Thermal analysis of an Eyring fluid in elastohydrodynamic traction

Recent research into elastohydrodynamic (EHD) traction has shown that under high pressure and isothermal conditions the flow properties of typical lubricants follow the Eyring relation between shear stress τ and shear rate /.γ: $\text{η/.γ = τ}{}_0\text{sinh(}\text{τ}\text{τ}{}_0\text{)}$ where η is the Newtonian viscosity and τ₀ a representative stress. The maximum in the traction curve arises from shear heating, and Crook's thermal analysis for a Newtonian lubricant has been modified to apply to an Eyring lubricant.In an EHD contact the pressure and hence the viscosity η vary from inlet to outlet, but it is shown that under the conditions of maximum traction it is sufficiently accurate to use the average values of η and τ₀ associated with the average values of pressure and temperature through the length of the contact. A simple formula can then be derived for the maximum traction coefficient in terms of the properties of the fluid (viscosity, pressure and temperature indices, and the representative stress τ₀ and the operating conditions (contact pressure, speed and film thickness).     

On the Temperature Effect on the Parameters of the Specific Friction Force of Metals

Temperature relationships of the maximum coefficient of static friction, maximum specific static friction force, and its parameters τ₀ and β at the ball-plane contact are experimentally investigated. A ball indenter with a radius of 0.5 mm made of ZlM80 alloy contacted a flat gold sample (99.99%). The range of contact loads was 0.5–4 mN, and the temperature range was 24–160°C. The experiments have shown that the coefficient of friction, specific friction force, and parameter β increase with increasing temperature, while parameter τ₀ decreases.     

Molecular structure of synthetic hydrocarbon oils and their rheological properties governing traction characteristics

Correlations between rheological properties governing traction and the molecular volume or structure of synthetic hydrocarbon oils are presented. A simplified thermal theory is applied to the traction curves experimentally determined on a four-roller machine, and characteristic parameters are obtained. It is shown that effects of molecular volume on the parameters are small and that the parameters are primarily related to the molecular structures. Further, the maximum traction coefficients of the oils are critically dependent on the effective viscosity—pressure coefficient among the parameters.     

Lubricant oils additivated with polymers in EHD contacts: Part 1. Rheological behaviour

This paper reports on the influence of a polymer additive on the traction behaviour of a mineral oil investigated using a two‐disc machine at different temperatures and contact pressures. A semi‐empirical approach was used for determining the effective lubricant rheological parameters ‐ the elastic shear modulus, the viscosity of the lubricant, and the limiting and Eyring stresses ‐ in elastohydrodynamic contacts. Using this approach, the effect of polymer concentration on the rheological parameters that appear in both the Johnson‐Tevaarwerk and Bair‐Winer models was quantified. The influence of operating conditions, such as pressure, oil temperature, and polymer concentration, on the traction coefficient, limiting shear stress (from the Bair‐Winer model), Eyring stress (from the Johnson‐Tevaarwerk model), shear modulus, and apparent viscosity was also investigated.     

Base fluid parameters for elastohydrodynamic lubrication and friction calculations and their influence on lubrication capability

In this study, base fluid parameters for elastohydrodynamic lubrication (EHL) and friction analyses have been determined experimentally. The viscosity at atmospheric pressure, η₀, the pressure‐viscosity index, α, and the EHL friction coefficient, γ, are important parameters in EHL theory and they are crucial in the selection of efficient lubricants for different applications. This investigation focuses on three important lubrication mechanisms: the capability of forming a separating lubricant film, the friction generated in a lubricated contact, and the height of pressure peaks, such as the outlet pressure spike and pressure ripple caused by surface roughness. The influence of different lubricant parameters on these three mechanisms is discussed. The value of α is measured in a Couette high‐pressure viscometer, and the value of γ is obtained from a jumping‐ball device. Other parameters discussed are temperature‐viscosity coefficient, β, bulk modulus, B₀, thermal conductivity at atmospheric pressure, λ₀, and heat capacity unit volume, ρc_p0. A comparison between traditional mineral base oils and environmentally adapted oil based on rapeseed oil and synthetic esters contributes to the further understanding of the performance of these new materials in lubrication applications. It is shown that rapeseed oil and synthetic esters have good lubricating properties and are, in most cases, better than mineral oils.     

Bulk Modulus of Lubricating Oils as Predominant Factor Affecting Tractional Behavior in High-Pressure Elastohydrodynamic Contacts

The phase diagrams corresponding to transition from liquid to viscoelastic solid and that from viscoelastic solid to elastic-plastic solid of Santotrac100 (SN100), mineral oil, synthetic naphthenic oil, polybutene, and tetradecane were first made up by high-pressure density measurements and others. The bulk modulus of lubricating oils under a quasi-static condition was evaluated using a phase diagram. The results indicated that the bulk modulus of lubricating oils is closely related to the oil molecular packing parameter T _VE ?T (where T _VE is the viscoelastic solid transition temperature at pressure p, and T is the oil temperature). The constant values of the bulk modulus in the elastic-plastic range are different depending on the molecular structures of the oils. It has also been shown that SN100, mineral oil, synthetic naphthenic oil, and polybutene converted to amorphous solids at high pressures and tetradecane converted to molecular crystal. Next, the elastohydrodynamic lubrication tractions were measured by a ball-on-disk machine. The results indicated that the maximum traction coefficient is closely related to T _VE ?T. As a result, the importance of the bulk modulus as a predominant factor for traction characteristics of lubricating oil was pointed out.     

Polyethylene as an Additive for Mineral Oils — Part II: EHL Traction Behavior

In Part I of the paper ((1999), Trib. Trans., 42, pp. 851–859) we investigated the effect of the polyethylene concentration on the film forming properties in a rolling bearing. This second part presents the influence of the polymer additive concentration on the traction behavior experienced using a two-disk machine at different temperatures and contact pressures.

By using the traction data, a semi-empirical approach for determining the effective lubricant theological parameters in EHL contacts was performed. Using this approach, the effect of polymer concentration upon rheological parameters that appear in the Johnson and Tevaarwerk model with Eyring stress was quantified.     

Investigation into the traction coefficient in elastohydrodynamic lubrication

The elastohydrodynamic traction coefficients of two Chinese aviation lubricating oils were investigated for various loads, rolling velocities, and lubricant inlet temperatures using a self‐made test rig. Traction coefficient versus slide‐to‐roll ratio curves were generated. The concept of critical load varying with the lubricant temperature is proposed. This paper presents a new empirical formula for the dynamic performance design of high‐speed rolling bearings, that relates traction coefficient with normal load, rolling velocity, and lubricant inlet temperature. The coefficients of the formula may be computed by regression analysis of the experimental data. Two example calculations are presented. The predicted results from the formula agree well with experimental observations.     

Molecular interaction originating from polar functional group in lubricants and its relationship with their traction property under elastohydrodynamic lubrication

The correlation between molecular interaction and traction properties was investigated using a traction tester and in situ observation of elastohydrodynamic lubrication film with a micro‐Fourier transform infrared spectrometer. The sample oils used were polypropylene glycols (PPGs) with the end‐group of alcohol or ether and a synthetic hydrocarbon oil, poly‐α‐olefin. From the traction tests, it was found that the traction coefficient of PPG was sensitive to the end‐group. PPG with alcohol as the end‐group showed a higher traction coefficient than that with the ether group. In situ observation with a micro‐Fourier transform infrared was performed in order to investigate the molecular interaction of the lubricant oil. It was found that the hydrogen bonding of hydroxyl groups in PPG was strengthened by high pressure in the Hertzian contact region. These results suggest that the rheological properties in the elastohydrodynamic lubrication contact region were affected by the strengthened hydrogen bonding. Copyright © 2014 John Wiley & Sons, Ltd.     

Effect of EHL Contact Conditions on the Behavior of Traction Fluids

New infinitely variable transmission (IVT) systems are under development for the automotive industry as a means to achieving significant fuel economy benefits. These systems rely on the lubricating fluid to transmit the drive train loads across the interface of the transmission components. This requires the development of new fluids that exhibit high traction properties under elastohydrodynamic lubrication (EHL) conditions. However, it has been reported recently that the traction performance of some fluids can reduce dramatically as temperature is reduced. This may place severe operational limits on IVT systems and suggests that the low-temperature traction properties of fluids for these systems should be studied in order to understand the mechanism for the observed reduction in traction.

The work reported here is an experimental study aimed at identifying whether low temperature traction reduction is related to a fundamental change in rheological behavior specific to the fluids tested or to more generic changes in the EHL contact conditions. A series of model experiments were performed using a mini traction machine (MTM) on three high-viscosity polybutene samples. The results have been mapped against previously reported non-dimensional parameters used to identify different EHL regimes. The results show that dramatic reductions in traction occur when the contact transitions from the rigid piezo-viscous (RP) toward the rigid iso-viscous (RI) region. Similar results were also found for two other high-viscosity fluids of different molecular structure and lower traction properties. The results support the hypothesis that the reduction in traction observed at low temperature is due to a change in EHL contact conditions rather than being solely due to a change in the rheological performance of the test fluids.     

Energy conservation in stainless steel cold rolling applications

In order to predict the performance of rolling oils in actual production mills, from tests in laboratory mills, the influence of various factors, such as shape factors work roll diameter (D), strip thickness (h₁), operating conditions (reduction rate (r), peripheral velocity of roll (U₀), strip velocity (U₁)) and kinematic viscosity of the rolling oil (υ₀) was investigated. A parameter RLI (Rolling Lubrication Index = u₀(U₀+U₁)(1−r)(D/2h₁.r)^½) was found to be useful in predicting lubricating conditions in actual production mill applications. The coefficients of friction of mineral oils, some synthetic hydrocarbons including polybutene, and several kinds of additives were obtained from laboratory mills under the same condition of RLI value as that for finish rolling in actual production mills. With hydrocarbons, paraffins showed the lowest coefficient offriction, while aromatics exhibited a higher coefficient of friction, with naphthenes showing the highest. A high-quality rolling oil was formulated using a combination of ester and paraffinic mineral oil. It is observed that this new oil can save 14% of energy consumed by a laboratory mill compared with conventional rolling oils. In production mills, nearly the same energy conservation level can be achieved.     

航空润滑油拖动特性动态数据库的建立

建立的润滑油拖动特性动态数据库具有查询、计算、绘图、比较、维护和设置步长等多项功能.通过该数据库,可以查到多种航空润滑油在多种工况条件下的拖动系数及拖动系数计算公式中的系数值,可以对不同润滑油的拖动系数进行比较及同一种油的计算值和试验值进行比较.     

Influence of the size,geometry, and material of the rollers on EHD traction

The influence of the parameters relating to the rolling elements on traction in EHD contacts is experimentally studied on a two-roller machine, in which experiments with point contacts are conducted for two paraffinic mineral oils, a synthetic naphthene, and a synthetic ester. Firstly, it is shown that the same traction curves are obtained in both internal and external contacts when the effective radius in rolling direction of the rollers is equal. The effect of an increase in the size of the rollers is to increase the film thickness and this results in a gentle decline in the maximum traction coefficient. As the effective radius in transverse direction is increased, so the traction decreases for a paraffinic mineral oil, while that for a synthetic naphthene remains constant independent of the geometry of the rollers. Finally, the effect of the material of the rollers is studied, employing rollers made of steel, ceramics, phosphorus bronze, brass, and aluminium alloy. The traction obtained under an identical normal load can be arranged according to the effective elastic modulus of the rollers for each oil. However, under identical contact pressure the same maximum traction curve is obtained independent of the material, but the decline in traction in the thermal region is slightly steeper with the ceramic than with the steel rollers because of the difference in the temperature rise of the fluid film.     

Non-newtonian thermal analysis of an EHD contact lubricated with MIL-L-23699 oil

A thermal and non-Newtonian fluid model under elastohydrodynamic lubrication conditions is proposed, integrating some particularities, such as the separation between hydrodynamic and dissipative phenomena inside the contact. The concept of apparent viscosity is used to introduce the non-Newtonian behaviour of the lubricant and the thermal behaviour of the contact into the Reynolds equation, acting as a link element between the hydrodynamic and dissipative components of the EHD film, independently of the rheological and thermal models considered. The apparent viscosity enables the application of the rheological model better adapted to each lubricant, without appealing to special formulations of the EHD problem.The Newton–Raphson technique is used to obtain the lubricant film geometry and the pressure distribution inside the EHD contact. The shear stresses developed in the fluid film are evaluated assuming the non-linear Maxwell rheological model. The surfaces and lubricant temperature distributions are determined using the simplified Houpert's method, applied to the inlet contact zone, and the thermal method proposed by Tevaarwerk is applied in the high pressure contact zone.The non-Newtonian thermal EHD model is applied to the analysis of a contact lubricated with MIL-L-23699 oil. Significant results are obtained for the centre and minimum film thickness, for the inlet shear heating and film thickness reduction factor (φ_T), for the temperature rise of the lubricant and of the surfaces and for the friction coefficient inside the contact, considering wide ranges of the operating conditions (maximum Hertzian pressure, inlet oil temperature, rolling speed and slide-to-roll ratio).Finally, the numerical traction curves determined are compared with the corresponding experimental results, showing very good correlation.     

Experimental and computational investigation of the traction coefficient of a ball traction drive device

Traction drive is a new kind of drive manner in which the power is transmitted by a thin oil film between transmission elements. This paper describes a ball traction drive device. The quasi-dynamics analysis was carried out for the transmission components of the ball traction drive device. The traction coefficients of oils Ub2 and HH-20 were calculated respectively with different rheological models. The elastohydrodynamic lubrication (EHL) film thickness and the traction coefficient between traction drive elements were measured. The results of the calculations are consistent with experiments.     

The effect of non-equilibrium condensation on the coefficients of force with the angle of attack in the transonic airfoil flow of NACA0012

A transonic flow with a non-equilibrium condensation past NACA0012 profile whose aspect ratio AR is 1.0 with the angle of attack was analyzed by numerical analysis using a TVD scheme, and investigated using an intermittent indraft type supersonic wind tunnel. Transonic flows of 0.70–0.90 in free stream Mach number with variations of Φ₀ and α were tested. For the same M_∞ and α, the increase in stagnation relative humidity Φ₀ caused a decrease in the drag coefficient of profile (that is total) which is composed of the components of form, viscous, wave and condensation; however, the lift coefficient up to Φ₀ = 50% increased in the opposite direction. As an example, in the case of M_∞ = 0.83, Φ₀ = 50%, α = 3○ and T₀ = 298 K, the decreasing rate of the coefficient of profile drag and the increasing rate of the lift coefficient compared to the case of Φ₀ = 0% caused by non-equilibrium condensation amounted to 65% and 52%, respectively. In addition, for the same Φ₀ and α, as the free stream Mach number M_∞ increased, at first, the lift coefficient increased slightly, and then suddenly severely dropped, and finally remained nearly constant. The suddenly dropped free stream Mach number in C_L became larger with an increase of Φ₀. It turned out that the drag coefficients of form and viscous were almost independent of Φ₀. The contribution of wave drag to the coefficient of profile drag for M_∞ = 0.83, Φ₀ = 30%, α = 3° and T₀ = 298 K amounted to approximately 79%, and in the case of Φ₀ = 60%, the contribution of the non-equilibrium condensation to the reduction in the coefficient of the profile drag compared to the case without condensation amounted to 75%. Especially, for the case of Φ₀ = 0% and α = 0°, there was an oscillatory flow region around M_∞ = 0.87.     

Reduction in axle oil operating temperatures by fluids with optimized torque transfer efficiencies

Effective axle oils must efficiently transfer torque from the drive‐train to the wheels, while maintaining low axle oil operating temperatures. Previous studies have shown that fluids, which form thicker elastohydrodynamic (EHD) films and have lower EHD friction, have higher torque transfer efficiencies (TE) and lower axle oil operating temperatures (OT). In general, oils with higher viscosities form thicker films and those with lower viscosities have lower EHD friction. Therefore, optimizing oil's rheological properties to maximize TE and minimize OT is difficult. In this paper, we examine two approaches to maintaining high TE while reducing OT. One approach is to minimize boundary friction since previous studies have shown that the boundary frictional properties of oils influence OT and not TE. A second approach is to more thoroughly examine the effect of rheology on film thickness and EHD friction. Film thickness and EHD friction are related to the high temperature high shear viscosity and pressure‐viscosity coefficient of oils. We have found that oils with high pressureviscosity coefficients and low high temperature high shear viscosities will form thick films and have low EHD friction. This optimized combination of physical parameters, along with lowering the boundary friction coefficient of axle oils, results in oils with high TE and low OT. Copyright © 2006 John Wiley & Sons, Ltd.     

A non-Newtonian model based on limiting shear stress and slip planes—parametric studies

Parametric studies and corresponding results are presented using a rheological model based on the limiting shear stress and possible occurrence of slip planes. The model is applied to elastohydrodynamically lubricated line contacts with smooth surfaces and isothermal conditions. A few investigations are carried out where different parameters are varied. The first study investigates the influence on the film thickness distribution due to a variation of the maximum Hertzian pressure when the slide-to-roll ratio is constant. The second study investigates how far the non-Newtonian region propagates at low slide-to-roll ratios for a few different values of the Hertzian pressure. The results show that it is a remarkably small slide-to-roll ratio necessary to cause slip planes in a large part of the Hertzian contact zone. A third study regards the influence of the entrainment velocity on the film thickness generation at different slide-to-roll ratios. Finally some rheological parameters are varied. First, only the limiting shear stress at atmospheric pressure (τ₀) is varied, and second, a few different lubricants are studied, each with their own set of rheological parameters.     

Temperature dependency of the fill factor in PV modules between 6 and 40 °C

The definition of the fill factor (FF) and a more accurate formula were used to study the temperature dependency of FF. To investigate FF changes as a function of the temperature in the photovoltaic (PV) modules, we used an equivalent circuit diagram that considers series and parallel resistances. Using a measurement setup that allows precise temperature control of the PV modules, the parameters V_oc, I_sc, V_m, I_m were measured between 6 and 40 °C. Using the theoretical model, a formula for the FF temperature gradient, ∂FF/∂t, could be found. The experimental results show that FF decreases with increasing temperature, and fitting the obtained data points results in a straight line. The FF has a negative temperature coefficient. Specifically, the obtained “defined value” for ∂FF/∂t is −0.00093 1/°C, while the theoretical value is −0.0015 1/°C.

     

Traction Characteristics of High-Temperature Powder-Lubricated Ceramics (Si3N4/αSiC)

As part of a high-temperature, dry-lubricated bearing technology and lubricant system development program, a high-speed, high-temperature disk-on-disk tribometer was utilized and a matrix of traction data covering a range of load, speed and temperature was obtained. The influence of dry powder lubricants, TiO₂ and MoS₂, on the traction coefficients between two ceramic materials, Si₃N₄ and SiC, was investigated. The most important results of this investigation are characteristic curves for the traction coefficient vs. the slide/roll ratio with dry powders which are reminiscent of fluids, and the observation of dry powder lubricants' lower traction coefficients and wear. Measured tractions are found to be a strong function of powder lubricant type and values decrease moderately with slide-to-roll ratio and load. The data, show a weak sensitivity to temperature.