Computational fluid dynamics and full elasticity model for sliding line thermal elastohydrodynamic contacts

Classically, the EHD problem is solved using the Reynolds assumptions to model the fluid behaviour, and the Boussinesq elastic deformation equation to model the solid response, both being coupled with the load balance equation. The development of an alternative approach is presented here in order to solve at once the Navier-Stokes equations (mass conservation and momentum equilibrium), the full elasticity and energy equations for the line EHD problem in a fluid-structure interaction approach.The Finite Element Method is used to solve the mathematical formulation in a fully coupled way, inspired from Habchi et al. (2008) [1]. After linearisation with the Newton procedure, all the physical quantities (pressure, velocity field, deformations and temperature) are solved together in a unique system. An important benefit of this approach is the possibility to implement in a simple manner the non-Newtonian and thermal effects; in fact all the quantities can vary through the film thickness. The extension to non-Newtonian rheology and the pressure and temperature dependencies for the viscosity and density are taken into account in a direct way to allow an acceptable prediction of the friction coefficient. Gradients across the film thickness and temperature fields in both the fluid and the two solids are naturally computed and analysed. As a case study, we focus first on the pure sliding cylinder-on-plane contact. It is shown that thermal effects due to friction in the central zone of the contact play a role in heating the lubricant at the inlet zone, via heat conduction in the solids. By increasing the Slide-to-Roll Ratio (SRR), the occurrence of dimples and the subsequent effects in different parts of the contact under zero entrainment velocity conditions are then studied.     

Quantitative Viscosity Mapping Using Fluorescence Lifetime Measurements

Lubricant viscosity is a key driver in both the tribological performance and energy efficiency of a lubricated contact. Elastohydrodynamic (EHD) lubrication produces very high pressures and shear rates, conditions hard to replicate using conventional rheometry. In situ rheological measurements within a typical contact are therefore important to investigate how a fluid behaves under such conditions. Molecular rotors provide such an opportunity to extract the local viscosity of a fluid under EHD lubrication. The validity of such an application is shown by comparing local viscosity measurements obtained using molecular rotors and fluorescence lifetime measurements, in a model EHD lubricant, with reference measurements using conventional rheometry techniques. The appropriateness of standard methods used in tribology for high-pressure rheometry (combining friction and film thickness measurements) has been verified when the flow of EHD lubricant is homogeneous and linear. A simple procedure for calibrating the fluorescence lifetime of molecular rotors at elevated pressure for viscosity measurements is proposed.     

Experimental Study of Elastohydrodynamic Lubrication

This paper describes experimental measurements of the conditions occurring in the conjunctive region of two lubricated cylindrical disks which roll or roll and slide on their peripheral surfaces under load. The results of these measurements are compared with those of the recent elastohydrodynamic theory, including thermal effects. The measured quantities include lubricant film pressure distribution, surface temperature distribution, and the shape and thickness of the lubricant film, all measured in the direction of rolling. The results suggest several improvements and modifications of the thermal elastohydrodynamic theory including an improved analysis of the inlet region and modification of the lubricant rheological model to include effects of shear or time dependence.     

Elastohydrodynamic Lubrication of Rough Surfaces under Oscillatory Line Contact with Non-Newtonian Lubricant

This paper presents the results of a transient analysis of elastohydrodynamic lubrication (EHL) of two parallel cylinders in line contact with a non-Newtonian lubricant under oscillatory motion. Effects of the transverse harmonic surface roughness are also investigated in the numerical simulation. The time-dependent Reynolds equation uses a power law model for viscosity. The simultaneous system of modified Reynolds equation and elasticity equation with initial conditions was solved using the multigrid, multilevel method with full approximation technique. The film thickness and the pressure profiles were determined for smooth and rough surfaces in the oscillatory EHL conjunctions, and the film thickness predictions were verified experimentally.

For an increase in the applied load on the cylinders or a decrease in the lubricant viscosity, there is a reduction in the minimum film thickness, as expected. The predicted film thickness for smooth surfaces is slightly higher than the film thickness obtained experimentally, owing primarily to cavitation that occurred in the experiments. The lubricant film under oscillatory motion becomes very thin near the ends of the contact when the velocity goes to zero as the motion direction changes, but a squeeze film effect keeps the fluid film thickness from decreasing to zero. This is especially true for surfaces of low elastic modulus. Harmonic surface roughness and the viscosity and power law index of the non-Newtonian lubricant all have significant effects on the film thickness and pressure profile between the cylinders under oscillatory motion.     

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.     

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 hydrodynamic liquid lubrication analysis of slider/disk interface

A numerical solution for ultrathin hydrodynamic liquid lubrication of slider/disk interface is introduced. Both surface roughness effects and non-Newtonian behavior of the liquid lubricant are incorporated into the hydrodynamic lubrication analysis. A non-Newtonian liquid is used as the lubricant, and its behavior is described by a power-law rheological model. The contact pressure is calculated for a Gaussian surface roughness. The hydrodynamic load capacity is calculated by using an averaged form for the Reynolds equation. The finite difference scheme, with Gauss–Seidel iterative-relaxation method, is applied to solve the average Reynolds equation. The effects of surface roughness parameter, surface pattern parameter, and the power-law exponent on hydrodynamic pressure distribution, hydrodynamic load capacity are studied and discussed.     

Thin film lubrication of sliding point contacts of AISI 52100 steel

The mechanism of thin film lubrication of sliding point contacts of AISI 52100 steel has been studied as a function of load, sliding speed, composition and temperature of the lubricant.Below certain critical combinations of Hertzian pressure, speed and temperature the surfaces are kept apart by an elastohydrodynamic lubricant film. The load carrying capacity of this film depends primarily on the effective viscosity of the lubricant in the contact region which decreases with bulk oil temperature and with increasing sliding speed, because of friction induced thermal effects. After breakdown of the EHD film, boundary lubrication may still prevent severe adhesive wear. The transition from the boundary lubricated regime towards the regime of severe adhesive wear is a function of load (normal force), speed and bulk oil temperature and possibly depends on the conjunction temperature. Irrespective of the initial lubrication condition, oxidation of the steel surfaces leads to the (re)establishment of low friction, mild wear conditions.     

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.     

Analysis of viscosity interaction on the misaligned conical–cylindrical bearing

Viscosity is an essential property in hydrodynamic lubrication. In general, the lubricant is not considered to have uniform viscosity within a given bearing. The viscosity of the lubricant is affected by both pressure and temperature. The viscosity of the lubricant increases with pressure and for most lubricants, this effect is much larger than that of temperature or shear when the pressure is significantly above than the atmospheric pressure. This study analyzes the thermal effect of conical–cylindrical bearing performance parameters via the viscosity–pressure–temperature relationships of lubricants. The results reveal that pressure increases both the film viscosity and temperature as well.     

Modeling Bearing and Shear Forces in Molecularly Thin Lubricants

Under the effects of high shear rate and confinement between solid surfaces, the behavior of a thin lubricant film deviates from that of the bulk, resulting in significant increases of lubricant viscosity and interfacial slip. A semi-empirical model accounting for the breakdown of continuum theory at the nanoscale is proposed—based on film morphology and chemistry from available experimental and molecular dynamics simulation data—to describe lubricant behavior under shear. Viscosity stiffening and interfacial slip models are introduced into the formulations of the normal (bearing) and shear forces acting on a sphere that moves within a thin lubricant film parallel to a rigid plane. The experimentally measured ‘apparent’ viscosity confounding the effects of both stiffening and slip is used to predict the hydrodynamic forces acting on a fully or partially submerged sphere for the purposes of describing lubricant contact in magnetic storage. The proposed sphere-on-flat model forms the basis of a future, dynamic contact with friction model that will account for lubricant contact in the context of molecularly thin lubricated rough surface contact.     

Effect of coatings on thermal conditions of EHL

The thermal EHD model of rectangular contact has been applied to analysing the effect of coatings on thermal conditions in EHL. The model takes into account variation of oil viscosity along and across the oil film according to the Barus formula. The solution has been obtained by means of the Newton-Raphson method. The effect of the coating has been examined by comparison of the temperature distributions in the oil film and on the surfaces of rollers for the cases with and without coating. In addition, the oil film shapes and minimum values, the pressure distributions and traction coefficients, have also been compared.     

Analysis of Viscosity Interaction and Heat Transfer on the Dual Conical-Cylindrical Bearing©

Viscosity is an essential property in hydrodynamic lubrication. In general, the lubricant is not considered to have uniform viscosity within a given bearing. The viscosity of the lubricant is affected by both pressure and temperature. The viscosity of the lubricant increases with pressure and, for most lubricants, this effect is much larger than that of temperature or shear when the pressure is significantly above atmospheric pressure. This study analyzes the thermal effect of dual conical-cylindrical bearing performance parameters via the viscosity-pressure-temperature relationships of lubricants. The results reveal that pressure increases both the film viscosity and temperature.     

TRIBOS: A Performance Evaluation Tool for Traction-Transmitting Partial EHD Contacts

The details are given of a computer model for performing a state-of-the-art tribological assessment of the performance of a lubricated concentrated rolling/sliding/spinning/contact comprising general anisotropic rough surfaces. The name chosen for this program is TRIBOS.

It computes: 1. The contact ellipse dimensions and area

2. The elastohydrodynamic (EHD) film thickness both at the plateau and at the constriction that forms at the rear of a lubricated concentrated contact under fully flooded (un-starved) and isothermal lubricant inlet conditions

3. The apportionment of the applied load between the asperities and the lubricant film

4. The magnitude and direction of the tractive force transmitted between the contacting bodies by the combined effects of (a) shearing of the fluid film and (b) coulomb friction between contacting asperities

5. The mean number of asperity contacts and the real contact area, i.e. the total contact area of the elastically deformed asperities

6. A film thickness correction factor accounting for lubricant starvation in the contact inlet

7. A film thickness correction factor accounting for a viscosity decrease of the inlet oil due to fluid heating

8. An index of surface fatigue behavior

The program is a synthesis of computational tools from the current literature for the computation of fluid film thickness and traction, and a general asperity simulation model for the elastic contact of anisotropic rough surfaces. In the example given, it is used to perform a comparative evaluation of the performance of 18 combinations of 9 surface roughnesses and 2 lubricants in a traction drive contact.     

线接触弹流润滑综合数值分析

应用多重网格法和多重网格积分法数值求解rNewton流体和Ree-Eyring流体线接触等温和热弹流润滑问题,分析了滑滚比对摩擦因数的影响,指出了润滑油的流变性和热效应对线接触弹流润滑油膜粘度的影响,以及不同滑滚比时压力、膜厚和温度的分布规律。结果表明：等温润滑时的摩擦因数随着滑滚比的增加而增加,热弹流润滑时的摩擦因数随着滑滚比的增加先增加后减小,热效应和非牛顿流体的剪稀作用均会使润滑油的等效粘度降低,从而影响摩擦因数;热效应的存在使油膜变薄,且在所讨论的工况条件下Newton流体的膜厚比Ree-Eyring流体的稍薄,热效应使第二压力峰变矮,且Ree-Eyring流体的第二压力峰矮于Newton流体的第二压力峰;纯滚动时,Ree-Eyring流体的温度比Newton流体的温度高,有滑滚比时,Newton流体的温度比Ree-Eyring流体的温度高,且油膜的温度随滑滚比的增加而增加。     

Measurement of the Rheology of Lubricant Films Within Elastohydrodynamic Contacts

There is growing need for a reliable model of the rheological response of lubricants in elastohydrodynamic (EHD) contacts, not only to predict behaviour in full-film EHD conditions, but also for use in modelling mixed-film lubrication. One barrier to developing such a model is that measurements of friction actually represent averaged values over the whole, lubricated contact under study. However the fluid film conditions of temperature, pressure and strain rate generally vary over such contacts, which makes it difficult to determine constitutive shear-stress equations from friction measurements. This paper examines the various different techniques used to study the origins of EHD friction and the underlying film rheology. It then describes and applies a technique for obtaining the temperature rise maps of both solid surfaces in a rolling-sliding EHD contacts and thus shear-stress and friction maps. The work shows that the shear stress of the traction fluid studied increases approximately linearly with pressure and decreases approximately linearly with temperature in the high-pressure central region of EHD contacts.     

Non-Newtonian Temperature and Pressure Effects of a Lubricant Slurry in a Rotating Hydrostatic Step Bearing

The purpose of this research was to investigate the pressure and temperature effects of graphite powder lubricant when added to a Newtonian carrier fluid and applied in a rotating hydrostatic step bearing. Temperature and pressure profiles were determined both analytically and experimentally. The rheological behavior of the non-Newtonian lubricant was modeled using a power law model previously shown to approximate experimental data for this fluid. Ethylene glycol was used as the Newtonian lubricant, providing a check on the test apparatus and a base line for comparison with the non-Newtonian graphite slurry.

Data revealed a temperature increase with bearing rotational speed for both fluids and compared favorably with the mathematical predictions. A significantly higher temperature rise was seen in the non-Newtonian lubricant due to the higher shear rates. The pressure profile was not directly dependent on bearing rotational speed in the mathematical model, but experimental data demonstrated a reduction in pressure at higher rotation speeds. This loss was greater for the non-Newtonian lubricant and attributed to temperature dependence of power law constants. It was concluded that the effects of operating speed and temperature on a non-Newtonian lubricant should be considered as well as their greater load-carrying capacity.     

The Influence of Lubricant Upon EHD Film Behavior During Sudden Halting of Motion

Although steady state elastohydrodynamic (EHD) lubrication is quite well understood both from the theoretical and from the experimental point of view, studies of transient effects in EHD are currently far less developed. This paper describes an experimental investigation into EHD film behavior during sudden halting of motion. A technique has been devised which enables both central lubricant film thickness and film thickness profiles to be measured every millisecond during halting of a ball on flat, sliding contact. This has enabled detailed information of influence of lubricant on film collapse during halting to be obtained. It is shown that film collapse occurs in two stages. The first is a very rapid reduction in film thickness with only very small changes in film geometry and thus pressure distribution. This is followed, as soon as entrainment ceases, by the formation of a lubricant entrapment, and subsequent slow leakage of fluid from the central film region. This paper focussed on the formation of this entrapment and the influence of the rheological properties of the lubricant, i.e. viscosity and pressure-viscosity coefficient, on its development and behavior.     

Molecular Dynamics of Synthetic-Based Lubricant System by Spectroscopic Techniques—Part 1

This article describes the structure–property relationships of synthetic pentaerythritol polyol esters (PEE) and polyalphaolefins (PAO) as established by the diffusion and mobility measurement and tilt angle results obtained by nuclear magnetic resonance (NMR) and infrared (IR) spectroscopic techniques, respectively. The diffusion coefficients (D) were found to be dependent on the molecular structure, alkyl chain length, shape and size, hydrodynamic volume, and alignment of the molecules in a lubricant system constituting these base stocks. The viscosity–temperature and viscosity–pressure properties such as viscosity index (VI), pour point (PP), elastohydrodynamic (EHD) film thickness, pressure–viscosity coefficient (α), hydrodynamic volume, and radius are explained on the basis of the variation in D with temperature and tilt angle on the smooth surfaces. The study has enabled us to propose a molecular structure of a synthetic molecule that can be molecularly engineered to have high-performance physicochemical properties.