A Film Thickness Correction Formula for Double-Newtonian Shear-Thinning in Rolling EHL Circular Contacts

Lubricants which contain a polymeric thickener will often display a second Newtonian plateau in measured flow curves. Like other manifestations of shear-dependent viscosity, this shear response will lead to an inaccurate prediction when the classical film-thickness formulas are employed. A correction formula has been developed from numerical experiments for a range of parameters of the double-Newtonian modified Carreau equation. The parameters of this shear-thinning model were selected from measurements for real lubricants obtained in Couette viscometers and a capillary viscometer. In addition, a full EHL film thickness formula has been derived from the same numerical experiments. The correction formula and the full formula were successfully validated using published film thickness data and published viscosity data for an EHL reference liquid, a polymer solution. Clearly, viscometer measurements of shear-dependent viscosity which contain the inflection leading to the second Newtonian are essential for a film-thickness calculation when a high-molecular-weight component of the lubricant is present.     

The Elastohydrodynamic Traction of Synthetic Base Oil Blends

The aim of this study was to investigate the elastohydrodynamic (EHD) properties of lubricant blends. Three base fluids of very similar viscosities, a polyalphaolefin, a diester and an alky lated aromatic, have been obtained and their EHD film thickness and traction behavior measured at a range of pressures. Blends of these fluids have been prepared and the influence of blending on film thickness and traction has been investigated. Traction measurements were conducted at film thicknesses between 100–200 nm and thermal analysis was incorporated to correct for in-contact shear heating. The blends showed a broadly linear relationship between the inlet pressure-viscosity coefficient and blend composition. Isothermal traction comparisons revealed that traction is not an additive property of lubricant blends.     

A Quantitative Solution for the Full Shear-Thinning EHL Point Contact Problem Including Traction

We present a realistic elastohydrodynamic lubrication (EHL) simulation in point contact using a Carreau-like model for the shear-thinning response and the Doolittle-Tait free-volume viscosity model for the piezoviscous response. The liquid lubricant modeled is a high-viscosity polyalphaolefin which has been shown by high-pressure viscometry to possess a relatively low threshold for shear-thinning as a single-component liquid lubricant. As a result, the measured EHL film thickness is about one-half of the Newtonian prediction. We derived and numerically solved the two-dimensional generalized Reynolds equation for the modified Carreau model based on Greenwood. In this simulation, viscosity was not treated as an adjustable parameter; the models used for the pressure and shear dependence of viscosity were obtained entirely from viscometer measurements. Truly remarkable agreement is found in the comparisons of simulation and experiment for traction coefficient and for film thickness in both pure rolling and sliding cases.     

A Rough Shear-Thinning Correction for EHD Film Thickness

A film thickness correction for shear-thinning in elastohydrodynamic contacts has been available that requires parameters obtained from flow curves generated for the specific liquid. For instances for which reduced accuracy is acceptable, a new rough film thickness correction has been formulated for pure rolling and a moderate amount of sliding based on Van Krevelen's graphical technique of estimating shear-thinning from the molecular weight. It has been shown to be useful for high-molecular-weight base oils, when lubricant specific shear-thinning data is absent, although it should most often overestimate the film thinning.     

A More Complete Description of the Shear Rheology of High-Temperature,High-Shear Journal Bearing Lubrication

High-pressure viscometers, which have in the past been used mainly to obtain rheological properties for elastohydrodynamics, can be used to obtain flow curves for motor oils that extend much deeper into the shear-thinning regime than conventional high-temperature, high-shear (HTHS) viscometers and the constitutive information obtained should be immensely helpful in journal bearing calculations. A simple infinite journal bearing calculation shows that the effect of pressure on viscosity is at least as important as the effect of shear rate and that shear rate alone is a poor measure of the extent of shear thinning in a bearing under HTHS conditions. Then variability in piezoviscous response should be at least as important as variability in shear thinning.

Sufficiently accurate theory exists to possibly design lubricants for both high load capacity and low friction by balancing pressure and shear rate effects.     

Effect of Starvation on Traction and Film Thickness in Thermo-EHL Line Contacts with Shear-Thinning Lubricants

The effect of starvation on traction and film thickness behavior in thermo-EHL rolling/sliding line contacts has been studied using full EHL simulations. The simulations employed the free volume equation for viscosity–pressure–temperature relationship and Carreau viscosity model to describe the shear-thinning behavior of the EHL lubricant. The simulation results were used to develop equations for estimating the factors by which the traction coefficient increases and film thickness decreases as a function of the degree of starvation. For the situations involving inadequate lubricant supply at the inlet, these factors can be used to correct the traction coefficient and central film thickness predicted with the assumption of fully flooded condition.     

Central film thickness formula for shear thinning lubricants in EHL point contacts under pure rolling

Based upon an extensive set of full EHL point contact simulations, this paper offers a central film thickness formula pertaining to shear-thinning lubricants with Carreau-type behavior. In order to develop a more generic and accurate version of film thickness formula, a recent work is extended by carrying out the simulations for widely varying operating loads and piezo-viscous coefficients along with the more realistic Doolittle's free volume based pressure–viscosity model. This equation is found to conform very well with the published experimental data for EHL lubricants with widely varying rheological and piezo-viscous behaviors, i.e., polyalpha olefins and polydimethyl siloxane.     

流变模型对剪切稀化流体弹流油膜厚度影响的研究

基于Carreau流变模型和Ree—Eyring流变模型,对剪切稀化流体线接触弹流润滑进行了完全数值分析,得到了同一种润滑油在不同流变模型下的弹流油膜厚度。将理论分析得到的油膜厚度、经典弹流膜厚公式计算的油膜厚度以及实测的油膜厚度进行了对比,结果表明：基于Carreau流变模型的理论分析结果更能反映剪切稀化流体的实际弹流油膜厚度;在相同工况下,基于Ree—Eyring流变模型的理论分析结果低估了剪切稀化流体的油膜厚度,经典弹流膜厚公式过高地估计了剪切稀化流体的油膜厚度。研究结果表明：幂函数形式的流变模型更能反映剪切稀化流体的流变特性。     

The Effect of Load (Pressure) for Quantitative EHL Film Thickness

New quantitative numerical simulations of the elastohydrodynamic lubrication (EHL) film thickness using realistic pressure and shear-dependent rheology and realistic compressibility have indicated that the dependence of central film thickness upon Hertz pressure (or load) for the classic Newtonian, slightly compressible solution is merely a lower limit with magnitudes three times as great being possible. Experimental measurements of central film thickness employing Hertz pressures from 1.0 to 2.6 GPa confirm that for a neat mineral oil, the classical pressure dependence is accurate, while for two gear oils the experimental pressure dependence is much larger. Shear-dependent viscosity is a major factor and compressibility plays a lesser role, while there is evidence that mechanical degradation is also important. New experimental evidence of the enhanced scale sensitivity resulting from shear-thinning has also been obtained. These results for the pressure and scale dependence have dire implications for the usual practice of extrapolation of film thickness from experimental measurements at large scale and low pressure using effective pressure–viscosity coefficients. For machines of small scale and high pressure, the extrapolation will sometimes result in substantially overestimated film thicknesses.     

The First Normal Stress Difference in a Shear-Thinning Motor Oil at Elevated Pressure

Currently, the only aspect of non-Newtonian behavior being modeled in lubrication is the shear dependence of viscosity. However, shear thinning is accompanied by a large difference between the normal stress in the flow direction and the cross-film direction. This stress difference can increase the load capability of a lubricant film without increased frictional penalty.

A commercial 10W-40 motor oil was characterized at elevated pressures. Three different high-pressure instruments were employed: a falling-body viscometer, a thin-film Couette viscometer, and a parallel-plate rheogoniometer. Ordinary shear thinning with a second Newtonian inflection was observed. A first normal stress difference of 0.6 MPa was measured under what may be mild conditions for a crankshaft journal bearing. Elevated pressures are essential to the measurement of rheological properties that govern hydrodynamic film thickness and friction in automotive components.

Time–temperature–pressure superposition was validated for the first normal stress difference. The first normal stress difference in the terminal regime may be estimated from the upper-convected Maxwell model, where the shear modulus is assumed to be equal to the Newtonian limit shear stress obtained from a measurement of shear thinning. The first normal stress difference in the shear-thinning regime may be estimated from an extant empirical rule.

These results will be of substantial importance when analytical techniques are developed for hydrodynamic lubrication with real non-Newtonian shear response. The results are immediately useful for calculating the shear stress for cavitation in ambient pressure high-shear viscometers.     

Obtaining the pressure spike and maximum shear stress from optical interferometry data

In order to predict and optimise highly loaded contact performance, accurate lubricant data is crucial. The lubricant's high-pressure rheological behaviour is by far the least known parameter. However, this is the key factor to realistic modeling of non-Newtonian Elasto-Hydrodynamic lubrication. In this paper a new approach is described to extract such data from optical interferometric film thickness measurements of EHL contacts. The approach is relatively straightforward and cheap compared to “out of contact” rheological experiments using specialized equipment.A measured high-resolution film thickness distribution was positioned using a computed film thickness distribution as a reference. The reference is computed using the same operating conditions as the measurement. Subsequently, from the computed film thickness difference, a pressure difference file is obtained by deconvolution. Adding this pressure difference to the computed pressure file associated with the computed reference film thickness, provides a corrected pressure distribution, as it has appeared in the experimental contact. In this paper results are presented for the pressure spike region of the contact, in which significant shear stresses occur. The basic approach and its difficulties are described as well as some “tricks”, such as the reduction of (local) noise resulting from the ill-posedness of the deconvolution. It is shown that simple averaging over a circle segment in the pressure spike zone, results in significant noise reduction and a very good ‘measured’ pressure spike.     

Effect of lubricant selection on EHL performance of involute spur gears

As the gear oils usually undergo shear-thinning even in the inlet zone, an accurate EHL analysis requires realistic rheological models. This is necessary for gear oil selection so as to prevent scuffing failure. This paper demonstrates the effect of rheology on the EHL characteristics of spur gears using full transient thermal EHL simulations with Carreau shear-thinning model and Doolittle's free volume based pressure-viscosity relationship. The PDMS oil considered here is found to exhibit severe film thinning with 74% thinner EHL film as compared to a moderately shear-thinning PAO oil which, on the other hand, undergoes a larger thermal reduction.     

极限剪切状态下的线接触Reynolds方程

本文导出了考虑极限剪切状态的线接触流变热弹流Reynolds方程,该方程以Evans—Johnson流变模型为基础,可用于求解线接触流变热弹流润滑问题的油膜厚度、压力分布、剪应力分布和牵曳系数曲线。计算实例表明,润滑油的流变特性对弹流润滑的油膜形状和压力分布影响不大,但对Hertz接触区的剪应力分布有显著影响。     

Mechanical Degradation of the Liquid in an Operating EHL Contact

Elastohydrodynamic lubrication (EHL) calculations using the real pressure and real shear dependence of viscosity have revealed that the shear and load dependences of film thickness are often greater than the classical prediction. Experimental measurements have confirmed the increased sensitivity to scale and load; however, the sensitivities are even greater than would be expected from shear-thinning. Time-dependent film thickness measurements and stress-history-dependent flow curves are employed to show that molecular degradation may occur at nominal rolling EHL stress levels and that this degradation affects the film thickness.     

The nature of the logarithmic traction gradient

Great significance has been attached to the logarithmic traction gradient in elastohydrodynamic lubrication. It has been used to justify the assumption of logarithmic constitutive behavior.We have calculated viscous traction curves from the viscous shear response that is observable by simulation or experiment out of contact. This response includes Newtonian, shear-thinning of the ordinary power-law type, and rate independent behavior. The calculated traction curves can be reasonably described by a sinh law using fictitious viscosity and Newtonian limit. These system model parameters behave as expected from cases where the same system model was applied to measured traction.We conclude that for point contact, the logarithmic gradient results from rate-independent (limiting stress) behavior combined with greater than exponential pressure-viscosity behavior. Shear-thinning has little effect on this gradient in point contact. On the other hand for line contact, shear-thinning of the ordinary type (Carreau) is essential for the appearance of a logarithmic gradient.     

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.     

Thermal Elastohydrodynamic Lubrication of Point Contacts Using a Newtonian/Generalized Newtonian Lubricant

The classical ElastoHydroDynamic (EHD) theory assumes a Newtonian lubricant and an isothermal operating regime. In reality, lubricating oils do not behave as perfect Newtonian fluids. Moreover, in most operating conditions of an engineering system, especially at high speeds, thermal effects are important and temperature can no longer be considered as constant throughout the system. This is one reason why there has always been a gap between numerical results and experimental data. This paper aims to show that this gap can be reduced by taking into consideration the heat generation that takes place in the contact and using appropriate rheological models. For this, a unique thermal ElastoHydrodynamic lubrication model is developed for both Newtonian and non-Newtonian lubricants. Pressure, film thickness and traction results are then compared to their equivalent isothermal results and experimental data. The agreement between thermal calculations and experiments reveals the necessity of considering thermal effects in EHD models.     

Film Formation by Colloidal Overbased Detergents in Lubricated Contacts

It has been reported in the literature that overbased detergents can possess good antifriction and antiwear properties although the origins of these properties are not fully clear. In practice, over-based detergents are colloidal dispersions and this may be important in determining their properties and mechanism of action.

In the current study, the lubricating properties of commercial, overbased magnesium and calcium sulfonates were measured in thin film, lubricated conditions and compared to a neutral sulfonate additive. A range of techniques was employed to evaluate the tribological performance of solutions of these additives. Film thickness measurements were carried out using optical interferometry and in-contact visualization, while friction and wear measurements complemented the study.

It has been found that, when operating in thin film conditions, overbased detergents deposit solid-like boundary films on the rubbing surfaces. These films form in both rolling and mixed rolling/sliding conditions and, unlike many other colloidally-formed boundary films, are able to survive in high speed, thick film conditions. During formation, the film rapidly reaches a thickness corresponding to one colloid particle diameter, between 10 and 20 nm. After prolonged rubbing, however, the film thickness reaches the equivalent of three particle diameters. No such thick boundary films are observed with the neutral sulfonate.

The boundary films formed by overbased detergents produce a significant reduction in wear. However, for the very smooth surfaces used in this study, they also result in an effective roughening of the very smooth surfaces studied. This leads to an increase in friction in the intermediate speed region by promoting solid-solid contact in thin fluid film conditions.     

An efficient numerical analysis of starved thermohydrodynamically lubricated rolling line contacts

Effect of starvation in thermohydrodynamically lubricated high rolling speed line contacts has been investigated numerically by using an efficient numerical method in which temperature variations across the lubricant film is approximated by the second-order of Legendre polynomial. Mechanism of starvation at the contact has been set by creating gradual reduction in the length of the computational domain from the inlet side. In the solution, the lubricant has been assumed to be a Newtonian fluid. Minimum film thickness and rolling traction coefficient under fully flooded and starved conditions have been computed in this work. The rolling traction coefficient, minimum film thickness, and maximum mid film temperature rise in the starved line contact are found to be lesser than the fully flooded contact condition.     

On-line acoustic viscometry in oil condition monitoring

The paper describes the theoretical standpoints of developing magnetoelastic viscometers and a concept of viscosity measurement. The magnetoelastic viscometer has shown the readings close to the capillary viscometer. Testing of the oils with PMMA viscosity-index improvers by viscometers has indicated changes in rheological properties observed in the non-Newtonian behavior of the oils. With increase in content or molecular weight of the improver, the non-Newtonian behavior of the oil appeared at lower frequencies of viscosity measurements.