LUBRIICATION

Systematic Investigations on theInfluence of Viscosity Index

Improvers on EHL Film ThicknessBernd-Robert H,ohn, Ktaus Michaelis andilFranz KO,patsch

ACC

INomen claturedeformed area of disk capacitorcapacitance of disk capacitorthermal correction factor ace,MurchIWilson (Ref. 12)Young's modulus of contact bodiesreduced Young's modulusno rma I fore eEHL-parameter 01 elasticitythermal load factor ace. MurchIWilson(Ref. 121weight average molecular weightpolymer correction factorreduced radius of curvatureshear stability indexEHL parameter of velocityviscosity indexEHL parameter of loaddeformed Hertzian contact widthtJpcirclebase circlepitch circlefrequency of resonance circuit.measured lubricant film thicknessminimum film thickness calculated ace.Dawson/Higginson (ReI. 5)film thickness in the parallel gap calcu-lated acc. ErteVGrubin (Refs. 6 and ,8)disk widthHertzian contact pressureradius of curvature of contact bodiesslip ratio (s =1 - v/vI)

surface velocity of contact bodies[v1 <11:1)

hydrodynamic velocity (VI" VI + v2)

press uta-vise osity coefficienttemperature coefficient of dynamicviscosityshear raterelative dielectric coefficient 01 the oilelectric field constant(eo = 8.8542 •.10.12 C/(Vm})dynamic viscositydynamic viscosity at bulk temperaturetemperatureaverage bulk temperature(19M: (ill + 192M!)bulk temperature of contact bodiesoil inlet temperatureheat conductivity of lubricant(mineral oil: A '" 0.133 W/(m" K)jkinematic viscosityPoisson's ratio of contact bodiesangle velocity

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Printed with permission 'of the ,copy-rigbt holder, the American GearMa'nuf,acturers Association.. 1500 KingStreet. Suite 201. Alexandria. V:irg,inia22314. Copies of the paper are avail'abl'efrom the assnciatinn

Statements presented in this paper ar,ethose of the ,authorsand may not representthe position or oplnicn of the AmericanGear Manufacturers Association ..

IntroductionMineral-oil-base lubricants show a

significant. decrease of kinematic viscos-ity with rising temperature, as exempli-fied in Figure I by lubricants for vehiclegears. An important attribute of lubri-cant is their viscosity index (VI),according to DIN/ISO 2909 (Ref. 4).Viscosity index is a calculated coeffi-cient, which characterizes the change ofviscosity of lubricants as a function oftemperature. A high viscosity index rep-resents a low variation of viscosity due totemperature and vice versa. A low vis-cosity-temperature-dependence is re-quired for lubricants that are operated atsignificantly varying temperature condi-tions, such as vehicle engine and gearlubricant in slimmer and winter time.This way, [he oil remain flowing andpumpable at low temperatures on the onehand; and on the other hand, ufficientlythick lubricant films can be formed athigher temperatures for a safe epararionof the surfaces,

A deliberate improvement of the vis-cosity temperature behavior can beachieved by blending an oil with poly-

mer additives as viscosity-index im-provers, such as polyalkylrnethacrylate(PMA), olefin copolymer (OCP), styrenebutadiene copolymer (SBC) or poly-isobutylene (PIB), This way, polymer-free monograde oils can be convertedinto multigrade oil , which are used inlarge quantities as engine oils in vehicles(e.g. SAE 15W-40), as gear oils ill man-ual transmissions in vehicles (e.g. SAE7SW-90, see Fig. 1) or in automatictransmissions (e.g. ATF DEXRON®type oils). Universal oils for tractors andearth-movers (e.g. UnO), which can beused for hydraulics and gears, are multi-grade oils as well.

The viscosity-increasing effect ofpolymer additives at laboratory condi-tions is known and can be proved.However, their efficiency at EHL condi-tions of high pressure, high shear rateand rugh temperature, such as in gear orroller-bearing contacts, is questionable.Polymer-containing oils can suffer froma temporary viscosity loss by high shearrates in an EHL contact, and they cansuffer from a permanent viscosity loss by11 partial mechanical destruction ofthepolymers during operation. That re ultsin a lower operating viscosity and,hence, worse lubricating conditions thanone would expect according to the vis-cosity data determined at laboratory COli-

dnions with the fresh oil,The lubricant film thickness signifi-

cantly influences the mlcropitting andwear performance of gear applicationsand. to a smaller extent, it also affects thepitting and scuffing performance,Knowledge of the actual lubricant filmthickness in a gear contact is therefore

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es ential fOJ a reliable e timation of thefailure risks of wear and micropitting,which are recently more and more thefocus of interest.

For lllat reason. the efficiency of vis-co~ity index (VW)impr1lversin EHL con-lacl~ was mvestigated by "Y tematicmeasurement of Ute lubricant film thick-nes s, Various type of polymers with var-lou molecular weights and concentra-tiens in the base oil were included in the 20 mm;o ). in order 10 gel measurablete t program in order to determine theinfluence of each parameter on Lhe for-mation oflubricant films separately fromeach other.

Test LubricantsThe investigations were carried out

with more than 20 te t lubricants, whichwere blended especially for thi re earchproject, The base oils were two straight-paraffin-ba e mineral OIls. M32 andM 100. of the vi co i.ly grades ISO VG 32a:ndmso VO 100. The polymers that wereused consisted of PMA (polyalkyl-methacrylate), pm (polyisoburylenc), !o P (olefin copolymer). SBC ( tyrone I"

butadiene copolymer) and STAR (star-shaped styrene i oprene copolymer), For ieach type of those polymers, a .et of five !different blend was inve tigaled, which i

is hown in Table 1 for the polymer I.

PMA. a an example. Each polymer typewas available wilh low molecular weight .11.

{designated by the code PMAI. OCPI.etc.) and high molecular weight (PMA2. !ocez, ete.), The polymers with low Imolecular weight were added in low con- 1

central ion (PMAIL. OCPIL. etc.) and!high concemration (PMAIH. OCPIH. !

etc.) to the base oil M 100 and in veryhigh concentration to the bas e oil M32(PMAJVH, OCPIVH. etc.), The poly-mers with high molecular weight wereadded in low concentration 110 base oiIMIOO (PM 2L. OCP2L, etc.) and inhigh concentration to ba e oil. M32(PM 2H. OC~H. etc.),

The potymer coacentration ill eachblend was chosen with respect 10 equalkinematic vi. cositie 1'100 of all test lubri-cants at !OODC, 0 that. the lubricant film

Code',oftest oil

PMAIL X. XPMA1H X XPMA2L X XPMA1H X XPMA1VHI X.

x Xx xX X

X. XX X X

film thickncsse at rugh temperatures up I

to IIODC. at which the investigationswere performed. For a direct comparisonwith a straight mineral oil, a. straight-pareffin-basemineral oil M240 with thesame kinematic vi cosily of vlOO = 20mm2/ at ]oODC was included in the et

of te t lubricants.The investigation of a set of five dif-

ferent blends, as shown in Table I foreach type of polymers, give informationabout:

.' the influence of !he concentrationof polymers with the same molecularweight in the same bu. e oil (PMA ILandPMAIH).

• the influence of the molecularweighl. of the polymers in blends withthe same viseosity at lOoDe and with the. arne base oil. and

• the influence of the base oil viscos-ity in blends with the same polymer 'Iype(low and high molecular weight.) andwith the same viscosity at '(X)DC.

The STAR-type polymer wereinvestigated ill two blend only. whichwere equivalent. to the blends with highmolecular weight ( ... 2L, ... 2H).

hear Stabi.liC.y of InvestigatedPolymers

containing oils can suffer a penn anentvi cosily 10 when being subject tomechanical loads. which can hred thepolymer chains. That proce s is notreversible.

An polymer-containing test oil weresubjected to a 20-hour tapered-roUer-bearing shear lest (KRL-shear te 0according to CEC L-45-A-99 (Ref. 2). in

j

II Professor Dr:-'lng. IBemd-!Robert IHohn

is head of tile Institun: 01 MOe/lIlll' £lellll'lIIf and! the Gear Reseon.:1r Centre. hmh 011111'Technical!I University of Mllnic!l. Germany. TIJI' centre Pt'r-

forms basic and appiied research ill flrl! fields ofI luati·curryill8 capacity and (rib%gy of RM,.S

Permanent Viscosity Loss. Polymer- i anti (11l1011l0Iil'l' components.

! Professor Dr:~!lng. IKlaus Michae'lis,i iJ "searr/l group mana}1l!rat the Gear Researcl:! Centre. HI! is responsible for experimental ela •! tohydrodynamics and Iribol(8)' and their appli·I cation 10 gear lcl/ffing and "'ear 1'/'!r/wmrna.

! Dlr.~lng.F,rsnz K,opstscht is head of Ihe calculouon gf[lliP al leinlxJCIi

I·GmbH. a GennaII' mannfocturer of etectric fort/ifttrucks. A. mechanical engineer; Ill' worked from

i 1994 /0 2()()f) as a scielllifk asJislllnt til IIII' Gearthicknes e of all oils could be directly order to determine the permanent viscos- I' Research C,mtl"l'. As all fUJi.HOIrl. Ire performedcompared at high temperature. Emphasis iry 10 s by shearing. In this test. a tapered two research projects on the illfluence o/l'lscosiry-was put on higher-viscous blend. ""100" roller bear.ing 32008XQ is lubricated ! index improvers on EHL·fllm thickness .

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_L~w -J!~WJ

,~ /_It~ ...., 01 I

. ,~ ~II mono9"odti oa) "~["-..,.'!b

,

").,..~ t'--.: :1.0

~. -'3.,. 90

SAE ftKail-t)' dat.t;iflc:oUanlJ f',::-

far' 'iit'h1cl'1 'TOI'I- .... I... 011 :1T-oeeJ" TU.1 J I

10.000-'I.'.000

I. i 100

,~ eeI ~! j 10

I 3

1,1 1L...._·_!iO_·_-·_O_-.2_0_l:.._P_:_.t_ ..._:D_~_10_110_._'OQ_"C_.. ....J0

t Flouf'a 1-'Differen·ce between monogradei andl multigr,adellgeall' IOil'S, for vehicl'es.

I

shear-s,tabllity-indn SSl al 100'C

Figura 2-Shearstability iindices 0,1 Ihe,I,est oil's after a KHI!.-shear test.

Figure 3-Arrangement of pol:ymers in 1fIeinlet shear field of an EHI!.eantaet,

I ~ CI ,",,_IUd-..1)1' mMIUI'tmtnl 0' ,-,ar ,,-'I

I

",,,,,11 • HTHS. __ otiIt, mtftiKtm .. 1 ,ot 1- 0. ... 0' .-'!: I f tI -

J 10~!!. -l ------il

~ - --~ .q

§ I~ §~ ~0 s

I ~'i ~ 'I~ ~ ..; :!.. ,0

J: :J; ....J ....J ....J ....J

~iii N N N N<[, ID Q. U'0:: ::I; 0:: g .Sl' IQ.

IFigure4--Results of HTHS ViSCDSity meas·urements.

L

Figure, !i--JP!rim:iple, ,of capacitance fU'mthickness; lest method.

LUBRICATI!ONwith 40 ml of the te t fluid by dip' lubri-cation at60°C. The bearing is run for 20hours at ] ,450 rpm and at a load of 5 kN.The kinematic viscosity "too of the testoil is measured before and after the testat lOO°C. With this information and thevi cosity of the ba e oil VIOO.JxLt~ oi1" theshear stability index (SSI) of the polymerin the blend can be calculated. 11 isdefined as:

(v - v )SSl .. . 100,(;. .... /, . lOO.KRL(VICKI!,..,..},- vIOOJx ... "') 0)

wi,lhvIOO!",slJ ::: kinematic viscosiry in mrn2/sof the fresh polymer-containing oil.determined at a 'temperature of 100DC byusing a capillary viscometer."IOII.KRL::: kinematic vi cosily in mm2fs.ofthe polymer-contai:ning oil after a KRL-shear test according to CEC L-45-A-99(Ref. 2). determined at a temperature of100°C by using a capillary vi cometer,amiIlIOO,horeni( .. kinematic viscosity in nl.ln2fsof the base oil. determined at aternpera-ture of IOODCby using a capillary vis-cometer.

The hear-stability index is an indica-lor for (be shear-stability of the poly-mers. SSl :::0% means that the polymer-containing oil has the same viscosityafter the KRL-shear test as before. so thepolymers are hear-stable. SS] ::: 100%means that the polymer-containing oilha only the viscosity oflhe base .oil afterthe KRL-shear test, 0. the viscosity-increa ingeffect of the polymers hascompletely di appeared after the test, Inthis case, the polymers are unstableagainst hear.

The shear-stability indices of thepolymer-containing oils. which werederived from the KRL-shear te t , areshown in Figure 2. Tile shear-stability

polymers that were investigated havemolecular weight M", of more than90,000 glmole am fresh-oil. condition. Theshear-stability indices of the correspondingoils are all more than 70%, That. meansthat :uter the KRL-shear te l,the polymerchamsare broken into pieces and hardlyable to ignificanlly increa e the blend vi •cosily above the base oil visco ity,

Temporary Viscosity LossLong-stretched polymer chains tend

to arrange them elves in parallel within ashear field, as shown in Figure 3. Th.31way. the probability of the polymersbecoming tangled with each other isreduced and so is 'the thickening effect ofthe polymers. This process is reversible,Sucha shear field exists ill the inlet regiono[;:IIIY oil-lubricated EHL contact. Wtiseaus ed by the back -flow of the surplu oil.

To gel iafermatien about the tempo-rary vi cosily loss, high-temperature-high-hear (HTHS) vi cosity measurements

were carried out with some of the lest oils.

A capillary viscometer aided by air pres-sure was used to increase the velocity ofthe oils flowing through the capillary. Thatway, 'the hear ratio of the o.il. in the capil-lary could be increased from '¥.., 1()2s·lalpure-gravity-induced flow to. some 0..4 ,.111's-1at air-pressure-aided flow.

The results of the HTHS visco itymeasurement are shown ill Figure 4 forthe oil' PMA1H. PIBIH, PMA2 •pm2L, OCP2L and SBe2L. The tempo-rary viscosity .105s of the oils containinglong-chain polymers is significantlyhigher than that of the oils containingshort-chain ones. The BC polymersappear 1.0 be especially u ceptible totemporary vi cosiry 10 , as they .10 eabout half of their thickening power atthe high hear ratio ill F.igure 4 ..

.Resnlts of Film Th~ckness,Measurements

Tess Principle. The measurementswere carried out ill a 'twin-disk test rig.Th core of 'the test rig consisl of twocylindrical steel disks, each aile 8'0 mmin diameter. They can be driven eparate-Iy from each other with continuouslyvariable peeds and can be loaded with anormal force F,., The lest oil is injectedbetween both disks. The bulk tempera-

! trongly depends on the average molecu-I lar weight of the polymer. For example.i the te: toil containing the polymers! PIBil and PMAl. which have a molecu-

III

lar weight M,., of less than 20,000 g/moleeach, show the lowest shear-stabiljty

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indices after the KRL-shear test, 0 tho epolymer. are relatively stable agailOStpermanent shearing. All of the other

The "disk capacitor" is inlegrated

into a resonance circuit, the frequency fof which depend on the capacitance Cand ,I known inductivity L By using acapacitance-frequency-calibration curve,the capacitance C can be derived fromthe resonance circuit' ~ frequency f,which

is determined by using a frequencycounter.

Tile relative dielectric coefflclent of

the oil £oil is measured in a high pres urecell as a function of pre sure and tem-perature. The deformed Henzian contact

width b can be calculated with theHertzian equations. With thai data, thelubricant film thickness h~Q.J of 'the oilcan be calculated from the capacitance Cof the disk capacitor by nurneri al inte-granen, The calculation method used isbased on Equation 2, It divides thecon-laet zone into five' eparaie ection withdifferent portions of the entire capaci-'lance and also 'lakes into account theinfluence of an insulating layer madefrom AIPr which is applied to one 01" thedi k surfaces by ion beam sputtering inorder to prevent electric hortcursbetween the di ks, More detailed infor-mation about the measuring techniqueused is given in Reference 13.

FilT" Thickness of Po.lymer-COlJtai"irlg Oils.. In the following, themost important results of the film thick-ne s mea urement of the test oil blends... IH. and ... 2L (see Table 1) are pre-sented, A detailed de cription and di .-

cussion of all Ie t result gained ~D thiwww.powllrrrsfls·mlssion com' www,gear.rot'hno.rogy.com " GEAR TECHNOLOGY" NOVEMBER/DECEMBER 2001 33

tures ~I and "2 of both disks are meas-ured with temperature en ors lin bore-

holes 2 mm belo the running urCace.A detailed de criptien of the lest rig and0:1 the te t di i given in Reference 9.

When loaded and tbuselasticallydeformed. both disks and the lubricant

between them form a capacitor ( ee Fig.5), the capacitance C of which dependon the lubricant film thickne ';""UJ' therelative dielectric coefficient Eud of thelubricant, the deformed Hertzian contact

width b and the di k width Irff accon:ling1.0 Equation 2.

C == .£0 '. £",1 '. (AIh .....as)with A = 2 • b .I ../f (2)

-- - -------

project can be found in Reference '9.Tne visco ity-temperature curves of

the blends ... IHand ... 2L are shown infigures 6 and 7. All polymer-containingtest oils were blended with equal kine-

matic viscosities at 100" of v100 = 20mm2fs which is the value of the- refer-

ence mineral oil M240, The base oilM 100 ha a kinematic vi co ity al IOODeof appr-oximately ]0 mm2J .

thicknes e .of the te 1oils wuh polymershaving low molecular weight and highconcentration (pmIH. OCP11H, SBC[H.PMAIH) and of the. traigbt mineral oilsMI.OO and M240 plotted against. the bulktemperature "M of the disks. iJM= (01 -I-

{}2)/2 is the average measured bulk tem-perature of both clisks. At high tempera-ture • the oils PIB]H. and PMA IH. formfilm thicknesses similar to the mineral oil

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LUBRICATION

1.,OOO ........... ...-~.....,.----~4-~-+--~--+-~--~_mnf/s I

1100-I_:--"'"t'l"""'III!---II--I--d

~ 5O~-----~~~~~-+--~1...-;;;e'U''WI'S;

.I~

'0 10 ClIIPIB1HI -I------,I--~Ir__Ii 'OloOP1iHc 'VSBC1HIli,6. PidA1H

:; 0 fJI240 ':!-il--I---I---I

20 40 eo 80 ~ 120oil tem,pt"roture'

IFig,ure6--Viscos'itytemperature curves 01test oils ... , HI.

OPIB2LaOCP2LvSElC2L

I" AIPMA2Ls- -..:r STA_R':L ,-+---If---I

'" --20 40 60 ,SO, '~aUi te:mpero,tur,e "

1201

Figure 1-Viscosity temper,aMe curves 'of itest aib;, ... 2L i

I

I1~C: i

~ :~~ I I!ctl- I~~~-1--1---1---1----1---1.

- 0.0340 50 ,50 .c -I 0, I i-I

Figure 8---Measured film tliic"-nesses 'of 'tes10ils .. , IIH. !, 2.0 I,riftJ ::t-,-..j..:: .... ~ ......4-- i

+~oo I,t 1.12-40,1I1'11!21.

i I• OCP2I. !

0.1 - I~ t----t--I1--4-4---d I., SfAiI-i. , I

cosity 11100 as the polymer-containingoiuls. At low temperatures" however. thefilm thicknesses of PIBIH and PMAI.Hare lower than those of M240. The V[-improving effect of the polymer PIB Iand PMAI cen be seen quite clearlyhere,

On t1te other hand, the oils OCPIHand SBCI.H show only very littleincrea e of the film thi.ckness comparedto the ba e oil MIOO. Within the accura-cy of measurement, Ute oil OCPI.H

(Ref. 5) and 'u according to Ertel/Grubin(Ref. 6 and 8) in an EHL contact can becalculated for line contact condition. asfollows:h

miJl= 2.65 • R • (jO.54.lP·7 • ~.IJ (3)

doesn't even show an increase of the filmthicknes compared to MIOO .3:1. all. Thatis a consequence of the ability of the ipolymers SHC and OCP to form physical i

I~

I!III,IIii

I

!i

II

II

The nondimensional EHL parameters,G, U and W in the above equations wedefined as:G = a·.1f (5)

U = (71M•· v,)I(2 • R .•E) (6)

and chemical! network structures. Thosenetworks have a higbthickeoingeffect atstandard condition . At. high. pressure,

(7)

temperatureand hear rate. as in an.EHLcontact. however. those network struc-ruresare obviously not very stable andtherefore lose a great part of their thick-ening power.

Figure 9 shows the measured filmthicknesses of the test oils with polymersof high molecular weight and low con-centration PIB2L, OCP2L, SBC2L,PMA2L. STAR-L and of the two miner-al!oils M I00 and M240 at the same COD-

ditions as in Figure 8. None of the poly-mer-containing oils reaches the filmthicknesses of the mineral oil M240despite equal kinematic viscosine "100'

Thai isa consequence of the high molec-ular weight of those polymers, whichcausesa hightemporaryviscesity lossunder the influence of a shear field. asshown in Figure 3. As the viscosity of anoil in the inlet region of an EHL contactis decisive for the height of the filmthickness and as the viscosities of the testoils containing long-chain polymers arereduced to some extent within the hlghshear field in the inlet region of the diskcontact. tho etest oils fonn lower filmthickne es than expected according totheir vi co ity data gained at standardlaboratory conditions.

Film Thickness CalculationFilm Thickness Calculation in

General.The lubricant film thicknessesh"'ifl according to Dowson/Higginson

The reduced Young's modulus It andthe reduced radius of curvature R are cal-culated as follows:If = 2[(l-vf/E'l) + 0-V2/E2)]-1 (8)

(9)

According to Murch/Wilson (Ref.12), the accuracy of film thickne s calcu-lation can be improved by thermal cor-rection, which takes into account thetemperature rise of the oil in the inletregion of the contact, the ri e beingcaused 'by the bacldlow of the surplus oil.

hm,·". thermal = h",/n • C (10)

(U)

withc= 3.'94/(3.94 + [9.62) (]2)

(13)

(14)

ModijicatiolJ ,oJ Film Th'icknessCalculation for Polymer. ContainingOils. A the film thickness mea urementsprove. polymer-containing oils hardlyever rom film thic.knesses as high as astraight m:inerall oil of equal viscosity,ThaI. means that the usual kinematic vis-cosity, which is determined in a capillaryvi cometerat tandard conditions, is nolsufficient as an indicator for the filmthicknes es to be expected :for polymer-containing oils. As the usual film thick-

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ness calculation methods according toDow oIllKi.ggil!lon (Ref. 5) or lErteJjGrubin (Ref. 6 and 8) include only thestandard laboratory viscosity data. devia-tioas between calculated and actual filmthicknesses cannot be avoided for poly-mer-containing oils.

An improvement of the accuracy offilm thickness calculation for polymer-conta:ining oils requires modifying the,calculation equations with a factor thatcorrectly reflects the effective viscosityincrease of polymers in an EHL contactPolymer-specific properties, such astype, conceatration or molecular weightof the polymers, cannot be n ed for sucha factor, because tho e properties areusually not available to the user.

So a nondimensional polymer-cor-rection factor P was derived fromthefilm thickness test results. The factortakes into account the viscosijy loss of a

ILUIB,RIICATIOIN;polymer-containing oilaiter a KRL-shear lest. This term seems to be apt 10

specify the efficiency ofpolymers in aliiEHL contact a the measurementsshowed a good correlation of high vis-cosity los e after a KRL-shear test withpoor film thickness performance andvice ver a. Besides, the KRL-shear testis a common and simple test method andits te t devices are available in many lab-oratories,

The polymer-correction factor,which was derived from the test results,is defined as:

P'"' (v100• KRL!v1OO./rt!sh'P·1 (15)

The exponent IJ.7 in the above equa-tion wa chosen with respect to theweighting of the dynamic viscosity 11inthe usual film thickness equations.

The polymer-correction factor P isused to calculate the film thickness of

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CIRCLE 130

polymer-containing oils as follows:

~i". thel7f¥ll. poL = h",in,IMmtlJl .' P (] 6.)

" - /T.. .1''t!. 111"""",/. ptJl. - . U. th"mal . 07)

Tho e equations can, of course, alsobe used to calculatethe film thickness oftraight mineral or synthetic oil . In thi

case, the polymer-correction factorequals I, because polymer-free oils prac-tically don 'I. Iose any viscosity during aKRL-shea:r test. So the correction factorP is universally applicable for ell lubri-

cating oils,The improvement of the accuracy of

film thicknes calculation by u ing thepolymer-correction factor Pi hown inFigures H1-I3.

]n Figure ID, the film thicknesses'tl_henrwl' which were calculated withoutthe polymer-correction factor P; aft plaI-ted against the measured film thicknes -

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LUBRI:CATIION

ccLc.ul.f;Jhon .,thou(

pol)'TIet' -<0tT..,1"",-f~I'" /

",' r1? /0% (!' /

//

//

111 10''''

5~'i!= 10e0:;;

1:;;~ 05c

0101100oPISIHOQCP1H<t58CIH"'PMAlH

o¥-~~----~----+---~o 0.5 10 "m 2.0

fl'il'Ql\!l'td film thletnHS ~

IFlgure UJ,-Comparison between measured,and calculated film thicknesses oUest oils... 1'IHwithout polVll1er-correction .actor.

_ ...1....... 1/1

PC!I!"'*-c",",.cllm- facl""

0101100CI P!II!HO0Cl'1H'l'S8CIH6!'WAiIH

"'""'_ lin'! Ih!dlMSI ""-'

Figure 11-Comparison between measuredand calculated film thicknesses of test oils,... 1iHwith polymer-correction factor.

CGlodalioni w;ti"tCutp61-J!ft"4f-C(PKEIOI'i-focl.or

Figure U-Comparison between measur,edand calculated film thicknesses of test oil's,....2l without polymer-conectio.n factor ..

20

IL' pm

J5 '.0~,

i0:10 '0 Ifl!'!'t~td'flmthl!:kntll!lh....,

Figure 13--Com,parison between measuredand ca'iculated film thicknesses ot test oils... 21 with pol,ymer-correction factor;

es h",ea., of the test oils .... I.H. All filmthickness measurements at all conditions

that had been carried out were regarded.

The calculation overestimates the fumthicknesses of the polymer-containing

oils, especially those of SBCm and

OCPIH. For the polymer-free base oil

M 100, there is already a good correlationbetween measured and calculated film

thicknesses. When modifying the calcu-

lation with the polymer-correction factorP; the accuracy of film thickness predic-tion improves considerably, as can be

IFi!lure 14---=Lineof contact ,of C·PT-type'!leafS,

,....

seen in Figure 11, where measured and

calculated film thicknesses correlatequite well within the marked scatter

range of ± 0.2 Jim. even for the polymer-

containing oils. For the majority of themeasurements, the calculated film thick-

nesses are still slightly higher than themeasured ones. That is a consequence ofthe difference between the bulk: tempera-

ture 0M,which is measured 2 mm belowthe disk surfaces and used for film thick-ness calculation, and the actuaJ-slightly

higher=-temperature jn the inlet region

ofthe EHL contact, So the actual viscos-ity in the inlet region of the contact and

thus also the actual film thickness areslightly lower than calculated.

The use of applying the polymer-cor-rection factor Ptofilm thickness cal.cula-

tion for oils containing Iong-chaiet poly-

mers is shown in Figures [2 and 13. The

test oils ... 2L with long-chain polymersuffer from a high temporary and perma-

nent viscosity loss by shearing. Using thepolymer-correction factor Pleads to a

considerable improvement of the accura-cy of film thickness calculation for thepolymer-containing oils.

Altogether. the proper applicabilityof the polymer-correction factor P hasbeen checked with approximately 3,000

film thickness measurements with 32 dif-ferent polymer-containing oils. and itprovided good results.

Application of tile Modified FilmThickness Calcnlatioll to GearContacts. Figure 14 shows the line ofcontact of a CoPT-type spur gear pair as

:it is used for the standard pitting test PTCf9f90 (Ref. 7). Pinion 1 has 1.6 teeth.gear 2 has 24 teeth and the module is 4.5

mm. The base circles dbl and dlil' the pitch

circles '~'land~2 and the tip circles d,,1and da2 are shown in Figure 14 as well.The path of contact is limited on the lineof contact by the beginning A and end Eof contact The points B and D representthe beginning and end of the range ofsingle contact. C is the pitch point. Theline of contact touchesthe base circles in

points T 1 and T 2'

For calculating the lubricantfilrnthickness within a gear contact, the dis-tributions of the reduced radius ofcurva-

Figurel '15-Some gear-specific Iparameters,along the path of contact

IFig.uro16--Calculatod film thicknesses 01test oils .... 1H' at Ipitting-test. conditions.

I ....

r~:1• Ol~

i50.10

~J oO!J f"::f ~:;fi 0 ~~._<""_t_oc_t~_--!c__ ~...;<_on...;\O<...;I~

po'h o. conto.cl

36, NOVEMBER/DECEMBER 2001 • GEAR TECHNOLOGY' www.ge8ItBchnology.com ., www.powsrtransmlsslon.com

Figur,e 17-Calculaled film thicknesses oftest ells ... 2t at pitting-test conditions .

ture .R,. the hydrodynamic velocity ~zand

the Henzian pressure PH along the path ofcontact need to be known. A an exam-ple. tho e paramet.erare hown in

Figure ]5 for a C-PT-type gear pair and

for the conditions of the standard pitting-

test PT Cl9/90. The reduced radius ofcurvature .R forms a parabola along the

line of contact, which equals 0 in T.and ~

T 2' The hydrodynamic velocity ~E Iincreases linearly from A to E. For the I,'

calculation of the Hertzian contact pre -

sure, the normal tooth force FN was !assumed to be 100% in the range of sin-

gle contact and to be 50% in the range ofdouble-tooth contact. That i a simplifi-cation. which does not consider dynamic

tooth forces, If the course of dynamic

tooth forces along the path of contact isknown by measurement or by calcula- r

tion, the Hertzian contact pressure can be :calculated more accurately. !

With 'that gear data. the filmthick- !ne . can be calculated along the path of Icontact of a gear me h. An example is ishown in Figure 16. The film thickness!

'u.llu>mr(lI.p<JI.' which was calculated accord- .~=5::n~~;~::;:~~f~;1",.1

correction factor P. is plotted against the

path of contact of a C-PT-type gear pairfor the conditions of the standard pitting-lest PT C/9/90 for the test o.ils with short-chain polymers and high concentrations.

The relevant tooth bulk temperature wasassumed to be constant at loo°C.Wi.thout using the polymer-correctionfactor P. the filmthicknesse of all poly- I

Ii

mer-correction factor P, the calculated ..,l;",.

film thickne ses of the polymer-coruam-ing oil represent the actuaIJy measuredvalues better (see Fig. 8). I

Another calculation example in 1Figure 17 shows the film thicknesses of !the test oils ... 2L with (he long-cham :polymers in low concentration. Again, ;

calculation would provide film thick- :

me e equal to M240 for aI.l polymer- I,.

containing oil without u ing the poly-

mer-correction factor. With the factor, the :...1

calculated film thickne es how much

mer-containing oils would be calculatedequal to that of M240. Using the poly-

LUBR'ICATI,ONbetter correlation with the measured ones(see Fig. 9).

styrene isoprene copolymers (STAR),

each with two different molecularweights. In addition, the ba e ail. vi co -

ity and the coacentration of the poly-mers in the bai e oil were varied. forinformation about the shear-stability ofthe polymers. the 'temporary and perma-nent viscosity loss by shearing weredetermined separately from each otherby means of HTHS-viscosity measure-ments and KRL-shear-stability tests.

SummaryThe lubricant film th.ickne se of a

number of polymer-containing oil andtheir base oils were measured systemati-

cally in a twin-disk: test rig. The investi-gated polymers were polyalkylmelhacry-lares (PMA). polyi.sobutylene (PIB),

olefin copolymers (OCP). tyrene buta-diene copolymers (SBC) and slar-shaped

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References1. Bartz, W.-J. "Bewertung des reversiblen

und irreversiblen Viskositatsverlustes vonMebrbereichsolen," Tribologie undSchmierungstechnik; 41. Jahrgang, 41.1994,

S.214--218.

2. CEC L-45-A-99, "Viscosity Shear

Stability Test Procedure for the TaperedRoller Bearing Test Rig." 1999.

3. CEC L-37-T-85, "Shear Stability ofPOlymer-Containing Oils (FZG Spur GearTest Rig)," 1986.

4. D]Nnso 2909. "Berechnung deViskositiitsindex aus der kinematischenViskosiliil," July 1979.5. Dawson, D, and G.R. Higginson.

Elastohydrodynamic Lubrication, Oxford.Pergamon Press. 1966.

6. Ertel-Mohrenstein. A. "Die Berechnungder hydrodynamischen Schmierunggekrummter Oberflachen unter hoherBelastung und Relativbewegung," VDI-Fortschrutsberichs Reihe I,Nr. 115, 1984.

7. FVA-lnformationsblatt ZUlli For-schungsvorhaben Nr. 2nV: "Pittingtest -

EinflllB des Schmierstoffes auf die

G rubcheulebensdauer ei nsatzgeh arteter

Zaharader im Einsnrfen- und imLastkellektivversuch," 1997.

8. Grubin, A.N. and I.E. Vinogradova,

tnvestigation of th« contact machine com-ponents, Cent. Sci. Res. Inst, Tech. Mech.Eng .., MosCQw, Book No. 30, 1949.

9. Kopatsch. F. "Systematische Unter-suchun-gen ZUlli Einflu13von polymeren Zusatzen aufdie EHD-Schmierfilmdicke," DGMK·

Forsdllmgsbericht Nr. 466-01. 1999.38; NOVEMBER/DECEMBER 2001 • GEAR TECHNOl.OGY . www.ge/lttechnQlogy.com • www.powenrensmtsston.cam

................ _1 LUBRICATIO,NIAll. polymer-containing oils formed

lower film thicknesses than a straigiltmineral oil. of the same kinematic vis-

cosily "100 over a wide range of operat-ing conditions. Short-chain polymers in

high concentration in the base oil turned

out to be significantly more effective inthe contact than long-chain polymers in

low concentration witb the same viscosi-

ties. Polymers with thickening powermainly based on the formation of net-

work structures, such as SBC, providedpoor film forming properties. Those find-ings are in good accordance with tbe

findings of other authors, for instanceProfessor Spikes (Refs. U, 14 and is)from tile Imperial College in London,

who carried out a great number of optical

film thickness measurements with vari-

ous polymer-containing oils.A correction factor P was derived

from the test results, by which the accu-

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CIRCLE 129

racy of film thickness calculation can beimproved significantly for polymer-con-

tainjng oils. The application of the cor-

rection factor is demonstrated and irspractical use is exemplified by calculat-

ing the film thicknesses of some poly-

mer-containing oils in a gear contact,Admowledgments

This research project was ponsoredby the German Society for Petroleumand Coal Science and Techaology(DGMK) ill the German Federation of

Industrial Cooperative Research Associ-ations (AiP) by funds of the German

Federal Ministry of Economics andTechnology (BMWi). 0

LUBRICATIOINI10. Mann, U. "Me ung von Sehmier-filmdicken im EHD-Kontnkt. .EinnuB vee-chiedener Orundole und Viskositats-

Index- Verbesserer." .DGMK-Forschungs-bericht Nr, 466, 1995.11. Mitsui, N. and H.A. Spikes, "PredictingEHD Film Thickness of Lubricant PolymerSolutions," fr.iboloK)! Transactions, Vol.41, 1, 1998. PI'. 1-10.[2. Murch. L.E.and W.R.n. Wilson. "A

Thermal ElasLohydrodynamic .Inlet ZoneAnaly is," Tram. ASME F. J. Lubr. Techr:91,2, 1975. pp. 212-2[15,.13. Simon. M. Messung 1'071 elasto·hydro.dynamis hen Parametem und ihreA.IIswirklmg auf die Griib hentragfiihigkeirl!ergiiJell'r Scheiben lind' Zahnrtider, Diss.TU Munchen, 11984.14. Srneeth, M., H.A. Spikes and S. Gunsel,"The Formation of Viscoll Surface Filmsby Po lymer SO.luliolls: Boundary orElastohydmdynamic Lubrication?"

fribology Transactions, Vol 39'. 3, 1996,pp.72i0-725.15. Smeejh, M., H.A. Spikes and S. Gunsel,"Bound.ary Film Formation by Viscosity

Index Improvers:' Tribology Transactions,Vol. 39, 3, 1996, pp. 726-734.

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