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IN THIS ISSUE

### RESEARCH PAPERS

J. Tribol. 2006;128(3):445-459. doi:10.1115/1.2194913.

An average Reynolds equation considering the effects of a pad’s annular grooves and surface roughness is developed in this study to examine mixed lubrication in the chemical mechanical polishing (CMP) of a copper-film silicon wafer. This equation is obtained on the basis of the principle that the pressure gradients and volume flow rates in the direction normal to the border of a groove and a plateau as well as on two sides of the border must be equal. The continuities of volume flow rates and hydrodynamic pressure on two sides of the border as well as in the direction normal to the border of a groove and a plateau are satisfied in order to develop this Reynolds equation. The removal rate model is obtained by taking the concentration of active abrasives in the slurry and the pad grooves into account. Theoretical results are also shown in order to investigate the effects of changing the groove depth and width on the removal rate and the nonuniformity of a copper-film wafer. The application of concentric grooves in general can lower the suction pressure (negative pressure) formed between the pad and the wafer, elevate the wear rate, and reduce the nonuniformity. However, the influences of the groove depth on wear rate and nonuniformity become insignificant when the depth is excessively large. The removal rate is reduced by increasing the groove width such that it finally approaches to the result of a nongrooved pad.

Commentary by Dr. Valentin Fuster
J. Tribol. 2006;128(3):460-468. doi:10.1115/1.2197841.

Premature failure of materials in sliding contact is often a result of the buildup of frictional heat at the contact interface. The interface temperature is an important parameter affecting the friction and wear process, and it is a function of the operating conditions as well as the heat that is dissipated through the material pair and the nearby surroundings. Possible solutions to alleviate thermal wear mechanisms include using more thermally robust materials and providing better cooling or heat dissipation to reduce the elevated temperatures. The latter is the subject of this paper. The micro heat sink ring $(μHSR)$ is a patented approach to interface cooling in which a micro heat sink is constructed within millimeters of the contact interface. The ramifications of this are that temperature can be treated during wear testing as an independent variable and is only a very small function of speed and load. Using this approach, this work investigates the impact of the $μHSR$ on the wear behavior of a tungsten carbide and carbon graphite material pair under dry running conditions at various rotational speeds and face pressures. Ring-on-ring experiments are performed using a thrust washer rotary tribometer within and in excess of the PV limit of the material pair $(17.5MPa*m∕s)$. Results show the potential of the $μHSR$ to allow for reliable operation of materials in sliding contact in harsh operating conditions. The ability to reduce the interface temperature shows a shift in the region of acceptable operating parameters normally defined for the material pair. This shift is attributed to the prevention of the onset of thermally induced wear transitions and thermal failures otherwise prone to occur under certain operating conditions.

Commentary by Dr. Valentin Fuster
J. Tribol. 2006;128(3):469-475. doi:10.1115/1.2197843.

Degradation of materials due to solid particle erosion is encountered in a variety of engineering industries, either at room temperature or elevated temperatures. Nickel-based coatings are commonly used in applications where wear resistance, combined with oxidation or hot corrosion resistance, is required. In the present work, $NiCrAlY$ and $Ni-20Cr$ metallic coatings were deposited on an iron-based superalloy by a shrouded plasma spray process. The coatings were characterized by scanning electron microscopy, optical microscopy, microhardness testing, and x-ray diffractometry. Erosion studies were conducted using an air-jet erosion test rig at a velocity of $40ms−1$ and impingement angles of 30 and $90deg$. Scanning electron microscopy was used to analyze the eroded surfaces. 3D surface roughness profiles of the eroded samples were taken using a Veeco Optical Profilometer. $NiCrAlY$ coatings had slightly lower average porosity and lower microhardness as compared to $Ni-20Cr$ coatings. The observed erosion rate of the $NiCrAlY$ coatings, however was lower than that of the $Ni-20Cr$ coatings at both 30 and $90deg$ impingement angles. $Ni-20Cr$ coating had shown higher erosion rate at $90deg$ impingement angle than that at $30deg$, whereas the effect of impingement angle on the erosion rate is negligible for plasma sprayed $NiCrAlY$ coating. The higher bond strength of $NiCrAlY$ coating might be one of the major contributing factors for lower erosion rate of $NiCrAlY$ coating as compared to $Ni-20Cr$ coating under the tested conditions. Erosion mechanisms of plasma sprayed coatings are discussed.

Commentary by Dr. Valentin Fuster
J. Tribol. 2006;128(3):476-485. doi:10.1115/1.2194917.

This paper presents a fast and robust three-dimensional contact computation tool taking into account the effect of cyclic wear induced from fretting solicitations under the gross slip regime. The wear prediction is established on a friction-dissipated energy criteria. The material response is assumed elastic. The contact solver is based on the half-space assumption and the algorithm core is similar to the one originally proposed by Kalker (1990, Three Dimensional Elastic Bodies in Rolling Contact, Kluwer, Dordrecht) for normal loading. In the numerical procedure the center of pressure may be imposed. The effect of surface shear stress is considered through a Coulomb friction coefficient. The conjugate gradient scheme presented by Polonsky and Keer (1999, Wear, 231, pp. 206–219) and an improved fast Fourier transform (FFT) acceleration technique similar to the one developed by Liu (2000, Wear, 243, pp. 101–111) are used. Results for elementary geometries in the gross slip regime are presented. It is shown that the surface geometry influences the contact pressure and surface shear stress distributions found after each loading cycle. It is also shown that wear tends to be uniformly distributed. This process continuously modifies the micro- and macrogeometry of the rubbing surfaces, leading after a given number of cycles to (i) an optimum or ideal contact geometry and (ii) a prediction of wear.

Commentary by Dr. Valentin Fuster
J. Tribol. 2006;128(3):486-492. doi:10.1115/1.2197522.

Machine design and electrical contacts involve frequently elastic circular contacts subjected to normal loads. Depending on geometry, these may be Hertzian or surface contacts. Both possess highly nonuniform pressure distributions which diminish contact load carrying capacity. The achievement of a uniform pressure distribution would be ideal to improve the situation, but this violates stress continuity. Instead, the generation of a uniform pressure over most of contact area can be sought. Generally, equivalent punch profile which generates this pressure is found by numerical evaluation of double integrals. This paper simplifies the derivation of punch profile by using an existing correspondence between a polynomial punch surface and elastically generated pressure. First, an improved pressure profile is proposed seeking to avoid high Huber-Mises-Hencky stresses near contact surface. Then, this is approximated by the product between typical Hertz square root and an even polynomial, which yields directly the punch profile. Formulas for normal approach and central pressure are derived.

Commentary by Dr. Valentin Fuster
J. Tribol. 2006;128(3):493-504. doi:10.1115/1.2197523.

The contact area and pressure distribution in a wheel/rail contact is essential information required in any fatigue or wear calculations to determine design life, re-grinding, and maintenance schedules. As wheel or rail wear or surface damage takes place the contact patch size and shape will change. This leads to a redistribution of the contact stresses. The aim of this work was to use ultrasound to nondestructively quantify the stress distribution in new, worn, and damaged wheel-rail contacts. The response of a wheel/rail interface to an ultrasonic wave can be modeled as a spring. If the contact pressure is high the interface is very stiff, with few air gaps, and allows the transmission of an ultrasonic sound wave. If the pressure is low, interfacial stiffness is lower and almost all the ultrasound is reflected. A quasistatic spring model was used to determine maps of contact stiffness from wheel/rail ultrasonic reflection data. Pressure was then determined using a parallel calibration experiment. Three different contacts were investigated; those resulting from unused, worn, and sand damaged wheel and rail specimens. Measured contact pressure distributions are compared to those determined using elastic analytical and numerical elastic-plastic solutions. Unused as-machined contact surfaces had similar contact areas to predicted elastic Hertzian solutions. However, within the contact patch, the numerical models better reproduced the stress distribution, as they incorporated real surface roughness effects. The worn surfaces were smoother and more conformal, resulting in a larger contact patch and lower contact stress. Sand damaged surfaces were extremely rough and resulted in highly fragmented contact regions and high local contact stress.

Commentary by Dr. Valentin Fuster
J. Tribol. 2006;128(3):505-514. doi:10.1115/1.2194915.

For several decades, asperities of nominally flat rough surfaces were considered to be points higher than their immediate neighbors. Recently, it has been recognized that this model is incorrect. To address the issue, a new multiple-point asperity model, called the $n$-point asperity model, is introduced in this paper. In the new model, asperities are composed of $n$ neighboring sampled points with $n-2$ middle points being above a certain level. When the separation between two surfaces decreases, new asperities with higher number of sample points, $n$, will come into existence. Based on the above model, the height and curvature of $n$-point asperities are defined and their distributions are found. The model is developed for Gaussian surfaces and for the general case of an autocorrelation function (ACF). As a case study, the exponential ACF is applied to the new model, which is shown to produce remarkably good agreement with measurements from real and simulated surfaces.

Commentary by Dr. Valentin Fuster
J. Tribol. 2006;128(3):515-524. doi:10.1115/1.2197839.

Instead of a general consideration of the fractal dimension $(D)$ and the topothesy $(G*)$ as two invariants in the fractal analysis of surface asperities, these two roughness parameters in the present study are varied by changing the mean separation $(d*)$ of two contact surfaces. The relationship between the fractal dimension and the mean separation is found first. By equating the structure functions developed in two different ways, the relationship among the scaling coefficient in the power spectrum function, the fractal dimension, and topothesy of asperity heights can be established. The variation of topothesy can be determined when the fractal dimension and the scaling coefficient have been obtained from the experimental results of the number of contact spots and the power spectrum function at different mean separations. A numerical scheme is developed in this study to determine the convergent values of fractal dimension and topothesy corresponding to a given mean separation. The theoretical results of the contact spot number predicted by the present model show good agreement with the reported experimental results. Both the fractal dimension and the topothesy are elevated by increasing the mean separation. Significant differences in the contact load or the total contact area are shown between the models of constant $D$ and $G*$ and variable $D$ and $G*$ as the mean separation is reduced to smaller values.

Commentary by Dr. Valentin Fuster
J. Tribol. 2006;128(3):525-533. doi:10.1115/1.2194914.

Characterization of slider motion induced by contact is becoming a critical aspect of developing advanced head-disk interfaces. While vertical motion induced by contact has been studied, very little is known about off- and down-track motions. We have applied three separate laser Doppler vibrometers to measure slider movement in three orthogonal directions simultaneously. We have measured the position of a slider as it undergoes a transition from flying to making full contact with the media surface. We find that slider motion varies considerably with varying levels of contact and that motion in all three directions is considerable. Spectral decomposition is used to identify the vibration modes that are excited in each direction, and we find that for most of the test velocities, modes excited in the vertical direction give rise to motion in the two orthogonal directions. In addition, we present a depiction of the vertical, down-track, and off-track position changes by plotting the position of the slider in real space coordinates to help visualize more completely how the slider moves in space. These trajectories depict the periodic, elliptical path the slider takes and identify how the paths change with contact. Analysis of motion identifies that at some levels of contact, a majority of motion is repeatable, but that nonrepeatable components increase with the amount of contact. Additionally, down-track motion is the only component whose magnitude increases monotonically with increasing contact.

Topics: Motion , Disks
Commentary by Dr. Valentin Fuster
J. Tribol. 2006;128(3):534-541. doi:10.1115/1.2197526.

A thermohydrodynamic model is developed for predicting the three-dimensional (3D) temperature field in an air-lubricated, compliant foil journal bearing. The model accounts for the compressibility and the viscosity-temperature characteristic of air and the compliance of the bearing surface. The results of numerical solutions are compared to published experimental measurements and reasonable agreement has been attained. Parametric studies covering a fairly wide range of operating speeds and load conditions were carried out to illustrate the usefulness of the model in terms of predicting the thermal performance of foil journal bearings.

Commentary by Dr. Valentin Fuster
J. Tribol. 2006;128(3):542-550. doi:10.1115/1.2197838.

Foil bearings are a key enabling technology for advanced and oil-free rotating machinery. In certain applications, they provide a level of performance that is difficult or impossible to match with other technologies. A number of reasonably successful analytical techniques to predict bearing load capacity, power loss, and stiffness have been developed. Prediction of damping, however, has remained problematic. This work presents a fresh look at the damping problem. Using a simplified representation of a bump foil, this work considers explicitly adding the load dependence of the friction force. This approach is shown to provide a good match to previous experimental data. Parametric study results for the various model parameters are presented to examine the characteristics of this model. It is concluded that the load-dependent frictional force is important to consider for a bump foil damping model.

Commentary by Dr. Valentin Fuster
J. Tribol. 2006;128(3):551-558. doi:10.1115/1.2194918.

Gas film bearings offer unique advantages enabling successful deployment of high-speed microturbomachinery. Current applications encompass micro power generators, air cycle machines, and turbo expanders. Mechanically complex gas foil bearings are in use; however, their excessive cost and lack of calibrated predictive tools deter their application to mass-produced oil-free turbochargers, for example. The present investigation advances the analysis and experimental validation of hybrid gas bearings with static and dynamic force characteristics desirable in high-speed turbomachinery. These characteristics are adequate load support, good stiffness and damping coefficients, low friction and wear during rotor startup and shutdown, and most importantly, enhanced rotordynamic stability at the operating speed. Hybrid (hydrostatic/hydrodynamic) flexure pivot-tilting pad bearings demonstrate superior static and dynamic forced performance than other geometries as evidenced in a high-speed rotor-bearing test rig. A computational model including the effects of external pressurization predicts the rotordynamic coefficients of the test bearings and shows good correlation with measured force coefficients, thus lending credence to the predictive model. In general, direct stiffnesses increase with operating speed and external pressurization, whereas damping coefficients show an opposite behavior. Predicted mass flow rates validate the inherent restrictor-type orifice flow model for external pressurization. Measured coast-down rotor speeds demonstrate very low-friction operation with large system time constants. Estimated drag torques from the gas bearings indirectly validate the recorded system time constant.

Commentary by Dr. Valentin Fuster
J. Tribol. 2006;128(3):559-565. doi:10.1115/1.2197845.

The flow inside a seal chamber as induced by the influx of the flush fluid and the rotation of the primary ring is analyzed. The 3-D flow characteristic around the mating ring and the rotating ring are predicted by solving the Navier-Stokes equations in cylindrical coordinates. For this purpose, the pressure correction method was used in conjunction with the SIMPLE algorithm. A series of numerical solutions is presented that show the flow mechanism within the gap between the rings and the gland. The implication of the flow characteristic on the cooling of the rings is discussed.

Commentary by Dr. Valentin Fuster
J. Tribol. 2006;128(3):566-574. doi:10.1115/1.2195461.

A theoretical study of thin fluid film flows between rotating and stationary disks is presented. Inertia terms are included using an averaged method. It is assumed that inertia effects do not influence the shape of velocity profiles. It is shown that this assumption applies in many cases encountered in fluid film lubrication. The model is validated by comparison with experimental data and previous theoretical studies. A thermoelastohydrodynamic analysis of a hydrostatic seal is performed. The substantial influence of inertia terms on leakage rate prediction is demonstrated.

Commentary by Dr. Valentin Fuster
J. Tribol. 2006;128(3):575-584. doi:10.1115/1.2197525.

When a liquid lubricant film fractionates into disjointed liquid bridges, or a unique liquid bridge forms between solid surfaces, capillary forces strongly influence the action of the fluid on the solid surfaces. This paper presents a theoretical analytical model to calculate the normal forces on the solid surfaces when squeezing a flat liquid bridge. The model takes into account hydrodynamic and capillary effects and the evolution of the geometry of the liquid bridge with time. It is shown that the global normal force reverses during the squeezing motion except in the case of perfect nonwetting; it is attractive at the beginning of the squeezing motion, and becomes repulsive at small gaps. When the external load is constant, capillary suction tends to accelerate the decrease in gap dramatically.

Commentary by Dr. Valentin Fuster
J. Tribol. 2006;128(3):585-593. doi:10.1115/1.2197524.

Recently, herringbone-grooved journal bearings have had important applications in miniature rotating machines. The scribed grooves, on either the rotating or stationary member of the bearing, can pump the lubricant inward, which generates supporting stiffness and improves the dynamic stability, especially for concentric operation. Most of the previous investigations that dealt with herringbone grooved journal bearings and grooved thrust bearings were theoretical. Few experimental attempts for the investigation of the performance characteristics of herringbone grooved journal bearings (HGJBs) and grooved thrust bearings have been done. All these investigations concentrated on rectangular and circular groove profiles of HGJBs. In order to improve the performance characteristics of HGJBs, a new design of the groove profile, the beveled-step groove profile, is introduced. The introduced groove profile is capable of increasing the pressure recovery at the divergence of the flow over the step. In addition, it increases the amount of oil pumped inward over the circular groove profile. Optimization processes were carried out experimentally, in order to obtain the optimal geometry of the introduced groove profile. The optimum geometrical parameters of the groove (groove angle $α$, groove width ratio $β$, and groove depth ratio $Γ$) are $29deg$, 0.5, and 2.0, respectively, which give maximum radial force and maximum radial stiffness of the beveled-step HGJB. In order to check the effectiveness of the introduced beveled-step groove profile, the obtained results were compared with that for rectangular groove profile. The comparison shows that the introduced beveled-step HGJBs have higher radial force, higher load carrying capacity, and lower friction torque than the rectangular HGJBs.

Commentary by Dr. Valentin Fuster
J. Tribol. 2006;128(3):594-603. doi:10.1115/1.2197842.

The effects of rotor stiffness on the bifurcation regions of a flexible rotor supported by two identical fluid-film journal bearings are presented. It is shown that the rotor stiffness has a pronounced influence on the bifurcation characteristics at the instability threshold speed. For short bearings, two bifurcation regions exist if the dimensionless rotor stiffness $K¯⩾4.3$. On the other hand, three bifurcation regions exist if the dimensionless rotor stiffness $K¯<4.3$. Information is presented that allows one to easily predict both the instability threshold speed and its bifurcation type of a rotor-bearing system with any specific set of operating parameters. The results presented have been verified by laboratory experiments as well as several published results in the open literature. Several examples are presented to illustrate the application of the results for design purposes.

Commentary by Dr. Valentin Fuster
J. Tribol. 2006;128(3):604-611. doi:10.1115/1.2197527.

A three-dimensional dynamic simulation analysis of a tapered roller bearing was performed using commercially available software. Without cage pocket shape simplification, the dynamic motion of the cage and rollers was calculated in six degrees of freedom. The motion of the cage and rollers was measured experimentally to verify the analysis. Under all axially loaded conditions, cage whirl was analytically predicted and experimentally confirmed. Whirl amplitude increased as the inner-ring rotational speed and axial-load magnitude increased. The maximum whirl amplitude reached the radial clearance between a roller and its pocket. Under combined load conditions, the cage also whirled. However, the whirl amplitude was smaller than only under axial load. Load distribution due to the addition of radial load to axial load equalized roller distribution. Equally distributed rollers limited the cage’s movable distance to circumferential clearance between a roller and its pocket.

Commentary by Dr. Valentin Fuster
J. Tribol. 2006;128(3):612-618. doi:10.1115/1.2197848.

A lubricant-film monitoring system for a conventional deep groove ball bearing (type 6016, shaft diameter 80 mm, ball diameter 12.7 mm) is described. A high-frequency (50 MHz) ultrasonic transducer is mounted on the static outer raceway of the bearing. The transducer is focused on the ball-raceway interface and used to measure the reflection coefficient of the lubricant in the “contact” ellipse between bearing components. The reflection coefficient characterizes the lubricant film and can be used to calculate its thickness. An accurate triggering system enables multiple reflection measurements to be made as each lubricated contact moves past the measurement location. Experiments are described in which bearings were deliberately caused to fail by the addition of acetone, water, and sand to the lubricant. The ultrasonic reflection coefficient was monitored as a function of time as the failure occurred. Also monitored were the more standard parameters, temperature and vibration. The results indicate that the ultrasonic measurements are able to detect the failures before seizure. It is also observed that, when used in parallel, these monitoring techniques offer the potential to diagnose the failure mechanism and hence improve predictions of remaining life.

Commentary by Dr. Valentin Fuster
J. Tribol. 2006;128(3):619-623. doi:10.1115/1.2198211.

The lubrication mechanisms with oil-in-water emulsions have been extensively investigated based on the measurements of film thickness and/or tractions in the past few decades. However, direct observation of the emulsion flow, as a more direct method of evaluating suggested explanations, has been greatly restricted by the available instruments, especially the cameras used in collaboration with high-speed bearing simulators. In this paper, a newly devised digital video camera and a microscope were used to directly observe the emulsion flow in an elastohydrodynamic lubrication (EHL) inlet region at a wide range of speeds ($0.012m∕s$ up to $1.5m∕s$). Both EHL line and point contacts were considered. Previous observations of low speed oil droplet “stay,” “reverse,” and “penetration” behavior for low-speed line contact were confirmed and extended into high-speed line and point cases, and the results were compared with point contact where significant side flow was observed. Three tight emulsions with different mean droplet sizes were examined on an EHL rig to clarify the droplet behavior and investigate the effect of droplet size on entrainment.

Commentary by Dr. Valentin Fuster
J. Tribol. 2006;128(3):624-631. doi:10.1115/1.2197846.

There has been a long-standing need for a piezoviscous parameter $αfilm$ that, together with the ambient viscosity $μ0$, will completely quantify the Newtonian rheology so that the film thickness for liquids that do not shear-thin in the inlet may be calculated as $h=h(μ0,αfilm,…)$, regardless of the details of the pressure-viscosity response. It seems that Blok’s reciprocal asymptotic isoviscous pressure has certain advantages over the conventional pressure-viscosity coefficient, which is poorly suited for this purpose. The first detailed review of piezoviscous models for low pressures is provided. A simulation code that is apparently stable for all realistic pressure-viscosity response was utilized with diverse piezoviscous models and model liquids to develop a satisfactory definition of $αfilm$ that reads $αfilm=[1−exp(−3)]∕[∫03∕α*μ(0)dp∕μ(p)]$; $1∕α*=∫0∞μ(0)dp∕μ(p)$. In the case of $μ=μ0exp(αp),αfilm=α$ and formulas are provided for other models.

Commentary by Dr. Valentin Fuster
J. Tribol. 2006;128(3):632-640. doi:10.1115/1.2194919.

Previous studies about pure squeeze elastohydrodynamic lubrication (EHL) have disclosed a film profile with a central dimple. Two problems about pure squeeze EHL are numerically solved in this paper. One is for a very small initial impact gap, and the other is the response of a squeezed EHL conjunction under stepwise loads. None of them result in the familiar film with a central dimple, which can be attributed to the local squeeze effect generated in the periphery region. In the first problem, it has been found that when there is adequate oil present on the plate, with a decrease in the initial impact gap, a shallow circumferential dimple occurs at the periphery of the conjunction instead of the primary central dimple presented in previous studies. Correspondingly the minimum film thickness occurs at the central region. The effect of the initial impact velocity on the periphery dimple is also investigated. In the second problem, the response of a conjunction subjected to a prescribed stepwise load is studied. When the first step load is applied, a central dimple film is produced. When the applied load is increased with a second step load, a periphery dimple appears, similar to that in the first problem. The local squeeze effect for the present numerical periphery dimple has been observed in previous experiments under similar conditions.

Commentary by Dr. Valentin Fuster
J. Tribol. 2006;128(3):641-653. doi:10.1115/1.2194916.

This paper investigates the effects of differential scheme and mesh density on elastohydrodynamic lubrication (EHL) film thickness based on a full numerical solution with a semi-system approach. The solution variation with different schemes and mesh sizes is revealed based on a set of numerical cases in a wide range of central film thickness from several hundred nanometers down to a few nanometers. It is observed that when the film is thick, the effects of differential schemes and mesh density are not significant. However, if the film becomes ultra-thin, e.g., below 10–20 nanometers, the influence of mesh density and differential schemes becomes more significant, and a proper dense mesh and differential scheme may be highly desirable. The present study also indicates that the solutions from the 1st-order backward scheme give the largest film thickness among all the solutions from different schemes at the same mesh size.

Commentary by Dr. Valentin Fuster

### TECHNICAL BRIEFS

J. Tribol. 2006;128(3):654-659. doi:10.1115/1.2197853.

In this paper Spartan 02, a molecular dynamics software, is used to analyze and predict the tribological properties of coconut oil in a qualitative manner on the basis of carbon chain length of the constituent fatty acids, their polarity (net electrostatic charge, $Qr$), the energies of the molecular orbitals $E_HOMO$ (energy of the highest occupied molecular orbital), and $E_LUMO$ (energy of the lowest unoccupied molecular orbital), and the heats of formations (H-Form) of the iron soaps of respective fatty acids. Tribological properties of the constituent fatty acids of coconut oil were evaluated using a four-ball tester as per ASTM D4172 method. The experimental results showed good correlation to the selected quantum chemical descriptors. The influence of an anti-wear additive on the tribological performance of coconut oil and the optimum additive concentration were also evaluated experimentally.

Commentary by Dr. Valentin Fuster
J. Tribol. 2006;128(3):660-664. doi:10.1115/1.2197850.

In rolling bearing analysis Hertzian contact theory is used to compute local contact stiffness. This theory does not have a closed form analytical solution and requires numerical calculations to obtain results. Using approximations of elliptical functions and with a mathematical study of Hertzian results, an empirical explicit formulation is proposed in this paper and allows us to obtain the dimensions, the displacement, and the contact stress with at least 0.003% precision and it can be applied to a large range of ellipticity of the contact surface.

Commentary by Dr. Valentin Fuster
J. Tribol. 2006;128(3):665-669. doi:10.1115/1.2197852.

The load/unload behavior of the hard disk drive slider is studied in terms of the air bearing static characteristics. The application of numerical continuation methods to calculate spacing diagrams is proposed. The algorithm that detects multiple flying height states and fold points is developed. The relationship between suspension force $x$-offset and critical preload is found for femto size sliders. The second fold corresponding to the critical preload for unloading is found in the negative air bearing force area. The range of $x$-offsets and preloads where bi-stable phenomenon exists is depicted on the stability diagram. The perturbation method is used to check the dynamic system characteristic values near the fold points and to determine the stability of the solution branches. The present procedure can be employed to study the multiple flying height states in the terms of any other pair of parameters besides the preload and $x$-offset.

Commentary by Dr. Valentin Fuster
J. Tribol. 2006;128(3):670-673. doi:10.1115/1.2197851.

Commercial oil-free microturbomachinery implements gas foil bearings (GFBs) for reliable performance with improved efficiency. However, GFB modeling is still largely empirical, lacking experimental validation. An analysis of simple GFBs operating at large shaft speeds (infinite speed number) follows. The bearing ultimate load and stiffness coefficients are derived from simple algebraic equations for the gas film pressures at the equilibrium journal position and due to small amplitude journal motions, respectively. GFBs without a clearance or with assembly interference are easily modeled. The underlying elastic structure (bump foil strip) determines the ultimate load capacity of a GFB as well as its stiffnesses, along with the limiting journal displacement and structural deformation. Thus, an accurate estimation of the actual minimum film thickness is found prior to performing calculations with a complex computational model, even for the case of large loads that result in a journal eccentricity well exceeding the nominal clearance, if applicable. An initial assembly preload (interference between shaft and foil) increases the GFB static stiffness at both null and infinite rotor speeds. At infinite speed, cross-coupled stiffnesses are nil, and thus, GFBs are impervious to hydrodynamic whirl instability.

Commentary by Dr. Valentin Fuster
J. Tribol. 2006;128(3):674-676. doi:10.1115/1.2197849.

The effects of textured tubes on the tribological performance in tube hydroforming (THF) are discussed. Textured surfaces, namely sand blasted, knurled, electrical discharge machined (EDM), and as rolled surfaces, were tested under various interface pressure conditions. Sand blasted textured tubes were found to have the best tribological performance. The study has demonstrated that the increase in the interface pressure between the tube and the die can result in either lower or higher interface friction depending on the surface texture conditions. The study has also shown that different surface texture treatment methods can alter the hardness of the tube surface with significant influence on the tribological performance.

Commentary by Dr. Valentin Fuster
J. Tribol. 2006;128(3):677-680. doi:10.1115/1.2198209.

This short paper describes a theoretical platform for modeling the boundary lubrication of nominally flat metallic contacts. The platform is of a general structure with four interrelated modules, each governing one of the four key processes of the problem. It is envisioned to be open ended allowing individual modules to be updated and/or replaced. The product and the outcome may provide an infrastructure for fundamental research in boundary lubrication among theoreticians and experimentalists and across several science/engineering disciplines.

Commentary by Dr. Valentin Fuster