Prediction Of Film Thickness Research Articles

Elastohydrodynamic lubrication analysis of metal-on-metal hip-resurfacing prostheses

The elastohydrodynamic lubrication analysis was carried out in this study for a typical metal-on-metal hip-resurfacing prosthesis under a simple steady-state rotation. Both the Reynolds equation and the elasticity equation were coupled and solved numerically by the finite difference method. The finite element method was used to determine the elastic deformation of both the femoral and the acetabular components required for the lubrication analysis. The effect of the radial clearance between the femoral head and the acetabular cup on the predicted film thickness and pressure distribution was investigated. The predicted minimum lubricating film thickness was found to compare favourably with the prediction using the Hamrock and Dowson [J. Lubrication Technol. 100 (1978) 236] formula based on the assumption of ball-on-plane semi-infinite solids. This implies that the non-metallic materials such as bone and cement underlying the metallic components have a small effect on the predicted lubrication performance for the particular metal-on-metal hip-resurfacing prosthesis considered in this study. Under realistic physiological walking conditions, a decrease in the radial clearance from 150 to 50 μm resulted in a 137% increase in the predicted minimum film thickness from 19 to 45 nm. Consequently, given a surface roughness of 0.01 μm for both the metallic femoral and acetabular bearing surfaces, the predicted mixed lubrication regime for the larger clearance was changed to a full fluid film lubrication regime for the smaller clearance. This clearly highlighted the importance of the design and manufacturing parameters on the tribological performance of these hard-on-hard hip prostheses.

Sources, properties, recovery, treatment

Models for the temperature and pressure dependence of density, temperature and pressure dependence of the low-shear viscosity, and shear dependence of viscosity are directly applicable to elastohydrodynamic simulations. The models provide a means to relate the tribological behavior of the lubricated contact to the properties of the liquid lubricant. The success of the Newtonian assumption for the film thickness of squalane can be typical for neat, low-molecular-weight liquids that are used as lubricants such as naphthenic mineral oils, polybutenes, and low-viscosity paraffinic mineral oils. The assumption is reasonable for squalane to a shear stress of at least 5 MPa, which is not exceeded in the inlet zone. It is possible to produce an accurate prediction of the central elastohydrodynamic film thickness without solving simultaneously the Reynolds equation and the elastic film-shape equation.

Free coating of a non-Newtonian liquid onto walls of a vertical and inclined tube

The one-dimensional approximate equations governing flow in a free coating and a gas-assisted displacement of liquid in a vertical or inclined tube is derived using asymptotic techniques. These techniques are employed to place the free coating flow and mass conservation equations, utilized in previous studies, on a firmer theoretical ground. The derived one-dimensional flow equation for the motion of a long bubble rising steadily in a vertical or inclined tube filled with a power-law fluid is found to be identical to that of Gutfinger and Tallmadge [AIChE 11 (1965) 403] for a free coating on a flat plate withdrawn vertically from the liquid reservoir. The theoretical analysis indicated that the residual liquid film thickness increases with decreasing power-law index. This trend is similar to that observed experimentally by Huzyak and Koelling [J. Non-Newt. Fluid Mech. 175 (1997) 73] for Boger fluids. The prediction of the liquid film thickness from this analysis qualitatively agrees with the experimental results of Huzyak and Koelling [J. Non-Newt. Fluid Mech. 175 (1997) 73].

Effect of evaporation on thin film deposition in dip coating process

Evaporation from the free surface is an important phenomenon that occurs during dip coating process. Accounting for evaporation is crucial for correct prediction of film thickness during this process when evaporation rate is large. This paper suggests a method to extend the classical free meniscus theory to account for evaporation from the free surface in a two-component system. The governing equations are solved utilizing a finite difference method. The effects of evaporation on the free surface profile and solute concentration distribution are investigated.

Nano-lubricant film formation due to combined elastohydrodynamic and surface force action under isothermal conditions

This paper presents the results of numerical prediction of the lubricant film thickness and pressure distribution in concentrated counterformal point contact under isothermal conditions. The operating conditions, which include load and speed of entraining motion, promote the formation of ultra-thin films; these are formed under the combined action of elastohydrodynamic lubrication (EHL), the surface contact force of solvation and molecular interactions due to the presence of Van der Waals forces. A numerical solution has been carried out, using the low-relaxation Newton-Raphson iteration technique, applied to the convergence of the hydrodynamic pressure. The paper shows that the effect of surface forces become significant as the elastic film (i.e. the gap) is reduced to a few nanometres. The numerical predictions have been shown to conform well to the numerical work and experimental findings of other research workers.

Models for Marangoni drying

Marangoni drying is a new ultra-clean drying process, which relies on surface-tension gradient forces, so-called Marangoni stresses. This method is of particular use in the semiconductor industry wherein obtaining ultra-clean surfaces is of paramount importance. The present work provides a mathematical description of this novel process involving four coupled partial differential equations, derived in the thin-layer approximation, for the film thickness, the concentration of chemicals in the air, at the air–liquid interface and in the bulk of the liquid film. Numerical solution of these equations yields prediction of typical profiles that accompany the spreading and drying processes. Particular attention is aimed at the prediction of the minimum film thickness as a function of system parameters with a view to optimizing the drying process.

Viscosity–pressure–temperature behaviour of mineral and synthetic oils

AbstractA new high‐pressure viscometer that can measure viscosity at pressures up to 0.8 GPa has been developed in the authors' laboratory. The ‘modulus equation’ has been used to compare the behaviour of mineral and synthetic lubricants. Among the oils investigated there was one ester that biodegraded rapidly both before and after ageing in a long‐term test‐rig operation. To facilitate a comparison or application of the results to other oils, an analysis of the correlation between the viscosity—pressure coefficient and the kinematic viscosity measured at atmospheric pressure has been provided. A prediction of lubricant film thickness based on high‐pressure viscosity data is compared with film thickness measurements in a roller bearing.

Elastohydrodynamic lubrication analysis of ultra-high molecular weight polyethylene hip joint replacements under squeeze-film motion

Elastohydrodynamic lubrication was analysed under squeeze-film or normal approach motion for artificial hip joint replacements consisting of an ultra-high molecular weight polyethylene (UHMWPE) acetabular cup and a metallic or ceramic femoral head. A simple ball-in-socket configuration was adopted to represent the hip prosthesis for the lubrication analysis. Both the Reynolds equation and the elasticity equations were solved simultaneously for the lubricant film thickness and hydrodynamic pressure distribution as a function of the squeeze-film time was solved using the Newton-Raphson method. The elastic deformation of the UHMWPE cup was calculated by both the finite element method and a simple equation based upon the constrained column model. Good agreement of the predicted film thickness and pressure distribution was found between these two methods. A simple analytical method based upon the Grubin-Ertel-type approximation developed by Higginson in 1978 [1] was also applied to the present squeeze-film lubrication problem. The predicted squeeze-film thickness from this simple method was found to be remarkably close to that from the full numerical solution. The main design parameters were the femoral head radius, the radial clearance between the femoral head and the acetabular cup, and the thickness and elastic modulus for the UHMWPE cup; the effects of these parameters on the squeeze-film thickness generated in current hip prostheses were investigated.

Effects of electroless plating chemistry on the synthesis of palladium membranes

The effects of plating chemistry on palladium deposition, plating efficiency and membrane microstructure have been studied for two palladium electroless plating solutions, hydrazine-based and hypophosphite-based plating baths. The electroless plating kinetics of palladium onto seeded supports have been determined for hypophosphite-based plating bath, and a simple kinetic model has been developed. The model provides an accurate prediction of deposition rate and film thickness as a function of plating parameters. Most importantly, the experimental results demonstrated that plating chemistry plays a vital role on both plating performance and film microstructure.

Elastohydrodynamics of a Worm Gear Contact

The paper is concerned with prediction of elastic contact and elastohydrodynamic film thickness in worm gears. Using the undeformed geometry of the gap between gear teeth in contact a three-dimensional elastic contact simulation technique has been developed for calculation of the true area of elastic contact under load relative to the wheel and worm surfaces. A parallel investigation of elastohydrodynamic lubrication effects has been carried out using a special non-Newtonian, thermal solver which takes account of the nonsymmetrical and spin aspects of worm contacts. An interesting feature of the results obtained is the discovery of regions of poor film forming due to entrainment failure at the edges of the contact.

Elastohydrodynamic Film Collapse During Rapid Deceleration. Part II—Theoretical Analysis and Comparison of Theory and Experiment

This paper presents a theoretical model for the behavior of elastohydrodynamic films subjected to transient speed conditions, based on Grubin’s analytical solution for elastohydrodynamic lubrication. This model is applied to predict film thickness in high deceleration conditions. The model’s predictions are compared with the experimental results presented in an accompanying paper entitled “Elastohydrodynamic Film Collapse During Rapid Deceleration. Part I: Experimental Results.”

Film thickness predictions for elastohydrodynamic elliptical contacts over a wide range of radius ratios with consideration of side starvation

The paper presents numerical solutions obtained for a wide range of elliptical elastohydrodynamic lubrication (EHL) problems. The conditions considered encompass relative principal radii of curvature ratios from 20:1 with entrainment in the minor axis direction, to 50:1 with entrainment in the major axis direction. The problems considered derive from investigations of practical machine elements where the width of contact (perpendicular to entrainment) is limited by the extent of the metal surfaces on either side. Two sets of results have been obtained: one with the width of the lubricated contact approximately twice that of the Hertzian dry contact, and the other where the ratio of these widths is 1.2. Taken as a whole the results present a complete range of conditions obtained using the same numerical model throughout. The film thickness predictions are compared with those given by well-known published formulae and design charts.

The Analysis of the Lubrication Condition and Friction Losses of a Single Acting Cross Head Guide Shoe of a Low Speed Cross Head Diesel Engine: Part I—An Alogrithm For The Prediction of Oil Film Thickness

The lubrication condition pertaining to the cross head guide shoe of a low speed cross head diesel engine is evaluated in this paper under the principles of hydrodynamic lubrication. The Reynolds differential equation which describes the pressure and oil film thickness distribution of the cross head guide shoe system operating under unsteady load will be solved using a finite difference method. The influence of the width to length ratio of the rectangular cross head guide shoe plate will be considered in terms of variation of the pressure distribution within the bearing and its load carrying capacity.

Modeling of Spray-Wall Interactions Considering Liquid Film Formation

The main purpose of this article is to propose and assess a new spray impingement model considering film formation, which is capable of describing the droplet distribution and film flows in direct injection diesel engines. The spray-wall interaction model includes several mathematical formulae, newly made by the energy conservation law and some experimental results. The model consists of three representative regimes, rebound, deposition and splash. In addition, the film flow is described in the present model by solving the continuity and momentum equations for film flows using the integral method. To assess the new spray impingement model, the calculated results using the new model are compared with several experimental data for the normally impinging diesel sprays. The film model is also validated through comparing film radius and thickness against experimental data. The results show that the new model is generally in better agreement with experimental data and acceptable for prediction of the film radius and thickness.

The Analysis of the Lubrication Condition and Friction Losses of a Single Acting Cross Head Guide Shoe of a Low Speed Cross Head Diesel Engine: Part II — A Practical Model for the Determination of the Oil Film Thickness

The cross head guide shoe plate of a large diesel engine operates under a large normal force which presses it against the rails between which it executes both axial and transverse motion. In order to ensure the safe operation of an unconventional bearing such as the guide shoe system of the cross head engine, an algorithm that can be used to predict accurately the oil film thickness that can be achieved for all the engine's operating regimes, is invaluable. A solution of the three dimensional form of Reynolds differential equation can provide the requisite oil film thickness. However, with even the availability of very fast computers and large computer storage capacity this solution for a large axial bearing such as the guide shoe becomes impractical in terms of computation time and computer core requirements. This paper describes alternative simplified algorithm for accurate prediction of the oil film thickness developed in the guide shoe bearing at different operating regimes of the engine.

Effect of sol rheology on the uniformity of spin-on silica xerogel films

Spin-on xerogels, which are promising candidates for use as interlayer dielectric materials in future microelectronic devices, change from a Newtonian liquid to a solid gel during processing. Since the rheology of the sol may affect the uniformity of the xerogel films produced, here we relate the rheology of a two-step, acid-base catalyzed, sol-gel system to the thickness and porosity profiles across xerogel films of importance to the microelectronics industry. We also analyze the effect of spin speed on the thickness and porosity of the films. Our rheological studies of the xerogel sol demonstrated that the sol changes from Newtonian far from the gel point, to shear thinning close to the gel point. On films spin coated with shear-thinning sols there is a region of uniformity extending for a distance of about 5 mm from the center. The film thickness and porosity are highest in this region and both quantities decrease towards the edge. If the sol is spun in its Newtonian regime, the resulting films are uniform (<3% thickness and porosity). The predictions of film thickness and uniformity based on simple models for spin coating a Newtonian and truncated power law fluid were found to be in good agreement with the experimental observations. The film thickness was varied from 0.485 to 1.9 μm by adjusting the spin coating speed from 5900 to 1000 rpm. Over this sixfold range of speed, the porosity was almost constant and varied by less than 10% while the thickness varied by about a factor of 4.

Elastohydrodynamic Film Thickness in Elliptical Contacts With Spinning and Rolling

In this paper, a theoretical model for the film thickness prediction of elastohydrodynamic lubrication of elliptical contacts with spinning and rolling/sliding motions is presented, in which 1) an effective ellipticity ratio ke is introduced to present the ellipse feature instead of the normal ellipticity ratio k in case of that the entraining velocity at the center of contact ellipse is at an angle with minor axis, 2) Roelands and Dowson-Higginson’s equations are adopted to express the influence of pressure upon lubricant viscosity and density, 3) multilevel/multigrid techniques, with low complexity and good stability, are used for the purpose of reducing computing time in the complex numerical analysis. With this model the characteristics of film shape and pressure distribution of elastohydrodynamic lubrication of elliptical concentrated contacts with spinning and rolling/sliding were discussed. The results showed that the spinning motion has significant influence on the film shape and pressure distribution. Based on a large number of numerical results of elastohydrodynamic lubrication analysis of elliptical concentrated contacts with spinning and rolling/sliding, new expressions for the minimum and central film thickness prediction were regressed. Their accuracy was analyzed by comparisons with numerical results of an evaluation set and others’ expressions under pure rolling and/or sliding condition. The comparisons showed that the two new expressions have satisfactory accuracy and potential application to engineering analysis and design.

Palladium composite membranes by electroless plating technique: Relationships between plating kinetics, film microstructure and membrane performance

Thin supported palladium membranes were prepared using electroless plating technique. The intrinsic plating kinetics were determined for hydrazine-based palladium plating baths. Mathematical models were developed to predict film thickness and plating rate as a function of plating parameters (i.e., reactant concentrations, temperature and time). Analyses of film surface microstructure indicate that grain structure is dependent on both plating chemistry and plating rate. The evolution of film morphology during electroless plating was also investigated. Hydrogen permeation study demonstrated that film structure has a significant influence on the permeation performance of the palladium membrane.

Film-Thickness Distribution for Annular Flow in Directional Wells: Horizontal to Vertical

Summary An experimental and theoretical investigation has been carried out on two-phase annular flow in inclined pipes. The study focused on the effect of the inclination angle on the liquid film thickness distribution. A conductance multiprobe instrument was utilized to measure the local liquid film thickness around half of the pipe periphery for inclination angles of 90°, 75°, 60°, and 45° from the horizontal. A simple analytical model has been developed for the prediction of the liquid film thickness at the top and bottom of the pipe. The model is applicable for the entire range of inclination angles, from horizontal to vertical. Good agreement is observed between the prediction of the model and the experimental data collected in this study and from the literature.

Effect of the Behavior of Generated Vapor on the Minimum-Heat-Flux Point During Rapid Quenching of a Thin Horizontal Wire.

Heat transfer characteristics and minumum heat flux point (MHF point) condition during rapid quenching of a thin horizontal wire were studied both experimentally and theoretically. Experiments were conducted with ethanol as a quenching liquid. The wire was either fixed or moving downward at a constant speed in an ethanol bath. When the wire was heated instantly to a high temperature, bead like bubbles were formed along the wire. This was in contrast to the previous results for a heated wire that was dipped into the ethanol bath at a relatively high velocity, where a vapor sheet was formed in the wake of the wire. Consideration was given to the effect of film boiling mode on the MHF point condition. A linear stability analysis of vapor film for natural convection film boiling on a horizontal cylinder was presented. The theoretical prediction of the critical vapor film thickness compared well with the measured value at the MHF point for the fixed wire.