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VERSATILE SELF-HEALING COATINGS Researchers from the University of Illinois Urbana-Champaign developed a tougher ultrathin material by merging thin-film and self-healing technologies. They found that the rapid evaporative qualities of a [...]

On the basis of ongoing research conducted on the clarification of processes responsible for lubricant degradation in the environment of piston grooves in exhaust gas recirculation (EGR) diesel engines, an experimental investigation was aimed to develop a kinetic model, which can be used for the prediction of lubricant oxidative degradation correlated with endurance test conducted on engines. Knowing that base oils are a complex blend of paraffins and naphthenes with a wide range of sizes and structures, their chemistry analysis during the oxidation process can be highly convoluted. In the present work, investigations were carried out with the squalane ([C.sub.30][H.sub.62]) chosen for its physical and chemical similarities with the lubricant base oils used during the investigations. Thermooxidative degradation of this hydrocarbon was conducted at atmospheric pressure in a tubular furnace, while varying temperature and duration of the tests in order to establish an oxidation reaction rate law. The same experimental procedures were applied to squalane doped with two different phenolic antioxidants usually present in engine oil composition: 2,6-di-tert-butyl-4-methylphenol and octadecyl-3-(3,5-di-tert-butyl-4 hydroxyphenyl)propionate. Thus, the effect of both antioxidants on the oxidation rate law was investigated. Data analysis of the oxidized samples (Fourier transform infrared spectroscopy and gas chromatography/mass spectrometry) allowed rationalization of the thermo-oxidative degradation of squalane. The resulting kinetic modeling provides a practical analytical tool to follow the thermal degradation processes, which can be used for prediction of base oil hydrocarbon aging. If experiments confirmed the role of phenolic additives as an effective agent to lower oxidation rates, the main results lie in the observation of a threshold temperature where a reversed activity of these additives was observed. [DOI: 10.1115/1.3155797]

A model for oil-in-water emulsion has been developed in this paper. A group of viscosity coefficients transiting smoothly and incessantly from the thick film region to the thin film region is defined. The contributions from disperse and continuous phases to the total lubricant pressure and pressure gradient are functions of the oil concentration and the film thickness. The parameters used in these functions are determined by a series of computational fluid dynamics simulations. The onset of inversion and the viscosity after inversion are also investigated. It is found that the critical volume fraction of oil in the inception of inversion is dependent on the oil viscosity and a factor regarding the combined effects from the emulsifier, pH value, droplet size, and the shear rate. A series of simulations using the proposed model has been carried out and compared with the experimental results, such as the film thickness and the extension of oil pool for various rolling speeds and supply oil concentrations. The numerical outputs are basically in agreement with the experiments. [DOI: 10.1115/1.4000274] Keywords: emulsion, phase inversion, effective viscosity, Reynolds equation, hydrodynamic lubrication

In this study, a transient, non-Newtonian, mixed elastohydrodynamic lubrication (EHL) model of involute spur gear tooth contacts is proposed. Unlike the contact between two cylindrical rollers, spur gear contacts experience a number of time-varying contact parameters including the normal load, radii of curvature, surface velocities, and slide-to-roll ratio. The proposed EHL model is designed to continuously follow the contact of a tooth pair from the root to the tip to capture the transient characteristics of lubricated spur gear contacts due to these parameter variations, instead of analyzing the contact at discrete positions assuming time-invariant parameters. The normal tooth force along the line of action is predicted by using a gear load distribution formulation and the contact radii and tangential surface velocities are computed from the kinematics and geometry of involute profiles. A unified numerical approach is adapted for handling asperity interaction in mixed EHL conditions. The differences between the transient and discrete EHL analyses are shown for a spur gear pair having smooth surfaces and different tooth profile modifications. The transient behavior predicted by the proposed model is found to be mainly due to the squeezing and pumping effects caused by sudden load changes. The lubrication behavior under rough conditions is also investigated at different operating conditions. [DOI: 10.1115/1.4000270] Keywords: gear lubrication, transient EHL, mixed EHL

A numerical algorithm for fully dynamical lubrication problems based on the Elrod--Adams formulation of the Reynolds equation with mass-conserving boundary conditions is described. A simple but effective relaxation scheme is used to update the solution maintaining the complementarity conditions on the variables that represent the pressure and fluid fraction. The equations of motion are discretized in time using Newmark's scheme, and the dynamical variables are updated within the same relaxation process just mentioned. The good behavior of the proposed algorithm is illustrated in two examples: an oscillatory squeeze flow (for which the exact solution is available) and a dynamically loaded journal bearing. This article is accompanied by the ready-to-compile source code with the implementation of the proposed algorithm. [DOI: 10.1115/1.3142903] Keywords: dynamical lubrication, cavitation, Elrod--Adams model, oscillatory squeeze flow, journal bearings

A lubrication theory that includes the effects of electrokinetics and surface microstructure is developed. A porous layer attached to the impermeable substrate is used to model the microstructure on a bearing surface. The Brinkman-extended Darcy equations and Stokes equations are modified by considering the electrical body force and utilized to model the flow in porous media and fluid film, respectively. The stress jump boundary conditions on the porous media/fluid film interface and the effects of viscous shear and electric double layer (EDL) are also considered when deriving the modified Reynolds equation. Under the usual assumptions of lubrication and Debye--Huckel approximation for low surface potential, the velocity distributions, the apparent viscosity, and the modified Reynolds equation are then derived. The apparent viscosity is expressed explicitly as functions of the Debye length, the electroviscosity, the charge density, the stress jump parameter, and the porous parameters (permeability, porosity, and porous film thickness). The considerations of EDL near the interface and the charge density of the flow in the porous media increase the apparent viscosity. The existence of porous film also increases the apparent viscosity as well. Both effects are important for flow within microspacing and lubrication problems. The apparent viscosity and the performance of ID slider bearings are analyzed and discussed. The results show that the apparent viscosity and the load capacity increase as the permeability decreases, the stress jump parameter decreases, the charge density increases, the inverse Debye length decreases, or the porosity decreases. [DOI: 10.1115/1.3140610] Keywords: stress jump, electrokinetics, EDL, Brinkman-extended Darcy's equation, lubrication theory.

As the head-disk spacing reduces in order to achieve the areal density goal of 1 Tb/[in.sup.2], the dynamic stability of the slider is compromised due to a variety of proximity interactions. Lubricant pickup by the slider from the disk is one of the major reasons for the decrease in the stability as it contributes to meniscus forces and contamination. Disk-to-head lubricant transfer leads to lubricant pickup on the slider and also causes depletion of lubricant on the disk. In this paper, we experimentally and numerically investigate the process of disk-to-head lubricant transfer using a half-delubed disk, and we propose a parametric model based on the experimental results. We also investigate the dependence of disk-to-head lubricant transfer on the disk lubricant thickness, lubricant type, and the slider air bearing surface (ABS) design. It is concluded that disk-to-head lubricant transfer occurs without slider-disk contact and there can be more than one timescale associated with the transfer. Furthermore, the transfer increases nonlinearly with increasing disk lubricant thickness. Also, it is seen that the transfer depends on the type of lubricant used and is less for Ztetraol than for Zdol. The slider ABS design also plays an important role, and a few suggestions are made to improve the ABS design for better lubricant performance. [DO]: 10.1115/1.3139045] Keywords: hard disk, tribology, reliability, head-disk interface, ABS design, lubricant

The concept of load sharing between asperities and fluid film is applied in conjunction with lubricated sliding wear formulation proposed by Wu and Cheng (1991, 'A Sliding Wear Model for Partial-EHL Contacts,' ASME J. Tribol., 113, pp. 134-141; 1993, 'Sliding Wear Calculation in Spur Gears,' ASME J. Tribol., 115, pp. 493-500) to predict the steady state adhesive wear in gears. Thermal effects are included using a simplified thermoelastohydrodynamic analysis. The prediction of the model is verified by comparing simulation results with published experimental data pertinent to steady state wear rate. The main advantages of this method are the accuracy and the remarkable computational efficiency. The results of parametric simulation study are presented to investigate the effect of speed and surface roughness on a portion of load carried by asperities and wear rate. [DOI: 10.1115/1.3075859] Keywords: spur gear, line of action, load sharing, adhesive wear, surface roughness

Over the years, the deterministic elastohydrodynamic lubrication (EHL) approach has been widely used. This technique is very powerful in capturing details of asperity deformation and interaction. The probabilistic EHL methodology is still used when the main interest of the engineer is directed toward computations of bulk properties. During recent years, the results of many deterministic analyses have been published. The reduction of the waviness amplitude in EHL contacts under rolling-sliding was systematically studied and it was shown that the amplitude reduction is completely described by a single parameter that includes relative wavelength and the operating conditions. This approach, usually referred to as the amplitude reduction technique, has opened the way for developing improved probabilistic EHL models by incorporating the effects of fluid-induced roughness deformation, which is calculated using the fast fourier transform. In this paper we provide a review of the latest developments in the amplitude reduction technique and we present a probabilistic EHL algorithm for the computation of the load supported by the fluid, the elastically deformed asperities and the plastically deformed asperities, in a mixed EHL contact with either isotropic on nonisotropic roughness. The fluid-induced roughness deformation is incorporated into the probabilistic model via the use of the amplitude reduction technique. [DOI: 10.1115/1.2961919] Keywords: mixed elastohydrodynamic lubrication (EHL), amplitude reduction technique

This paper presents a nonlinear theoretical model to study the effect of laser surface texturing on the tribological performance in soft elastohydrodynamic lubrication. Both geometrical and physical nonlinearities of the elastomer are considered by using a logarithmic strain and the Mooney-Rivlin constitutive law, respectively. The results of the present nonlinear model are compared with a previous linear one over a wide range of operating conditions. It is found that the simpler linear elasticity model predicts results that are only slightly different from these predicted by the more accurate nonlinear one. Hence, the linear elasticity model can be practically considered valid over the entire range of operating conditions. [DOI: 10.1115/1.3071973] Keywords: elastohydrodynamic lubrication, nonlinear elasticity, surface texturing

A numerical soft elastohydrodynamic lubrication model of a reciprocating hydraulic seal has been used to simulate the performance of a U-cup seal and a step seal in a conventional actuator. The model consists of coupled steady state fluid mechanics, deformation mechanics, contact mechanics, and thermal analyses, with an iterative computational procedure. The results indicate that for a given seal roughness and stroke length there is a critical rod speed above which the seal will not leak. The critical speed is dependent on both seal roughness and sealed pressure. [DOI: 10.1115/1.3063820] Keywords: reciprocating seal, rod seal, hydraulic Seal, elastohydrodynamics

Chemical mechanical polishing (CMP) is a manufacturing process that is commonly used to planarize integrated circuits and other small-scale devices during fabrication. Although a number of models have been formulated, which focus on specific aspects of the CMP process, these models typically do not integrate all of the predominant mechanical aspects of CMP into a single framework. Additionally, the use of empirical fitting parameters decreases the generality of existing predictive CMP models. Therefore, the focus of this study is to develop an integrated computational modeling approach that incorporates the key physics behind CMP without using empirical fitting parameters. CMP consists of the interplay of four key tribological phenomena--fluid mechanics, particle dynamics, contact mechanics, and resulting wear. When these physical phenomena are all actively engaged in a sliding contact, the authors call this particle-augmented mixed lubrication (PAML). By considering all of the PAML phenomena in modeling particle-induced wear (or material removal), this model was able to predict wear-in silico from a measured surface topography during CMP. The predicted material removal rate (MRR) was compared with experimental measurements of copper CMP. A series of parametric studies were also conducted in order to predict the effects of varying slurry properties such as solid fraction and abrasive particle size. The results from the model are promising and suggest that a tribological framework is in place for developing a generalized first-principle PAML modeling approach for predicting CMP. Keywords: mixed lubrication, chemical mechanical polishing, contact mechanics, particle dynamics, computational fluid dynamics, abrasive wear

The Eyring sinh law, which is the most widely used model to describe the shear-thinning behavior of elastohydrodynamic lubrication (EHL) lubricants, fails to replicate the experimentally measured flow curves for shear-thinning lubricants. Interestingly, this law was rejected by Eyring for shear-thinning fluids and, in fact, it was found useful only for fluids thought to exhibit thixotropy. The 'actual Ree--Eyring model' for shear-thinning involves multiple flow units with appropriate relaxation times. This paper presents an extensive set of full EHL line and point contact simulations to investigate the usefulness of the actual Ree--Eyring model in EHL applications with shear-thinning lubricants. Comparisons with published experimental data establish the validity of the actual Ree--Eyring model Also presented is the application of an appropriate shifting rule expected to improve the agreement between simulations and experiments. Keywords: EHL, shear thinning, Ree--Eyring, non-Newtonian, shifting rule

Tilting-pad gas bearings are widely used in high-speed rotating machines due to their inherent stability characteristics. This paper advances the analytical method for prediction of the dynamic performances of tilting-pad gas bearings. The main advantage of the analytical method is that the complete set of dynamic coefficients of tilting-pad gas bearings can be obtained. The predictions show that the perturbation frequency has the strong effects on the dynamic coefficients of gas bearings. In general, at lower perturbation frequency, the equivalent direct stiffness coefficients increase with frequency, whereas equivalent direct damping coefficients dramatically reduce. For higher perturbation frequency, the dynamic coefficients are nearly independent of the frequency. Moreover, the equivalent dynamic coefficients of four-pad tilting-pad gas bearing obtained by the method in this paper are in good agreement with those obtained by Zhu and San Andres [(2007), 'Rotordynamic Performance of Flexure Pivot Hydrostatic Gas Bearings for Oil-Free Turbomachinery,' ASME J. Eng. Gas Turbines Power, 129(4), pp. 1020-1027] in the published paper. The results validate the feasibility of the method presented in this paper in calculating the dynamic coefficients of gas-lubricated tilting-pad bearings. Keywords: dynamic coefficients, tilting-pad beatings, perturbation frequency, partial derivative method

Journal bearings are widely used for supporting high-speed rotating machinery, such as turbine, compressor, and HDD spindle, because of their high load carrying capacity, stability, and durability. Recently, the engineering trend is oriented to higher speed and smaller sizes of rotating machinery, and then it is important to enhance stabilities for the small-bore journal bearings. Tilting pad journal bearing is generally used for high-speed rotating machineries because of their advantages of stabilization. However, there are some problems using compact size rotating machineries for their high manufacturing cost and complicated structure. Therefore, it is necessary to enhance the stability of more simple bearings compared with tilting pad bearing in order to use for small-size rotating machinery. This paper describes the stabilization method of the small-bore journal bearing based on the combination mechanism with starved lubrication and orientation angle change. It is found that the stabilization of small-bore journal bearings is improved drastically by hybrid lubrication combining these two kinds of mechanism. Keywords: journal bearing, stability, oil supply groove, bearing orientation angle, starved lubrication, flooded lubrication, small bore

The negative squeeze lubrication problem is investigated by means of numerical simulations that account for the dynamics of vaporization. The model is based on bubble dynamics, governed by the Rayleigh--Plesset equation, and the Reynolds equation for compressible fluids. Unlike most existing simulation models our model can predict tensile stresses in the fluid film prior to its rupture, which is in accordance with experimental evidence. Keywords: negative squeeze behavior, vaporization, bubble dynamics, Rayleigh--Plesset equation

This paper reports the development of a novel three-dimensional (3D) deterministic model (3D L-EHL) for rough surface line-contact mixed-elastohydrodynamic lubrication (EHL) problems. This model is highly demanded because line contacts are found between many mechanical components, such as various gears, roller and needle bearings, cams and followers, and work rolls and backup rolls in metal-forming equipment. The macro aspects of a line-contact problem can be simplified into a two-dimensional (2D) model; however, the topography of contacting rough surfaces, microasperity contacts, and lubricant flows around asperities are often three-dimensionaL The present model is based on Hu and Zhu's unified 3D mixed-EHL model (Hu and Zhu, 2000, 'Full Numerical Solution to the Mixed Lubrication in Point Contacts,' ASME J. Tribol., 122(1), pp. 1-9) originally developed for point contacts and the mixed fast Fourier transform (FFT)-based approach for deformation calculation formulated by Chen et al. (2008, 'Fast Fourier Transform Based Numerical Methods for Elasto-Plastic Contacts With Normally Flat Surface,' ASME J. Appl. Mech., 75(1), 011022-1-11). It is numerically verified through comparisons with results from the line-contact Hertzian theory and the conventional 2D line-contact smooth-surface EHL formulas. Numerical examples involving 3D sinusoidal and digitized machined surfaces are also analyzed. Sample cases indicate that transverse roughness may yield greater film thickness than longitudinal roughness. This observation is qualitatively in agreement with the trend predicted by Patir and Cheng's stochastic model (1978, 'Effect of Surface Roughness on the Central Film Thickness in EHL Contacts,' Proceedings of the Fifth Leeds-Lyon Symposium on Tribology, London, pp. 15-21). However, the roughness orientation effect does not appear to be quantitatively as great as that shown in the work of Patir and Cheng for the same range of h ratio. Keywords: three-dimensional line-contact, mixed elastohydrodynamic lubrication, deterministic modeling, rough surface contact, surface topography, tribology

In this paper, we numerically study the lubricant migration on a flying slider air-bearing surface in a hard disk drive. The lubricant dynamics is based on a continuum thin film lubrication theory with inter-molecular forces and a precursor film model. It includes air-bearing pressure, air-bearing shear stress, the Laplace pressure, the disjoining pressure, and the shear stress caused by the surface free energy gradient. Using this model we investigate the lubricant migration behavior on a modern negative pressure type slider surface. We also reveal the correlation between the lubricant migration behavior and the air-bearing shear stress. We further perform the lubricant migration analysis for various different slider designs, radii, and skew angles. Index Terms--Flying head slider, hard disk drives, lubricant, migration.

An elastohydrodynamic lubrication (EHL) model for coated surfaces in point contacts has been developed by combining the elastic deformation formulation for the coated surfaces with an EHL model. Inverse fast Fourier transform (IFFT) is employed first to obtain the influence coefficients (ICs) from the frequency response function (FRF). The subsequent calculation of elastic deformation is performed using the efficient algorithm of discrete convolution and fast Fourier transform (DC-FFT). The coating EHL model is verified by the comparison to available numerical results. The effects of coating on lubrication under various loads, speeds, rheological models, and pressure-viscosity behaviors are numerically investigated. Similar to the observations from dry contact, stiffer coatings in EHL tend to reduce the nominal contact radius but increase the maximum contact pressure, and vice versa for more compliant coatings. However; as coating thickness increases, the influence of coatings on film thickness, including the central and the minimum film thicknesses, does not follow a monotonic variation, and therefore, cannot be predicted by any simple film thickness equation. The reason for that is the pressure viscosity effect which tends to counterbalance the effect of coating. The average friction coefficient in lubricant film increases in stiff coating cases but decreases for compliant coating cases. Furthermore, two possible approaches to improving the minimum film thickness thus reducing friction and wear in mixed lubrication are indicated: a thin stiff coating for conventional EHL and a thick compliant coating for soft EHL. [DOI: 10.1115/1.2736433] Keywords: EHL, coating, FFT

The Stribeck curve plays an important role in identifying boundary, mixed, elastohydrodynamic, and hydrodynamic lubrication regimes. Recent advances in elastohydrodynamic lubrication together with rough surface interaction have made it possible to develop a methodology for predicting the trend of the Stribeck curve. In this paper, we report the results of a series of experiments performed on a journal bearing together with a theoretical prediction of the Stribeck-type behavior. Various loads and oil temperatures are considered. The comparison between the experimental results with a mixed elastohydrodynamic lubrication model for line contacts is indicative of good agreement. [DOI: 10.1115/1.2345406]

The analysis of the mixed lubrication phenomena in journal and axial bearings represents nowadays the next step towards a better understanding of these devices, subjected to more and more severe operating conditions. While the theoretical bases required for an in-depth analysis of the mixed-lubrication regime have long been established, only small-scale numerical modeling was possible due to computing power limitations. This led to the appearance of averaging models, thus making it possible to generalize the trends observed in vein small contacts, and to include them in large-scale numerical analyses. Unfortunately, a lack of experimental or numerical validations of these averaging models is observed, so that their reliability remains to be demonstrated. This paper proposes a deterministic numerical solution for the hydrodynamic component of the mixed-lubrication problem. The model is applicable to small partial journal bearings, having a few centimeters in width and diameter. Reynolds' equation is solved on a very, thin mesh, and pad deformation due to hydrodynamic pressure is taken into account. Deformation due to contact pressure is neglected, which limits the applicability of the model in those cases where extended contact is present. The results obtained with this deterministic model are compared to the stochastic solution proposed by Patir and Cheng, in both hydroclynamic and elastohydrodynamic regimes. The rough surfaces used in this study are numerically generated (Gaussian) and are either isotropic or oriented, having different correlation lengths. It is shown that the stochastic model of Patir and Cheng correctly anticipates the influence of roughness over the pressure field, for different types of roughness. However, when compared to the smooth surface solution, the correction introduced by this model only partially compensates for the differences observed with a deterministic analysis. [DOI: 10.1115/1.2345404] Keywords: mixed lubrication, elastohydrodynamic lubrication, surface roughness effects, journal bearings

The effects of lubricant film flow, pressurized and sheared between two parallel sinusoidal wavy surfaces in sliding motion is studied analytically. Results are presented using a flow factor model which provides an average description of the surfaces roughness impact. Two distinct cases are studied in order to compare stationary or time dependent local aperture configurations. Flow factors are computed respectively for each case through spatial or spatio-temporal average, revealing striking differences. The results shed light on the relevance of the composite roughness concept. Special attention is paid to the flow factor analytical behavior when surfaces are near contact. [DOI: 10.1115/1.1467084]

In ElastoHydrodynamic Lubrication (EHL), transient processes are much more common than stationary ones. Predicting the film thickness under steady state conditions has become straight forward. Using numerical methods, the effect of transient conditions on the film thickness profile can be computed. However, those analyses are very time consuming even using advanced numerical techniques. As such, they are inadequate for industrial applications as design and development. This paper shows that under certain assumptions, an approximate formula of the transient film thickness profile can be derived under transient operating conditions. The variations can occur in the geometry, the load or the hydrodynamic velocity. The theory can handle all variations separately, or even a combination of several parameters varying simultaneously. The analytical approximation obtained is rather good apart from the constriction at the contact edge(s). This approach can be applied to any set of time dependent conditions (load, speed, geometry). As an example an EHL contact is studied in which reversal of the entrainment velocity occurs. [DOI: 10.1115/1.1454105]

Formulation of a three-dimensional, quasi-static lubrication model of an artificial hip joint is proposed which includes the inclination angle of the acetabular cup. This is performed by deriving a transformed Reynolds equation accounting for this cup tilt angle. The numerical simulation also addresses mass conservation at the location of film rupture. A 3-D spherical representation of the articulating surfaces of the hip prosthesis is mapped onto a cartesian coordinate system of the entire geometry of the 'ball and socket' joint. Results include the lubricating fluid pressure distributions for various inclination angles of the acetabular cup demonstrating that the greatest pressures occur for large eccentricities in the upward vertical direction.

The use of lubrication equations in studying thin fluid films driven by surface tension has been studied. Landau and Levich were the first to study the phenomenon in 1942 and have facilitated the study of bubble flow, fluid motion on heat exchangers, soap films and contact lens motion. Significant progress still has to be made before surface tension in thin fluid films is fully understood. This is especially true for foam breakdown and contact line motion.

In certain applications where the lubricant is subjected to rapidly changing conditions along its flowing path (such as an elastohydrodynamic contact), the inherently time dependent nature of the lubricant may be significant. The simplest type of model to correctly account for such time dependence is the second-order fluid, which is a systematic small departure from Newtonian behavior, involving higher order rate-of-rate-of strain tensors. As in a companion paper using the Maxwell model, the formalities of applying such a model to thin film flow are emphasized. Using a regular perturbation in the Deborah number, with the conventional lubrication solution as the leading term, a solution can be obtained. Viscoelasticity may raise or lower pressure depending on the nature of edge boundary conditions.

This paper examines a class of experimental techniques used to develop constitutive models for lubricants, by simulating the shearing of a thin lubricant layer while accounting for transient phenomena. The complete transient thermal problem with fully nonlinear constitutive relations is solved, and heat conduction is accounted for both in the lubricant layer and into the walls. Numerical simulations are used to examine the shear stress history, the velocity profile, and the temperature profile as functions of time. As a particular example, the high-rate torsional Kolsky bar rheometer (Feng and Ramesh, 1993) is simulated. The computations indicate that the Kolsky bar experiments, which are able to examine the time-histories of the stresses and of the motion, can be used to obtain material properties for lubricants at high shear rates. A full numerical analysis may be required to properly interpret some of the data available from the Kolsky bar experiments, since at longer times (greater than that associated with the peak shear stress) the thermal softening may dominate the response and the velocity field may become strongly inhomogeneous. The numerical simulations are performed using both rate-dependent and limiting stress constitutive laws, and the effects of the layer thickness and the rise time of the relative velocities are examined. The simulations show that the film thickness and the rise time of the relative velocities can have strong effects on the character of the solution when the transient phenomena are included in the analysis. The computations also demonstrate that highly inhomogeneous and even localized flows may occur within rheometers as a result of transient effects. The development of these flows depends on the layer thickness, the rise-time of the boundary velocity, the thermal boundary conditions, and the constitutive behavior of the lubricant.

A new modified Reynolds equation for solving the ultrathing film gas lubrication is proposed to overcome the complicated and time-consuming difficulties of solving the linearized Boltzmann equation. The model equation is based on modified high-order slip-flow velocity distribution with three adjustable coefficients, which are corrected according to the Boltzmann model. The results are compared to those obtained using other kinds of currently employed modified Reynolds equations. It shows that the present model produces a closer approximation to that of the exact Boltzmann model than do other models, in a wider range of inverse Knudsen number. In addition, the newly derived equation is widely applicable to practical use.