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Shearing of Adsorbed Polymer Layers in an Elastohydrodynamic Contact in Pure Sliding
Lubrication at the Frontier / D. Dowson et al. (Editors) © 1999 Elsevier Science B.V. All rights reserved.
493
Shearing of Adsorbed Polymer Layers in an Elastohydrodynamic Contact in Pure Sliding D. Mazuyer% E. Varenne ", A.A. Lubrecht b, J.-M. Georges ", B. Constans c q~cole Centrale de Lyon, Laboratoire de Tribologie et Dynamique des Syst6mes UMR CNRS 5513, B.P. 163, F69131 l~cully Cedex, France, bINSA Lyon, Laboratoire de M6canique des Contacts, UMR CNRS 5514, 20, Boulevard Albert Einstein, F69621 Villeurbanne Cedex, France, CCentre de Recherche Elf-Solaize, Chemin du Canal, B.P. 22, F-69360 Solaize
The valve train wear of automotive diesel engines mainly depends on the kinematics of the contact, the metallurgy of the rubbing surfaces and the lubricant [1]. The presence of soot in the oil causes a dramatic increase in wear of the cam/tappet contact [2-3]. It has been shown, in this case, that the interactions between the soot particles and the rubbing solid surfaces are very important in the understanding of the wear and lubrication process. These interactions are partially governed by the dispersant polymer in solution in the automotive lubricant. Then, the tribological and the rheological behaviour of the boundary films anchored on to the surfaces must be considered. This paper focusses on the shearing of polymer films inside an elastohydrodynamic contact. The application of low speed alternative motions of the contact with successive periods of pure rolling (vanishing sliding speed) and pure sliding (vanishing entrainment speed) leads to the formation of film accumulations that are always entrained by the lubricant flow . The shearing and the geometry of these aggregates strongly depend on their adherence to the solid surfaces. The agglomeration process is stopped when the adsorbed layers of polymers have been consumed and totally peeled off from the solids. A numerical simulation including the peculiar kinematics of the contact in a pure sliding elastohydrodynamic lubrication regime gives the evolution of the oil film thickness versus time. The results of this model are compared to the experimental results. The consumption and the adherence of these layers to the substrates can be related to the wear process of the valve train.
1. INTRODUCTION The wear mechanisms of valve trains are very different between a diesel engine and a gasoline one. The higher working temperature in diesel engines and especially the presence of soot particles in the lubricant are the main reasons explaining the different wear processes. So the main question is to find out the mechanisms that are responsible for the increase in wear with soot particles. All the hypotheses developed in the literature are based on the interaction of the particles with the rubbing surfaces or with the additives of the formulated lubricant. According to the physical nature of these interactions, several wear models can be built. The
models based on physico-chemical interactions usually consider the interactions between the soot particles and the anti-wear additives [4-6] that can destroy the equilibrium between the formation of adherent anti-wear films and their consumption Among the hypotheses that could explain the role of soot in the wear of diesel engines, their aggregation in the inlet of the contact creating an oil starvation is often advanced [3], [7]. Parallel to these observations, Rounds [2] and Colacicco [3] show the beneficial role of dispersants and the VII (Viscosity Index Improver) polymers on the wear. The dispersant properties of the oil to avoid sedimentation and aggregation of the colloidal particles [8] (soot, wear and oxidation particles,...)
494
become fundamental. Then, the knowledge of the interparticle forces (steric, electrical, van der Waals forces) whose equilibrium governs the stability of the particles in the lubricant is very important to understand the wear mechanisms. The steric stabilisation by adsorbed or polymer layers is often used to control the aggregation process in the lubricant. Besides the particle/particle and the surface/particle interactions, the dwell time of the contact point and the sliding distances run by the surfaces due to the global kinematics of the contact must also be considered [ 1]. To simulate the tribological and cinematic conditions of a reciprocating motion characteristic for several real contacts, a tribometer with an elastohydrodynamic lubricated contact between a ball and a disc has been developed, in which the slide/roll ratio of the contact can be controlled accurately. The work presented in this paper concerns the behaviour of adsorbed dispersant polymer layers sheared in an EHL regime under successive cycles of pure rolling (vanishing sliding speed) and pure sliding (vanishing rolling speed).
Their structure, rheological and tribological properties which are key parameters because they govern the soot/surface interactions mainly responsible for the wear process are investigated at molecular level with a surface force apparatus. In these experiments the evolution the lubricated contact is visualised. Because of the lower entrainment speed of the lubricant inside the ball/plane contact, the oil film thickness is less than the resolution of the interferometric measurement, the thickness of the lubricant is deduced from a theoretical approach. The numerical simulation compared to the experiments is able to explain the evolution of the contact under pure rolling/sliding conditions but is not sufficient to describe the shearing of the adsorbed polymer layers in the pure sliding interval. Nevertheless the local evolution of the pictures contrast of the EHL contact is interpreted as local thickness evolution. They are able to give qualitative information on the balance between the adherence of the layers on the surfaces and their shearing behaviour in a concentrated contact. 2. E X P E R I M E N T A L T E C H N I Q U E
To the spectrometre
=,ITVl
c o o
..........
....
White light
Silica disc
Stepping motors Figure 1. Principle of the EHL machine used for the experiments. The ball and the disc are accurately and independently entrained by 2 stepping motors in the range 0.5 mm/s to 3 m/s. The applied load is between 0 and 25 N (contact pressure < 0.5 GPa).
2.1. The Elastohydrodynamic tribometer The Elastohydrodynamic tribometer used for these experiments and presented in figure 1 has been developed in the Laboratory. Its main principle is similar to the EHL machines already described in the literature [9-10]. Nevertheless, this apparatus is not only devoted to the measurement of the oil film thickness with an optical method but to the visualisation of the lubricated contact. This one is realised between a 52100 ball steel and a silica disc coated with a thin chromium layer (thickness: 10 nm). This disc in contact with the steel ball, forms an optical resonant cavity that allows us to precisely measure the oil film thickness [11]. The diameters of the ball and the disc are 25.4 mm and 60 mm respectively. Before each test, the ball is polished with a diamond dispersion (the mean size of the particles is 0.1 ~tm) to obtain a peak to valley roughness of 20 nm. The roughness of the silica disc is less than 5 nm. After cleaning the glass disc (heating in a blue flame and ultrasonic bath), the semi reflective chromium layer is obtained by a cathodic sputtering of 45 s. The coating is made under a partial pressure
495
of argon of 5.10 .7 bar in the vacuum chamber. The thickness of the metallic layer is then evaluated at 10 nm. The contact is loaded through a spring with a known stiffness in the range 0-25 N. Accounting for the mechanical properties of the steel and the silica, the contact pressure can be varied from 0 to 400 MPa. In the work presented in this paper, the load is maintained constant at its maximum giving a 280 gm hertzian contact diameter and a mean contact pressure of 400 MPa. The ball and the plane are driven independently over a speed range of 500 gm/s to 3 m/s by 2 stepping motors mechanically insulated from the ball/plane contact. The stability of the rotational motion without any vibration is assured by the use of peculiar motor drivers working until 50800 steps per revolution. These indexers can be automatically driven by a personal computer. Because of the coupling of a precise guiding of the 'turning pieces' with this type of motorization, the kinematics of the contact is controlled with great accuracy : the resolution in speed is 0.001 revolution per second in the range 0.01 revolutions per second50 revolutions per second. Therefore, numerous combinations of motions can be monitored either continuous or changing from pure rolling to pure sliding. 2.2.
The kinematics of the contact
As shown by Bell [1], the valve train wear is very dependent upon the dwell time of each point of the rubbing surface inside the contact and the length of the counterface that it sees during one path in the contact in other words, its cinematic length. These parameters are a function of the entrainment speed and the sliding speed. The shearing of the adsorbed lubricant layers is also governed by the kinematics of the contact but with time scales of a few hundred milliseconds, which is one order of magnitude higher than the time scale involved in the wear process (about 10 ms) [ 1]. Therefore, the previously described EHL tribometer allowing a precise speed control of ball and disc is used to study the influence of the dwell time and the sliding distance of the contact on the lubrication. A particular speed cycle made of alternative motions at low entrainment speed with successive periods of pure rolling and pure sliding has been chosen to exhibit the shear behaviour of the boundary polymer films under high pressure (400 MPa).
+ speed of the ball x speed of the disc ...... entrainment speed - - sliding speed ]
3,2
...... 1,6 E vE
-g X o ¢.t)
""""'...... 2
3
i
-1,6 0,96
1,92
Me
....."""'
"........................
t
2,88
~
3,84
__
_d!sc 4,8
5,76
T i m e (s)
Figure 2. Evolution of the characteristic speeds of the contact during one pure rolling/pure sliding cycle. The period between points 2 and 3 is pure rolling. The pure sliding period is between points 5 and 6. Point 4 is the time when the speed of the disc is vanishing. Figure 2. shows the evolution of the speed of the disc and the ball, Ud and Ub respectively, for one cycle. From these two speeds, the entrainment speed Ue and the sliding speed Us are defined by the relation (1) and (2) respectively : U e -- ( g d +
Ub)/2
U s -- ( U d - U b )
(1) (2)
During the whole experiment, the ball has a constant speed Ub = 1.6 mm/s. The cycle can be divided in 6 steps (points 1, 2, 3, 4, 5 and 6 referred on figure 2.) according to the motion of the disc (the time separating two consecutive steps is 960 ms) : a- At the beginning of the cycle, the disc is stationary and the contact spot is located at the left side of friction track (point 1 in figure 2.), b- The disc reaches, at point 2, the speed Ud = Ub with a constant acceleration, c- Between point 2 and point 3, the speed of the disc is maintained constant. Therefore, during this period, Ud = Ub and the contact works in pure rolling (Us- 0), d- Then, between points 3 and 5, the disc is slowed down with a constant deceleration. Ud vanishes at point 4, e- The disc reaches the speed Ud = -Ub at point 5. Ud is constant between the points 5 and 6.
496
During this period, the contact is in pure sliding and the entrainment speed Ue = 0, At point 6, disc is slowed down to zero speed and a new cycle starts from the point onwards. The dwell time and the sliding distance for a contact point belonging either to the disc or to the ball are computed according to a method detailed by Bell et al. [1] from the speeds Ud, Ub, U e and Us. These calculations show that the sliding distance and the dwell times are maximum at each side of the friction path. The sliding distance varies for the disc between 0 and 1.2 mm, while the dwell time of the contact on the disc varies between 0 and 800 ms.
30°C, is [11] = 22 cm3/g. The "hydrodynamic" radius RH is therefore equal to about 8.4+0.5 nm. The radius of gyration is evaluated to be 5.28 nm. The ratio "hydrodynamic" radius to gyration radius RH/RG, is considered as a criterion for the solvent quality [14]. It is concluded that 175NS, is a good solvent for the PMA solution at 25°C. The critical concentration of polymer, i.e. the concentration c* at which overlap of the polymer starts, is estimated by the formula • c * -
The In]" theoretical critical concentration is found to be c* = 45 mg.cm -3. Therefore the concentration c is less than c* (c/c* = 0.50), thus corresponding to the dilute regime.
2.3. The lubricant The lubricant that has been used in this paper is a solution of a dispersant polymer (DPMA) in a base oil. Experiments are carried out with pure solvent and polymer solutions. The solvent is a 175 Neutral Solvent base oil (175 NS, from Esso Port J4r6me, France) whose kinematic viscosities are 33.60 cSt at 40°C and 5.65 cSt at 100°C (its dynamic viscosity is 60 mPa.s at 25°C). Its density at 15°C is 0.8707 and dielectric constant is 2.188 at 24°C. The molecular weight of 175NS is 416 g.mo1-1, and it is composed of 4.30% of aromatic carbon, 68.85% of parafinic carbon and 26.85% of naphtenic carbon. The sulfur level is 0.55% weight. The polymer used in solution in the 175 NS is a polyalkylmetacrylate (PMA) with a dispersant function, DPMA, diluted in a 150NS base stock and supplied by Rohm & Haas. The product is used as received. This polymer is obtained by polymerization of metacrylate esters of different aliphatic alcohols containing grafted nitrogen compounds. The weight-average molecular weight of the pure polymer Mw, was measured by gel permeation chromatography (GPC) against polystyrene standards. The nitrogen concentration determined by chemilunescence is 0.43% w/w in pure polymer. Its final molecular weight is Mw=177000 g.mol 1. The concentration of the polymer in the base oil is 2.6 % w/w which gives a bulk solution viscosity of 95 mPa.s at 25°C [12]. The pressure-viscosity coefficient is evaluated to 2.45.10 .8 Pa -1 [13]. The intrinsic viscosity [rl] ([11]= limc_.o - ~ )
measured at the temperature o f
1
Cobalt substrate DPMA layer
2RH = 33 nm
~
L=34nm
100 175NS+DPMA kk, [-[ 100kTexp(rCD"] "'- ~ = $3 \-£-J with s = 6.3+0,3nm \\ \ ". \ x ~ . 4+0 5nm .~.. 175 NS
nl0 L._ 00
~- 1 13.
0.1 0
I
I
I
10
20
30
I'~%
40
I
50
60
Distance D (nm)
Figure 3. Plot of contact pressure against distance D, for DPMA layers in SFA experiments. From Alexander-de Gennes theory [16], the thickness and the density of the polymer layers can be calculated. The structure, the adsorption and the nanorheological properties of the DPMA layers have been studied by surface force experiments in a
497
sphere/plane contact of cobalt surfaces whose characteristics are described in the literature [15]. After an adsorption of 20 hours, the measurement of the static normal force versus the normal displacement of two cobalt surfaces lubricated with the DPMA solution becomes repulsive for a sphere/plane distance of 68 nm corresponding to the beginning of the interpenetration between the adsorbed polymer layers. This distance leads to a thickness L of the polymer layer on each cobalt surface of 34 nm [15]. This value is close to the hydrodynamic layer (33.5 nm) [15] which means that the surfaces are uniformly covered by the DPMA polymer. During the approach, the force continuously increases due to the squeeze of the polymer layers. During the separation of the surfaces, the normal force decreases with a slight hysteresis. This evolution shows that the layers of adsorbed DPMA polymer are quite homogeneous with an elastic behaviour [15]. The figure 3. describes the mean pressure H, in semi logarithmic scale, given by the DPMA layers adsorbed on a metallic surface, that can be deduced from the results of squeeze tests with a surface force apparatus. Comparison with the pure solvent, the base oil is given. The base oil forms a thin layer adsorbed on the surface that resists to the pressure and is 5 nm thick. In the case of DPMA, an experimental law is followed, for the normal force : H= 1.85 exp(nD/L)
(3)
where H is expressed in MPa, and L=34.0+lnm. As already proposed [16], the adsorbed polymer may be considered as a relatively thin layer of loops and trains with tails of polymer extending considerably further from the surface. It is assumed that the adsorbed layer is due to an hexagonal packing of polymer spheres. Each sphere fixed on the surface leaves two terminal tails elongated in the solution with a length L and a mean distance between two tails equal to s. This correspondance to a brush polymer invites comparison with the force-distance profiles, which have been developed for the brush polymer with anchored chain ends [16]. The pressure profile can be approximated by the following relation :
FI _ lOOkT ( - r i D 1 exp L
(4)
with kT = 4.10 -21 J, at room temperature. Identification of the two relations (3) and (4), leads to the distance s=6.3+0.3 nm, value less than 2RH = 17nm. Each tail will occupy a surface area of some 31.2 nm 2, therefore the surface density is 32" 1015"tails".m -2. If we assume a hexagonal packing of polymer molecules and two tails per adsorbed molecules, then we conclude that there are 16" 1015 molecules of DPMA adsorbed per m 2. This value is close to that found from chemical analysis of the adsorption 8.2.1015 per m 2.
2.4. Experimental procedure The experimental procedure carried out for this test with the elastohydrodynamic tribometer is as follows: a- The lubricant is tested in pure rolling at different entrainment speeds varying between 0.1 m/s and lm/s. The variation of the lubricant film thickness is measured against the rolling speed and is compared to the Hamrock-Dowson's law. This first test allows us to calibrate the EHL tribometer (see figure 4.), b- A droplet of lubricant is put in the gap between the ball and the disc. The ball is entrained in order to spread the lubricant all around the ball. Then, the lubricant is allowed to adsorbed in the unloaded contact for 10 hours, c- The lubricant is submitted to the kinematics defined in section 2 during 10 minutes, d- The visualisation of the contact during the test exhibits the decohesion of the adsorbed layers, e- Finally, the possible wear of the chromium layer due to shearing of the lubricant can be observed along the friction path.
3. THEORETICAL MODEL The varying entrainment velocity was modelled as an extension of the standard transient EHL line contact problem described in [ 17]. The dimensionless Reynolds equation written as :
498
OX with
OX
OT
boundary
:0
conditions
(5) for
P"
Comparing transient results on different levels, it was found that the numerical error in the film thickness was better than 0.1Hc, that especially during the buffer and the restart phase, the errors tended to be largest.
P(Xa, T ) : P(Xb, T ) = 0 whatever T, Furthermore, the pressure must always be larger or equal to zero, then :
4. E X P E R I M E N T A L RESULTS
P(X,T)>0
4.1. Behaviour of the polymer in pure rolling
for
X e[Xa,Xb] ,
whatever
T
(cavitation conditions). s is defined as : =
~H 3 12q0Ub R2 _ with X = q;L b3ph '
)
where Ub is the constant ball velocity.
The first series of experiments have been made on the elastohydrodynamic tribometer with the polymer solutions in a situation of pure rolling. In this case, the entrainment is strictly equal to the linear speed of both the ball and the disc which leads to a vanishing sliding speed. The entrainment speed is then varied between 0.1 m/s and 1 m/s.
The variations of the entrainment speed Ue are introduced through the variable y, which varies with time between zero and one. When ~/ is zero, the c3(~H) wedge term is suppressed, leaving only the OX buffer term active. The density p is assumed to depend on the pressure according to the DowsonHiginson relation [18] and the Roelands [19] pressure viscosity relation is used. The dimensionless thickness equation, including the elastic deformation of the surfaces reads :
H(X, T) = H 0 (T) + -X2 - _ l ~ b p(X,T)ln~X_X,i~ X, 2 ~ x, and the dimensionless balance equation becomes • Xb
I P(X)dX = Xa These three equations are discretised up to the second order precision and the dimensionless time and space increments AT and AX are taken equal. Multilevel techniques are used to accelerate the convergence and rapidly calculate the deformation integrals [20]. The calculation domain is -2.5 <_ X < 1.5 and on the finest level it uses 1024
1
points, giving AX = AT = ~ = 0.0039 .... 256
I • Base oil (175 NS)
r/
,ooo
I iiiiii i
i
o B a s e oil (175 NS) + D P M A
I11
I1!
i q baseoil = 7' mPa.s q b. . . . il + DPMA - 103 mPa.s I IIIII
E" E
I ~
I! ill I
o~_ 100 ~•
-"
6, l!
..,-," i i i"H ...... , , . , J " Extrapolat~ limiting thickness
E
!
I AcO~ I I I
" " " ""
i illLit Uppel
=• u_
~ 10
0,001
limit of the entrainment speec ~u: ing the cycle ~ R~~
l
i
T= 23"C
0,0~1 0,1 E n t r a i n m e n t s p e e d (m/s)
1
Figure 4. Oil film thickness against the entrainment speed. An increase in thickness is observed for the polymer solution compared to the base oil. The full line is the Hamrock-Dowson law and fits the behaviour of the lubricants at high speed. At lower speed the thickness of the polymer film tends to a limiting value estimated at 50 nm. The thickness of the lubricant film is measured according to the entrainment speed by the interferometry method [ 11 ]. The experimental points in figure 4 follow the Hamrock-Dowson law [21 ] • 0.67 ( )-0.067 h = 1.9(rl0Ue) W (orE') 0"53 (6) r E'r E,r 2
1-v1
where r = R/2 and --1 =-1 1 - v 2 + E' 2 Eb Ed
499
............U . entrainment (m/s) ~
U sliding (m/s)l
3,2 I
16 ,
~
E
...............................................................~................................... /I ~:~ ................. ilil~ .........../...
vE 0,8 -.................
ili!i.~...... .. ~ ' i:~
I
~
Formation I of crescents
\1
..i:.................~.:": ... Eiection ~ _Stable from the
..................-..~ - A c l
i state r ~ ~ .
cumulations
I
t'3
....
................... .......
0
lilt
N
[Pure rollingJ -
0
~,
0,96
1,92
I
I ................................................................................................ I.......................................................... !
,!
Ii
•
2,88 Time (s)
~
[Pure sliding I ~:..~"..~i~,
3,84
F
4,8
~'~"='~i~i
5,76
Figure 5. The pictures show the different steps of the shearing of the polymer film during the successive phases of pure rolling and pure sliding. During the pure sliding period, the polymer film is first compacted and remains stable in the contact. This behaviour is characteristic for the relative adherence of the polymer layer to the metal surfaces. with the bulk viscosity q0 of the polymer solution at high speed. In this relation, all the parameters are expressed in the international unit system. At lower speeds (< 0.1 m/s), a deviation from this theoretical law is observed. It seems that the film thickness becomes constant at a value extrapolated at 50 nm. But, for this range of speeds, we are within the limits of the interferometric method with the use of the chromium layer. For a more precise evaluation of the limiting thickness of the polymer film layer that can be related to the thickness of the boundary layer of the polymer [22], the use of an additional silica spacer layer on the chromium surface is required [23]. Nevertheless, this limiting value is in agreement with the thickness of the immobile layer obtained in a nanorheology experiment. The continuity of the behaviour of the polymer film inside the EHD contact and in confinement has also been observed for other lubricants [22].
4.2. Behaviour of the polymer layer in pure sliding Figure 5 shows successive snapshots of the contact during each of the described periods of the cycle. During the first period (between point 2 and 3), the contact is working in pure rolling, the entrainment speed reaches its maximum and is equal to 1.6 mm/s. Inside the hertzian zone of the contact, the light is completely reflected and the image of the contact is white during the pure rolling phase (Figure 6-A). Therefore, the thickness of the lubricant film in central zone is too thin to be measured with the semi-reflective chromium layer only (the oil film thickness is less than 60 nm). Nevertheless, the calculation issued from the equations described in the previous part allows us to make an accurate evaluation of the distribution of the oil film thickness in the whole contact. Under these conditions, an air meniscus due the decrease in the lubricant pressure appears at the outlet.
500
When the disc is slowed down (Figure 6-B), the size of the meniscus in the cavitation zone decreases steeply and completely disappears during the period of pure sliding. At this step it is interesting to notice the appearance of a more contrasted zone with a crescent shape. This is certainly due to a local variation of the lubricant film thickness. The figure 6-C represents the time when the entrainment speed is vanishing. The contact is then in pure sliding. This situation leads to the build-up of a dark crescent-shaped accumulation. Two important remarks can be made concerning this <>: a- the crescent-shaped zone appears in the hertzian contact when the entrainment velocity begins to decrease, b - t h i s one stays immobile inside the contact during the whole phase when Ue = 0. This last observation shows that this dark zone does not move relative to the hertzian contact which means that the matter contained in this area slides relative to both the ball and the disc (figure 6-D). It can be reasonably concluded that the adsorbed layers are not adherent to the couple of metallic surfaces chromium/steel. This crescent can then be due to either a variation of the refractive index of the oil or to an increase in the lubricant film thickness. Anyway, this can be considered as a compaction of the boundary layers of polymer. This point will be discussed in the next part of the paper. When the entrainment speed has completely vanished, another phenomenon can be observed. Some lines normal to the direction of the sliding speed are clearly visible. Their width is about 10 gm and their length has the same order of magnitude as the hertzian diameter (figure 6-D). At the neighbourhood of these dark lines, the contact zone is more brilliant and more light is reflected. As for the crescent-shaped area, the lines are immobile relative to the contact and are also sliding relative to the metallic surfaces. It seems that during the sliding, these lines become more and more contrasted as shown by the pictures 6-C and 6-D. Between these two snapshots, the ball and the disc have moved one millimetre (about four times the diameter of the hertzian contact). From these observations, it is assumed that these lines can result from the tearing of the boundary layers of polymer. The dark areas are able to bear the load
and are supposed to be fed by lumps of film peeled out from the adsorbed layers. Then, the clearer zone of the contact correspond to areas where the films have been removed. It is interesting to notice that when the ball has completed one revolution i.e. after 8 complete cycles, these aggregates are no longer observed. After the pure sliding phase (figure 6-E), when the entrainment speed is increased again the dark areas of the contact (crescents and lines) are expulsed out of the contact in the direction of the entrainment speed (figure 6-E-F). This confirms that these " accumulations " are related to the boundary layers of polymer adsorbed onto the metallic surfaces.
5. DISCUSSION To go further in the understanding of the shearing of the adsorbed DPMA layers in the EHL regime, it is necessary to link the interferometric pictures of the EHD contact during the successive periods of pure rolling and pure sliding to a physical information characteristic from the contact. Actually, during these speed cycles, contrast variations that are observed are significant from the optical properties of the contact. The following hypotheses conceming the origin of these variations attributed to the polymer shearing can be made: a- The agglomerates formed in the contact do no transmit the light signal, b- The agglomerates transmit the light and then behaves like a bulk lubricant. Therefore, a peculiar wavelength of the spectrum of the white light is reflected and is representative either from the variation of the refractive index of these accumulations or from their thickness. If these lumps of polymer film are thinner than the optical resolution, then they appear as dark areas in interferometry. The assumption a) is not possible because in some cases the accumulations formed during the pure sliding period grows inside the contact and become blue which means that they reflect the corresponding wavelength and afortiori that they transmit the light. This behaviour is confirmed when a silica spacer layer is used [23]. In this case these agglomerates have light yellow colour.
501
t = 1.92 s " end of the pure rolling phase 1
0,75
0,5 J
0,25
i
I
i
-1,5
-1
-0,5
0
0
(x)/(b)
i
i
i
0,5
1
1,5
Ue = 1.6 mm/s and U, = 0 mm/s
t = 3.36 s " deceleration phase 1
0,75
0,5
0,25
!
|
-1,5
-1
' ~ 0
-0,5
0
1
I
I
0,5
1
1,5
(x)/(b)
Ue = 0.4 mm/s and Us = 2.4 mm/s
t = 3.84 s : beginning of the pure sliding phase 1
0,75
0,5
0,25
-1,5
-1
-0,5
0
(x)/(b)
0,5
1,5
Ue = 0 and Us = 3.2 mm/s
Figure 6 (A-B-C). Evolution of the theoretical oil film thickness profile during the pure rolling phase (A) until the beginning of the pure sliding period. These curves are compared to the pictures of the contact at each of the steps A, B and C. When the sliding starts at non zero entrainment speed, the shape of the meniscus at the oulet is changing and a dark crescent-shape area appear close to the contact (B). When the entrainment speed has just vanished, some polymer film is accumulated in the zone created in (B).
502
t = 4.8 s • end of the pure sliding phase 1 -
0,75
0,5
0,25
i
-1,5
-1
-0,5
0
(x)/(b)
0,5
i
1
1,5
Ue = 0 and Us = 3.2 mm/s
t = 5.16 s " acceleration phase
0,75
0,5
0,25
,
I
I
-1,5
-1
-0,5
0
(x)/(b)
0,5
1
1,5
Ue = 0.3 mm/s and Us = 2.6 mm/s
t = 5.76 s " acceleretion phase with Ud = 0 1 -
0,75
0,5
<.
0,25
I
I
I
-1,5
-1
-0,5
0 (x)/(b)
I
I
I
0,5
1
1,5
Ue = 0.8 mm/s and Us = 1.6 mm/s
Figure 6 (D-E-F). Location of the polymer aggregates during (D) and just after the sliding phase (E) in the hertzian contact. These areas are compared to the oil film thickness from the computations of Reynolds'equation. During the whole pure sliding period (D), the aggregates formed normal to the sliding direction are very stable (the sliding distance is in this case about 4 times the contact diameter) do not move relative to the observation point and are not deformed. When the entrainment is positive again, the aggregates are entrained (E) by lubricant and ejected from the contact (F).
503
Besides, as the refractive index of the DPMA polymer solution is equal to that of the base oil (about 1.48) and is independent of its concentration, the contrast variations observed in the contact can be related to local thickness changes. It is possible to get more precise informations concerning these evolutions, the images of the contact are numerized and in an HSI (HueSaturation-Intensity) representation, the intensity component representative from the contrast variation of the image is extracted. For each step of the speed cycle, the evolution of this parameter is plotted along a line in the direction of the entrainment speed containing the centre of the contact and correlated to the non dimensional thickness evolution, as shown in figure 7. These experimental data are consistent with the theoretical thickness issued from the calculations developed in the previous part, for the pure rolling period except for the thickness restriction zone. The numerical simulation applied to the pure sliding phase (the entrainment speed is zero and the inlet zone cannot be distinguished from the outlet zone) shows that the thickness is not vanishing in pure sliding, remains constant during all this period and is limited by two lateral thickness restriction zones.
D .....iill
[
•~
]
•,I° :!ii!iN!N!ii :i!::!ii '~ i.::.'~!~i~~!!!i !i!~!i
I
o -8
::~:::'::.~:~i'~
~uJ
]
~i ~ i:,i!i::i:.i: .
0~,5
:"=
Intensity Component
~ l i ~ i ~ ~ i i i i i i
~..;.E~.~~ ! ~ "
I~~i
ii~N~il Oe(t)/2
Ue(t )
.....::iiiii@~:.i:' .....x i' .............. .......... t ;' .~;i:~.~..~:::.....::~.~i!i~ii~i~::i!i~i~!~7..~:i~i7~:~...7::~..:~ii~iiiiii~i~i :Nii:i:i:i:~:~:}...........
'~("'
"~
q
; Time (Arbitrary units)
ii~:~i~:~i~i~: Position
0,5
1,5
Figure 7. Intensity variation considered as thickness variation during each step of the rolling/sliding cycle. The polymer agglomerate formed in the pure sliding phase is moving at the entrainment speed while the second one built when Ue becomes positive again has a half speed.
The variation of the intensity signal interpreted in terms of thickness is not correlated to the predicted thickness variation. Figure 7 shows the time dependence of the thickness variation (deduced from the intensity signal extracted from the successive snapshots) in the EHL contact from the pure sliding period until the speed of the disc is vanishing (Ud = 0 and Ue = U b / 2 ) . It appears clearly in figure 7 that the accumulations are first compacted and then stay stable in the contact (that confirms the non-adherence boundary conditions on the walls). Consequently, for the DPMA polymer adsorbed onto a chromium surface, the accumulations stay immobile relative to the point of observation which means that the polymer film slides identically relative to both the surface of the ball and the surface of the disk. This result shows that the shear plane is mainly localised at the film/metal surface interface. When the entrainment speed becomes strictly positive, the polymer film agglomerates are moved in the lubricant flow with a velocity equal to the entrainment speed. It is worth noticing that a second dark crescentshaped zone may appear at the inlet of the contact (figure 6-E). This region is bounded by the theoretical thickness restriction predicted by the solving of the Reynolds' equation and located in the inlet of the contact. The speed of this new polymer film aggregate is moving at half the mean entrainment speed. These experiments also show that the shearing of adsorbed lubricant films results from the balance between the visco-elastic properties of the layer of lubricant formed under pressure at the neighbourhood of the surfaces and their adherence properties to the surfaces themselves. This different behaviour observed for such polymer layers has some consequence on the wear of the surface of the disk. For example, in the case of the chromium when the polymer layer is not sufficiently adherent to the metallic surface, the surface of the disc is slightly worn with a very low wear rate (few nanometer per run meter).
6. CONCLUSIONS These experiments carried in an alternative EHL contact allows to characterise the shearing behaviour of thin boundary layers for polymer
504
whose thickness that should be more accurately measured. The pure rolling experiments can be correlated to the structure and the nano-rheological properties described at molecular level with a surface force apparatus. In pure sliding, some agglomerates are formed resulting from the peeling of the adsorbed polymer layers from the metallic surfaces. They are then compacted and remain very stable in the contact for a sliding distance of about six hertzian contact diameters. This kind of behaviour is characteristic of a weak adherence of the polymer on both the surfaces and should be related to its local visco-elastic properties. Then, the physico-chemical properties of the solid surfaces on which the boundary layers of lubricant is anchored should be considered. The same phenomenon is observed under pure sliding conditions for other formulations of lubricant including engine oils and additives with their own kinetics and boundary conditons (adherence or non-adherence onto the surfaces, thickness and adsorption rate of the layers of lubricant).
REFERENCES
1. J.C. Bell, T.A. Colgan, Tribology International, 2-24 (1991) 77. 2. R.G. Rounds, SAE Technical Paper Series n°770829 (1977). 3. K. Yoshida, T. Sakurai, Journal of JSLE, International Edition n°10 (1989) 133. 4. I. Berbezier, J.-M. Martin, Ph. Kapsa, Tribology International, 1- (1986) 115. 5. K. Hosonuma, K. Yoshida, A. Matsunaga, Wear, 123 (1988) 297. 6. M. Kawamura, T. Ishioguro, K. Fujita, H. Morimoto, Wear, 123 (1988) 269.
7. Ph. Colacicco, D. Mazuyer, STLE Trans., 38-4 (1995) 959. 8. K. Narita, K. Kakugawa, T. Miyaji, Proceedings of the International Tribology Conference (1995), 9. F.J. Westlake, A. Cameron, ASLE Trans., 2-15 (1971) 81. 10. H.A. Spikes, C.J. Hammond, ASLE Trans. 4-24 (1980) 542. 11. C.A. Foord, W.C. Hammann, A. Cameron, ASLE Trans., 11(1968) 31. 12. E. Georges, Th6se de doctorat, n ° ECL 96.35 (1996) 107. 13. E. Varenne, Th6se de doctorat, n ° ECL 96.34 (1996) 91. 14. J.-F. Joanny, S.J. Candau in C. Booth and C. Price (eds.), Comprehensive Polymer science, Pergamon Press, 1989. 15. E. Georges, J.-M. Georges, C. Diraison, SAE paper n°961218, (1996). 16. P.-G. de Gennes, Macromolecules, 14-6 (1981) 1639. 17. C.H. Venner, A.A. Lubrecht, ASME Trans., J. of Tribology, 116 (1994) 186. 18. D. Dowson, G.R. Higginson in, Elastohydrodynamic Lubrication, The Fundamentals of Roller and Gear Lubrication, Pergamon Press, Oxford, Great Britain, 1966. 19. C.J.A. Roelands, Ph.D. thesis, Technical Univeristy Delft, Delft, 1966. 20. A. Brandt, A.A. Lubrecht, J. of Computational Physics, 90 (1990) 348. 21. B.T. Hamrock, D. Dowson in, Ball Bearing Lubrication : The Elastohydrodynamics of Elliptical contacts, John Wiley (ed.), New York, 1981. 22. G. Guangteng, H.A. Spikes, Trib. Tans., 39 (1996) 448. 23. G.J. Johnston, R. Wayte, H.A. Spikes, Trib. Trans., 34 (1991) 187.
493
Shearing of Adsorbed Polymer Layers in an Elastohydrodynamic Contact in Pure Sliding D. Mazuyer% E. Varenne ", A.A. Lubrecht b, J.-M. Georges ", B. Constans c q~cole Centrale de Lyon, Laboratoire de Tribologie et Dynamique des Syst6mes UMR CNRS 5513, B.P. 163, F69131 l~cully Cedex, France, bINSA Lyon, Laboratoire de M6canique des Contacts, UMR CNRS 5514, 20, Boulevard Albert Einstein, F69621 Villeurbanne Cedex, France, CCentre de Recherche Elf-Solaize, Chemin du Canal, B.P. 22, F-69360 Solaize
The valve train wear of automotive diesel engines mainly depends on the kinematics of the contact, the metallurgy of the rubbing surfaces and the lubricant [1]. The presence of soot in the oil causes a dramatic increase in wear of the cam/tappet contact [2-3]. It has been shown, in this case, that the interactions between the soot particles and the rubbing solid surfaces are very important in the understanding of the wear and lubrication process. These interactions are partially governed by the dispersant polymer in solution in the automotive lubricant. Then, the tribological and the rheological behaviour of the boundary films anchored on to the surfaces must be considered. This paper focusses on the shearing of polymer films inside an elastohydrodynamic contact. The application of low speed alternative motions of the contact with successive periods of pure rolling (vanishing sliding speed) and pure sliding (vanishing entrainment speed) leads to the formation of film accumulations that are always entrained by the lubricant flow . The shearing and the geometry of these aggregates strongly depend on their adherence to the solid surfaces. The agglomeration process is stopped when the adsorbed layers of polymers have been consumed and totally peeled off from the solids. A numerical simulation including the peculiar kinematics of the contact in a pure sliding elastohydrodynamic lubrication regime gives the evolution of the oil film thickness versus time. The results of this model are compared to the experimental results. The consumption and the adherence of these layers to the substrates can be related to the wear process of the valve train.
1. INTRODUCTION The wear mechanisms of valve trains are very different between a diesel engine and a gasoline one. The higher working temperature in diesel engines and especially the presence of soot particles in the lubricant are the main reasons explaining the different wear processes. So the main question is to find out the mechanisms that are responsible for the increase in wear with soot particles. All the hypotheses developed in the literature are based on the interaction of the particles with the rubbing surfaces or with the additives of the formulated lubricant. According to the physical nature of these interactions, several wear models can be built. The
models based on physico-chemical interactions usually consider the interactions between the soot particles and the anti-wear additives [4-6] that can destroy the equilibrium between the formation of adherent anti-wear films and their consumption Among the hypotheses that could explain the role of soot in the wear of diesel engines, their aggregation in the inlet of the contact creating an oil starvation is often advanced [3], [7]. Parallel to these observations, Rounds [2] and Colacicco [3] show the beneficial role of dispersants and the VII (Viscosity Index Improver) polymers on the wear. The dispersant properties of the oil to avoid sedimentation and aggregation of the colloidal particles [8] (soot, wear and oxidation particles,...)
494
become fundamental. Then, the knowledge of the interparticle forces (steric, electrical, van der Waals forces) whose equilibrium governs the stability of the particles in the lubricant is very important to understand the wear mechanisms. The steric stabilisation by adsorbed or polymer layers is often used to control the aggregation process in the lubricant. Besides the particle/particle and the surface/particle interactions, the dwell time of the contact point and the sliding distances run by the surfaces due to the global kinematics of the contact must also be considered [ 1]. To simulate the tribological and cinematic conditions of a reciprocating motion characteristic for several real contacts, a tribometer with an elastohydrodynamic lubricated contact between a ball and a disc has been developed, in which the slide/roll ratio of the contact can be controlled accurately. The work presented in this paper concerns the behaviour of adsorbed dispersant polymer layers sheared in an EHL regime under successive cycles of pure rolling (vanishing sliding speed) and pure sliding (vanishing rolling speed).
Their structure, rheological and tribological properties which are key parameters because they govern the soot/surface interactions mainly responsible for the wear process are investigated at molecular level with a surface force apparatus. In these experiments the evolution the lubricated contact is visualised. Because of the lower entrainment speed of the lubricant inside the ball/plane contact, the oil film thickness is less than the resolution of the interferometric measurement, the thickness of the lubricant is deduced from a theoretical approach. The numerical simulation compared to the experiments is able to explain the evolution of the contact under pure rolling/sliding conditions but is not sufficient to describe the shearing of the adsorbed polymer layers in the pure sliding interval. Nevertheless the local evolution of the pictures contrast of the EHL contact is interpreted as local thickness evolution. They are able to give qualitative information on the balance between the adherence of the layers on the surfaces and their shearing behaviour in a concentrated contact. 2. E X P E R I M E N T A L T E C H N I Q U E
To the spectrometre
=,ITVl
c o o
..........
....
White light
Silica disc
Stepping motors Figure 1. Principle of the EHL machine used for the experiments. The ball and the disc are accurately and independently entrained by 2 stepping motors in the range 0.5 mm/s to 3 m/s. The applied load is between 0 and 25 N (contact pressure < 0.5 GPa).
2.1. The Elastohydrodynamic tribometer The Elastohydrodynamic tribometer used for these experiments and presented in figure 1 has been developed in the Laboratory. Its main principle is similar to the EHL machines already described in the literature [9-10]. Nevertheless, this apparatus is not only devoted to the measurement of the oil film thickness with an optical method but to the visualisation of the lubricated contact. This one is realised between a 52100 ball steel and a silica disc coated with a thin chromium layer (thickness: 10 nm). This disc in contact with the steel ball, forms an optical resonant cavity that allows us to precisely measure the oil film thickness [11]. The diameters of the ball and the disc are 25.4 mm and 60 mm respectively. Before each test, the ball is polished with a diamond dispersion (the mean size of the particles is 0.1 ~tm) to obtain a peak to valley roughness of 20 nm. The roughness of the silica disc is less than 5 nm. After cleaning the glass disc (heating in a blue flame and ultrasonic bath), the semi reflective chromium layer is obtained by a cathodic sputtering of 45 s. The coating is made under a partial pressure
495
of argon of 5.10 .7 bar in the vacuum chamber. The thickness of the metallic layer is then evaluated at 10 nm. The contact is loaded through a spring with a known stiffness in the range 0-25 N. Accounting for the mechanical properties of the steel and the silica, the contact pressure can be varied from 0 to 400 MPa. In the work presented in this paper, the load is maintained constant at its maximum giving a 280 gm hertzian contact diameter and a mean contact pressure of 400 MPa. The ball and the plane are driven independently over a speed range of 500 gm/s to 3 m/s by 2 stepping motors mechanically insulated from the ball/plane contact. The stability of the rotational motion without any vibration is assured by the use of peculiar motor drivers working until 50800 steps per revolution. These indexers can be automatically driven by a personal computer. Because of the coupling of a precise guiding of the 'turning pieces' with this type of motorization, the kinematics of the contact is controlled with great accuracy : the resolution in speed is 0.001 revolution per second in the range 0.01 revolutions per second50 revolutions per second. Therefore, numerous combinations of motions can be monitored either continuous or changing from pure rolling to pure sliding. 2.2.
The kinematics of the contact
As shown by Bell [1], the valve train wear is very dependent upon the dwell time of each point of the rubbing surface inside the contact and the length of the counterface that it sees during one path in the contact in other words, its cinematic length. These parameters are a function of the entrainment speed and the sliding speed. The shearing of the adsorbed lubricant layers is also governed by the kinematics of the contact but with time scales of a few hundred milliseconds, which is one order of magnitude higher than the time scale involved in the wear process (about 10 ms) [ 1]. Therefore, the previously described EHL tribometer allowing a precise speed control of ball and disc is used to study the influence of the dwell time and the sliding distance of the contact on the lubrication. A particular speed cycle made of alternative motions at low entrainment speed with successive periods of pure rolling and pure sliding has been chosen to exhibit the shear behaviour of the boundary polymer films under high pressure (400 MPa).
+ speed of the ball x speed of the disc ...... entrainment speed - - sliding speed ]
3,2
...... 1,6 E vE
-g X o ¢.t)
""""'...... 2
3
i
-1,6 0,96
1,92
Me
....."""'
"........................
t
2,88
~
3,84
__
_d!sc 4,8
5,76
T i m e (s)
Figure 2. Evolution of the characteristic speeds of the contact during one pure rolling/pure sliding cycle. The period between points 2 and 3 is pure rolling. The pure sliding period is between points 5 and 6. Point 4 is the time when the speed of the disc is vanishing. Figure 2. shows the evolution of the speed of the disc and the ball, Ud and Ub respectively, for one cycle. From these two speeds, the entrainment speed Ue and the sliding speed Us are defined by the relation (1) and (2) respectively : U e -- ( g d +
Ub)/2
U s -- ( U d - U b )
(1) (2)
During the whole experiment, the ball has a constant speed Ub = 1.6 mm/s. The cycle can be divided in 6 steps (points 1, 2, 3, 4, 5 and 6 referred on figure 2.) according to the motion of the disc (the time separating two consecutive steps is 960 ms) : a- At the beginning of the cycle, the disc is stationary and the contact spot is located at the left side of friction track (point 1 in figure 2.), b- The disc reaches, at point 2, the speed Ud = Ub with a constant acceleration, c- Between point 2 and point 3, the speed of the disc is maintained constant. Therefore, during this period, Ud = Ub and the contact works in pure rolling (Us- 0), d- Then, between points 3 and 5, the disc is slowed down with a constant deceleration. Ud vanishes at point 4, e- The disc reaches the speed Ud = -Ub at point 5. Ud is constant between the points 5 and 6.
496
During this period, the contact is in pure sliding and the entrainment speed Ue = 0, At point 6, disc is slowed down to zero speed and a new cycle starts from the point onwards. The dwell time and the sliding distance for a contact point belonging either to the disc or to the ball are computed according to a method detailed by Bell et al. [1] from the speeds Ud, Ub, U e and Us. These calculations show that the sliding distance and the dwell times are maximum at each side of the friction path. The sliding distance varies for the disc between 0 and 1.2 mm, while the dwell time of the contact on the disc varies between 0 and 800 ms.
30°C, is [11] = 22 cm3/g. The "hydrodynamic" radius RH is therefore equal to about 8.4+0.5 nm. The radius of gyration is evaluated to be 5.28 nm. The ratio "hydrodynamic" radius to gyration radius RH/RG, is considered as a criterion for the solvent quality [14]. It is concluded that 175NS, is a good solvent for the PMA solution at 25°C. The critical concentration of polymer, i.e. the concentration c* at which overlap of the polymer starts, is estimated by the formula • c * -
The In]" theoretical critical concentration is found to be c* = 45 mg.cm -3. Therefore the concentration c is less than c* (c/c* = 0.50), thus corresponding to the dilute regime.
2.3. The lubricant The lubricant that has been used in this paper is a solution of a dispersant polymer (DPMA) in a base oil. Experiments are carried out with pure solvent and polymer solutions. The solvent is a 175 Neutral Solvent base oil (175 NS, from Esso Port J4r6me, France) whose kinematic viscosities are 33.60 cSt at 40°C and 5.65 cSt at 100°C (its dynamic viscosity is 60 mPa.s at 25°C). Its density at 15°C is 0.8707 and dielectric constant is 2.188 at 24°C. The molecular weight of 175NS is 416 g.mo1-1, and it is composed of 4.30% of aromatic carbon, 68.85% of parafinic carbon and 26.85% of naphtenic carbon. The sulfur level is 0.55% weight. The polymer used in solution in the 175 NS is a polyalkylmetacrylate (PMA) with a dispersant function, DPMA, diluted in a 150NS base stock and supplied by Rohm & Haas. The product is used as received. This polymer is obtained by polymerization of metacrylate esters of different aliphatic alcohols containing grafted nitrogen compounds. The weight-average molecular weight of the pure polymer Mw, was measured by gel permeation chromatography (GPC) against polystyrene standards. The nitrogen concentration determined by chemilunescence is 0.43% w/w in pure polymer. Its final molecular weight is Mw=177000 g.mol 1. The concentration of the polymer in the base oil is 2.6 % w/w which gives a bulk solution viscosity of 95 mPa.s at 25°C [12]. The pressure-viscosity coefficient is evaluated to 2.45.10 .8 Pa -1 [13]. The intrinsic viscosity [rl] ([11]= limc_.o - ~ )
measured at the temperature o f
1
Cobalt substrate DPMA layer
2RH = 33 nm
~
L=34nm
100 175NS+DPMA kk, [-[ 100kTexp(rCD"] "'- ~ = $3 \-£-J with s = 6.3+0,3nm \\ \ ". \ x ~ . 4+0 5nm .~.. 175 NS
nl0 L._ 00
~- 1 13.
0.1 0
I
I
I
10
20
30
I'~%
40
I
50
60
Distance D (nm)
Figure 3. Plot of contact pressure against distance D, for DPMA layers in SFA experiments. From Alexander-de Gennes theory [16], the thickness and the density of the polymer layers can be calculated. The structure, the adsorption and the nanorheological properties of the DPMA layers have been studied by surface force experiments in a
497
sphere/plane contact of cobalt surfaces whose characteristics are described in the literature [15]. After an adsorption of 20 hours, the measurement of the static normal force versus the normal displacement of two cobalt surfaces lubricated with the DPMA solution becomes repulsive for a sphere/plane distance of 68 nm corresponding to the beginning of the interpenetration between the adsorbed polymer layers. This distance leads to a thickness L of the polymer layer on each cobalt surface of 34 nm [15]. This value is close to the hydrodynamic layer (33.5 nm) [15] which means that the surfaces are uniformly covered by the DPMA polymer. During the approach, the force continuously increases due to the squeeze of the polymer layers. During the separation of the surfaces, the normal force decreases with a slight hysteresis. This evolution shows that the layers of adsorbed DPMA polymer are quite homogeneous with an elastic behaviour [15]. The figure 3. describes the mean pressure H, in semi logarithmic scale, given by the DPMA layers adsorbed on a metallic surface, that can be deduced from the results of squeeze tests with a surface force apparatus. Comparison with the pure solvent, the base oil is given. The base oil forms a thin layer adsorbed on the surface that resists to the pressure and is 5 nm thick. In the case of DPMA, an experimental law is followed, for the normal force : H= 1.85 exp(nD/L)
(3)
where H is expressed in MPa, and L=34.0+lnm. As already proposed [16], the adsorbed polymer may be considered as a relatively thin layer of loops and trains with tails of polymer extending considerably further from the surface. It is assumed that the adsorbed layer is due to an hexagonal packing of polymer spheres. Each sphere fixed on the surface leaves two terminal tails elongated in the solution with a length L and a mean distance between two tails equal to s. This correspondance to a brush polymer invites comparison with the force-distance profiles, which have been developed for the brush polymer with anchored chain ends [16]. The pressure profile can be approximated by the following relation :
FI _ lOOkT ( - r i D 1 exp L
(4)
with kT = 4.10 -21 J, at room temperature. Identification of the two relations (3) and (4), leads to the distance s=6.3+0.3 nm, value less than 2RH = 17nm. Each tail will occupy a surface area of some 31.2 nm 2, therefore the surface density is 32" 1015"tails".m -2. If we assume a hexagonal packing of polymer molecules and two tails per adsorbed molecules, then we conclude that there are 16" 1015 molecules of DPMA adsorbed per m 2. This value is close to that found from chemical analysis of the adsorption 8.2.1015 per m 2.
2.4. Experimental procedure The experimental procedure carried out for this test with the elastohydrodynamic tribometer is as follows: a- The lubricant is tested in pure rolling at different entrainment speeds varying between 0.1 m/s and lm/s. The variation of the lubricant film thickness is measured against the rolling speed and is compared to the Hamrock-Dowson's law. This first test allows us to calibrate the EHL tribometer (see figure 4.), b- A droplet of lubricant is put in the gap between the ball and the disc. The ball is entrained in order to spread the lubricant all around the ball. Then, the lubricant is allowed to adsorbed in the unloaded contact for 10 hours, c- The lubricant is submitted to the kinematics defined in section 2 during 10 minutes, d- The visualisation of the contact during the test exhibits the decohesion of the adsorbed layers, e- Finally, the possible wear of the chromium layer due to shearing of the lubricant can be observed along the friction path.
3. THEORETICAL MODEL The varying entrainment velocity was modelled as an extension of the standard transient EHL line contact problem described in [ 17]. The dimensionless Reynolds equation written as :
498
OX with
OX
OT
boundary
:0
conditions
(5) for
P"
Comparing transient results on different levels, it was found that the numerical error in the film thickness was better than 0.1Hc, that especially during the buffer and the restart phase, the errors tended to be largest.
P(Xa, T ) : P(Xb, T ) = 0 whatever T, Furthermore, the pressure must always be larger or equal to zero, then :
4. E X P E R I M E N T A L RESULTS
P(X,T)>0
4.1. Behaviour of the polymer in pure rolling
for
X e[Xa,Xb] ,
whatever
T
(cavitation conditions). s is defined as : =
~H 3 12q0Ub R2 _ with X = q;L b3ph '
)
where Ub is the constant ball velocity.
The first series of experiments have been made on the elastohydrodynamic tribometer with the polymer solutions in a situation of pure rolling. In this case, the entrainment is strictly equal to the linear speed of both the ball and the disc which leads to a vanishing sliding speed. The entrainment speed is then varied between 0.1 m/s and 1 m/s.
The variations of the entrainment speed Ue are introduced through the variable y, which varies with time between zero and one. When ~/ is zero, the c3(~H) wedge term is suppressed, leaving only the OX buffer term active. The density p is assumed to depend on the pressure according to the DowsonHiginson relation [18] and the Roelands [19] pressure viscosity relation is used. The dimensionless thickness equation, including the elastic deformation of the surfaces reads :
H(X, T) = H 0 (T) + -X2 - _ l ~ b p(X,T)ln~X_X,i~ X, 2 ~ x, and the dimensionless balance equation becomes • Xb
I P(X)dX = Xa These three equations are discretised up to the second order precision and the dimensionless time and space increments AT and AX are taken equal. Multilevel techniques are used to accelerate the convergence and rapidly calculate the deformation integrals [20]. The calculation domain is -2.5 <_ X < 1.5 and on the finest level it uses 1024
1
points, giving AX = AT = ~ = 0.0039 .... 256
I • Base oil (175 NS)
r/
,ooo
I iiiiii i
i
o B a s e oil (175 NS) + D P M A
I11
I1!
i q baseoil = 7' mPa.s q b. . . . il + DPMA - 103 mPa.s I IIIII
E" E
I ~
I! ill I
o~_ 100 ~•
-"
6, l!
..,-," i i i"H ...... , , . , J " Extrapolat~ limiting thickness
E
!
I AcO~ I I I
" " " ""
i illLit Uppel
=• u_
~ 10
0,001
limit of the entrainment speec ~u: ing the cycle ~ R~~
l
i
T= 23"C
0,0~1 0,1 E n t r a i n m e n t s p e e d (m/s)
1
Figure 4. Oil film thickness against the entrainment speed. An increase in thickness is observed for the polymer solution compared to the base oil. The full line is the Hamrock-Dowson law and fits the behaviour of the lubricants at high speed. At lower speed the thickness of the polymer film tends to a limiting value estimated at 50 nm. The thickness of the lubricant film is measured according to the entrainment speed by the interferometry method [ 11 ]. The experimental points in figure 4 follow the Hamrock-Dowson law [21 ] • 0.67 ( )-0.067 h = 1.9(rl0Ue) W (orE') 0"53 (6) r E'r E,r 2
1-v1
where r = R/2 and --1 =-1 1 - v 2 + E' 2 Eb Ed
499
............U . entrainment (m/s) ~
U sliding (m/s)l
3,2 I
16 ,
~
E
...............................................................~................................... /I ~:~ ................. ilil~ .........../...
vE 0,8 -.................
ili!i.~...... .. ~ ' i:~
I
~
Formation I of crescents
\1
..i:.................~.:": ... Eiection ~ _Stable from the
..................-..~ - A c l
i state r ~ ~ .
cumulations
I
t'3
....
................... .......
0
lilt
N
[Pure rollingJ -
0
~,
0,96
1,92
I
I ................................................................................................ I.......................................................... !
,!
Ii
•
2,88 Time (s)
~
[Pure sliding I ~:..~"..~i~,
3,84
F
4,8
~'~"='~i~i
5,76
Figure 5. The pictures show the different steps of the shearing of the polymer film during the successive phases of pure rolling and pure sliding. During the pure sliding period, the polymer film is first compacted and remains stable in the contact. This behaviour is characteristic for the relative adherence of the polymer layer to the metal surfaces. with the bulk viscosity q0 of the polymer solution at high speed. In this relation, all the parameters are expressed in the international unit system. At lower speeds (< 0.1 m/s), a deviation from this theoretical law is observed. It seems that the film thickness becomes constant at a value extrapolated at 50 nm. But, for this range of speeds, we are within the limits of the interferometric method with the use of the chromium layer. For a more precise evaluation of the limiting thickness of the polymer film layer that can be related to the thickness of the boundary layer of the polymer [22], the use of an additional silica spacer layer on the chromium surface is required [23]. Nevertheless, this limiting value is in agreement with the thickness of the immobile layer obtained in a nanorheology experiment. The continuity of the behaviour of the polymer film inside the EHD contact and in confinement has also been observed for other lubricants [22].
4.2. Behaviour of the polymer layer in pure sliding Figure 5 shows successive snapshots of the contact during each of the described periods of the cycle. During the first period (between point 2 and 3), the contact is working in pure rolling, the entrainment speed reaches its maximum and is equal to 1.6 mm/s. Inside the hertzian zone of the contact, the light is completely reflected and the image of the contact is white during the pure rolling phase (Figure 6-A). Therefore, the thickness of the lubricant film in central zone is too thin to be measured with the semi-reflective chromium layer only (the oil film thickness is less than 60 nm). Nevertheless, the calculation issued from the equations described in the previous part allows us to make an accurate evaluation of the distribution of the oil film thickness in the whole contact. Under these conditions, an air meniscus due the decrease in the lubricant pressure appears at the outlet.
500
When the disc is slowed down (Figure 6-B), the size of the meniscus in the cavitation zone decreases steeply and completely disappears during the period of pure sliding. At this step it is interesting to notice the appearance of a more contrasted zone with a crescent shape. This is certainly due to a local variation of the lubricant film thickness. The figure 6-C represents the time when the entrainment speed is vanishing. The contact is then in pure sliding. This situation leads to the build-up of a dark crescent-shaped accumulation. Two important remarks can be made concerning this <
and are supposed to be fed by lumps of film peeled out from the adsorbed layers. Then, the clearer zone of the contact correspond to areas where the films have been removed. It is interesting to notice that when the ball has completed one revolution i.e. after 8 complete cycles, these aggregates are no longer observed. After the pure sliding phase (figure 6-E), when the entrainment speed is increased again the dark areas of the contact (crescents and lines) are expulsed out of the contact in the direction of the entrainment speed (figure 6-E-F). This confirms that these " accumulations " are related to the boundary layers of polymer adsorbed onto the metallic surfaces.
5. DISCUSSION To go further in the understanding of the shearing of the adsorbed DPMA layers in the EHL regime, it is necessary to link the interferometric pictures of the EHD contact during the successive periods of pure rolling and pure sliding to a physical information characteristic from the contact. Actually, during these speed cycles, contrast variations that are observed are significant from the optical properties of the contact. The following hypotheses conceming the origin of these variations attributed to the polymer shearing can be made: a- The agglomerates formed in the contact do no transmit the light signal, b- The agglomerates transmit the light and then behaves like a bulk lubricant. Therefore, a peculiar wavelength of the spectrum of the white light is reflected and is representative either from the variation of the refractive index of these accumulations or from their thickness. If these lumps of polymer film are thinner than the optical resolution, then they appear as dark areas in interferometry. The assumption a) is not possible because in some cases the accumulations formed during the pure sliding period grows inside the contact and become blue which means that they reflect the corresponding wavelength and afortiori that they transmit the light. This behaviour is confirmed when a silica spacer layer is used [23]. In this case these agglomerates have light yellow colour.
501
t = 1.92 s " end of the pure rolling phase 1
0,75
0,5 J
0,25
i
I
i
-1,5
-1
-0,5
0
0
(x)/(b)
i
i
i
0,5
1
1,5
Ue = 1.6 mm/s and U, = 0 mm/s
t = 3.36 s " deceleration phase 1
0,75
0,5
0,25
!
|
-1,5
-1
' ~ 0
-0,5
0
1
I
I
0,5
1
1,5
(x)/(b)
Ue = 0.4 mm/s and Us = 2.4 mm/s
t = 3.84 s : beginning of the pure sliding phase 1
0,75
0,5
0,25
-1,5
-1
-0,5
0
(x)/(b)
0,5
1,5
Ue = 0 and Us = 3.2 mm/s
Figure 6 (A-B-C). Evolution of the theoretical oil film thickness profile during the pure rolling phase (A) until the beginning of the pure sliding period. These curves are compared to the pictures of the contact at each of the steps A, B and C. When the sliding starts at non zero entrainment speed, the shape of the meniscus at the oulet is changing and a dark crescent-shape area appear close to the contact (B). When the entrainment speed has just vanished, some polymer film is accumulated in the zone created in (B).
502
t = 4.8 s • end of the pure sliding phase 1 -
0,75
0,5
0,25
i
-1,5
-1
-0,5
0
(x)/(b)
0,5
i
1
1,5
Ue = 0 and Us = 3.2 mm/s
t = 5.16 s " acceleration phase
0,75
0,5
0,25
,
I
I
-1,5
-1
-0,5
0
(x)/(b)
0,5
1
1,5
Ue = 0.3 mm/s and Us = 2.6 mm/s
t = 5.76 s " acceleretion phase with Ud = 0 1 -
0,75
0,5
<.
0,25
I
I
I
-1,5
-1
-0,5
0 (x)/(b)
I
I
I
0,5
1
1,5
Ue = 0.8 mm/s and Us = 1.6 mm/s
Figure 6 (D-E-F). Location of the polymer aggregates during (D) and just after the sliding phase (E) in the hertzian contact. These areas are compared to the oil film thickness from the computations of Reynolds'equation. During the whole pure sliding period (D), the aggregates formed normal to the sliding direction are very stable (the sliding distance is in this case about 4 times the contact diameter) do not move relative to the observation point and are not deformed. When the entrainment is positive again, the aggregates are entrained (E) by lubricant and ejected from the contact (F).
503
Besides, as the refractive index of the DPMA polymer solution is equal to that of the base oil (about 1.48) and is independent of its concentration, the contrast variations observed in the contact can be related to local thickness changes. It is possible to get more precise informations concerning these evolutions, the images of the contact are numerized and in an HSI (HueSaturation-Intensity) representation, the intensity component representative from the contrast variation of the image is extracted. For each step of the speed cycle, the evolution of this parameter is plotted along a line in the direction of the entrainment speed containing the centre of the contact and correlated to the non dimensional thickness evolution, as shown in figure 7. These experimental data are consistent with the theoretical thickness issued from the calculations developed in the previous part, for the pure rolling period except for the thickness restriction zone. The numerical simulation applied to the pure sliding phase (the entrainment speed is zero and the inlet zone cannot be distinguished from the outlet zone) shows that the thickness is not vanishing in pure sliding, remains constant during all this period and is limited by two lateral thickness restriction zones.
D .....iill
[
•~
]
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I
o -8
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]
~i ~ i:,i!i::i:.i: .
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:"=
Intensity Component
~ l i ~ i ~ ~ i i i i i i
~..;.E~.~~ ! ~ "
I~~i
ii~N~il Oe(t)/2
Ue(t )
.....::iiiii@~:.i:' .....x i' .............. .......... t ;' .~;i:~.~..~:::.....::~.~i!i~ii~i~::i!i~i~!~7..~:i~i7~:~...7::~..:~ii~iiiiii~i~i :Nii:i:i:i:~:~:}...........
'~("'
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q
; Time (Arbitrary units)
ii~:~i~:~i~i~: Position
0,5
1,5
Figure 7. Intensity variation considered as thickness variation during each step of the rolling/sliding cycle. The polymer agglomerate formed in the pure sliding phase is moving at the entrainment speed while the second one built when Ue becomes positive again has a half speed.
The variation of the intensity signal interpreted in terms of thickness is not correlated to the predicted thickness variation. Figure 7 shows the time dependence of the thickness variation (deduced from the intensity signal extracted from the successive snapshots) in the EHL contact from the pure sliding period until the speed of the disc is vanishing (Ud = 0 and Ue = U b / 2 ) . It appears clearly in figure 7 that the accumulations are first compacted and then stay stable in the contact (that confirms the non-adherence boundary conditions on the walls). Consequently, for the DPMA polymer adsorbed onto a chromium surface, the accumulations stay immobile relative to the point of observation which means that the polymer film slides identically relative to both the surface of the ball and the surface of the disk. This result shows that the shear plane is mainly localised at the film/metal surface interface. When the entrainment speed becomes strictly positive, the polymer film agglomerates are moved in the lubricant flow with a velocity equal to the entrainment speed. It is worth noticing that a second dark crescentshaped zone may appear at the inlet of the contact (figure 6-E). This region is bounded by the theoretical thickness restriction predicted by the solving of the Reynolds' equation and located in the inlet of the contact. The speed of this new polymer film aggregate is moving at half the mean entrainment speed. These experiments also show that the shearing of adsorbed lubricant films results from the balance between the visco-elastic properties of the layer of lubricant formed under pressure at the neighbourhood of the surfaces and their adherence properties to the surfaces themselves. This different behaviour observed for such polymer layers has some consequence on the wear of the surface of the disk. For example, in the case of the chromium when the polymer layer is not sufficiently adherent to the metallic surface, the surface of the disc is slightly worn with a very low wear rate (few nanometer per run meter).
6. CONCLUSIONS These experiments carried in an alternative EHL contact allows to characterise the shearing behaviour of thin boundary layers for polymer
504
whose thickness that should be more accurately measured. The pure rolling experiments can be correlated to the structure and the nano-rheological properties described at molecular level with a surface force apparatus. In pure sliding, some agglomerates are formed resulting from the peeling of the adsorbed polymer layers from the metallic surfaces. They are then compacted and remain very stable in the contact for a sliding distance of about six hertzian contact diameters. This kind of behaviour is characteristic of a weak adherence of the polymer on both the surfaces and should be related to its local visco-elastic properties. Then, the physico-chemical properties of the solid surfaces on which the boundary layers of lubricant is anchored should be considered. The same phenomenon is observed under pure sliding conditions for other formulations of lubricant including engine oils and additives with their own kinetics and boundary conditons (adherence or non-adherence onto the surfaces, thickness and adsorption rate of the layers of lubricant).
REFERENCES
1. J.C. Bell, T.A. Colgan, Tribology International, 2-24 (1991) 77. 2. R.G. Rounds, SAE Technical Paper Series n°770829 (1977). 3. K. Yoshida, T. Sakurai, Journal of JSLE, International Edition n°10 (1989) 133. 4. I. Berbezier, J.-M. Martin, Ph. Kapsa, Tribology International, 1- (1986) 115. 5. K. Hosonuma, K. Yoshida, A. Matsunaga, Wear, 123 (1988) 297. 6. M. Kawamura, T. Ishioguro, K. Fujita, H. Morimoto, Wear, 123 (1988) 269.
7. Ph. Colacicco, D. Mazuyer, STLE Trans., 38-4 (1995) 959. 8. K. Narita, K. Kakugawa, T. Miyaji, Proceedings of the International Tribology Conference (1995), 9. F.J. Westlake, A. Cameron, ASLE Trans., 2-15 (1971) 81. 10. H.A. Spikes, C.J. Hammond, ASLE Trans. 4-24 (1980) 542. 11. C.A. Foord, W.C. Hammann, A. Cameron, ASLE Trans., 11(1968) 31. 12. E. Georges, Th6se de doctorat, n ° ECL 96.35 (1996) 107. 13. E. Varenne, Th6se de doctorat, n ° ECL 96.34 (1996) 91. 14. J.-F. Joanny, S.J. Candau in C. Booth and C. Price (eds.), Comprehensive Polymer science, Pergamon Press, 1989. 15. E. Georges, J.-M. Georges, C. Diraison, SAE paper n°961218, (1996). 16. P.-G. de Gennes, Macromolecules, 14-6 (1981) 1639. 17. C.H. Venner, A.A. Lubrecht, ASME Trans., J. of Tribology, 116 (1994) 186. 18. D. Dowson, G.R. Higginson in, Elastohydrodynamic Lubrication, The Fundamentals of Roller and Gear Lubrication, Pergamon Press, Oxford, Great Britain, 1966. 19. C.J.A. Roelands, Ph.D. thesis, Technical Univeristy Delft, Delft, 1966. 20. A. Brandt, A.A. Lubrecht, J. of Computational Physics, 90 (1990) 348. 21. B.T. Hamrock, D. Dowson in, Ball Bearing Lubrication : The Elastohydrodynamics of Elliptical contacts, John Wiley (ed.), New York, 1981. 22. G. Guangteng, H.A. Spikes, Trib. Tans., 39 (1996) 448. 23. G.J. Johnston, R. Wayte, H.A. Spikes, Trib. Trans., 34 (1991) 187.