Calculated Film Thickness Research Articles

Discussion: “Modeling of Film Thickness and Traction in a Variable Ratio Traction Drive Rig,” (Sharif, K. J., Evans, H. P., Snidle, R. W., and Newall, J. P., 2004, ASME J. of Tribology, 126(1), pp. 92–104)

Ordinary shear-thinning affects EHL film thickness by reducing the central thickness from the theoretical Newtonian value 1 and ordinary shear-thinning affects traction in point contacts by shifting the logarithmic traction gradient to higher rates 2 in a manner indistinguishable from a reduction in pressure dependence of low shear viscosity at high pressure 2. The models selected by the authors for shear-thinning are not recognizable as ordinary shear-thinning. The authors’ Eq. (10) was Eyring’s sinh law model for thixotropy 3. Thixotropy should not be an issue here since the traction fluid is not known to contain wax and in any event the waxy structures studied by Eyring were quite weak with approximately τo=0.01 MPa3. Eyring made very clear his opinion that the sinh law, Eq. (10), is not an accurate description of shear-thinning 4. The authors’ Eq. (11) is not constitutive as it results from inhomogeneous shear 5. The viscosity extrapolation rule selected by the authors also has no physical basis. Two years ago, at the request of one of the authors for an accurate extrapolation, one of the discussers (S.B.) provided the authors with the parameters of the Tait-Doolittle free volume formulation for the same early version of Santotrac 50 6. This free volume formulation has been used by physical chemists to extrapolate viscosity to the glass transition pressure 7 in order to calculate pressure fragility. We have found it to be accurate for pressure extrapolations for another traction fluid 8. The authors neglected this formulation in favor of exponential extrapolation and thus discount the greater-than-exponential response that is known to be a feature of glass forming liquids and that the authors acknowledge to be important. Numerical simulations should ideally provide traction and film thickness predictions from the best available viscosity-temperature-pressure correlation, but these simulations should include shear-thinning. For example the fluid studied in this paper, Santotrac 50, is known to contain a high molecular weight additive. Then even a central film thickness calculation must include shear-thinning to accurately predict the film thickness. To illustrate, the film thickness of the subject traction fluid was measured in rolling point contact at INSA Lyon and the data points are plotted in Fig. 1. The Newtonian solution of Hamrock and Dowson 9 using rheological properties obtained at INSA from the same sample is plotted as a straight curve which can be see to overestimate the film thickness. The same film-thinning effect was reported by Makala et al. 10 for the same traction fluid. Shear-thinning of the ordinary power-law type is required to explain this film-thinning 11 that increases with sliding. The sinh law is inadequate for this purpose as the effect of sliding becomes drastic 11. Also, in Fig. 4 of the original paper, the viscosity of a glass is calculated with a free volume model that assumes a liquid equation of state. Free volume models are useful for their accuracy and for the fact that many of the parameters such as the glass transition temperature have physical meaning and may be obtained by other measurements.

Modeling and measurement of shear stress for a slug flow inside a capillary

AbstractThe aim of the present study is to characterize wall shear stresses generated by a gas–liquid two‐phase flow inside a capillary tube. In this case the flow is a slug flow. Two different approaches were used. The first one constituted a calculation of the shear stresses by a two‐phase model in which some parameters characteristics of the flow were introduced. These parameters had been determined experimentally in a previous study. The second approach constituted a direct and local measurement of wall shear stresses by an electrochemical method. The shear stresses near liquid and gas slugs were obtained for different operating conditions. Moreover, a calculation of the liquid film thickness around the gas slugs demonstrated that this thickness does not depend on gas velocity. © 2005 American Institute of Chemical Engineers AIChE J, 2005

ESCA-thickness metrology and head-medium spacing impact of disk lubricant

Electron spectroscopy for chemical analysis (ESCA) has been commonly used as a metrology tool for lubricant film-thickness measurement on magnetic hard disks. The accuracy of the ESCA-thickness measurement rests solely with the calibration accuracy of the characteristic photoelectron attenuation length in the lubricant film. Several past studies on this subject yielded widely divergent results, due to the difficulty in obtaining an accurate, absolute lubricant film-thickness measurement. In this paper, we revisited the calibration issue and, instead of following the same paths pursued in the past, used a derivative method to yield an accurate calibration of the photoelectron attenuation length. We also compared the various methods for lubricant film-thickness calculation based on ESCA measurements and determined that the most accurate method is to use only the photoemission signal from the lubricant film. In addition, by studying the lubricant film-thickness effect on the electrical readback signal, we found that the lubricant film leads to an increase in the head-medium spacing by an amount greater than one times, but less than two times, its physical thickness.

Shear thinning correction for rolling/sliding elastohydrodynamic film thickness

A film thickness correction for shear-thinning in rolling elastohydrodynamic (EHD) contacts has been available for about 8 years that uses parameters obtained from flow curves. Newly acquired shear-thinning data from experiment and simulation allow for a more narrow and more realistic range of parameters for ordinary lubricant base oils. Line contact film thickness calculations were performed over a wide range of conditions to arrive at a new film thickness correction that includes the sliding effect. This correction may be applied to any classical Newtonian prediction of film thickness for single-component liquids having ordinary power-law response to high shear rate or stress.

Actual Eyring Models for Thixotropy and Shear-Thinning: Experimental Validation and Application to EHD

The Eyring sinh law is presently the most well-accepted model for shear-thinning of EHD lubricants at high pressure. It was, however, not accepted for this purpose by Eyring, who found it to be of only limited usefulness for thixotropy. Then, it is extremely important that these models receive a critical review using data obtained by modern methods to evaluate the actual Eyring models and show how they differ from the model in use today. Data from high-pressure viscometers were used to validate the actual Eyring models. The Ree-Eyring model for shear-thinning obeys time-temperature-pressure superposition. A film thickness calculation shows it to suffer from the same anomalous behavior in sliding contact as does the sinh law.

Mathematical modeling of contact of two surfaces in the first order of tangency

The topic of the paper is in the area of mathematical modeling of the contact of two smooth regular surfaces in the first order of tangency. The paper is aiming to develop an approach for the mathematical description of the geometry of tangency of two smooth regular surfaces, which share a common point, and in such way to describe geometry of contact of two surfaces not only qualitatively, but quantitatively as well. Various approaches of the first-, second-, and higher-order approximation are discussed. To resolve the problem under consideration, a characteristic curve of new kind is introduced. We refer to this characteristic curve as the so-called indicatrix of conformity of two surfaces, which are tangent to each other at a point. Application of the indicatrix of conformity enables one developing an appropriate quantitative and qualitative description of the geometry of contact of two smooth regular surfaces in the first order of tangency. The results presented in the paper will have many practical applications in science and engineering: 1. (i) for optimal tool-path generating in machining sculptured surfaces on multiaxis CNC milling machine, from which the problem arose; 2. (ii) for developing a perfect TCA ( tooth contact analysis) computer programs for gear pairs and for gear trains; 3. (iii) for improving accuracy of solving the problem of two rigid bodies contact; 4. (iv) for fitting two surfaces while designing blend surfaces; 5. (v) when performing elastohydrodynamic film thickness calculations, etc .

Mathematical simulation of catalytic paste flow in a ram extruder

A mathematical model was developed for the stage of catalyst paste preparation. The mathematical model allows the calculation of solvate film thickness and volume content of the solid phase at any moment of time. Functional dependencies were found, which correlated the solvate film thickness and volume content of the solid phase with the plastic strength and viscosity of catalyst pastes. A range of plastic strength was determined, which ensures the optimum forming properties of the pastes. The mathematical model allowed the determination of the concentrations of the components of the continuous and dispersed phases, which ensured the optimum paste forming rheological properties, which, in turn, influence the end properties of an a-FezOs catalyst. The significant role of the solvate film thickness in the forming properties of pastes was demonstrated.

Film thickness calculations

The wear and friction behaviour of self-mated silicon nitride pairs in lubricated ball-on-flat reciprocating sliding conditions is the subject of the present work, using diesel fuel and soybean biodiesels as lubricants. The results show that the friction coefficient is considerably higher for the diesel fuel than for biodiesels in the stationary regime (about 0.14 and 0.06, respectively). The wear coefficient values are in the range 10−8–10−9 mm3/N·m, denoting a mild wear regime, in agreement with the high lubricity of these fuels assessed by the ASTM D 6079 standard. The observed wear mechanisms were mainly mechanically dominated, consisting of transgranular and intergranular fractures, and the formation of a tribolayer by plastic deformation of the wear debris.

Tungsten Oxide Coatings from the Aerosol-Assisted Chemical Vapor Deposition of W(OAr)6 (Ar = C6H5, C6H4F-4, C6H3F2-3,4); Photocatalytically Active γ-WO3 Films

Tungsten hexaaryloxide complexes of formula W(OAr)(6) (Ar = C6H5, 1; C6H4F-4, 2; C6H3F2-3,4, 3) have been synthesized by the reaction of W(O)Cl-4 and ArOH in 22-28% yield. The complexes were characterized by H-1, C-13, F-19, and W-183 NMR (1, delta = -474.8; 2, delta = -416.3; 3, delta = -446.3), melting point (1, 95 degreesC; 2, 101 degreesC; 3, 105 degreesC), IR, microanalysis, and single-crystal X-ray diffraction (octahedral coordination). Aerosol-assisted chemical vapor deposition of W(OAr)6 using acetone and toluene solvents and substrate temperatures from 300 to 500 degreesC produced blue tungsten oxide films on glass substrates. The films were analyzed by glancing angle powder diffraction and shown to be amorphous at 300 degreesC, but consisted of crystalline WO3-x at higher deposition temperature. Annealing the films from 1 at 550 degreesC in air for 30 min produced yellow gamma-WO3 with preferred growth in the [020] direction. Raman analysis of the as-formed films showed WO3-x with evidence for W-V-W-VI paired ions. Annealed samples produced Raman patterns for gamma-WO3 (807, 715, 273, and 133 cm(-1)). The films were adhesive to the substrate, conformal, passed the Scotch tape test, and gave good coverage. Typical growth rates were 20-50 nm min(-1). SEM showed uniform films consistent with an island growth mechanism. Energy dispersive analysis confirmed the presence of only tungsten and oxygen. XPS showed that the as-formed films were WO3-x (x approximate to 0.22) with binding energy shifts for W 4f(5/2) at 37.2 and 4f(7/2) 34.4 eV and for oxygen Is at 532.6 eV. The as-formed films had an absorption maxima at 320-360 nm (dependent on film thickness) and an onset for absorption at 400 nm. Reflectance/transmission measurements produced interference fringes that enabled a calculation of film thickness. In general the films showed good transmission from 500 to 1000 nm (60%) and some reflectivity (ca. 20%) over the same region. After annealing, the absorption edge was pushed more into the visible and the films showed evidence for some scattering associated with haze. The blue WO3-x films showed negligible photocatalytic activity. The annealed, yellow WO3 films were active photocatalysts and readily destroyed an overlayer of stearic acid.

Analytical Formulas for Film Thickness in Compacted Asphalt Mixture

Recently, several researchers have proposed asphalt film thickness as a criterion for ensuring the durability of asphalt mixtures. However, they suggested that the standard film thickness equation, which dates back to the 1940s, needs to be examined by modern technology and improved. A presumable background on which the Asphalt Institute surface area factors are based was recovered and analyzed in detail. A fundamentally sound model for film thickness calculation was developed using a model of asphalt concrete in which the aggregates are spherical but have an arbitrary size distribution. A recent result from statistical geometry is applied to determine the film thickness for any volume fraction of aggregates and any volume fraction of effective asphalt. The analytical formulas are presented, the details of the calculation are summarized, and examples are provided.

Electron probe microanalysis (EPMA) measurement of thin-film thickness in the nanometre range.

The thickness of thin films of platinum and nickel on fused silica and silicon substrates has been determined by EPMA using the commercial software STRATAGEM for calculation of film thickness. Film thickness ranged in the order 10 nm. An attempt was made to estimate the confidence range of the method by comparison with results from other methods of analysis. The data show that in addition to the uncertainty of the spectral intensity measurement and the complicated fitting routine, systematic deviation caused by the underlying model should be added. The scattering in the results from other methods does not enable specification of a range of uncertainty, but deviations from the real thickness are estimated to be less than 20%.

Modified split Hopkinson pressure bar method for determination of the dilatation-pressure relationship of lubricants used in elastohydrodynamic lubrication

In theoretical calculations of film thickness, pressure distribution and friction in an elastohydrodynamically lubricated (EHL) conjunction it is necessary to model the physical/ mechanical behaviour of the lubricant. It is important to know, for example, the dilatation-pressure or the density-pressure relationship. In this paper a modified split Hopkinson pressure bar system for determination of the compressibility of oil is presented. It makes it possible to test oils under conditions similar to those found in real EHL contacts: loading duration in the range of 100–300 μs and pressures of almost 2 GPa. An empirical model has been suggested for mathematical description of the dilatation-pressure relation of the specific oils. A naphthenic mineral oil and a synthetic oil, 5P4E, have been tested under adiabatic conditions and at pressures up to 1.5 and 1.9 GPa respectively. The adiabatic results have been recalculated to isothermal conditions for comparison.

Characterization and properties of lignocellulosic fibers with thin-film deposited cationic precursor

Cationic pulp has been prepared by depositing ultra-thin films of a cationic silane precursor on the pulp surface. The deposited thin film has been characterized by relative measurement of film thickness and also by determining the charge behavior of the modified fiber surface in an aqueous suspension by streaming current, ionic mobility and charge density measurements. Although the calculated film thickness was found to be less than 30 Å, a significant difference in the calculated thickness values between X-ray photoelectron spectroscopy and ellipsometry was observed. Streaming current measurements confirmed that the cationic charge carrying capacity of cellulosic fibers depends on the hydrophobicity of the fibers. The charge density of the cationic fibers was found to be lower than conventional polyelectrolytes that are used as flocculants in wet-end papermaking. Effect of pH on the ionic mobility of the precursor deposited fibers demonstrated the more pH tolerant character of the cationic fibers compared to the unmodified fibers. Effect of precursor concentration on cationic charge behavior of cellulose, stoned ground wood and thermomechanical pulp demonstrated that, for most of the cation modified fibers, there was a marginal increase in charge with higher precursor concentration. Temperature and pH have little effect on charge properties. A partial replacement of anionic fiber by silane deposited cationic fiber in a fiber slurry improved fines and filler retention properties. Microscopic analyses of floc structure suggested that the improved retention properties exhibited by the cationic fibers could be due to the formation of smaller but stronger flocs at higher shear rates.

Simultaneous Thickness and Refractive Index Determination of Monolayers Deposited on an Aqueous Subphase by Null Ellipsometry

For the first time, the thickness and refractive index of monolayers at the air/water interface have simultaneously been determined by null ellipsometry. Separation of refractive index from film thickness has been achieved by highly precise measurements of the two ellipsometric angles Ψ and Δ. In the solid state, film thicknesses of arachidic acid and valine gramicidin A obtained by ellipsometry are comparable with those obtained by the X-ray techniques. For arachidic acid in the condensed state, our results suggest that only the thickness of the hydrophobic moiety is measured. When highly hydrated, the thickness of the polar headgroup is not detected. This is presumably due to its refractive index being the same as that of the bulk water; hence, the calculated film thickness corresponds to the thickness of the hydrophobic part only. As molecular area is reduced, the polar headgroup gradually loses hydration water molecules causing its refractive index profile to become different from that of the bulk wat...

A Computer Program Package for the Prediction of EHL and Mixed Lubrication Characteristics, Friction, Subsurface Stresses and Flash Temperatures Based on Measured 3-D Surface Roughness

A complete computer program package has been developed in the present work based on a recently developed unified numerical approach for point contact problems. This approach is capable of simulating the entire transition from the full film EHD, mixed, down to boundary lubrication, using measured 3-D roughness. The numerical solution can cover a full range of λ ratio, from infinity down to zero. Based on the calculated film thickness (or gap) and pressure distribution in the contact, subsurface stresses can readily be predicted. Also, friction and flask temperatures can be computed by using a non-Newtonian fluid model in the hydrodynamic regions and a measured (or assumed) coefficient of friction for boundary lubrication in the contact regions. Sample cases show that this computer program package is robust with no convergence problems encountered even under severe operating conditions. It appears to be a useful engineering tool for industrial applications.

Analysis of EHL Circular Contact Start Up: Part I—Mixed Contact Model With Pressure and Film Thickness Results

In this paper a model is presented to investigate the start up condition in elastohydrodynamic lubrication. During start up the lubrication condition falls into the mixed lubrication regime. The transition from solid contact to lubricated contact is of importance when investigating the start up process and its effects on bearing performance. The model presented uses the multigrid multilevel method to solve the lubricated region of the contact and a minimization of complementary energy approach to solve the solid contact region. The FFT method is incorporated to speed up the film thickness calculation. An iteration scheme between the lubrication and the solid contact problems is used to achieve the solution of the mixed lubrication contact problem. The results of start up with smooth surfaces are provided for the case when speed increases from zero to desired speed in one step and the case when speed is linearly increased to desired speed. The details of the transition from full solid contact to full lubricated contact in EHL start up are presented. The change of pressure and film thickness as well as contact forces and contact areas are discussed.

2205 VOF モデルを用いたスワールインジェクタの内部流れ解析

A two-phase analysis of air and fuel flow through a swirl injector was performed by using a volume of fluid (VOF) model. This model makes it possible to calculate the cavity that is formed at the exit of the nozzle, thereby facilitating calculation of the liquid film thickness which strongly influences fuel atomization. The calculated results were compared with experimental data for fully developed spray characteristics, including the flow coefficient, cone angle and cavity factor. Moreover, the initial spray development process was also calculated. The calculated results were compared with visualizations of the initial spray development process. They showed relatively good agreement with the experimental data.

A Simple and Accurate Method to Calculate Transient EHL Film Thickness in Machine Components Undergoing Operation Cycles

This paper presents a new method to calculate EHL film thicknesses for contacts operating in transient conditions. The method approximates the EHL pressure distribution by its corresponding Hertz distribution. The transient Reynolds equation is simplified to a partial differential equation governing wave propagation of the film thickness from the inlet to the outlet of the Hertz contact region. The film thickness at the Hertz inlet is calculated by the Dowson-Toyoda formula in which the parameters are determined by the current operating conditions. These modeling techniques greatly enhance the robustness and computational efficiency of the method. A wide range of practical EHL problems can be solved, and film thicknesses for a full cycle of machine operation can be calculated on a PC in a few seconds of CPU time. The accuracy of the method is evaluated by comparing its results with those obtained by a full transient EHL model. The comparison is fairly favorable for a wide range of operating conditions with large variations of load and speed parameters and with a frequency of variation up to 1000 cycles per second. This method of transient film thickness calculations can be easily implemented into design programs for EHL machine elements. it also establishes a platform upon which other design calculations and analyses can be performed such as asperity contacts, temperature and traction. Presented at the 53rd Annual Meeting in Detroit, Michigan May 17–21, 1998

Influence of lubricant properties on elastohydrodynamic lubrication

In hard EHL, encountered in, e.g., gears, rolling element bearings etc. the properties of the lubricant play a significant role in the forming of a lubricating film and reducing friction between the contacting surfaces. The influence of pressure and temperature on viscosity, limiting shear stress and density, has to be taken into account when creating lubricant models to be used in numerical calculations of film thickness and friction. This paper describes some experimental methods to determine these properties of a number of different lubricating oils, both from mineral, vegetable and synthetic origin. The results show that, apart from 5P4E, naphthenic mineral oil has the highest values of pressure–viscosity as well as limiting shear stress–pressure coefficients. It also exhibits the highest density increase with pressure. Rapeseed oil has a rather high pressure–viscosity coefficient but a low limiting shear stress–pressure coefficient as well as a low density increase with pressure. Thus, rapeseed oil is a strong alternative to naphthenic (and also paraffinic) oil since it has the ability to form a relatively thick oil film and at the same time give a low coefficient of friction. Ester, polyglycol and polyalphaolefin oils also exhibit low values of friction but are not equally good as rapeseed oil to form a lubricant film as a result of their lower pressure–viscosity coefficients.

Wetting and Non-Wetting Behaviour of Silicon Carbide Grain Boundaries

Silicon carbide (SiC) grain boundaries have been observed to be free from intergranular films. On the basis of equilibrium film thickness calculations, it has been proposed elsewhere that because SiC has very high refractive index, the attractive forces are very large and thin amorphous films cannot exist at SiC grain boundaries. However, in our studies, we have observed film-free grain boundaries together with grain boundaries containing intergranular films. Possible reasons for the wetting and non-wetting behaviour of SiC grain boundaries are briefly discussed.