Pressure-viscosity Coefficient Research Articles

Derivation of basic rheological parameters from experimental elastohydrodynamic lubrication traction curves of low-viscosity lubricants

The rheological parameters characterizing the non-linear viscosity of lubricants having a low viscosity at a Hertzian contact were determined on an assumption of a parallel film, a Hertzian pressure distribution and the Eyring model expressing the relationship between the shear stress and the shear rate in an elliptical contact. Making a reasonable approximation and taking the variation in viscosity with pressure in the Hertzian contact into account, an approximate formula expressing the mean shear stress with shear rate was derived as a function of a viscosity-pressure coefficient and the representative stress determining the onset of non-Newtonian behaviour. Traction characteristics of two kinds of paraffinic mineral oil were determined with an elastohydrodynamic lubrication tester. Then, a regression analysis using a least-squares method with the proposed formula was applied to the traction measurements, from which the available rheological parameters and the effective pressure were obtained. The viscosity-pressure coefficients derived from traction measurements fall on the extrapolated line from the relation between the viscosity-pressure coefficient and the pressure in the pressure range from atmospheric pressure to 0.3 GPa obtained with a high-pressure viscometer.

Influence of load and lubricants on EHD film thickness and rolling‐contact fatigue lives of AISI 52100 steel balls

AbstractThis work has evaluated the influence of load and type of lubricant on the thickness of the elastohydrodynamic (EHD) film and the rolling‐contact fatigue lives of AISI 52100 steel balls. The lubricants studied have various viscosities and included two mineral oils and five synthetic oils from three families. Firstly, the central film thickness was determined in order to predict the lubrication regime. The stress—number of cycles fatigue curves were then calculated by means of Weibull plots, and the fatigue mechanism was evaluated.The test machine used for the analysis was a Seta‐Shell 1980 four‐ball EP lubricant tester. The 12.7 mm diameter test balls were made from a single batch of carbon‐vacuum‐deoxidised AISI 52100 steel with hardness RC65.Elastohydrodynamic film thickness estimation was carried out using pressure—viscosity coefficients (a). In this study, to calculate (X), a new interferometric technique, ultrathin film interferometry, was employed to measure the film thickness. A practical method was developed for evaluating EHD, mixed film, and solid lubrication processes. Micrographic mapping and energy dispersive spectroscopy (EDS) were used to analyse the rolling track of the test balls.

The Elastohydrodynamic Friction and Film Forming Properties of Lubricant Base Oils

The stringent and often competing requirements of high fuel economy and low emissions are placing increasing emphasis on the selection of appropriate base oils for modem engine lubricants. Two properties now recognized as important in engine oil design are the elastohydrodynamic (EHD) traction coefficient and the pressure-viscosity coefficient. The former determines the level of friction in high pressure contacts such as cams, while the latter plays a major role in determining the EHD film thickness. Unfortunately, for many fluids there is a broad correlation between the two properties so that a low traction coefficient implies a low pressure viscosity coefficient and thus film thickness. This paper measures the traction and film-forming properties of a wide range of base oil types at realistic engine oil temperatures in order to both explore the extent of this correlation and to determine the dependence of EHD lubricant properties on base oil compositions. Presented as a Society of Tribologists and Lubrication Engineers paper at the World Tribology Congress in London, United Kingdom, September 8–12, 1997

The Lubricity of Gasoline

A study has been made of the lubricating properties of gasoline fuel. A conventional HFRR diesel fuel lubricity tester has been modified to measure gasoline wear. Using this test equipment, a number of features of gasoline lubricity have been investigated, including the comparative lubricating behavior of gasoline, the influence of detergent additives and oxygenates on wear and the wear behavior of a series of refinery streams employed in gasoline blending. The lubricity of a range of pure organic chemicals known to be present in gasoline has also been studied. From these measurements it has been shown that, except for components such as dienes and diaromatics, the HFRR lubricating properties of most gasoline hydrocarbon constituents are broadly independent of chemical structure bur depend significantly on viscosity. Using these measurements, predictive wear equations based on gasoline group analysis have been developed. Because it has been found that viscosity plays a role in determining the wear properties of gasoline, the elastohydrodynamic (EHD) film-forming and friction properties of gasoline have been measured and compared to those of diesel fuels. This shows that the combination of gasoline's very low viscosity and low pressure-viscosity coefficient results in very thin EHD film thickness generation and also very low friction in full-film EHD conditions. Presented at the 53rd Annual Meeting in Detroit, Michigan May 17–21, 1998

The Effects of a Transversely Oriented Bump and Groove on Reciprocating EHL Films.

The behavior of elastohydrodynamic lubrication (EHL) films is directly observed with all oil having rather high pressure-viscosity coefficient under conditions of rolling or sliding reciprocating motion using the optical interferometry technique. The EHL conjunction is formed by an oscillating glass disk and a steel ball having a transversely oriented long bump and a groove. Under pure rolling conditions, the effects of the surface irregularity is localized to a region around it. Under pure sliding conditions, each bump and groove which stays at the entrance of the EHL conjunction causes a reduction ill film thickness. Its reduction rate is larger for the bump than for the groove. It has however been found that under pure sliding reciprocation with a short length of stroke, the collapse of the oil film and consequently the surface damage easily occur when the groove exists in the inlet of the contact.

High-pressure rheology of lubricants and limitations of the Reynolds equation

A review of high pressure rheology leads to the conclusion that the results from rheometers may be used to generate empirical rate equations which are useful in modelling elastohydrodynamic traction. However, an analytical treatment of piezoviscous liquids reveals that the Reynolds equation adequately captures the mechanics of the piezoviscous liquid only when the shear stress is much less than the reciprocal of the pressure viscosity coefficient. Otherwise the cross film pressure gradient may be significant and secondary flows result.

On the Choking of the Flow of Piezoviscous Liquids

Experimental evidence for choking of a piezoviscous fluid in a capillary tube is presented. It is shown that under a nearly isothermal condition, it is possible for the flow to experience choking whereby increasing the inlet pressure ceases to affect the flow rate. The occurrence of this phenomenon can be predicted by noting a singularity in the flowrate equation in a capillary tube under typical conditions encountered in injection molding (cf. Denn, 1981). Further examination of the general equations governing the shear flow of laminar, incompressible, linearly viscous (Newtonian) liquids under high pressures reveals a singularity in the solution for the pressure gradient. This apparently unreported phenomenon is shown to occur in liquids whose viscosity, μ, increases exponentially with pressure, p, as μ = μ0eαp, where α denotes the pressure-viscosity coefficient. For a two-dimensional configuration with the shearing action taking place in the x direction and with p = p(x, y), the singularity is shown to take place when: τyx=±(1/α)1+α2τxxτyy, at which case both δp/δx and δp/δy →∞. The occurrence of such a singularity in the pressure gradient may have an important physical implication in lubrication flows particularly in concentrated contacts such as elastohydrodynamic lubrication of rolling element bearings and gears.

A study of temperature rise in oil due to compression

Temperature rises of various oils were measured in both impact tests and quasi-adiabatic compression tests. A steel ball impacted against an oiled sapphire glass in the impact test. It was found that the maximum temperature rise was 45 °C in impact tests. A close relationship between temperature rise and α amax was found for oils of relatively low viscosity, where α was the pressure-viscosity coefficient and amax was the maximum acceleration of the hammer during impact; namely, the temperature increased with each increase in the product of the contact force and the pressure-viscosity coefficient. In the compression tests, the temperature increased almost linearly with increase in the volumetric strain regardless of the type of oil. The order of the temperature rise for the corresponding oil in each experiment was reversed; i.e. a higher temperature increase was observed for an oil of smaller pressure-viscosity coefficient in the compression test. On the contrary, a higher temperature rise was noted in the case of a larger pressure-viscosity coefficient in the impact test. As far as the temperature rise is concerned for entrapped oil in the impact tests, there exists an optimum combination of viscosity and pressure-viscosity coefficient.

The optical EHD method applied to the study of ageing of biodegradable oils

AbstractIn the present study, modifications of the lubricating properties of vegetable oils, which had undergone accelerated ageing, were quantified, using the optical EHD method. Each oil sample was examined in an optical viscometer in order to measure film thickness vs. contact speed. From these results the pressure—viscosity coefficient was calculated, by adjusting theoretical values. The modifications were related to molecular changes, which were observed with various tools of chemical analysis, including gel permeation chromatography (GPC).

Friction and Wear Characteristics of Polyvinylether(PVE) as a Lubricant for Alternative Refrigerant.

The tribological characteristics of a synthetic lubricating oil of polyvinylether (PVE) for a alternative refrigerant have been studied using three different friction testers with polyolesters (POE), polypropylene glycols (PPG), hydrogenated coal-tar oil and traction oil. In boundary lubrication regime, PVE gave higher friction coefficient and lower wear amount than POE and PPG. The high friction and low wear of PVE with high viscosity-pressure coefficient were attributed to a solidified film formed in a conjunction zone of high contact pressure. Although the solidified film had a high shear strength leading to a high coefficient of friction, it had a high ability to prevent the direct contact between rubbing surfaces compared with a boundary film consisting mainly of the adsorbed molecules of POE. The tribological characteristics in boundary lubrication are effected by two kinds of boundary films, adsorbed film and solidified film.

Lubricant characterization by molecular simulation

Lubrication is a phenomenon of immense practical importance and fundamental scientific interest, and the automobile engines of the future are envisioned by the Partnership for a New Generation Vehicle will require the development of improved lubricants that perform well at higher operating temperatures and higher engine speeds. The rheological properties of liquid alkanes of intermediate molecular sizes (C20H42-C40H82) are among the most important properties in lubricant performance. Though realistic study of these systems by molecular simulation has previously been limited by both high computational costs and the lack of potential models accurate over a wide range of physical conditions, the advent of massively parallel supercomputers has now made such studies possible. As an illustration of the ability of molecular simulation as a useful tool for lubricant development, we present the first molecular-simulation-based calculation of the kinematic viscosity index of an alkane liquid, viz. 2,6,10,15, 19,23-hexamethytetracosane, commonly called squalane. In the mass range of interest, squalane is one of the few commercially available isoparaffins and has been the subject of previous studies by molecular simulation (Mondello and Grest 1995; Mundy et al., 1997). Though numerous properties of a lubricant are important to end-use applications, the viscosity is considered most significant. Mundy et al. (1996) investigated the variation of decane’s viscosity with pressure, calculating its pressureviscosity coefficient by equilibrium molecular dynamics simulations. The kinematic viscosity index (VI) is another widelyused industrial characterization of automotive lubricants. It was proposed by Dean and Davis (1929) as an indication of an oil’s viscosity-temperature characteristics in terms of its Saybolt viscosities at 311 K (100°F) and 372 K (210°F). Two series of reference lubricating-oil fractions (H and L) were used for comparison. Series H exhibited little change of viscosity with temperature while the viscosities of series L oils exhibited large variation with temperature. Series H and L represented, respectively, the best and worst oils available in 1929. Series H oils were assigned a VI of 100, series L a

Strain-controlled fatigue properties of Ti 3Al based alloy : Cao, J., Sun, F., Cao, C. and Gao, Y. Xiyou Jinshu Cailiao yu Gongcheng (Rare Metal Materials and Engineering) (1996) 25, 17–20

This work has evaluated the rolling-contact fatigue lives of AISI 52100 steel balls with several mineral and synthetic oils with and without additive using a four-ball tester. The studied lubricants include S.N.-350 (mineral oil), S.N.-600 (mineral oil), TMP-05 (synthetic polyol ester), TMP-05 + 2%ZnDDP, P.A.G.-9 (synthetic polyalkyl glycol), P.A.G.-12 (synthetic polyalkyl glycol) and Breox-B-135X (synthetic polyalkyl glycol). Weibull plots and S-N (stress-number of cycles) of L10 and L50 are given to all the tested oils. Pressure-viscosity coefficients for different tested oils are estimated experimentally for understanding the fatigue test results. The results indicate: (1) synthetic polybutene HYVIS-07 gives the longest rolling-contact fatigue life to AISI 52100 steel balls among all the mineral and synthetic oils studied in the present work, which may be attributed to its highest pressure-viscosity coefficient among the tested oils; (2) the rolling fatigue performance of a synthetic oil can be better or worse than that of a mineral oil, depending on the nature of the synthetic oil family. The capability of improving the rolling fatigue lives of tested mineral and synthetic oils increases in the order synthetic polyol ester, synthetic polyalkyl glycol, mineral oil, and synthetic polybutene; (3) a higher viscosity oil will lead to a longer rolling life, but the influence of viscosity in synthetic oil on the rolling fatigue life of steel balls will be less than that of changing synthetic oil family; (4) synthetic oil with E.P. antiwear additive has al longer rolling fatigue life compared with the case without additive.

The Elastohydrodynamic Properties of Lubricants in Refrigerant Environments©

The elastohydrodynamic (EHD) film-forming properties of several refrigeration oils placed in pressurized refrigerant environments were investigated by an interferometric EHD tester equipped with a pressurized vessel. It has been shown that the oils with dissolved refrigerants formed EHD films at the point of contact in the same manner as lubricant base fluids. It was also found that greater amounts of dissolved refrigerant in the oil decreased not only the viscosity but also the viscosity-pressure coefficient of the oil. In this paper, the authors describe a method to predict the viscosity-pressure coefficient of oils with dissolved refrigerants. Presented as a Society of Tribologists and Lubrication Engineers paper at the ASME/STLE Tribology Conference in San Francisco, California, October 13–17, 1996

Rolling-contact fatigue lives of steel AISI 52100 balls with eight mineral and synthetic lubricants

This work has evaluated the rolling-contact fatigue lives of AISI 52100 steel balls with several mineral and synthetic oils with and without additive using a four-ball tester. The studied lubricants include S.N.-350 (mineral oil), S.N.-600 (mineral oil), TMP-05 (synthetic polyol ester), TMP-05 + 2%ZnDDP, P.A.G.-9 (synthetic polyalkyl glycol), P.A.G.-12 (synthetic polyalkyl glycol) and Breox-B-135X (synthetic polyalkyl glycol). Weibull plots and S-N (stress-number of cycles) of L 10 and L 50 are given to all the tested oils. Pressure-viscosity coefficients for different tested oils are estimated experimentally for understanding the fatigue test results. The results indicate: (1) synthetic polybutene HYVIS-07 gives the longest rolling-contact fatigue life to AISI 52100 steel balls among all the mineral and synthetic oils studied in the present work, which may be attributed to its highest pressure-viscosity coefficient among the tested oils; (2) the rolling fatigue performance of a synthetic oil can be better or worse than that of a mineral oil, depending on the nature of the synthetic oil family. The capability of improving the rolling fatigue lives of tested mineral and synthetic oils increases in the order synthetic polyol ester, synthetic polyalkyl glycol, mineral oil, and synthetic polybutene; (3) a higher viscosity oil will lead to a longer rolling life, but the influence of viscosity in synthetic oil on the rolling fatigue life of steel balls will be less than that of changing synthetic oil family; (4) synthetic oil with E.P. antiwear additive has al longer rolling fatigue life compared with the case without additive.

Evaluation of film-forming capability of refrigeration lubricants in pressurized refrigerant atmosphere

In order to investigate the effect of refrigerant on the film-forming capability of refrigeration lubricant, we have developed an apparatus to measure oil film thickness under pressurized atmosphere. As a result of comparison among several types of lubricants, mineral oils (particularly naphthenic mineral oil) which were currently used showed superior ability of film-formation to new synthetic ones, polyalkylene glycol (PAG) or polyol ester (PE), in a vacuum. However, the level of superiority reduced as the refrigerant pressure increased, thus the capability was identical to that of synthetics at a pressure of 0.6 MPa. On the other hand, there was little difference between PAG and PE at the atmospheric pressure of vacuum to 0.6 MPa. It was estimated that the pressure-viscosity coefficients of these new refrigeration lubricants were almost identical.

Rheology of Perfluoropolyalkylether Fluids in Elastohydrodynamic Lubrication

The rheological characteristics of two branched and two linear, commercial perfluoropolyalkylether (PFPAE) fluids were studied under high pressures and temperatures. The effects of branching and carbon-to-oxygen (C :O) ratio on the pressure-viscosity-temperature behavior and on the non-Newtonian behavior of these fluids were studied experimentally under high pressures and temperatures. The branching and the higher C :O ratio seemed to increase the pressure-viscosity coefficients of these fluids. The effects of the viscosity and the pressure-viscosity coefficient on the capabilities of these fluids to generate elastohydrodynamic lubrication (EHL) film thickness were studied and compared with experimental measurements. All of the fluids studied seemed to follow the Roelands viscosity model and classical EHL theory (1). The C :O ratio also influenced the temperature dependence of the limiting-shear-strength proportionality constant. The results show that for similar-viscosity fluids, the linear PFPAE with higher C :O ratio is most desirable for wide temperature use.

Bulk Modulus of Solidified Oil at High Pressure as Predominant Factor Affecting Life of Thrust Ball Bearings

In a previous paper, it was pointed out that the solidification behavior of mineral oils at high pressures exceeding glass transition points plays an important role on bearing life. Further detailed investigations have been carried out based upon actual observations of solidification phenomena of traction oils and mineral oils. Traction oils characterized by large pressure-viscosity coefficients and high friction result in shorter bearing life, in spite of their excellent separating film formation ability, in particular, under solidified conditions. The general tendency of mineral oils shows that bearing life increases with the film parameter. However, the beneficial effect of high film parameters of traction oils is considered to be disturbed by high friction, which is found to increase linearly with the bulk modulus of solidified oil. In view of this fact that brittleness of solidified oils is estimated by the temperature difference from the viscoelastic solid transition to the initiation of cracks under lowering temperature condition. Since this is inversely proportional to the bulk modulus, the high modulus is considered to promote lowering of the bearing life. In particular, thrust ball bearings operate with ball spinning which acts to cause brittle failure of solidified films. Both factors, i.e. expectation of the beneficial effect to improve bearing life and the detrimental one to increase friction and temperature rises, are in conflict with each other, but are both characterized by a high bulk modulus under the elastic-plastic condition. The present investigation was carried out in order to clarify merits or demerits of the high bulk modulus of supplied oil concerning bearing life. Conversely, it is noted that mineral oils and polyalphaolefins show shorter life at high temperatures exceeding the glass transition points.

Elastohydrodynamic lubrication at pure squeeze motion

Experimental and theoretical studies of elastohydrodynamically lubricated contacts normally assume static or quasi-static conditions. Non-steady conditions are, however, common. In this paper the case of a ball impacting a flat lubricated surface is investigated theoretically. This case implies transient conditions and the lubricating effect is due to pure squeeze action. Pressure and film thickness distributions are computed during impact and rebound. The results of the analysis show the effects of ball mass, initial impact velocity, lubricant properties and the thickness of the applied lubricant layer on the minimum film thickness. Increased impact velocity increases the minimum value of film thickness achieved during the bounce. The damping capacity of the lubricating film is very high at low impact velocity and small ball mass. In fact, the damping is so high that no rebound occurs if the velocity or the ball mass are smaller than certain critical values. The thickness of the lubricant layer has no influence on the results if it is greater than a certain value. If the pressure-viscosity coefficient is increased, the film becomes thicker.

Elastohydrodynamic Lubrication at Impact Loading

Experimental and theoretical studies of elastohydrodynamically lubricated contacts normally assume static or quasi-static conditions. Nonsteady conditions are, however, very common, e.g., in machine elements such as ball bearings, gears, and cam-follower mechanisms. In this paper, the case of a ball impacting a flat lubricated surface is investigated theoretically. This case implies transient conditions and the lubricating effect is due to pure squeeze action in the contact. Pressure and film thickness distributions are computed during impact and rebound. The results of the analysis show the effects of ball mass, initial impact velocity, lubricant properties, and the thickness of the applied lubricant layer on, for example, minimum film thickness, maximum impact force, and maximum pressure. Increasing impact velocity increases the minimum value of film thickness achieved during the total impact time. The damping capacity of the lubricating film is very high at low impact velocity and small ball mass. In fact, the damping is so high that no rebound occurs if the velocity or the ball mass are smaller than certain critical values. The thickness of the lubricant layer has very little influence on the results if it is thicker than a certain value. If the pressure-viscosity coefficient is increased, the film becomes thicker.

Behavior of Traction Oils under Impact Loads

The squeeze film forming ability of traction fluids is studied under impact load by a falling bearing steel ball against a stationary cylindrical surface or flat anvil made of mild steel, bearing steel, or aluminum. The effect of the pressure-viscosity coefficient and of the viscosity is investigated for plastic and elastic impact. For soft materials, oils with high pressure-viscosity coefficients maintain much greater surface separation under impact load. The time fraction of separation by the oil film increases linearly with the product of the pressure-viscosity coefficient and the yield pressure of the anvil material. It decreases with an increase in surface roughness. Similar results are observed under impact on stationary or rotating surfaces. These results can be used to estimate the solidification behavior of traction oils. In the case of the elastic impact for hard materials, the coefficient of restitution of the ball is influenced mainly by the squeeze film effect, which is governed by viscosity ...