High-Pressure Viscosity Measurements of Polyalphaorefins at Elevated Temperature

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1 Tribology Online, 11, 2 (2016) ISSN DOI /trol Short Communication High-Pressure Viscosity Measurements of Polyalphaorefins at Elevated Temperature Yuichi Nakamura 1)*, Shota Hiraiwa 2), Fumiaki Suzuki 2) and Masahito Matsui 1) 1) Division of Physics Engineering, Graduate School of Engineering, Mie University 1577 Kurimamachiya-cho, Tsu-shi, Mie , Japan 2) Student, Graduate School of Engineering, Mie University 1577 Kurimamachiya-cho, Tsu-shi, Mie , Japan *Corresponding author: nakamura.yuichi@mie-u.ac.jp ( Manuscript received 11 August 2015; accepted 12 January 2016; published 30 April 2016 ) ( Presented at the International Tribology Conference Tokyo 2015, September, 2015 ) In order to provide detail data on polyalphaorefin(pao) s viscosity for the tribological analysis under EHL lubrication conditions, viscosity-pressure-temperature correlation relation of wide range viscosity grade PAOs (from PAO2 to PAO100) was investigated employing a special compact pressure-generating apparatus called diamond-anvil cell. Pressure-viscosity coefficients were resulted to gradually decrease with increasing pressure and temperature up to 1 GPa at up to 150 C, and the values at 150 C were about a half of those at 40 C for all PAOs. The two representative temperature-pressure-viscosity correlation formulations were well regressed with the high-pressure viscosity data. By substituting the regression formulations for Blok s pressure-viscosity coefficient, gradually increasing coefficient with viscosity grade were found out, and that of high viscosity PAO100 was about 1.5 times larger than that of low viscosity PAO2. Keywords: viscosity, lubricating oils, EHL, polyalphaorefin, high-pressure, pressure-viscosity coefficient 1. Introduction Mechanical design of power unit like engine, transmission and differential gears in vehicles and gear train in other machine such as wind turbine is getting complicated and its requirement on lubricant oil is becoming severe as progress of mechanical design. One way to satisfy that requirement is the application of polyalphaorefin (PAO) as base oil instead of mineral oil to guarantee thermal stability and cleanliness of oil and this has been adopted in many industrial fields such as automobile manufacturing. PAO has various kinds of viscosity grade and all of them show good miscibility with mineral oil in spite of its low solubility with additives. Traditionally, high viscosity PAO has been provided for gear oil as viscosity index improver to guarantee hardware protection. In contrast, low viscosity PAO is likely to be preferred as engine base oil in order to achieve good fuel economy performance, In the analysis of elastohydrodynamic lubrication (EHL) and traction coefficients on the machine elements suffering from high contact pressure like spur gears, rolling bearings and engine valve trains, rheological behavior should be well understood including shear-thinning, viscoelastic and elastic-plastic properties around solidification pressure. Among these properties, it is fundamental and essential to grasp high-pressure viscosity behavior and pressure-viscosity coefficient, quantitatively. However, high-pressure viscosity data are insufficient due to the difficulty of construction and manipulation of conventional high-pressure viscometoric apparatus. One of representative compiled data is ASME pressure viscosity report [1] and the other is in the published book by Bair [2]. As described above, PAO is one of common base oil or viscosity index improver in industrial fields, and its wide range data on high-pressure viscosity should be provided. High-pressure viscosity data of PAO are few and viscosity grade is limited [3,4], and systematic data ranging wide viscosity grade have not been found. Nakamura et al. have been studying those rheological properties employing a special compact pressuregenerating apparatus called diamond-anvil cell (DAC) which can easily pressurize up to 6 GPa. With a falling sphere viscometry together with the DAC, pressureviscosity correlation relation has been investigated for traction oils [5] and vegetable oils up to 2.7 GPa at up to 200 C [6]. In the present study, we would like to investigate viscosity-pressure-temperature correlation relation of Copyright 2016 Japanese Society of Tribologists 444

2 High-Pressure Viscosity Measurements of Polyalphaorefins at Elevated Temperature wide range viscosity grade polyalphaorefins (from PAO2 to PAO100) with the DAC up to 1 GPa at up to 150 C. Dependence of pressure-viscosity coefficient on viscosity grade would be evaluated with the aid of regression analyses employing two representative temperature-pressure-viscosity correlation formulations. 2. Experimental methods High-pressure viscosity measurements were carried out for PAO2, PAO4, PAO6, PAO10, PAO40 and PAO100 and their properties are listed in Table 1. Cross-sectional view of the DAC is illustrated in Fig. 1. The pressure is generated by compressing a drilled pressure chamber in a phosphor bronze gasket sheet clumped by opposed diamond anvils (0.2 carats) in Fig. 1(b). The dimension of the pressure chamber is small (the initial diameter of the drilled hole D = 0.9 mm, its thickness T = 0.8 mm), so thus only one drop of sample oil and a 90 μm diameter zirconium sphere occupy the space within the pressure chamber. The pressure was determined by the originally constructed pressure calibration diagram concerning the loading screw angle (M38 1 in Fig. 1) up to 1 GPa, which is almost independent of the kind of oils [7]. High-pressure viscosity was measured by a falling-sphere method with the DAC. By rotating the DAC embedded stage in Fig. 2 instantaneously upside down around a horizontal axis, the sphere is positioned at upper part of the pressure chamber and falls by gravity along the diameter of the chamber. The image of the falling sphere can be detected by a CCD camera and recorded in a HDD recorder incorporating 1/100 sec. time display. The viscosity is calculated by substituting the falling velocity v for the following equation derived from the hydrodynamic relation (Stokesʼ law etc.). 2 d S L g (1) 18v where g and d are the gravity acceleration and the sphere diameter: S and L are the sphere and fluid mass densities. Pressure variation of L is estimated by the equation expressed by Dowson et al [8]. is called wall factor proposed by Munro et al [9] for eliminating the effect of the wall of the DAC pressure chamber on the sphere velocity because Stokesʼ law Fig. 1 Fig. 2 Diamond anvils and pressure chamber in DAC Photograph of a falling-sphere viscometry with DAC holds in the infinite media of fluid. Therefore, depends on the above dimensions D, T and d, and it is about 0.8 in our measurement. Temperature is raised with a flexible band heater wound round the DAC and is regulated at 24 C, 40 C, 70 C 100 C and 150 C ± 1 C. Through these procedures, the calculated viscosity is low-shear-rate Newtonian one under small sphere gravity force. 3. Results and discussion 3.1. High-pressure viscosity measurements Some of measured high-pressure viscosity isotherms at each temperature are shown in Fig. 3 for PAO40, Fig. 4 for PAO4 and Fig. 5 for PAO2 in semi-logarithmic scale Table 1 The properties of sample PAOs Japanese Society of Tribologists ( Tribology Online, Vol. 11, No. 2 (2016) / 445

3 Yuichi Nakamura, Shota Hiraiwa, Fumiaki Suzuki and Masahito Matsui Fig. 3 Fig. 4 Pressure viscosity isotherms for PAO40 Pressure viscosity isotherms for PAO4 the expression and available properties such as viscositytemperature property, molecular weight, cohesive energy density etc. by investigating high-pressure viscosity up to 0.32 GPa for 64 kinds of lubricating oils. The predicted curve was also reported to fit well with the specific published measured data over 1 GPa. The consistency between our data and their prediction reconfirms that both methods are effective for the evaluation of high-pressure viscosity. The most plots of the logarithmic viscosity vs. pressure are like concave downward (convex) shape together with the prediction curves. However, the data of PAO2 at around 0.8 GPa at 24 C slightly deviate from the curve, and the viscosity increases like a straight line or slightly a concave upward curve above some inflection pressure in contrast to a concave downward curve at low pressure (sigmoidal shape in the plot of all pressure range). This feature was reported by Bridgman [11] and Bair [4]. They pointed out that the upturn of the concave shape appears at relatively high pressure and high viscosity and that the sigmoidal shape is remarkable for some liquids which often have low molecular weight. Probably in the case of PAO2 at 24 C, there may be some concern to comparatively low molecular weight of PAO2. Sargent expression expresses only convex characteristic in the plot mathematically. Pressure-viscosity coefficients αs were obtained by substituting each data points for Barus equation and those for PAO40 are shown in Fig. 6. They are also consistent with Hata and Tamotoʼs predictions. Obtained pressure-viscosity coefficients are gradually decreasing with increasing pressure and temperature. α at maximum pressure at 24 C is 15 GPa -1, whereas that at 150 C is about 7 GPa -1, which is about a half of that at 24 C. These features were almost the same for all PAOs. High-pressure viscosity isotherms of all PAOs at only 100 C are shown in Fig. 7. With increasing viscosity grade, the data line gradually varies upward in parallel fashion in the plot. Fig. 5 Pressure viscosity isotherms for PAO2 up to 0.9 GPa, 150 C, 10 5 Pa s. They are almost consistent with Hata and Tamotoʼs predicted curves based on Sargent expression [10]. Their prediction approximates correlation relations between constants of Fig. 6 Variation of Pressure-viscosity coefficient α with pressure and temperature for PAO40 Japanese Society of Tribologists ( Tribology Online, Vol. 11, No. 2 (2016) / 446

4 High-Pressure Viscosity Measurements of Polyalphaorefins at Elevated Temperature Fig. 7 Pressure viscosity isotherms for all PAOs at 100 C Fig. 8 Fitness of two regression curves with measured data for PAO Regression analyses and dependence of pressureviscosity coefficient on viscosity grade Temperature-pressure-viscosity correlation formulation is convenient to get the value at ambient pressure and temperature, and has been required for precise EHL and traction analysis. Roelands equation has been extensively utilized and is effective for the EHL analysis of inlet pressure-boosting region (near zero pressure). Yasutomiʼs formulae (modified WLF equation derived from free volume theory) [12] has been also utilized especially for traction analysis, because it can well express sigmoidal (convex and concave) plot of wide range viscosity variation up to the maximum EHL pressure over 1 GPa. Regression analyses were performed with Yasutomiʼs formulae and Roelands equation, and some plots are shown in Figs. (8,9) for PAO40 and PAO100, respectively. Both equations are regressed well with data points, however some deviations around 1 GPa can be seen between the two curves, especially at 24 C. This might be because Roelands equation expresses only convex characteristic in the plot mathematically in contrast to both convex and concave plot capability of WLF formulae. Substituting these regression formulations for the high-pressure viscosity η p of the following Blokʼs pressure-viscosity coefficient α * (reciprocal of asymptotic isoviscous pressure) [13], α * was obtained. 1 0 dp (2) 0 p where η 0 is atmospheric viscosity. Temperature dependence of α * is shown in Fig. 10 together with α at maximum pressure (αpmax). α * from WLF equation is slightly larger than that from Roelands equation and α pmax is about 30% smaller than α * for all PAOs at every temperature. This may be caused by the convex curve feature of high-pressure viscosity isotherms described above. The variation of α * and αpmax with viscosity are shown in Figs. (11,12) at 40 C and 100 C, respectively. α * and αpmax of PAO2 in Figs. 11 are 12.5 and 9.5 and Fig. 9 Fitness of two regression curves with measured data for PAO100 gradually increase with viscosity grade and those of PAO100 are 19.5 and 14.5, respectively, which are both about 1.5 times larger than those of PAO2. The same feature can be seen in Fig Conclusions High-pressure viscosity measurements of wide range viscosity grade polyalphaorefins were carried out up to 1 GPa, 150 C, 10 5 Pa s, and the plots of the logarithmic viscosity vs. pressure exhibited like concave downward (convex) shape. Consequently, pressure-viscosity coefficients gradually decreased with increasing pressure and temperature, and the values at 150 C were about a half of those at 40 C for all PAOs. The two representative temperature-pressure-viscosity correlation formulations were well regressed with the high-pressure viscosity data. By substituting the regression formulations for Blokʼs pressure-viscosity coefficient, gradually increasing coefficient with viscosity grade were found out, and that of high viscosity PAO100 was about 1.5 times larger than that of low viscosity PAO2. This investigation is expected to provide detail data on PAO s viscosity for the Japanese Society of Tribologists ( Tribology Online, Vol. 11, No. 2 (2016) / 447

5 Yuichi Nakamura, Shota Hiraiwa, Fumiaki Suzuki and Masahito Matsui (a) PAO2 (b) PAO40 (c) PAO4 (d) PAO100 Fig. 10 Variation of Blokʼs pressure-viscosity coefficient α * and αpmax with temperature Fig. 11 Variation of pressure-viscosity coefficient with increasing kinematic viscosity ν (40 C) tribological analysis under EHL lubrication conditions. Acknowledgments This study was supported by JSPS KAKENHI Grant Number The authors would like to thank Mr. Kenichi Murai of Mie University for their technical assistance. References [1] ASME Research Committee on Lubrication, Pressure Viscosity Report, ASME, New York, Fig. 12 Variation of pressure-viscosity coefficient with increasing kinematic viscosity ν (100 C) [2] Bair, S., High Pressure Rheology for Quantitative Elastohydrodynamics, Elsevier, Amsterdam, 2007, [3] Nakamura, K. and Muraki, M., Analysis of Shear Behaviour of a Low-Viscosity Oil Film at EHL Conditions, Transactions of the Japan Society of Mechanical Engineers, Series C, 72, 718, 2006, (in Japanese). [4] Bair, S., Pressure-Viscosity Behavior of Lubricants to 1.4 GPa and Its Relation to EHD Japanese Society of Tribologists ( Tribology Online, Vol. 11, No. 2 (2016) / 448

6 High-Pressure Viscosity Measurements of Polyalphaorefins at Elevated Temperature Traction, STLE Tribology Transactions, 43, 1, 2000, [5] Nakamura, Y., Sanda, A. and Matsubo. H., High-Pressure Viscosity Measurements of Traction Oils up to 2 GPa and up to 200 C, Journal of Japanese Society of Tribologists, 50, 4, 2005, (in Japanese). [6] Nakamura, Y., Matsubo. H., Yoshizaki, K. and Komiya, H., High-Pressure Viscosity Measurements of Vegetable Based Biodegradable Lubricant Oils up to 2.5 GPa and Tribological Characteristics, Proc. Austrib 2006, Brisbane, Australia, CD-ROM, 2006, 1-6. [7] Dowson, D. and Higginson, G. R., Elastohydrodynamic Lubrication, Pergamon, London, 1966, 89. [8] Munro, R. G., Piermarini, G. J. and Block, S., Wall Effects in a Diamond-Anvil Pressure-Cell Falling Sphere Viscometer, Journal of Applied Physics, 50, 5, 1979, [9] Nakamura, Y., Ito, T. and Matsui, M., Establishment of Simple Pressure Evaluation in Diamond-Anvil Pressure Cell Apparatus and High-Pressure Viscosity Measurements of Lubricant Oils, Journal of Japanese Society of Tribologists, 53, 5, 2008, (in Japanese). [10] Hata, K. and Tamoto, Y., Prediction of High- Pressure Viscosity of Various Lubricants, Journal of Japanese Society of Tribologists, 55, 10, 2010, (in Japanese). [11] Bridgman, P. W., Viscosities to 30,000 kg/cm 2, Proceedings of the American Academy of Arts and Sciences, 77, 4, 1949, [12] Yasutomi, S., Bair, S. and Winer, W. O., An Application of a Free Volume Model to Lubricant Rheology I, Transactions of the ASME, Journal of Tribology, 106, 2, 1984, [13] Blok, H., Inverse Problems in Hydrodynamic Lubrication and Design Directives for Lubricated Flexible Surfaces, Proc. International Symposium on Lubrication and Wear, Houston, 1963, Japanese Society of Tribologists ( Tribology Online, Vol. 11, No. 2 (2016) / 449