1、12FTM06AGMA Technical PaperVirtual Optimization ofEpicyclic GearboxPlanet Bearings inWind TurbinesBy D. Raju and S. Vasconi, SKFVirtual Optimization of Epicyclic Gearbox Planet Bearings inWind TurbinesDayananda Raju and Silvio Vasconi, SKFThe statements and opinions contained herein are those of the
2、 author and should not be construed as anofficial action or opinion of the American Gear Manufacturers Association.AbstractDemand for higher reliability, robustness and performance in epicyclical gearboxes have led SKF to developDesign for Six Sigma (DFSS) based simulation tools and methods.This pap
3、er will illustrate the advantages of using simulation driven design in the development of planetarygearboxes for multi megawatt wind turbines. The simulation example will show the influence of the housingflexibilityandofthenon-linearbearingandgearstiffnessonthegearboxperformanceundertransientload. I
4、nparticular the load distribution and deformation of the planetary gears and bearings will be analyzed.The flexibility and accurate stiffness description led to non-intuitive results. The gear deformation and loaddistribution led to significantly different results compared to results obtained by usi
5、ng traditional calculationtoolsandmethods. Acomparisonbetweenadvancedandstandardcalculationmethodsisgivenasevidencethat advanced analyses should be used to design reliable, robust and high performing gearboxes.A virtual design of experiments was used to determine the most influential parameters affe
6、cting the gearboxperformance. This paper will highlight the results of this DFSS study.Copyright 2012American Gear Manufacturers Association1001 N. Fairfax Street, Suite 500Alexandria, Virginia 22314October 2012ISBN: 978-1-61481-037-73 12FTM06Virtual Optimization of Epicyclic Gearbox Planet Bearings
7、 in Wind TurbinesDayananda Raju and Silvio Vasconi, SKFIntroductionOptimization of design parameters in wind turbine gearboxes has become increasingly important to achievelonger bearing service life. To answer the demand for improved performance a detailed simulation model ofan epicyclical gearbox w
8、as created. By means of numerical simulations the computer model was used toanalyze the performance at different loading conditions. The simulation model was also used to perform aDesign and Analysis of Simulation Experiments (DASE). TheDASE analysis consistedof avirtual designofexperiments aimed at
9、 understanding the relationship between various design parameters and the maximumcontactpressureatthebearingracewaylocation. Byapplyingvirtualoptimizationmethodologiesitispossibletoexplorethedesignspacewithoutinvestinginexpensiveprototypesandwithoutbiasesfrommanufacturingerrors. An optimized choice
10、of design parameters makes the system more robust to variation in its noisefactors and loading conditions.Bearing fatigue lifeThischapterwillpresenttwodifferentlife calculations. Thefirst isthe Basicrating lifemethod. The secondisthe DIN ISO 281 addendum 4 method. The bearing life referenced to in t
11、his report is the calculated L10raceway fatigue life. L10 bearing life is defined as 90% of the bearings exceeding the calculated value.ISO basic rating lifeThe basic rating life in hours is calculated according to ISO 281 without environmental effects and operatingconditions considered as:L10h =CPp
12、 16667N(1)whereC is basic dynamic load rating, kN;P equivalent dynamic bearing load, kN;p is exponent of the life equation;N is revolutions/minute.Fatigue life DIN 281 addendum 4The second life calculation method presented here is the DIN ISO 281 Addendum 4 method. This methodconsiders the individua
13、l rolling element loads to calculate the equivalent dynamic load. This life method isbased on rolling element load and does not include rolling element contact stress integration. Themodification factor for lubrication and contamination aDINis averaged over all roller elements.The NREL collaboration
14、 projectTheNationalRenewableEnergyLaboratoryinGolden,CO,USAstartedawindenergyprogram,theGearboxReliability Collaborative (GRC), to address reliability issues on wind turbine gearboxes . Theinput datausedin this article was provided by NREL. This includes 3D models, 2D drawings and loading conditions
15、. Thisallows the simulation to be representative of real operating conditions in wind turbines.Gearbox modelThegearboxiscomposedofthreestages:anepicyclicstageandtwoparallel,helicalstages. The mainfocusof this analysis was the low-speed epicyclical stage as shown in the following pictures. To achieve
16、 a betterunderstanding of thesystem interactions and a higher modelingaccuracy thesimulation modelhas beende-veloped including all stages and the housing. The modelwas createdusing SKFAdvanced Simulator,whichis an SKF-proprietary simulation software. See Figure 1.4 12FTM06Optimization using numerica
17、l simulationTheapproachfollowedinthisstudyisshowninFigure 2. Note:TheyellowboxinFigure 2coveringBoundarydiagram all the way through to Variation modes and effects analysis are the tools that require brain stormingsessions with different key participants.Figure 1. Wind turbine gearboxFigure 2. Approa
18、ch5 12FTM06The design for six sigma approachThe design for six sigma, DFSS, approach addresses quality when it is easiest and cheapest to improve,whenthedesignisstillonpaper. Byassessingthevariationsthataproductexperiencesduringmanufacture,shipping,storage,installationanduse,itispossibletominimizeth
19、eeffectsasaproductperformsitsintendedfunction regardless of these variations;such aproduct is“robust.” DFSSis aprocess todetermine theextenttowhichuncertaintiesinthemodelaffecttheresultsofananalysis. Basedonaprobabilisticcharacterization,DFSS enables users to quantify the quality of product, address
20、ing issues such as functional performance,minimization of warranty costs and reliability. DFSS goes one step further than a probabilistic characteriza-tion by allowing users to optimize individual design variables to achieve system optimization including theproduct performance, material, and manufac
21、turing costs.Boundarydiagram:Theboundarydiagramisadiagramwhichdefinesandlistsoutthedifferentcomponentsinthesystem andtheir interaction. Itis importantat thisphase tolist outall thecomponents inthe system,theirinteraction mode with each other and its surrounding environment.Parameterdiagram:Isadiagra
22、mthatliststheinputstothesystemandthedesiredoutputs. Thisdiagramalsocontainsthedetailsofthedesignparametersandthenoiseparameters/factorsthatcouldpotentiallyaffectthedesired output.Variation modes and effects analysis, VMEA: All the noise factors that affect the particular control parameterarerankedac
23、cordingtoitsinfluencingeffectonthedesiredoutput. Thisrankingprocesshelpssystematicallyisolate the most important parameters to be considered for the sensitivity analysis.Design of experiments, DoE: Now that the most relevant parameters are chosen and the limits on itsextremes decided, a design of ex
24、periments analysis will be performed on the selected parameters usingvirtual simulation.System boundary diagramInordertobeabletodefinetheimportantparametersinfluencingthecalculatedbearingL10fatigueLifeoftheplanetbearings,atoolknownastheboundarydiagramwasutilized. Aboundarydiagramdefinestheinterac-ti
25、ons of the components of the planetary stage and its immediate surrounding components, including the in-puts and desired responses. During the design of the diagram, it was decided to focus on the ISO/TS 16281(DINISO281addendum4)L10fatiguelifeandtheBasicratingL10fatiguelifeoftheplanetbearingsFigure
26、3belowshowstheboundarydiagramfrom theplanet stage. Theinteractions betweendifferent componentsintheplanetstageareshownwithinthedottedred box. Theinputs arelisted onthe left,and theoutput fromthesystem and the desired response are listed on the right.System parameter diagramTheboundarydiagramdevelope
27、dfacilitatesusinginformationforadditionalprocessingusingatoolcalledtheParameter diagram (P-Diagram), Figure 4. This diagram helps identify and sort the control (or design para-meters)andthenoiseparametersthatcouldpotentiallyaffectthedesiredresponse. Thecontrol/designpara-meters are parameters that c
28、an be controlled (control parameters) and factors that cannot be controlled ornoise in the system are (noise factors/parameters). This structure helps to identify all the control and noiseparameters that can be of importance for the desired outcome (Calculated planet bearing L10 fatigue life).The no
29、ise factors are further divided into five different categories, Figure 5.Variation modes and effects analysis, VMEAIn the variation modes and effects analysis, VMEA, tool each of the noise factors was ranked for its ability toaffect the desired response. Table 1 below presents a portion of the VMEA
30、spread sheet. The ranking num-bers in the sheet were determined together with experts in the field of gearbox design, bearing consultants,wind turbine manufactures, testing experts and othermembers ofthe NRELanalysis collaborative. Thefinalrisk priority number for the different design parameters and
31、 noise factors are calculated based on theserankings. Based on the prioritization created in the VMEA, six parameters were identified as most critical.6 12FTM06Figure 3. Boundary diagramFigure 4. P-DiagramFigure 5. Noise parameters7 12FTM06Table 1. Variation modes and effects analysis (VMEA)Function
32、alrequirement,FRDesignparameters,DP(referencecase)FRsensitivityto DPNoise factor,NFDPsensitivityto NFNFvariationsizeVRPNVRPN(DP)VRPN(NF)Lower limit Upper limitPlanetbearingfatigue lifeOperatinglubricantconditions10Lubricantcleanliness9 8 518400 - - 0 c=0.4 c=0.8Planetbearingfatigue lifeOperatinglubr
33、icantconditions10Lubricanttemperature8 8 409600 967285 409600 60C 80CPlanetbearingfatigue lifeOperatinglubricantconditions9Carrier supportbearingalignment9 7 321489 - - 321489 0 4 min of arcPlanetbearingfatigue lifeOperatinglubricantconditions9Carrier supportbearingoperatingclearance9 6 236196 - - 2
34、361961) -44.5 microns(downwindbearing)2) 157.6 microns(upwind bearing)1) 75.5 microns(downwindbearing2) 267.6 microns(upwind bearingPlanetbearingfatigue lifeOperatinglubricantconditions9Planet bearingoperatingclearancevariation8 3 46656 46656 46656 63 microns 113 micronsThese parameters are:1. Lubri
35、cant temperature (sump temperature)2. Planet bearing operating clearance3. Carrier upwind bearing operating clearance4. Carrier downwind bearing operating clearance5. Lubricant cleanliness6. Carrier downwind bearing misalignmentTheseparametersareshowninTable 1,includingtheirupperandlowerlimits. Uppe
36、randlowerlimitsforeachof the shortlisted parameters were selected based on experience.Virtual design of experimentsThe design of experiments was created based on the five chosen parameters. A high and low value wasselected for the different parameters.1. Lubricant cleanliness, c.a. High 0.8b. Low 0.
37、4A high value of crepresents a clean lubricant compared to the lower value. These limits were based on thelimits specified in the bearing catalogue for a similar size and type of bearing.2. Lubricant operating temperature or sump temperature.a. High 80 Cb. Low 60 CThe inner ring and outer ring tempe
38、ratures of each bearing in the gearbox were based on the sumptemperature according to ANSI/AGMA/AWEA 6006-A03.3. Carrier misalignment.a. High 4 minutes of arcb. Low 0 minutes of arc.8 12FTM064. Carrier bearing operating clearance.PLC-Aa. High 226.6 micronsb. Low 157.6 micronsPLC-Ba. High 75.5 micron
39、sb. Low 44.5 micronsThese values were chosen based on the operating clearance specifications provided by NREL.5. Planet bearing operating clearancea. High 113 micronsb. Low 63 micronsThese values were chosen based on the operating clearance specifications provided by NREL.Simulation resultsWith thes
40、e parameters and and their chosen limiting values a full factorial design of experiments, DoE, wassetup. ThisDoEwouldhelpidentifysignificantandnonsignificantfactorsthatwouldaffectthedesiredoutput:theplanetbearingupwindanddownwindradialloads;thebasicratingL10fatiguesystemlife;andtheISO/TS16281 L10 fa
41、tigue system life calculations. This resulted in 64 different simulations for the six parameters inquestion. Table 2 shows these simulations along with their parameter settings.The simulations were setup and solved for the response. The following section describes the statisticalresults of this full
42、 factorial analysis.Table 2. Full factorial DoESimulationsLubricantcleanliness, cSumptemperature, CCarriermisalignment,min of arcPLC-A Clea1),mmPLC-B Clea2),mmPL-Clea3), mm1 0.4600157.6-44.5 632 0.83 0.4804 0.85 0.46046 0.87 0.4808 0.89 0.4600267.610 0.811 0.48012 0.813 0.460414 0.815 0.48016 0.817
43、0.4600157.6 75.5 6318 0.819 0.48020 0.821 0.460422 0.823 0.48024 0.8(continued)9 12FTM06Table 2 (concludedSimulationsLubricantcleanliness, cSumptemperature, CCarriermisalignment,min of arcPLC-A Clea1),mmPLC-B Clea2),mmPL-Clea3), mm25 0.4600267.6 75.5 6326 0.827 0.48028 0.829 0.460430 0.831 0.48032 0
44、.833 0.4600157.6-44.511334 0.835 0.48036 0.837 0.460438 0.839 0.48040 0.841 0.4600267.642 0.843 0.48044 0.845 0.460446 0.847 0.48048 0.849 0.4600157.675.550 0.851 0.48052 0.853 0.460454 0.855 0.48056 0.857 0.4600267.658 0.859 0.48060 0.861 0.460462 0.863 0.48064 0.8NOTES:1)PLC-A Clea, carrier upwind
45、 bearing operating clearance.2) PLC-B Clea, carrier downwind bearing operating clearance.3)PL-Clea, planet bearing operating clearance.10 12FTM06Pareto-effects analysis: Planet bearing basic rating L10 fatigue system lifePareto-effectsplotswerealsoanalyzedforupwindanddownwindplanetbearingswithbasicr
46、atinglifeastheresponse. Figure 6andFigure 7showtheParetoeffectsplotsforupwindanddownwindplanetbearingbasicrating life. It is observed that the planet bearing operating clearance, the carrier misalignment and the down-windcarrieroperatingclearancehasthemostsignificanteffectontheupwindplanetbearingbas
47、icratinglives.NOTE:Thebasicratinglifecalculationmethodisbasedontheequivalentbearingload. Hence,lubricantcleanlinessand the lubricant sump temperatures are not included in the Pareto effects plots for Basic rating life.Basic rating L10 system fatigue life for the downwind planet bearings are influenc
48、ed mostly by the carrierbearing operating clearance followed by the planet bearing operating clearanceand thecarrier bearingoper-ating clearance. It is also observed that the combination of the different factors/parameters have significanteffect.Figure 6. Pareto effects upwind planet bearing, basic
49、rating L10 fatigue lifeFigure 7. Pareto effects downwind planet bearing, basic rating L10 fatigue life11 12FTM06Pareto-effects analysis: Planet bearing ISO/TS 16281 L10 system fatigue lifeSince the basic rating L10 fatigue life calculation method does not consider the lubrication cleanliness andbearing contact load distribution, Pareto effects plots for ISO/TS 16281 (DIN ISO 281-4) L10 fatiguesystemlife method was also analyzed. The ISO/TS 16281 L10 fatigue system life calculations also consider thelubricant cleanliness and
