Paper VI (ii) On the Prediction of the Occurrence of Wear on Automotive Camshafts

133

Paper VI (ii)

On the Prediction of the Occurrence of Wear on Automotive Camshafts F. Jarnias, G. Monteil and C. Coddet

This work presents a forecastlng model of the wear risk for an automotlve overhead camshaft and Its confrontationto experimental results.Thls model was built on the specifk oil film thkkness calculationand on the subsequent cakulatbn of the coeffklents of frktbn and stresses, the correspondlngvalues belng then compared with threshold values. Organized as a plece of computer software, the model permits the cakulatlon of overall wear factors ;the most slgnllcant parameters are thus presented as curves related to the cam proflles In such a way that the occurence and locallzatbnof wear Is predkted with a rather good agreement with results obtalned on rigs, for different operating condltbns. 1 INTRODUCTION

W v e train of automotive engines Is contributlng substantlally to the Internal combustion englnes friction bsses and wear. With the increasing rate of solllcltatlon, its definitlon becomes a major preacc-tbn of engines designers and justlfles the development of models, able to confirm a choke of cam proflle or materials that the speclficatbns sheets have imposed to engineers, from the tribobgk point of view. The caiculatlon of the oil film thkkness by the elastohydrodynamk lubrlcatlon theory gives the frame of the model. Its association with a stress calculation taklng Into account frktlon allows the predlctbn of the bcatbn of plttlng on the cam surface; It Is also possible to determine Its Intensity and the lnitiatbn mechanism, srbsurface or surface Initiated cracks. This study considers a pivoting OHC conflguratbn, figure (l),but it is possble to extend the model to other types of conflguratbn as to other wear f0nnS. 1.1. Notatbn

A : S p e c k oll fllm thkkness hcen,hmin,:Centraland mlmlmal oil film thkkness hv : Squeeze fllm thkkness rOQhneSS = mcam+bfd U,W, G :Adlmensbnal terms of veloclty, bad and material, for EHL cakulatbns Ucam, Ufd :Velocities of the point of contact on cam and rocker surfaces : Equivalent radius at contad point abng Ry Ry each plane of maximum curvature E : Equlvalent Young modulus ~ R M S: Composite

V Fu, Fv

( 1 - v & ~ f o i ) ~ I-’ :Vebclty of vertical separatbn of surfaces :Statbnary and instatbnary parts of bad

= (((1+am2

+

supported by oil fllm :Excentrkty ratio of contact elllpse p : Coeklent of frktbn pasp,plub.Extremai values of the coefficient of frktbn Z,,,, . Maximum shear stress Zs . Maximum superfklal shear stress Po,P, . Hertz pressure and maximurn pressure on the cam surface Rc, Rs :Yield stresses in compressbnor pure shear zo :Depth of absolute maximum shear stress p, Fls, Fs : Normal bad, Inertialand spring t o m s I,b :Lengthand half-width of Hertzlan contact k, :Sprlngstlfft~~~ 6 :coefkknt of thermovlscosity Q : coemclent of plezoviscoslty vo, 110 : Kinematk and dynam k vlcrcositles at test temperature and atmospherk pressure Barn, Bfd: (p Ct kt)”*, Where p IS the density Of material, q and 6 its thermal capacity and conductlvlty N :Camshafl rotational speed AO, EO : Cam profiles, without spring overbadlng A50,ESO : Cam proflles with overloadlng of 50%

k

2 TESTS CONDITIONS

The study of the tribobgy of valve trains was not yet accompilshed for the great variety of operating systems, except in a recent attempt 111. If the cam tappet configuration is now well known 12, 31, the one by osclllatlng rocker generated few studies, altough If Is more and more frequent because it albws a larger engine compacity. On thls system the wear of cams Is often more severe than with a tappet counterface : thls because kads and stresses are generally higher, even though the entralnment vebcilles are smaller. Thus, we focused our attention w n the fatigue wear

-

I34

or pitting of cams. We used for practical support parts of a current standard engine. Materials were, for the rubbing pad of the rocker, a tool steel, and for the cam, white cast Iron, obtained from flacky gray Iron. Materiais compositions and mechanical characteristics are summarized in table 1. E 1 : Characteristics of materials and oil Materials Poisson's ratio Elastic modulus (QPa) Hardness (Hv) Rc (MPa) Rs (MPa) Specific wight (kglm3) Composition: C% s i% Mn% CPA P% S% NI % Mn %

: : : : :

: :

: : :

: :

Cam

Rocker

0.26 160 540 900 145 7200 3.62 2.55 0.64 0.05 0.08 0.08

0.30 210 710 900 450 7700 2.16 0.4 0.26 12.25 0.02 0.02 0.12 0.26

Lubricant(Paraffinic) SAE Classification 1OW40 : 95.6 ~ 4 0 (10-6Pa.s) 0 ~

Composition Ca(Wm): 1430

v 1oooc (10'6 Pa.s): 14.6

Mg

: 185

a(10'8Pa)at850C : 1.79

E

: 130

S(1U6 Pa.s.K-l)

: 2.94

P

: 1085

p(1U6 kg.rn-3)

: 0.83

Zn S (%)

: 780 : 0.4

Tests were made on a motored cylinder head, the camshaft beeing driven by an electric motor fitted with a speed variabr. A heating oil tank let a pressure and temperature regulationof the Iubricant. Standard valve springs were replaced by ones of higher stiffnessso as to increase the load of 50%. Standard tests conditions are a low speed (900 rpm), a test duration of 7.2 1O6 cycles and a temperature of 85OC. Visual cotations were used for the comparison of pitting damages of the cam sufface. The area extension of pits, their depth and proximity enter In the evaluation of the "NID%"criterion whith marks from 0 to 20. (See on figure (2)). The pits repartition on the cam nose were also classified in five typical wear facies as shown in figure (3). After tests, SEM observations and top transversa1 inspections with a profilometer, as shown on figure (41, were made in order to reach a better knowledge of the aspect of pitting and of the average depth of pits. 3 MECHANISMS OF PllTlNQ

The litterature on this subject is abundant, and we

shall relate here the proposals whlch seem the best confirmed by our experiments. This form of wear occurs when the yield strength of the material, for pure shear stress, is locally passed beyond : the accumulation of plastic micro-strain at each cycle induces an increasing damage, which consists in the splitting up d the material, after a time which depends on the conditions of sollicitation, for a given material. Defects such as microcracks, heterogeneities, inclusions or voids are points of stress concentration which increase the degradation process, (4). The initiating phase is distinct from the propagation one, which determines the erective resistence of the system to the pitting, [5].Twr, distinct mechanisms must be considered : - The initiation of piking o b n begins under the surface, at the point where the 45" shear stress reaches its maximum. This depth is smaller than the one wich can be calculated using the static HerWan theory. The Tresca equivalent stress criterion was adopted, at flrst because It fit more easily with the present form of our model than the Yon Mises one and also because it is more severe. The maxim um alternative shear stress, which acts at lower depths and reaches higher ranges of variation, was not retained because while in the cases of pure rolling or impact contacts it seems well correlated, when sliding appears on the surface, its capacity of Interpretation becomes limited, (61. Cracks propagate with inclinations which evolve with the variations of the maximum shear Stress direction. When the section of the material separated from the bulk by the crack cannot support the imposed stresses, a sudden rupture occurs and the particule dissociates from the surface. This way of pitting is highly predjudiciable but its rate is low. - Meanwhile, the Initiatingphase can occur at the surface, [7, 8, 91 when the asperities of opposite surface can interactfrequently or when defects due to the mechanical machining of the surface, for example, pre-exist. It has been demonstrated with simples models [ I 0,l I ] that shear stresses can reach values similar to those at the depth of the maximum shear sb-ess, beneath asperities, when the lubricant cannot separate efficiently the surfaces. Cracks propagates then with typical angles of 25-30 degrees to the surface, the driving forces for the crack extension being not only the research of the maximum shear stress but alsosolllcitatlons In mode I and 11, according to the tension stresses at the outlet of the contact at first (- 2 p, P o), and by the possible effect of enhppement and compression of the lubricant In the opened crack. This way of pitting seems to be associated to boundary lubrication conditions and high friction forces. It is by the way dependant on the microgeomeby of surfaces and if its rate is high, the depths of pits are usually small. 4 CONSTRUCTION OF THE MODEL It was not intended in this work to generate a heavy software, with an analysis by finite elements of the contact, for example, but a simple tool, easy to use on a desk-size computer. Thus, the different

I35

formulations of the oil film thickness were employed rather than Reynolds, elasticity, or thermal fundarnenlaI equations and the model was built on the EHL theory and postulates that the ratio

A

made by Caubet and Cattier, [19,20]. The oil film thickness expression always takes the following form : h=KRxUUGg Ww

= IWMWS

is a good indication of a wear risk, as it was demon&-ated by many wrkers aRer Dawson [ 12 1. The values necessary for the oil film thickness calculation are taken from simple geometrical informations, obtained from technical drawings or metrologic inspections, ( cam profiles, with a degree per degree definition, or assembly quotations of pieces), and mechanical datas. At the first step of the calculation, we can, for example, localize the contact points on the cam and the follower, acceed to the cam radius, the contact speed and the valve speed, the inertial forces, the m I bad and the torque. These calculations can be achieved for a cylinder-cylinder hypothesis of contact, as for an elliptical area of contact. The second level of the model concerns the oil film thickness and the stresses (upon and under the surface) calculations, (with different propositions), and also a friction evaluation. It is well established that the friction increases with the rate of contacts between asperities [13,14,15]. We thus adopted a simple law of dependance of the friction t o i l as represented in figure (71, which fits reasonably with the experiment. The friction cMlclent expression becomes : p = ksp(2.5 - A 112.2 + q&A - 0.3) I 2.2 0.3 and 2.5 being respectively the values for which

w consider that boundary lubrication and full fllm

lubrication occur. hspdepends on the boundary properties of the lubrlcant, hub from the bulk properties of the oil.Such values are difficult to appreciate, so, i n a first approach, we consider values of 0.1 5 and 0.005, which can be obtained for valve hins, for an anti-wear formulated mineral oil, (1, 15, 161. If the conditions of a strictEj Hertzian contact are chosen, the coefficient of friction is nil and constant for the whole calculation. The value of CIws is an average of measures realized on several pieces, alter running-in. For the first calculationthe value ofp is always 0.001, but for all successive sequences of A calculation the values of the friction coefficient differ along the position of the contact on the cam profile. After 3 iterations, the values of p are yet quite constant, so the loop is stopped. The new Fiction coefficients affects, at every stage of the calculation, the normal loads on cam, the flash temperatures and the stresses. The sbesses caIculation, without friction, res u b t o m the general formulation Ibr an elastic contact, (171. With the hypothesis of tangential and normal forces, it is based upon the wrks of Smith and Liu, [ 181 and its hnscription, of more practical use for us,

U = TO('J-m '&I W = p I ( E RX I) G=aE k = 1.03 (RY I Rx) +

1 (2 E Rxl

Dowson and Al. have calculated these coefficients, (table 2), for linear and elliptical contacts, [21, 221. This calculation constitutes the first obligatory EHL hypothesis. )

T

Linear hcen hmin h, Elliptic hcen hmin

thickness calculation : U

g

w

0.69 0.70 0.47

0.56 0.54 0.40

0.10 0.13 0.087

2.69 (1 - 0.61 e-0.73k) 0.67

0.53

0.067

3.63 (1 - e-o.68k)

0.49

0.074

K

3.06 2.65 1.86

0.68

On a camrocker system, there is a cyclic load variation : a first complementary proposal consists in taking into account the simultaneous speeds of the vertical separation of surfaces, that generates a "squeeze fiim" component in the total oil film thickness. From the initial calculation of hmi, we can have access to the vertical speed dhmi,./dt, and so, using the principle of superposition of the two parts of the load postulated by Holland, 1231, to the pure squeeze thickness to be added to the value resulting from entrainment of lubricant by surfaces only. As the vertical speed is determined from erroneous inltlal values, the calculation proceeds by a convergence method, [24), in such a way to obtain the resultant oil film thickness.

P = Fv(hcen) + Fu(hv)

The second offered posbility is a non isothermal calculation, based upon the commonly used equation of Blok for cylindrical contacts, 1201, giving the frictional temperature rise :

The friction induces high temperatures in the materials, which increase, by conduction, the oil

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temperature at the contact Inlet. The piezo-viscosity index (and the new viscosities of the oil), along the cam profile, for bulk temperatureplus flash temperature, are re-evaluated before each new loop of cakulatlon using the Klaus and So equation [25] :

We are thus far from an exact solution of the thermo-elasto hyd rody namic problem and s uc h hypothesis raise the question of the potential weight of the temperature of the lubricant certainly In an important way, but It is a very simple mean to evaluate the extreme variations which could be attributed to the fall of the lubricant viscosity with a temperature increase. Such an hypothesis has been proved to be reasonable accordlng to our previous results, (21 and other wrks [161. A general flow chart of the saltware is presented in figure (6). 5 PRES ENTATON OF RESULTS

It is possible, at the conclusion of any calculation, to express any parameter as a function of an other, in a listing or in a graphic form. Howver 4 diagrams can be drawn systematically : the first, shows A on a cam profile, fgure (1la). It appears from experiment that w a r Is not severe until A > 0.3, so the portions of the surface where there Is an bnportant rlsk of wear occurence can be predicted. The second, figure (llb), gives the friction coeff kient along the profile. A first level at 0,08 wds chosen as a reference, independant from the studied system and near clasp ;the upper boundary has the value of wasp in the model. As the friction Increases, the wear forms encountered are : deep pittlng, superficialpitting and then scuffing. The third graph, figure (1lc], shows the depth of maximum shearing, (and flash temperature if this option has been chosen). It allows to predlct the severity of the pitting : when the depth is nil, surface initiated pittlng is predominant. As a matter of fact, when the friction becomes greater, the positionof the maximum shear stress position moves from the center of the contact area towards the inlet and from the depth to the surface. The depth of maximum shear stress seems to be wII correlated with the maximum depth of pits measured after tests. Howver it Is always leading to associate Vle depth of pits with the shear dress maximum rather than with the alternative shear stress maximum, with only a simple analysis of S EM observationsor mlcro-geornetrlcalvarlatlons on pitted zones, because these methods always give a partial view of the real cracking pattern. This graph confirms, in the case of thin superfiiial treatments, their validKy, from the shearing point of view. The flash temperature informs upon the portions of profile where chemical reactivity of the lubricant is

enhanced, wlch Is partlcularly Interest1ng for scufflng studies. The last graph, figure (lld), expresses the maximum pressure, the maximum shear stresses at the surface or beneath, normalized using their respective elastic yields for the considered material (Rc and Rs).When the pressure on a portion of cam profile exceeds the simple conpression strength of the white cast iron, we note that every kind of wear can occur; it depends principally on the friction and the sliding velocity. With the Tresca equivalent shear stress the probability of pitting occurence can be predicted and when correlated with the second and third graphs, the predominent mechanism of pitting can also predict. Tension forces at the outlet of the contact can also exceed the tensile strength of the material and authorlze the development of a superfiiial pitting or scuffing. 6 COMPARISON OF TESTS RESULTS AND MODEL

FORECASTINQS

Two profiles are presented here to illusbate the use of the model, figures (1la) and (8). A calculatlonwith, as flrst typothesls, no frlctlon, for a linear as well as for an elliptical area of contact, does not agree qualitatively with experiment. K kw include the friction in the calculation, the agreement is rather good In the predlction of wear patterns and depth of shear stress. For the assumption of an elliptical contact, the calculatedpressures are greater, from 12% to SO%, depending on conditions of calculation, than for a llnearone, and thus the oll fllm thickness is lightly thinner. If these values seem to be ovemted, the qualitative predictionsare quite similar. We observe also that the consideration of the transversal curvature of rocker pads does not enhance the accuracy of the calculation, versus the computation with perfectly cylindrical pads. We must consider that followers, (as cams), are mass produced and that some disperslon In the effective shapes of pads, some misalignments and flexure of the axles and mainly some evolution of the shapes of surfaces during the test mortgage the results obtained, as much as does the approximation of a linear contact for the real elliptical one. So we prefered to make calculations with a linear contact hypothesis, which gives a betteraccuracy for the stresses calculation in plane shin, bearing in mind that the effectlve stresses are certainly greater. Unstationary hypothesis do not seem to be determining. Lowest values of the oil film thickness are increased, but the model conclusions are not sensitive to these modifications. A t the opposite, thermal effects reduce the oil film thickness and thus increase the contribution of the asperity to the friction. The model predicts that superficial pltting should be enhanced much more than the experiment shows, but the effects of the anti-wear additives in the oil are not yet taken into account. As an illustratlon of the usefulness of the model a comparison between the effects of different factors such as : the temperature, the spring rate and the camshaft rotational speed, resulting from model

137

calculations and rig tests, are presented in figure (5) and (8) to (12). 6.1 Effects of load Profiles A and E are very different : it can be observed that increasing loads leads to increasing damage but with profiles dependent proportions. TARLE 3 : Datas and results of experiments : Cams Preload(N)

kS (kN I m)

Peakload (N) Mean NID% Aspect

normal springs A0 EO

50% of overload A50 E50

560 38 1435 1405 5,3 3,8 D CsE

660 71 2175 2075 12,l 6,8 B,C,D B s D

In spite of the great increase of the load between the htests, ca kulation results show that the speclfic oil film thickness and the coefficient of tktion are only slightly modiied. However, the values of the stresses, (pressure and shear], have been risen by near 25%, so greater is the area where elastic &ength Is accomodated, figure (9) and (1ld). TABLE 4 : Values and repartitionsof calculated shear stresses (* Repartitionon two distinct sites) Extends on cam nose in degrees A0 ED A50 E50 ZM> Rs ts > RS

37 38

40 35,s

IS 'ZM

40,5 11* Boundarylubrkatin 17 4* ZMmaximum(MPa) 231 208 ZSmaxknum(MPa) 233 205

46 45

45 42,s

40,s 18 280 285

12* 5" 252 252

The area of supremacy of superficial shear stress is large for profiles A and very small for E ones, and approximativeiy independent of the load. Under small loads the aspects of worn surfaces result from the preponderance of superficial pitting, according to the specificities of each profile. On A0 the whole cam nose is under boundary lubrication conditions, so the "0"form is finally obtained. On EO, superficial shear overcomes sharply near the top, and around the point of the maxlmum curvature of the profile, f lgure (10), such is the repartition of pits. Under heavy loads the great variations of shear sbesses, on a same point, at every cycle, lead to a higher relative weight of deep pltting and so the aspects of pitted surfaces evolve towards "B"types, for A50 as for E50 profiles. 6.2 Effects of the camshaft speed The profile A, as describedon figure (1la) is sensitive to wear by steps. For high values of the oil film thickness, the damage is quite insignificant. For

smaller ones, pitting occurs in a restrkted area between the maximum curvature and the top of the cam. If the oil film thickness becomes smaller the pitting area grows to reach the entire cam nose region. During running-in those conditions are predominant : numerous sites for the starting of superficial pitting are generated, over the whole summit surface. They will evoke to cracks and flakes with unfavourablesteady state conditions of contact. In a first approach we can expect a decrease of the damage, as the velocity rbes, owing to the fact that the specific oil film thickness is increased and the load reduced. This is wll observed for small loads but not with a 50% overload, Mere the maximum damage seems to be reached near the 900 rpm regime speed. TABLE 5 : Experimentalresults N (rpm) 500 900 1200

Cams

NID%

Aspect

A50 NID% Aspect

686 5,3 2,3

D, B, C D A, B, D

7,O 12,l 6,2

A0

B>D 8, C, D D

For the considered range of speeds, we can reject the hypothesis that onb inertial forces acts, as it is illustratedin figure (5) :the load decrease between 500 to 1200 rpm do not exceed 3% with A50 and 5 % with A0 and these forces are very small all over the top of the cam. The locations where the decrease of the load due to inertial effects are noticeable are the cam ramps on which the geomeby leads to a good protectionagainst high pressures or oil film ruptures. The oil film thickness depends little on the load, as it is known ;with the speed, tiction curves show that, altough the area of boundary lubrication decreases (extended upon 39" at 500 rpm, 3 7 at 900 tpm and 33" at 1200 rpm), there is no disruption of the film until a speed of 1200 rpm. We can note that the average of the oil film thickness increases more tom 900 to 1200 rpm than from 500 to 900 rpm, indicating that a threshold is overcome. The variation of the pressure or shear stresses intensities are small, (1 to 2 % , between extremal speeds), because of the size of the profile under boundary lubrication conditions. The absolute superficial maximum shear decreases with velocity and the superficial pitting is reduced faster as the speed rises, faster than the deep shear stress, in intensity and in length. The aspect and intensities of the pittlng obtalned can be discussed as follows : under heavy loads :at lowcamshaltregimes, the interactions between asperities are frequent but the energy dissipatedat eac h contact remains weak. On the other hand, the 45" shear stress reach high values beneaththe surface, so the pits are deep and disposed as "8"form. At 900 rpm, deep pitting is quite unaffected and lot of initiatbn sites of superficial pitting encounter favourable conditions for their extension, so the NID% average increases and he aspects of the pitted zone on surface are m e

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138

dlverslfled. At 1200 rpm a lot of Inllatlon sites on the surhce are moving towards superficial pitting : the energy involved at each asperly contact is high ; these locations are only dependant from the microgeometrlca I characteristks. However the gap between the surfaces is significantly larger than for the precedent cases, because a level Is overcome. Superficial stresses are also less important. Deep pitting always occurs but It appears less clearly because surface initiated pits are randomly distributed. - Under light loads : lnteractlons between asperities are less strenuo us, (we noted correlatively, that scuffing, which was often present In other cases had almost totally disapeared) : with reduced speed, deep pitting propagates on an area which remains nearly as extended as in the former case (39"versus 46'). The large stresses attenuation involves a reduction of the area of deep pitting predominence ; so the relative variation of the superficial pitting with speed takes more evldent welght on the flnal aspect (types "A"or W). It Is also Interrestingto note that the depth of maximum shear stress decrease on this portion of profile from 70-75 w to 50-60 pm, consequently the time to pittingwas clearly reduced. 6.3 Effectsof regulated oil temperature

The effects of the 011 temperature are rather spectacular because of the large difference In the lubricant viscosity between the two temperatures considered here, (table 6). TABLE 6 : Results and conditions of tests Temperature("C) 60 Cams A50 E50

A50

NID% Aspects qo (10'6 Pas)

6.3 7.8 B>D E>E 4

p (1 kg.m-3) a ( 1 ~ Pa-') 8

5.3 3.2 B C>B 28

120 E50

0.85

0.80

2.0~

1.53

These tests were made with honed cams, the roughness of which seems to be largely favourable because during the running-inperiod there are less initiation sites on the cam surface. This good mlcrogeometrical finishing has also comp leteiy removed scuffing occurrence. Stresses are not affected by the temperature if the considered portions of the profile are under boundary lubrication conditions. They increase sligthly when the oil film thickness decreases significantly. The results are once again cam profile dependant, as shown in figure (12). For A50 profiles, even at low temperature an area behveen the summit and the maximum nose curvature is under boundary Ibrication conditions, with high superficial and subsurface shear dresses. In that case, deep pitting still prevails because of the quite good surfaces separation maintained by the oil film, [the minimum oil film thickness was below 0.2 prn

over less than 2" for the whole profile, versus 17" at 85OC). For higher temperatures, the boundary lubrication area is extended b the entire nose cam reglon. However, the stresses decrease towards the opening ramp prevents an heavy increase of the damaged surface area. This certainly w u l d have not been the case with non honedcams. For E50 profiles the stresses Increase due to the friction rising up k more evident and deep pitting prevails. lmust also be noted that the minimal depths of the maximumshear is decreasingas the coefficient of hlctlon Is Increasing.These facts explain the great difference between the rate of pitting expansion for A an E profiles. 6.4 S ummaty of some other test results a nd model

evolutian Other operatingparameters have been experimented, (8 cam profiles, different speed or loads under other conditions, of lubricant for example, temperature variations during test...). Of course, we can not sum up here all these results, but the importantpoint is that for each conditions, our model has given satisfactory confirmationsof experimentalresuIts. It can also procure Informationson the effects of roughness : the Importance of the mlcrogeomeby of the surfaces has been evoqued, from the crack initiation point of view. It seems possible to delay or even to prevent, by an appropriated state of surface finish, the superficial pitting or seyere wear forms as scuPfing, but the composite roughness criteria lacks of significance for such a study. Nowadays it is possible to simulate the effects of running-In, excepted for the tribochemical aspects, by calculations taking into account the initial roughness of the pieces and non isothennaI hypothesis. The antiwar properties of a lubricant can also be evaluated, by the use of friction curves with different thresholds for ksp and plubIn spite of some evident carencies of our model in its present form, results can be obtained which agree with experiments made with the same oil formulated with a small quantity of antipitting additives, simply by the use of a Val ue of k s p = O .09. This approach wi II provide full satisfaction when an effective mean to quantify reactivity effects of lubricantwill be available.

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The presentmodel having given proof of its capacity to explain tests results in fatigue wear conditions, it is expected now to employ It for a validation of designers proposals on a large extent. It can be objected that the calculations were correlatedto results of "postmortem"ana1ysis of cams while wear Is always a dynamic phenomena. In fact, the knowledge of the wear facbrs variations during the tests, has always been one of our main preoccupation ;we shall soon improve the situation since a fully instrumented monocarn test rig will become progressively operational. It will allow measurements of the oil film thickness and of the

I39

coefficients of hlction, at any point on the cam profile. Such tests of course will be of further importance for the validation of our friction hypothesis for example. At last, it may be noted that the abrasive wear, on cam as on rocker, can also be predicted using the Beii model [25] approach, with an excellent qualitative agreement. while there is not yet effective fully satiactory model for scuffing w a r , our calculations already procure numerous Informations which authorize b formulate reasonable hypothesis for the scuffing resistance of cams.

REFFRENCES BALL, A. D. ‘A tribological study of the design and pertormanceof automotive cams’, Ph. D. Thesis, University of Leeds, 1988. MONTEiL, G. ‘Etude tribologique du systeme came-poussoit‘, Ph. D. Thesis, University of Franche Comte, BesanGon, 1987. HARRISON, P. ‘A study of the lubrication of automotive cams’, Ph. D. Thesis, University of Leeds, 1985. KEER, L. M. and CHENG, H. S. ‘Stress analysis and crack growth in concentrated contacts’, Proc. of the 12 th LyonlLeeds Symp.on Tribology “Mechanisms and Surface Distress”, Lyon 3-6 Sept. 1985, Paper I(i), 23-28. LONGCHING, C., QING, C. and ERYU, S. ‘Study on i n i t i t i n and propagationangles of subsurface cracks in GCr 15 bearing steel under rolling contact.’, Wear, 1989,133. 205-21 8 BROSZEIT, E. ‘Internal stresses and their influenceon material stresses in Hertzian contacts - calculations with different stress hypotheses’, Proc.of the 1 2 th LyonlLeeds Symp. on Tribology - ‘Mechanlsms and Surface Dlstress”, Lyon 3-6 Sept. 1985, PaperVlll(i), 189-197. KEER, L. M. and BRYANT, M. D. ’A pitting model for rolling contact fatigue’, Trans. of the ASME, Journ. of Lubr. Techn., m 1 9 8 3 , 198-205. ICHlMARU K., NAKAJIMA, A. and HIRANO, F. ’Effect of asperity interaction on pitting in rollers and gears’, ASME, 1981, 482-491. GANG, D., CHUI, X. and YANG, Y. ‘An investigationof the mechanismof micropits on the case-hardenedtooth surface’, Proc. of the Eurotrii Int. Cong., Ecully, Sept. 1985,-V01.3. paper 1.4. (1 0) IOANIDES, E. and KUIJPERS, J. C. ‘Elastic stresses below asperities in lubricated contacts’, ASME, 1985, Trib-3. (1 1) BERTHE, D. ‘Les Mets hydrodynamiques sur la fatigue des surfaces dans les contacts Hertziens’, Ph. D. Thesis, University C. Bernard of Lyon,l974 (1 2) DAWSON, P. H. ‘Effects of metallic contact on the pitting of lubricated rolling surfaces’, J. Mech. Eng. Sc., 9.,No 1,1962. (1 3) HOLMBERQ, K. ‘A suney of applications of EHL on machine elements’, Trib. Int., June 1982, 123131. (14) ZHU, G. ‘A theoretical and experlmental study of the biology of a cam and followt‘, Ph. D. Thesis, University of Leeds, 1988.. (1 5) STARON, J. T. and WLLERMET, P. A. ‘An

a nalysIs of va Ive tra In hlctlon In terms of lubrificationprinciples’, SAE Trans. paper, No 8301 65,1983. (16) VAN HELDEN, A.K., VAN DER MEER, R.J., VAN STAADEN, J.J. and VAN GELDEREN, E. ‘ Dynamic friction in cam 1 tappet lubrication‘, SAE Paper 850441,1985. (1 7) TIMOSHENKO, S . and GODDIER J.N. ‘Theory of elasticity’, Mac Graw-Hill Book Company, New York, 1951. (1 8) SMITH, J. 0.and LiU, C. K. ’Stresses due to tangential and normal loads on a elastic solid with application to some contact stress problems ’,J. of Appl. Mech., ASME Paper 52, 1953,157165 (1 91 CAUBET, J.J. and CARTIER, M. ‘ Analyse des Conhintes r4sultant du Contact de deux Corps frobants- Courbes Intrinsequesdu Frottement, Premiere Partie-’ Les Memoires Techniques du Cetim, Nol, 1970. (20) CAUBET, J.J., CARTIER, M., RACINE R. and REYMOND, A. ‘ Analyse des Contraintes resultantdu Contact de deux Corps frobantsDeuxieme Pattie : emploi pratique des Coubes lnbinseques du Frottement-’ Les M h o i r e s Techniques du Cetim, N*4,1970. (21) WINER, W.O. and CHENG, H.S. ‘Wear control handbook- Film thickness, contact stress and surface temperature-‘, ASME, New York, 1980. (22) BOOSER, E. R. ‘CRC Handbook of lubricationTheory and practice of tribology- Vol II ’, CRC Press, Boca Raton, 1984. (23) HOLLAND, J. ‘Die Instationareelastohydrodynamich’, Konsb-uktlon 30,g1978,363-369 (24) STEINFUHRER, G. ‘Calculation of film thickness for variable velocity’, Wear,& 1980,195-201. (25) KLAUS, E.E. and SO, B.Y .C ‘Viscoslty pressure correlation of liquids’, AS LE Trans., a4,409-421. (26) BELL, J. C. ’Critical conditions for wear in pivotedfollower valve train systems’, I I I CEC ~~ Symposium, 1989.

a

1 F T YP FOLLOWER VALVE TRAiN SYSTEM

I40

r I

.....

-I

I . . . . .

Polisnea o y wear surface c a m nose surface

.......

~ a 9 kael!rnltlng a I X I cm' a r e a ( A ) Area wnere scurrrng may occurs 5 u p c r l l c I 1 ~p l l t l n g

OP

( f r o m camera v l e w a t Y 9

or tne cam m

d " . ,

SUE IOOX&I/

Coruantntlon 01pnn turn C :

D

A

NID % = S% + C + D If S% + C + D r 20 then NID%=20

E

FIGURE 3 :TYPICAL ASPECTS OF PITTING

b p t h 01 @la tbnD:

Hlph : + 4 PI8 Ymdlurn :+ 2 PI. Llghl : 0 f l a

I

-

wltn a g r l d )

SURFACE INITIATED PllTlNG : POPULATION OF PITS 0 5 10 15 20

I

FIGURE 2 : DESCRIPTION OF THE NID% PITTING DEMERIT COTATION

fl

-

cbn 4

-

Cbrn 2

w

p

'CzOrm

\

Y

v

MAXIMU DEEPPllTlNG ; POPULATION OF PITS 0 5 10 ...........................................................

190- \ .............................................................

5100-\

C

FIGURE 5 : vARlATDNS OFp WITH THE POINT OF CONTACT [CAM A5Q P'SlTlON. FOR DIFF-mDS

E

DEPTHOF PITS FOR TYPICAL DEEP AND S UPl3FICIAI PllTl NG ; a) From Hommel T20 inspection on cam top - b) Disbibutions of maximum depth of pits established tom (a]

141

........ .. ..... I.............. Contents o t a t r l e . .* Geomn 01 mcker Pssembbd Inpl1lrd;rhsad Valve sprin charMerlc1Ica ' Geomel c! m c b r pad ' ( whh cy%ddul *hap or ' Imnwema cuwmun) :Physlul pmpniar :Mechanical propnles * Complrilbn '* R o u g h m

.:

! !

. *

0,1

*

0.0

. . . . . . . . . . . . . d

I

A

","*

FIGURE 7 : COEFFICIENT OF FRICTIONVS S PECIFIC OIL FILM THICKNESS BL : Boundary Lubrication ML : Mixed Lubrication EHL, HL : Elastohydrodynamicand Hydrodynamic Lubrications

FIGURE 6 : SIMPLIFIED FLOW CHART OF THE COMPUTER SOFTWARE

\

..L....... ...... j plub

FIGURE 8 : S PEClFlC OIL FILM THlCKNESSflOO% : A = 2.5) CAM EO ;N = 900 rpm ;T= 85OC

I

FIGURE 9 : STRESSES NORMALIZEDTO Rc OR Rs (1 OO%] : CAM AO, N= 900 rpm, T = 85*C

FIGURE 10 : DEPTHOF ABSOLUTE MAXIMUM SHEAR STRESS : CAM EO, N=900 rpm, T=85'C

I42

FIGURE 11 :

CAM A50 ; N = 900 rpm ; T = 85'C a)A( 100%= 2.5) b ) u ( 100%= 0.151 ( deDth x 40 relatively to cam DroDortion 1 d) Pp$ Rc and T~ / Rs

... I,

FIWRE 12 : EFFECTS OF TFMPE RATURE ON u FOR A50 [c. dj AND F50 [a. bj CAMS : 60 OC : (a, c) 120°C: (b,d) N = 900 rpm