numerical simo

8/17/2019 Numerical Simo

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Numerical simulation of oil and air two-phase flow in aplanetary gear system using the overset mesh technique

Jaeyeol Cho1, Nahmkeon Hur

1*, Jongrak Choi

, Jiwon !oon

ISROMAC 2016

International

Symposium on

Transport

Phenomena and

Dynamics o

Rotatin! Machinery

"a#aii$ "onolulu

April 10%1&$ 2016

A'stract

"lanetary gear systems are widely used in differentials, transmissions and #rake systems of manyindustrial machineries$ %ften, the components inside such a system are fully or partially su#merged inoil, which serves for simultaneous lu#rication and cooling$ Hence, this oil recirculation is a key elementfor the dura#ility and performance$ &he focus of this paper is two-phase flow analysis of a planetarygear system at different initial oil level and, also, its application in a transa'le #rake assem#ly$ (sually,due to the comple' multi-phase flow phenomena inside the transa'le cham#ers, their simulation isarduous, and hence, little technical information e'ist a#out the details of their multi-phase phenomena$)n order to imitate a real case situation, the numerical simulations are solved in an unsteady frameworkusing the *eali+a#le k-ε tur#ulence model together with the volume of fluid %./ method$ %versetmesh technique is used to simulate the rotating planetary gear and the #rake pad, which allows morerealistic simulation of gears engagement$ &he aims are to predict flow characteristics, quality of lu#rication and also heat transfer inside the #rake during its operation$ &he results are presented anddiscussed in terms of lu#rication and cooling efficiency$ &he outcomes can #e used to improve the

design of e'isting #rake oil lu#rication$$

(ey#ords

"lanetary gear0&ransa'le #rake0C.02ultiphase0Heat transfer03u#rication

1Department of Mechanical Engineering, Sogang University, Seoul, Ko re a

Department of Research and Development, LS Mtron, Gunpo, Korea

*Correspondin! author 4 nhur 5 sogang $ac$kr

I)TROD*CTIO)

"lanetary gears are usually used for com#ination of power shafts with different types of gears which might #e used indifferentials, transmissions and transa'le #rake systems in many machineries, such as automo#iles and trains$ 6 planetary gear is composed of a sun gear at the center, planet gears and a ring gear$ %ften oil is used for the lu#rication and cooling of themechanical parts engaged in the rotation, including gears, #rake pads and shafts$ 7ince, the mechanical part might #e partiallysu#merged in the oil, the oil and air form two-phase phenomena, which are rather impossi#le to #e fully predicted andunderstood without numerical simulations$ )n this case C. method can #e an appropriate solution$

&adashi !amada 819 simulated thermal characteristics of the the coolant inside of the powertrain$ He predicted oil and air multiphase flow characteristics and con:ugate heat transfer using a mesh regeneration method for rotating gears and %.olume of .luid/ method$ &his numerical method was validated #y comparing with e'perimental data, and the results were usedfor improving powertrain performance and efficiency$ !a+dani and 7oteriou 89 studied oil :et effect at the simple gear systemusing a mesh regeneration technique and %. method$ &hey compared cooling efficiency of oil according to velocity of oil :et$7tosic 8;9 investigated oil and air multiphase flow and temperature characteristic inside of compressor using screw gears$ 7imilar to the previous works, mesh regeneration method and %. method were applied$ Nirvesh 2ehtha et al$ 89 investigated relation #etween oil churning loss and oil level #y gear simulation using mesh regeneration method$

=ased on the difficulties and limitations of the e'isting numerical techniques, simulation of a compact rotating gear system inthe presence of circulating oil and considering heat transfer pro#lem in a single framework needs a very high computationalresource$ )n addition, these kinds of simulations have to #e carried out using unsteady multiphase flow assumptions$.urthermore, an appropriate mesh technique with sufficient mesh resolution is required, which usually results in a larger num#er of computational cells, which has #een a draw#ack for many scholars$ 2oreover, the 2*. method which is usually used for thesimulations is not inherently appropriate for these simulations, which is due to the fact that 2*. requires some simplifications inthe overlapped regions, which causes considera#le discrepancies #etween the simulations and the e'periments$ Hence, a fewcomprehensive sources and reports are availa#le, in which all of the previous important simulation parameters are appropriatelyconsidered$

&his research aims at investigation of the effects of initial oil level in planetary gear and unsteady heat transfer and oilcirculation inside a transa'le #rake$ &o do so, first, the required mesh resolution for overset mesh technique and other necessaryC. factors such as timestep are inverstigated during the planetary gear simulation$ 3ater, the transa'le is simulated taking into

ATIN

SIAONRO

T

S Y MPO

GMACHINER Y

mailto:[email protected]:[email protected]:nhur@sogang.


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account the results of the planetary simulations, and the predictions a#out the two-phase interaction of the oil and air, in thepresence of heat transfer are investigated$ &he study is carried out using a commercial C. solver, 7&6*-CC2? 1@$@ on thecomputer cluster of C.-A*C of 7ogang (niversity, Borea$ &he typical solution times for the planetary gear and transa'le are@ hours and 1D@ hour using D@ cores )ntel Eeon A>-FF@ v, $@ GH+ C"(s/$

1+ ,O-.R)I), ./*ATIO)S

&he numerical simulations consider the mass and momentum conservation equations for incompressi#le flows$ )n addition,

for the pressure and velocity coupling, the 7)2"3A scheme is adopted$ &his scheme consider relation #etween velocity andpressure correlations to enforce mass conservation and to o#tain pressure distri#ution$ &he mass conservation equations can#e e'pressed as4

( ) 0 j j

u x

ρ ∂

=∂

1/

&he momentum conservation equation is 4

( )i j i ij i j i

u pu u s

t x x

ρ ρ τ

∂ ∂ ∂+ − = − +

∂ ∂ ∂

/

&he %. method is used for oil and air multiphase flow simulation$ &his model considers the volume fraction for each fluidand tracks free surface of the immisci#le fluid regions$ &he location of interface #etween oil and air can #e determined fromthe distri#ution of volume fraction in domain$ .luid properties such as density and viscosity are calculated #ased on volumefractional average$&he equations physical properties are calculated as 4

i i i ρ ρ φ = ∑

; - a /

i i i µ µ φ = ∑

; - # /

( ) p i i p i i

c

c

ρ

φ ρ = ∑ ; - c /

wherei

φ

is the volume fraction of phase ) and evidently4

1iφ =∑ /

=ecause of fast rotating gears, the flow regime is tur#ulent, *eI1@,@@@,@@@/$ &o take into account the effects of tur#ulent flows

inside, the *eali+a#le k-ε

tur#ulence model is used$ &his model is #ased on transport equation for tur#ulent kinetic energyand dissipation rate and has #een reported to have certain advantages in the modeling rotating and swirling flows$ &hetransport equations of kinetic energy and dissipation rate can #e presented as4


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,

( ) [ ( ) ]

1 ( )

2 ( )

3

i j

j k j

i iij

j h t i

i it

i i

k k u k

t x x

u g S

x x

u uk

x x

µ ρ ρ µ

σ

ρ µ ρε

σ ρ

µ ρ

∂ ∂ ∂+ − +

∂ ∂ ∂

∂ ∂= − −

∂ ∂

∂ ∂− +

∂ ∂ F/

1

2

3 2 4

,

( ) [ ( ) ]

2 [ ( ) ]

3

1 ( )

t j

j j

i it t

i

i it

h t i i

ut x x

u uC P k

k x

g uC C C

k x k x

ε

ε

ε

ε ε ε

µ ε ρε ρ ε µ

σ

ε µ µ ρ

σ

ε ρ ε µ ρ ρε

σ ρ

∂ ∂ ∂+ − +

∂ ∂ ∂

∂ ∂= − +

∂

∂∂− − +

∂ ∂

/

where

k 1

2 3 4

0.009, 1.0, 1.22, 0.9, 0.9, 1.44,

C 1.92, C 1.44, C 0.419

h mC C µ ε ε

ε ε ε

σ σ σ σ = = = = = =

= = =

%verset mesh, also known as Chimera, is used to discreti+e a computational domain with multiple differentmeshes that overlap each other in an ar#itrary manner$ %verset mesh does not need any mesh modification after generating the initial mesh$ 6n overset mesh simulation needs #ackground cells enclosing the entire solutiondomain and multiple smaller regions containing the #odies with in the domain$ )n overset mesh, cells are consistof active, inactive and acceptor types$ 6t the active cells, discreti+ed governing equations are solved$ 6t theinactive cells, no equation is solved$ &he active cells and inactive cells change interactively #y motion of #odies$ )naddition, acceptor cells separate active and inactive cells #etween #ackground region and overset region andthese cells are used to couple solutions #etween two overlapping grids$ 7olution values at donor cell at#ackground region and overset region transferred to acceptor cell through interpolation$ &he donor cells are theactive cells from other mesh that are nearest the acceptor cell$ 6ll the solution #etween donor cell and acceptor

cell are calculated simultaneously$ &his means all the meshes are implicitly coupled$

2+ ,.OM.TR A)D M.S" R.SO*TIO)

"lanetary gears are one su#-assem#ly part in the transa'les$ Hence, prior to the simulations of the transa'le, aseries of simulations for a panletary gear has #een conducted in order to provide a technical C. foundation for the transa'le$ "lanetary gear consists of a sun gear, planet gears and a ring gear$ &he dimensions of thesimulated planetary gear are sun gear diameter I1@> mm, plane t gear diamete r


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i!ure 1+ Geometry of planetary gear

;IF1 mm and ring gear diameter 1I> mm$ )n the present model, num#er of ring gear teeth is F< and num#er of sun gear teeth is 1


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i!ure 3+ Geometry of transa'le #rake

i!ure 4+ 2esh arrangement of transa'le #rake

&he C. mesh domain is composed five rotational and one stationary su#-domains$

i!ure &+ =rake heat generation region


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3+ R.S*TS A)D DISC*SSIO)S

.or the C. simulations, the oil density, specific heat, conductivity and viscosity are assumed as @$D@, @/

3+1 Planetary !ear simulation&he planetary gear simulations are continued until the steady state condition is achieved the steady state condition

:udged #y instanteneous volume fraction of oil distri#ution, the heat transfer coefficient of planetary gear surfaceand churing energy loss of oil in whole domain and is o#served after appro'imate operational time of sec$/$ &hevalues of steady state volume of fraction distri#ution, velocity magnitude and also heat coefficient versus the initialoil level are showen in .igures F-D, respectively$ 6s it can #e seen, for the cases with higher oil level, more oil isdispersed on the gears$ )n the .igure F, volume fraction of oil distri#ution according to initial oil level are shown$ )ncase of ;@, oil does not considera#ly reach to the central and upper regions of planetary gear, and merely triviallyscattered oil reachs to middle and u p p e r

i!ure 5+ 7teady state velocity distri#ution in planetary gear according to oil level ;@, >@, @/


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i!ure + "redicted heat transfer coefficient according to oil level

i!ure 7+ "redicted churning energy loss according to oil level

regions$ )n case of >@, oil reaches higher, #ut still only relatively low amount of oil reachs to the upper region$However, when the initial level of oil is @, all regions are noticea#ly effected #y lump of oil$ )n the .igure ,velocity magnitude distri#ution after the operational time of second are shown$ Near the sun gear teeth, velocity

magnitude is highest #ecause of the effects of sun gear rotation$ )n the .igure D, average heat transfer coefficientof gear surface is shown according to initial oil level$ )n case of ;@,>@ and @ the heat transfer coefficientsare claculated as @@@ OLmMB, 11@@@ OLmMB and 1@@@ OLmMB, respectively$ &hese results show that initial oillevel is a crucial factor for improving the cooling effects in a planetary gear assem#ly$ Hence, to enhance thecooling effect, increasing the amount of oil can #e considered$ )n the .igure , churning energy loss at steadystate is shown according to initial oil level$ )n case of ;@ churning energy loss is calculated a#out @$@@@ JLkg,a#out @$@@@> JLkg for >@ and a#out @$@@1 JLkg for @ initial oil level$ &hese results show that the higher oillevel cause more energy loss of rotating gear$ Ohen initial oil level increases ;@ to @, energy loss increasesmore then si' times higher$ &his energy loss is related to the oil resistance against the rotation of the gears$ 6 verysimilar trend has #een reported #y other scholars81,>9, in which the increasing the oil level causes increasingchurning energy loss$

3+1 $ Transa8le 'ra9e simulation

.or the transa'le #rake simulations, oil properties are same with the planetary gear system, the and initial oil levelis assumed to #e >@$ otation speed of the planetary gear of #rake is same with previous planetary gear simulation$ =rake pad is engaged with planet gear cover and it rotates at the same rotating speed$ Ohen #rake isoperating, the heat is generated on #rake pad and gears surfaces$ &he heat generation during the


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i!ure 10+ olume fraction of oil inside of #rake


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i!ure 11+ &emperature contour inside of #rake

operation is calculated and assumed to #e 1>@@ O for #rake pad and F@@O for gear surface t hese values are assumed to#e close to the real case situation/$ 6s shown in .igure ;, there e'ists a cold oil reservoir at the left side and planetarygears at the right side of the #rake pad$ )n addition, four holes are designed on the #rake pad for oil transfer #etween the leftand right sides for the sake of cooling$ 6lso these holes are made to increase surface attached with oil and air for effectivecooling whole #rake pad$ However, the pro#lem of overheating still e'ists, which is caused #y ineffective oil flow #etween thecold oil reservoir and the planetary cham#er$ &his issue is related to the churning of the oil around the #rake pad and oildespersion apart form the #rake pad as a result of centrifugal forces$ 7imilar to the previous part, the simulation iscontinued until the results of %. distri#ution #ecome steady state after appro'imately sec$/ $ Hence, as it can #eseen in .igure 1@d/, when the flow reaches its steady state condtion, the oil flow #etween the two sides is severly decreased+

6s shown, there e'ist only the air phase around the #rake pad$ 7o, there is no oil recirculation #etween cold reservoir regionand planetary gear cham#er$ =y heat generation of #rake pad, left side of the #rake is heated first$ 6t first, #ecause of therotation of planetary gear, heat of planetary gear dissipates well$ However, as the rotation continues, the temperature inside theplanetary cham#er increases$

&his pro#lem is also addressed #y !an+hong Oang et al$ 8F9 as Pspin flow effectP$ &hey simulated one pair of rotating gearswith stationary oil and oil :et and concluded that rotation of the gears decreases the quality of lu#rication and oil circulationinside the cham#er$ 6ccordingly, in the present research the Pspin flow effectP increases with the rotational speed of the #rakepad$ 6s a inevita#le consequence of this Pspin flow effectP, heated oil remains in the the planetary cham#er of the #rake andthe amount of heat trnasfer rate is very lower than the required amount of heat transfer for cooling planetary cham#er of the

#rake$ 6s time increases, this phenomenon causes the oil temperature rise inside the planetary cham#er as depicted in .igure11/$

&o over come this pro#lem, several methods are suggested$ 6ccording to planetary gear result, using more oil and filling the oilreservoir to a higher level is one solution to increase cooling effect$ )t is also helpful to devise a #y-pass pipeline for oile'change #etween the oil reservoir and planetary cham#er, in order to compensate the spin flow effect$

4+ CO)C*DI), R.MAR(S

)n the present research, the unsteady tur#ulent multiphase flow analysis of a planetary gear system and a transa'le #rake aresimulated in the presence of heat transfer using the overset mesh technique$ "rior to run the transa'le simulation, theplanetary gear is simulated using similar fluid properties at different initila levels of oil in order to achieve the appropriateresolution for the overset mesh technique and other C. settings$ &he planetary gear simulations are carried out for oil levelsof ;@,>@ and @$ &he heat transfer coefficient versus oil level has #een calculated$ )n addition, the oil churning energy

loss versus oil level is plotted$ (sing the same mesh resolutin, the transa'le #rake simulation has #een conducted with >@ oillevel, and the phase distri#ution and heat characteristics inside the #rake are o#tained$ .urthermore, the reason of overheatingpro#lem of transa'les is found to #e the #lockage of oil circulation inside the cham#er #etween two sides of the #rake pad spinflow effect/$ &his phenomenon is mainly caused #y the #rake pad fast rotation$ 6ccording to the results, it is suggested to add a#y-pass oil pipe to connect two oil cham#ers on #oth sides of the #rake pad in order to compensate the spin flow effect$

R..R.)C.S

:1; &adashi !amada, 2easurement and prediction technology of cooling capa#ility for hy#rid drivetrain components, 6utomotive simulation world congress, @1-, @11->;@,@1>$

4; Nirvesh 2ehta, *avi B$ ayatar, Nilesh J$ "arekh, C. analysis of gear#o', )nternational Journal of Angineering*esearch Q &echnology, o 4)ssue ;, @1;$

&; 3i 3i, Henk B versteeg, Graham B hargreve, Numerical investigation on fluid flow of gear lu#rication, )nternationalJournal of Heat and 2ass &ransfer, 141F-1;, @11$

6; !an+hong Oang, Oinstao Niu, 7ong Oei, Guanhua 7ong, )nfluence of spin flow on lu#ricating oil :et designmethod of oil spray parameters to high speed spur gears, &ri#ology )nternational, @4@-;@@, @1>$


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5; .ranco Concil, Corlo Gorla, 6 new methodology for the prediction of the no-load losses of gears 4 C. ande'perimental investigation of the efficiency of a planetary gear#o', )nternational Conference on Gears, ol, @11$

; 6ndrea acca, 2arco Guidetti, 2odeling and e'perimental validation of e'ternal spur gear machines for fluidpower application, 7imulation 2odeling "ractice and &heory, 14@@-@;1, @11$

7; $ del Campo, *$ Castilla, G$ 6$ *aush, Numerical analysis of e'ternal gear pumps including cavitation, Journalof .luids Angineering, ol 1;


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Article Title


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Article Title /

=ecause of fast rotating gears, the flow regime is tur#ulent,*eI1@,@@@,@@@/$ &o take into account the effects of

tur#ulent flows inside, the *eali+a#le k- ε tur#ulence modelis used$ &his model is #ased on transport equation for tur#ulent kinetic energy and dissipation rate and has #eenreported to have certain advantages in the modeling rotatingand swirling flows$ &he transport equations of kinetic energyand dissipation rate can #e presented as4

,

( ) [ ( ) ]

1 ( )

2 ( )3

i j

j k j

i iij

j h t i

i it

i i

k k u k

t x x

u g S

x x

u uk x x

µ ρ ρ µ

σ

ρ µ ρε

σ ρ

µ ρ

∂ ∂ ∂+ − +

∂ ∂ ∂

∂ ∂= − −

∂ ∂

∂ ∂− +∂ ∂

F/

1

2

3 2 4

,

( ) [ ( ) ]

2 [ ( ) ]

3

1 ( )

t j

j j

i it t

i

i it

h t i i

ut x x

u uC P k

k x

g uC C C

k x k x

ε

ε

ε

ε ε ε

µ ε ρε ρ ε µ

σ

ε µ µ ρ

σ

ε ρ ε µ ρ ρε

σ ρ

∂ ∂ ∂+ − +

∂ ∂ ∂

∂ ∂= − +

∂

∂∂− − +

∂ ∂

/

where

k 1

2 3 4

0.009, 1.0, 1.22, 0.9, 0.9, 1.44,

C 1.92, C 1.44, C 0.419

h mC C µ ε ε

ε ε ε

σ σ σ σ = = = = = =

= = =

%verset mesh, also known as Chimera, is used todiscreti+e a computational domain with multipledifferent meshes that overlap each other in anar#itrary manner$ %verset mesh does not need anymesh modification after generating the initial mesh$ 6noverset mesh simulation needs #ackground cellsenclosing the entire solution domain and multiple

smaller regions containing the #odies with in thedomain$ )n overset mesh, cells are consist of active,inactive and acceptor types$ 6t the active cells,discreti+ed governing equations are solved$ 6t theinactive cells, no equation is solved$ &he active cellsand inactive cells change interactively #y motion of #odies$ )n addition, acceptor cells separate active andinactive cells #etween #ackground region and oversetregion and these cells are used to couple solutions#etween two overlapping grids$ 7olution values atdonor cell at #ackground region and overset regiontransferred to acceptor cell through interpolation$ &hedonor cells are the active cells from other mesh that

are nearest the acceptor cell$ 6ll the solution #etweendonor cell and acceptor cell are calculated

simultaneously$ &his means all the meshes areimplicitly coupled$

2+ ,.OM.TR A)D M.S" R.SO*TIO)

"lanetary gears are one su#-assem#ly part in thetransa'les$ Hence, prior to the simulations of thetransa'le, a series of simulations for a panletary gear has #een conducted in order to provide a technical C.foundation for the transa'le$ "lanetary gear consists of a sun gear, planet gears and a ring gear$ &hedimensions of the simulated planetary gear are sungear diameter I1@> mm, planet gear diameter

i!ure 1+ Geometry of planetary gear

;IF1 mm and ring gear diameter 1I> mm$ )n thepresent model, num#er of ring gear teeth is F< andnum#er of sun gear teeth is 1


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Article Title @$ &he rotation rate of planetary gear system in transa'le #rake is same withplanetary gear simulation$ &his operating condition for the

transa'le is defined to #e very close to the highest speedcondition of an industrial transa'le #rake$


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Article Title @, @/

3+2 Planetary !ear simulation&he planetary gear simulations are continued until thesteady state condition is achieved the steady statecondition :udged #y instanteneous volume fraction of oildistri#ution, the heat transfer coefficient of planetary

gear surface and churing energy loss of oil in wholedomain and is o#served after appro'imate operationaltime of sec$/$ &he values of steady state volume of fraction distri#ution, velocity magnitude and also heatcoefficient versus the initial oil level are showen in.igures F-D, respectively$ 6s it can #e seen, for thecases with higher oil level, more oil is dispersed on thegears$ )n the .igure F, volume fraction of oil distri#utionaccording to initial oil level are shown$ )n case of ;@,oil does not considera#ly reach to the central and upper regions of planetary gear, and merely trivially scatteredoil reachs to middle andu p p e r

i!ure 5+ 7teady state velocity distri#ution inplanetary gear according to oil level ;@, >@,

@/

i!ure + "redicted heat transfer coefficient accordingto oil level

i!ure 7+ "redicted churning energy loss according tooil level

regions$ )n case of >@, oil reaches higher, #ut still only

relatively low amount of oil reachs to the upper region$However, when the initial level of oil is @, all regionsare noticea#ly effected #y lump of oil$ )n the .igure ,velocity magnitude distri#ution after the operational timeof second are shown$ Near the sun gear teeth,velocity magnitude is highest #ecause of the effects of sun gear rotation$ )n the .igure D, average heat transfer coefficient of gear surface is shown according to initialoil level$ )n case of ;@,>@ and @ the heat transfer coefficients are claculated as @@@ OLmMB, 11@@@OLmMB and 1@@@ OLmMB, respectively$ &hese resultsshow that initial oil level is a crucial factor for improvingthe cooling effects in a planetary gear assem#ly$ Hence,

to enhance the cooling effect, increasing the amount of oil can #e considered$ )n the .igure , churning energyloss at steady state is shown according to initial oillevel$ )n case of ;@ churning energy loss is calculateda#out @$@@@ JLkg, a#out @$@@@> JLkg for >@ anda#out @$@@1 JLkg for @ initial oil level$ &hese resultsshow that the higher oil level cause more energy loss of rotating gear$ Ohen initial oil level increases ;@ to@, energy loss increases more then si' times higher$&his energy loss is related to the oil resistance againstthe rotation of the gears$ 6 very similar trend has #eenreported #y other scholars81,>9, in which the increasingthe oil level causes increasing churning energy loss$


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Article Title @$ otation speed of theplanetary gear of #rake is same with previousplanetary gear simulation$ =rake pad is engaged withplanet gear cover and it rotates at the same rotating

speed$ Ohen #rake is operating, the heat is generatedon #rake pad and gears surfaces$ &he heat generationduring the

i!ure 10+ olume fraction of oil inside of #rakei!ure 11+ &emperature contour inside of #rake

operation is calculated and assumed to #e 1>@@ O for #rakepad and F@@O for gear surface these values are assumedto #e close to the real case situation/$ 6s shown in .igure;, there e'ists a cold oil reservoir at the left side and planetarygears at the right side of the #rake pad$ )n addition, four holesare designed on the #rake pad for oil transfer #etween the leftand right sides for the sake of cooling$ 6lso these holes aremade to increase surface attached with oil and air for effective

cooling whole #rake pad$ However, the pro#lem of overheating still e'ists, which is caused #y ineffective oil flow#etween the cold oil reservoir and the planetary cham#er$ &hisissue is related to the churning of the oil around the #rake padand oil despersion apart form the #rake pad as a result of centrifugal forces$ 7imilar to the previous part, thesimulation is continued until the results of %.distri#ution #ecome steady state after appro'imately sec$/$ Hence, as it can #e seen in .igure 1@d/, when the flowreaches its steady state condtion, the oil flow #etween the twosides is severly decreased+ 6s shown, there e'ist only the air phase around the #rake pad$ 7o, there is no oil recirculation#etween cold reservoir region and planetary gear cham#er$ =y

heat generation of #rake pad, left side of the #rake is heated


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Article Title

numerical simo

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