EHL Traction Analysis of Perfluoropolyether Fluids Based on Bulk Modulus

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1 1 EHL Traction Analysis of Perfluoropolyether Fluids Based on Bulk Modulus N. Ohno 1 *, T. Mawatari 1, B. Zhang 1, M. Kaneta 2, P. Sperka 2, I. Krupka 2, M. Hartl 2 1: Saga University, 1 Honjo Saga Japan. 2: Brno University of Technology, Tecknicka 2896/2, Brno, Czech Republic. Abstract High pressure density measurements of three kinds of commercial PFPE fluids were done at temperatures from 293K to 333K and pressure up to 1.2 GPa. The tangent bulk modulus - pressure - temperature relation and secant bulk modulus - pressure - temperature relation of PFPE fluids were proposed. The traction coefficient was also measured using a ball on disk machine. It was found that the maximum traction coefficient and the limiting shear stress are closely related to the tangent bulk modulus and the secant bulk modulus, respectively. That is, the traction characteristics are mainly influenced by the bulk modulus of the oil. Keywords: PFPE fluid, rheology, bulk modulus, traction, EHL. *Corresponding author: Nobuyoshi Ohno (ohno@me.saga-u.ac.jp). 1. INTRODUCTION Perfluoropolyether (PFPE) fluid are used in magnetic recording media [1], aerospace industry and satellite instruments [2] satisfactorily. Recently these oils have been introduced as hydraulic fluids, high temperature liquid lubricants in turbine engines [3] and base oils of high-temperature greases. Despite considerable research on PFPE, the rheological characteristics at high pressure and EHL traction have not been understood yet. That the lubricating oils solidify at sufficiently high pressure as the amorphous or glassy solids has been verified by a number of studies [4]. On the other hand, in view of the significance of the behavior of lubricants at high pressures, in particular, in relation to traction drives a number of theoretical and experimental investigations were developed []. Recently, the measurement of EHD traction for a half-toroidal CVT fluid were carried out by the authors [6] under the conditions of the mean Hertzian pressure of up to 2. GPa, rolling speed of up to 3 m/s, oil temperature in the range of 313~393 K. The maximum traction coefficient was closely related to T VE -T (T VE : viscoelastic solid transition temperature at pressure p, T : oil temperature) that is free volume parameter. However, it is not yet clear from the perspective of mechanical properties of traction fluid. The authors previous investigation was carried out to clarify the predominant factor affecting the traction characteristics of lubricating oil. Ten kinds of lubricating oil were tested. As result, the importance of the bulk modulus as a predominant factor for traction characteristics of lubricating oil was established [7]. The purpose of this paper is to investigate the predominant factor affecting the traction characteristics of PFPE fluid. As result, it was found that the maximum traction coefficient and the limiting shear stress are closely related to the tangent bulk modulus and the secant bulk modulus, respectively. 2. PROPERTIES OF PFPE FLUIDS Three kinds of PFPE fluids are tested. These are Fluid Table 1: Properties of PFPE fluids Fluid ρ, g/ml ν, mm 2 /s VI M 288 K 313 K 373 K g/mol K (GPL) D (S2) F (M2) Molecular structures: Fluid K (GPL): F[C(CF 3 )FCF 2 O] n CF 2 CF 3 Fluid D (S2): F(CF 2 CF 2 CF 2 O) n CF 2 CF 3 Fluid F (M2): CF 3 [(OCF 2 CF 2 ) p (OCF 2 ) q ]OCF 3

2 K S, K T, GPa K S, K T, GPa K S, K T, GPa, g/ml K (GPL), Fluid D (S2) and Fluid F (M2). Their properties and molecular structures are given in Table 1 [8]. 3. HIGH PRESSURE RHEOLOGY 3.1. Bulk Modulus and Phase Diagram The high-pressure density measurement of the test fluids was measured in the high-pressure densitometer shown in Fig. 1 [9]. Two milliliters of the test fluid was poured into the test machine and pressure was applied in the upper plunger by a hydraulic power unit. The lower plunger rests on a load cell which records the total force on lower plunger. The chamber pressure p is given by (W 1 +W 2 )/2A, where W 1 is the force on hydraulic power unit, W 2 is the force on load cell, and A is the area of the bore in the high pressure chamber. The volume of lubricant in the chamber corresponding to a pressure is determined from the displacement of the upper plunger by using a linear gauge. A correction for the volume of lubricant was done to take account of the elastic deformation of upper plunger, lower plunger and bore area high pressure. Fluid volume measurements at test temperature and pressures were converted to density. pressure, T the temperature, K the tangent bulk modulus and δ the coefficient of thermal expansion. The change in density ρ against pressure p at 293 K, Figure 2: Density-pressure relation of fluid D. 1 Fluid D Fluid K K T K S 1 (a) Fluid K Fluid D K T K S. 1. Figure 1: High-pressure densitometer One of the basic equations for the solidification of oils is the equation of volumetric change that is used in the strength of materials. The volumetric strain ε is defined as the ratio of the decrease in volume to the original volume []: 1 Fluid F K T K S (b) Fluid D. 1. dv ln ln 1 dp dt dp 3dT V p T P K T (Eq. 1) where V represents the volume, ρ the density, p the (c) Fluid F Figure 3: Tangent bulk modulus K T and secant bulk

3 Viscosity, Pa s modulus K S relationship with pressure p. 313 K and 333 K of fluid D is shown in Fig. 2. Differentiating the pressure-density curve, the tangent bulk modulus K T = (dlnρ/dp) -1 are estimated as shown in Fig. 3. And also, secant bulk modulus K S = (ρ/(ρρ ))p is shown in Fig. 3, where ρ represents density at atmospheric pressure. The viscoelastic solid transition point p VE of fluid D is obvious from the abrupt change of dk T /dp in Fig. 3 (b). The viscoelastic transition point are.73 GPa at 293 K and.9 GPa at 313 K, respectively. The equation related to the temperature and pressure of the viscoelastic solid transition point T VE is represented in the following equation formula: T T A ln A p (Eq. 2) VE VE where A 1 and A 2 represents parameters that depend on fluid properties. The parameters obtained are listed in Table 2. The viscoelastic solid transition temperature T VE at atmospheric pressure was estimated by the occurrence of photoelasticity effect at lowering temperature using liquid nitrogen gas. Determined T VE are given in Table 2. Table 2: Rheological parameters of PFPE fluids Fluid T VE, A 1, A 2, name K K GPa -1 B 1 B 2 C 1 C 2 K D F Viscosity-Pressure-Temperature Relation The schematic diagram of the falling ball viscometer is shown in Fig. 3 [9]. The basic principle is that a solid body having higher density than the liquid to be tested slowly falls through a liquid filled tube. A steel ball of 7.94 mm diameter was dropped into the viscometer with oil which passed through the 3. mm diameter sapphire observation window. The falling ball passing time through the sapphire window was measured by a sensor. As a result of having compared our data [9] with the data by Sargent [11] about high pressure viscosity of the castor oil for calibration of viscometer, all the data were in good agreement. In Fig. 4, viscosity as a function of the pressure and temperature is shown for fluid D. The values of the Barus pressureviscosity coefficient α (GPa -1 ) were calculated using the least squares method. The variations of the pressure-viscosity coefficient α can be described by the equation C1 C2 log (Eq. 3) where ν represents the kinematic viscosity (mm 2 /s) under atmospheric pressure. The parameter C 1 and C 2 are shown in Table Fluid D Figure : comparison of predicted and observed values of high-pressure viscosity of fluid D. A very useful viscosity-pressure-temperature correlation on the basis of free volume and phase diagram was derived by the authors []. The viscosity pressure-temperature relationship is given below: B1 log 7 B 2 T TVE T VE / TVE T T T / T VE VE VE (Eq. 4) Figure 4: High pressure viscometer A high pressure falling body viscometer is used to determine high-pressure viscosity up to.4 GPa and at temperature from 293 K to 313 K in the range of viscosity η< 3 Pas, where is the absolute viscosity. Results of regression analysis of the viscosity data are in Table 2. In Fig.4, solid lines are the theoretical curves by Eq. (4), which matches closely with the experimental data. 4. EHL TRACTION MEASUREMENT 3

4 4.1. Experimental Method The tractional properties of the PFPE fluids were measured using a mini traction machine MTM (PCS Instruments, London, UK). In this, a rolling-sliding lubricated contact is formed between a steel ball with 19. mm diameter and the flat surface of a polished steel disc with 46 mm diameter. The ball shaft is tilted so as to provide nominally zero spin in the contact, and ball and disc are driven by two independent DC motors. In the current study, the balls and discs were both AISI2 bearing steel (Young s modulus E=2 GPa, Poisson s ratio ν=.3) and root mean square surface roughness -13 nm for the balls and 2-3 nm for discs [12]. The load applied was w = 4.2 N, 12.4 N, 26.4 N and 62.6 N, corresponding to maximum Hertzian pressure of p H =. GPa,.7 GPa,.9 GPa and 1.2 GPa, respectively. Tests were carried out over the entrainment speed u =. m/s and at three temperatures, 293 K, 313 K, and 333 K. To obtain conventional EHL traction measurements in this study, the slide-roll ratio was increased at a fixed entrainment speed of. m/s to produce traction coefficient versus slide-roll ratio plots. GU 1/ Results of Traction Measurement IR (isoviscous rigid) IE (isoviscous elastic) p=13 PR (piezoviscous rigid) p=2 PE (piezoviscous elastic) 1 1 p Figure 6: Experimental points in liquid/solid transition lubrication diagram For measurement of traction forces and observation of It was considered very important to be sure that traction measurements were being taken in the full EHL regime and not in the mixed lubrication regime where a component of traction might depend on boundary lubrication. It is common practice for identification of the lubrication regime of the point contacts to use Hamrock-Dowson [13] diagram in which the regimes are divided as follows: isoviscousrigid IR. piezoviscous-rigid PR, isoviscous-elastic IE, and piezoviscous-elastic PE. The authors [14] previously pointed out that the most suited representation for estimated of the solidified film 4 thickness at high pressure EHL contacts is concluded to use the liquid/solid transition lubrication diagram, where the product of pressure-viscosity coefficient α Fluid K, 313 K 1, % (a) Fluid K Fluid D, 313 K P H :.GPa, :.7GPa :.9GPa, :1.2GPa 1, % (b) Fluid D Fluid F, 313 K P H :.GPa, :.7GPa :.9GPa, :1.2GPa 1, % (c) Fluid F Figure 7: Effect of slide-roll ratio Σ and Hertzian pressure ph on the traction coefficient μ at temperature 313 K and. m/s entrainment speed. and mean Hertzian pressure p as the abscissa and dimensionless parameter GU 1/4 as the ordinate are used. It is composed by combining Greenwood diagram [ ]. Hamrock-Dowson diagram and liquid/solid transition condition given by αp, i.e., liquid αp < 13, for viscoelastic solid 13 < αp < 2, and elastic-plastic solid 2 < αp [16]. The experimental ranges for circular contact k = 1 are plotted in Fig. 6. In our experimental range, the state of the lubricants are liquid to elastic-plastic solid and lubrication regime is PE, therefore, the minimum film thickness calculated by the formula of Hamrock-Dowson for P H :.GPa :.7GPa :.9GPa :1.2GPa

5 Viscosity, mpa s max, GPa EHL. The range of lambda ratio Λ, the ratio of the minimum film thickness to composite surface roughness are 1 to 4. Figure 7 shows a set of traction coefficient versus slide-roll ratio for fluid K, fluid D and fluid F at four Hertzian pressures and a fixed entrainment speed. m/s at 313 K. The results show classical traction behavior, with traction coefficient increasing slide-roll ratio to reach a limiting value before falling slightly due to thermal effects. It can be seen that this limiting traction coefficient increases as Hertzian pressure increases. The authors [16] previously pointed out that the product of pressure-viscosity coefficient α and mean Hertzian pressure p are closely related to the oil molecular packing parameter. The maximum traction coefficient μ max obtained from Fig. 7 and αp value at 313 K is summarized in Table 3. The results show that μ max increases as αp increases. The tangent bulk modulus K T and secant bulk modulus K S of each fluid at each mean Hertzian pressure p = 2p H /3 can be read from Fig. 3. K T and K S of tested fluids at 313 K is listed in Table 3. It shows the variation of maximum traction coefficient of PFPE fluid with kind of fluid, Hertzian pressure p H, αp, tangent bulk modulus K T and secant bulk modulus K S. Table 3: Results of αp, maximum traction coefficient μ max, limiting shear stress τ max, tangent bulk modulus K T and secant bulk modulus K S for all Hertzian pressure at 313 K. fluid p H αp μ max τ max K T K S name GPa GPa GPa GPa K D F DISCUSSIONS Figure 8 shows the relation of μ max and the tangent bulk modulus K T at the operating condition for all experiments. The significant correlation exists between μ max and the tangent bulk modulus K T ; greater K T indicates greater μ max. Figure 9 shows the relation between limiting shear stress τ max and the secant bulk modulus K S at the operating condition for all experiments. Here, the limiting shear stress τ max is calculated from equation τ max = μw/a, where w represents load and A the Hertzian contact area. A significant correlation also exists between the limiting shear stress τ max and secant bulk modulus K S. Greater secant bulk modulus K S would give greater τ max. It was found that a significant physical property for.1 max.. P H =.-1.2GPa mm/s K 1 2 K T, GPa Figure 8: Relationship between maximum traction coefficient μ max and tangent bulk modulus K T for all experiments P H =.-1.2GPa mm/s K K S, GPa Figure 9: Relationship between limiting shear stress τ max and secant bulk modulus K S for all experiments K Absolute viscosity 6 7 Share rate, s -1 Figure : Measuring results of fluid viscosity at high shear rates. tractional behavior of lubricating oil is bulk modulus. The values of fluid viscosity under high shear rate conditions are indicated in Fig.. In order to measure the viscosity at high shear rate in the range of 1.8 s -1 to 6. 6 s -1, the ultra shear viscometer of PCS instruments was used. The measuring temperature was fixed at 393 K. Marks in the figure are corresponded to test results. The broken line, dotted line and chain line

6 indicate the viscosity values of fluid K, fluid D and fluid F, respectively. As shown in this figure, each viscosity was almost constant independent of the shear rate. In the case of fluid K and fluid D, each viscosity at the high shear rates is almost the same as the absolute viscosity. On the other hand, it was found that the viscosity of fluid F clearly decreases in comparison with the absolute viscosity. All traction tests with fluid F were performed in the liquid region where αp is less than 13, and the traction coefficient and the maximum shear stress became lower than the other fluids as shown in Figs. 7, 8 and 9. Therefore, it is suggested that such traction properties of fluid F is caused by the decline of the viscosity at the EHL contact region exposed to the relatively high shear rates. Furthermore, in the case of fluid F showing the decline of viscosity at high shear rates compared with the absolute viscosity, it was found that both the tangent bulk modulus K T and the secant bulk modulus K S related closely to the fluid molecular structure become smaller than the other fluids. 6. CONCLUSIONS Summarizing the experimental results, the following conclusions are drawn concerning the bulk modulus and traction coefficient of PFPE fluids. 1. The maximum traction coefficient is closely related to the tangent bulk modulus. 2. The limiting shear stress is closely related to the secant bulk modulus. 3. The traction characteristics are mainly influenced by the bulk modulus of the oil. ACKNOWLEDGEMENT The authors would like to express their sincere thanks to Dr. K. Matsumoto, Honda R&D Co. Ltd., Japan for the enormous cooperation of the fluid viscosity measurements at high shear rates. REFERENCE 1. B. Bhusan, Tribology and Mechanics of Magnetic Storage Devices, Springer, New York, W. R. Jones, Jr., Properties of Perfluoropolyethers for Space Applications, STLE Trib. Trans, 38 (3) (199) J. C. Liang, L. S. Holmick, Tribochemistry of a PFPAE Fluid on M- Surfaces by FTIR Spectroscopy, STLE Trib. Trans, 39 (3) (1996) M. Alsaad, S. Bair, D. M. Sanborn, W. O. Winer, Glass Transition in Lubricants: Its Relation to Elastohydrodynamic Lubrication (EHD), ASME J. Lubr. Technol., (3) (1978) C. R. Evans, K. L. Johnson, Regimes of Traction in Elastohydrodynamic Lubrication, Proc. IMech E, 2 (C) (1986) N. Ohno, H. Achiha, S. Natsumeda, S. Aihara, F. Hirano, High Pressure Rheology and Traction Characteristics of Traction Oil, Journal of Japanese Society of Tribologists, 44 (12) (1999) N. Ohno, MD. Z. Rahman, K. Kakuda, Bulk Modulus of Lubricating Oils as Predominant Factor Affecting Tractional Behavior in High Pressure Elastohydrodynamic Contacts, STLE Trib. Trans, 48 (2) N. Ohno, MD. Z. Rahman, S. Yamada, H. Komiya, Effect of Perfluoropolyether Fluids on Life of Thrust Ball Bearings, STLE Trib. Trans, 2 (29) T. Mawatari, R. Fukuda, H. Mori, S. Mia, N. Ohno, High Pressure Rheology of Environmentally Friendly Vegetable Oils, Tribology Letters, 1 (2) (213) N. Ohno, F. Hirano, High Pressure Rheology Analysis of traction Oils Based on Free Volume Measurement, Lubr. Eng., 7 (7) (21) L. B. Sargent, Jr., Significance of Viscosity Studies of Fluid Lubricants at High Pressure, Lubr. Eng.,July-August, (19) M. Muller, K. Topolovec-Miklozic, A. Dardin, H. A. Spikes, The Design of Boundary Film- Formation PMA Viscosity Modifiers, STLE Trib. Trans., 49 (26) B. J. Hamrock, D. Dowson, Ball Bearing Lubrication, Wiley and Sons, Inc., New York (1981). 14. N. Ohno, N. Kuwano, F. Hirano, Diagrams for Estimation of the Solidified Film Thickness at High Pressure EHD Contacts, Dissipative Processes in Tribology, Eds, D. Dowson, C.M. Taylor, T.H.C. Childs, M. Godet, and G. Dalmaz, Elsevier, Amsterdam (1994) J. A. Greenwood, Film Thickness in Circular Elastohydrodynamic Contacts, Proc. IMech E, 22 (C1) (1988) N. Ohno, N. Hattori, N. Kuwano, F. Hirano, Some Observations on the Relationship between Rheological Properties of Lubricants at High Pressure and Regimes of Traction (Part 1) The Rheological Properties of Lubricants at High Pressure -, Journal of Japan Society of Lubrication Engineers, 33 (12) (1988)