Surface Effects on Boundary Friction with Additive Free Lubricating Films: Coupled Influence of Roughness and Material Properties

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1 ORIGINAL PAPER Surface Effects on Boundary Friction with Additive Free Lubricating Films: Coupled Influence of Roughness and Material Properties Julien Bonaventure 1 Juliette Cayer Barrioz 1 Denis Mazuyer 1 Received: 25 April 2018 / Accepted: 19 May 2018 / Published online: 12 June 2018 Springer Science+Business Media, LLC, part of Springer Nature 2018 Abstract This work deals with the friction mechanisms of non-conforming contacts lubricated with additive-free poly-alpha olefins in the boundary regime at mean pressures between 0.3 and 0.9 GPa. To analyse the coupled influence of surface roughness and material, the surfaces involved in these experiments were made of steel or DLC-coated steel with a roughness from the nanometer to the micrometer. On the one hand, DLC DLC contacts presented the lowest friction level with hardly any influence of the surface roughness on the boundary friction coefficient: we showed that the high hardness of these surfaces prevented from significant wear and that boundary friction arose from the shearing of a nanometric fluid layer, physisorbed on the surfaces. On the other hand, steel steel and steel DLC contacts presented roughness-dependent higher friction coefficients. Two trends arose according to the contact composite roughness. For rough ones, friction was controlled by the plastic deformation of micrometric asperities. For smooth ones, the dulled asperities did not allow significant local pressure rises, but they occupied a large fraction of the contact area. The boundary friction level was then controlled by the area left available for the lubricant between these conforming asperities and valleys. Keywords Boundary lubrication Friction Stribeck Random roughness Steel DLC Abbreviation S qc composite RMS roughness S 2 q1 + S2 q2 (m) a H Hertz contact radius (m) β s summit curvature radius (m) std(x) standard deviation of X BL boundary lubrication SRR Sliding rolling ratio u s u e COF coefficient of friction u b, d surface speeds (ball and disc) (m/s) DLC Diamond-like carbon u e Entrainment speed (u b + u d ) 2 (m/s) dx sampling interval (x and y) (m) u s Sliding speed u b u d (m/s) EHD, L elastohydrodynamic, - lubrication η 0 inlet viscosity (Pa s) F f Couette Couette friction force (or traction) (N) η 0 u BL ML Entrainment product at the BL ML transition e H material hardness (Pa) (Pa m) L c cut-off length ( m) η 0 u ML EHL entrainment product at the ML EHL transition (Pa m) e MTM Mini Traction Machine n s summit density ( m 2 ) σ s summit height standard deviation (m) p a mean asperity pressure (Pa) τ Couette shear stress F f Couette πa 2 H (Pa) p m mean Hertz pressure ( Pa) <τ Bl > Boundary shear stress (Pa) P.A. probing area ( m 2 ) Y material yield strength, Y = H 3 (Pa) RMS root mean square S q height standard deviation (m) 1 Introduction * Juliette Cayer Barrioz juliette.cayer barrioz@ec lyon.fr 1 Laboratoire de Tribologie et Dynamique des Systèmes, UMR 5513 CNRS, École Centrale de Lyon, 36 Avenue Guy de Collongue, Écully Cedex, France Lubricated concentrated contacts are present in many industrial applications such as ball bearings or cam-follower contacts. When the surfaces move fast enough, a hydrodynamic lift is generated through the lubricant and the bodies are Vol.:( )

2 84 Page 2 of 11 fully separated. This is the regime of elastohydrodynamic lubrication (EHL). In this regime, the origin of friction is viscous and can be reliably predicted provided the fluid rheology be known [1, 2]. The least understood lubrication regimes are the mixed (ML) and the boundary (BL) regimes. These occur when the film thickness is comparable with the surface roughness. ML is an intermediate state between EHL and BL, hence, it seems primordial to understand the nature of the BL regime. Part of the lacking knowledge on the BL regime results from the fact that it was defined differently according to the authors in the past century. Initially, the term of boundary lubrication referred to the lubrication due to a layer of chemicals strongly bonded to the metal surfaces [3], which yield friction coefficients close to 0.1, whereas the same unlubricated surfaces have friction coefficients close to 0.6 [4]. The BL regime is thus often associated with the presence in the lubricant of chemically active compounds that are likely to adsorb on the surfaces, forming layers of a few molecules on the solids. Since these additives constitute generally less than 1% of the formulated lubricant [5], and since they behave more like solids than fluids, it is often stated that boundary friction cannot be predicted from the bulk fluid properties [5]. Another definition of BL, also widely present in the tribology literature, corresponds to the state reached at the friction plateau on the top-left part of the Stribeck curve, i.e. when the entrainment speed is not sufficient to separate the bodies. This definition thus does not involve the presence of chemical adsorption. Although it is less restrictive, the latter definition is more useful in practice because it is technically difficult to measure in situ the presence of these adsorbates and to ensure that friction only originates from their presence. In BL, the surfaces are generally so close to each other that considerable asperity contact occurs [5], which makes this regime propitious to wear. However, the experimental studies that discuss the influence of roughness features on the boundary friction mechanism are scarce. During sliding rolling experiments with rough ridged surfaces, 1 [6] noticed boundary friction peaks up to COF = 0.25, correlated with plastic deformations. Coating one of the steel bodies with a 2 μm-thick Diamond-Like Carbon (DLC) layer allowed a significant reduction of plasticity, correlated with lower friction peaks. It thus seemed to indicate that plastic deformations play a role on boundary friction. This paper is an attempt to understand the role played by surface in boundary-lubricated contacts. In order to discuss the origin of friction in boundary regime, Stribeck tests were performed using steel surfaces with topographies representative of nowadays typical industrial applications, i.e. 1 R a 0.3 μm Tribology Letters (2018) 66:84 with roughnesses from the nanometer to the micron [7] for, respectively, wide and moderate ranges in velocity and contact pressure. The plasticity hypothesis was also investigated through the use of a hard DLC coating in DLC DLC and steel DLC contacts, which were confronted to steel steel experiments. Additive-free fluids with a wide range of viscosity, extending over three decades, were used to identify the role of roughness, alone, on the boundary friction origin. 2 Experimental Procedure 2.1 Friction Tests Tribometers Sliding rolling experiments were performed on two discball tribometers. The first one was the PCS Mini Traction Machine (MTM), which allows to cover speeds in the range [ ;3] m s, loads in the range [1 ; 75] N and a sampling rate of 1 Hz. The second one was the IRIS tribometer, a homemade tribometer described in [8, 9] that allows to cover speeds in the range [ ;1] m s, loads in the range [0.5 ; 15] N and a sampling rate of 1 khz. This tribometer also permits in situ contact visualization and film thickness distribution measurement in real time with one transparent disc, using interferometry technique. This advantage was used in the last part of the paper Friction Procedures The majority of the friction tests presented here are Stribeck procedures, which consist in imposing a constant sliding rolling ratio, a constant load and covering a given range of entrainment speed between u e = 1mm s and u e = 1m s. Speed ramps where u e is linearly increased in time at an acceleration between 3 and 8 mms 2 and speed steps where u e is kept constant during 30 s where both used and gave the same friction evolution towards u e. The duration of the friction tests did not exceed 1 h in order to limit the evolution of surface roughness. This was confirmed by a systematic observation and analysis of the surface topography before and after the friction test Lubricants Additive-free poly-α olefins (PAO2, PAO4 and PAO40) were used during the friction tests in order to avoid issues coupling chemically adsorbed films with the roughness. The dynamic viscosity of each fluid was measured with a cone/ plane AR2000 rheometer at 0.1 s 1 from 17 to 60 C. The range of viscosity extends over three decades, from to

3 Page 3 of Table 1 Topographical parameters of the balls measured using interferometry with a cut-off length L c = 200 μm for measurements using dx = μm and L c = 47 μm for those using dx = μm Balls S q σ s β s n s dx P.A Mode Dispersion All lengths are in μm, n s is in μm 2 and P.A. is in mm Pa s according to the chain length of the PAO and the room temperature. 2.2 Surfaces The surface topography analysis was carried out using Bruker interferometer in vertical shifting interferometry with a resolution of ± 1 nm. The balls used in the experiments were AISI steel balls having a radius of mm, with or without an a-c:h DLC layer of about 3 μm coated by HEF group. Both kinds of balls were polished with a constant process so they have all the same smooth topography. Each polished ball topography was measured before the friction test on six different probing areas with a sampling interval dx = μm and sometimes also on six areas using dx = μm. All the values are reported in Table 1. All discs (see Table 2) were characterized before any friction test using the planar detrending operation [10, 11] on square windows of lateral extent L c = 200 μm. This constitutes a high-pass filtering operation with a cut-off length L c. The value for L c was chosen for its closeness to the Hertz length during the experiments. 2 Then, for each topographical parameter among the RMS height deviation ( S q ), the fivepoint summit RMS height deviation ( σ s ), their density ( n s ) and their curvature radius β s were calculated over the whole survey. The local curvature radius of a summit is defined as ( β s (x 0, y 0 )= z x ) z x 2 where (x 0, y 0 ) refers to the location of a five-point summit. The most probable value or mode of these parameters over the probing area (P.A.) was then calculated and added to Table 3. Unless otherwise specified, the RMS roughness S q refers to values measured using dx = μm as these values correspond to the largest probing area. The M2 and ( 1 + z y 2 z y 2 ) 3 2, (x0,y 0 ) (1) Table 2 Disc materials and surface shaping process Name Disc Steel A Polished-by-hand AISI B Pickled steel 1 AISI C Pickled steel 2 AISI D Finished steel AISI E MTM rough + smoothing AISI M2 F MTM rough AISI M2 G Finished steel + roughening AISI H Sandblasted steel Hardened steel I Rectified steel AISI J MTM rough + roughening AISI M2 K-DLC Pickled steel + DLC + polishing AISI L-DLC Pickled steel + DLC AISI M-DLC Pickled steel + DLC AISI N-DLC Rectified steel + DLC AISI AISI steel hardnesses were approximately equal to 8 GPa. Nanoindentation tests, performed with a continuous stiffness measurement module, on the DLC coating 3 down to depths equal to 0.8 μm indicated a hardness of 21 ± 3 GPa, and a Young modulus of 2.2 ± Pa. 3 Results 3.1 Different Stribeck behaviours according to materials Figure 1 shows Stribeck tests at SRR = 0.25, p m = 440 MPa with DLC DLC contacts (black symbols) and with steel DLC contacts (blue symbols). The entrainment product, viscosity x entrainment velocity, was plotted in abscissa as it takes into account the possible variation in 2 According to the operating pressure, 2 a H [120 ; 334] μm. The majority of the friction tests were performed at p m = 440 MPa, i.e. using 2 a H = 170 μm. 3 Based on seven indents.

4 84 Page 4 of 11 Tribology Letters (2018) 66:84 Table 3 Topographical parameters (most probable values) of the discs measured using interferometry with a cutoff length L c = 200 μm Disc S q σ s β s n s dx P.A A B C D E x x x x F x 0.10 x x x G H 0.14 x x I J x 0.39 x 0.28 x x K-DLC L-DLC M-DLC x x x x x N-DLC All lengths are in μm, n s is in μm 2 and P.A. is in mm 2 Fig. 2 Viscosity velocity product of the transition between the lubrication regimes for different Stribeck tests using steel and DLC-coated surfaces in additive-free PAOs (from [11]). (Color figure online) Fig. 1 Stribeck tests performed between DLC-coated steel balls and steel discs with or without a DLC coating, in PAOs. Vertical lines correspond to the BL ML transition. (Color figure online) room temperature between tests. The temperature was indicated in the inset. These experiments cover the lubrication regimes from BL to EHL. Each symbol corresponds to a range of surface roughness from 0.01 to 0.16 μm. These tests show that for a given composite surface roughness S qc, the friction evolution in the EHD and mixed regime are roughly the same between steel DLC (in blue) and DLC DLC contacts (in black). However, the evolution of friction in the BL regime (see Fig. 1) as well as the effect of roughness on the transition from ML to BL (defined with vertical straight lines on Fig. 1 and reported with filled symbols on Fig. 2) are different between DLC DLC contacts and contacts with

5 Page 5 of Fig. 3 Evolution of the shear stress in the BL regime versus the mean Hertz pressure. These points were obtained with Stribeck tests at SRR=0.25. (Color figure online) one or two steel bodies. This appears more clearly on Fig. 2: the entrainment product η 0 u ML EHL that corresponds to the e transition from EHL to ML (empty symbols) follows the same trend towards the RMS roughness between steel steel, steel DLC and DLC DLC contacts (see [10, 12] for more details on this transition). However, this result does not hold for the transition from ML to BL: steel DLC and steel steel contacts enter in BL at a lower entrainment product than DLC DLC contacts. Figure 3 shows the evolution of the boundary shear stress defined as the Couette friction force divided by the Hertz area πa 2, averaged over the speeds that correspond to H the BL regime for steel steel, steel DLC and DLC DLC contacts, versus the mean Hertzian pressure. For all couples of materials, this shear stress increases in proportion with pressure, which is a classical behaviour in the BL regime [13]. However, DLC DLC contacts yield a much lower boundary shear stress ( <τ Bl> = 0.05 ) than contacts with steel p m = according to the surface roughness). This ( <τ Bl> p m leads to study separately the boundary regime for these two sets of materials. 3.2 BL with DLC DLC Contacts Several experimental observations in the boundary regime of DLC DLC contacts are listed below. They give a better Fig. 4 Boundary friction coefficients averaged from the lowest speed ( u e = 1 mm s ) to the BL ML transition ( u BL ML ) during Stribeck e tests, versus the composite RMS roughness S qc, measured using dx = μm. Blue symbols correspond to tests with at least one steel body, black ones correspond to DLC DLC contacts. The error bars correspond to the standard deviation of the friction coefficient over the speed range corresponding to the BL regime. The single point filled in cyan corresponds to the maximum friction coefficient obtained in the ML regime using disc A against a steel ball in PAO4 at 22 C, since no BL regime could be obtained with this disc. (Color figure online) understanding of the origin of the boundary friction with such contacts. After the tests, the surfaces were observed using optical and interferometric microscopy. None of the two rubbing bodies did present any quantifiable wear. Scars in the sliding direction, with a width inferior to 10μm and a depth less than 0.03 μm, could sometimes be found on some DLC-coated balls, indicating that abrasion occurred during the test. Yet, these surface modifications were not important enough to change the surface RMS roughness. On the discs, no traces of wear could be distinguished from the overall topography. However, after the tests, the disc rubbing tracks usually appeared shiny. This enhanced reflectivity could be attributed to the removal of very sharp asperities 4. This certainly explains the slight friction decrease up to 30% often observed in the BL regime between the beginning and the end of 40-minute-long Stribeck tests on the same rubbing track. The black symbols on Fig. 4 represent the friction coefficient averaged on the speeds lying in the BL regime. The error bars correspond to the standard deviation of COF over this speed range. These friction coefficients are plotted versus the RMS composite roughness S qc of discs K-DLC, L-DLC, M-DLC and N-DLC. These discs have 4 Private communication with Dr. C. Héau, HEF group.

6 84 Page 6 of 11 Tribology Letters (2018) 66:84 Fig. 5 a Exponents of COF versus η 0 u e during Stribeck tests with the L-DLC disc against a DLC-coated ball, in PAO4. b Stribeck curves corresponding to p m = 0.31 GPa, SRR=0.05 and SRR=1 very different topographical features, in particular in terms of height deviations and of asperity sharpness (see Table 3), but surprisingly, they yield about the same friction coefficient:< COF BL >= ± If this does not prove that the solid solid contribution to boundary friction is null or close to zero, it can be stated that this contribution does not vary with the surface heights or with the asperities sharpness. It can be seen from the Stribeck tests on DLC DLC contacts (Fig. 1) that the boundary friction presents a slight increase with the entrainment product η 0 u e. This behaviour was already observed in the literature [14 16]. To quantify this, the evolution of COF with η 0 u e was fitted with power laws on Stribeck tests performed at mean pressures between 0.31 and 0.50 GPa and sliding rolling ratios between 5 and 100%. These exponents are plotted in Fig. 5a: the higher SRR and p m, the less speed-dependent the friction is. Fig. 6 Traction tests on PAO4 performed using smooth AISI steel balls against polished M2 steel discs ( S qc = μm ), except for the test at p m = 0.27 GPa for which a silica disc ( S q = μm ) was used. From the highest pressure to the lowest one, the nominal film thickness lies between 0.06 and 0.07 μm 3.3 Boundary Friction Mechanism in DLC DLC Contacts Beyond a certain shear rate, the viscous shear stress of most lubricants saturates [17]. This limiting shear stress, τ max, does not vary much with temperature and is proportional to the fluid pressure, p [17 22]. For poly-α olefins, plastic shearing occurs at shear rates superior to typically s 1 for pressures around GPa, and the ratio τ max is p equal5 to ± ([11, 23]). Traction tests on PAO4, plotted on Fig. 6, illustrate this as Newtonian, shear-thinning and plastic rheological regimes are schematically indicated. The boundary shear stress of DLC DLC contacts is thus approximately equal to the lubricant shear strength. With these contacts, increasing the sliding speed results in a higher friction even in the boundary and mixed regimes, as it arises from the comparison of the Stribeck tests at SRR=0.05 and SRR=1, Fig. 5b. This dependence towards sliding would not be observed if friction was dominated by solid solid contacts, according to the Amontons Coulomb laws. These observations lean towards a scenario where the 5 For some high molecular weight poly-α olefins like the PAO40, this ratio might reach higher values, superior to 0.07.

7 Page 7 of Fig. 7 Stribeck test between two DLC-coated surfaces covering the three lubrication regimes. The drawings illustrate the shear rates applied to the fluid and the film thickness between the surfaces. The colour spectrum from red to green indicates the level of shear rates from the highest to the lowest. (Color figure online) boundary friction of DLC DLC contacts originates from the viscous shearing of the lubricant layer remaining between the surfaces, just like in EHL, except that in the BL regime, the surface separation is no longer affected by η 0 u e, as it is schematically represented on Fig. 7. Boundary friction decreases as η 0 u e is reduced because of the corresponding decrease in sliding speed u s = SRR u e, which reduces the shear rate applied to the fluid layer and thus makes it quit its plastic shear regime. Within this interpretation, we implicitly assume that the fluid shear stress versus shear rate dependence is not affected by its thickness. On the traction tests shown in Fig. 6, the dashed straight lines separate roughly the Newtonian, shear-thinning and plastic shear regimes of the lubricant. In these shear regimes, the influence of the shear rate (or of the sliding speed) on the viscous shear stress is, respectively, large, medium and absent. In DLC DLC contacts, a low SRR implies low shear rates applied to the fluid layer, which gets further away from its plastic shear regime (and closer to its Newtonian behaviour) than when the SRR is large. Similarly, for even shear rates applied to the fluid layer (i.e. for even SRR, during a Stribeck procedure in the BL regime), an increase in fluid pressure shifts towards lower shear rates the boundaries between plastic and shear-thinning regimes as it may be seen from the top-right dashed line, Fig. 6. This explains why the speed dependence of boundary friction is more pronounced at low than at high pressure on Fig. 5. Fig. 8 Mean asperity pressures, calculated for a Gaussian distribution of the asperity heights (Eq. (3)) showing the influence of the asperity RMS heights σ s and of their curvature radius β s. The horizontal dashed lines represent the yield strength of the DLC and of the AISI steel 3.4 Boundary Regime with steel steel and steel DLC Contacts General Observations on Boundary Friction with Steel The blue symbols on Fig. 4 correspond to boundary friction coefficients with a steel disc, versus the initial composite RMS roughness. These contacts follow a Coulomb Amontons behaviour in the BL regime: the boundary shear stress is proportional to the pressure (see Fig. 3) and the friction coefficient does not vary with the sliding speed (see Fig. 1). The two plausible causes of this Coulomb behaviour are either plastic shearing of the lubricant, or friction dominated by solid solid contacts. For these contacts, the boundary shear stress is higher than the lubricant shear strength as COF BL lies between 0.09 and 0.2, whereas PAOs yield τ max p m = This leads to consider that solid solid contacts contribute significantly to boundary friction. A major effect of roughness on boundary friction, in steel contacts, is shown in Fig. 4 (see the blue dotted lines). Two trends were exhibited according to the surface roughness of contacts with steel, illustrated with the two blue dotted lines in Fig. 4. These two trends define a critical surface

8 84 Page 8 of 11 Tribology Letters (2018) 66:84 roughness at S qc = 0.03 μm. The trend labelled (ii) shows that the boundary friction coefficient increases with increasing roughness, as long as S qc > 0.03 μm. On the contrary, the trend (i) shows that as surfaces get smoother than 0.03 μm, boundary friction increases sharply when the surface roughness decreases Asperity Considerations Usually, for profile measurements, the ratio between the standard deviation of the peak height with the height standard deviation is approximately 0.7 [24]. For the present 3D measurements, using dx 0.1 μm, the comparison of S q with σ s yields: σ s = 0.6 ± 0.2 S (2) q The asperity heights thus increase roughly in proportion with the surface heights. Although there is no general relationship between the asperity curvature radius β s and the asperity height, Table 3 shows that rougher surfaces have sharper asperities. Figure 8 shows the evolution of the mean pressure withstood by asperities, assuming their heights are Gaussian, with a standard deviation σ s and a curvature radius β s. The reduced elastic modulus E of bulk steel surfaces was used. These pressures were calculated using the Greenwood Williamson modelling [24] between a rough surface (the disc) and a perfectly smooth one (the ball) according to p a = 2 E σs 3π β d σ s du e ( 1 2 u2 u d ) π σ s, where d is the separation between the smooth surface and the mean plane of the rough surface asperities. Figure 8 shows that steel plastic deformations are likely to occur for asperity radii around β s = 1 μm, provided these asperities have RMS heights superior to σ s = 0.01 μm Role of Surface Roughness in Boundary Lubricated Contacts with Steel This can explain the trend (ii) observed in Fig. 4: as surfaces get rougher, the asperity pressures get higher, which causes plastic deformations to occur more often in the steel body, and rises locally the contact shear stress. After the friction tests of contacts corresponding to S qc 0.04 μm, the rubbing track was generally visible on the ball and sometimes on the disc, even if no modification of the topography parameters could be detected, which confirms that (3) Fig. 9 Stribeck tests at SRR = 0.25 in PAOs using at least one steel body. Brown circles correspond to the roughest steel steel contact and black triangles, to the smoothest steel steel contact. (Color figure online) solid solid contacts and wear likely occurred. Still, the boundary friction increase with S q was small ( d COF BL 0.09 d S q for trend (ii)) because, depending on the load, the surface asperities cannot be completely squeezed, which prevents the surface separation from reaching values well inferior to σ s. For surfaces smoother than S qc = 0.03 μm, the composite RMS roughness was generally unchanged between the beginning and the end of the tests. No visible rubbing track appeared on the solids after the test, which confirms that wear occurrences were scarce. Table 3 shows that these surfaces have summit curvature radii superior to a few tens microns. The absence of wear can be explained by the fact that asperities were not sharp enough to cause plastic deformations. Hence, the values of < COF BL > and the friction increase when the surfaces get smoother (trend (i) on Fig. 4) are not related to plastic deformations of steel. The lowamplitude asperities imply that the surface separation can be reduced down to lower values, which explains the ML EHL transition occurring at lower entrainment product for smooth than for rough surfaces. When asperities make contact, the smooth surfaces are more conforming than rough ones and the contact area becomes populated with wide solid solid contact spots, as it is schematically drawn on the left part of Fig. 9. [25] studied experimentally and theoretically the influence of roughness parameters on the adhesion between silicon surfaces. Their work indeed reveals that the most significant parameter that influences adhesion is the surface RMS roughness, and they showed that significant adhesion occurs when surfaces get smoother than S q 0.01 μm. It is thus possible that adhesion explains friction coefficients close to 0.2 since these were only obtained with smooth

9 Page 9 of Fig. 10 a Evolution of the friction coefficient with SRR during 30-s-long speed ramps where the entrainment and sliding speeds were linearly varied between pure sliding and pure rolling, using a transparent silica disc ( S q disc = 0.001μm ) against a smooth steel ball ( S q ball = μm ) in PAO2, at p m = 0.27 GPa. b.1 b.4 In situ interferograms taken during these speed ramps. b.5 In situ interferogram taken during a pure sliding step. c Time-averaged friction coefficient obtained during 3-min-long pure sliding steps ( u e = 0 ± 10 3 m s, u s =constant) with the same contact steel steel contacts ( S qc 0.02μm ), as it was suspected [26] in earlier experimental work with base stock fluids and smooth surfaces. For very smooth contacts such as those performed with the manually polished disc A ( S qc = 0.027μm, see triangles on Fig. 9) or with silica steel contacts ( S qc = 0.008μm, see pentagrams on Fig. 9) no friction saturation towards low entrainment speeds, i.e. no onset of BL, could be measured with the present tribometers. 3.5 Oil Supply Mechanism at Zero Entrainment Speed in Smooth Contacts In order to evaluate whether a boundary friction regime could occur with the smoothest contacts, a different kinematic procedure was applied to a silica/steel contact using the least viscous lubricant (PAO2, η 0 = 0.006Pa s ). In these tests, the entrainment speed was reduced from u e max to zero (with u e max = 0.4, 0.2 and 0.02 m s ), while the sliding speed was increased from zero to u s =±2u e max, with linear ramps lasting 30 s each. This procedure corresponds to going from pure rolling to pure sliding and the opposite. Fig. 11 a Evolution of the friction coefficient with SRR during 30-s-long speed ramps where the entrainment and sliding speeds were linearly varied between pure sliding and pure rolling in a contact between a smooth DLC-coated disc (K-DLC, S q disc = μm ) and a smooth DLC-coated ball ( S q ball = μm ) with PAO2 at p m = 0.44 GPa. b Time-averaged friction coefficient obtained during 3-minute-long pure sliding steps ( u e = 0 ± 10 3 m s, u s =constant) with the same contact The COF measured during the ramps where the disc moves faster are displayed in red, on Fig. 10a, those where the ball is faster are shown in blue. In terms of history, going from pure rolling (SRR = 0 ) to pure sliding (SRR = ± ) and from pure sliding to pure rolling yield the same friction curves. Although, a repeatable difference was observed according to the sign of the sliding speed: when the smooth silica disc was faster than the steel ball, the friction coefficient presents a peak up to 0.14 in SRR 30. In situ interferograms, shown Fig. 10b, reveal that from low SRR to SRR , the experimental film thickness decreased down to 1 nm, which is the maximum vertical resolution. It is thus possible that solid contacts explain the friction coefficient peaking at Yet, at larger sliding rolling ratios, the film thickness gets slightly higher than the vertical resolution ( h c = 2 nm, see in situ interferogram Fig. 10b.5) and the friction coefficient decreases from 0.14 down to about 0.05 and remains stabilized to this value during 3-minutelong pure sliding steps ( u e = 0, u s = constant) performed in between the speed ramps, as it is shown on Fig. 10c This indicates the reformation of a protective fluid layer between the surfaces. Since the entrainment product is nominally zero, the presence of this protective layer must be due to a different mechanism than that predicted by the EHD theory. The most plausible explanation is that in pure sliding, the contact is supplied with lubricant brought out of the surface valleys. This phenomenon was observed for EHL contacts

10 84 Page 10 of 11 between a smooth disc and a ball textured with shallow cavities [27]. The friction peak observed when the smooth silica is faster would then correspond to a transient state between the two lubricating mechanisms, where neither the classical EHD film-forming mechanism nor the amount of lubricant brought by the surfaces valleys would be sufficient to prevent solid contact spots. The speed ramps where the ball was faster than the silica disc (in blue, Fig. 10a) did not present any friction peak, which indicates that at the end of the EHD film-forming regime, there was always enough lubricant brought by the second supply mechanism. Given the silica disc RMS roughness ( S q disc = μm ), it can be considered that most of the reservoirs were on the ball ( S q ball = μm ). On the one hand, the [rougher] ball motion supplies the contact with lubricant reservoirs. On the other hand, the [smoother] silica disc motion only spreads the available fluid on the rubbing track. As a consequence, when the rougher surface (the ball, here) was faster than the smoother one (the silica disc, here), the contact was more unlikely to lack of lubricant, which explains qualitatively that in the former case, the contact did not dry-up and friction remained low, with a friction coefficient compatible with the lubricant shear strength. To question this presumed oil supply mechanism, the same kinematic was performed using a ball smoother than the counter disc, with two DLC-coated surfaces. The friction tests are shown Fig. 11a. These experiments indeed exhibit a friction peak of COF 0.08 when the smoother surface was the fastest, and no peak when the rougher one was the fastest, which agrees with the presumed valley-induced feeding mechanism. The smaller amplitude of the friction peak is certainly due to both surfaces being rough enough ( S q = μm for the DLC-coated ball and S q = μm for the K-DLC disc) to provide lubricant reservoirs in the contact. Finally, during 3-min-long speed steps in pure sliding, the friction coefficient with these DLC-coated surfaces remained stable and equal to ± for u s = 0.04, 0.4 and 0.8 m/s, as shown in Fig. 11b. 4 Conclusions This work showed that the friction in the boundary regime with synthetic base oils presents a dependence towards roughness when one of the bodies is made of steel. For contacts rougher than S qc = 0.03 μm, solid solid contacts occur in a transient way between the asperity tops and the counter surface. This causes locally high pressure and plastic deformations of the steel surface asperities, leading to local tangential stresses significantly higher than in lubricant-protected areas. For smoother contacts, these local pressures are too low to cause plastic deformations, but the low asperity amplitude implies wide solid solid Tribology Letters (2018) 66:84 contact spots and little space remaining for the fluid associated with friction coefficient up to 0.2, either because of adhesion or simply because solid solid friction is always higher than when the solids are protected with a fluid layer. In situ visualization of smooth silica steel contacts showed that the fluid nanometric layer can be recovered provided the roughness of the fastest body exceeds 1 nm: its valleys can work as lube reservoirs, and this surface moves fast enough to renew the amount of fluid between the surfaces. The a-c:h DLC DLC contacts present the most interesting features. Even when the contact involves sharp asperities, the high material hardness prevents the occurrence of plasticity and friction remains governed by the lubricant shear strength. Contrary to the view of BL usually found in the literature, the boundary friction can arise from the bulk fluid shear properties. This can only be fulfilled if the solid hardness is significantly higher than the asperity pressures, preventing from solid plastic deformations. The science of hard surface coatings thus has a promising future not only for the extension of workpieces lifetime but also with respect to the energetic efficiency of lubricated contacts. Acknowledgements This work benefits from financial funding of DGCIS via the project GMPDLC 2. The authors thank Dr. Anthony Chavanne (HEF group) for providing surfaces used in this work. We also thank Sophie Pavan (LTDS) for performing nanoindentation experiments. References 1. Spikes, H.A., Jie, Z.: History, origins and prediction of elastohydrodynamic friction. Tribol. Lett. 56(1), 1 25 (2014) 2. 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