1、11FTM13AGMA Technical PaperInvestigations on theFlank Load CarryingCapacity in the NewlyDeveloped FZGBack-to-Back Test Rigfor Internal GearsBy B.-R. Hhn, K. Stahl,J. Schudy, T. Tobie, andB. Zornek, Gear Research Centre(FZG)Investigations on the Flank Load Carrying Capacity in theNewly Developed FZG
2、Back-to-Back Test Rig for InternalGearsProf. Dr.-Ing. B.-R. Hhn, Prof. Dr.-Ing. K. Stahl, Dr.-Ing. J. Schudy, Dr.-Ing. T. Tobie,and Dipl.-Ing. B. Zornek, Gear Research Centre (FZG)The statements and opinions contained herein are those of the author and should not be construed as anofficial action or
3、 opinion of the American Gear Manufacturers Association.AbstractMicropitting,pittingandweararetypicalgearfailuremodes,whichcanoccurontheflanksofslowlyoperatedandhighlystressedinternalgears. Howeverthecalculationmethodsfortheflankloadcarryingcapacityhavemainly been established on the basis of experim
4、ental investigations on external gears.The target of a research project was to verify the application of these calculation models to internal gears.Therefore two identical back-to-back test rigs for internal gears have been designed, constructed andsuccessfully used for gear running tests. These gea
5、r test rigs are especially designed for low and mediumcircumferential speeds and allow the testing of the flank load carrying capacity of spur and helical internalgearsfordifferentpairingsofmaterialsatrealisticstresses. Thethreeplanetgearsofthetestrigarearrangeduniformly across the circumference. Ex
6、perimental and theoretical investigations regarding the loaddistribution across the face width, the contact pattern and the load sharing between the three planet gearshave been carried out.Furthermore substantial theoretical investigations on the characteristics of internal gears were performed.Ther
7、efore internal and external spur gears were compared regarding their geometrical and kinematicaldifferencesaswellastheirimpactontheflankload. Basedontheresultsofthesetheoreticalinvestigationsanextensive test program of load stage tests and speed stage tests on internal gears of different material,di
8、fferentfinishingoftheflanksanddifferentoperatingconditionshasbeencarriedout. Themainfocusofthistest program was on the fatigue failures micropitting and wear at low circumferential speeds.Thepaperdescribesthedesignandfunctionalityofthenewdevelopedtestrigsforinternalgearsandshowsbasic results oftheth
9、eoreticalstudies. Furthermoreitpresents basic examples ofexperimental testresults.Copyright 2011American Gear Manufacturers Association1001 N. Fairfax Street, 5thFloorAlexandria, Virginia 22314October 2011ISBN: 978-1-61481-012-43 11FTM13Investigations on the Flank Load Carrying Capacity in the Newly
10、 Developed FZGBack-to-Back Test Rig for Internal GearsProf. Dr.-Ing. B.-R. Hhn, Prof. Dr.-Ing. K. Stahl, Dr.-Ing. J. Schudy, Dr.-Ing. T. Tobie,and Dipl.-Ing. B. Zornek, Gear Research Centre (FZG)IntroductionTransmissions for windturbines andlowspeedindustrialgearunits oftenfeatureaslowly operatedpla
11、netarygear stage. Theflanksof thesegears canbeatrisk ofmicropitting, pittingandwearduetothelowcircumfer-ential speeds. The increase in power density, especially in transmissions for wind turbine gear boxes,enhances the risk of flank damages.However, the calculation methods for the flank load carryin
12、g capacity have mainly been established on thebasis of experimental investigations on external gears. These calculation methods possibly consider theadvantages of internal gears regarding geometrical, kinematical and tribological conditions only in a limitedform. Thus far, findings of systematic inv
13、estigations on the flank load carrying capacity of internal gears arescarcely existent.Thescopeoftheresearchprojectwastoenlargethestateofknowledgeontheflank loadcarryingcapacityofinternal gears and to verify the application of the calculation models to internal gears. Therefore substantialtheoretica
14、linvestigations onthecharacteristics of internals gears wereperformedandanextensiveprogramof gear running tests on internal gears has been carried out.FZG back-to-back test rig for internal gearsIn order to carry out the gear running tests on internal gears, two identical back-to-back test rigs for
15、internalgears were designed and constructed (Figure 1). These gear test rigs are especially designed for low andmedium circumferential speeds and allow the testing of the flank load carrying capacity of spur and helicalinternal gears for different pairings of materials at realistic stresses. The ess
16、ential component of thisback-to-backtestrigisthetestgearbox,inwhichbothtestgearanddrivegeararesituated. Thetestgearisaplanetary gear whose planet carrier is driven by a continuously variable electric motor via a shiftablecountershaft transmission. The three stepped planet gears of the test rig are a
17、rranged uniformly across thecircumference and are engaged with the test ring gear as well as the drive ring gear.Figure 1. FZG back-to-back test rig for internal gears (schematic representation)4 11FTM13By means of thesectionalrepresentationof thetest gearbox (Figure 2) thedesignandfunctioningof the
18、testrigisexplained. Thehydrostaticbracingdevice(Figure 1)twiststhebracingring(2)relativelytothetwohous-ingparts (1a, 1b). Springelements (3) areused toapply astatic torqueto thedrive ringgear (4). Thespringelements (3) aremounted uniformly across thecircumference andtransmit theperipheral forces. Th
19、ey alsoprovidealargerbracingdisplacementandtherebyallowadefinedadjustmentofthebracingtorque. Thedriveringgear (4) canadjust itself freely inradialdirectionwhereby auniform loadsharingbetweenthethreeplan-ets (5) is promoted. Thebracingtorqueis transmittedtothetest ringgear (6)by theplanetary gears(5)
20、. Thestagesofthegearings(4)-(5)and(5)-(6)exhibitthesamegearratio. Thesymmetricaldesignoftheplanetarygears (5) allows to test the rear flanks simply by reversing the planets without changing the orientation ofbracing. Theplanetsaswellastheplanetshaftsareofrigiddesigntoreduceirregularloaddistributiona
21、crossthefacewidthinthecontactbetweenplanets(5) andtest ringgear (6)causedbyshaft deflection. Thepowerloss of the test rig is induced via the two-piece planet carrier (8).Figure 2. Sectional representation of the test gearbox5 11FTM13Inorder toensureauniform distributionof theinducedtorquetothethreep
22、lanetarygears, thedriveringgear(4) ismountedradiallyfreeinthetestgear box. Thespringelements(3) substantiallysupport onlyperipheralforces. The axial force occurring in helical gears can be supported by thrust washers (9) mounted in thehousing.Despitetherigidityoftheplanetgears(5)andtheplanetshafts(7
23、)aslightdeflectionofthesecomponentshastobetakenintoaccount. Inthesamewayaslighttorsionoftheplanetcarrier(8)duetothetiltingtorquehastobe considered. For this reason an optimization with FEM-analysis has been performed.Torque and rotational speed of the continuously variable electric motor are being m
24、onitored. Variations intorque and/or rotational speed can serve as switch-off criterion. The countershaft transmission (Figure 1)allows the achievement of the required low rotational speeds.The oil feed, with a constant oil temperature, is implemented with oil spray lubrication by an external oil un
25、it.Due to the low rotational speeds the test and drive gears are wetted around full perimeter by means ofannularly arranged spray nozzles.Thetwohousingparts(1a,1b)arescrewedtogetherwiththegroundingtoallowtheapplicationof thebracingtorque. The bracing ring (2) is twisted relatively to the housing (1a
26、, 1b) by two hydraulic cylinders. Amonitoring system by means of strain gages was installedin order to keepthe requiredstatic bracingtorqueconstantwhileoperating. Thestraingagesareappliedtomultiplespringelementsarrangeduniformlyacrossthe circumference.Table 1 shows the specifications of the FZG back
27、-to-back test rig for internal gears. The range of thecircumferentialspeedfrom vt= 0.05 - 10m/s allowstheevaluationof micropittingandwearresistanceatlowspeedsaswellastheperformingoftestrunsundertestconditionscomparabletostandardizedtestmethods,like the pitting test (vt= 8.3 m/s). The dimensioning of
28、 the maximum bracing torque was based on thecalculativepittingresistanceofthepairingof acasehardenedplanet withcasehardenedringgearaccordingto ISO 6336 3, 4.The deflection of the planet shafts due to the radial forces resulting from the bracing torque Trg(Figure 3) aswellas thedeformationofplanet wh
29、eelandplanetshaft duetothetiltingtorqueresultingfromthedoubleringgear design can affect the load distribution across the face width in an unfavorable way. This problemespecially occurs in transmissions with stepped planets. An increasing misalignment of the planets resultsfromanincreasingbracingtorq
30、ue. Atransverseloadfactorof KH=1.08wascalculatedforthetestgear atabracing torque of Trg= 1500 Nm, which corresponds to a pitting safety factor of SH 1.0 for the pairing of acasehardened planet and athrough hardenedring gear. Consideringthe twistingof theplanet carrier (FEMcalculation)atransverseload
31、factor ofKH=1.09wascalculated. However foramaximumbracingtorqueofTrg= 6000Nm anevenbetter transverseloadfactor of KH= 1.06wascalculated(consideringthetwistingoftheplanetcarrieralsoKH=1.06)despitealargermisalignmentoftheplanets. Thisisduetoamorefavorableratio of the maximum force per tooth width to t
32、he average force per tooth width (Equation 1).(1)KH=FbmaxFmbTable 1. Specifications of the FZG back-to-back test rig for internal gearsParameter Unit Valuerotational speed of the carrier ncarriermin- 15 - 1000circumferential speed vtm/s 0.05 - 10rated motor torque (power loss) TmotorNm 200maximum br
33、acing torque (test ring gear Trg,maxNm 60006 11FTM13Figure 3. Schematic representation of the assembly of the test gear unitStraingages havebeenappliedcloseto thefillet onboth sides of atest ringgear inorder toanalyze theloadsharing between the three planetary gears (Figure 4). The strain gages have
34、 been aligned with the 60tangentsofthefilletbecause,accordingtoISO63363,4,thisisthelocationofthemaximumbendingstressforinternalgears. ThefourstraingagesarewiredinaWheatstonebridgefortemperaturecompensation. Theresulting signal gives information about tooth root bending stress of the test ring gear c
35、aused by the threeplanets. Ideally the maximum amplitudes of the three signals (planet 1 - 3) are identical for a constant load.Figure 5 shows the results of the measurements on the load sharing for different loads at a circumferentialspeedofvt=2.0m/s. Thethreecurvesofoneloadshowthesignalbehavioroft
36、hestraingaugemeasurementduringonerevolutionof theplanet carrier whichis proportionaltothemaximum toothroot bendingstress. Inthis case, thesecondtoothcontact causedaslightly higher bendingstress thanthetwoother toothcontacts.However, the measurement indicates a good load sharing behavior between the
37、three planets.Inorder toevaluatethe contact pattern of the test gears inthe FZG back-to-back test rig for internal gears, acontact pattern check with contact pattern paint was performed at a medium load (pC= 400 N/mm2). Thecontactpatternpaintwasremovedrelativelyconsistentlyacrossthefacewidthofalltee
38、thofthethreeplanetsand the ring gear. Therefore, the good load distribution across the face width as well as the consistent loadsharing between the three planets could be attested.Figure 4. Application of the strain gauges (schematic representation)7 11FTM13Figure 5. Measurement of the load sharing
39、between the three planetsat vt= 2.0 m/s for different loadsTheoretical investigations on the characteristics of internal gearsThetheoreticalinvestigationswereperformedbycomparinganexternalgeartoaninternalgear. TheexternalgearforthesetheoreticalstudiesisofthestandardFZGtestgeartypeC,whichisalsousedin
40、multiplestand-ardgearrunningtestsliketheFZG-FVA pittingtest, theFZG-FVA micropittingtest andtheFZG-DGMKweartest. Thepinionoftheexternalgearandtheplanetoftheinternalgearhavethesametoothgeometry. Table 2summarizes the main gear data of both gears. The internal gear was also used for the gear running t
41、estswithin the experimental investigations.For the external gear the beginning of contact (point A) is in the area of the dedendum flank of thepinion. Incontrastthebeginningofcontact(pointA)fortheinternalgearwaslaidintheareaofthededendumflankofthering gear. These drive directions are consistent with
42、 the most common applications in practice. For theexternal gear this is the configuration with a driving pinion, while internal gears, especially in the applicationrange of wind turbines, are often operated with a reverse drive direction (driving ring gear).Atfirstitshouldbenotedthatexternalgearsare
43、apairingofconvex/convexflanks,whereasinternalgearsarea pairing of convex/concave flanks. Because of these geometrical conditions thepinion of the externalgearshows an increasing radius of curvature (1) along the transverse path of contact (AE), while the radius ofcurvatureof thewheel(2) isdecreasing
44、(Figure 6). Thisleads toanequivalentradius ofcurvature(eq)thatcanberegardedasbeingnearlyconstantincomparisontointernalgear. Theabsolutevaluesof theradiusesof curvature of planet (1) and ring gear (2) of the internal gear, both starting at highvalues, aredecreasingalongthetransversepathofcontact(Figu
45、re 7). Thisleadstoahighequivalentradiusofcurvature(eq)inthebeginningof contact whichcontinuously decreases over AE. The equivalent radius of curvature inpoint A ofthe external gear is comparable to the equivalent radius of curvature in the equivalent point E of the internalgear.Table 2. Gear data of
46、 external and internal gear for the theoretical studiesParameter UnitExternal gear Internal gearPinion Wheel Planet Ring gearnormal module mnmm 4.5number of teeth z 16 24 16 - 42face width b mm 14.0pressure angle n 20.0helix angle 0addendum modification coefficient x 0.1817 0.1715 0.1817 -0.2962tipc
47、irclediameter damm 82.5 118.4 82.5 -185.0center distance a mm 91.5 -59.08 11FTM13Figure 6. Radius of curvature of the external gear(beginning of contact: dedendum flank of the pinion)Figure 7. Radius of curvature of the internal gear(beginning of contact: dedendum flank of the ring gear)Figure 8 and
48、 Figure 9 show that negative specific sliding occurs in the area of the dedendum flank of pinionand wheel of the externalgear as well as planet andring gear of theinternal gear. Comparedto theexternalgear, the absolute values of the specific sliding for the internal gear are significantly lower. How
49、ever, for theinternalgear,thenegativespecificslidingoftheplanetismoredistinctthanthenegativespecificslidingofthering gear.Figure 8. Specific sliding and tangential speed of the external gear9 11FTM13Figure 9. Specific sliding and tangential speed of the internal gearThemeansumofvelocityforbothgearscanbecalculatedbyaddingthetangentialspeedsofthetwoengagedgearwheels. Figure 8shows that thetangentialspeedof thedrivinggear of the externalgear increases overthe transverse path of contact (AE) while the tangential speed of the driven gear equally
