1、09FTM07AGMA Technical PaperOptimizing GearGeometry for MinimumTransmission Error,Mesh Friction Lossesand Scuffing RiskThrough ComputerAided EngineeringBy R.C. Frazer and B.A. Shaw,Newcastle University, andD. Palmer and M. Fish, DontyneSystems LtdOptimizing Gear Geometry for Minimum Transmission Erro
2、r,Mesh Friction Losses and Scuffing Risk Through ComputerAided EngineeringRobert C. Frazer and B.A. Shaw, Newcastle University, and David Palmer andMichael Fish, Dontyne Systems LtdThe statements and opinions contained herein are those of the author and should not be construed as anofficial action o
3、r opinion of the American Gear Manufacturers Association.AbstractMinimizing gear losses caused by churning, windage and mesh friction is important if plant operating costsand environmental impact are to be minimized. The paper concentrates on mesh friction losses andassociatedscuffingrisk. Itdescrib
4、esthepreliminaryresultsfromusingavalidated3DFiniteElementAnalysis(FEA) and Tooth Contact Analysis (TCA) program to optimize cylindrical gears for low friction losses withoutcompromising Transmission Error (TE), noise and power density. Some case studies are presented andgeneric procedures for minimi
5、zing losses are proposed. Future development and further validation work isdiscussed.Copyright 2009American Gear Manufacturers Association500 Montgomery Street, Suite 350Alexandria, Virginia, 22314September 2009ISBN: 978-1-55589-960-83Optimizing Gear Geometry for Minimum Transmission Error, Mesh Fri
6、ctionLosses and Scuffing Risk Through Computer Aided EngineeringRobert C. Frazer and B.A. Shaw, Newcastle Universityand David Palmer and Michael Fish, Dontyne Systems LtdIntroductionCylindrical involute gears have many advantagesover other gears. They are relatively easy tomanufacturewithstandardtoo
7、ls,insensitivetocen-ter distance change, can accommodate modifica-tions in micro-geometry to account for elasticdeflection and manufacturing errors, have geome-try that is mathematically straight forward andrelatively easy tomeasure. Standards coveringtherating and analysis of cylindrical gears such
8、 as theISO 6336 suite of standards and ANSI/AGMA2101-D04 are well developed and appliedworldwide.Users of cylindrical gears demand continuous im-provement such as increased power density, lowerweight, reduced manufacturing costs, reducednoise, increased reliability and reduced operatingcosts. In rec
9、ent years it has become more impor-tant to reduce environmental impact from plant op-eration. Cylindrical involute gears are inherentlyvery efficient, typically 98-99.5% per mesh. How-ever,smallimprovements inefficiency willminimizeoverall system losses and reduce lubricant andcooling system require
10、ments.Gearbox losses occur from a number of sources:S Churning losses due to lubricant agitation aregeometry and speed (pitch line velocity) depen-dent. These can be minimized by using spraylubrication, dry sumps and internal gearboxbaffles to minimize gear immersion as well asusing smaller module a
11、nd higher helix anglegears.S Windage losses are geometry and speeddependent and can be minimized by modifica-tion to geometry (smaller module and higherhelix angle) running in partial vacuums or lightgases.S Mesh friction losses which are affected byspeed, load, coefficient of friction and gear geo-
12、metry.S Bearing losses which are affected by speed,load and gear geometry.S Seal losses seal type and speed dependent.The work described in this paper concentrates onmeshfrictionlosses. Ina2MWinstallation,lossesof between 10 to 40 kW occur with efficiencies of98-99.5%. This power is lost as heat whi
13、chrequires external cooling systems and controlsystems addingtothecost oftheplant. Lowergearfriction improves operational efficiency and if ap-plied carefully it will reduce plant manufacturingcosts and lubrication requirements.Minimizing the mesh friction loss is of particularimportance because it
14、will also reduce the risk ofscuffing failure and help to eradicate the need forlubricant additive packages which are costly andenvironmentally harmful. Scuffing risk is difficult toassess and although there are two ISO TechnicalReports 5,6 and the ANSI/AGMA standard6011-l03, annex B 7 published onth
15、e subject, thesafety factors that result from the analysis proce-dures often conflict, reducing confidence in theresults and evaluation procedure. The accuratemodellingof meshfriction ingears includingmicro-geometry correction, manufacturing and alignmenterrors and accounting for elastic deflection
16、underload is therefore important to minimize the meshfrictionlossesincylindricalgeardesignandimprovegear reliability.The preliminary results from the development of afriction loss model are described in this paper. Thework to model and minimize mesh friction losseswas undertaken as part of a wide ra
17、nging projectfunded by the European Union named X-GEAR.This targeted specifically Wind Turbine and Auto-motivegearapplications. However,theresultsfrom4thisworkaregenericandapplicabletoallcylindricalgear transmissions.BackgroundGear mesh frictionFigure 1 illustrates that as the tooth pair movesalong
18、the line of action, the combination of slidingand rolling changes throughout the mesh cycle.Pure rolling occurs at the pitch point (point C inFigure 1),butascontactmovesawayfromthepitchpoint sliding increases. Meshing gear pairs requirealubricatingfilmtoseparatethegearsurfaces butifthis film breaks
19、down,afailuremodecalledscuffingoccurs as illustrated in Figure 2. When the lubrica-tion film breaks down the gear tooth surfacesinstantaneously weld together and are then pulledapart due to the combination of rolling and slidingthat occurs during the mesh cycle. Gear lubricantshave been developed ov
20、er many years to preventthiswithEPadditives,generallysulphurbased,thatbondtothegear surfacesandthusprevent metaltometal contact. However the additive packagesmakegearoilunpleasanttohandleandsignificantlyincrease the environmental impact of the lubricantwhen it is disposed.Figure 1. Variation in driv
21、e gear sliding speed with mesh phase (position)Figure 2. Scuffed gear sample from Design Units 160mm center test rig5Gear scuffing is difficult to predict but severalstandards(DIN3991,ISO/TR13989-1andISO/TR13989-2 5,6,7) provide procedures to estimate asafetyfactorforscuffing. Theseproceduresusetheg
22、ear macro-geometry, the calculated load distribu-tion factors from the gear accuracy, and the esti-mated shaft deflections to estimate scuffing risk.The standards provide good general guidance butfail to consider the important effect gear micro-geometry has on the local tooth surface loads andthus t
23、he localized scuffing risk. The micro-geometry of agear is theintentional departurefroma standard gear form that can optimize theperformanceofagearbyimprovingloaddistributionand minimizing transmission error and noise bycompensating for deformation and misalignmentspresent in all loaded systems. It
24、is important thatthis is considered as part of the modelling process.Minimizingfrictionlossesingearsisstraightforwardin principle:S Minimize sliding speed m/s by reducing theheightofthegearteeth,eitherbyusingasmallermodule or simply reducing the addendum anddedendum of the gear, sometimes known as a
25、stub tooth gear form.S Reduce the peak tooth loads by applying flankcorrectionsforcalculatedelasticdeflectionsandimproving the gear accuracy and alignmentwithin the gear case.S Reduce self induced dynamic loads by minimiz-ing transmission error.S Reduce the mesh friction coefficient by improv-ing lu
26、bricant additives, surface finish andapplying low friction coatings.Inpractice,considerationhastobegiventobalancethe requirements of low friction loss gears with keyrequirements of maintaining power density, reliabil-ity, low noise, low cost and minimize sensitivity tomanufacturing and alignment err
27、ors.Friction power lossFriction power losses (PL) in gears are dependenton the normal force (FN), coefficient of friction (m)and the sliding speed of the surfaces (g) shown inequation 1.PL= m N g(1)Each of these quantities vary through the meshcycle, depending on the instantaneous position ofthe mes
28、h point between A (start of active profile)and E (end of active profile) shown in Figure 1, butthey also vary across the face width (b)asdiscussed below:S Thenormalforce(FN)dependsonthenumberofteethinmesh(affectedbytransversecontactra-tioandoverlapratio)andloaddistributionduetomanufacturing errors a
29、nd elastic deflection ofthegearteeth,thegearshaftsandhousing. Theactual loadis requiredat eachphaseof thegearmeshalongthepathof contact (x) from(A-E)inFigure 1 to accurately estimate gear losses.S Thecoefficient of friction(m) willvary withslidingspeed. It is likely that the coefficient of frictionw
30、ill be higher at the entry to the mesh and thestatic friction at the pitch point will be different.S The sliding speed (g) varies linearly withdistance along the path of contact from A to E,with g= 0at thepitchpoint C inFigure 2. Thiscanbecalculateddirectly.Thustheequationderivedforpower loss(W) inr
31、ealgears, with geometry errors, flank relief and elasticdeflection effects is given by equation 2.PL=1bPetz = boEAm(x) F(x) g(x)dxdzW(2)wherePetbase pitch (transverse), mmm (x) coefficient of frictionF (x) local mesh load, Ng(x) sliding speed, mm/sb facewidth, mmThe accurate assessment of equation 2
32、 requiresaccurate knowledge of the instantaneous meshloadF(x). Thisisbeyondthescopeofstandardgearstress analysis procedures defined in ISO 6336(gear stress analysis standard) as detailed meshdeflection values, gear geometry (including pre-dicted errors andthe gear designers specifiedhelixand profile
33、 correction), and dynamic loads are notaccurately modelled in the standard.Existing workThere has been much work in recent years to mini-mizemeshfriction. TheEUfundedresearchproject6Oil Free Powertrain (IPS-2001-CT-98006), aproject coordinated by the VDMA in Germany,completed a systematic review of
34、gear losses withthe ambitious target of producing a lubricant freepowertrain 1. The effect of geometry parameters,namely module (tooth size), addendum modifica-tion, ratio, helix angle, pressure angle and facewidth on total gear losses was investigated and theresults showed:Module(Mn): reducingthemo
35、dulereducesslidingspeed but increases root bending stress. This ef-fect canbeminimizedby controlledshot peeningorincreasing the helix angle.Pressure angle (n): increasing the pressureangle reduces the contact stress, but reduces thetransverse contact ratio which can increase themean tooth load and b
36、earing loads.Addendum (ha): decreasing the addendumreduces the sliding speed but reduces the contactratio and increases tooth stiffness (resulting in anincreased sensitivity to geometry errors).Helix angle (): Increasing the helix angleincreases the overlap ratio, increases the trans-verse pressure
37、angle and reduces transversecontact ratio but increases axial bearing loads.Addendum modification factor (x): increasingthe addendum modification factor will increase theoperating pressure angle and increase slidingspeed at the tip unless the mating gear is alsoadjusted.Toppingfactor(k): changingthe
38、outsidediameterwithout changing the cutting tool is called toppingthe gear. It allows gear geometry to be changedwithout changing the manufacturing tool. Positive(+) toppingreduces theoutside diameter (da)ofthegear.Reviewing the data published by the Oil FreePowertrain project shows that the stronge
39、st cor-relationbetweenreducingpowerlossandgeometrymodifications is by either minimizing module orreducing the transverse contact ratio by using astub tooth gear geometry. Both have the sameeffect of reducing sliding speed but the stub toothgeometry does not suffer fromthereducedbendingstrength that
40、affects the smaller module size.Thesechanges reducethe loadcontact linelength,increasingcontactloadsandthereforealsoincreas-ingcontactstress. Twomethodstocompensateforthis are to either to increase the face width, with aresultingincreaseingearmanufacturingcosts(duetolarger bearingspans,gear blanks,g
41、ear caseandincreasedweight) or toincreasethepressureangleof the gears (which increases the relative radius offlank curvature and thus reduces the Hertziancontactstress). Itshouldberealizedthatforagivenmaterial andmanufacturingroute, theloadcarryingcapacity of a gear is proportional to its volume.Thu
42、s a change in a one geometry parameterrequires a proportional change in a secondgeometry parameter.Many of these changes in geometry can havepotentially conflicting effects on gear performance.Throughout this work to minimize losses it isimperative that good gear design practice is fol-lowed and tha
43、t Transmission Error is minimized toreduce dynamic loads and gear noise.Implementation of the loss calculationGATESIntheearly1990s,TheDesignUnitidentifiedaneedto improve the modelling of cylindrical gears anddeveloped a 3D FEA and TCA program tooptimizethe gear macro-geometry (module, helix angle,pr
44、essure angle etc), and gear micro-geometry(flank relief- profile tip/root relief and helix correc-tion and crowning). It is used to estimate meshforces, bending stresses, contact stresses andloaded transmission error (TE). The model, knownas DU-GATES (Gear Analysis for TransmissionError and Stress)
45、was initially validated by a seriesof tests using aninstrumented power re-circulatingtest rig (back-to-back configuration), which canberunat6000rev/minand8MW3,8,9. TransmissionError was verified by measuring dynamic bearingloads, and mesh stiffness by measuring load dis-tributionacrossthefacewidthwi
46、thstraingauges. Ithas since been successfully used for optimizinggear designs in conjunction with ISO 6336analysismethods on a wide range of applications includingmarine gear, automotive, aerospace and industrialtransmissions over a 15 year period.In 2007 the software was transferred to DontyneSyste
47、ms Ltd and renamed GATES. The develop-ment of the model continued with significant7improvement in the usability, visualization of theresults andtheextension of its analysis range toin-clude the estimation of mesh friction losses.The model works in two stages:S A 3D FEA to establishthe stiffness matr
48、ix of thegear flank. This requires the definition of thegear macro-geometry, bore or shaft size, andtorque direction and rotation directions. Pro-vided the geometry is unchanged, it requiresrunning only once and takes typically 5 to 15minutes to run. Post processing the FEAcompliancedataintoaseries
49、of curves for com-pliance and stress is performed, thus definingthecomplianceofanypointonthetoothsurface.Itallowsupto120pointspercontactlinebeusedin the subsequent TCA analysis. A TCA that includes the arrangement, loadconditions, gear geometry errors, mountingerrors anddetailedmicro-geometry. This takestypically 1 minute to run and is used to investi-gate the relief strategy, sensitivity to alignmenterrors and gear manufacturing errors. It calcu-lates contact loads, bending stress, contactstress (by analytical method
