large portions of agear tooth. Way 1 also proposed the theory ofhydraulic-pressure-propagation to explain thegrowth of PSO
9、macropits. Lubricant viscosity is animportant parameter influencing PSO macropitting,and it has been shown 2 that low viscositylubricants promote PSO macropitting by hydraulic-pressure-propagation. PSO macropitting ispromoted by the combination of low viscositylubricant, low specific film thickness,
10、 and tangentialshear stresses from sliding 2. PSO macropittingcan originate from surface flaws such as:S Tip-to-root interferenceS Debris dentS Handling nickS Edge of macropittingS Edge of micropittingS Surface flaws from manufacturingS Surface non-metallic inclusionS Surface carbideS Corrosion pitT
11、his paper discusses PSO macropitting originatingfrom tip-to-root interference. If involute gear teethwere perfectly rigid and without manufacturingerrors they would begin contact at the ideal start-of-active-profile, SAP, point and end contact at theideal end-of-active-profile, EAP, point. However,r
12、eal gears are not rigid, and even without manufac-turing errors, tooth deflection causes the teeth tostart contact earlier than the ideal SAP, and endcontact later than the ideal EAP. In the areas ofextended contact at the ends of the path of contact agear tooth is loaded on its tip corner (intersec
13、tionbetween the tooth flank and tooth topland) and thecontact stresses are very high because ofgeometric stress concentration, GSC. Therefore,to avoid corner contact and the associated high con-tact stresses, it is common practice to design gearteeth with tip relief that is sufficient to compensatef
14、or tooth deflection and manufacturing errors.However, FZG type C test gears, FZG-C, spurgears are manufactured accurately but without tiprelief. Consequently, they inevitably have cornercontact when they are tested at high loads. FZG-Cgears are discussed in this paper because theydemonstrate the con
15、sequences of inadequate tiprelief.ObjectiveThis paper demonstrates how gears without tiprelief suffer tip-to-root interference that causesGSC and PSO macropitting.Corner contactFigure 1 shows the path of contact for FZG-C gearsthat was calculated with KISSsoft software 3. Itshows corner contact occu
16、rs when early contactoccurs between the gear tip and the pinion involuteat point A and continues along the gear tip circle topoint A on the line of action. The path of contactbetween points A and A is non-conjugate and isknown by many names such as:S Tip-to-root interferenceS Corner contactS Contact
17、 outside the normal path of contactS Early contactS Edge contactS Extended contactS Non-conjugate actionS Premature contactS Prolonged contactS Top contactS Tooth interference4GeardrivenPiniondriverFigure 1. Gear tip approaching pinion involuteMechanism of tip- to- root interferenceFigure 2 shows ho
18、w the gear tip corner approachesthe pinion involute along a trochoidal path that inter-sects the pinion involute at a point above the usualpinion SAP. Contact between the gear corner andthe pinion involute results in very high Hertzianstress especially if the gear has sharp corners at thetips of its
19、 teeth. The high stress and scraping actionof the gear corner undercuts the pinion involute byremoving the material shown shaded in Figure 2and plowing material toward the pinion root. Theintersection between the undercut and involuteforms a cusp on the pinion flank at point A.Inthispaper, damage ca
20、used by corner contact will becalled tip-to-root interference.GeardrivenPiniondriverFigure 2. Mechanism of tip-to-rootinterferenceContact on pinion cuspCorner contact undercuts the pinion involute andremoves the usual SAP (point A) and delays thecontact between the pinion and gear until they con-tac
21、t at point A onthelineofactionasshowninFigure 3. The edge contact that occurs on thepinion cusp causes GSC as shown by the localmaximum Hertzian stress shown in Figure 4.Figure 3. Contact on the pinion cuspFZG- C test gearsAn FZG-C gearset was tested at load stage 9 inaccordance with the FZG pitting
22、 test PT C/9/90 pro-cedure 4 except the oil temperature was set to120C. Table 1 gives the lubricant properties. Thelubricant prevented adhesive and abrasive wear.However, after only 60 hours, the test had to bestopped because macropitting occurred on teeth 1,9, and 15.5Angle of rotation, N/mm2250020
23、0015001000500- 2 5 - 2 0 - 1 5 - 1 0 - 5 0 5 1 5100Figure 4. Local maximum Hertzian stress at pinion cuspTable 1. Lubricant propertiesType Mineral oil including 325 Neutraland 650 Neutral Group IAdditives VI-improver, pour pointdepressant, mild S-P antiscuffViscosity at40C157.2 cStViscosity at100C18
24、.3 cStDamage caused by tip- to- rootinterferenceFigure 5 shows tooth number 1 of the FZG-C pinionwith damage caused by tip-to-root interference. Tothe unaided eye, the damage might appear as apolished line along the SAP, and it is often referredto as a “line of hard contact.” However, as will beshow
25、n, the damage in this example consists ofplastic deformation, micropitting, and PSO macro-pitting. In more severe cases the damage caninclude material transfer resulting from scuffing.Figure 5. Damage caused by tip-to-root interference on pinion6PSO macropittingFigure 6 is an enlarged view (scanning
26、 electronimage) of Figure 5 showing the largest PSO macro-pit that measures about 2 x 3.5 mm.Figure 7 is an enlarged view at the entrance of thePSO macropit, which initiated at the upper edge ofthe tip-to-root damage, corresponding to the cuspat point A shown in Figure 2. Below the cusp, thetip-to-r
27、oot damage produced a 0.5 mm high bandof plastically deformed material and a dense field ofmicropitting. All pinion teeth had similar tip-to-rootdamage, but in the short run time of 60 hours onlythree teeth developed relatively large PSOmacropits that in each case initiated at the cusp.Figure 6. Enl
28、arged view of PSO macropit on pinionFigure 7. Enlarged view at entrance of PSO macropit on pinion7Figures 5, 6, and 7 show there are many other PSOmacropits that have initiated at the cusp but havenot yet grown significantly. Figure 8 is an enlargedview at the exit of the PSO macropit. Original grin
29、dmarks can be seen above the macropit proving thatthere was no significant adhesive or abrasive wearon the pinion flanks.Figure 9 is an enlarged view at the tip of toothnumber 1. It shows micropitting caused by tip-to-root interference between the pinion tip and the gearroot. Original grind marks ar
30、e evident below themicropitting proving that there was no significantadhesive or abrasive wear on the pinion flanks.Figure 8. Enlarged view at exit of PSO macropit on pinionFigure 9. Enlarged view at tip of tooth 1 on pinion8Figure 10 shows a PSO macropit that occurred ontooth 15 that measures about
31、 1.8 x 2.8 mm. Twoother macropits can be seen initiating at the cusp(upper edge of the tip-to-root damage).Figure 11 shows a PSO macropit that occurred ontooth 9 that measures about 1.5 x 1.5 mm. At leasttwo other macropits can be seen initiating at thecusp (upper edge of the tip-to-root damage). Th
32、emicropitting within the band of tip-to-root interfer-ence is not as obvious in this light micrograph as it isin the other scanning electron images (Figures 6, 7,and 10). However, the abrasion within thetip-to-root interference and the original grind markson the flank are more obvious.Figure 10. PSO
33、 macropit on tooth 15 on pinionFigure 11. PSO macropit on tooth 9 on pinion9Gear tooth slidingFigure 12 shows the directions of the rolling (R) andsliding (S) velocities on the driving and driven gearteeth. Contact on the driver tooth starts near theroot of the tooth, rolls up the tooth, and ends at
34、 thetooth tip. Sliding is away from the driving gear pitch-line. Contact on the driven tooth starts at the toothtip, rolls down the tooth, and ends near the toothroot. Sliding is towards the driven gear pitchline.Hertzian fatigue cracks, either macropitting ormicropitting, that start at the gear too
35、th surfacegrow at a shallow angle to the surface, and grow op-posite to the slide directions. Consequently, asshown in Figure 12, the cracks converge near thepitchline of the driver and diverge near the pitchlineof the driven gear.Hydraulic pressure propagationGear teeth dedenda have negative slidin
36、g (directionof rolling velocity is opposite sliding velocity).Negative sliding is significant because it promotesHertzian fatigue by allowing oil to enter surfacecracks where it accelerates crack growth by thehydraulic-pressure-propagation mechanism firstproposed by Stewart Way 1 and verified manyti
37、mes by experiments such as Littmanns 2.Hertzian stress resulting from GSCGSC associated with contact on the pinion cuspcreates a Hertzian stress that is theoreticallyinfinite, but is actually limited to the yield strength ofthe pinion material. Therefore, the cusp plasticallydeforms and the GSC is r
38、educed. However,carburized gears have high yield strength, and eventhough subsequent cyclic stresses are elastic, thestresses are generally high enough to initiatemacropitting. Li et al. 5 tested FZG PT-C macro-pitting gears and found that in all cases PSOmacropits initiated at the cusp of the tip-t
39、o-rootdamage. Furthermore, they measured the radius ofthe cusp on several damaged teeth of a pinion andfound it averaged 1.54 mm. They assumed themating gear radius of curvature at point A was26.76 mm, and calculated the relative radius ofcurvature was 1.46 mm. For unworn teeth theycalculated a rela
40、tive radius of curvature of 6.26 mm.According to Hertzian theory, the difference inrelative radius of curvature doubles the Hertzianmaximum shear stress and reduces its depth to onlyhalf as deep. Consequently, the stress increaseresulting from GSC is very significant and it explainswhy PSO macropits
41、 initiate at the cusp.DrivenDriverFigure 12. Rolling, R, and sliding, S, directions10Jao et al. 6 tested FZG PT-C macropitting gearsand FZG GF-C micropitting gears, which are thesame in all respects except PT-C gears have atooth surface roughness of Ra = 0.3 mm, whereasGF-C gears have tooth surface
42、roughness of Ra =0.5mm. With PT-C gears, PSO macropits initiate atthe cusp formed by tip-to-root interference. In con-trast, the GF-C gears form a band of micropitting atthe SAP similar to PT-C gears, except it continuesto spread toward the pitchline until it forms a wideband of severe micropitting.
43、 PSO macropits initiateat the top of the micropitting band because of GSCcaused by the step in the tooth profile at the upperedge of the micropitting crater. This macropittingoccurs at a later time than with the PT-C gears. Theauthors concluded that the failure mechanism is dif-ferent for GF-C gears
44、 because their rougher sur-faces cause more severe micropitting that removesthe cusp at the SAP and thereby prolongs the mac-ropitting life.ConclusionsS The root cause of PSO macropitting is the GSCcaused by tip-to-root interference, or GSCcaused by edge discontinuities such as the edgeof a band of
45、micropitting.S Tip-to-root interference is caused by cornercontact that occurs in gears without adequate tiprelief.S Tip-to root interference undercuts the involuteprofile and creates a cusp on the active flank thatacts as a point of GSC.S With FZG PT-C gears, PSO macropits initiateat the cusp forme
46、d by tip-to-root interference.S With FZG GF-C gears, their rougher surfacescause more severe micropitting that removesthe cusp at the SAP and thereby prolongs themacropitting life until PSO macropitting occursnear the pitchline because of GSC caused bythe step in the tooth profile at the upper edge
47、ofthe micropitting crater.S PSO macropitting is promoted by the combina-tion of low viscosity lubricant, low specific filmthickness, and tangential shear stresses fromsliding.S Negative sliding promotes rapid growth of PSOmacropitting by the hydraulic-pressure-propagation mechanism.References1. Way,
48、 S., Pitting Due to Rolling Contact, ASMETrans., J. Appl. Mech., Vol. 57, pp. A49-A114,1935.2. Littmann, W.E., The Mechanism of Contact Fa-tigue, in Interdisciplinary Approach to the Lub-rication of Concentrated Contacts, SP-237,NASA, pp. 309-377, 1970.3. 09FTM06, Kissling, U., Dependency of thePeak
49、-to-Peak-Transmission-Error on theType of Profile Correction and the TransverseContact Ratio of the Gear Pair, AGMA, 2009.4. FVA-Information Sheet No. 2/IV, Pitting Test,Forschungsvereinigung Antriebstechnik E.V.(7/1997).5. SAE Paper 2003-01-3233, Li, S., et al., Invest-igation of Pitting Mechanism in the FZG PittingTest, 2003.6. 04FTM04, Jao, T.C., et al., Influence of SurfaceRoughness on Gear Pitting Behavior,AGMA,2004.11Appendix AFigure A.1. FZG test mac
