1、12FTM05AGMA Technical PaperCombined Effects ofGravity, BendingMoment, BearingClearance, and InputTorque on WindTurbine Planetary GearLoad SharingBy Y. Guo and J. Keller, NationalRenewable Energy Laboratoryand W. LaCava, University ofMassachusettsCombined Effects of Gravity, Bending Moment, BearingCl
2、earance, and Input Torque on Wind Turbine Planetary GearLoad SharingYi Guo and Jonathan Keller, National Renewable Energy Laboratory andWilliam LaCava, University of MassachusettsThe 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.AbstractThis computational work investigates planetary gear load sharing of three-mount suspension wind turbinegearboxes. A three-dimensional multibody dynamic model is established, addressing gravity, bendingmoments, fluctuating mesh stiffness,
4、 nonlinear tooth contact, and bearing clearance. A flexible main shaft,planetary carrier, housing, and gear shafts are modeled using reduced degrees-of-freedom through modalcondensation. This drivetrain model is validated against the experimental data of the Gearbox ReliabilityCollaborative for gear
5、box internal loads.Planet load sharing is a combined effect of gravity, bending moment, bearing clearance, and input torque.Influences of each of these parameters and their combined effects on the resulting planet load sharing areinvestigated. Bending moments and gravity induce fundamental excitatio
6、ns in the rotating carrier frame,whichcanincreasegearboxinternalloadsanddisturbloadsharing. Clearanceincarrierbearingsreducesthebearing stiffness, and thus the bending moment from the rotor can be transmitted into gear meshes. Withbearing clearance, the bending moment can cause tooth micropitting an
7、d can induce planet bearing fatigue,leading to reduced gearbox life. At low input torque, planet bearings are susceptible to skidding. At ratedtorque and beyond, planet bearings are at risk of fatigue.Copyright 2012American Gear Manufacturers Association1001 N. Fairfax Street, Suite 500Alexandria, V
8、irginia 22314October 2012ISBN: 978-1-61481-036-03 12FTM05Combined Effects of Gravity, Bending Moment, Bearing Clearance, and InputTorque on Wind Turbine Planetary Gear Load SharingYi Guo and Jonathan Keller, National Renewable Energy Laboratoryand William LaCava, University of MassachusettsIntroduct
9、ionWindturbineshavetraditionallyexperiencedprematuregearboxfailures1. Thecostofgearboxrebuilds,aswell as the down time associated with these failures, has elevated the cost of wind energy. The NationalRenewable Energy Laboratory Gearbox Reliability Collaborative (GRC) was established by the U.S.Depa
10、rtmentofEnergyin2006;itskeygoalistounderstandtherootcausesofprematuregearboxfailuresandimprovetheirreliabilityusingacombinedapproachofdynamometertesting,fieldtesting,andmodeling2. Amajor modeling activity of the GRC is to evaluate assumptions and uncertainties in current design practicesthat could a
11、ffect gearbox reliability. As a part of the GRC program, this paper investigates planetary gearload-sharing in three-mount suspension wind turbine drivetrains that affects the load path and gearboxcomponent life.Compared to parallel axis gears, planetary gear systems provide high power density by sp
12、litting the inputtorque into multiple, parallel sun-planet and ring-planet load paths. Planetary gear systems are commonlyused in wind turbine drivetrains and they use nearly or exactly equally-spaced planet gears, theoreticallyleading to equally shared loads at each planet. However, in reality plan
13、et gear loads are not always equallyshared among planets 3 4 5 6 7 8 9 10 11. With unequally shared loads, planet bearing forcesincrease, leading to reduced bearing life and potential premature failure. Planetary gear load sharing is animportant design parameter for drivetrain reliability. The degre
14、e of unequal load sharing has implications fortolerance schemes and gearbox loads.Early studiesby Hidakaand Terauchi3 investigateddisturbed loadsharing bymanufacturing andassemblyerrorsonaStoekichtplanetarygear. Thisunequalloadsharingwas notsignificant whenthe meshfrequencywas lower than 1000 Hz. Ha
15、yashi 5 developed a method to measure the planet gear shearing stress andstudied the influences of gear tooth profile error and eccentricity on load sharing. Ligata 6 investigated theeffectofpinpositionerroronplanetloadsharingandamethodforcomputingtheplanetloadsharingfromrootstrain-timehistorieswasp
16、roposed. Singh12foundthatthetangentialpinpositionerrorhasagreatereffecton the load sharing compared to the radial error. It was also shown that the sensitivity to pin position errorincreases as the number of pinions in the planetary gear set increases 6 12. Singh 13 14 developed aformulation to esti
17、mate load sharing considering the unequal planet spacing for three to seven planetarygears. Theanalyticallypredictedloadsharingfactorwascomparedagainstafiniteelementanalysisusingtheprogram developed by Vijayakar 15.Various techniques have been investigated to improve load sharing. Studies show using
18、 a flexible ring gearimproved load sharing when a number of manufacturing and assembly errors were present 4 16.Kahraman investigated the effects of ring gear flexibility on planetary gear loads using a finite elementmodeland experiments and found contradictory results 15 17. They found that adding
19、flexibility to the ring gearwas not as effective as a floating sun in improving load sharing. Kahraman 9 developed a two-dimensionallumped-parameter model to calculate tooth and bearing loads of planetary gears. The study also investig-ated the effect of a floating sun on load sharing and found it d
20、id not improve disturbed load sharing due to pinposition errors. Similar results were shown in the study by Singh 12.This aforementioned research on load sharing is limited to unequally spaced planets due to manufacturingerrors and eccentricity. Input torque is considered as the only applied load to
21、 these planetary gears in priorstudies. Nearly all horizontal-axis wind turbine gearboxes carry various combinations of input torque andnon-torque loads. The non-torque loads include bending moments caused by the rotor weight and tower4 12FTM05shadow, wind induced moments, moments caused by the cont
22、roller, thrust, etc. Three-mount suspensiondrivetrainsstudiedbyNRELGRCshowsignificantbendingmomentonthemainshaft,whichismainlycausedby the rotor weight and aerodynamic forces 2. This bending moment has the same order of magnitude asinput torque 2 18. Other wind turbine designs adopt a two main beari
23、ng configuration to reduce thetransmission of these non-torque loads into gearboxes. These turbines still have a small amount of bendingmoment present on the main shaft.ThemeasuredloadspectrumoftheGRCturbineconsideringvariouswindandweatherconditionsisshowninFigure 1. Over 90% of the time, the GRC wi
24、nd turbine operates below rated torque. Within the entire loadspectrum, the turbine operates below 10% of rated torque over 50% of testing period. Gearbox reliability atlow input torque hasreceived littleattention inthe pastbecause priorresearch hasmainly focusedon thelowbearing and tooth loads with
25、 low input torque. Influences of bending moment are not considered for the lowload conditions.With the increasing size of wind turbines, gravity induced excitation in the rotating carrier frame becomes animportant vibration source. Gravity led to tooth wedging, apotential sourcefor prematureplanet b
26、earingfail-ure, in a wind turbine planetary gear investigated by Guo and Parker 19. Clearance is introduced in rollingelementbearings toaccount forthermal expansion,interference fit,and surfaceroughness duringoperation.Clearancesinwindturbinebearingsarelargeandcancausegeartoothmisalignment,leadingto
27、uneventoothand bearing load distribution and increased bearing vibration 19 20 21.Thisstudyinvestigatesthecombinedeffectsofgravity,bendingmoment,bearingclearance,andinputtorqueon planetary load sharing of three-mount suspension wind turbine gearboxes. Gearbox internalloads atlowinput torque - a wind
28、 turbine operating condition that is rarely considered - are also studied under effects ofbending moment.GRC wind turbine drivetrain descriptionThis studyinvestigates the750 kWturbine drivetrainused bythe NRELGRC. This drivetrainhas asphericalroller main bearing that supports the main shaft and roto
29、r weight, and two trunnion mounts that support thegearbox. The gearbox includes a helical planetary stage with three equally-spaced planets and two parallelstages, with stage ratios of 5.71, 3.57, and 4.00, respectively. The rated input speed is 22.2 rpm. A cutawayviewofthegearbox isshown inFigure 2
30、. There aretwo parallelcarrier bearingssupporting thecarrier. Eachplanet gear is supported by two identical cylindrical bearings. The sun shaft is connected to the intermediateshaft through a spline connection with 300 mm backlash to partially float the sun. The ring is bolted to thegearbox housing.
31、 This drivetrain configuration represents the majority of the existing three-mountsuspensionwindturbinedrivetrains. KeyparametersoftheplanetarysectionarelistedinTable 1andTable 2.Additional details of this gearbox are described in 22.Figure 1. Torque distribution throughout measurement campaign on N
32、EG Micon NM48/750turbine 2 185 12FTM05Figure 2. Cut-view of the GRC gearbox configurationTable 1. Geometric parameters of the planetary gearSun Planet RingNumber of teeth 21 39 99Pitch diameter, mm 215.6 400.4 1016.4Root diameter, mm 186.0 372.9 - -Base diameter, mm 198.8 369.3 937.4Whole depth cons
33、tant 2.4 2.4 2.4Tooth thickness, mm 16.84 18.80 8.55Module, mm 10.0 10.0 10.0Helix angle, degrees 7.4947 (right) 7.4947 (left) 7.4947 (left)Backlash, mm 0.25/0.29 0.25/0.29 0.30/0.36Pressure angle, degrees 20.0Center distance 308.0Table 2. System parameters of the planetary gearSun Carrier Planet Ri
34、ng HousingMass, kg 181.6 756.9 104.0 480.0 1213.0Ixx,kgm21.26 59.1 3.20 144.2 340.0Iyy,kgm224.0 60.3 2.04 75.4 554.4Izz.kgm224.0 60.3 2.04 74.4 424.8Experimental setup and instrumentationTheGRCprojectinstrumentedtwoidentical750kWwindturbinegearboxes fordynamometer (Figure 3)andfield testing. Interna
35、l measurements include gear tooth loads, main shaft torque and bending, internal com-ponent deflections and misalignments, and planet bearing loads. The full description of instrumentation isdetailed in 2.6 12FTM05Figure 3. 750 kW wind turbine drivetrain of NREL GRCMain shaft torque and bending were
36、 measured using three sets of strain gauges in full bridge arrangements.These measurements are taken nearthe centerof themain shaftbetween themain bearingand gearbox2.Theshafttorqueandbendingmeasurementservesasareferencefortheinputloadbeingappliedtothegear-box from the rotor side, and can also be us
37、ed as the time series input for dynamic simulations. The bendingmomentscausedbythebladesandhubweightandaerodynamicforcesweremeasuredinthefieldtests,andare 29.2% to 64.6% of rated input torque 2.For each planet bearing, three axial slots were machined into the inner diameter of the inner ring andinst
38、rumentedwithstrainandtemperaturegauges2. Twooftheslotswerelocatedatdifferentlocationsinthebearing load zone for each planet, and the third slot for every bearing was oriented 90 from the sun-planetaxis, referred to here as top dead center (TDC). Two gauge sets in each TDC slot and two bearings on ea
39、chplanet provided an axial distribution of four radial loadsalong eachplanet pin. Thesegauges werecalibratedto loads applied to the fully assembled planet pins and bearing pairs in a bench top test setup 23.Dynamic drivetrain modelingThe three-dimensional dynamic model of the wind turbine drivetrain
40、 is established in SIMPACK 24. Thismodelincludesthemainshaft,lowspeedplanetarygear,planetarycarrier,andhousingasshowninFigure 4aand Figure 4b. The parallel stages are not included in this study.a) Side view b) Axial viewFigure 4. Multibody model of the examined gearbox with flexible carrier and hous
41、ing7 12FTM05Gears are modeled as rigid bodies with six degrees-of-freedom x, y, z, x, yand z. The gear contactanalysis considers the time varying tooth meshing when the gears rotate by modeling the fluctuating meshstiffness according to the ANSI/AGMA/AWEA 6006-A03 25. The gears are modeled using a s
42、licingapproach to determine the load distribution across the gear tooth facewidth, which accounts for tooth profileandleadmodification,toothcontactloss,andfluctuatingmeshstiffness. Thetoothloaddistributionofthesungear teeth with tooth modifications is shown in Figure 5. This model also considers shu
43、ttling contact andsliding friction forces 26.Bearingsaremodeledusingdiagonalstiffnessmatrices. RadialbearingclearanceisincludedinthemodelasshowninFigure 6. Radialforcesdeveloponlywhentherelativedisplacementbetweentheconnectedbodiesexceeds a specified clearance. For instance, the radial forces of the
44、 carrier bearings are:fjc= mcjkcjjc jh c, j = y, z(1)wherekcj, j = y, z are the bearing stiffnesses;jc, jhare the displacements of the carrier and housing; andmcj, j = y, z tracks if the bearings are in contact according to:mcj=1 111(2)1if(jc- jh)c- 1 if (jc- jh)-c0if|jc- jh| cFigure 5. Tooth load d
45、istribution with profile and lead modification at .the sun-planet 1 meshFigure 6. Nonlinear bearing model8 12FTM05The model includes the flexibilities of the main shaft, planet carrier, shafts, and gearbox housing, which areimportantstructuralcomponentsinthedrivetrainthatcouldaffectgeardynamics. The
46、gearboxfrontandrearhousingsandplanet carrierare includedas reducedfinite elementflexible bodies. Finiteelement modelsarecreated in Abaqus and reduced using the Craig-Bampton method 27. Master degrees-of-freedom,referredtohereas“nodes”,areselectedateachinterfacepoint. Fortheplanetcarrier,nodesatthema
47、inshaftconnection, upwind and downwind carrier bearing connections, the planet-pin upwind and downwind bores,and planet pins are retained for the drivetrain model. Housing nodes were retained at each bearing location,theringgearinterfacecenter,andtheyokemountcenters(Table 3). Alltheeigenfrequenciesb
48、elow1,000Hzof the housing and carrier are included for the super element creation in Abaqus. This cut-off frequency(1,000 Hz) is selected to include higher than 25thharmonic of the planetary stage mesh frequency at ratedspeed. After creating the super elements and performing modal analyses on the re
49、duced matrices, theflexible bodies are imported into the multibody drivetrain model. The ring is modeled as a rigid body due tosoftware limitations. Shafts are modeled using beam elements.The sun spline connection is modeled using its diagonal stiffness matrix obtained through a finite elementanalysis in RomaxWIND 28 (Table 4). Spline facewidth, crowning, applied load, and surface lubricationaffect these stiffnesses. Trunnion mounts are mode
