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NASA TECHNICAL NASA 'TM -73851MEMORANDUM

U'N00Mtii

QunQZ

( 'NASA-TI-739 1) £TARING, GFA61N.;, AND N7ti-173 9

1 11nPICATUN ?FChNCLOGY (NASA) 24 F NC

A02/MF AC1 CSCL 131U nc 1i s

3/37 04473

I BEARING, GEARING, AND LUBRICATION TECHNOLOGY

by William J. AndersonLewis Research CenterCleveland, Ohio 44135

TECHNICAL PAPER to be presented at the1978 Automotive Engi,ieering Congress and Exposmo nsponso - )y the Society of Automotive Engineers, Inc.Detroit, ? i chiga-n, February 27 - Mar---h 3, 1978 <x/

Well, g

- --.._

BEARING, GEARING, AND LUBRICATION TECHNOLOGY

by William J. Anderson

National Aeronautics~ and Space Administration

Lewis Research Center

Cleveland, Ohio 44135

F:

-7- U

r

ABSTRACT

kesults Lf selected NASA research programson rolling-element and fluid-film bearings,gears, and elastohydrodynamic lubrication arereported. Advances in rolling-element bearingmaterial technology, which have resulted in asignificant improvement in fatigue life, andwhich make possible new applications for rollingbearings, are discussed. Re„earch on whirl-resistant, fluid-film bearings, suitable for veryhigh-speed applications, is discussed. An im-proved method for predicting gear pitting lifeis reported. An improved formula for calc-.11atingthe thickness of elastohydrodynamic films (theexistence of which help to define the operatingregime of concentrated contact mechanisms suchas bearings, gears, and cams) is described.

ORIGINNI,ov POo

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l'IIF NAS A LEWIS RE:SE:ARC11 CENri-,R h.ts e,upportcd asustained MD effort in Mecllaili. - ,II Componentstechnology since the 1940's. 'Chi c research hasbeen both fundamental and applied, with the ap-

plications centering on rocket engine Lurbopumps,aerospace power generation s y sLems, and iircraltgas turbine engines and transmissions. These

• are, in the nr. ► i11, high-perlormance hrod% • cts whichrequire soplhisti. • .iced research and developmentprograms, and in which cost is usually secondary

to perlorntance and reliability. Despite the fact

that the goals of NASA's R&D efforts in mechani-

cal components :Ire somewhat different from thoseof 1t&D efforts on highly Cost competitive com-mercial products, m.iny of the results of NASA's

research .ire being utilized in the conrnercialsector.

I'he objective of title, paper iw to report rv-,ults of selected NASA research programs onrolling-clement and fluid-film beatings, gears,

and elasLohydrodvnamic Itlbri.'.iLion which nkty beof interest and v: ► lue to the automotive industry.These results are presented in greater detail in

Kk't::. 1 to K. in p.trticular, it is hoped 1.11atthe research reported can be ipplitd to improvetilt , designs of gear systems and high-.,peed rot.i-Ling systems such as turbine engines and Lurbo-ch.irgers .

S YMBOLS

a st-minha_jor axis of contact t- l l ipso,ill (in.)

b semiminor axis of contact ellipse,m (in. )

C jout•nal hearing r.hdial clearance,ill (in. )

D journal diameter, ill (in.)

E modulus of elasticity, N/m 2 (psi)

G 1 modified modulus of elasticity,

,

> )I - v 1 ^ l /1

e 1<, ; bu l 1 slope:lndrrstill

F normal .ipplaed load, N (lb)

I gear tooLh tare width, ill (in.)

G dimensionless matcri.11 parameter, E'/P2

s

flit

If min

dimensionless minimum film thickness,h/Rx

h film thickness, m (in.)

k ellipticity parameter, a/b

L .journal bearing length, m (in.)

• L life of gear mesh, millions of revolu-gm tions

I involute profile are length, in (in.)

L length of gear contact line, m (in.)

M rotor mass, kg ((lb sect)/in.)

M dimensionless mass, Ml' (C/R)'/2u2Li a

N rotative speed, rpm

IN 1 number of teeth, driving gear

N2 number of teeth, driven gear

P ambient pressure, N/m2(psi)a

P asymptotic is:iviscous pressure,s

N/m (psi) (Ref. 3)

p load-life exponent

R effective radius of curvature, in (in.)

journal bearing radius, m (in.)r

radius of curvature, m (in.)

r i ,r 2 pitch circle radii of driving anddriven gears, in (in.)

U dimensionless speed parameter,(U.A a )/ (R' Rx)

IU surface velocity in x direction,

m/sec (in./sec)

W dim^!nsionless load parameter,P p/(LIRX)

W t gear tangential load, N (lb)

Wtingear mesh dynamic capacity, N (lb)

q, fraction of journal bearing lobe thatis convergent

w angular velocity, rad/sec

r stability parameter, (M2 iR3 )/(P C2L)

µ dynamic viscosity, N sec/m 2aAnderson

((lb sec)/in.2)

gear transverse pressure angle, radL

3

. b gear base helix angle, r;id

ORIGINAL PAGE IS zOF POOR (QUALITY

6

gift

:Anderson

gear tooth curvature (Minn,(t • Ci s . i^l(l/r I + 1 r ` ) /(ti in a't)

SubN^ri;ire

l , ^ eul 1.1 N l amt

.I atmottpher ► c pressurt•

W whirl

x,v t• oortllllatt' tit rectiotlrl

RESULTS AND I ► ISLTSS It ►N

HOLLING-EL"IENT MAKINGS - 1111 • t ai ltire molt,

for which rolling-elvinctit (ball and cvlindrit•tll,t.yered, spheri c.I I, mul net,dic roller) hearings.irt , tlornmli y designt,d in fatigue. l'll_` cond,irta-t ioil t i t high- c.ml.let titrt`osvi+ beLweell tilt' rot l ing

clements and r.ic vs .md Litt` large number of strexsevcleN which art , a:cunnilated ill relat ive iv

8110l• t pt,t'iod of time call lead to lat ► gue cr.Icksllild Nlll'I.Jt't' pittillg of lilt' 1'.1008 Jild'Or rolllllgelemt• nts. i'hus, rolling-elviticit bearings have afinite taligut, lite expectanc y in contrast toSliding bearin ►;N which are not stlbit,ct Lo t.ltigueunless Ni ►tnitic.mt dvnanlic loads ,Ire pt•eNt'11t.For this: reason dt:.t l,nt,t'N OfLt'n avoid tli: use Ofrt+l t inr;-element he ' ll- ings in many appl ic.it ionswhere they otter .1dV.int.lgVS which more (11.111 olt-Nl't the pott'llti.11 diNadv,nital't,s of .I tillltt' 1.1-

Li gue I i. 1t'.RVSt`.It'ch Over tilt, past thret , dt,cades has,

ilowt,vvr, rostiI t &I d i i i i i c w rot I illl; - e ic tit ellt be.irillgltuiLerials which II.ivv SigniIic. lilt IV Z;rt'.Ilt'r rt-sistance to pittirl^; 1,lLi t;uo. As i result, mo-teri.ilN ,ire now .iv.iil.ibIc on i production basis,t.tr tilt' manuiacturt, of rolling - element hearings

which will provide service lives as Itinr; .Is twoorders tit m.iLtnitude grt,:lter 01.111 those t i t bear-ings mmuitactured ill F'igur'e I shows Lilt-., It rollo l ol; it'. i l Improvement. in re tat ive bt'.Ir ingIift, .1lhl some of the tiietors til.it have re8111 Ledin tilt, tIr. lilt. it i c 1 i t v Im l 1rove lilt , t1L . Me m.1 jorport lull of the improved llo.irl ng 111 He ll.is ro-

sitILed from tilt , use 0 y•lt'llllnl melted s,tt,c'IN.

V.Icil tim melting sign Iis:nitl y reduces or &'l

n.ILes Lht' formation t11 hard oxide inclusions.111.1t, pills carotut cotiLrol t i t Lilt, melt: process

to clilt.in.lte retractories and other loreign (nat-ter, rt,NUlts in bearitlg matorialN which :Ire frocti t the h.lrtl inclusiotls mid stringers which serve:1N Il l I C 1 t,. l L i t i ll sitt's for t.iL. iglle cr.i cks.

As shown t i ll ig. 1, L%, I is tAthab lc Cleft rod

vacuum mfr (titit, i nt roduced re-sutted ill a tivt — loll improvenlcnt ill

fatigue life. Then vacuum induction melting fol-lowed by vacuum arc remelting (VIMVAR) resultedin a further, very significant improvement inlife. Details of the VIMVAR bearing testing arereported in Rei. 8. All of these tests were con-ducted with bearings of M-50 steel (0.8C, 4Cr,4.3Mo, 0.2551, 1V, Bal. Fe), which has become thestandard material for aircraft turbine engine,mafnshaft bearings. VIMVAR M-50 steel is avail-able at a small premium in cost over that of SAE52100 steel.

The principal advantage in using rolling-element rather than sliding (fluid-film) bearingsin high-speed turbo machines such as gas turbinesand turbochargers is in reduced power loss. In atypical automotive size turbine engine, bearingpower loss would be reduced by several horse-power. A lesser advantage would be lower start-ing torque. The disadvantages would be in cost,since rolling-element bearings are more expensivethan sliding bearings. Fatigue life would not bea factor with today's improved materials.

FLUID-FILM BEARIN,;S - Conventional fluid-filmjournal bearings, although they of far cost andpossibly life advantages over rolling-clementbearings, are subject to destructive, self-excited whirl instabilities when they support ro-tors running at speeds above twice the first cri-tical speed of the rotor-bearing system. Self-excited fractional frequency whirl can result inalmost instantaneous bearing :ailure. The trendtoward smaller, more compact higher power densitymachines has led to higher operating speeds, andmany cases of rotors operating at several timesthe first critical speed of the rotor-bearingsystem. Figure 2 illustrates three common typesof whirl resistant journal bearings: elliptical,lobed, and tilting pad. The most effective ofthese is tt-^ tilting pad bearing, but it is ex-pensive and its complexity sometimes leads toassembly problems. NASA carried out a researchprogr.im (Refs. 4 and 5) to thoroughly investigatethe whirl characteristics of several types offixed geometry journ.^l bearings. The bearingtests were conducted in water to simulate thev..sccsity characteristics of liquid metals usedin Rankine cycle power systems, and in a low vis-cosity oil. They are applicable to bearings op-erating in any fluid.

Tests were run on herringbone grooved jour-nals (Fig. 3), Rayleigh step journals (Fig. 4),lobed journals (Fig. 5), and lobed bearings withboth converging-diverging sectors or lobes andfully converging sectors or tilted lobes (Fig. 6).

Anderson

5

()WGIN AL PACE IS()P' PU()R QUALITY,

a

I

-- _L_ "I

k *.

l'he whirl onset speed for each of these bear-ing geometries was detennined for it ofclearances in each bearing type. Tests were runwith the bearing axis vertically oriented and .IL

zero radial load. As shown in Fig. 7, thetilted-lobe bearing with fully convergent lobes(1 - 1.0) was the most stable of the five bearingtypes investigated. Me region ut stable opera-tion for each bearing is below and to the left ofeach curve. 'these Last conditions represent themost severe eondiLians possible for int!iaeinghearing instability. It ir• recognized that sohnebearing loads exist in all practical applicationsso that the results obtained are conservative.It must .also be recognized, however, Lh..t periodsof bearing unloadinf, even though very brief, canoccur in any application and can be of suffietenLduration to induce whirl and cause failure.

With the results at Fig. 7 in hand, it wasdecided to conduct a thorough investigation ofthe tilted-lobo bearing to determine the ioflu-ence of the number of lobes and the :ength-diameter ratio as well as the clearance on sta-bility. Kitrings with 3, 5, and 7 lobes andlength-diameter ratios of 0.), 0.5, 0.75, and 1.0were tested in bath oil and water (Ref. 5). thisr.inge of length-diameLer raL ios encomimsses thosewhich would be expected In almost .all .ipplic.i-tions. Ilse results of these tests are illtastra-ted in Fig. ti. The results are platted as dimen-sionless mass M vs dimensionless stability pa-rameter r. A .1 tit rn.al be.iring stability analvsia(Ret. y ) indicated that these are the importantp.tramleters to t.onsider. Variables included inthese parameters are rotor mass ld, ambient pres-sure 1'. 1 , bearing radial clearance C, bearingradius R, bearing length 1., vluid viscosityand rotative speed lit Lerills at m .Ind I',the data for all hearings can be approximated asit litre on a lug-log plat. Although itwas intended that these bearings all have fullyconver t ,'tlt tilted Lobes, the average ottset fac-tor was 0.77 rather than l 0. rhis means thatthe :aver.ige lobe was 77';, convergent and ?3". di-vergenL instead of fully convergent. Test re-sult:: wiLh tilted-lobe bearings indicated thatbearings with fully converged lobes were the moststable. Therefore, the re sit ILs obtained withthese bearings are conservative.

The experimental bearings used in this pro-grain were fabricated by offset mi1Iin'i;. In pro-duction lots Lilt • bearings would be broached ironsan undersized circular bore to Lhe finished p,eo-metry. They cart tie produced at a ver y nominal

Anderson

b

f

y.

f

cost premium above conventional circular sleevebearings and offer a practical economically com-petitive whirl - resistant bearing for many high-speed applications.

Intensive governiw nt-sponsored programs forthe development of gas bearings for applicationin turbine engines are underway (Refs. 10 and11). Gas bearings will be required in locationswhere the temperatures exceed the maximum capa-H lily of engine oils. A complete gas-bearingengine would offer the obvious advantages ot re-duced complexity through the elimination of sev-eral oil-lubricated bearings. This would, how-ever, require a significant advance in gas-bearing technology.

GEAR LIFE PREDICTION - Gears may fail byscoring, tooth breakage, or tooth pitting (sur-face fatigue). Both scoring and tooth breakagecan be avoided by proper design and lubricationpractice. Under such circumstances, surface fa-tigue will determine the life of the gear set.

Current methods of designing gears to resistsurface fatigue are b a sed on the concept of asurface fatigue endurance limit. The currentmethod (Refs. 12 to 14) of predicting gear toothpitting failures is similar to that used for pre-dicting tooth breakage. The Hertzian contactstress is estimated, and then modified with ser-vice condition and geometry factors to become thestress number. When the stress number is lessthan the surface fatigue endurance limit, thepitting fatigue life is assumed to be infinite.There is controversy among gear researchers re-garding the existence of an endurance limit(Refs. 15 to 17).

In contrast, rolling-element bearing endur-ance life prediction, as developed by Lundbergand Palmgren (Refs. 18 and 19), assumes that fa-tigue life is a function of

(1) The maximum orthogonal shear stress(2) The depth below the surface at which the

maximum shear stress occurs

(3) The stressed volume(4) The number of stress cycles

It assumes that an endurance limit does notexist. An easily applied gear life predictionmethod, based on the Lundberg-Palmgren theory,is developed in Ref. 6.

In essence, the life prediction method ofRef. 6 states that the life of the gear mesh interms of the dynamic capacity of the mesh Wtmand the transmitted load W t is

7

Anderson

ORIGINAL PAGE, ISOI" POOR QUALITY

l^

I

al^r^rr _

I'

W tanL^;M a't

fhe dynamic capacity of the gear-pinion mesh iscalculated as foIIows:

Wtma ' K2 , ,, cos c,t(cot; , b )

I ^ i9 ( )-35/27

r -^-./9

N 1 I

In Rot. b values of p 3/2, v - 3, and

K2 t 132 000 English units (lhl-in.)

5.28 SI unit~ (N-m)

were derived based on theory and rolling-elementbearing; experience.

Experiments were conducted in Ref. 7 withvacuum arc remelted (VAR) 9310 stvvl spur guars.The results were ti8ed to modify the exponents pand e and tilt' constant K,- To obtain these

values the gears were run to pitting failure atthree tangential load levels. Results are shownin Fig. 9, plotted on Weibull coordinates. Tlicdata indicate that life is inversely proportionalto load to the 4.3 and 5.1 powt^r at tilt' L10 and

L50 life levels, respectively, its shown inFig, 10. Thus, the value of p - 3/2 derivedin Rel. 6 appe,irs to be too low for gears. Piecorrelation of the revised NASA gv.ir life pre-diction theory with test results is shown inFig. II - Life prediction nt all three load lev-els is excellent. Comparison of the A(;%< Stand-ard 411.02 (Ref. 17) with experiment is shown inFig. 12. 11tc test data show a steeper slope forthe load- life di.igram them assumed by the ALMAStandard 411.0:.

FLASToll1URODYNA?i1CS - Elastohydrodynamic(EIIU) lubrication duals wit)' the development ofthin films of lubricant in the contacts betweennonconfotmal machine elements in relative motion.Examples of nonconformal machine clenicuts .ire thehalls or rollers and racewa ys in hail l .ind roller

hearings, gear teeth and cams, and cam tollowers.The development of hydrodynamic lubricationtheory, which deals with conformal machine cle-qtent-; such as sliding hearings (journal and

Anderson

8

R

I

thrust) began in the 1880's. In contrast, thefirst significant publication on HID luuricationtheory was in 1949 (Ref. 21). This was followedby fLrther work on the line contact problem(Refs. 12 and 13) and publication of methods forcalculating film thicknesses in point (ellipticalit circular) cortacts (Refs. 24 and 25).

None of the research reported in Refs. 21to 25, however, deals with the detailed contourof the contact area, and,

fit with the

minimum f.im-thickness region. The minimur, filmthickness developed is critical to Lite perform-ance, reliability, and life expectancy of the ma-chine element. 11ie thickness of the separatingfilm must exceed, by a factor of two or three,the composite surface roughness of the contactingsurfaces if the full fatigue life potential is tobe achieved. Otherwise, surface distress such asmicropitting, smearing, or scuffing occurs andthe machine-element life is drastically short-ened.

A comprehensive elastohydrodynamics analysiswas undertaken at the NASA Lewis Research Center,The analysis (Refs. i and 26 to 28) was done inpartial fulfillment if the requirements for adoctorate degree at Leeds University, England.A coupled solution to the elasticity and hydro-dynamics equations was obtained (Ref. 26) and ap-plied to the calculation of film thickness in EHDcontacts with a wide range of ellipticity ratios(Ref. 27). Easily applied film-thickness equa-tions for the cases of fully flooded contacts(Ref. 3) and contacts partially starved of lubri-cant (Ref. 28) were developed. For the fullyflooded case the dimensionless minima'- filmthickness is given by

min3.b3U

0.68C0.49W'-0.073 (1 --0.68k)

F

A simplified expression for the ellipticity pa-rameter is

R 0.64

k 1.03 -yIt x

For a discussion of Lite consequences of partialstarvation in the contact, the reader is referredto Ref. 28. While lubricant starvation and itseffect on film thickness can be easily defined ina mathematical sense, there is no easy way topredict when it occurs in real machine elements.

Anderson

9

For well-lubric;-ted bearings and gears, it issuggested that fully flooded conditions be as-sumed.

The critical parameter of importance is theratio. f film thickness to composite surfaceroughness

A ha

where

2 ,21 t 2

For full film conditions without asperity con-tact, A should exceed three. For values of Abetwc?n one and three some asperity contact willoccur and some surface distress, with a conse-quent reduction in pitting fatigue life, may oc-cur. For values of A less than --le, gross sur-face distress is likely to occur w i th a very sig-nificant reduction in component life.

St'I MARY

Significant advances have been made inrolling-element bearing materials technology overthe pest three decades. These have resulted inimprovements in bearing fatigue life of two or-ders of magnitude and open up many new possibili-ties for applying rolling-element bearings. 111erelative whirl resistance of several journalbearing geometries was investigated experimen-tally. The tilted-lobe .Journal bearing was loundto have superior whirl resistance. it can bemade inexpensively in production quantities, andoffers promise for turbine engine and turbochar-ger applications. A new method for predictinggear pitting life, based on the Lundberg-I'almgrenbearing fatigue life theory, was developed. Itagrees well with pitting life data obtained withspur gears.

An improved formula for calculating; elasto-hydrodynamic (E:IiD) film thickness in concentratedcontact machine elements was developed. Propercalculation of EAID films is necessary in orderto Fredict the operating regime of bearings andgears. The lack of a sufficiently thick EHD filmcan result in surface distress and reduced life.

ACKNOWLE:DChtE-Wr - The author is indebted toJohn Coy, Bernard Hamrock, Frederick Schuller,Dennis Townsend, and Erwin/.aretsky who conduc-ted the original research reported in this paper.

Anderson

10

0MGINAT, PAGE 1SUr' YUUIt QUAIXfy

Ih="

REFERENCES

1. D. P. Townsend, and E. V. Zaretaky, "ALife Study of AISI M-50 and Super Nitralloy SpurGears With and Without Tip Relief." Journal ofLubrication Technology, Vol. 9b, October 1974,

pp. 583-590.2. D. P. Townsend, E. N. Bamberger, and

F.. V. ZareLsky, "A Life Study of Austorged,Standard Forged, and Standard Machined AISI M-50Spur Cears." Journal of Lubrication technology,\'ol. 98, July 1976, pp. 418-425.

3. B. J. Hamrock, and D. Dowson, "Isother-mal Elastohydrodynamic Lubrication of Point Con-tacts, Part III - Fully Flooded Results." Jour-nal of Lubrication Technology, Vol. 99, April1977, pp. 264-27b.

4. F. T. Schuller, "Experiments on the Sta-bility of Various Water-Lubricated Fixed Geome-try Hydrodynamic Journal Bearings at 'Zero Load."Journal of Lubrication Technology, Vol. 95,October 1073, pp. 434-446.

5. F. T. Schuller, " E ffect of Number of

Lobes and Length-Diameter Ratio on stability ofrilted Lobe Hydrodyrami, Journal Bearings atZero Load." NASA rN D-1902, 1175.

6. I. J. Coy, D. P. Townsend, and i?. V.Zaretsky, "Dynamic Capacity and Surface FatigueLife for Spur and Helical Gears." Journal ofLubrication rechnology, Vol. 98, April 1976,pp. 267-270.

7. D. P. Townsend, J. J. Coy, and E. V.Zaretsky, "Experiment.il and Analytical Load-LiceRelation for AISI 9310 Steel Spur tears." NASArM x-73590, 1977.

S. E. N. Bamber,;er, F. V. Zaretsky, and II.Signer, "Endurance- and Failure Characteristicsof Mainshalt Jet Engine Bearing at 3 . 10' DN."Journal of Lubrication Technology, Vol. 98,October 1976, pp. 580-585.

9. F. T. Schuller-, D. P. Fleming, and W. J.Anderson, "Experiments on the Stability of WaterLubricated Nerringhone-Groove Journal Bearings,I - theoretical Considerations and ClearanceEffects." NASA TN D-4883, 1968.

10. S. Gray, "Applying; Resilient Foil AirBearings to rurbomachinery - Techniques andChallenges." Paper 751070 presented at SAE. No-tional Aerospace Engineering 6 ManufacturingMeeting, Los Angeles, November 1475.

11, S. Gray, J. McCormick, and N. Sparks,"'the Application of Gas and oil Lubricated FoilHearings for the FRDA%Chrvhl r :Automotive GasTurbine Engine." Paper 76-Gr-115 presented at

Anderson

ASME Gas Turbine h Fluids Engineering Confer-ence, New Orleans, March 1976.

12. "Surface Durability (Pitting) of Spur

Gear reeth." ACMA Standard Nu. 210.02 - 1965.

13. "Surfac:a Durability (Pitting) of Hciical

r anC Herringbone :;ear Teeth." ALMA Standard No.

211.02 - 1969 (41974).14. "Information Sheet for Surface Dura-

bility (Pitting) or Spur, Helical, Herrlcigbune,and Bevel Gear Teeth." ALMA Standard No.

215.01 - 1966 (R1974).15. A. Ishibashi, T. Ucno, and S. Tanaka,

"Surface Durability of Spur Gears at HertzianStresses Ovvr Shakedown Limit." Journal ofEngineering for lndtrstry, Vol. 98, Mav 1974,pp. 359-372.

16. W. E. Shilke, "The Reliability Evalua-tion of Transmission Gears." raper 670725 pre-

sented at SAE Farm, Construction and industrialMachinery Meeting, Milwaukee, September 1967.

17. G. 1:. Huffaker, "Compressive Failuresin Transmission Gearing." SAE Transactions,Vol. 68, 1960, pp. 53-59.

18. G. Lundberg, and A. Prinrgrcn, "DynamicCapacity of Rolling Bearings." Ingenious

Vetenskaps Akademien, Ilandlinger, No. 196, 1947.19. G. Lundberg, and A. Palmgren, "Dynamic

Capacity of Roller Bearings." ingeniuersVetenskaps Akademien, Handlinger, No. 210, 1952.

2U. "Design Procedure for Aircraft Engineand Power Takeoff Spur and Helical Gears." ALMAStandard Nu. 411.02 - 1966 (111974).

2.. A. N. Grubin, and 1. E. Venogradova,"Im;estigation of the Contact of Machine Compo-

ner;s." Department of Scientific and IndustrialResearch (Great Britain), CTS 235, 'Translationof Tsentral'nvi NaUCI1110- Isslcdovatel'skiiInstitUt Tekhnologii i Mashinostrocniya (I'SSR),

Kniga 30, Kh. F. Ketova, ed., Moscow, 1949.(SLA R-3554.)

22. D. Dowson, and G. R. Iligginson, "Nu-incrical Solution to the Elastohydrodynamic 1 1 rob-lem." Journal of Mechanical Engineering Sci-ence, Vol. 1, Junc 1959, pp. 6-15.

23. D. Dowson, and G. R. Higginson, "NewRoller Bearing Lubrication Formula." Engineer-ing (London), Vol. 192, August 4, 1961, pp.158-i59.

24. .1. F. Archard, and F. W. Cowking,"Elastohydrodynamic Lubrication of Point Con-tacts." Proceedings Institution of MechanicalEngineers, London, V.I. 180, fart ill, 1965-1966,pp. 47-56.

ORIGINAL PAGE" ISOF N x w QU,W'1'14

Anderson

12

it

25. It, S. Cho ng, "A Nluu :ri, al Soltlt ion vtt11. Film I'1llcktivss in anFll li l t Ica I Contact." Journal of Lubricat i•`n•{'c`rhnologv. V.+I. 4., . .I.,,wary 197o, l ip. 155-1b2.

N). It. .I. Ilamro:k, and 1). Dowson. "Ie+.+thc`r-uul I'.1.11t++hvdrudvnaml: Lubricat ion of Point t'on-Iacts, Part I - 1'livorot Ica I Formulation." Jour-tial of I. ill ri cat ion TvvluloIo• Vol. QK. Apri 1

'I. It. J. Nanlro:{., and 1). Uowsotl, "hiother-mal I la-itohvdrodynamic Lubrl cat loll of Point Con-tactti, fart it - Ellipti cit y Par. ►m.`tc`r R.`ru1tN."Journa l tit I uhricat ion VOI . 1 18, JulyI^)16. pp. 1; +- 3N 1.

.ti. It. .I. Ilamr++, • L, .111.1 1). 1)owson.

nul F I.AsIA y dlociviiami: Lubrication of Point l'otl-ta:trt, Part IV - Stirva( ion Rcsult4." .lournaIof Lubri:at ion '1'rchnolog ,,, Vol. `)' ► , Januar y 1977.

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Figure 12. - Comparison of experimental lifP of(VAR) AISI 9310 steel spur gears with ALMAlife prediction.

ORIGINAL PAGE. IS

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