Embed Size (px)
Citation preview
CFD Analysis of Gear Windage Losses: Validationand Parametric Aerodynamic Studies
Matthew J. Hill ∗
The Pennsylvania State UniversityUniversity Park, [email protected]
Robert F. Kunz †
The Pennsylvania State UniversityUniversity Park, [email protected]
Richard B. Medvitz ‡
The Pennsylvania State UniversityUniversity Park, PA
Robert F. Handschuh§
NASA Glenn Research CenterCleveland, OH
Lyle N. Long ¶
The Pennsylvania State UniversityUniversity Park, PA
Ralph W. Noack ‡
The Pennsylvania State UniversityUniversity Park, [email protected]
A CFD method has been applied to gear configurations with and without shrouding. The goals of thework have been to validate the numerical and modeling approaches used for these applications and to developphysical understanding of the aerodynamics of gear windage loss. Several spur gear geometries are consideredfor which experimental data are available. Various canonical shrouding configurations and free-spinning (noshroud) cases are studied. Comparisons are made with experimental data from the open literature, and datarecently obtained in the NASA Glenn Research Center Gear Windage Test Facility. The results show goodagreement with experiment. The parametric shroud configuration studies carried out in the Glenn experimentsand the CFD analyses elucidate the physical mechanisms of windage losses as well as mitigation strategies dueto shrouding and newly proposed tooth contour modifications.
Nomenclature∀ volumer radial vectorV velocity vector in the relative frame of refer-
enceAθ tangential projection of the area of the grid
faceCp pressure coefficientD wall damping coefficientdn measure of the normal distance to the nearest
wallk turbulence kinetic energyLre f reference lengthp pressurep∞ freestream pressureq
√k
r radial coordinate of grid face centroidrbase base radius of gearS areaT ∗(x) torque per unit width
∗Ph.D. Candidate, Department of Aerospace Engineering†Senior Scientist, Applied Research Laboratory‡Research Associate, Applied Research Laboratory§Aerospace Engineer¶Professor of Aerospace EngineeringPresented at the American Helicopter Society 66th Annual Forum, Phoenix,
Arizona, May 11-13, 2010. Copyright c© 2010 by the American Helicopter SocietyInternational, Inc. All rights reserved.
V ∗ local normalized projected relative velocitymagnitude
Vx velocity x-componentVy velocity y-componentVre f reference velocityCµ,C1,C2,α turbulence model coefficientsPrq,Prω turbulent Prandtl numbersε turbulence dissipation rateµ molecular viscosityµt eddy viscosityω ε/kρ densityω angular velocityτ shear stress tensor
Introduction
Gearbox windage losses refer to the power losses asso-ciated with rotational deceleration torques exerted on spin-ning gears by aerodynamic forces (pressure and viscous)within the air-oil atmosphere present within a gearbox.Windage losses are a source of significant heating and fuelconsumption in rotorcraft and other VTOL systems. Theweight and packaging constraints inherent in these systemsrequire the gearing components to be both lightweight andheavily loaded. Attendant to this, the gears are requiredto operate at high rotational speeds where windage losses
become significant with respect to other gearbox losses(rolling, sliding, and lubrication losses).
A host of experimental studies of gearbox windage haveappeared in the literature.1–9 These studies employ ei-ther closed loop systems5–9 or treat isolated gears1–4 wherewindage (and other) losses are determined by measuringspin-down velocities once the gear and shaft assembly isdisconnected from the drive torque. Generally, these stud-ies parametrize gear geometry elements, rotational speed,enclosure geometry, and lubrication system characteristics(flow rate, jet location, lubricant rheology), and use dimen-sional analysis to develop correlations for the power losseswhich have proven useful in the design process.
It has been shown experimentally by Winfree1 and Daw-son2, 3 that geometric modifications of the near-gear flowpath, such as shrouding and baffle configurations, can sig-nificantly reduce both windage losses and lubricating oilconsumption (80% and 40% reductions observed, respec-tively, in Ref. 1). Such modifications are therefore ofsignificant interest in rotorcraft transmission design, but todate, only these empirical studies are available. Accord-ingly, there is a need for more systematic and prototypicalexperimental data and a need for improved understandingof the physical mechanisms involved in the schemes usedto reduce these aerodynamic losses.
Recently, a gear windage test facility has been developedat the NASA Glenn Research Center. This facility is ex-pected to produce the most comprehensive set of gearboxwindage data to date, and is providing CFD validation datarequired in the present NASA sponsored research effort.The test facility is designed to parametrize the effects ofspur gear geometry, shroud geometries, different lubrica-tion system configurations, system pressures and temper-atures, and gear meshing on windage loss. The first datasets from the Glenn rig are published here. This data in-cludes a single spur gear spinning in air for a set of fouraxisymmetric axial/radial shroud configurations.
CFD practitioners have also recently begun to analyzegear windage aerodynamics towards the goal of develop-ing a more general design approach. Recent 2-D studies10
were performed using the commercial flow solver FLU-ENT, where a side correlation factor was used to to accountfor 3-D effects (although these authors state that work is un-der way to extend their simulations to 3-D11). Marchesse etal.12 used a similar approach as Al-Shibibl et al.,10 but useda structured grid with the flow solver ANSYS CFX. Theyalso extended their 2-D model into three dimensions, us-ing one tooth passage with periodic boundary conditions astheir computational domain. Imai et al.13 investigated 3-D bevel gears in mesh in an air-oil atmosphere, modelingthe gears as porous bodies. Hill et al.,14 implemented a 3-D, unstructured, overset moving mesh method and appliedit to isolated spur gears in air and validated the methodagainst data due from Diab et al.4
The validated capability developed in our earlier work14
has motivated, among other things, the focus of the presentstudy: to use a CFD model to interrogate the physics as-
sociated with gear windage aerodynamics. The attendantgoal of this is to develop design guidance principles formethods to minimize these power losses in rotorcraft, andpotentially other high speed gear systems. This has beenand will continue to be enabled by the availability of theGlenn Research Center data sets.
The paper is organized as follows: First, the governingequations and numerical procedures are reported. Next aseries of numerical studies are performed that provide in-sight into several of the physical mechanisms of windagelosses including the role of gear shrouding. Next, anoverview of the NASA Glenn Gear Windage Test Facil-ity is provided along with a selection of data obtained todate. CFD simulation of the Glenn windage loss tests arepresented and discussion of these comparisons are pro-vided. Lastly, we present results of a numerical experi-ment, guided by the findings described in the paper, thatdemonstrate a benefit in windage performance beyond thatobserved with shrouds alone.
Theoretical FormulationGoverning Equations
We focus in this paper on the physical mechanisms ofgear windage loss, and mitigation schemes for reducingthem. The available data1–4 shows that windage lossesalready become significant at low subsonic tip Mach num-bers. Accordingly, in this work we restrict ourselves toincompressible analysis. Also, as will be shown, much canbe learned from systems that are either shroud-free or havecompletely axisymmetric shrouds (i.e., fully enclosed ra-dial shrouds) so we consider single-tooth domains that areperiodic and steady in the frame of reference of the spin-ning gear. The conservation of mass and momentum canbe written in integral conservation law form for a systemrotating with constant angular velocity ω as:Z
S
ρV ·dS = 0 (1)
ZS
ρVV ·dS = −ZS
pdS +ZS
τ ·dS−Z∀
ρω× (ω× r)d∀
−Z∀
2ρ(ω× r)d∀ (2)
where V is the velocity vector in the relative frame ofreference. It was shown in Hill et al.14 that a sublayerresolved two-equation turbulence model performed betterthan a high-Reynolds number form with wall-functions inpredicting viscous losses on a spinning disk. Accordingly,in this work we adopt τ = (µ+µt)(∇V +(∇V )T ) and a sub-layer resolved q-ω turbulence model due to Coakley15 isused. The dependent variables in this model are related tothe turbulence kinetic energy, k, and the turbulence dissi-pation rate, ε, through q =
√k and ω = ε/k. In this model,
the eddy viscosity is obtained from:
µt = ρCµDq2/ω (3)
where Cµ = 0.09 and D is the near wall damping function:
D = 1− e−αρqdn/µ (4)
where α = 0.02 and dn is a measure of the normal distanceto the nearest wall. The modeled transport equations for qand ω are:ZS
ρqV ·dS =ZS
(µ+
µt
Prq
)∇q ·dS+
Z∀
ρq2
(CµD
Sω−ω
)d∀
(5)ZS
ρωV ·dS =ZS
(µ+
µt
Prω
)∇ω ·dS+
Z∀
ρ(C1CµS−C2ω
2)d∀
(6)
CFD Code and NumericsOVER-REL
OVER-REL is a parallel, cell-centered, incompress-ible, finite-volume code based on structured overset multi-block grids and the time-marching, pseudo-compressibilityformulation of Chorin.16 Inviscid fluxes are formulatedfrom the Roe-approximate Riemann solver17 and extendedto third-order accuracy through the MUSCL scheme.18
Second-order accurate central differences are utilized forthe viscous fluxes. Numerical derivatives are used to calcu-late the flux Jacobians. A symmetric Gauss-Seidel methodis applied to solve the resulting linear system of equa-tions. In the present application, the code’s turbomachineryanalysis instrumentation is employed; all simulations arecarried out for a single gear tooth, with periodic bound-ary conditions, in a non-inertial frame-of-reference rotat-ing with the gear. OVER-REL is not the code used forour other gear-windage research, NPHASE-PSU,14 sinceit does not support compressible flow, multiphase flow, orunstructured meshes (necessary for complex gearbox ge-ometries). However, it is better suited than NPHASE-PSUto the present physics exploration analyses due to its effi-ciency for cases where a single ”blade-row”/gear tooth canbe used (i.e., axisymmetric shroud).
Overset meshing: SUGGAR and DiRTlibAs illustrated below, the tight shroud clearances stud-
ied lead to mesh topology constraints that in turn lead topoor quality block-structured meshes. OVER-REL is in-strumented with overset meshing capability, which enableshigh quality meshes for these configurations.
The overset assembly process is performed using theSUGGAR code,19 a general overset grid assembly codewith the capability to create the domain connectivity in-formation at node and/or element centers for general gridtopologies. For static grid assemblies with no motion be-tween component grids (as here) the grid assembly is apre-processing step. The inter-grid interpolations producedby SUGGAR use an unweighted least square procedure.
OVER-REL is instrumented with DiRTlib,20 a solverneutral library that encapsulates the functionality requiredby the solver to utilize the overset domain connectivity
information (DCI) produced by SUGGAR. DiRTlib is in-dependent of the CFD solver’s data structures, and cantherefore be used with any solver. The CFD code callsa few functions to initialize the library, load the DCI in-terpolation, transfer the data to appropriate processors in aparallel execution environment, and apply the interpolateddata as boundary values at inter-grid boundary points.
Results
Loss Mechanisms and Budgets in Gear WindageIn their 2004 paper, Diab et al.4 studied four unshrouded,
spur gears and a disk spinning freely in air (i.e., no shroud-ing). The gears varied in diameter, width and tooth count- as summarized in Figure 1. Figure 2 shows resultspublished previously by the present authors.14 There itis observed that the NPHASE-PSU simulations exhibitedvery good agreement with experiment in modeling windagelosses for these configurations.
In this work, free spinning simulations were first carriedout for Diab Gear 1 and disk using OVER-REL. Non-overset multiblock structured meshes were employed forboth as shown in Figure 3. Near-wall grids were con-structed to return wall cell y+ values < 1 and wall normalstretching ratios < 1.2 everywhere in order to adequatelyresolve the high Reynolds number boundary layers thatarise. The grid topologies, near-wall grid spacing, andgrid stretching ratios were maintained as closely as pos-sible between the gear and disk meshes. Per the periodicboundary conditions employed, one tooth passage (2π/72)is modelled for both configurations. In order to stablytime-march the OVER-REL solution, a very small inflowvelocity and a pressure outflow boundary were included inadjacent to the maximum and minimum axial boundariesupstream and downstream of the rotating elements. Thisartificial through-flow velocity was successively reduced towhere no perceptible changes in loss values were returned.
Fig. 1 Diab Gears 1-4. (Only one side of symmetry plane isshown for each gear.) Adapted from Hill et al.14
Figure 2 includes the OVER-REL results for Gear 1and very good agreement with experiment is seen there as
Fig. 2 Comparison of results from experiment,4 NPHASE-PSU,14 and OVER-REL for Diab Gears 1-4.
Fig. 3 Comparison of Diab Gear 1 and disk grids.
well. Figure 4 shows that for Gear 1 the pressure torqueassociated with the integrated pressure difference betweenleading and trailing tooth surfaces, dominates the loss bud-get. As the rotation rate increases, viscous losses remain anearly constant fraction of total loss (10%). Figure 5 showsa comparison of loss results between Gear 1 and the disk.The total losses are much smaller for the disk, which bysymmetry are due to viscous shear alone. This large differ-ence between disk and Gear 1 is particularly striking if wecompare their similar geometries shown in Figure 6.
In Figure 7, the torque per unit span contributed by vis-cous shear is compared for the disk (up to its outer radius)and Gear 1 (up to its base radius). The geometry of thesesystems requires that the all pressure spin-down torque isdue to the pressure differences between the leading andtrailing tooth surfaces. Figure 7 illustrates that the vis-cous losses are very similar between these configurations(indeed the small differences in predicted viscous powervalues are due to very small grid differences) indicating that3D effects (i.e.non-axisymmetric) associated with pressureforces are almost completely responsible for the significant
Fig. 4 Comparison of results from experiment4 and OVER-REL for Diab Gear 1, including viscous and pressure lossbudgets.
Fig. 5 Comparison of Diab Gear 1 and disk measurementsand OVER-REL solutions.
increase in loss for the gear.The physical mechanisms associated with the dominant
spin-down pressure torque are studied by interrogating theCFD results. In Figures 8- 11, several 3D visualizationsare presented for the 850 rad/s case. In Figure 8, a numberof relative frame-of-reference streamlines, colored by localstatic pressure, are plotted. These streamlines are seededclose to the gear face and teeth and integrated in both di-rections. Some of the high speed (in the relative frame)tangential flow near the gear face plane is diverted intothe tooth passage, where strong secondary flows are evi-dent. By symmetry this axial transport arises on both sidesof the gear and therefore leads to impingement of oppo-
Fig. 6 Comparison of Diab Gear 1 and disk geometries.
Fig. 7 Comparison of predicted torque per unit span con-tributed by viscous shear for the Diab disk (up to its outerradius) and Gear 1 (up to its base radius).
sitely directed flow and radial ejection of momentum nearthe gear centerline. Figure 9 shows an axial view of thesame streamlines illustrating the complex secondary mo-tions and an indication of the radial ejection angle. Alsoevident is the radially outward component of flow close tothe face for r < rbase. An axial projection of relative ve-locity vectors is shown in Figure 10 at a plane halfwaybetween the gear face and gear centerline. A vector den-sity of 0.5 (vector plotted for approximately every othergrid point) is applied for clarity. Contours of local nor-malized projected relative velocity magnitude are included(V ∗ =
√V 2
y +V 2x /ωr). Two counter-rotating passage vor-
tices are present. Peak normalized secondary velocity mag-nitudes near 1
2 ωr are observed indicating the strength ofthese secondary motions. The flow at this axial location isreminiscent of a rearward facing step and/or cavity flowwith attendant vortical recirculation regions. Figure 11shows the same plot but near the gear centerline. Here onesees the very significant radial ejection quite clearly. Theflow has a component directed upstream (against the rel-
ative flow) near the leading surface at the tip radius. Themagnitude of the ejection flow induces significant block-age and we see values of V ∗ much less than 1 well beyondthe tip radius.
Fig. 8 Three-dimensional relative frame streamlines coloredby static pressure for Diab Gear 1, 850 rad/s.
Fig. 9 Three-dimensional relative frame streamlines coloredby static pressure for Diab Gear 1, 850 rad/s.
Fig. 10 Axial projection of velocity vectors halfway betweengear face and gear centerline. Diab Gear 1, 850 rad/s. Vec-tor density of 0.5. Background contours of local normalizedprojected relative velocity magnitude.
In Figure 12 contours of static pressure coefficient,CP = (p− p∞)/0.5ρV 2
tip) are plotted for the leading geartooth surface. As seen above, some of the high speedtangential flow near the gear face plane is diverted intothe tooth passage. There is a stagnation where this flow
Fig. 11 Axial projection of velocity vectors near gear cen-terline. Diab Gear 1, 850 rad/s. Vector density of 0.5. Back-ground contours of local normalized projected relative veloc-ity magnitude.
impinges on the leading surface, near the face. The lead-ing surface pressure field can be compared with the muchlower surface pressures on the trailing surface shown inFigure 13. The net spin-down torque due to pressure effectscan be represented by the difference between the leadingand trailing surface pressure coefficients, which is shownin Figure 14. Clearly the net torque is dominated by theimpingement observed in Figures 8 and 12. In Figure 15the torque per unit width is plotted vs. distance from thegear face. Here, torque is nondimensionalized as:
T ∗(x) =
R rtiprinner
∆pdAθdr
dx
[1
12 ρV 2
re f L2re f
](7)
where ∆p is the pressure difference between the gridfaces on the leading and trailing surfaces (which have iden-tical x-r vertex coordinates), dAθ is the tangential projec-tion of the area of the grid face, and r is the radial coordi-nate of the grid face centroid. We see that indeed it is thenear face region that dominates the pressure windage losstorque.
Gear ShroudingAs mentioned in the introduction, several reseachers
have measured improvements in gear windage loss per-formance when shrouds of various configurations are em-ployed.1–3 In this section we study the aerodynam-ics of shrouding in the context of geometrically sim-ple configurations and draw several conclusions thatmay impact design considerations. The Diab Gear 1configuration is studied. Four notional shrouding ar-rangements are considered, nominally Large-Axial-Large-Radial, Small-Axial-Large-Radial, Large-Axial-Small-Radial, and Small-Axial-Small-Radial. Table 1 and Fig-ure 16 quantify the shroud dimensions. These four shroudconfigurations were chosen to be representative of the ex-trema of the full-shroud NASA Glenn tests as detailedfurther below. The smaller axial and radial shrouds clear-ances gave rise to mesh topology constraints that in turnlead to poor quality block-structured meshes unless overset
Fig. 12 Static pressure coefficient contours on the gear lead-ing tooth surface (1/2 of symmetrical gear shown). Diab Gear1, 850 rad/s.
Fig. 13 Static pressure coefficient contours on the gear trail-ing tooth surface (1/2 of symmetrical gear shown). Diab Gear1, 850 rad/s.
meshes are used. Figure 17 shows a cross-sectional viewof the overset mesh topology for a Small-Radial case.
Table 1 Diab Shroud Clearances
Axial Clearance (/Rtip) Radial Clearance (/Rtip)0.0970 0.17330.0044 0.0044
In Figure 18, the predicted windage loss vs. rotationrate is plotted for the free wheel case, validated and stud-ied above, and the four shrouded configurations. All fourof the shrouds give rise to very significant improvements
Fig. 14 ∆CP between gear leading and trailing tooth surfaces(1/2 of symmetrical gear shown). Diab Gear 1, 850 rad/s.
Fig. 15 Pressure torque per unit width vs. axial coordinate(1/2 of symmetrical gear shown). Diab Gear 1, 850 rad/s.
in windage losses. The Large-Axial-Large-Radial shroudprovides a 68% decrease in loss at 850 rad/s; the Small-Axial-Small-Radial shroud approximately a 81% decreaseat this speed. Indeed, distinguishing the performance gainsbetween the shrouded cases is facilitated by not includingthe free spinning results as in Figure 19. Examining thisplot we see that reducing the axial and radial clearancesfrom large to small provide approximately the same level ofadditional benefit over the Large-Axial-Large-Radial case,with the reduction of the radial clearance providing some-what more benefit in this particular case. Applying bothclearance reductions together provides the maximum ben-efit.
Figures 20- 22 show the same three pressure coefficient
Fig. 16 Four notional shroud configurations for Diab Gear 1geometry. Figure is to scale. Black lines define the gear face,tip radius and base radius, dark blue and red lines indicate theLarge-Axial and Small-Axial shrouds, green and cyan linesindicate the Large-Radial and Small-Radial shrouds.
Fig. 17 Cross-section of overset mesh topology for Small-Radial shroud.
plots reported above, but here for the Large-Axial-Large-Radial shroud case, again at 850 rad/s. Several observa-tions are forthcoming. Firstly, the load distribution on theleading surface shown in Figure 20 is qualitatively similarto the unshrouded case (Figure 12), including the stagna-tion region associated with near-face flow diverted into thetooth passage. However, the range of CP values here aremuch smaller than for the free wheel case. (Note that theabsolute values of CP should not be compared betweencases here as this level is determined in the incompress-ible flow solver using a domain ”exit” value of p∞ = 0).
Fig. 18 Comparison of predicted windage losses between freespinning Diab Gear 1 and four shrouded configurations.
Fig. 19 Comparison of predicted windage losses between andfour shrouded Diab Gear 1 configurations
The trailing surface (Figure 21) exhibits a much more axi-ally uniform pressure distribution than the free wheel case(Figure 13), and again the range of CP values here aremuch smaller. Most importantly, in Figure 22 we observea highly edge loaded ∆CP between leading and trailing sur-faces, as observed for the free wheel case, but with a veryreduced range of ∆CP which of course leads to reducedtorque. Figure 23 shows contours of pressure and sur-face shear stress lines on the leading surface for the fourshrouded cases at 850 rad/s. There is can be seen that thegeneral features of impingement/stagnation near the faceremain present for all of the configurations.
In Figure 24, the torque per unit width is plotted vs. dis-tance from the gear face for all four shrouds at 850 rad/s.
Fig. 20 Static pressure coefficient contours on the leadingtooth surface (1/2 of symmetrical gear shown). Diab Gear 1,Large-Axial-Large-Radial shroud, 850 rad/s.
Fig. 21 Static pressure coefficient contours on the gear trail-ing tooth surface (1/2 of symmetrical gear shown). Diab Gear1, Large-Axial-Large-Radial shroud, 850 rad/s.
All four configurations exhibit edge loaded profiles, withtheir integral consistent with the net loss trend reportedin Figure 19. Comparison with Figure 15 shows the dra-matic reduction in pressure torque that has been achievedfor these configurations, but with retention of the basic fea-tures of the pressure torque distribution.
A final exploration study of viscous losses was per-formed on the shrouded Diab gears. Figure 25 shows acomparison of viscous losses per unit span for the un-shrouded case, illustrating the increase in shear torque withrotation rate and span. The viscous loss per unit span isplotted for each of the four shrouded cases and the un-shrouded case at 850 rad/s in Figure 26. There is it ob-
Fig. 22 ∆CP between gear leading and trailing tooth surfaces(1/2 of symmetrical gear shown). Diab Gear 1, Large-Axial-Large-Radial shroud, 850 rad/s.
served that face shear is smaller for all of the shroud casesdue to the ”couette-flow-like” rotational boundary layerthat arises in the presence of an outer axial boundary. Alsoof interest in this figure is the increase in viscous lossfor the Small-Axial shrouds compared to the Large-Axialshrouds. These losses are smaller than for the unshroudedcase but suggest that viscous losses can increase a percent-age of total loss for very small axial shroud clearances.
NASA Glenn Gear Windage Test Facility
Recently, a gear windage test facility has been devel-oped at the NASA Glenn Research Center. This facil-ity is expected to produce the most comprehensive setof gearbox windage data to date, and is providing theCFD validation data required in the present NASA spon-sored research program. The test facility is designed toparametrize the effects of spur gear geometry, shroud ge-ometries and sizes, different lubrication system configura-tions, system pressures and temperatures, and gear meshingon windage loss. It is instrumented to provide data onwindage power loss (spin-down tests), oil fling-off tem-peratures, and pressure (at baffle walls). The test standemploys an open loop regenerative torque system to spintwo gears in mesh. It can also be used to test individualisolated gears. Figure 27 is a diagram of the test facil-ity. Figure 28 is a photograph of the gearbox assemblywith the top cover removed, showing the test gears withoutshrouds. In this work we report data from the first series ofexperiments: air-only, single-gear, fully enclosed axial andradial shrouds. The single gear that is studied is a 13 inchpitch diameter spur gear, the topmost gear in Figure 28.The gear has 52 teeth and a tooth width of 1.12 inches.The gear has some modest geometric complexities com-pared to the idealized Diab gear studied above, including
Fig. 23 Contours of pressure and surface shear stress lines onthe leading surface for the four shrouded cases at 850 rad/s.
Fig. 24 Plot of torque per unit width from the gear face forthe four shrouded cases.
Fig. 25 Comparison of viscous losses per unit span for DiabGear 1 at various spin rates.
Fig. 26 Comparison of viscous losses per unit span for DiabGear 1 at 850 rad/s for unshrouded and four shreouded con-figurations.
tooth chamfering, root rounding and narrowing of the gearwidth below the base radius to reduce gear weight/inertia.These features are shown in Figure 29 and were accom-modated in the CFD model. The test fixture was designedto accommodate numerous shroud spacing configurations.Specifically, the baffle housing, pictured in Figure 30, hasadjustable axial and radial wall clearances. The housingallows for up to 36 different fully-enclosed baffle config-urations to be tested in the facility - report the data forand analyze the four extrema: Large-Axial-Large-Radial,Large-Axial-Small-Radial, Small-Axial-Large-Radial, andSmall-Axial-Small-Radial. Table 2 lists these four axialand radial clearance dimensions.
Table 2 Shroud Wall Clearances Studied
Axial Clearance (in.) Radial Clearance (in.)0.030 0.0301.170 0.655
Fig. 27 CAD model of the NASA Glenn Gear Windage TestFacility.
Fig. 28 Photograph of the NASA Glenn Gear Windage TestFacility gearbox assembly with the top cover removed and noshrouds.
Speed data is measured using inductive pickups that reada 60 tooth disc on the end of each of the shafts. The outputfrom the sensor (pulse / sine wave) is sent to a frequencyto voltage converter. The output from the convertor is thensent to a National Instruments card and read by Labview.Data was taken at 10 Hz.
Data from the NASA Windage Test Stand was measuredin the following manner. In the tests reported here, therewas only an input gear and the gear was operated in a to-tally enclosed shroud (no drain holes in the shroud). Duringthe operation of the test facility discrete speeds were main-tained and data (speed, torque, oil fling-off temperatures,and pressure at shroud walls) were taken. This was also
Fig. 29 View of the spur gear studied (on the right), illus-trating the chamfer, root rounding, and gear width reductionbelow the base radius.
Fig. 30 Shroud configurations in the NASA Glenn GearWindage Test Facility.
done at the same speeds for a shaft-only configuration (thetest gear was removed). Driving torque data was taken attwelve discreet speeds with and without the gear present.The net effect of the gear was found by subtracting the shaftonly torque from the total torque to operate the shaft andgear shroud arrangement together. Windage loss power iscomputed using the known rotational intertia of the gear(measured separately in a pendulum fixture).
Experimental and Computational Results forthe Glenn Facility Tests
Grids were developed for the 13-inch pitch diameterspur gear configuration using similar topologies as the Diabcases. To date three shrouded configurations have been se-lected for study. Table 2 lists the four baffle configurationsstudied computationally; the ”Small-Axial-Large-Radial”configuration has not yet been run in the NASA test rig.
Figure 31 shows comparison of the Glenn data andOVER-REL predictions for the Large-Axial-Large-Radial,Large-Axial-Small-Radial and Small-Axial-Small-Radialshroud configurations. Between 5 and 12 experimental datapoints were taken for each speed line. These data werecurve fit using a cubic polynomial - resulting R values wereall above 0.997 - and these curves are plotted in Figure 31.The data shows the same trends as the idealized Diab gearCFD studies reported above. Specifically, the Large-Axial-Large-Radial shrouding exhibits the highest loss levels, andthe Small-Axial-Small-Radial shrouding exhibits the low-est loss levels. The benefit realized by reducing both clear-ances is somewhat more substantial than for the Diab case.The CFD results are seen here to provide fairly good agree-ment with measured values. An interesting observation inthe CFD results is that the Large-Axial-Small-Radial andSmall-Axial-Large-Radial results are nearly identical alongthe entire speed line.
The qualitative correspondence between the Glenn andidealized Diab cases presented earlier, suggests that thesame physical loss mechanisms are acting. Figure 32shows a view of predicted relative streamlines colored bypressure for the Large-Axial-Large-Radial shroud case at700 rad/s. This image exhibits several of the features ob-served for the idealized case including diversion of the nearface flow into the tooth passage and impingement uponthe leading surface, strong axial secondary vorticity in thetooth passage, strong ejection of this flow near the toothcenterline and radial flow of the near-face streamlines be-low rbase.
Design Alternatives
It was demonstrated above that axial and radial shroud-ing can reduce windage losses. Some of the physics ofthese loss reduction schemes were studied there. Despitethe experimentally and computationally observed differ-ences in loss magnitudes between unshrouded and various
Fig. 31 Experimental results And CFD results for the 13”pitch diameter NASA spur gear.
Fig. 32 Three dimensional relative frame streamlines coloredby static pressure for the 13” pitch diameter NASA spur gear,Large-Axial-Large-Radial shroud, 700 rad/s.
shrouded configurations, in all cases a significant compo-nent of the torques associated with spin down arose fromimpingement onto the leading surface of the high veloc-ity relative-frame flow drawn into the tooth passage. Ac-cordingly, in this section we return to the geometricallyidealized Diab Gear 1 configuration, and experiment nu-merically with four proposed tooth geometry modificationsaimed at mitigating this impingement and attendant spindown torque. Figure 33 shows an oblique view of thefour alternative geometries considered: 1) leading surfacetooth-edge rounding, 2) leading+trailing surface tooth-edgerounding, 3) double slots on the top of the teeth and, 4)trailing surface ramp.
Figure 34 shows a comparison of these four simula-tions with the baseline Large-Axial-Large-Radial case. Theleading surface rounding and double slot geometries returnnearly identical windage loss. The leading+trailing sur-
Fig. 33 Tooth geometry alternatives - from top: leadingsurface rounding, leading+trailing surface rounding, slot andtrailing surface ramp.
face rounding returns somewhat higher loss. However, thenet loss obtained using the trailing surface ramp is approx-imately 30% lower than the baseline configuration. Thetorque per unit width for the five geometries are plotted inFigure 35. There it can be seen that the ramp configurationexhibits much smaller torques within the tooth channel andthis clearly results in the reduced integrated loss for the en-tire gear.
To further elucidate the physics involved in these numer-ical studies, Figures 36- 40 are presented. In each of thesefigures, predicted surface pressure coefficients contours areplotted along with selected surface skin friction lines. Thebaseline and two rounded geometries exhibit largely samequalitative flow features, with the rounded cases ”smear-ing” the leading face impingement and trailing face detach-ment gradients. The tooth slots were conceived to ”flush”the peak axial vorticity/low pressure regions with highervelocity incoming relative flow thereby reducing the axialpressure gradient and thereby the diverting the high rela-tive velocity near-face flow into the passage. This appearshere to not have achieved the desired result. The trailingsurface ramp geometry did have a significant impact on theaerodynamics. Specifically, the relative flow near the faceis turned away from the gear. This turning induces a localpressure rise on the ramp which contributes to spin-downtorque. However, this flow has been diverted away from thetooth enough that subsequent diversion of this flow into thetooth passage has been virtually eliminated, resulting in al-most no pressure rise on the leading surface. This gives riseto the much small torques shown in Figure 35. So the im-proved net performance of the ramp configuration observedin Figure 34 is clearly due to the reduced integrated toothpassage torque more than offsetting the increased torqueassociated with the ramp turning itself.
Fig. 34 Windage loss predictions for the baseline tooth ge-ometry (Diab Gear 1 with Large-Axial-Large-Radial shrouds)and four geometric alternatives.
Fig. 35 Torque per unit width predictions for the baselinetooth geometry (Diab Gear 1 with Large-Axial-Large-Radialshrouds) and four geometric alternatives at 850 rad/s.
Fig. 36 Predicted surface pressure coefficient and skin fric-tion lines for baseline tooth geometry.
Fig. 37 Predicted surface pressure coefficient and skin fric-tion lines for tooth geometry alternative: leading surfacerounding.
Fig. 38 Predicted surface pressure coefficient and skin fric-tion lines for tooth geometry alternative: leading+trailing sur-face rounding.
Fig. 39 Predicted surface pressure coefficient and skin fric-tion lines for tooth geometry alternative: tooth slot.
Fig. 40 Predicted surface pressure coefficient and skin fric-tion lines for tooth geometry alternative: trailing surfaceramp.
ConclusionThis paper has summarized a number of CFD studies fo-
cused on the aerodynamics of gear windage losses. Thegoals of the work have been to validate the numerical andmodeling approaches used for these applications and to de-velop physical understanding of the aerodynamics of gearwindage loss. Comparisons are made with experimentaldata from the open literature, and data recently obtained inthe NASA Glenn Research Center Gear Windage Test Fa-cility. Parametric shroud configuration studies carried outin the Glenn experiments and the CFD analyses elucidateimportant physical mechanisms of windage losses as wellas mitigation strategies due to shrouding and newly pro-posed tooth contour modifications.
The following conclusions apply: 1) The Glenn data andCFD analyses show that axial and radial gear shrouding areeffective in significantly reducing gear windage losses bothindependently and when employed together. 2) For all con-figurations studied, the dominant physical mechanism con-tributing to windage losses is the pressure field associatedwith diversion and impingement of the high speed relativeflow on the leading tooth surface. 3) Shrouding mitigatesthe magnitude of this mechanism but not its dominancein the loss budget. 4) The CFD results show good agree-ment with the Glenn experiments. 5) The Glenn data showsquite similar loss trends to the idealized shrouded gear con-figurations studied computationally. 6) Viscous losses arereduced by shrouding as well, but are a small componentof the total loss so this effect is not important. However,small axial clearances were observed computationally toincrease viscous losses compared to larger shroud clear-ances, suggesting that this effect could become importantfor even smaller clearances and at higher speeds. 7) TheCFD studies suggested a set of possible geometric toothmodifications to further reduce windage loss. One of theseappears quite promising and the authors anticipate studyingthis in the Glenn facility.
Our continuing work in the gear windage aerodynamicsarea focuses on: 1) Further validation for shrouded gears asmore Glenn data becomes available, 2) Multi-phase flows,3) Overset gridding in the context of gear tooth contact,and 4) Further evolution of design guidance for minimizingwindage losses.
AcknowledgmentsThis work was supported by NASA under NASA Coop-
erative agreement NNX07AB34A.
References1Don D. Winfree, “Reducing Gear Windage Losses from High Speed
Gears,” AME Power Transmission and Gearing Conference, ASME, Bal-timore, MD, Sept. 2000.
2P. H. Dawson, “Windage loss in larger high-speed gears,” Proc InstnMech Engrs, Vol. 198A, No. 1, 1984, pp. 51–59.
3P. H. Dawson, “High Speed Gear Windage,” GEC Review, Vol. 4(3),1988, pp. 164–167.
4Y. Diab, F. Ville, P. Velex, and C. Changent, “Windage Losses inHigh Speed Gears - Preliminary Experimental and Theoretical Results,”Journal of Mechanical Design, Vol. 126, Sept. 2004, pp. 903–908.
5Neil E. Anderson and Stuart H. Loewenthal, “Spur-Gear-System Ef-ficiency at Part and Full Load,” Tech. rep., NASA, 10 Dec. 1979, TP 1622AVRADCOM TR 79-46.
6Neil E. Anderson and Stuart H. Loewenthal, “Effect of Geometryand Operating Conditions of Spur Gear System Power Loss,” Journal ofMechanical Design, Vol. 103, Jan. 1981, pp. 151–159.
7Neil E. Anderson and Stuart H. Loewenthal, “Efficiency of Nonstan-dard and High Contact Ratio Involute Spur Gears,” Fourth InternationalPower Transmission and Gearing Conference, ASME, Cambridge, MA,Oct. 1984, NASA TM 83725 USAAVSCOM TR 84-C-9.
8Robert F. Handschuh and Charles J. Kilmain, “Preliminary Inves-tigation of the Thermal Behavior of High-Speed Helical Gear Trains,”International Conference on Gears, International Federation for the The-ory of Machines and Mechanisms, Munich, Germany, March 2002,NASA/TM-2002-211336 ARL-TR-2661.
9Petra Heingartner and David Mba, “Determing Power Losses in theHelical Gear Mesh,” Gear Technology, Sept. 2005.
10K. Al-Shibl, K. Simmons, and C. N. Eastwick, “Modelling windagepower loss from an enclosed spur gear,” Journal of Power and Energy,Vol. 221, 2007, pp. 331–341, Proc. IMechE Part A.
11Carol N. Eastwick and Graham Johnson, “Gear Windage: A Re-view,” Journal of Mechanical Energy, Vol. 130, March 2008.
12Y. Marchesse, C. Changenet, F. Ville, and P. Velex, “Investigationson CFD Simulation fro Predicting Windage Power Losses in Spur Gears,”3rd International Conference on Integrity, Reliability and Failure, Porto,Portugal, July 2009.
13Hideyuki Imai, Tatsuhiko Goi, Hidenori Arisawa, and MotohikoNishmimura, “Reduction in Gear Windage and Churning Loss by Opti-mum Shroud Desing with aid of CFD,” JSME International Conference onMotion and Power Transmission, JSME, Matsushima Isles Resort, Japan,May 2009.
14Hill, M. J., Kunz, R. F., Noack, R. W., Long, L. N., Morris, P. J., andHandschuh, R. F., “Application and Validation of Unstructured OversetCFD Technology for Rotorcraft Gearbox Windage Aerodynamics Sim-ulation,” 64th Annual Forum of the American Helicopter Society, April2008.
15Thomas J. Coakley, “Turbulence Modeling Methods for the Com-pressible Navier-Stokes Equations,” 1983, AIAA 83-1693.
16Chorin, A. J., “A Numerical Method for Solving Incompressible Vis-cous Flow Problems,” Journal of Computational Physics, Vol. 2, No. 12,1967.
17Roe, P. L., “Approximate Riemann solvers, parameter vectors anddifference schemes,” Journal of Computational Physics, Vol. 43, 1981,pp. 357–372.
18van Leer, B., “Towards the ultimate conservative differencesscheme, V. A second order sequel to Godunov’s methods,” Journal ofComputational Physics, Vol. 32, 1979, pp. 101–136.
19Noack, R. W., “SUGGAR: a General Capability for Moving BodyOverset Grid Assembly,” 17th AIAA Computational Fluid Dynamics Con-ference, AIAA, Toronto, Ontario, Canada, June 2005, AIAA 2005-5117.
20Ralph W. Noack, “DiRTlib: A Library to Add an Overst Capabilityto Your Flow Solver,” 17th AIAA Computational Fluid Dynamics Confer-ence, AIAA, Toronto, Ontario, Canada, June 2006, AIAA 2005-5116.
