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Rheological response of fatty alcohols in sliding elastohydrodynamic contacts
Tribology International 49 (2012) 58–66
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Rheological response of fatty alcohols in sliding elastohydrodynamic contacts Kazuyuki Yagi a,n, Joichi Sugimura a, Philippe Vergne b a b
Department of Mechanical Engineering, Kyushu University, Japan Universite´ de Lyon, CNRS, INSA-Lyon, LaMCoS UMR5259, F-69621, Villeurbanne, France
a r t i c l e i n f o
a b s t r a c t
Article history: Received 27 September 2011 Received in revised form 15 December 2011 Accepted 26 December 2011 Available online 29 December 2011
In this study, the authors investigated the appearance of anomalous film shapes in highly sliding circular contacts when fatty alcohols such as 1-decanol, 1-dodecanol, and 1-tetradecanol were used as lubricants. The film thickness distribution between a steel ball and a glass disc was measured via whitelight optical interferometry. The experimental results revealed film thickening under high sliding conditions for all three fatty alcohols. It was observed that for 1-decanol, which has the lowest melting point, the thickened part of the film was the smallest; 1-tetradecanol, which has the highest melting point, produced the largest variation of the film shape. & 2011 Elsevier Ltd. All rights reserved.
Keywords: Elastohydrodynamic Film shape Solidification Rheology
1. Introduction The lubrication regime recognised as elastohydrodynamic (EHD) lubrication is found in non-conforming contacts of machine elements such as gears, rolling bearings, traction drives, and cam-follower systems. In the contact area operated under EHD conditions, the load is supported locally and the fluid pressure can increase up to or beyond 1 GPa. This significant pressure increase leads to an elastic deformation of the bounding surfaces that exceeds the film thickness in the contact area. The viscosity of the lubricant also increases drastically by the piezoviscous effect [1]. The thickness of the film formed under EHD conditions is nearly constant in the central zone of the contact, whereas some constriction occurs in the exit zone [2]. When a sliding motion takes place between the bounding surfaces, a high shear rate is imposed into the lubricant film during its passage through the contact area. This produces two significant effects on the pressurised film. First, heat is generated within the film because of viscous dissipation, which decreases the viscosity [3,4]. Second, non-Newtonian effects such as the shear thinning, visco-elastic behaviour, and elastic–plastic behaviour appear, depending on the operating conditions [5]. It has been widely recognised that both the shearing heat and the nonNewtonian effects influence the traction behaviour, whereas the film thickness and shape are believed to be less affected, as described in the literature on EHD research [6].
n
Corresponding author. E-mail address: [email protected] (K. Yagi).
0301-679X/$ - see front matter & 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.triboint.2011.12.012
Recently, the authors discovered the development of anomalous film shapes in EHD lubrication when using fatty alcohols such as lauric alcohol and pure 1-dodecanol as lubricants in circular contacts [7,8]. The film shape and overall thickness changed drastically with an increase in sliding speed at a fixed entrainment speed. In the present study, the development of such anomalous film shapes is investigated using other fatty alcohols such as 1-decanol and 1-tetradenanol, in addition to 1-dodecanol.
2. Background Under pure rolling conditions, the shape and thickness of the EHD lubricant film can be quantitatively estimated by considering only the flow in the inlet zone on the basis of a Newtonian model. Grubin [9] considered only the piezoviscous effect of the fluid and the elastic deformation of the bounding surfaces in the inlet zone. In his model, it was assumed that the two surfaces were separated by a lubricant film of constant thickness, and that they were elastically deformed according the Hertzian theory. Using the film thickness profile obtained on the basis of these assumptions, the flow in the inlet zone was then calculated considering the piezoviscous effect. Although his approach was rather simple, the film thickness equation thus derived was remarkably consistent with safety operation of gear teeth. Later, Dowson and Higginson [10] succeeded in obtaining a full numerical solution of the Reynolds equation for line contacts incorporating the piezoviscous effect and the elastic deformation of the two surfaces. Their full numerical solution indicates that the lubricant film thickness is uniform in most of the central contact area, and that a constriction occurs only at the contact exit. The distribution
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of film thickness is close to the assumed uniform film shape proposed in Grubin’s model, except for the constriction. In other words, the central film thicknesses equation [11] proposed on the basis of the full numerical simulation is more accurate than Grubin’s equation; however, both are essentially similar. Under rolling and sliding conditions, shear heating and nonNewtonian effects are pronounced within the contact area where the lubricant is pressurised to the order of gigapascals. It is widely accepted that the non-Newtonian and heating effects influence the traction behaviour in EHD contacts [3–5]. On the other hand, the influence of these effects on film thickness has not been investigated in detail because Grubin’s work [9] has influenced subsequent studies on the central film thickness, with an emphasis on flow in the inlet zone [12–15]. However, two supplementary mechanisms that affect lubricant film thickness and shape in EHD contacts under sliding conditions, i.e., shear heating and non-Newtonian effects, have been reported. The shear heating occurring in the contact area produces a complex temperature distribution in the film under high sliding conditions. The thermal conditions of the two sliding surfaces are significantly different in such systems due to the difference in relative speed, even if the materials of the bounding surfaces are the same. As a result, the temperature distribution produced in the lubricant film becomes asymmetrical, resulting in the appearance of viscosity gradients across the film. Cameron [16] referred to the changes in Couette flow owing to viscosity gradients recognised as the ‘viscosity wedge’ action, which Yagi et al. [17] subsequently showed to be responsible for a significant drop in film thickness under rolling and sliding conditions compared with that obtained under pure rolling conditions. Anomalous film shapes have also been discovered in glass–steel contacts [18] and under oppositely sliding conditions [19]. Non-Newtonian effects on film thickness include those observed by Chiu and Sibley [20], who found that a conical depression developed in circular contacts using high-viscosity polybutene as the lubricant when entrainments speeds were lower than 1 mm/s (i.e. negligible heat generation). More recently, Guo and Wong [21,22] observed similar effects using several types of polybutene and explained this phenomenon schematically using a limiting shear stress model [23]. Recently, the authors discovered the development of another anomalous film shape in circular contacts when using lauric alcohol and pure 1-dodecanol as the lubricant [7,8]. Under pure rolling conditions, the lubricant film developed a conventional shape with a zone of uniform film thickness at the centre of the contact and a constriction at the exit. Increasing the sliding speed at a fixed entrainment speed resulted in a gradual increase in the film thickness at moderate slide-to-roll ratios. Under conditions close to simple sliding where one surface remained stationary, the film became thinner around the exit zone, coincident with the zone of constriction under pure rolling. An estimate of the increase in temperature of both the oil film and the surfaces by a simple calculation using measured traction coeffficients revealed an average increase in the contact close to 20 K. This low temperature rise indicates that the appearance of the anomalous film shape cannot be explained by the viscosity wedge action. On the other hand, given the relatively high melting point of 1-dodecanol (24 1C) at ambient pressure and its proximity to the operating temperature of 40 1C, it is considered that the anomalous film shape may have been produced by solidification of the pressurised film in the contact area. If such a phase change is responsible for the anomalous change in film shape, the degree of change can be expected to be higher for lubricants with higher melting points. In the present study, the influence of lubricant melting point on the appearance of anomalous film shape is investigated by conducting experiments using three fatty alcohols with different melting points.
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3. Experimental procedure Experiments were conducted using a ball-on-disc apparatus as shown schematically in Fig. 1. The set-up puts into contact a steel (SUJ2, equivalent to AISI 52100) ball with a diameter of 25.4 mm and an optically flat BK7 glass disc with a diameter of 80 mm and a thickness of 10 mm. The composite root mean square (RMS) roughness of both surfaces was approximately 3 nm. The properties of the steel and glass are listed in Table 1. The contact side of the glass disc was coated with a thin semi-reflective layer of chromium to augment the contrast of the interferograms recorded during the experiments. The moving assembly was set in a temperature-controlled chamber partially filled with the lubricant, and lubricant was supplied to the contact area by the partially immersed rotating ball. The moving parts were driven independently using AC servo motors at prescribed rolling and sliding conditions. Traction forces and normal load were recorded using a gimbal mechanism. Molecular diagrams of the three fatty alcohols tested in the present study (1-decanol, 1-dodecanol and 1-tetradecanol) are shown in Fig. 2, and the melting points are listed in Table 2. Fig. 3 shows the variation in viscosity of these fatty alcohols with temperature under ambient pressure. Lubricant film thickness in the contact area was measured by white-light interferometry, as described in detail elsewhere [8]. White light delivered via a microscope mounted above the test rig was reflected at both the glass/chromium and fluid/steel interfaces and recorded by a high-speed digital camera attached to the microscope. The red–green–blue (RGB) intensities for each pixel
Objective lens
Glass disc
Chromium layer
Lubricant
Steel ball
Fig. 1. Schematic diagram of ball-on-disc test rig.
Table 1 Properties of ball and disc. Properties
Steel
Glass
Young’s modulus (GPa) Poisson’s ratio Density (kg/m3) Thermal conductivity (W/mK) Specific heat (J/kg K)
210 0.3 7850 46 470
81 0.208 2510 1.11 840
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All tests were conducted under negative slide-to-roll ratios (S) at a fixed entrainment speed (um) of 1.8 m/s. S is expressed as follows. S¼
ub ud : um
ð1Þ
where ub and ud are the speeds of the ball and disc surfaces, and um is defined as um ¼(ub þud)/2.
4. Results
Fig. 2. Molecular structures of (a) 1-decanol, (b) 1-dodecanol, and (c) 1-tetradecanol.
Table 2 Melting points of fatty alcohols. Lubricant
Chemical formula
Melting point
1-decanol 1-dodecanol 1-tetradecanol
C10H22O C12H26O C14H30O
7 1C 24 1C 38 1C
15 1-tetradecanol
viscosity (mPas)
12
1-dodecanol 9
6
1-decanol
3
0 20
40
60 temperature (°C)
80
100
Fig. 3. Viscosity of fatty alcohols as a function of temperature.
were converted into film thickness using a calibration table constructed in advance from a static contact. The experimental protocol was as follows. The steel ball, glass disc, chamber, and other parts of the rig that could come into contact with the lubricant during the tests were cleaned in an ultrasonic bath filled with heptane for 20 min followed by acetone for the same period. After cleaning and prior to each experiment, interference images were recorded on a static contact for film thickness calibration. Four images were stored at each operating condition to check the repeatability of the interferograms.
Fig. 4 shows the optical interferograms of the film obtained for the three lubricant at various slide-to-roll ratios under conditions of fixed entrainment speed and contact pressure. The inlet temperature was adjusted such that the central film thickness matched that obtained under pure rolling conditions. The viscosities of the three lubricants under these conditions have similar values, 10.8 mPa s for 1-decanol (at 27 1C), 9.6 mPa s for 1-dodecanol (at 40 1C), and 11.0 mPa s for 1-tetradecanol (at 45 1C). For 1-dodecanol, the pressure–viscosity coefficient is 8.6 GPa 1 according to the curve-fitting results from central film thickness measurements conducted under pure rolling conditions [8]. The pressure– viscosity coefficients of 1-decanol and 1-tetradecanol are 7.3 GPa 1 (at 27 1C) and 7.1 GPa 1 (at 45 1C) according to the film thickness equation [11]. The present experiments showed that the development of film shape under rolling and sliding conditions is dependent on the chain length of the fatty alcohol. The film thicknesses of all three lubricants under pure rolling, however, were identical. For 1-decanol, the colour of the optical interferograms became orange in a limited region immediately upstream of the exit zone at S¼ 40%, and the orange colouration remained at the same location with further increases in S. At S¼ 180%, however, the shape of the changed colour was unstably changed during the test. The unstable change in film shape may be attributed to small vibration of the spindles during the test. For 1-dodecanol, as reported in previous studies [7,8], the colour changed from S¼0 to S¼–150%, indicating an increase in film thickness in the central part of the contact, with the colour variation moving towards the inlet zone. For 1-tetradecanol, the variation in colour was more prominent than for the other two lubricants. At S¼ 40%, the thickness of the entire film increases at the leading side as well as at the centre. In contrast, the film thickness in the inlet zone did not increase for the other two fatty alcohols. From S¼ 70% to 150%, the colour changed dramatically in all areas except in the constriction zone. At S¼ 180%, the zone of colour change moved towards the inlet zone and the black region in the exit zone expanded over the entire contact area. Fig. 5 shows the film thickness profiles on the central line in the sliding direction as converted from the optical interferograms presented in Fig. 4. As expected, the film thickness profiles of all three fatty alcohols are almost identical under pure rolling conditions. Under sliding conditions, however, differences become apparent among these three lubricants. At S¼ 70%, it can be seen that film thickening becomes more pronounced as the chain length of the fatty alcohol increases. For 1-tetradecanol, the film thickness reached around 200 nm in the inlet zone, and the region of uniform film thickness extended into the usual constriction zone. For 1-dodecanol, the film thickness was about 150 nm in the inlet zone and was the same as that at S¼0, increasing to 200 nm in the contact area. For 1-decanol, the film profile is the same as that at S¼0 at the inlet zone. The film thickness increases locally to about 170 nm immediately adjacent to the constriction zone. At S¼ 100%, for 1-tetradecanol, the film thickness in the inlet zone remains the same as at S¼ 70%, but increases locally near
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S = 0%
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S = 0%
S = -40%
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S = -150%
S = -180%
S = 0%
S = -40%
S = -70%
S = -100%
S = -120%
S = -150%
S = -180%
Fig. 4. Optical interferograms for various slide-to-roll ratios at an entrainment speed of 1.8 m/s and a maximum Hertzian pressure of 0.52 GPa for (a) 1-decanol (27 1C), (b) 1-dodecanol (40 1C), and (c) 1-tetradecanol (45 1C).
the contact to 290 nm. For 1-dodecanol and 1-decanol, the films are slightly thicker than at S¼ 70%. At S ¼ 150%, the 1-tetradecanol film thickness reaches almost 400 nm. The thickness of the 1-dodecanol film is similar, but the region of the uniform film thickness around the centre is smaller than for 1-tetradecanol. At S¼ 180%, the film thickness drops markedly for 1-tetradecanol and the thin film zone expands over the entire contact area. For 1-dodecanol, the film remains thick on the inlet side of the contact, reaching a maximum film thickness of about 800 nm. For 1-decanol, the film thickness was unstable during the tests, but was of the order of 100 nm. The influence of applied load is shown for 1-docecanol under various slide-to-roll ratios in Fig. 6. In pure rolling, as expected, it can be seen that the film shape develops according to the classical pattern with a uniform film in the central contact region and a constriction shape in the exit zone. With increasing slide-to-roll ratio, the colour of the optical interferograms changes gradually. At S¼ 180%, the region of colour change moves towards the inlet zone, while the black-colour region, corresponding to a film thickness of less than 100 nm, expands over the exit zone. The most important observation in Fig. 6 is that the film thickness is not significantly sensitive to the applied load. In pure rolling, the contact area expands but the film thickness and shape remain relatively unchanged with an increasing load. Under rolling and sliding conditions, the colour in the central contact region remains the same with an increasing load, while the contact area increases. Fig. 7 shows the influence of applied load for 1-tetradecanol. The inlet temperature was set at 45 1C to afford the same film thickness under pure rolling conditions as observed for 1-dodecanol at S ¼0. The variations in film thickness with the slide-toroll ratio for 1-tetradecanol appears largely similar to that for 1-dodecanol: a change in colour in the central region occurs when S is increased, and the region of film thinning in the exit zone
expands at S¼ 180%. As the applied normal load is increased, the film thickness varies while the film shape remains unchanged. At S ¼0 and 40%, the film thickness decreases slightly with an increasing applied load. Under moderate sliding conditions, from S ¼ 70% to 120%, the change in colour is more pronounced on the leading side of the central contact area for phmax ¼0.3 and 0.4 GPa, whereas the colour becomes more uniform at phmax ¼0.52 GPa. These colour variations indicate that the film thickness increases with the applied load. Under high sliding conditions, from S¼ 150% to 180%, the change in colour with an increasing load is almost undetectable. Fig. 8 shows the influence of the inlet temperature on the film shape for 1-dodecanol under constant entrainment speed (1.8 m/s) and the maximum Hertzian pressure (0.52 GPa), and Fig. 9 shows the corresponding film thickness profiles on the central line along the sliding direction. In the case of S ¼0, the central film thickness is 220 nm at 27 1C and 110 nm at 40 1C. It can be observed from Fig. 8 that the film shape follows the same trend in terms of film thickness distribution as a function of the slide-to-roll ratio for both temperatures. According to the film thickness profiles shown in Fig. 9, it can be deduced that the thickness at 27 1C increases more at the inlet zone as well as at the centre with increasing slide-to-roll ratio in comparison with that at 40 1C. From S¼0 to 150%, the entire film thickness increases with increasing inlet temperature. At S¼ 180%, the maximum film thickness reaches 900 nm at 27 1C and is greater than that at 40 1C, while the minimum film thicknesses are almost the same (100 nm) at all temperatures.
5. Discussion The anomalous EHD lubricant film shape originally observed for 1-dodecanol was also observed for 1-decanol and 1-tetradecanol in the present study. It is found that the film shape was dependent on
K. Yagi et al. / Tribology International 49 (2012) 58–66
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Fig. 5. Film thickness profiles on the contact central line converted from the optical interferograms in Fig. 4 for slide-to-roll ratios of (a) 0, (b) 70%, (c) 100%, (d) 150%, and (e) 180%.
both the operating conditions and the chain length of the fatty alcohol. For the three fatty alcohols with different melting points tested in the present study, the film thickness increased in the contact area with increasing slide-to-roll ratio at a fixed entrainment speed. For 1-decanol, having the lowest melting point, the
region of thickening with increasing slide-to-roll ratio was the smallest among these three lubricants and was located just upstream of the exit zone (Fig. 4). For 1-tetradecanol, having the highest melting point, the variation in film shape was the most pronounced. The film thickness increased at the inlet zone as well
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63
S = 0%
S = -40%
S = -70%
S = -100%
S = -120%
S = -150%
S = -180%
S = 0%
S = -40%
S = -70%
S = -100%
S = -120%
S = -150%
S = -180%
S = 0%
S = -40%
S = -70%
S = -100%
S = -120%
S = -150%
S = -180%
Fig. 6. Influence of applied load on film shape for 1-dodecanol at an entrainment speed of 1.8 m/s and a temperature of 40 1C: (a) 0.3 GPa, (b) 0.4 GPa, and (c) 0.52 GPa.
S = 0%
S = -40%
S = -70%
S = -100%
S = -120%
S = -150%
S = -180%
S = 0%
S = -40%
S = -70%
S = -100%
S = -120%
S = -150%
S = -180%
S = 0%
S = -40%
S = -70%
S = -100%
S = -120%
S = -150%
S = -180%
Fig. 7. Influence of applied load on film shape for 1-tetradecanol at an entrainment speed of 1.8 m/s and a temperature of 45 1C: (a) 0.3 GPa, (b) 0.4 GPa, and (c) 0.52 GPa.
as at the centre (Fig. 5). With increasing applied load, the film thickness increased at moderate slide-to-roll ratios for 1-tetradecanol (Fig. 7), whereas the film thickness remained largely unchanged for 1-dodecanol under the same conditions (Fig. 6).
In a previous paper [8], the authors discussed the mechanism of development of this anomalous film shape for 1-dodecanol and they concluded that this behaviour could be attributed to the solidification of the lubricant as a result of phase change. The anomalous film shapes observed in the present study also appear
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S = 0%
S = -40%
S = -70%
S = -100%
S = -120%
S = -150%
S = -180%
S = 0%
S = -40%
S = -70%
S = -100%
S = -120%
S = -150%
S = -180%
Fig. 8. Influence of inlet temperature on film shape for 1-dodecanol at an entrainment speed of 1.8 m/s and an Hertzian pressure of 0.52 GPa: (a) 27 1C and (b) 40 1C.
to support the solidification hypothesis. The melting point of fatty alcohols increases with chain length, as indicated in Table 2. The fatty alcohol with the highest melting point tested in the present study, 1-tetradecanol (38 1C), showed the most remarkable anomalous film shapes. The difference between the melting temperature and the inlet temperature (45 1C) was the lowest for this alcohol among those tested, and thus would have most easily undergone solidification. As shown in Fig. 5, the film thickness increased in the inlet zone even at moderate slide-to-roll ratios for 1-tetradecanol whereas the film profile at the inlet zone did not change at moderate slide-to-roll ratios for 1-dodecanol and 1-decanol. This may imply that the lubricant has already been solidified at the inlet zone for 1-tetradecanol. At high slide-to-roll ratios, the region of film thickening moved towards the inlet zone for 1-dodecanol and disappeared for 1-tetradecanol. These observations suggest that the solidified lubricant at the inlet zone may result in lubricant starvation. Generally, the melting point is expected to increase with pressure and thus it is possible that the lubricant could solidify in the inlet zone and/or in the central contact zone. However, the influence of pressure on the melting point was not the focus of the current work. The flow of solidified lubricant should be different from that of a viscous fluid. Under pure rolling conditions, the lubricant solidified can flow through the contact area. Therefore, the film thickness distributions in pure rolling for all alcohols have the commonly accepted shape with flat centre and outlet constriction. Under rolling and sliding conditions, the lubricant is subjected to high shear stress, which causes slippage to change the Couette flow along the sliding direction. As a result, such anomalous film shapes are produced so that the continuity of the flow should be satisfied. Three relevant slippage mechanisms have been proposed. Smith [23] stated that solidified lubricant slips at the interface between the viscous fluid because of heat generation. Slippage could also occur between the solidified lubricant and the sliding surfaces as suggested by Ehret et al. [24]. Stahl and Jacobson [25] and Zhang and Wen [26] introduced a wall slip model related to the limiting shear stress of the lubricant. Ehret et al. [24] reported the occurrence of a thickened part in the film thickness distribution based on a plug flow model. Zhang and Wen [26] showed a local film thickening in the inlet zone followed by a gradient in the film thickness. Bair and McCabe [27], on the other hand, captured pictures of shear bands within pressurised lubricants and suggested a third mechanism
by which mechanical shear bands occur within the solidified film. The film shapes reported and discussed in the present study, however, do not show why and how the Couette flow changes, which is dominant in the contact area, explored by Bair and McCabe [27]. The appearance of anomalous film shape in this present study can be qualitatively explained as due to lubricant solidification phenomena. However, some unresolved points still remain, such as the effect of the lubricant nature, the relationship between the melting point and pressure, and the transient features of lubricant solidification during its passing through the contact area in less than 1 ms. Further study is needed to investigate the mechanism of the anomalous film shape.
6. Conclusions In the present study, the authors investigated the development of anomalous lubricant film thickness shapes in glass–steel contacts under rolling and sliding conditions when fatty alcohols were used as lubricants. From the results and discussion presented above, the following conclusions can be drawn: 1) When the lubricant melting point is high, the anomalous film shape appears remarkably under rolling and sliding conditions. For 1-decanol, which has the lowest melting point among the three fatty alcohols tested, the thickened part of the film appears around the contact centre. For 1-tetradecanol, which has the highest melting point, the thickened part of the film is the thickest. For 1-dodecanol, which melting point value is in-between the previous ones, the thickness is intermediate. 2) At moderate slide-to-roll ratios, the film thickness increases at the inlet zone as well as at the contact centre with increasing the melting point of the lubricant. For 1-decanol, the film thickness at the inlet zone does not change with increasing the slide-to-roll ratio. For 1-tetradecanol, the thickness increases at the inlet zone as well as at the central zone. For 1-dodecanol, the film thickness profile at the inlet zone does not change but increases when the ambient temperature decreases. 3) At high slide-to-roll ratios, the thickened part of the film moves towards the inlet zone when the melting point of
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Fig. 9. Film thickness profiles on the contact central line converted from the optical interferograms in Fig. 7 for slide-to-roll ratios of (a) 0, (b) 70%, (c) 100%, (d) 150%, and (e) 180%.
lubricant is high. For 1-decanol, the thickened part is kept around the centre. For 1-dodecanol and 1-tetradecanol, the thickened part moves towards the inlet zone while the thin film expands over the trailing side of the contact area. For 1-tetradecanol, this tendency is strongest.
4) The appearance of the anomalous film shapes for lubricants with high melting points suggests that the lubricant is solidified under high pressure, and the high shear stress causes slippage of the lubricant to give rise to the anomalous behaviour.
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Acknowledgement The current study was conducted with the financial support of the Japan Society for the Promotion of Science (JSPS) via a Grantin-Aid for Young Scientists (B) (no. 19760102). References [1] Bridgman PW. Viscosities to 30,000 kg/cm2. Proceedings of the American Academy 1949;77:117–28. [2] Gohar R, Cameron A. Optical measurement of oil film thickness under elastohydrodynamic lubrication. Nature 1963;200:458–9. [3] Crook AW. The lubrication rollers III. A theoretical discussion of friction and the temperatures in the oil film. Philosophical Transactions of the Royal Society London Series A 1961;254:237–58. [4] Cheng HS, Sternlicht B. A numerical solution for the pressure, temperature and film thickness between two infinitely long, lubricated rolling and sliding cylinders, under heavy loads. Transactions of ASME Journal of Basic Engineering 1965;87:695–707. [5] Evans CR, Johnson KL. Regimes of traction in elastohydrodynamic lubrication. Proceedings of the Institution of Mechanical Engineering Part C 1986;200: 313–24. [6] Spikes HA. Sixty years of EHL. Lubrication Science 2006;18:265–91. [7] Yagi K, Vergne P. Film thickness changes in EHD sliding contacts lubricated by a fatty alcohol. Tribology Online 2006;1:5–8. [8] Yagi K, Vergne P. Abnormal film shapes in sliding elastohydrodynamic contacts lubricated by fatty alcohols. Proceedings of the Institution of Mechanical Engineers Part J 2007;221:287–300. [9] Grubin AN. Investigation of the contact of machine components. In: Ketova KhF, editor. Moscow: Central Scientific Research Institute for Technology and Mechanical Engineers; 1949. p. 30. (DSIR translation 337). [10] Dowson D, Higginson GR. A numerical solution to the elastohydrodynamic problem. Journal of Mechanical Engineering Science 1959;1:6–15. [11] Dowson D. Elastohydrodynamic. Proceedings of the Institution of Mechanical Engineers 1968;182:151–67. [12] Gecim B, Winer WO. Lubricant limiting shear stress effect on EHD film thickness. Transactions of ASME Journal of Lubrication Technology 1979;101: 258–265.
[13] Greenwood JA, Kauzlarich JJ. Inlet shear heating in elastohydrodynamic lubrication. Transactions of ASME Journal of Lubrication Technology 1973;95:417–26. [14] Wilson WRD, Sheu S. Effect of inlet shear heating due to sliding on elastohydrodynamic film thickness. Transactions of ASME Journal of Lubrication Technology 1983;105:187–8. [15] Salehizadeh H, Saka N. Thermal non-Newtonian elastohydrodynamic lubrication of rolling line contacts. Transactions of ASME Journal of Tribology 1991;113:481–91. [16] Cameron A. The viscosity wedge. ASLE Transactions 1958;1:248–53. [17] Yagi K, Kyogoku K, Nakahara T. Experimental investigation of effects of slip ratio on elastohydrodynamic lubrication film related to temperature distribution in oil films. Proceedings of the Institution of Mechanical Engineers Part J: Journal of Engineering Tribology 2006;220:353–63. [18] Kaneta M, Nishikawa H, Kanada T, Matsuda K. Abnormal phenomena appearing in EHL contacts. Transactions of ASME Journal of Tribology 1996;118:886–92. [19] Yagi K, Kyogoku K, Nakahara T. Relationship between temperature distribution in EHL film and dimple formation. Transactions of ASME Journal of Tribology 2005;127:658–65. [20] Chiu YP, Sibley LB. Contact shape and non-Newtonian effects in elastohydrodynamic point contacts. Lubrication Engineering 1972;28: 48–60. [21] Guo F, Wong PL. Experimental observation of a dimple-wedge elastohydrodynamic lubricating film. Tribology International 2004;37:119–27. [22] Guo F, Wong PL. An anomalous elastohydrodynamic lubrication film: Inlet dimple. Transactions of ASME Journal of Tribology 2005;127:425–34. [23] Smith FW. Lubricant behaviour in concentrated contact systems — the castor oil-steel system. Wear 1959;2(4):250–63. [24] Ehret P, Dowson D, Taylor CM. On lubricant transport conditions in elastohydrodynamic conjunctions. Proceedings of the Royal Society of London Series A 1998;454:763–87. [25] Stahl J, Jacobson BO. A lubricant model considering wall-slip in EHL line contacts. Transactions of ASME Journal of Tribology 2003;125:523–32. [26] Zhang YB, Wen S. An analysis of elastohydrodynamic lubrication with limiting shear stress: part I—theory and solutions. Tribology Transactions 2002;45:135–44. [27] Bair S, McCabe C. A study of mechanical shear bands in liquids at high pressure. Tribology International 2004;37(10):783–9.
Contents lists available at SciVerse ScienceDirect
Tribology International journal homepage: www.elsevier.com/locate/triboint
Rheological response of fatty alcohols in sliding elastohydrodynamic contacts Kazuyuki Yagi a,n, Joichi Sugimura a, Philippe Vergne b a b
Department of Mechanical Engineering, Kyushu University, Japan Universite´ de Lyon, CNRS, INSA-Lyon, LaMCoS UMR5259, F-69621, Villeurbanne, France
a r t i c l e i n f o
a b s t r a c t
Article history: Received 27 September 2011 Received in revised form 15 December 2011 Accepted 26 December 2011 Available online 29 December 2011
In this study, the authors investigated the appearance of anomalous film shapes in highly sliding circular contacts when fatty alcohols such as 1-decanol, 1-dodecanol, and 1-tetradecanol were used as lubricants. The film thickness distribution between a steel ball and a glass disc was measured via whitelight optical interferometry. The experimental results revealed film thickening under high sliding conditions for all three fatty alcohols. It was observed that for 1-decanol, which has the lowest melting point, the thickened part of the film was the smallest; 1-tetradecanol, which has the highest melting point, produced the largest variation of the film shape. & 2011 Elsevier Ltd. All rights reserved.
Keywords: Elastohydrodynamic Film shape Solidification Rheology
1. Introduction The lubrication regime recognised as elastohydrodynamic (EHD) lubrication is found in non-conforming contacts of machine elements such as gears, rolling bearings, traction drives, and cam-follower systems. In the contact area operated under EHD conditions, the load is supported locally and the fluid pressure can increase up to or beyond 1 GPa. This significant pressure increase leads to an elastic deformation of the bounding surfaces that exceeds the film thickness in the contact area. The viscosity of the lubricant also increases drastically by the piezoviscous effect [1]. The thickness of the film formed under EHD conditions is nearly constant in the central zone of the contact, whereas some constriction occurs in the exit zone [2]. When a sliding motion takes place between the bounding surfaces, a high shear rate is imposed into the lubricant film during its passage through the contact area. This produces two significant effects on the pressurised film. First, heat is generated within the film because of viscous dissipation, which decreases the viscosity [3,4]. Second, non-Newtonian effects such as the shear thinning, visco-elastic behaviour, and elastic–plastic behaviour appear, depending on the operating conditions [5]. It has been widely recognised that both the shearing heat and the nonNewtonian effects influence the traction behaviour, whereas the film thickness and shape are believed to be less affected, as described in the literature on EHD research [6].
n
Corresponding author. E-mail address: [email protected] (K. Yagi).
0301-679X/$ - see front matter & 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.triboint.2011.12.012
Recently, the authors discovered the development of anomalous film shapes in EHD lubrication when using fatty alcohols such as lauric alcohol and pure 1-dodecanol as lubricants in circular contacts [7,8]. The film shape and overall thickness changed drastically with an increase in sliding speed at a fixed entrainment speed. In the present study, the development of such anomalous film shapes is investigated using other fatty alcohols such as 1-decanol and 1-tetradenanol, in addition to 1-dodecanol.
2. Background Under pure rolling conditions, the shape and thickness of the EHD lubricant film can be quantitatively estimated by considering only the flow in the inlet zone on the basis of a Newtonian model. Grubin [9] considered only the piezoviscous effect of the fluid and the elastic deformation of the bounding surfaces in the inlet zone. In his model, it was assumed that the two surfaces were separated by a lubricant film of constant thickness, and that they were elastically deformed according the Hertzian theory. Using the film thickness profile obtained on the basis of these assumptions, the flow in the inlet zone was then calculated considering the piezoviscous effect. Although his approach was rather simple, the film thickness equation thus derived was remarkably consistent with safety operation of gear teeth. Later, Dowson and Higginson [10] succeeded in obtaining a full numerical solution of the Reynolds equation for line contacts incorporating the piezoviscous effect and the elastic deformation of the two surfaces. Their full numerical solution indicates that the lubricant film thickness is uniform in most of the central contact area, and that a constriction occurs only at the contact exit. The distribution
K. Yagi et al. / Tribology International 49 (2012) 58–66
of film thickness is close to the assumed uniform film shape proposed in Grubin’s model, except for the constriction. In other words, the central film thicknesses equation [11] proposed on the basis of the full numerical simulation is more accurate than Grubin’s equation; however, both are essentially similar. Under rolling and sliding conditions, shear heating and nonNewtonian effects are pronounced within the contact area where the lubricant is pressurised to the order of gigapascals. It is widely accepted that the non-Newtonian and heating effects influence the traction behaviour in EHD contacts [3–5]. On the other hand, the influence of these effects on film thickness has not been investigated in detail because Grubin’s work [9] has influenced subsequent studies on the central film thickness, with an emphasis on flow in the inlet zone [12–15]. However, two supplementary mechanisms that affect lubricant film thickness and shape in EHD contacts under sliding conditions, i.e., shear heating and non-Newtonian effects, have been reported. The shear heating occurring in the contact area produces a complex temperature distribution in the film under high sliding conditions. The thermal conditions of the two sliding surfaces are significantly different in such systems due to the difference in relative speed, even if the materials of the bounding surfaces are the same. As a result, the temperature distribution produced in the lubricant film becomes asymmetrical, resulting in the appearance of viscosity gradients across the film. Cameron [16] referred to the changes in Couette flow owing to viscosity gradients recognised as the ‘viscosity wedge’ action, which Yagi et al. [17] subsequently showed to be responsible for a significant drop in film thickness under rolling and sliding conditions compared with that obtained under pure rolling conditions. Anomalous film shapes have also been discovered in glass–steel contacts [18] and under oppositely sliding conditions [19]. Non-Newtonian effects on film thickness include those observed by Chiu and Sibley [20], who found that a conical depression developed in circular contacts using high-viscosity polybutene as the lubricant when entrainments speeds were lower than 1 mm/s (i.e. negligible heat generation). More recently, Guo and Wong [21,22] observed similar effects using several types of polybutene and explained this phenomenon schematically using a limiting shear stress model [23]. Recently, the authors discovered the development of another anomalous film shape in circular contacts when using lauric alcohol and pure 1-dodecanol as the lubricant [7,8]. Under pure rolling conditions, the lubricant film developed a conventional shape with a zone of uniform film thickness at the centre of the contact and a constriction at the exit. Increasing the sliding speed at a fixed entrainment speed resulted in a gradual increase in the film thickness at moderate slide-to-roll ratios. Under conditions close to simple sliding where one surface remained stationary, the film became thinner around the exit zone, coincident with the zone of constriction under pure rolling. An estimate of the increase in temperature of both the oil film and the surfaces by a simple calculation using measured traction coeffficients revealed an average increase in the contact close to 20 K. This low temperature rise indicates that the appearance of the anomalous film shape cannot be explained by the viscosity wedge action. On the other hand, given the relatively high melting point of 1-dodecanol (24 1C) at ambient pressure and its proximity to the operating temperature of 40 1C, it is considered that the anomalous film shape may have been produced by solidification of the pressurised film in the contact area. If such a phase change is responsible for the anomalous change in film shape, the degree of change can be expected to be higher for lubricants with higher melting points. In the present study, the influence of lubricant melting point on the appearance of anomalous film shape is investigated by conducting experiments using three fatty alcohols with different melting points.
59
3. Experimental procedure Experiments were conducted using a ball-on-disc apparatus as shown schematically in Fig. 1. The set-up puts into contact a steel (SUJ2, equivalent to AISI 52100) ball with a diameter of 25.4 mm and an optically flat BK7 glass disc with a diameter of 80 mm and a thickness of 10 mm. The composite root mean square (RMS) roughness of both surfaces was approximately 3 nm. The properties of the steel and glass are listed in Table 1. The contact side of the glass disc was coated with a thin semi-reflective layer of chromium to augment the contrast of the interferograms recorded during the experiments. The moving assembly was set in a temperature-controlled chamber partially filled with the lubricant, and lubricant was supplied to the contact area by the partially immersed rotating ball. The moving parts were driven independently using AC servo motors at prescribed rolling and sliding conditions. Traction forces and normal load were recorded using a gimbal mechanism. Molecular diagrams of the three fatty alcohols tested in the present study (1-decanol, 1-dodecanol and 1-tetradecanol) are shown in Fig. 2, and the melting points are listed in Table 2. Fig. 3 shows the variation in viscosity of these fatty alcohols with temperature under ambient pressure. Lubricant film thickness in the contact area was measured by white-light interferometry, as described in detail elsewhere [8]. White light delivered via a microscope mounted above the test rig was reflected at both the glass/chromium and fluid/steel interfaces and recorded by a high-speed digital camera attached to the microscope. The red–green–blue (RGB) intensities for each pixel
Objective lens
Glass disc
Chromium layer
Lubricant
Steel ball
Fig. 1. Schematic diagram of ball-on-disc test rig.
Table 1 Properties of ball and disc. Properties
Steel
Glass
Young’s modulus (GPa) Poisson’s ratio Density (kg/m3) Thermal conductivity (W/mK) Specific heat (J/kg K)
210 0.3 7850 46 470
81 0.208 2510 1.11 840
60
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All tests were conducted under negative slide-to-roll ratios (S) at a fixed entrainment speed (um) of 1.8 m/s. S is expressed as follows. S¼
ub ud : um
ð1Þ
where ub and ud are the speeds of the ball and disc surfaces, and um is defined as um ¼(ub þud)/2.
4. Results
Fig. 2. Molecular structures of (a) 1-decanol, (b) 1-dodecanol, and (c) 1-tetradecanol.
Table 2 Melting points of fatty alcohols. Lubricant
Chemical formula
Melting point
1-decanol 1-dodecanol 1-tetradecanol
C10H22O C12H26O C14H30O
7 1C 24 1C 38 1C
15 1-tetradecanol
viscosity (mPas)
12
1-dodecanol 9
6
1-decanol
3
0 20
40
60 temperature (°C)
80
100
Fig. 3. Viscosity of fatty alcohols as a function of temperature.
were converted into film thickness using a calibration table constructed in advance from a static contact. The experimental protocol was as follows. The steel ball, glass disc, chamber, and other parts of the rig that could come into contact with the lubricant during the tests were cleaned in an ultrasonic bath filled with heptane for 20 min followed by acetone for the same period. After cleaning and prior to each experiment, interference images were recorded on a static contact for film thickness calibration. Four images were stored at each operating condition to check the repeatability of the interferograms.
Fig. 4 shows the optical interferograms of the film obtained for the three lubricant at various slide-to-roll ratios under conditions of fixed entrainment speed and contact pressure. The inlet temperature was adjusted such that the central film thickness matched that obtained under pure rolling conditions. The viscosities of the three lubricants under these conditions have similar values, 10.8 mPa s for 1-decanol (at 27 1C), 9.6 mPa s for 1-dodecanol (at 40 1C), and 11.0 mPa s for 1-tetradecanol (at 45 1C). For 1-dodecanol, the pressure–viscosity coefficient is 8.6 GPa 1 according to the curve-fitting results from central film thickness measurements conducted under pure rolling conditions [8]. The pressure– viscosity coefficients of 1-decanol and 1-tetradecanol are 7.3 GPa 1 (at 27 1C) and 7.1 GPa 1 (at 45 1C) according to the film thickness equation [11]. The present experiments showed that the development of film shape under rolling and sliding conditions is dependent on the chain length of the fatty alcohol. The film thicknesses of all three lubricants under pure rolling, however, were identical. For 1-decanol, the colour of the optical interferograms became orange in a limited region immediately upstream of the exit zone at S¼ 40%, and the orange colouration remained at the same location with further increases in S. At S¼ 180%, however, the shape of the changed colour was unstably changed during the test. The unstable change in film shape may be attributed to small vibration of the spindles during the test. For 1-dodecanol, as reported in previous studies [7,8], the colour changed from S¼0 to S¼–150%, indicating an increase in film thickness in the central part of the contact, with the colour variation moving towards the inlet zone. For 1-tetradecanol, the variation in colour was more prominent than for the other two lubricants. At S¼ 40%, the thickness of the entire film increases at the leading side as well as at the centre. In contrast, the film thickness in the inlet zone did not increase for the other two fatty alcohols. From S¼ 70% to 150%, the colour changed dramatically in all areas except in the constriction zone. At S¼ 180%, the zone of colour change moved towards the inlet zone and the black region in the exit zone expanded over the entire contact area. Fig. 5 shows the film thickness profiles on the central line in the sliding direction as converted from the optical interferograms presented in Fig. 4. As expected, the film thickness profiles of all three fatty alcohols are almost identical under pure rolling conditions. Under sliding conditions, however, differences become apparent among these three lubricants. At S¼ 70%, it can be seen that film thickening becomes more pronounced as the chain length of the fatty alcohol increases. For 1-tetradecanol, the film thickness reached around 200 nm in the inlet zone, and the region of uniform film thickness extended into the usual constriction zone. For 1-dodecanol, the film thickness was about 150 nm in the inlet zone and was the same as that at S¼0, increasing to 200 nm in the contact area. For 1-decanol, the film profile is the same as that at S¼0 at the inlet zone. The film thickness increases locally to about 170 nm immediately adjacent to the constriction zone. At S¼ 100%, for 1-tetradecanol, the film thickness in the inlet zone remains the same as at S¼ 70%, but increases locally near
K. Yagi et al. / Tribology International 49 (2012) 58–66
61
S = 0%
S = -40%
S = -70%
S = -100%
S = -120%
S = -150%
S = -180%
S = 0%
S = -40%
S = -70%
S = -100%
S = -120%
S = -150%
S = -180%
S = 0%
S = -40%
S = -70%
S = -100%
S = -120%
S = -150%
S = -180%
Fig. 4. Optical interferograms for various slide-to-roll ratios at an entrainment speed of 1.8 m/s and a maximum Hertzian pressure of 0.52 GPa for (a) 1-decanol (27 1C), (b) 1-dodecanol (40 1C), and (c) 1-tetradecanol (45 1C).
the contact to 290 nm. For 1-dodecanol and 1-decanol, the films are slightly thicker than at S¼ 70%. At S ¼ 150%, the 1-tetradecanol film thickness reaches almost 400 nm. The thickness of the 1-dodecanol film is similar, but the region of the uniform film thickness around the centre is smaller than for 1-tetradecanol. At S¼ 180%, the film thickness drops markedly for 1-tetradecanol and the thin film zone expands over the entire contact area. For 1-dodecanol, the film remains thick on the inlet side of the contact, reaching a maximum film thickness of about 800 nm. For 1-decanol, the film thickness was unstable during the tests, but was of the order of 100 nm. The influence of applied load is shown for 1-docecanol under various slide-to-roll ratios in Fig. 6. In pure rolling, as expected, it can be seen that the film shape develops according to the classical pattern with a uniform film in the central contact region and a constriction shape in the exit zone. With increasing slide-to-roll ratio, the colour of the optical interferograms changes gradually. At S¼ 180%, the region of colour change moves towards the inlet zone, while the black-colour region, corresponding to a film thickness of less than 100 nm, expands over the exit zone. The most important observation in Fig. 6 is that the film thickness is not significantly sensitive to the applied load. In pure rolling, the contact area expands but the film thickness and shape remain relatively unchanged with an increasing load. Under rolling and sliding conditions, the colour in the central contact region remains the same with an increasing load, while the contact area increases. Fig. 7 shows the influence of applied load for 1-tetradecanol. The inlet temperature was set at 45 1C to afford the same film thickness under pure rolling conditions as observed for 1-dodecanol at S ¼0. The variations in film thickness with the slide-toroll ratio for 1-tetradecanol appears largely similar to that for 1-dodecanol: a change in colour in the central region occurs when S is increased, and the region of film thinning in the exit zone
expands at S¼ 180%. As the applied normal load is increased, the film thickness varies while the film shape remains unchanged. At S ¼0 and 40%, the film thickness decreases slightly with an increasing applied load. Under moderate sliding conditions, from S ¼ 70% to 120%, the change in colour is more pronounced on the leading side of the central contact area for phmax ¼0.3 and 0.4 GPa, whereas the colour becomes more uniform at phmax ¼0.52 GPa. These colour variations indicate that the film thickness increases with the applied load. Under high sliding conditions, from S¼ 150% to 180%, the change in colour with an increasing load is almost undetectable. Fig. 8 shows the influence of the inlet temperature on the film shape for 1-dodecanol under constant entrainment speed (1.8 m/s) and the maximum Hertzian pressure (0.52 GPa), and Fig. 9 shows the corresponding film thickness profiles on the central line along the sliding direction. In the case of S ¼0, the central film thickness is 220 nm at 27 1C and 110 nm at 40 1C. It can be observed from Fig. 8 that the film shape follows the same trend in terms of film thickness distribution as a function of the slide-to-roll ratio for both temperatures. According to the film thickness profiles shown in Fig. 9, it can be deduced that the thickness at 27 1C increases more at the inlet zone as well as at the centre with increasing slide-to-roll ratio in comparison with that at 40 1C. From S¼0 to 150%, the entire film thickness increases with increasing inlet temperature. At S¼ 180%, the maximum film thickness reaches 900 nm at 27 1C and is greater than that at 40 1C, while the minimum film thicknesses are almost the same (100 nm) at all temperatures.
5. Discussion The anomalous EHD lubricant film shape originally observed for 1-dodecanol was also observed for 1-decanol and 1-tetradecanol in the present study. It is found that the film shape was dependent on
K. Yagi et al. / Tribology International 49 (2012) 58–66
1000
1000
800
800
600
film thickness h (nm)
film thickness h (nm)
62
1-dodecanol 1-decanol
400 1-tetradecanol
600 1-dodecanol
400
200
200
-200
-100
0 100 x (µm)
200
0 -300
300
1000
1000
800
800 film thickness h (nm)
film thickness h (nm)
0 -300
1-decanol 1-tetradecanol
600 1-dodecanol 1-tetradecanol
400
-200
-100
200
300
1-tetradecanol
600 1-dodecanol
400
200
200
1-decanol
1-decanol
0 -300
0 100 x (µm)
-200
-100
0 100 x (µm)
200
0 -300
300
-200
-100
0 100 x (µm)
200
300
1000 1-dodecanol film thickness h (nm)
800 1-tetradecanol
600
400
200 1-decanol
0 -300
-200
-100
0 100 x (µm)
200
300
Fig. 5. Film thickness profiles on the contact central line converted from the optical interferograms in Fig. 4 for slide-to-roll ratios of (a) 0, (b) 70%, (c) 100%, (d) 150%, and (e) 180%.
both the operating conditions and the chain length of the fatty alcohol. For the three fatty alcohols with different melting points tested in the present study, the film thickness increased in the contact area with increasing slide-to-roll ratio at a fixed entrainment speed. For 1-decanol, having the lowest melting point, the
region of thickening with increasing slide-to-roll ratio was the smallest among these three lubricants and was located just upstream of the exit zone (Fig. 4). For 1-tetradecanol, having the highest melting point, the variation in film shape was the most pronounced. The film thickness increased at the inlet zone as well
K. Yagi et al. / Tribology International 49 (2012) 58–66
63
S = 0%
S = -40%
S = -70%
S = -100%
S = -120%
S = -150%
S = -180%
S = 0%
S = -40%
S = -70%
S = -100%
S = -120%
S = -150%
S = -180%
S = 0%
S = -40%
S = -70%
S = -100%
S = -120%
S = -150%
S = -180%
Fig. 6. Influence of applied load on film shape for 1-dodecanol at an entrainment speed of 1.8 m/s and a temperature of 40 1C: (a) 0.3 GPa, (b) 0.4 GPa, and (c) 0.52 GPa.
S = 0%
S = -40%
S = -70%
S = -100%
S = -120%
S = -150%
S = -180%
S = 0%
S = -40%
S = -70%
S = -100%
S = -120%
S = -150%
S = -180%
S = 0%
S = -40%
S = -70%
S = -100%
S = -120%
S = -150%
S = -180%
Fig. 7. Influence of applied load on film shape for 1-tetradecanol at an entrainment speed of 1.8 m/s and a temperature of 45 1C: (a) 0.3 GPa, (b) 0.4 GPa, and (c) 0.52 GPa.
as at the centre (Fig. 5). With increasing applied load, the film thickness increased at moderate slide-to-roll ratios for 1-tetradecanol (Fig. 7), whereas the film thickness remained largely unchanged for 1-dodecanol under the same conditions (Fig. 6).
In a previous paper [8], the authors discussed the mechanism of development of this anomalous film shape for 1-dodecanol and they concluded that this behaviour could be attributed to the solidification of the lubricant as a result of phase change. The anomalous film shapes observed in the present study also appear
64
K. Yagi et al. / Tribology International 49 (2012) 58–66
S = 0%
S = -40%
S = -70%
S = -100%
S = -120%
S = -150%
S = -180%
S = 0%
S = -40%
S = -70%
S = -100%
S = -120%
S = -150%
S = -180%
Fig. 8. Influence of inlet temperature on film shape for 1-dodecanol at an entrainment speed of 1.8 m/s and an Hertzian pressure of 0.52 GPa: (a) 27 1C and (b) 40 1C.
to support the solidification hypothesis. The melting point of fatty alcohols increases with chain length, as indicated in Table 2. The fatty alcohol with the highest melting point tested in the present study, 1-tetradecanol (38 1C), showed the most remarkable anomalous film shapes. The difference between the melting temperature and the inlet temperature (45 1C) was the lowest for this alcohol among those tested, and thus would have most easily undergone solidification. As shown in Fig. 5, the film thickness increased in the inlet zone even at moderate slide-to-roll ratios for 1-tetradecanol whereas the film profile at the inlet zone did not change at moderate slide-to-roll ratios for 1-dodecanol and 1-decanol. This may imply that the lubricant has already been solidified at the inlet zone for 1-tetradecanol. At high slide-to-roll ratios, the region of film thickening moved towards the inlet zone for 1-dodecanol and disappeared for 1-tetradecanol. These observations suggest that the solidified lubricant at the inlet zone may result in lubricant starvation. Generally, the melting point is expected to increase with pressure and thus it is possible that the lubricant could solidify in the inlet zone and/or in the central contact zone. However, the influence of pressure on the melting point was not the focus of the current work. The flow of solidified lubricant should be different from that of a viscous fluid. Under pure rolling conditions, the lubricant solidified can flow through the contact area. Therefore, the film thickness distributions in pure rolling for all alcohols have the commonly accepted shape with flat centre and outlet constriction. Under rolling and sliding conditions, the lubricant is subjected to high shear stress, which causes slippage to change the Couette flow along the sliding direction. As a result, such anomalous film shapes are produced so that the continuity of the flow should be satisfied. Three relevant slippage mechanisms have been proposed. Smith [23] stated that solidified lubricant slips at the interface between the viscous fluid because of heat generation. Slippage could also occur between the solidified lubricant and the sliding surfaces as suggested by Ehret et al. [24]. Stahl and Jacobson [25] and Zhang and Wen [26] introduced a wall slip model related to the limiting shear stress of the lubricant. Ehret et al. [24] reported the occurrence of a thickened part in the film thickness distribution based on a plug flow model. Zhang and Wen [26] showed a local film thickening in the inlet zone followed by a gradient in the film thickness. Bair and McCabe [27], on the other hand, captured pictures of shear bands within pressurised lubricants and suggested a third mechanism
by which mechanical shear bands occur within the solidified film. The film shapes reported and discussed in the present study, however, do not show why and how the Couette flow changes, which is dominant in the contact area, explored by Bair and McCabe [27]. The appearance of anomalous film shape in this present study can be qualitatively explained as due to lubricant solidification phenomena. However, some unresolved points still remain, such as the effect of the lubricant nature, the relationship between the melting point and pressure, and the transient features of lubricant solidification during its passing through the contact area in less than 1 ms. Further study is needed to investigate the mechanism of the anomalous film shape.
6. Conclusions In the present study, the authors investigated the development of anomalous lubricant film thickness shapes in glass–steel contacts under rolling and sliding conditions when fatty alcohols were used as lubricants. From the results and discussion presented above, the following conclusions can be drawn: 1) When the lubricant melting point is high, the anomalous film shape appears remarkably under rolling and sliding conditions. For 1-decanol, which has the lowest melting point among the three fatty alcohols tested, the thickened part of the film appears around the contact centre. For 1-tetradecanol, which has the highest melting point, the thickened part of the film is the thickest. For 1-dodecanol, which melting point value is in-between the previous ones, the thickness is intermediate. 2) At moderate slide-to-roll ratios, the film thickness increases at the inlet zone as well as at the contact centre with increasing the melting point of the lubricant. For 1-decanol, the film thickness at the inlet zone does not change with increasing the slide-to-roll ratio. For 1-tetradecanol, the thickness increases at the inlet zone as well as at the central zone. For 1-dodecanol, the film thickness profile at the inlet zone does not change but increases when the ambient temperature decreases. 3) At high slide-to-roll ratios, the thickened part of the film moves towards the inlet zone when the melting point of
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lubricant is high. For 1-decanol, the thickened part is kept around the centre. For 1-dodecanol and 1-tetradecanol, the thickened part moves towards the inlet zone while the thin film expands over the trailing side of the contact area. For 1-tetradecanol, this tendency is strongest.
4) The appearance of the anomalous film shapes for lubricants with high melting points suggests that the lubricant is solidified under high pressure, and the high shear stress causes slippage of the lubricant to give rise to the anomalous behaviour.
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