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The Lubrication ofGears - Part IIR obert E rriichelfo

'G E A R T E C H , A lb a n y . C A

IntroductionWbat. follows is Part 2 of a three-partarticle

covering the principles of gear lubrication.Part 2 gives an equation for calculatingth e lu brica nt film th ick nes s, w hich d eterm in eswhether the gears operate in the boundary,elastobydrodynarnic, or f ul l- fi lm l ub ri ca ti on r e-gime. An e qu at io n f or B l ok 's f la sh t emper at ur e,w hic h is u se d fo r p red ictin g th e rislt o f s cu ffin g,is a ls o g iv en .

E :l as to hyd ro dyn am i c Lubr :i ca ti onG ea r te eth a re s ub je cte d to e no rm o us c on ta ct

pressures on the order of the ultim ate tensilestrength of hardened steel, yet theyare quites uc ce ss fu ll y l ub ri ca te d w it h o il f ilm s t ha t a re l es s

- IE l iDPRESSURE

_ _ _ _ h n u n,INLET H E R TZ IA N _ EXI ,. _R E G I O N R E G I O N

I Fig. I1 8 GE"H TECHNOLOGY

than one m icrom eter th ick, 'This is possib leb ec au se a f or tu it ou s p ro pe rt y o f l ub ri ca nt s c au se sth eir v is co sity to in cre ase d ra matic ally w ith in -creased pressure, F ig . 1 depicts the region ofco ntact b etw een m ating gear teeth. I t show s th eshape of the elastically deform ed teeth and th ep re ss ure d is trib utio n d ev elo pe d w ith in the con-tact zone. The m olecular adsorption of the lu-b ric an t o nto th e g ea r to oth s urf ac es c au se s it to bed ra gg ed i nt o t he i nl et r eg io n o f U te c on ta ct , wh er eits p re ss ur e is in cr ea se d d ue to th e c on ve rg en ce o fth e to oth su rfac es. T he v is co sity in crea se o f th elubricant caused by t he i nc re as in g p re ssur e h el psto entrain the lubricant into the contact zone.Once it is w ithin the high pressure, H ertzianregion ef t he c on ta ct , t he l ub ri ca nt c an no t e sc ap eb eca use its v is co sity b as in crea se d to th e ex ten tw here th e lu brica nt is v irtu ally a rig id so lid .

T he follow ing equatio n, fro m D ow soa andHigginson' g iv es th e m in iu mu m filin th ick ne ssth at o cc urs n ea r th e ex it o f th e c on tac t.

M i nim u m film th ic kn es s:1.63a;0.54(1l V )0.7 0.43

. 0 e p l 1 .hmin = = - - -- - -- - -- (X )0.13E .0.03. rW N rThe spe ci fi c f ilm t hi ck ne ss is given by

whereo =cemposite su rfac e roughne ss

01,02'" s ur fa ce r oughne ss , rm s ( pi ni on ,.gear)

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1 - 1 0 =absolute viscosity, Reyns (lb sec/hh Fig. 2 gives average valuesof viscosity versus temperaturefo r typical mineral gear lubricantswith viscosity index of 9 5 ..

0: = pressure-viscosity coefficient, (in21lb),The pressure-viscosity coeffi-cient ranges from 0: = 0.5 x l

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Descr,iption UnitsNomenclatu re Tab le

SymbolSymbol Descfliption UnitsBM

b IH

d

E r

h .mm

L.mmnpqS

TbTb.test

I Tc

T fTttest

Ts

-thermal contactcoeffleient- semi-width ofHlertzian contactband-eenstant 'I SeeT a b'le 3 .1 '-specific hea t pe runit mass

i V

in

hp/gpm

11 bf i n W b O F ]

-operating pitch indiameter o f p i nlio n-modulus ,of Ibf~in2elasticity (pinion,g:ear)- reduced modulusof elasticity-minimum film

J bf/in2

inthickness-minimum contact iinlength-pinion speed rpm-transmittad Ipower hp-oil now rate g!pm-avera'g,e surface ,uin:roughness, rms-bulk temperature O F-bulk ternpsretureof test gears

-contacttempersture-flssh temperature O F-maximum flash O Ftemperature oftest gears-scuffingt e m p e r a t u r e-opera ting p itch !line ftlminvelocity

2 0 GEAR TECHNOLOGY

V eV r 1, V r 2

W NrWNrXwX I

-entra ininq ve lo city in/s-rolling velocity

,I p i n io n"g!ear )-norrnal ,operatingload

in/s

Ibf

Ibtlinnormalunit load-wel'ding factor- t oad sharing factor-pressure-viscositv in2/11b2coefficient-specific fHmthickness

-heat conductivity-mean ceefflclentof friction-absolute viscosity R evns

Ubs/in2)

Ibf/[s O F ] ,

-Po lsscn's ratio'(pin!ion,gealf)-kina rna tic vis .c as ity cStof 40C-transverse Ifad,ius inof curvature(pinion, gealrl,-densltv Ib/in3-normal relative inradius of curvature- compos ite surface ttinrouqhness. rms-s urtae e ro ughne ss , p inrms (pinion, gear)-hase helix angle deg-anqular v,eioeity(pinion, gear)

rad/s

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p era tu re o f th e g ea r teeth reach es a critic al m ag -n itu de. T he co ntact tem pe ratu re is th e su m o f tw oco mp on en ts, the bulk tem peratu re and th flashtemperature; i.e., Tc::: Tb +Tf.

B lok's flash tem perature equation as fom m-lated inA GMA 2C KH~ B8 8. Appendix A3 for SpU1an d h elical g ears is

wheref,1 = m ea n c oe ffic ie nt o f f ric tio ne mX :::Loadsha ring fac to rr _W =normal u nl it l o ad'N r - .V = r ollin g v elo city o f th e p un onr[ -V ::: r o l l i J l - 8 : v elo city o f th e ge ar1 "2B -- = t he rma l contac t coef fi ci en t._-b ::: sem i-width of H ertzian contactH band

Mean Coefficient of Friction, f, 1 mThe following equaticngives a typical value

ef 0 ,06

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Table 26S y nth etic L ub ric an t M e an S c uffin g T em pe ra tu ee , T s

I Lubricant IMean ScuffingI Temp. 1s ( O F I ' I

Mlll-6081 '(gra,del0051 I, 2 ,64MIL-L-JaIlS, 400MIL-l-23699 425m~RD2487 440D E R : D 2 . 4 9 7 I 4ti5I,

ID O D - L - B 5 7 3 4 5 0 0

IM OBil S HC 624 540ID EX R O N I I 550

II

U NM O DIF IE D TO O TH P R O FILE S

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iL . ' _ _ ---1. L-__ ~c , . 2 . " e,P INIO N R O LL ANG LE

X r M O DlF IE .D TO O TH P R O FI L E S=P INIO N DR M NG

ORWING

il!72 4 5

P INIO N R O LL .ANG LE, Fig. 41-2 2 GEAR TECHNOL.OGY

Ts'" 146 -I - 591nv .wF

F or m in eral o ils w ith low c on ce nt ra tio ns o f a nt i-s cu ff a dd itiv es , th e m ea n s cu ff mg 'te mp er atu re isgiven by

Ts '" 245 -I - 591nv 40 of

wherev 40 =k in em atic v isco sity a t 4 0 C , cS tT he scu ffin g tem peratu re d eterm in ed fro m

iFZG t es t g ea rs f or m i ne ra l o il s w it ho ut a nt i- sc uf fa dd it iv es o r w it h [ ow eon ce nt ra ri on s o fa nti -s cu ffaddi ti ve s may be e xt en de d t o d i ff er en t g ea r s te els ,heat tre atm en ts , o r surface treatments by intro-ducing an empirical. we ld ing fac to r:

Ts=T +X T.b'test w f testwhereX . = w eld in g fa cto r ( S ee T ab le 1.)wTb, .. '" bulk tempera tu re o f test gears!esl -Tr =maximum. flash temperature oflest test gears.

for synthetic lubricants and carburized gearstypical of t he a er ospa ce industry, the scuffingt emperatures are shown ill Tab le 2 .

F or m in erali o ils w ith h ig h co ncen tratio ns o fanti-scuff additives. such as hypoid gear oils,research is still needed to determine whether thescuff ing tempera ture is d ep en de nt o n the materi-a ls a nd /o r o pe ra ti ng c ondi ti on s. S p e ci al a tte nt io nha s to be paid to the correlation betw een testc ondi ti on s a nd actual o r d es ig n c ondi ti on s.Acknowledgement: Reprinted by permission of SocietyofTribologists and Lubrication Engineers.

References:1. DOWSON, D. "Elastonydrcdynamics." Paper: o,1 0. P ro c, I ns t. M ec h. E ng rs . V o l. 182, PT3A, 1967..pp.151-167.2. BLOK, H. "Les Temperatures de Surface dans lesConditions de Graissage sons Pressions Extreme."S e co nd . Wo rl d P etr ol eu m C o ng re ss , P a ri s, J un e, 1937.3. AGMA 2oo1-B88. "Fundamental Rating Factorsand Calculation Methods fo r lnvolu teSpur and HelicalG ea r T ee tlt." 1 98 8 .4. A KA ZA W A , M ., T EJIM A, T.&N A RI TA , T . " Fu llScale Test of High Speed, High Powered Gear Unit -Helical Gears of 25,000 PS at 200 m/s PLV." ASMEPaper N o. 8 0-C 2 /D ET -4 , 1 98 0.5. AGMA op.cit.6 . D R A GO , R.J. " C o m pa ra tiv e L oa d C a pa city E va lu -ation of CBN-Finished G ea rs ." A G M A Paper No. 88FfM8 . .O c t, 1 98 8 .