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Differential Colorimetry: A tool for the analysis of fluid film lubrication
Mécanique & Industries 3 (2002) 571–581
Differential Colorimetry: A tool for the analysis of fluid film lubrication Colorimétrie Différentielle : Un outil pour l’étude de la lubrification fluide J. Molimard a,∗ , M. Querry b , P. Vergne b , I. Krupka c , M. Hartl c , R. Poliscuk c , M. Liska c a Centre SMS, ENSMSE, 158, cours Fauriel, 42 027 Saint-Etienne cedex 02, France b LMC/IET, UMR CNRS/INSA n◦ 5514, INSA bât. 113, 69621 Villeurbanne cedex, France c Brno University of Technology, Faculty of Mechanical Engineering, 616 69 Brno, Czech Republic
Received 6 July 2001; accepted 6 March 2002
Abstract In the field of elastohydrodynamic (bearing, gears, etc.) or aerodynamic (hard disks, tape recorders, etc.) lubrication, optical interferometry is the most popular method for film thickness measurement. In 1994, for the first time an image analysis method allowing the automatic treatment of the interferograms was presented. Since then, various teams published numerous literature on this subject. This work aims to sum up the improvements realised. Various methods are described and analysed, then different applications in lubrication ensuing from these works are evoked. They show that image analysis associated to differential colorimetry allows not only to obtain results of better quality and of greater user-friendliness, but that this technique opens a field of studies impossible or difficult to achieve until then. At last, two tendencies are outlined for the near future: differential colorimetry seems to be a very promising tool for the understanding of the mixed lubrication regime and for the in situ study of lubricant behaviour under pressure. 2002 Éditions scientifiques et médicales Elsevier SAS. All rights reserved. Résumé L’interférométrie est la méthode de mesure des épaisseurs de film la plus utilisée pour l’étude de la lubrification élastohydrodynamique (roulements, engrenages. . . ) ou aérodynamique (disques durs, enregistreurs à bande. . . ). En 1994, pour la première fois, une méthode d’analyse d’images permettant le traitement automatique des interférogrammes est présentée. Depuis, différentes équipes ont publié une nombreuse littérature à ce sujet. L’objet de ce travail est de lister les améliorations réalisées. Diverses méthodes sont décrites et analysées, puis les différentes applications découlant de ces travaux sont évoquées. Elles montrent que l’analyse d’images associée à la colorimétrie différentielle permet non seulement d’obtenir des résultats de meilleure qualité avec une plus grande souplesse d’utilisation, mais que cette technique ouvre également un champ d’études impossible ou difficile à atteindre auparavant. Enfin, deux tendances sont soulignées pour le futur : la colorimétrie différentielle semble être un outil très prometteur pour comprendre la lubrification en régime mixte et pour l’étude in situ du comportement d’un lubrifiant sous pression. 2002 Éditions scientifiques et médicales Elsevier SAS. All rights reserved. Keywords: Contact mechanics; EHD lubrication; Thin film lubrication; Film thickness; Optical interferometry; Differential colorimetry; Image analysis Mots-clés : Mécanique des contacts ; Lubrification élastohydrodynamique ; Lubrication en film mince ; Épaisseur de film ; Interférométrie optique ; Colorimétrie différentielle ; Analyse d’images
* Correspondence and reprints.
E-mail addresses: [email protected] (J. Molimard), [email protected] (M. Querry), [email protected] (P. Vergne), [email protected] (I. Krupka), [email protected] (M. Hartl), [email protected] (R. Poliscuk), [email protected] (M. Liska). 1296-2139/02/$ – see front matter 2002 Éditions scientifiques et médicales Elsevier SAS. All rights reserved. PII: S 1 2 9 6 - 2 1 3 9 ( 0 2 ) 0 1 2 0 2 - 2
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Nomenclature α ϕ η λ a E∗ (Ei , νi ) G h Hc Hmin
piezoviscosity coefficient . . . . . . . . . . . . . . . Pa−1 phase change du to the metallic reflection dynamic viscosity . . . . . . . . . . . . . . . . . . . . . . Pa·s wavelength of the incidental light . . . . . . . . . . m contact radius . . . . . . . . . . . . . . . . . . . . . . . . . . . . m reduced Young’s modulus. . . . . . . . . . . . . . . . . Pa elastic parameters of each solid . . . . . . . . . Pa, – dimensionless material parameter G = 2αE ∗ local film thickness . . . . . . . . . . . . . . . . . . . . . . . m film thickness in the middle of the contact area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . m minimum film thickness . . . . . . . . . . . . . . . . . . m
1. Introduction During the past 10 years, high level film thickness measurement techniques were developed in conjunction with the necessity to explore new research fields in lubrication with oil or air. For example, many modern lubricated contacts operate in the mixed lubrication regime, in which the film thickness is close to the mean composite roughness of the two surfaces. This means that two basic mechanisms occur in the contact area: limit lubrication on the local asperity to asperity contacts and hydrodynamic lubrication around these local contacts. Usually, limit lubrication is explained by physicochemical considerations whereas hydrodynamic lubrication remains in the classical field of thin fluids mechanics. For the moment, the understanding of the mixed lubrication regime is poorly developed, and experiments have to be performed. Film thickness is one of the easiest information to measure. But the mixed lubrication regime implies some specific consequences: a wide range of thicknesses inside the contact zone and the presence of very thin films (about a few nanometers). This regime requires a good spatial resolution (a few micrometers) and a high thickness accuracy (about 1 nm). As the example above shows, film thickness knowledge is critical in lubrication studies. This paper deals with some recent applications of image analysis techniques to film thickness measurement. It aims at listing the main contributions and the identified applications. We will first recall the classical technique of optical interferometry. Then, the main different approaches for the numerical treatment of interferograms are presented. It is shown that these techniques fulfill the requirements mentioned above, opening new possibilities for researchers. In the second part of the paper, applications to various problems are presented. Film thickness measurements performed on a rough static contact, then on a smooth dynamic one, under EHD and thin film regimes, are reported. Finally, from
I I1 , I2 IA , IB n R∗ u U w W
luminous intensity . . . . . . . . . . . . . . . . . . . . . . . Cd luminous intensity of the two first outgoing beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cd luminous intensities in the approach of Luo Cd refractive index equivalent radius of curvature . . . . . . . . . . . . . . m mean rolling speed . . . . . . . . . . . . . . . . . . . m·s−1 dimensionless speed parameter U = η0 u/(E ∗ R ∗ ) total load applied in the contact . . . . . . . . . . . . N dimensionless load parameter W = W/(2E ∗ R ∗2 )
film thickness mapping, we show that it is also possible to evaluate other parameters, such as the pressure that can be determined everywhere in the contact with a very good spatial resolution.
2. Optical interferometry: a short review 2.1. Classical approach of optical interferometry Optical interferometry is the most common method used for film thickness measurement since Kirk or Gohar [1,2] first works. The experimental assembly is today well defined and is based on a ball-on-disk device. Contact is established between a reflecting specimen of spherical or ellipsoidal shape (generally in steel) and a flat, transparent disk generally made of glass or sapphire. Contact is observed by reflection through a microscope. Fig. 1 illustrates the very basic optical phenomenon. Only two beam interferometry is shown, and the normal incident light is not respected for the clarty of the picture, even if it is experimentally verified. Light is divided into two parts on
Fig. 1. Interference fringes formation in two beam theory.
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the lower surface of the disk. One part is directly reflected towards the upper surface of the disk (intensity I1 ) while the other part goes throw the oil, is reflected on the ball surface and then turns back (intensity I2 ). Interference fringes are formed at the lubricant/disk interface, according to Newton’s experiment. These fringes are representative of the distance separating the two reflecting surfaces. As to illustrate this purpose, in the very simple case of monochromatic light, with the two beams interferometry assumption, if these beams are totally coherent, the total intensity emitted by the optical system is 4πnh −ϕ (1) I = I1 + I2 + I1 I2 cos λ This equation shows that the intensity I varies periodically with the thickness h, explaining √ Newton’s fringes formation. Defining fringe visibility as 2 I1 I2 /(I1 + I2 ), the visibility is maximum if I1 = I2 , thus, it is necessary to control the light division between the glass and the oil. Classically, a thin layer of chromium (10–20 nm) deposited onto the lower surface of the disc increases significantly the fringe contrast. But this equation has some strong limitations. When h is growing, the temporal coherence becomes partial, thus, the fringe visibility decreases and Eq. (1) is no more valid. Furthermore, fine adjustments of the optical set-up must be carefully done (alignment of elements, punctual light source) otherwise the general periodic shape could change. Last, this very simple equation is unsuitable for white light interferometry. Thus, it is beter to use this equation only for basic understanding. For a detailed description of the optimal conditions, the reader should refer to Foord [3] and for a complete theoretical study of interference fringes formation to Tolansky [4]. The complete description of the classical “handmade” procedure is out of purpose here and the reader should refer to Foord’s paper [3], but it seems useful to describe some aspects of these former works. With monochromatic light, contact appears under the pattern of dark and bright alternated fringes corresponding to the various fringe orders. With white light or multi-chromatic light, fringes are more numerous and present more different colours. In the first case (monochromatic light), a simple relationship can be used for the determination of the thickness. In the second one, there is no existing relationship and a calibration between colour and thickness must be performed from a static contact. Two difficulties of interferometry have to be outlined. Firstly, it is necessary to know the fringe order to determine the thickness, especially with monochromatic light. Secondly, the resolution of this method is limited by the capacity of a human eye to detect a luminosity or chromaticity variation. Let us retain that this original treatment of interferograms leads to a minimal thickness of 100 nm and to a height between two consecutive fringes of 40 nm. The analysis of more recent and more severe lubricated contacts makes these performances too much limited. Because the method is performed from point to point and be-
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cause the fringe order must be known, it appears to be inadequate for the study of strongly disturbed contacts, due to the presence of grease, roughness, dents etc. Furthermore, the poor resolution of the human eye makes this technique unsuccessful for the study of very thin films. 2.2. Spacer layer and spectrometer introduction The first great improvement of the method was the use of a SiO2 layer sputtered on the chromium coating, known as a “Spacer Layer” [5]. Its refractive index is very close to the oil’s one, thus everything happens as if a constant thickness was added to the oil film thickness. This facility overcame the first limitation concerning the minimum detectable thickness. In spite of the use of a wedged spacer layer to get round the second limitation, the best solution for years appeared to be the use of a spectrometer [6,7]. For a given point of the interferogram, the light is split into its spectral components: the more intense wavelength corresponds to a constructive fringe and the thickness can be deduced from it with a simple formula, if the fringe order is known. The technique associating these two advances, known as “Ultra Thin Interferometry” or UTI, allowed film thickness measurements from one to hundreds of nanometers, with an accuracy about 1 nm. It has permitted to obtain many interesting results in the domain of thin film lubrication. The reader should refer to one of the reviews recently published [8]. But by using this method, one can only measure film thickness at a given point or line in the contact. Thus, it does not permit a complete film thickness mapping as a full field technique may do. As a consequence, the minimum film thickness is not found, even if it is very important to check if surface damages can occur. Furthermore, this method is not adapted to rough surfaces. With the emergence of more efficient CCD cameras and faster computers, the idea of a computerised treatment of the interferograms rose. The following section describes the main evolutions brought by image analysis techniques. 2.3. Further improvements In 1994, Gustafsson [9] proposed a first advance based on white light interferometry. He proceeded by analogy with the handmade technique used until then. First of all, the ball and the disk, both motionless, are moved close together in order to obtain a punctual contact between the two solids. In these conditions, the initial shape of the surfaces gives the film thickness at every point of the interferogram. So it is possible to establish a calibration associating film thickness to a colorimetric parameter representative of the observed colour, for instance, the hue value H of the video representation system HSI. This value is a nonlinear combination of the physical parameters recorded by the 3CCD camera, which are the intensities collected through wide bandwidth filters centred on red, green and
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Fig. 2. Typical calibration in the HSI system.
blue colours. However, the calibration is not unambiguous as it is shown Fig. 2: in this figure, the “Hue” value is represented versus thickness. There are many different thicknesses corresponding to a given hue value. The choice of the “right” thickness is done by using the other parameters (S and I ) at a reference point. Then, film thickness is deduced step by step from this reference point. As in the case of the handmade treatment of white light interferograms, the calibration curve is established at ambient pressure, while film thickness measurements are performed under the actual contact pressure. Gustafsson used a classic correction based on Lorenz–Lorentz’s law (connecting refractive index and density) and Dowson–Higginson’s relationship (linking density and pressure) described for example by Foord [3]. Finally, this method allowed measurements from 100 to 700 nm with an uncertainty of some nanometers. In 1996, Cann [10] combined both this technique and the spacer layer, in order to perform measurements below 100 nm (Spacer Layer Imaging Method, SLIM). The same year, Luo [11] proposed a method based on monochromatic interferometry with green light (Relative Optical Interference Intensity, ROII). A simple optical relationship, based on a two beams interferometry model, allows one to determine the luminous intensity I as a function of the interface thickness h: 4πnh (2) +ϕ I = IA + IB cos λ Wavelength λ and refractive index n can be determined besides. Only the parameters IA , IB and the phase change ϕ, due to the metallic reflection on the chromium layer, remain unknown. Luo shows that they can be previously determined by measuring minimal and maximal intensities as well as intensity in the centre of a static contact. Then, the luminous intensity I can be measured everywhere within the dynamic contact. If an order of interference is defined, h can be calculated by inverting relation (2). With this method, the wavelength λ must be known with high accuracy, that supposes a narrow spectral band of the incidental light. Furthermore, it is necessary to take into account the lubricant refractive index variation with pressure. Luo [11] used the same classical correction than Gustafsson, or previously
Foord. This technique turned out to be successful for very thin film thicknesses, but it worked well only within the first interference order. Furthermore, as Foord [3] mentioned, collimation defects change the relationship between height and luminous intensity. Thus, the optical set-up becomes hard to adjust for a precise thickness evaluation using Eq. (2). These first works were unable to take into account a rough surface because the interference order was still badly mastered. Besides, handled information (hue or intensity) presents sensitivity defects connected to its oscillating character [12]. As an example, for the green component, the sensitivity of the luminous intensity versus film thickness is 3 nm by degree of intensity at 146 nm, while it drops to 0.5 nm by degree of intensity at 180 nm, intensities being coded over a usual arbitrary scale of 256 levels. That is why Hartl and then Molimard [13,14] proposed to generalise the systematic use of the three components characterising the light intensity for every pixel of a colour image. This method allows both the determination of the film thickness independently of the interference order [12] and the minimisation of the sensitivity defects. This method, known as “Differential Colorimetry” (DC), is presented in Fig. 3. As in the approach of Gustafsson, the optics laws are not explicitly used and the luminous intensities versus film thickness relationships are calibration curves. For that purpose, a static contact is normally loaded first (Fig. 3(a)). Hartl and Molimard suppose that the shape of this static contact is Hertzian, in order to determine the film height everywhere in the interferogram. An analytic solution can be calculated, assuming the two solids are elastic and semi-infinite. For a given distance r from the centre of the contact, the gap between the two solids h is h=
r2 a2 1 − + ∗ ∗ 2R R πR ∗ 2 2 a a a × 2a − r 2 arcsin 1− + r2 r r r (3)
As Eq. (3) shows, this process requires the experimental determination of the contact radius a and the curvature radius R ∗ . Then, calibration curves can be drawn, as represented in Fig. 3(c). Each curve is oscillating, but their frequencies are different, so the sensitivity defect is reduced. Moreover, it is possible to show that a given triplet of intensities leads to a unique thickness. In a second step, the evaluation of film thickness is carried out in a dynamic contact Fig. 3(b). The three chromatic values (R, G and B) are recorded for each point and compared to the calibration curve, leading to a complete thickness map (Fig. 3(d)). The operations described above give a film thickness without correction of the refractive index variation with pressure: finally, the same classical corrections as before are used. Later, Hartl and Molimard [15], as Cann did [10], used
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Fig. 3. Schematic view of the differential colorimetry process: (a) static contact, (b) dynamic contact, (c) calibration chart deduced from the static contact, (d) result of differential colorimetry for the dynamic contact.
a space layer to perform measurements down to some nanometers. But, if the majority of the published works use the Hertz theory to calculate the pressure field and the Lorenz–Lorentz law to correct the refractive index, Marklund proposed a more precise approach [16]. This work is based on Astrom’s previous findings [17], showing that the pressure can be evaluated from out-of-plane displacements (thus, film thickness). Marklund related the pressure calculation based on thickness field, the refractive index versus pressure variation and last the thickness versus refractive index relationship in an iterative procedure. Consequently, the pressure in the contact and the film thickness field are both evaluated simultaneously. The correction on film thickness reaches 10%. Such a solution, heavy to finalise and to use, seems very interesting for thick EHD film or dimple cases but for the thin film cases, the pressure field tends to the Hertzian shape, and Marklund approach is no longer useful. Very recently, Lord proposed a method called “MultiChannel Interferometry” (MCI) based on a trichromatic lighting [18]. The relationships between intensities and thickness are deduced from the two-beam interferometry theory (Eq. (2)). Thus, this promising method combines some advantages of DC (fringe order independence, favourable sensitivity) and of Luo’s approach (very thin film measurement without spacer layer). Furthermore, contrary to classical white light interferometry for which the fringe contrast is very quickly lost (beyond 1 µm), the use of three
narrow-band light sources ensure a good contrast for thicker films. Today, this method has not given its full capacities. The previous works were developed for elastohydrodynamic lubrication; independently, some similar works were realised on head/tape contacts. Based at first on interferograms obtained in monochromatic light, the technique developed by Lacey [19] used a semi-empirical formula connecting film thickness and luminous intensity. This formula takes into account the possibility to have an inhomogeneous lighting due to misalignment in the optical set-up. The necessity to determine the interference order and the optimisation of the sensitivity, which varies according to both the measured thickness and the incidental wavelength, incited to the use of three red, green and blue monochromatic lights [20]. Large deviations between measured film thicknesses using only a single monochromatic light (with a red, green or blue filter) and those stemming from the trichromatic process have been revealed. Performances of the film thickness measurement techniques have not been clearly underlined yet. This point is discussed here for the particular case of DC. Some experiments were performed with oils previously studied by ultra thin interferometry [15]. From one to hundreds of nanometers, no evident deviation could be mentioned. Dispersion of the results is almost constant in this range and is less than 3 nm. Nevertheless, these values must be taken with care considering possible experimental effects: linearity defects, local variations in the properties of the optical coatings, presence of surfaces defects, variation of the lubricant refractive
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index due to modifications within the lubricating film [21]. As to finish this description, the highest measurable thickness by differential colorimetry is about 800 nm and the spatial resolution is nearby 1 µm.
3. Some recent applications of DC in tribology Most of publications mentioned before were dedicated to the development of the measurement techniques. Although image analysis applications in elastohydrodynamic contacts were proposed first in 1994 [22], results directly interesting tribology have been multiplied since 1998. This section will develop some recent applications, mostly performed by the DC method, although other methods could be used (ROII, SLIM, MCI).
Fig. 4. Topography of the rough surface model.
3.1. Topographic analysis of a static contact DC allows the film thickness determination at every pixel. So, it becomes easier to study a complete surface and not only some isolated points. This facility is particularly useful to quantify the roughness behaviour under normal loading. First tests were realised by Tan [23] for a head on tape contact. Some original results are presented here as an illustration of potential studies that can be conducted using differential colorimetry. A periodic unidirectional model roughness is printed on a glass plate. It is a rectangular wave characterised by a peak-to-valley amplitude of 210 nm and a wavelength of 96 µm (Fig. 4). This ideal surface profile has been pressed against a ceramic ball at various loads. Reduced Young’s modulus and equivalent curvature radius are respectively E ∗ = 64.9 GPa and R ∗ = 12.7 mm. Estimated pressures for a smooth contact under the same conditions vary from 0 to 610 MPa. An example of a 3D visualization is given Fig. 5. In this case, we can see that the load is supported both by the upper parts of the roughness (dark rectangles in Fig. 5(a)) and by the lower parts which have grown up (dark ellipses in Fig. 5(a)). It is possible, with this basic geometry but also with more realistic surfaces, to quantify the roughness evolution when the normal load varies. In this example, the mean value of the transverse roughness falls from σRMS = 103 nm down to σRMS = 10 nm (white plots, Fig. 6) whereas the relative area of contact increases from 0% to 85% (dark plots, Fig. 6). Such a tool has naturally an interest among studies carrying on the plastic or elastic deformation of rough surfaces in a static contact case, as in our example, or in a dynamic one (lubrication) if the high speed recording of pictures is mastered. Therefore, it is a first step toward the study of rough elastohydrodynamic lubrication or that of the mixed lubrication regime which is developed in Section 3.4.
(a)
(b) Fig. 5. Interferogram (a) and a 3D visualization (b) of a rough model surface under normal load (w = 20.2 N).
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Fig. 6. Variation with load of the contact area and the RMS roughness in a rough static contact.
Fig. 7. Hc /Hmin comparison versus speed: Hamrock and Dowson model does not fit the experimental results for low speed (i.e. low thickness).
3.2. Study of elastohydrodynamic lubrication
tonian, with an exponential viscosity–pressure law; lubrication (regime) has to be isothermal and fully flooded; experimentally, the speed is restricted to avoid shear heating at the contact inlet, referring to a basic thermal model (Crook) and a thermal transducer is placed near the contact for a rough control. Last, the oil used is free of additives otherwise non Newtonian behaviour could appear if the thickness is lower than 100 nm. We have recorded central and minimum film thickness, and Fig. 7 shows the variation of the ratio hc / hmin versus rolling speed. In this experiment, central film thickness varies from 32 nm to 375 nm. If the speed and consequently the film thickness are low, the efficiency of Moes– Venner formula is obvious, compared to that of Hamrock and Dowson. The experimental points are quite dispersed mainly because the minimum film thickness is strongly dependent on noise.
The example presented in this paragraph concerns a study possible without the contribution of the image analysis techniques, such as differential colorimetry. In this case, DC appeared to be necessary by its user-friendliness and its accuracy, especially for the finding of the minimum film thickness. In the field of elastohydrodynamic lubrication, many equations describing the evolution of central and minimum film thickness with the contact conditions were proposed. The two most popular were proposed by Hamrock and Dowson in 1977 and by Nijenbanning, Moes and Venner in 1994. The Hamrock and Dowson equation has been the object of numerous experimental comparisons. On the other hand, the approach proposed by Nijenbanning et al. [24] has been the object of less interest and experimental examination. Krupka et al. did it in the case of point [25,26] or elliptic [27] contact. Central and minimal film thicknesses were measured for various conditions of load, speed and material. Image analysis, by authorising a faster and more precise film thickness evaluation, allowed to confirm that the ratio between central and minimal film thickness is more important than the one given by Hamrock and Dowson model. Practically, this means that the minimum film thickness is lower than expected by Hamrock and Dowson model, which might be dangerous for the contact life. We have reproduced for this paper one single experiment with a paraffinic base oil in order to illustrate our purpose. Operating conditions of the two formulas are strictly respected experimentally. First, the dimensionless parameters (G = 2069, W = 1.366·10−6 , from U = 2.854·10−12 to U = 6.388·10−11 ) are within the definition range of these formulas. The contact has to be in pure rolling conditions; experimentally, the slide to roll ratio is lower than 0.1%. The two surfaces are supposed to be smooth; in practice, the RMS composite roughness is 2 nm, with no orientation, consequently the minimum film height according to this parameter should be 6 nm or less if Johnson model is considered. Last point, the lubricant behaviour should be New-
3.3. Thin film lubrication The results obtained with the static contact presented in Section 3.1 gains from the particularly high spatial resolution due to the introduction of the image analysis process in the treatment of the interferograms. But minimum measurable film thickness is also reduced. Luo [28,29] and Hartl et al. [15,30] used image analysis to study the behaviour of lubricants when a very thin film thickness occurs. It is possible to show the transition between elastohydrodynamic lubrication and a regime of lubrication in which the chemical structure of the lubricant determines its thin film behaviour [30]. We present here the main results of a previous work. The response of a mineral base oil (η = 11.3 Pa·s, α = 16.7 Pa−1 ) and the one of the same base oil with additives (η = 12.4 Pa·s, α = 10.5 Pa−1 ) are presented respectively in Figs. 8(a), (b). The central (square) and minimum (triangle) film thickness is recorded versus speed and presented in a log-log graph. In the presence of additives, results show an inflection in the evolution of the film thickness versus speed in the domain of very thin thicknesses whereas for the pure based oil a power law is valid for any thickness.
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with Hmin . So, it is observed that Hc and Hmin converge towards a single film thickness value at low speed. Owing to image analysis coupled with differential colorimetry, it is therefore possible to show the presence of adsorbed layers in different points of the contact, thus over all the contact area. 3.4. Toward mixed lubrication regime
(a)
(b) Fig. 8. Thin film lubrication (50 ◦ C, 0.5 GPa): (a) mineral base oil, (b) mineral base oil + additives.
This power law (a straight line in a log-log graph) is typical of the elastohydrodynamic regime, as shown by both models introduced above (Section 3.2). Consequently, the difference between the experimental curve and a power law fitted for high thickness range is representative of physico-chemical influence in the contact behaviour. These results have been explained with the model proposed by Moore [31] who suggested that film thickness in the contact is generated both by a viscous contribution, in agreement with the classical EHD theory, and by an immobile layer that may adhere onto one (or both) surface. Moore attributed this immobile layer to the adsorption of lubricant molecules. Comparing the immobile layer thickness for various lubricants to molecule dimensions, we confirmed Moore’s model [30] rather than the “apparent viscosity model”, based on the assumption of a viscosity change for thin films [32]. Some results presented in this paper have been obtained in a domain where ultra thin interferometry [33] has been already employed, but the technique presented here also allows to measure easily and simultaneously the central and the minimal thicknesses in the contact (respectively Hc and Hmin ). In Fig. 8(b), we put in evidence that the change already observed in the centre of the contact is clearly visible
Sections 3.1 and 3.3 clearly underline that differential colorimetry (proposed by authors), but also spacer layer imaging method (Cann) or relative optical interference intensity (Luo) are able to measure a film thickness map with a good lateral resolution (about 1 µm), a high accuracy (few nanometers) and a low minimum measurable thickness even in rough contacts. Thus, these methods seem to be very efficient to the study the mixed lubrication regime. A first promising work on mixed lubrication was recently realised by Guangteng [34] with the SLIM. An additivefree poly-alpha-olefin has been used. As SLIM could not allow measurements under 10 nm, the limit lubrication regime could not be put in evidence on the roughness peaks. Nevertheless, three different types of roughness were used (single, 1D or 2D periodic bumps) for a very complete study of rough EHD, including slide to roll ratio variations, compliance evolution with speed, or micro-EHD evidence. This first trial shows that the study of mixed lubrication regime is possible with a more accurate image analysis technique such as DC or ROII, even if the limit lubrication regime was not reached on the roughness peaks yet. 3.5. Local pressure estimation within the contact area Image analysis of interferograms supplies numerical data, directly exploitable either for visualisation or for a further treatment. The mechanical analysis of an EHD contact is based on the simultaneous resolution of elasticity (deformation of solids) and Reynolds (thin film fluid mechanics) equations for a given rheological model. Film thickness in an EHD contact arises from the initial shape of solids, from the elastic strain of surfaces and from a translation due to the resulting hydrodynamic forces. So, it is possible to deduce the surface displacements from the film thickness found experimentally within a constant. Afterwards, application of the elasticity laws leads to the normal stress, as firstly shown by Aström [17]. The example developed in this paper shows the interest of such an analysis. We present here our first results using a novel algorithm based on the Fast Fourier Transform [35, 36]: Johnson demonstrated that a sinusoidal load applied on a semi-infinite body induces a sinusoidal displacement and that the amplitude of this displacement is proportional to the one of the load. Thus, after deducing the displacement field from the thickness field, and developing it in Fourier
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(a)
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(b)
(c) Fig. 9. Analysis of a grease lubricated static contact: (a) interferogram, (b) measured film thickness, (c) calculated pressure.
series, the pressure can be easily reached in the frequency domain. A classical FFT algorithm has been used for the manipulations between the spectral and real spaces. A complete explanation of this method will be developed in a later communication [37]. This numerical approach is simpler to implement than the multigrid/multi-integration technique used by Aström [17], for a very reasonable calculation time. As an illustration, we study here a static contact between a glass disk and a stell ball lubricated with a complex lithium grease: the interferogram is reproduced in Fig. 9(a). Usually, the contact area corresponds to a grey circle, as Fig 5(a) shows. Here, the grey area is strongly reduced because of the presence of numerous soap particles. We can
deduce that these particles are transparent. So, assuming that their refractive index is close to that of the oil, it is possible to measure the film thickness map with DC (Fig. 9(b)). The transitions in thickness are marked, but there is no gap near the particles. So, our assumption on particles’ refractive index is realistic. Then, the pressure field is calculated (Fig. 9(c)) according to the method described above. Pressure engendered in this example is equal to 1.6 times the maximal pressure given by the Hertz theory in the case of a dry contact. This result is similar to Aström’s findings. This example shows the interest of our method: very localised and very intense pressure peaks occur because of the soap particles, voluntarily introduced in this case. So,
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the technique presented here allows to estimate engendered over-pressures and constitutes an interesting tool for the analysis of perturbed lubricated contacts particularly the mechanisms of surface degradation, either in the presence of wear, or in the case of solid pollution (dents). 3.6. Toward lubricant rheology Some authors pushed the inverse analysis farther down. The pressure calculation is only based on the elastic behaviour of contacting solids. Knowing film thickness and pressure fields, it may be possible then to deduce the flow properties of the lubricant by using the Reynolds equation. In particular, viscosity everywhere in the contact can be estimated. However, considering the measurement uncertainties, this parameter seems still difficult to reach [38] with confidence. On the other hand, the lubricant compressibility [39] and thus the variation of the refractive index with pressure could be estimated in satisfying numeric conditions. It should be underlined that these last two parameters change little with pressure, contrary to viscosity whose variation is exponential.
4. Conclusion After a brief review of existing methods devoted to film thickness measurements, this paper shows the advances that differential colorimetry has allowed in the field of the elastohydrodynamic lubrication. The help brought by the computerised analysis of interferograms has been underlined and various techniques and extensions were described and compared. As far as uncertainties are correctly mastered, the accessible film thicknesses in the contact cover a range between some nanometers and 800 nm, with a spatial resolution of the order of 1 µm. Applications of differential colorimetry performed in our laboratories were presented. They have been related to the main evolutions in the domains beyond EHD lubrication, and we have tried to identify two tendencies for further works: (1) The first one uses the high accuracy in the thickness evaluation and the full field capacity. It aims to understand phenomena governing mixed lubrication. It concerns the analysis of the thin film lubrication regime, with the determination of the height of adsorbed films, and the analysis of ideal rough lubricated contacts. (2) The second orientation involves the numerical exploitation of the film thickness fields, to calculate the pressure, for instance. This should be helpful for the analysis of surface degradation mechanisms. Even though his attempt failed, Ostensen [38] showed that contact mapping could lead to the knowledge, at the local scale, of the lubricant viscosity value.
Acknowledgements The work of the Czech part has been financially supported by the Grant Agency of the Czech Republic under grants Nos. 101/98/P105 and 101/98/P226. The work of the French part was carried out under the CPR “Mise en forme des matériaux: Contact métal-outillubrifiant” supported by CNRS, IRSID (USINOR), Pechiney Recherche, involving Paris Sud University (LMS), Collège de France (PMC), ECL (LTDS), INSA de Lyon (LMC), INPT (IMF), ENSMP (CEMEF), CNRS (SCA).
References [1] M.T. Kirk, Hydrodynamic lubrication of ‘perspex’, Nature 194 (1962) 965–966. [2] R. Gohar, A. Cameron, Optical measurement of oil film thickness under elastohydrodynamic lubrication, Nature 200 (1963) 458–459. [3] C.A. Foord, L.D. Wedeven, F.J. Westlake, A. Cameron, Optical elastohydrodynamics, Proc. Inst. Mech. Engrs. 184-1 (28) (1969– 1970) 487–505. [4] S. Tolansky, An Introduction to Interferometry, Longmans, London, 1955. [5] F.J. Westlake, A. Cameron, A study of ultra-thin lubricant films using an optical technique, Proc. Inst. Mech. Engrs. 182-3G (1967–1968) 75–78. [6] G.J. Johnston, R. Wayte, H.A. Spikes, The measurement and study of very thin lubricant films in concentrated contacts, Tribology Trans. 34 (2) (1991) 187–194. [7] J. Israelachvili, Thin films studies using multiple beam interferometry, J. Colloid Interface Sci. 44 (2) (1973) 259–272. [8] H. Spikes, Direct observation of boundary layers, Langmuir 12 (1996) 4567–4573. [9] L. Gustafsson, E. Hoglund, O. Marklund, Measuring lubricant film thickness with image analysis, Proc. Inst. Mech. Engrs. 208 (1994) 199–205. [10] P.M. Cann, H.A. Spikes, J. Hutchinson, The development of a spacer layer imaging method (SLIM) for mapping elastohydrodynamic contacts, Tribology Trans. 39 (4) (1996) 915–921. [11] J. Luo, S. Wen, P. Huang, Thin film lubrication, Part I: Study on the transition between EHD and thin film lubrication using a relative optical interference intensity technique, Wear 194 (1996) 107–115. [12] J. Molimard, Étude expérimentale du régime de lubrification en film mince, application aux fluides de laminage, Thèse de doctorat, INSA de Lyon, 1999, 199 p., n◦ 99 ISAL 0121 (in French). [13] M. Hartl, I. Krupka, M. Liska, Differential colorimetry: Tool for evaluation of the chromatic interference patterns, Opt. Eng. 36 (9) (1997) 2384–2391. [14] J. Molimard, M. Querry, P. Vergne, New tools for experimental study of EHD and limit lubrications, in: Proceedings of the 25th Leeds/Lyon Symposium on Tribology, Elsevier, Amsterdam, 1999, pp. 717–726. [15] M. Hartl, I. Krupka, R. Poliscuk, J. Molimard, M. Querry, P. Vergne, Thin film lubrication study by Colorimetric Interferometry, in: Proceedings of the 26th Leed/Lyon Symposium on Tribology, Elsevier, Amsterdam, 2000, pp. 695–704. [16] O. Marklund, L. Gustafsson, Correction for pressure dependence of the refractive index in the measurements of lubricant film thickness with image analysis, Proc. Inst. Mech. Engrs. J, J. Engrg. Tribology 213 (1999) 109–126. [17] H. Astrom, C.H. Venner, Soap-thickener induced local pressure fluctuations in a grease-lubricated elastohydrodynamic point contact, Proc. Inst. Mech. Engrs. Part J 208 (1994) 191–198.
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[18] J. Lord, O. Marklund, R. Larsson, Multi-Channel Interferometry for measurement of the thickness of very thin EHL lubricant films, in: Proceedings of the 26th Leeds/Lyon Symposium on Tribology, Elsevier, Amsterdam, 2000, pp. 711–717. [19] C. Lacey, F.E. Talke, Measurement and simulation of partial contact at the head/tape interface, J. Tribology 114 (October 1992) 646–652. [20] E. Baugh, J. Swenson, F.E. Talke, Simultaneous three-wavelength interferometry for head/tape spacing measurement, J. Tribology 120 (July 1998) 549–553. [21] S. Gunsel, H.A. Spikes, M. Aderin, In-situ measurement of ZDDP films in concentrated contacts, Tribology Trans. 36 (2) (1993) 276– 282. [22] E. Hoglund, EHL and the use of image analysis, Wear 179 (1994) 49– 56. [23] S. Tan, E. Baugh, F.E. Talke, Improved method for the measurement of asperity compliance of magnetic tapes, J. Tribology 121 (January 1999) 121–127. [24] G. Nijenbanning, C.H. Venner, H. Moes, Film thickness in elastohydrodynamically lubricated elliptic contacts, Wear 176 (1994) 217–229. [25] I. Krupka, M. Hartl, R. Poliscuk, M. Liska, Experimental study of the central and minimum elastohydrodynamic film thickness by colorimetric interferometry technique, Tribology Trans. 43 (4) (2000) 611–618. [26] I. Krupka, M. Hartl, R. Poliscuk, J. Cermak, M. Liska, Experimental evaluation of EHD film shape and its comparison with numerical solution, J. Tribology 122 (October 2000) 689–696. [27] I. Krupka, M. Hartl, R. Poliscuk, M. Liska, Experimental study of the central and minimum film thickness in elastohydrodynamic elliptic contacts, in: Proceedings of the 27th Leeds-Lyon Symposium on Tribology, Elsevier, Amsterdam, 2001 (to be published). [28] J. Luo, L. Qian, S. Wen L, Wen, L. Li, The failure of fluid film at nano-scale, Tribology Trans. 42 (4) (1999) 912–916.
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[29] J. Luo, P. Huang, S. Wen, L. Li, Characteristics of liquid lubricant films at the nano-scale, J. Tribology 121 (October 1999) 872–878. [30] M. Hartl, I. Krupka, R. Poliscuk, M. Liska, J. Molimard, M. Querry, P. Vergne, Thin film colorimetric interferometry, Tribology Trans. 44 (2) (2001) 270–276. [31] A.J. Moore, Nanometer elastohydrodynamic lubrication, in: Proceedings of the 25th Leeds/Lyon Symposium on Tribology, Elsevier, Amsterdam, 1997, pp. 57–67. [32] M. Smeeth, H.A. Spikes, S. Gunsel, The formation of viscous surface films by polymer solutions: Boundary or elastohydrodynamic lubrication?, Tribology Trans. 39 (3) (1996) 720–725. [33] G.J. Johnston, R. Wayte, H.A. Spikes, The measurement and study of very thin lubricant films in concentrated contacts, Tribology Trans. 34 (2) (1991) 187–194. [34] G. Guangteng, P.M. Cann, H.A. Spikes, Lubricant film thickness in rough surface, mixed elastohydrodynamic contact, J. Tribology 122 (2000) 65–76. [35] H.M. Stanley, T. Kato, A FFT-based method for rough surface contact, J. Tribology 119 (July 1997) 481–485. [36] K.L. Johnson, Contact Mechanics, Cambridge University Press, Cambridge, 1985. [37] J. Molimard, M. Querry, P. Vergne, M. Hartl, I. Krupka, Calculation of local pressure in point contacts from experimental interferogram analysis data, in: SEM Annual Meeting, Milwaukee, 2002 (accepted). [38] J.O. Ostensen, R. Larsson, C.H. Venner, Determination of viscosity and pressure in an elastohydrodynamic rolling contact by using optical interferometry: a theoretical study, Proc. Inst. Mech. Engrs. J, J. Engrg. Tribology 210 (1996) 259–268. [39] A. Jolkin, R. Larsson, Determination of lubricant compressibility in EHL conjunctions using the Hybrid Technique, in: Proceedings of the 26th Leeds/Lyon Symposium on Tribology, Elsevier, Amsterdam, 2000, pp. 589–596.
Differential Colorimetry: A tool for the analysis of fluid film lubrication Colorimétrie Différentielle : Un outil pour l’étude de la lubrification fluide J. Molimard a,∗ , M. Querry b , P. Vergne b , I. Krupka c , M. Hartl c , R. Poliscuk c , M. Liska c a Centre SMS, ENSMSE, 158, cours Fauriel, 42 027 Saint-Etienne cedex 02, France b LMC/IET, UMR CNRS/INSA n◦ 5514, INSA bât. 113, 69621 Villeurbanne cedex, France c Brno University of Technology, Faculty of Mechanical Engineering, 616 69 Brno, Czech Republic
Received 6 July 2001; accepted 6 March 2002
Abstract In the field of elastohydrodynamic (bearing, gears, etc.) or aerodynamic (hard disks, tape recorders, etc.) lubrication, optical interferometry is the most popular method for film thickness measurement. In 1994, for the first time an image analysis method allowing the automatic treatment of the interferograms was presented. Since then, various teams published numerous literature on this subject. This work aims to sum up the improvements realised. Various methods are described and analysed, then different applications in lubrication ensuing from these works are evoked. They show that image analysis associated to differential colorimetry allows not only to obtain results of better quality and of greater user-friendliness, but that this technique opens a field of studies impossible or difficult to achieve until then. At last, two tendencies are outlined for the near future: differential colorimetry seems to be a very promising tool for the understanding of the mixed lubrication regime and for the in situ study of lubricant behaviour under pressure. 2002 Éditions scientifiques et médicales Elsevier SAS. All rights reserved. Résumé L’interférométrie est la méthode de mesure des épaisseurs de film la plus utilisée pour l’étude de la lubrification élastohydrodynamique (roulements, engrenages. . . ) ou aérodynamique (disques durs, enregistreurs à bande. . . ). En 1994, pour la première fois, une méthode d’analyse d’images permettant le traitement automatique des interférogrammes est présentée. Depuis, différentes équipes ont publié une nombreuse littérature à ce sujet. L’objet de ce travail est de lister les améliorations réalisées. Diverses méthodes sont décrites et analysées, puis les différentes applications découlant de ces travaux sont évoquées. Elles montrent que l’analyse d’images associée à la colorimétrie différentielle permet non seulement d’obtenir des résultats de meilleure qualité avec une plus grande souplesse d’utilisation, mais que cette technique ouvre également un champ d’études impossible ou difficile à atteindre auparavant. Enfin, deux tendances sont soulignées pour le futur : la colorimétrie différentielle semble être un outil très prometteur pour comprendre la lubrification en régime mixte et pour l’étude in situ du comportement d’un lubrifiant sous pression. 2002 Éditions scientifiques et médicales Elsevier SAS. All rights reserved. Keywords: Contact mechanics; EHD lubrication; Thin film lubrication; Film thickness; Optical interferometry; Differential colorimetry; Image analysis Mots-clés : Mécanique des contacts ; Lubrification élastohydrodynamique ; Lubrication en film mince ; Épaisseur de film ; Interférométrie optique ; Colorimétrie différentielle ; Analyse d’images
* Correspondence and reprints.
E-mail addresses: [email protected] (J. Molimard), [email protected] (M. Querry), [email protected] (P. Vergne), [email protected] (I. Krupka), [email protected] (M. Hartl), [email protected] (R. Poliscuk), [email protected] (M. Liska). 1296-2139/02/$ – see front matter 2002 Éditions scientifiques et médicales Elsevier SAS. All rights reserved. PII: S 1 2 9 6 - 2 1 3 9 ( 0 2 ) 0 1 2 0 2 - 2
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Nomenclature α ϕ η λ a E∗ (Ei , νi ) G h Hc Hmin
piezoviscosity coefficient . . . . . . . . . . . . . . . Pa−1 phase change du to the metallic reflection dynamic viscosity . . . . . . . . . . . . . . . . . . . . . . Pa·s wavelength of the incidental light . . . . . . . . . . m contact radius . . . . . . . . . . . . . . . . . . . . . . . . . . . . m reduced Young’s modulus. . . . . . . . . . . . . . . . . Pa elastic parameters of each solid . . . . . . . . . Pa, – dimensionless material parameter G = 2αE ∗ local film thickness . . . . . . . . . . . . . . . . . . . . . . . m film thickness in the middle of the contact area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . m minimum film thickness . . . . . . . . . . . . . . . . . . m
1. Introduction During the past 10 years, high level film thickness measurement techniques were developed in conjunction with the necessity to explore new research fields in lubrication with oil or air. For example, many modern lubricated contacts operate in the mixed lubrication regime, in which the film thickness is close to the mean composite roughness of the two surfaces. This means that two basic mechanisms occur in the contact area: limit lubrication on the local asperity to asperity contacts and hydrodynamic lubrication around these local contacts. Usually, limit lubrication is explained by physicochemical considerations whereas hydrodynamic lubrication remains in the classical field of thin fluids mechanics. For the moment, the understanding of the mixed lubrication regime is poorly developed, and experiments have to be performed. Film thickness is one of the easiest information to measure. But the mixed lubrication regime implies some specific consequences: a wide range of thicknesses inside the contact zone and the presence of very thin films (about a few nanometers). This regime requires a good spatial resolution (a few micrometers) and a high thickness accuracy (about 1 nm). As the example above shows, film thickness knowledge is critical in lubrication studies. This paper deals with some recent applications of image analysis techniques to film thickness measurement. It aims at listing the main contributions and the identified applications. We will first recall the classical technique of optical interferometry. Then, the main different approaches for the numerical treatment of interferograms are presented. It is shown that these techniques fulfill the requirements mentioned above, opening new possibilities for researchers. In the second part of the paper, applications to various problems are presented. Film thickness measurements performed on a rough static contact, then on a smooth dynamic one, under EHD and thin film regimes, are reported. Finally, from
I I1 , I2 IA , IB n R∗ u U w W
luminous intensity . . . . . . . . . . . . . . . . . . . . . . . Cd luminous intensity of the two first outgoing beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cd luminous intensities in the approach of Luo Cd refractive index equivalent radius of curvature . . . . . . . . . . . . . . m mean rolling speed . . . . . . . . . . . . . . . . . . . m·s−1 dimensionless speed parameter U = η0 u/(E ∗ R ∗ ) total load applied in the contact . . . . . . . . . . . . N dimensionless load parameter W = W/(2E ∗ R ∗2 )
film thickness mapping, we show that it is also possible to evaluate other parameters, such as the pressure that can be determined everywhere in the contact with a very good spatial resolution.
2. Optical interferometry: a short review 2.1. Classical approach of optical interferometry Optical interferometry is the most common method used for film thickness measurement since Kirk or Gohar [1,2] first works. The experimental assembly is today well defined and is based on a ball-on-disk device. Contact is established between a reflecting specimen of spherical or ellipsoidal shape (generally in steel) and a flat, transparent disk generally made of glass or sapphire. Contact is observed by reflection through a microscope. Fig. 1 illustrates the very basic optical phenomenon. Only two beam interferometry is shown, and the normal incident light is not respected for the clarty of the picture, even if it is experimentally verified. Light is divided into two parts on
Fig. 1. Interference fringes formation in two beam theory.
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the lower surface of the disk. One part is directly reflected towards the upper surface of the disk (intensity I1 ) while the other part goes throw the oil, is reflected on the ball surface and then turns back (intensity I2 ). Interference fringes are formed at the lubricant/disk interface, according to Newton’s experiment. These fringes are representative of the distance separating the two reflecting surfaces. As to illustrate this purpose, in the very simple case of monochromatic light, with the two beams interferometry assumption, if these beams are totally coherent, the total intensity emitted by the optical system is 4πnh −ϕ (1) I = I1 + I2 + I1 I2 cos λ This equation shows that the intensity I varies periodically with the thickness h, explaining √ Newton’s fringes formation. Defining fringe visibility as 2 I1 I2 /(I1 + I2 ), the visibility is maximum if I1 = I2 , thus, it is necessary to control the light division between the glass and the oil. Classically, a thin layer of chromium (10–20 nm) deposited onto the lower surface of the disc increases significantly the fringe contrast. But this equation has some strong limitations. When h is growing, the temporal coherence becomes partial, thus, the fringe visibility decreases and Eq. (1) is no more valid. Furthermore, fine adjustments of the optical set-up must be carefully done (alignment of elements, punctual light source) otherwise the general periodic shape could change. Last, this very simple equation is unsuitable for white light interferometry. Thus, it is beter to use this equation only for basic understanding. For a detailed description of the optimal conditions, the reader should refer to Foord [3] and for a complete theoretical study of interference fringes formation to Tolansky [4]. The complete description of the classical “handmade” procedure is out of purpose here and the reader should refer to Foord’s paper [3], but it seems useful to describe some aspects of these former works. With monochromatic light, contact appears under the pattern of dark and bright alternated fringes corresponding to the various fringe orders. With white light or multi-chromatic light, fringes are more numerous and present more different colours. In the first case (monochromatic light), a simple relationship can be used for the determination of the thickness. In the second one, there is no existing relationship and a calibration between colour and thickness must be performed from a static contact. Two difficulties of interferometry have to be outlined. Firstly, it is necessary to know the fringe order to determine the thickness, especially with monochromatic light. Secondly, the resolution of this method is limited by the capacity of a human eye to detect a luminosity or chromaticity variation. Let us retain that this original treatment of interferograms leads to a minimal thickness of 100 nm and to a height between two consecutive fringes of 40 nm. The analysis of more recent and more severe lubricated contacts makes these performances too much limited. Because the method is performed from point to point and be-
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cause the fringe order must be known, it appears to be inadequate for the study of strongly disturbed contacts, due to the presence of grease, roughness, dents etc. Furthermore, the poor resolution of the human eye makes this technique unsuccessful for the study of very thin films. 2.2. Spacer layer and spectrometer introduction The first great improvement of the method was the use of a SiO2 layer sputtered on the chromium coating, known as a “Spacer Layer” [5]. Its refractive index is very close to the oil’s one, thus everything happens as if a constant thickness was added to the oil film thickness. This facility overcame the first limitation concerning the minimum detectable thickness. In spite of the use of a wedged spacer layer to get round the second limitation, the best solution for years appeared to be the use of a spectrometer [6,7]. For a given point of the interferogram, the light is split into its spectral components: the more intense wavelength corresponds to a constructive fringe and the thickness can be deduced from it with a simple formula, if the fringe order is known. The technique associating these two advances, known as “Ultra Thin Interferometry” or UTI, allowed film thickness measurements from one to hundreds of nanometers, with an accuracy about 1 nm. It has permitted to obtain many interesting results in the domain of thin film lubrication. The reader should refer to one of the reviews recently published [8]. But by using this method, one can only measure film thickness at a given point or line in the contact. Thus, it does not permit a complete film thickness mapping as a full field technique may do. As a consequence, the minimum film thickness is not found, even if it is very important to check if surface damages can occur. Furthermore, this method is not adapted to rough surfaces. With the emergence of more efficient CCD cameras and faster computers, the idea of a computerised treatment of the interferograms rose. The following section describes the main evolutions brought by image analysis techniques. 2.3. Further improvements In 1994, Gustafsson [9] proposed a first advance based on white light interferometry. He proceeded by analogy with the handmade technique used until then. First of all, the ball and the disk, both motionless, are moved close together in order to obtain a punctual contact between the two solids. In these conditions, the initial shape of the surfaces gives the film thickness at every point of the interferogram. So it is possible to establish a calibration associating film thickness to a colorimetric parameter representative of the observed colour, for instance, the hue value H of the video representation system HSI. This value is a nonlinear combination of the physical parameters recorded by the 3CCD camera, which are the intensities collected through wide bandwidth filters centred on red, green and
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Fig. 2. Typical calibration in the HSI system.
blue colours. However, the calibration is not unambiguous as it is shown Fig. 2: in this figure, the “Hue” value is represented versus thickness. There are many different thicknesses corresponding to a given hue value. The choice of the “right” thickness is done by using the other parameters (S and I ) at a reference point. Then, film thickness is deduced step by step from this reference point. As in the case of the handmade treatment of white light interferograms, the calibration curve is established at ambient pressure, while film thickness measurements are performed under the actual contact pressure. Gustafsson used a classic correction based on Lorenz–Lorentz’s law (connecting refractive index and density) and Dowson–Higginson’s relationship (linking density and pressure) described for example by Foord [3]. Finally, this method allowed measurements from 100 to 700 nm with an uncertainty of some nanometers. In 1996, Cann [10] combined both this technique and the spacer layer, in order to perform measurements below 100 nm (Spacer Layer Imaging Method, SLIM). The same year, Luo [11] proposed a method based on monochromatic interferometry with green light (Relative Optical Interference Intensity, ROII). A simple optical relationship, based on a two beams interferometry model, allows one to determine the luminous intensity I as a function of the interface thickness h: 4πnh (2) +ϕ I = IA + IB cos λ Wavelength λ and refractive index n can be determined besides. Only the parameters IA , IB and the phase change ϕ, due to the metallic reflection on the chromium layer, remain unknown. Luo shows that they can be previously determined by measuring minimal and maximal intensities as well as intensity in the centre of a static contact. Then, the luminous intensity I can be measured everywhere within the dynamic contact. If an order of interference is defined, h can be calculated by inverting relation (2). With this method, the wavelength λ must be known with high accuracy, that supposes a narrow spectral band of the incidental light. Furthermore, it is necessary to take into account the lubricant refractive index variation with pressure. Luo [11] used the same classical correction than Gustafsson, or previously
Foord. This technique turned out to be successful for very thin film thicknesses, but it worked well only within the first interference order. Furthermore, as Foord [3] mentioned, collimation defects change the relationship between height and luminous intensity. Thus, the optical set-up becomes hard to adjust for a precise thickness evaluation using Eq. (2). These first works were unable to take into account a rough surface because the interference order was still badly mastered. Besides, handled information (hue or intensity) presents sensitivity defects connected to its oscillating character [12]. As an example, for the green component, the sensitivity of the luminous intensity versus film thickness is 3 nm by degree of intensity at 146 nm, while it drops to 0.5 nm by degree of intensity at 180 nm, intensities being coded over a usual arbitrary scale of 256 levels. That is why Hartl and then Molimard [13,14] proposed to generalise the systematic use of the three components characterising the light intensity for every pixel of a colour image. This method allows both the determination of the film thickness independently of the interference order [12] and the minimisation of the sensitivity defects. This method, known as “Differential Colorimetry” (DC), is presented in Fig. 3. As in the approach of Gustafsson, the optics laws are not explicitly used and the luminous intensities versus film thickness relationships are calibration curves. For that purpose, a static contact is normally loaded first (Fig. 3(a)). Hartl and Molimard suppose that the shape of this static contact is Hertzian, in order to determine the film height everywhere in the interferogram. An analytic solution can be calculated, assuming the two solids are elastic and semi-infinite. For a given distance r from the centre of the contact, the gap between the two solids h is h=
r2 a2 1 − + ∗ ∗ 2R R πR ∗ 2 2 a a a × 2a − r 2 arcsin 1− + r2 r r r (3)
As Eq. (3) shows, this process requires the experimental determination of the contact radius a and the curvature radius R ∗ . Then, calibration curves can be drawn, as represented in Fig. 3(c). Each curve is oscillating, but their frequencies are different, so the sensitivity defect is reduced. Moreover, it is possible to show that a given triplet of intensities leads to a unique thickness. In a second step, the evaluation of film thickness is carried out in a dynamic contact Fig. 3(b). The three chromatic values (R, G and B) are recorded for each point and compared to the calibration curve, leading to a complete thickness map (Fig. 3(d)). The operations described above give a film thickness without correction of the refractive index variation with pressure: finally, the same classical corrections as before are used. Later, Hartl and Molimard [15], as Cann did [10], used
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Fig. 3. Schematic view of the differential colorimetry process: (a) static contact, (b) dynamic contact, (c) calibration chart deduced from the static contact, (d) result of differential colorimetry for the dynamic contact.
a space layer to perform measurements down to some nanometers. But, if the majority of the published works use the Hertz theory to calculate the pressure field and the Lorenz–Lorentz law to correct the refractive index, Marklund proposed a more precise approach [16]. This work is based on Astrom’s previous findings [17], showing that the pressure can be evaluated from out-of-plane displacements (thus, film thickness). Marklund related the pressure calculation based on thickness field, the refractive index versus pressure variation and last the thickness versus refractive index relationship in an iterative procedure. Consequently, the pressure in the contact and the film thickness field are both evaluated simultaneously. The correction on film thickness reaches 10%. Such a solution, heavy to finalise and to use, seems very interesting for thick EHD film or dimple cases but for the thin film cases, the pressure field tends to the Hertzian shape, and Marklund approach is no longer useful. Very recently, Lord proposed a method called “MultiChannel Interferometry” (MCI) based on a trichromatic lighting [18]. The relationships between intensities and thickness are deduced from the two-beam interferometry theory (Eq. (2)). Thus, this promising method combines some advantages of DC (fringe order independence, favourable sensitivity) and of Luo’s approach (very thin film measurement without spacer layer). Furthermore, contrary to classical white light interferometry for which the fringe contrast is very quickly lost (beyond 1 µm), the use of three
narrow-band light sources ensure a good contrast for thicker films. Today, this method has not given its full capacities. The previous works were developed for elastohydrodynamic lubrication; independently, some similar works were realised on head/tape contacts. Based at first on interferograms obtained in monochromatic light, the technique developed by Lacey [19] used a semi-empirical formula connecting film thickness and luminous intensity. This formula takes into account the possibility to have an inhomogeneous lighting due to misalignment in the optical set-up. The necessity to determine the interference order and the optimisation of the sensitivity, which varies according to both the measured thickness and the incidental wavelength, incited to the use of three red, green and blue monochromatic lights [20]. Large deviations between measured film thicknesses using only a single monochromatic light (with a red, green or blue filter) and those stemming from the trichromatic process have been revealed. Performances of the film thickness measurement techniques have not been clearly underlined yet. This point is discussed here for the particular case of DC. Some experiments were performed with oils previously studied by ultra thin interferometry [15]. From one to hundreds of nanometers, no evident deviation could be mentioned. Dispersion of the results is almost constant in this range and is less than 3 nm. Nevertheless, these values must be taken with care considering possible experimental effects: linearity defects, local variations in the properties of the optical coatings, presence of surfaces defects, variation of the lubricant refractive
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index due to modifications within the lubricating film [21]. As to finish this description, the highest measurable thickness by differential colorimetry is about 800 nm and the spatial resolution is nearby 1 µm.
3. Some recent applications of DC in tribology Most of publications mentioned before were dedicated to the development of the measurement techniques. Although image analysis applications in elastohydrodynamic contacts were proposed first in 1994 [22], results directly interesting tribology have been multiplied since 1998. This section will develop some recent applications, mostly performed by the DC method, although other methods could be used (ROII, SLIM, MCI).
Fig. 4. Topography of the rough surface model.
3.1. Topographic analysis of a static contact DC allows the film thickness determination at every pixel. So, it becomes easier to study a complete surface and not only some isolated points. This facility is particularly useful to quantify the roughness behaviour under normal loading. First tests were realised by Tan [23] for a head on tape contact. Some original results are presented here as an illustration of potential studies that can be conducted using differential colorimetry. A periodic unidirectional model roughness is printed on a glass plate. It is a rectangular wave characterised by a peak-to-valley amplitude of 210 nm and a wavelength of 96 µm (Fig. 4). This ideal surface profile has been pressed against a ceramic ball at various loads. Reduced Young’s modulus and equivalent curvature radius are respectively E ∗ = 64.9 GPa and R ∗ = 12.7 mm. Estimated pressures for a smooth contact under the same conditions vary from 0 to 610 MPa. An example of a 3D visualization is given Fig. 5. In this case, we can see that the load is supported both by the upper parts of the roughness (dark rectangles in Fig. 5(a)) and by the lower parts which have grown up (dark ellipses in Fig. 5(a)). It is possible, with this basic geometry but also with more realistic surfaces, to quantify the roughness evolution when the normal load varies. In this example, the mean value of the transverse roughness falls from σRMS = 103 nm down to σRMS = 10 nm (white plots, Fig. 6) whereas the relative area of contact increases from 0% to 85% (dark plots, Fig. 6). Such a tool has naturally an interest among studies carrying on the plastic or elastic deformation of rough surfaces in a static contact case, as in our example, or in a dynamic one (lubrication) if the high speed recording of pictures is mastered. Therefore, it is a first step toward the study of rough elastohydrodynamic lubrication or that of the mixed lubrication regime which is developed in Section 3.4.
(a)
(b) Fig. 5. Interferogram (a) and a 3D visualization (b) of a rough model surface under normal load (w = 20.2 N).
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Fig. 6. Variation with load of the contact area and the RMS roughness in a rough static contact.
Fig. 7. Hc /Hmin comparison versus speed: Hamrock and Dowson model does not fit the experimental results for low speed (i.e. low thickness).
3.2. Study of elastohydrodynamic lubrication
tonian, with an exponential viscosity–pressure law; lubrication (regime) has to be isothermal and fully flooded; experimentally, the speed is restricted to avoid shear heating at the contact inlet, referring to a basic thermal model (Crook) and a thermal transducer is placed near the contact for a rough control. Last, the oil used is free of additives otherwise non Newtonian behaviour could appear if the thickness is lower than 100 nm. We have recorded central and minimum film thickness, and Fig. 7 shows the variation of the ratio hc / hmin versus rolling speed. In this experiment, central film thickness varies from 32 nm to 375 nm. If the speed and consequently the film thickness are low, the efficiency of Moes– Venner formula is obvious, compared to that of Hamrock and Dowson. The experimental points are quite dispersed mainly because the minimum film thickness is strongly dependent on noise.
The example presented in this paragraph concerns a study possible without the contribution of the image analysis techniques, such as differential colorimetry. In this case, DC appeared to be necessary by its user-friendliness and its accuracy, especially for the finding of the minimum film thickness. In the field of elastohydrodynamic lubrication, many equations describing the evolution of central and minimum film thickness with the contact conditions were proposed. The two most popular were proposed by Hamrock and Dowson in 1977 and by Nijenbanning, Moes and Venner in 1994. The Hamrock and Dowson equation has been the object of numerous experimental comparisons. On the other hand, the approach proposed by Nijenbanning et al. [24] has been the object of less interest and experimental examination. Krupka et al. did it in the case of point [25,26] or elliptic [27] contact. Central and minimal film thicknesses were measured for various conditions of load, speed and material. Image analysis, by authorising a faster and more precise film thickness evaluation, allowed to confirm that the ratio between central and minimal film thickness is more important than the one given by Hamrock and Dowson model. Practically, this means that the minimum film thickness is lower than expected by Hamrock and Dowson model, which might be dangerous for the contact life. We have reproduced for this paper one single experiment with a paraffinic base oil in order to illustrate our purpose. Operating conditions of the two formulas are strictly respected experimentally. First, the dimensionless parameters (G = 2069, W = 1.366·10−6 , from U = 2.854·10−12 to U = 6.388·10−11 ) are within the definition range of these formulas. The contact has to be in pure rolling conditions; experimentally, the slide to roll ratio is lower than 0.1%. The two surfaces are supposed to be smooth; in practice, the RMS composite roughness is 2 nm, with no orientation, consequently the minimum film height according to this parameter should be 6 nm or less if Johnson model is considered. Last point, the lubricant behaviour should be New-
3.3. Thin film lubrication The results obtained with the static contact presented in Section 3.1 gains from the particularly high spatial resolution due to the introduction of the image analysis process in the treatment of the interferograms. But minimum measurable film thickness is also reduced. Luo [28,29] and Hartl et al. [15,30] used image analysis to study the behaviour of lubricants when a very thin film thickness occurs. It is possible to show the transition between elastohydrodynamic lubrication and a regime of lubrication in which the chemical structure of the lubricant determines its thin film behaviour [30]. We present here the main results of a previous work. The response of a mineral base oil (η = 11.3 Pa·s, α = 16.7 Pa−1 ) and the one of the same base oil with additives (η = 12.4 Pa·s, α = 10.5 Pa−1 ) are presented respectively in Figs. 8(a), (b). The central (square) and minimum (triangle) film thickness is recorded versus speed and presented in a log-log graph. In the presence of additives, results show an inflection in the evolution of the film thickness versus speed in the domain of very thin thicknesses whereas for the pure based oil a power law is valid for any thickness.
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with Hmin . So, it is observed that Hc and Hmin converge towards a single film thickness value at low speed. Owing to image analysis coupled with differential colorimetry, it is therefore possible to show the presence of adsorbed layers in different points of the contact, thus over all the contact area. 3.4. Toward mixed lubrication regime
(a)
(b) Fig. 8. Thin film lubrication (50 ◦ C, 0.5 GPa): (a) mineral base oil, (b) mineral base oil + additives.
This power law (a straight line in a log-log graph) is typical of the elastohydrodynamic regime, as shown by both models introduced above (Section 3.2). Consequently, the difference between the experimental curve and a power law fitted for high thickness range is representative of physico-chemical influence in the contact behaviour. These results have been explained with the model proposed by Moore [31] who suggested that film thickness in the contact is generated both by a viscous contribution, in agreement with the classical EHD theory, and by an immobile layer that may adhere onto one (or both) surface. Moore attributed this immobile layer to the adsorption of lubricant molecules. Comparing the immobile layer thickness for various lubricants to molecule dimensions, we confirmed Moore’s model [30] rather than the “apparent viscosity model”, based on the assumption of a viscosity change for thin films [32]. Some results presented in this paper have been obtained in a domain where ultra thin interferometry [33] has been already employed, but the technique presented here also allows to measure easily and simultaneously the central and the minimal thicknesses in the contact (respectively Hc and Hmin ). In Fig. 8(b), we put in evidence that the change already observed in the centre of the contact is clearly visible
Sections 3.1 and 3.3 clearly underline that differential colorimetry (proposed by authors), but also spacer layer imaging method (Cann) or relative optical interference intensity (Luo) are able to measure a film thickness map with a good lateral resolution (about 1 µm), a high accuracy (few nanometers) and a low minimum measurable thickness even in rough contacts. Thus, these methods seem to be very efficient to the study the mixed lubrication regime. A first promising work on mixed lubrication was recently realised by Guangteng [34] with the SLIM. An additivefree poly-alpha-olefin has been used. As SLIM could not allow measurements under 10 nm, the limit lubrication regime could not be put in evidence on the roughness peaks. Nevertheless, three different types of roughness were used (single, 1D or 2D periodic bumps) for a very complete study of rough EHD, including slide to roll ratio variations, compliance evolution with speed, or micro-EHD evidence. This first trial shows that the study of mixed lubrication regime is possible with a more accurate image analysis technique such as DC or ROII, even if the limit lubrication regime was not reached on the roughness peaks yet. 3.5. Local pressure estimation within the contact area Image analysis of interferograms supplies numerical data, directly exploitable either for visualisation or for a further treatment. The mechanical analysis of an EHD contact is based on the simultaneous resolution of elasticity (deformation of solids) and Reynolds (thin film fluid mechanics) equations for a given rheological model. Film thickness in an EHD contact arises from the initial shape of solids, from the elastic strain of surfaces and from a translation due to the resulting hydrodynamic forces. So, it is possible to deduce the surface displacements from the film thickness found experimentally within a constant. Afterwards, application of the elasticity laws leads to the normal stress, as firstly shown by Aström [17]. The example developed in this paper shows the interest of such an analysis. We present here our first results using a novel algorithm based on the Fast Fourier Transform [35, 36]: Johnson demonstrated that a sinusoidal load applied on a semi-infinite body induces a sinusoidal displacement and that the amplitude of this displacement is proportional to the one of the load. Thus, after deducing the displacement field from the thickness field, and developing it in Fourier
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(b)
(c) Fig. 9. Analysis of a grease lubricated static contact: (a) interferogram, (b) measured film thickness, (c) calculated pressure.
series, the pressure can be easily reached in the frequency domain. A classical FFT algorithm has been used for the manipulations between the spectral and real spaces. A complete explanation of this method will be developed in a later communication [37]. This numerical approach is simpler to implement than the multigrid/multi-integration technique used by Aström [17], for a very reasonable calculation time. As an illustration, we study here a static contact between a glass disk and a stell ball lubricated with a complex lithium grease: the interferogram is reproduced in Fig. 9(a). Usually, the contact area corresponds to a grey circle, as Fig 5(a) shows. Here, the grey area is strongly reduced because of the presence of numerous soap particles. We can
deduce that these particles are transparent. So, assuming that their refractive index is close to that of the oil, it is possible to measure the film thickness map with DC (Fig. 9(b)). The transitions in thickness are marked, but there is no gap near the particles. So, our assumption on particles’ refractive index is realistic. Then, the pressure field is calculated (Fig. 9(c)) according to the method described above. Pressure engendered in this example is equal to 1.6 times the maximal pressure given by the Hertz theory in the case of a dry contact. This result is similar to Aström’s findings. This example shows the interest of our method: very localised and very intense pressure peaks occur because of the soap particles, voluntarily introduced in this case. So,
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the technique presented here allows to estimate engendered over-pressures and constitutes an interesting tool for the analysis of perturbed lubricated contacts particularly the mechanisms of surface degradation, either in the presence of wear, or in the case of solid pollution (dents). 3.6. Toward lubricant rheology Some authors pushed the inverse analysis farther down. The pressure calculation is only based on the elastic behaviour of contacting solids. Knowing film thickness and pressure fields, it may be possible then to deduce the flow properties of the lubricant by using the Reynolds equation. In particular, viscosity everywhere in the contact can be estimated. However, considering the measurement uncertainties, this parameter seems still difficult to reach [38] with confidence. On the other hand, the lubricant compressibility [39] and thus the variation of the refractive index with pressure could be estimated in satisfying numeric conditions. It should be underlined that these last two parameters change little with pressure, contrary to viscosity whose variation is exponential.
4. Conclusion After a brief review of existing methods devoted to film thickness measurements, this paper shows the advances that differential colorimetry has allowed in the field of the elastohydrodynamic lubrication. The help brought by the computerised analysis of interferograms has been underlined and various techniques and extensions were described and compared. As far as uncertainties are correctly mastered, the accessible film thicknesses in the contact cover a range between some nanometers and 800 nm, with a spatial resolution of the order of 1 µm. Applications of differential colorimetry performed in our laboratories were presented. They have been related to the main evolutions in the domains beyond EHD lubrication, and we have tried to identify two tendencies for further works: (1) The first one uses the high accuracy in the thickness evaluation and the full field capacity. It aims to understand phenomena governing mixed lubrication. It concerns the analysis of the thin film lubrication regime, with the determination of the height of adsorbed films, and the analysis of ideal rough lubricated contacts. (2) The second orientation involves the numerical exploitation of the film thickness fields, to calculate the pressure, for instance. This should be helpful for the analysis of surface degradation mechanisms. Even though his attempt failed, Ostensen [38] showed that contact mapping could lead to the knowledge, at the local scale, of the lubricant viscosity value.
Acknowledgements The work of the Czech part has been financially supported by the Grant Agency of the Czech Republic under grants Nos. 101/98/P105 and 101/98/P226. The work of the French part was carried out under the CPR “Mise en forme des matériaux: Contact métal-outillubrifiant” supported by CNRS, IRSID (USINOR), Pechiney Recherche, involving Paris Sud University (LMS), Collège de France (PMC), ECL (LTDS), INSA de Lyon (LMC), INPT (IMF), ENSMP (CEMEF), CNRS (SCA).
References [1] M.T. Kirk, Hydrodynamic lubrication of ‘perspex’, Nature 194 (1962) 965–966. [2] R. Gohar, A. Cameron, Optical measurement of oil film thickness under elastohydrodynamic lubrication, Nature 200 (1963) 458–459. [3] C.A. Foord, L.D. Wedeven, F.J. Westlake, A. Cameron, Optical elastohydrodynamics, Proc. Inst. Mech. Engrs. 184-1 (28) (1969– 1970) 487–505. [4] S. Tolansky, An Introduction to Interferometry, Longmans, London, 1955. [5] F.J. Westlake, A. Cameron, A study of ultra-thin lubricant films using an optical technique, Proc. Inst. Mech. Engrs. 182-3G (1967–1968) 75–78. [6] G.J. Johnston, R. Wayte, H.A. Spikes, The measurement and study of very thin lubricant films in concentrated contacts, Tribology Trans. 34 (2) (1991) 187–194. [7] J. Israelachvili, Thin films studies using multiple beam interferometry, J. Colloid Interface Sci. 44 (2) (1973) 259–272. [8] H. Spikes, Direct observation of boundary layers, Langmuir 12 (1996) 4567–4573. [9] L. Gustafsson, E. Hoglund, O. Marklund, Measuring lubricant film thickness with image analysis, Proc. Inst. Mech. Engrs. 208 (1994) 199–205. [10] P.M. Cann, H.A. Spikes, J. Hutchinson, The development of a spacer layer imaging method (SLIM) for mapping elastohydrodynamic contacts, Tribology Trans. 39 (4) (1996) 915–921. [11] J. Luo, S. Wen, P. Huang, Thin film lubrication, Part I: Study on the transition between EHD and thin film lubrication using a relative optical interference intensity technique, Wear 194 (1996) 107–115. [12] J. Molimard, Étude expérimentale du régime de lubrification en film mince, application aux fluides de laminage, Thèse de doctorat, INSA de Lyon, 1999, 199 p., n◦ 99 ISAL 0121 (in French). [13] M. Hartl, I. Krupka, M. Liska, Differential colorimetry: Tool for evaluation of the chromatic interference patterns, Opt. Eng. 36 (9) (1997) 2384–2391. [14] J. Molimard, M. Querry, P. Vergne, New tools for experimental study of EHD and limit lubrications, in: Proceedings of the 25th Leeds/Lyon Symposium on Tribology, Elsevier, Amsterdam, 1999, pp. 717–726. [15] M. Hartl, I. Krupka, R. Poliscuk, J. Molimard, M. Querry, P. Vergne, Thin film lubrication study by Colorimetric Interferometry, in: Proceedings of the 26th Leed/Lyon Symposium on Tribology, Elsevier, Amsterdam, 2000, pp. 695–704. [16] O. Marklund, L. Gustafsson, Correction for pressure dependence of the refractive index in the measurements of lubricant film thickness with image analysis, Proc. Inst. Mech. Engrs. J, J. Engrg. Tribology 213 (1999) 109–126. [17] H. Astrom, C.H. Venner, Soap-thickener induced local pressure fluctuations in a grease-lubricated elastohydrodynamic point contact, Proc. Inst. Mech. Engrs. Part J 208 (1994) 191–198.
J. Molimard et al. / Mécanique & Industries 3 (2002) 571–581
[18] J. Lord, O. Marklund, R. Larsson, Multi-Channel Interferometry for measurement of the thickness of very thin EHL lubricant films, in: Proceedings of the 26th Leeds/Lyon Symposium on Tribology, Elsevier, Amsterdam, 2000, pp. 711–717. [19] C. Lacey, F.E. Talke, Measurement and simulation of partial contact at the head/tape interface, J. Tribology 114 (October 1992) 646–652. [20] E. Baugh, J. Swenson, F.E. Talke, Simultaneous three-wavelength interferometry for head/tape spacing measurement, J. Tribology 120 (July 1998) 549–553. [21] S. Gunsel, H.A. Spikes, M. Aderin, In-situ measurement of ZDDP films in concentrated contacts, Tribology Trans. 36 (2) (1993) 276– 282. [22] E. Hoglund, EHL and the use of image analysis, Wear 179 (1994) 49– 56. [23] S. Tan, E. Baugh, F.E. Talke, Improved method for the measurement of asperity compliance of magnetic tapes, J. Tribology 121 (January 1999) 121–127. [24] G. Nijenbanning, C.H. Venner, H. Moes, Film thickness in elastohydrodynamically lubricated elliptic contacts, Wear 176 (1994) 217–229. [25] I. Krupka, M. Hartl, R. Poliscuk, M. Liska, Experimental study of the central and minimum elastohydrodynamic film thickness by colorimetric interferometry technique, Tribology Trans. 43 (4) (2000) 611–618. [26] I. Krupka, M. Hartl, R. Poliscuk, J. Cermak, M. Liska, Experimental evaluation of EHD film shape and its comparison with numerical solution, J. Tribology 122 (October 2000) 689–696. [27] I. Krupka, M. Hartl, R. Poliscuk, M. Liska, Experimental study of the central and minimum film thickness in elastohydrodynamic elliptic contacts, in: Proceedings of the 27th Leeds-Lyon Symposium on Tribology, Elsevier, Amsterdam, 2001 (to be published). [28] J. Luo, L. Qian, S. Wen L, Wen, L. Li, The failure of fluid film at nano-scale, Tribology Trans. 42 (4) (1999) 912–916.
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[29] J. Luo, P. Huang, S. Wen, L. Li, Characteristics of liquid lubricant films at the nano-scale, J. Tribology 121 (October 1999) 872–878. [30] M. Hartl, I. Krupka, R. Poliscuk, M. Liska, J. Molimard, M. Querry, P. Vergne, Thin film colorimetric interferometry, Tribology Trans. 44 (2) (2001) 270–276. [31] A.J. Moore, Nanometer elastohydrodynamic lubrication, in: Proceedings of the 25th Leeds/Lyon Symposium on Tribology, Elsevier, Amsterdam, 1997, pp. 57–67. [32] M. Smeeth, H.A. Spikes, S. Gunsel, The formation of viscous surface films by polymer solutions: Boundary or elastohydrodynamic lubrication?, Tribology Trans. 39 (3) (1996) 720–725. [33] G.J. Johnston, R. Wayte, H.A. Spikes, The measurement and study of very thin lubricant films in concentrated contacts, Tribology Trans. 34 (2) (1991) 187–194. [34] G. Guangteng, P.M. Cann, H.A. Spikes, Lubricant film thickness in rough surface, mixed elastohydrodynamic contact, J. Tribology 122 (2000) 65–76. [35] H.M. Stanley, T. Kato, A FFT-based method for rough surface contact, J. Tribology 119 (July 1997) 481–485. [36] K.L. Johnson, Contact Mechanics, Cambridge University Press, Cambridge, 1985. [37] J. Molimard, M. Querry, P. Vergne, M. Hartl, I. Krupka, Calculation of local pressure in point contacts from experimental interferogram analysis data, in: SEM Annual Meeting, Milwaukee, 2002 (accepted). [38] J.O. Ostensen, R. Larsson, C.H. Venner, Determination of viscosity and pressure in an elastohydrodynamic rolling contact by using optical interferometry: a theoretical study, Proc. Inst. Mech. Engrs. J, J. Engrg. Tribology 210 (1996) 259–268. [39] A. Jolkin, R. Larsson, Determination of lubricant compressibility in EHL conjunctions using the Hybrid Technique, in: Proceedings of the 26th Leeds/Lyon Symposium on Tribology, Elsevier, Amsterdam, 2000, pp. 589–596.