1、08FTM11AGMA Technical PaperBending Fatigue Testsof Helicopter CaseCarburized Gears:Influence of Material,Design andManufacturingParametersBy G. Gasparini and U. Mariani,AgustaWestland and C. Gorla,M. Filippini and F. Rosa,Politecnico di MilanoBending Fatigue Tests of Helicopter Case Carburized Gears
2、:Influence of Material, Design and Manufacturing ParametersGiuseppe Gasparini and Ugo Mariani, AgustaWestland and Carlo Gorla, MauroFilippini and Francesco Rosa, Politecnico di MilanoThe statements and opinions contained herein are those of the author and should not be construed as anofficial action
3、 or opinion of the American Gear Manufacturers Association.AbstractAsingletoothbending(STB)testprocedurehasbeendevelopedtooptimallymaptheAgustaWestlandgeardesign parameters and a test program on case carburized, aerospace standard gears, has been conceivedandperformedinordertoappreciatetheinfluenceo
4、fvarioustechnologicalparametersonfatigueresistance,and to draw the curve shape up to the gigacycle region.Inafirstphase,testsupto10millioncycleshavebeenperformedonfourtestgroupsdifferingbymaterial(VARand VIM-VAR 9310, and VIM-VAR EX-53) and by manufacturing process (ground fillet versus ungroundfill
5、et);inthesecondphase,VIM-VAR9310groundfilletspecimenhavebeentestedupto100millioncycles.All the gear types were shotpeened.FEM analysis, strain gauge measurements and rating formula of AGMA standard are used to express testloads in terms of tooth root stresses.The program has been completed by failur
6、e analysis, based on SEM, on failed specimens and by ultimateload tests.Copyright 2008American Gear Manufacturers Association500 Montgomery Street, Suite 350Alexandria, Virginia, 22314October, 2008ISBN: 978-1-55589-941-73Bending Fatigue Tests of Helicopter Case Carburized Gears: Influence ofMaterial
7、, Design and Manufacturing ParametersGiuseppe Gasparini and Ugo Mariani, AgustaWestland andCarlo Gorla, Mauro Filippini and Francesco Rosa, Politecnico di MilanoIntroductionThe safety, performance and reliability required tohelicopter gearboxes are constantly increasing andgearsarethereforesubjected
8、toincreasingbendingfatigueloadsatthetoothrootwhileatthesametimelonger lives are demanded.1Many aspects of gear design and manufacturingmust be controlled in order to obtain such results,like material cleanliness, case depth and hardness,tooth root shape and roughness, compressive re-sidual stresses.
9、 Gear design and manufacturingprocesses, developed and optimized during manyyears, are therefore the key of the increasing per-formances of helicopter transmissions and a deepknowledge of the influence of each single designand manufacturing parameter on the fatiguestrength is also required. Moreover
10、, helicoptergears are designed to withstand loads in the veryhighcyclefield(108cycles)butarealsosubjectedto short duration overloads and therefore a preciseknowledge of the shapeof theS-N curveis ofgreatimportance for precisely assessing their in servicelife.Rating Standards, like AGMA 2101-D04 2 an
11、dISO 6336 3, provide methods to assess gearsbending fatigue performances, based on the com-parisonbetweenthestressinducedatthetoothrootand the material allowable stress. Both terms arecalculated in detail, taking into account with ap-propriate factors many influencing aspects, liketooth geometry, ge
12、ar mounting conditions, contactratio, overloads, velocity, number of cycles, rough-ness, dimensions, etc., but some limitations can bepointed out, and in particular:1. Material data provided are lower limits, whichcan be granted if the conditions specified by theStandard are respected, but cannot ta
13、ke intoaccount the actual performances which can beachieved through appropriate design,development and manufacturing.2. The stress cycle factor/life factor, which repre-sents the shape of the S-N curve, is notspecified in the highest number of cycle region,thatisrepresentedasarangebyashadedarea.In t
14、hat area the actual value of the factordepends on such items as material cleanliness,ductility,fracturetoughness andpitch lineveloc-ity (Figure 1). Therefore the responsibility ofselectingavalueislefttothedesigner,basedonhis specific knowledge. The range between thelower and the upper limit of the f
15、actor, at 1010cycles, varies from 0.8 to 0.9 according toAGMA and from 0.85 to 1.0 according to ISO.Figure 1. AGMA stress cycle factor (left) and ISO life factor (right)4For these reasons, in applications which require anaccurate evaluation of gearperformances, likeheli-copter transmissions, manufac
16、turers must performa systematic testing program in order to determinematerialfatiguelimits,whichmusttake intoaccountspecific design and manufacturing conditions, andthe shape of the S-N curve in the range of interest.Initialbendingfatigue testsare generallyperformedusing a STF (single tooth fatigue)
17、 scheme, insteadreproducing gearmeshing. The datafor actualrun-ningconditionscanthenbedeterminedbymeansofan appropriate factor, which can be explained as aconsequenceofadifferentloadratioRandofstatis-tical considerations depending on the teethnumberloaded during the tests 9. The load ratio R, whichi
18、sdefinedastheminimumtestloadversusthemax-imum test load in a load cycle, is R = 0 in runninggears and typically R = 0.1 in STF tests.Test setupSTF tests are usually performed by means ofhydraulic machines or resonance machines. Twobasic load application schemes, with severalvariations, are known:1.
19、In a “true” STF scheme, like in SAE J1619 4test rig for instance (Figure 2), the gear is sup-ported by a pin, one tooth is tested while a sec-ond one, which is loaded at a lower positionalong the profile, acts as a reaction tooth. Suchscheme is more common in the United States.With this scheme, some
20、 problems can arise ifthe tests are performed on mechanical reso-nance machines and the test are not stoppedbefore reaching the final breakage2. Asecondtestscheme,morecommoninEurope1211,inwhichactuallytwoteethareloadedatthe same time, is a consequence of the involuteprofileproperties,andofthespanmea
21、surement(the so called “Wildhaber span”) in particular. Inthis case the gear blank can be leftunsupportedsincethetwoequalandoppositesappliedforcesare perfectly balanced (Figure 3).The test fixture (Figure 4) designed specifically forthe present research program can be used for bothtesting schemes. B
22、y changing the length of the an-vil on the left side, the position of the load along theflanks of the tooth can be varied, thus changing thestresseson thetwo loadedteeth. With anappropri-ate length of the anvil the symmetric condition canbe obtained and the pin, which in this case is usedonlyforthep
23、ositioningofthegear,canberemoved:in this way no load can be absorbed by the pin andthe load and stress on the two teeth are the same.Figure 2. SAE J1619 test schemeFigure 3. Testing scheme without supportingthe gear blank (from 11)Figure 4. Fixture designed forAgustaWestland tests5The tests have bee
24、n performed on a mechanicalresonance 60 kN Schenck pulsator, without the pin(Figure 5).Figure 5. Gear specimen during testGear data and test groupsTable 1 summarizes the main gear data. For thistest program a specifically designed test gear wasdefinedandmanufacturedwithdifferenttechnologi-cal option
25、s. The gear proportions have been se-lected after several iterations optimizing test ma-chine capabilities and representation of typicalparameters of main power gears used on Agusta-Westland helicopter transmissions. This test gearhas now become the standard AgustaWestlandspecimen for gear technolog
26、y evaluation andscreening.The test gear has 32 teeth and the anvils span fiveteeth for the STF test. Consequently, eight inde-pendent test can be performed on each gear speci-men,becausetheteethnearestthose alreadybeentested are not used for testing.Table 1. Main gear dataNumber of teeth - 32Normal
27、module mm 3.773Helix angle 0.0Normal pressure angle 22.5Transversal pressure angle 22.5Transversal module mm 3.773Working pitch diameter mm 120.74Base diameter mm 111.55Effective face width mm 15.0Tip diameter mm 130.0Four test groups have been manufactured in orderto quantify the influence of desig
28、n, manufacturingand material parameters (Table 2).Table 2. Test groupsTest groupnumberMaterial Manufactur-ing451 VIM-VAR 9310 Ground fillet,shotpeened551 VIM-VAR 9310 Unground fil-let, shot-peened651 VAR 9310 Ground fillet,shotpeened751 VIM-VAR EX53 Ground fillet,shotpeenedInvestigations, like rough
29、ness and micro-hardnessmeasurements, have been performed to confirmthe compliance of the specimens to the designspecifications included in technical drawings.In a first phase of the research, the four test groupshavebeen testedand comparedup to10 millioncy-cles. In a second phase, the test group 451
30、 hasbeen selected to extend the testing range up to 100million cycles.Two ultimate load tests have also been performedon two specimens for each group, by fitting theanvils to an hydraulic universal testing machine(Figure 6).Figure 6. Ultimate load test6Test loads and tooth root stressesThe relation
31、between the applied load and the toothroot stress has been investigated trough differentapproaches: AGMA Standard, finite elementsanalyses and strain gauge measurements.The calculation according to AGMA Standard isbased on the following basic equation:F=Ftbmt1YJinwhichtheformfactorhasbeencalculatedb
32、ycon-sidering a virtual gear pair having the HPSC (highpoint of single tooth contact) for the z = 32 gear un-der consideration coincident with the point of loadapplication in the tests.In the FEM calculation (performed with ABAQUSsoftware), due to symmetry considerations, halfgear and one anvil in c
33、ontact have been modeled:the gear has been constrained on the symmetryplane and a displacement has been applied to theanvil (Figure 7).The tooth root stresses have also been determinedby means of Strain Gauges, which have also beenusedtoverifythealignmentofthetestgear. Forthisreason 8 strain gauges
34、corresponding to two teeth,two sides (compression and tension) and two endsof the face widths have been applied to two speci-mens, representing the two different fillet geome-tries (ground and unground). The details of thestrain gauges application are given in Figure 8.Table 3 summarizes the compari
35、son between theapplied load and the root stress, according todiffer-ent methods.Test resultsAsAgustaWestlandratingproceduresarebasedonthe use of a continuous S-N shape curve, the testresults have been analyzed by means of variouscurves, from both AgustaWestland experience andfrom other sources, that
36、 belong to the family:SSL=H+A (N+C)Bwhere S isthe stress,N is the number of cycles, SLis the fatigue limit, and H, A, B and C are constantswhich correspond to the different shapes.Figure 7. FEM model of the gear and the anvil, and example result of the FEM analysisTable 3. Load vs. root stress accor
37、ding to different calculation methodsTest group FilletgeometryLoad, kN FEM stress,MPaStrain gaugestress, MPaANSI/AGMA 2101-D04bending stress, MPa451, 651, 751 Ground 10 421.9 442.8 382.2551 Unground 10 417.6 427.3 361.67Figure 8. Strain gauges application sketchTwo curves, named GEAR05 and GEAR06, h
38、aveproved to best fit the experimental data and there-fore are plotted along with the test data (Figure 9 toFigure12). InthecurveGEAR05theparametersH,A, B and C are fixed and correspond to a shape-curve previously used and accepted by Agusta-Westland, while in the curve GEAR06 they havebeenoptimized
39、onthebasisofthepresenttestdata.Test results for test group 451 also include the dataof the second phase of the research, up to 100 mil-lioncycles. Veryhighfatiguecycletestresultshavenot been plotted separately because they are con-sistentwith theestimations doneon thebasis oftheshorter tests: the fo
40、recast of the fatigue limit basedontheshorterdurationtestsisonlyslightlymodifiedby the data obtained with gigacycle tests.The comparison between the four test groups ismade in terms of applied load in Figure 13, and interm of stress in Figure 14. The fatigue limit, that isthe asymptotic value of the
41、 shape curve, appearssimilarforthetestgroups451and751,withaslight-lyhighervalueforthe751. Thevaluesofthefatiguelimits estimation according to curve GEAR05 arereported in Table 4.8Figure 9. Test data, in terms of applied load, and curves GEAR05 and GEAR06 for test group 451Figure 10. Test data, in te
42、rms of applied load, and curves GEAR05 and GEAR06for test group 5519Figure 11. Test data, in terms of applied load, and curves GEAR05 and GEAR06for test group 651Figure 12. Test data, in terms of applied load, and curves GEAR05 and GEAR06for test group 75110Figure 13. Comparison, in terms of load (N
43、), among the four configurations by means of thecurves GEAR05 (left) and GEAR06 (right)Figure 14. Comparison, in terms of stress (MPa), among the four configurations by means of thecurves GEAR05 (left) and GEAR06 (right)Table 4. Fatigue limit estimations with curve GEAR05 (the values in term of stre
44、ss are derivedaccording to ANSI/AGMA 2101-D04)Test group 4511st phase4511st + 2nd551 651 751Fatigue limit, N 40,281 39,928 35,758 36,989 40,819Fatigue limit, MPa 1,540 1,526 1,293 1,414 1,560In the first phase, VIM-VAR EX53 and 9310 (bothaccordingtoAgustaWestland proprietaryspecifica-tions) have sho
45、wn the highest values of fatigue re-sistance with a slightly higher figure for EX53. Thefatiguelimitof9310VIM-VAR withunground filletisabout 8% lower while the fatigue limit of 9310 VAR(according to AMS6265 13) and form grinding isabout 11% lower.In the very high cycle fatigue tests on 9310 VIM-VAR,
46、 two failures occurred in the range between10and 100 million cycles. The results of the very highcycletestsconfirmthecurvedeterminedwiththeor-dinary tests and its asymptotic value.The fatigue limits obtained in the present test pro-gramaremuchhigherthanthoseincludedinAGMA11and ISO rating standards,
47、but the opinion of the au-thors is that a direct comparison with those data isnot meaningful, because they are not specific forthe aerospace applications and do not consider theinfluence of such parameters like shotpeening orresidualstresses. Besidesthe presentdata areob-tained with a STF test, whic
48、h have a different loadratio R and, also different statistical conditions, asexplainedin9. Literaturedataforasimilarmaterialandapplicationcanbefoundin8forthelowcyclesfield and they are consistent with those of thepresent research in the same cycle range.Furthermore, as already mentioned before, stat
49、ictests to breakage has been performed on the gearsto check the ratio between the static strength andtheendurancelimitandtheresultswereintherangeof1.93to2.17whicharereasonably consistentwiththe ISO and AGMA standard curves for carburizedgears (2.50 and 2.70 respectively, ref. Figure 1).Crack nucleation and propagationThe tooth failure surfaceshows thetypical shapeofcase hardened AISI 9310 gear teeth 6 8, with atypical cone-cup final fracture. An example offrac-ture surface is shown in Figure 15.From the SEM observation of the fractu
