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IN THIS ISSUE

RESEARCH PAPERS

J. Tribol. 2006;128(4):681-696. doi:10.1115/1.2345413.

Commentary by Dr. Valentin Fuster
J. Tribol. 2006;128(4):697-704. doi:10.1115/1.2345401.

Surface topography of harder mating surface plays an important role in metal forming operations as it predominantly controls the frictional behavior at the interface. In the present investigation, an inclined scratch tester was used to understand the effect of direction of surface grinding marks on interface friction and transfer layer formation. EN8 steel flats were ground to attain different surface roughnesses with unidirectional grinding marks. Al–Mg alloy pins were then scratched against the prepared EN8 steel flats. The grinding angle (angle between direction of scratch and grinding marks) was varied between 0 deg and 90 deg during the scratch tests. Scanning electron micrography of the contact surfaces revealed the transfer layer morphology. The coefficient of friction and transfer layer formation were observed to depend primarily on the direction of grinding marks of the harder mating surface, and independent of the surface roughness of harder mating surface. The grinding angle effect was attributed to the variation of plowing component of friction with grinding angle.

Commentary by Dr. Valentin Fuster
J. Tribol. 2006;128(4):705-710. doi:10.1115/1.2345394.

In the design of a magnetic recording disk file, pitch moment exerted by the flexure on the slider is usually treated as a product of flexure pitch static attitude and pitch-stiffness $(kp)$, both measured in the absence of preload (gram-load). However, a slider operates in the presence of preload, which permits a large dimple friction to exist. We shall show by elementary beam theory that the pitch moment due to dimple friction is appreciable. The lever-arm of dimple friction is proportional to the bow height, and is independent of the slope of the flexure. To minimize the pitch moment associated with dimple friction, hence improving fly-height distribution, the flexure must bow toward the disk. These results are confirmed by optical fly-height tests.

Commentary by Dr. Valentin Fuster
J. Tribol. 2006;128(4):711-717. doi:10.1115/1.2345395.

Ceramic seals are widely used in many severe applications such as in corrosive, high temperature and highly loaded situations especially in hot chemical water-based extreme environments for automobile water pumps. Presently, polymeric materials are used as the counter part for alumina ceramic seals to reduce the ceramic-to-ceramic wear. As a result, leaks are very commonly observed from water pump during services. Consequently, it is needed to improve the surface properties of the ceramic seals using a surface modification technique such as a thin film coating process to meet the increasing demand of more stability, more durability, and lower friction of coefficient in those extreme environments. To meet these challenges, we have applied DLC (diamond-like carbon) coatings on alumina using a PIID (plasma immersion ion deposition) technique intended for seal applications. The DLC-coated specimens were tested under a wide range of temperature conditions, from room temperature up to $400°C$, using a high temperature pin-on-disk tribo-tester. After that, the wear-tested specimens were analyzed using SEM with EDS to characterize the worn surfaces. Morphological changes of the DLC coated surfaces before and after the wear tests were studied. Under certain deposition conditions DLC performed very well up to $400°C$. However, under other conditions, DLC failed catastrophically. In this paper we will present the friction and wear characteristics of the DLC-coated alumina. Finally, we will discuss the failure mode of DLC coatings.

Commentary by Dr. Valentin Fuster
J. Tribol. 2006;128(4):718-724. doi:10.1115/1.2345412.

A finite element method is used to solve the problem involving thermoelastodynamic instability (TEDI) in frictional sliding systems. The resulting matrix equation contains a complex eigenvalue that represents the exponential growth rate of temperature, displacement, and velocity fields. Compared to the thermoelastic instability (TEI) in which eigenmodes always decay with time when the sliding speed is below a critical value, numerical results from TEDI have shown that some of the modes always grow in the time domain at any sliding speed. As a result, when the inertial effect is considered, the phenomenon of hot spotting can actually occur at a sliding speed below the critical TEI threshold. The finite element method presented here has obvious advantages over analytical approaches and transient simulations of the problem in that the stabilities of the system can be determined for an arbitrary geometry without extensive computations associated with analytical expressions of the contact condition or numerical iterations in the time domain.

Commentary by Dr. Valentin Fuster
J. Tribol. 2006;128(4):725-734. doi:10.1115/1.2345410.

A new equation has been formulated and found successful for modeling the wear rate of test specimens. It is capable of predicting the standard steady-state wear rate and the net steady-state wear rate with a $FA$ value, an exponential function, of 0.99 and 0.999, respectively; and with deviations of about 19% and 36%, respectively. A methodology has also been proposed in this paper to enable the steady-state wear rate to be determined more accurately, consistently, and efficiently. The wear test will be divided into three stages: (i) To conduct the transient wear test; (ii) to predict the steady-state wear rate with the required sliding distance based on the transient wear data by using the new equation; (iii) to conduct confirmation runs to obtain the measured steady-state wear rate. The proposed methodology is supported by wear data obtained previously on aluminium based matrix composite materials. It is capable of giving more accurate steady-state wear rates, as well as saving a lot of testing time and labor, by reducing the number of trial runs required to achieve the steady-state wear condition. It will also give more consistent results since a common $FA$ value will be used.

Commentary by Dr. Valentin Fuster
J. Tribol. 2006;128(4):735-744. doi:10.1115/1.2345414.

The role of microstructure is quite significant in fretting because the scale of plastic strain localization near the surface is on the order of key microstructure features. A dual-phase Ti-6Al-4V alloy that tends to be susceptible to fretting is considered as a model material. Fretting is simulated using a two-dimensional finite element analysis. A crystal plasticity theory with a two-dimensional planar triple slip idealization is employed to represent the hexagonal close packed structure of the $α$ phase of Ti. Modifications of the slip system strengths enable multiple phases to be considered. In this study, the effects of grain orientation distribution, grain size and geometry, as well as the phase distribution and their arrangement, are considered in simulations. Implications of the results are discussed.

Commentary by Dr. Valentin Fuster
J. Tribol. 2006;128(4):745-752. doi:10.1115/1.2345396.

Using modern EHL programs it is relatively simple to determine the pressures and clearances in rough EHL contacts. The pressures may then be used to calculate the subsurface stresses in the two contacting components. However, the results depend on the assumptions made about the fluid’s rheology. While it is possible to measure the clearances using interferometric techniques, measurement of either the pressures or stresses is extremely difficult. However it is these, rather than the clearances, that determine the life of the contact. In previous papers the authors have described how the inverse method may be used to validate the stress predictions for contacts with transverse roughness. This type of contact has fluid flow in only one plane and it remained necessary to check the results for more general rough surfaces where the flow is three-dimensional. Accordingly, the inverse method is extended, in this paper, to a situation where out-of-plane flow is significant. The paper describes the approach and presents some preliminary results for rolling contacts.

Commentary by Dr. Valentin Fuster
J. Tribol. 2006;128(4):753-760. doi:10.1115/1.2345398.

Over the last decade, the operating conditions of the Elastohydrodynamic lubricated (EHL) contact have become increasingly severe. Consequently, the average film thickness decreased and became comparable to the surface roughness. Under those conditions, the surface features can reduce the minimum film thickness and can thus increase wear. They can also increase the temperature and the pressure fluctuations, which directly affect the component life. In order to describe the roughness geometry inside an EHL contact, the amplitude reduction of harmonic waviness has been studied over the last decade. This theory currently allows a quantitative prediction of the waviness amplitude and includes the influence of wavelength and contact operating conditions. However, the model assumes a Newtonian behavior of the lubricant. The current paper contributes to the extension of the roughness amplitude reduction for EHL point contacts including non-Newtonian effects. A generalized model is derived that includes both types of behavior.

Commentary by Dr. Valentin Fuster
J. Tribol. 2006;128(4):761-770. doi:10.1115/1.2345402.

This paper presents a temporal study using dynamic finite element methods of the dynamic response of a 2D mechanical model composed of a deformable rotating disk (wheel) in contact with a deformable translating body (rail) with constant Coulomb friction. Under global sliding conditions, oscillatory states at specific frequencies occur in the contact patch even in the case of a constant friction coefficient. A parallel is drawn between the frequencies of these states and the modal analysis of the entire mechanical model. The influence on local contact conditions of parameters such as normal load, global sliding ratio, friction coefficient, and the transient value for applying sliding conditions is then evaluated. Finally, the consequences of these states on local rail plastic deformation are presented and correlated with rail corrugation occurring on straight tracks under acceleration and deceleration conditions.

Commentary by Dr. Valentin Fuster
J. Tribol. 2006;128(4):771-777. doi:10.1115/1.2345393.

The time-dependent thermal compressible elastohydrodynamic lubrication of a sliding line contact has been developed to investigate the effect of a sudden load change. The time-dependent modified Reynolds equation with non-Newtonian fluids has been formulated using a power law model. Properties of non-Newtonian dilatant fluids for solid-liquid lubricants have been studied experimentally using two common solid particles; namely, molybdenum disulfide and polytetrafluoroethylene. The simultaneous systems of modified Reynolds, elasticity, and energy equations with initial conditions were solved numerically using a multigrid multilevel technique. The performance characteristics of the thermoelastohydrodynamic line contact were presented with varying dimensionless time for the pressure distribution, temperature distribution, and oil film thickness. The transient response of the line contact between two infinitely long cylindrical surfaces was simulated under a heavy step load function. The coefficients of friction were also presented in this work at steady condition with varying particle concentration. This simulation showed a significant effect of solid particles on thermoelastohydrodynamic lubrication under heavy load conditions.

Commentary by Dr. Valentin Fuster
J. Tribol. 2006;128(4):778-788. doi:10.1115/1.2345404.

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 very 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 hydrodynamic 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.

Commentary by Dr. Valentin Fuster
J. Tribol. 2006;128(4):789-794. doi:10.1115/1.2345406.

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.

Commentary by Dr. Valentin Fuster
J. Tribol. 2006;128(4):795-800. doi:10.1115/1.2345400.

Many foodstuffs and personal care products consist of two-phase systems which, during use, are rubbed between compliant biosurfaces to form thin lubricating films. It is important to understand the nature and properties of the films thus formed since these contribute to the user’s sensory perception, and thus appreciation, of the products concerned. In this paper, the lubrication properties of simple oil-in-aqueous phase emulsions are studied in a steel/elastomer “soft-EHL” contact. It is found that overall behavior is strongly dependent on the ratio of the viscosities of the two phases. When the viscosity of the dispersed oil phase is lower or comparable to that of the continuous aqueous phase, the latter enters the contact and controls film formation and friction. However, when the dispersed phase has viscosity at least four times larger than the dispersion medium, the former enters the contact and determines its tribological properties. This effect is believed occur because at high viscosity ratios the droplets are nondeformable and are thus forced into the contact inlet region, where collisions occur that result in shear-induced coalescence. Once a pool of viscous fluid is formed, the lower viscosity bulk fluid is unable to displace it because the viscous shear stress is too small, so the pool acts as a reservoir to supply the contact.

Commentary by Dr. Valentin Fuster
J. Tribol. 2006;128(4):801-810. doi:10.1115/1.2345399.

Sub-$5nm$ flying head-disk interfaces (HDIs) designed to attain extremely high areal recording densities of the order of $Tbit∕in2$ are susceptible to strong adhesive forces, which can lead to subsequent contact, bouncing vibration, and high friction. Accurate prediction of the relevant interfacial forces can help ensure successful implementation of ultra-low flying HDIs. In this study, an improved rough surface model is developed to estimate the adhesive, contact, and friction forces as well as the mean contact pressure relevant to sub-$5nm$ HDIs. The improved model was applied to four different HDIs of varying roughness and contact conditions, and was compared to the sub-boundary lubrication rough surface model. It was found that the interfacial forces in HDIs undergoing primarily elastic-plastic and plastic contact are more accurately predicted with the improved model, while under predominantly elastic contact conditions, the two models give similar results. The improved model was then used to systematically investigate the effect of roughness parameters on the interfacial forces and mean contact pressure (response). The trends in the responses were investigated via a series of regression models using a full $33$ factorial design. It was found that the adhesive and net normal interfacial forces increase with increasing mean radius $R$ of asperities when the mean separation is small $(≈0.5nm)$, i.e., pseudo-contacting interface, but it increases primarily with increasing root-mean-square (rms) surface height roughness between 2 and $4nm$, i.e., pseudo-flying interface. Also, increasing rms roughness and decreasing $R$, increases the contact force and mean contact pressure, while the same design decreases the friction force. As the directions of optimization for minimizing the individual interfacial forces are not the same, simultaneous optimization is required for a successful ultra-low flying HDI design.

Commentary by Dr. Valentin Fuster
J. Tribol. 2006;128(4):811-816. doi:10.1115/1.2345397.

Load∕unload (L∕UL) technology has been widely applied in hard disk drives for a long period of time. One main promise of this technology compared with the contact start-stop (CSS) technology was no damage from the friction and stiction between sliders and disks during power on and off that exists in CSS. However, the friction between sliders and disks can still occur and has a strong effect on the L∕UL process because sliders may contact disks during loading. When friction is large and the pitch static attitude (PSA) is not in the preferred range, the loading process might fail. In this paper, a new simplified friction model was proposed based on experimental observations. The model was implemented into a L∕UL simulation code. Two cases were studied: a $10,000rpm∕84mm$ server drive and a $3600rpm∕25.4mm$ microdrive. The PSA and friction force effects on the loading process were simulated. A large PSA results in slider loaded onto a second stable state with a very large flying pitch angle. In this paper, a third stable state, which results from a small or negative PSA and a sufficiently large friction force, was discovered and investigated. It was found that the friction effect was smaller in the server drive case, while it was dramatic in the microdrive case. In the third stable state, the slider had a negative pitch angle, and its leading edge continuously dragged on the disk. In this state, reading∕writing operation was not possible, and disks and sliders could be damaged.

Commentary by Dr. Valentin Fuster
J. Tribol. 2006;128(4):817-827. doi:10.1115/1.2345405.

An approach based on proper orthogonal decomposition and Galerkin projection is presented for developing low-order nonlinear models of the gas film pressure within mechanical gas face seals. A technique is developed for determining an optimal set of global basis functions for the pressure field using data measured experimentally or obtained numerically from simulations of the seal motion. The reduced-order gas film models are shown to be computationally efficient compared to full-order models developed using the conventional semidiscretization methods. An example of a coned mechanical gas face seal in a flexibly mounted stator configuration is presented. Axial and tilt modes of stator motion are modeled, and simulation studies are conducted using different initial conditions and force inputs. The reduced-order models are shown to be applicable to seals operating within a wide range of compressibility numbers, and results are provided that demonstrate the global reduced-order model is capable of predicting the nonlinear gas film forces even with large deviations from the equilibrium clearance.

Commentary by Dr. Valentin Fuster
J. Tribol. 2006;128(4):828-840. doi:10.1115/1.2345407.

The theoretical background and the numerical modeling results of a ground-based verification activity of a critical space mission phase affected by adhesion issues are presented. Tribological models are first reviewed with an emphasis on the contact forces assessment and their relationship to the geometrical, material, and mechanical properties of the contacting metal bodies. An approach based on a finite element analysis of the contact, accounting for the adhesion forces, is then proposed for studying the contact behavior of smooth surfaces in vacuum. Some solutions aimed at reducing adhesion pull-off forces are discussed. Special emphasis is placed on the role of surface roughness in reducing adhesion. To this purpose, a fractal surface theory is used to estimate interaction forces. The obtained results are applied to discuss the role of adhesion on the release of a test mass under zero gravity as well as to suggest an appropriate detachment procedure that finds a specific application in a scientific space mission.

Commentary by Dr. Valentin Fuster
J. Tribol. 2006;128(4):841-850. doi:10.1115/1.2345392.

As the size of contacting and sliding tribosystems decrease, intermolecular or adhesive forces become significant partly due to nanometer size surface roughness. The presence of adhesion has a major influence on the interfacial contact and friction forces as well as the microtribosystem dynamics (microtribodynamics) and thus influences the overall dynamic friction behavior. In this paper, a dynamic friction model that explicitly includes adhesion, interfacial damping, and the system dynamics for realistic rough surfaces was developed. The results show that the amplitude and mean value of the time varying normal contact and friction forces increase in the presence of adhesion under continuous contact conditions. Also, due to the attractive nature of adhesion, its presence delays or eliminates the occurrence of loss of contact. Furthermore, in the presence of significant adhesion, dynamic friction behavior is significantly more complicated compared to the no adhesion case, and the dynamic friction coefficient predictions may be misleading. Thus, it is more appropriate to discuss dynamic friction force instead of dynamic friction coefficient under dynamic conditions.

Commentary by Dr. Valentin Fuster
J. Tribol. 2006;128(4):851-864. doi:10.1115/1.2345408.

Most contact analyses assume that the surface height distributions follow a single modal distribution. However, there are many surfaces with multi-modal roughness distributions, e.g., magnetic particulate tape, super alloys with precipitates, and hydrophobic leaves. In this study, an algorithm is developed to generate bimodal surfaces by superimposing particles with radii following a Gaussian distribution on a Gaussian rough surface. Two different cases are presented to produce composite surfaces with particles; the first case is particles sitting on a surface and the other case is particles sitting on the mean plane of a surface. Statistical analysis is carried out for the generated bimodal surfaces to study the effect of the bimodal roughness distributions on the surface’s probability density function shapes. Contact analysis is also conducted to identify optimum bimodal roughness distributions for low friction, stiction, and wear. It is assumed that particles and matrix have uniform elastic properties as it is a reasonable assumption in some applications such as magnetic tapes. Variation of fractional contact area, maximum contact pressure, and relative meniscus force as functions of relative mean radius and relative standard deviation of particles are studied for different values of particle densities. It is found that bimodal surfaces with lower particle density are beneficial to low friction and stiction, whereas those with higher particle density are beneficial to low wear. Relative mean radii of particles of 2–3 in bimodal surfaces with particles sitting on surface and 3–5 in bimodal surfaces with particles sitting on the mean plane of surface are desirable for low friction, stiction, and wear.

Commentary by Dr. Valentin Fuster
J. Tribol. 2006;128(4):865-875. doi:10.1115/1.2345411.

$Si3N4$ probes used for atomic force microscope exhibit large adhesion and friction resulting in artifacts of scanned image. In order to reduce adhesion and friction so as to reduce tip related artifacts, liquid lubricant (Z-TETRAOL) and fluorocarbon polymer (Fluorinert$™$) were applied on the $Si3N4$ probe. A comprehensive investigation of adhesion, friction, and wear of the uncoated/coated tips in both ambient air and various humidity levels as well as the influence of the coatings on the image resolution was performed. Experiments show that the coatings reduce the adhesion and friction of the $Si3N4$ tip, improve the initial image resolution, and exhibit less deterioration as compared to that of uncoated tip after scanning. The image degradation of an uncoated $Si3N4$ probe is also compared with that of an uncoated silicon probe. A probe cantilever deflection model was proposed to correlate the influence of the adhesion and friction with the image distortion.

Commentary by Dr. Valentin Fuster
J. Tribol. 2006;128(4):876-885. doi:10.1115/1.2345409.

The asperities of rough surfaces have long been considered to be points higher than their immediate neighbors. Based on this concept, theories were developed for quantitatively understanding the elastic and plastic nature of contact between rough surfaces. Recently it has been recognized that the above model for asperities is inadequate. Consequently, all the models that have been constructed based on that model are inadequate too. In this paper, based on a newly developed multiple-point asperity model, the elastic and plastic contact problem between nominally flat surfaces is reformulated. This leads to finding the deformed area, and load produced by the contact. The model is developed for the general form of isotropic rough surfaces with arbitrary height distribution and autocorrelation function (ACF). The microcontact areas generated by each asperity contact are considered to be circles. The Gaussian distribution of heights and exponential ACF are considered as a benchmark to compare the results of the new model with the existing models. Using results from numerical models developed by other groups, the new model is validated.

Commentary by Dr. Valentin Fuster

TECHNICAL BRIEFS

J. Tribol. 2006;128(4):886-890. doi:10.1115/1.2345415.

The contact of coated systems under sliding conditions is considered within the framework of elasticity theory with the assumption of perfect bond between coating and substrate. Formulation is introduced in the form of a system of coupled singular integral equations of the second kind with Cauchy kernels that describe contact problems for coated bodies under complete, semi-complete and incomplete contact conditions. Accurate and efficient numerical method for the solution of sliding contact problems is described. Explicit results are presented for the interpolative Gauss-Jacobi numerical integration scheme for singular integral equations of the second kind with Cauchy kernels. The method captures correctly both regular and singular behavior of the traction distribution near the edges of contact. Several cases of sliding contact are considered to demonstrate the validity of the method.

Commentary by Dr. Valentin Fuster
J. Tribol. 2006;128(4):891-894. doi:10.1115/1.2345416.

In this article, the heat treatment and dry sliding wear behavior of Al-based AA6063 alloy reinforced with both TiC and $Al2O3$ ceramic particles were studied. The particles were synthesized by self-propagating high temperature synthesis (SHS) technique. The prepared composite alloy contains $5vol.%$$Al2O3$ and $5vol.%$ TiC particles. The composite alloy was prepared by vortex method. To attain the peak hardness values of the alloys, age hardening behavior of the monolithic alloy and also the composite alloy was investigated. The wear tests were performed at room temperature using a pin-on-disk type apparatus. The results showed that the addition of TiC and $Al2O3$ particles increases the hardness of the AA6063 Al alloy and at the same time accelerates the aging kinetics. The sliding wear properties of AA6063 Al alloy were significantly improved by the addition of TiC and $Al2O3$ particles.

Commentary by Dr. Valentin Fuster
J. Tribol. 2006;128(4):895-897. doi:10.1115/1.2345417.

Boronized metals are potential candidate materials for various industrial applications as well as for joint arthroplasty. This is due to their high hardness and corrosion resistance. In the present research, we investigated the tribological performance of boronized chromium when worn against bearing steel E52100. Pure chromium was used as a control material and tested under similar conditions. Three test conditions were used—dry sliding, with water, and with simulated body fluid (SBF). The highest coefficient of friction obtained was for chromium boride under dry sliding conditions. Water and SBF acted as lubricants and lowered the coefficient of friction. The friction coefficient for Cr and chromium boride was lowest under SBF conditions. SEM analysis showed that the wear modes were different under different test conditions. TEM analysis showed a layered-like structure of debris that could have acted as a lubricant and caused a very low friction coefficient as the tests progressed.

Commentary by Dr. Valentin Fuster
J. Tribol. 2006;128(4):898-903. doi:10.1115/1.2345418.

When contact problems are solved by numerical approaches, a surface profile is usually described by a series of discrete nodes with the same intervals along a coordinate axis. Contact computation based on roughness datum mesh may be time consuming. An adaptive-surface elasto-plastic asperity contact model is presented in this paper. Such a model is developed in order to reduce the computing time by removing the surface nodes that have little influence on the contact behavior of rough surfaces. The nodes to be removed are determined by a prescribed threshold. The adaptive-surface asperity contact model is solved by means of the element-free Galerkin-finite element coupling method because of its flexibility in domain discretization and versatility in node arrangements. The effects of different thresholds on contact pressure distribution, real contact area, and elasto-plastic stress fields in contacting bodies are investigated and discussed. The results show that this model can help reduce about 48% computational time when the relative errors are about 5%.

Commentary by Dr. Valentin Fuster
J. Tribol. 2006;128(4):904-907. doi:10.1115/1.2345419.

The classical Reynolds theory reveals that a converging gap is the first necessary condition to generate a hydrodynamic pressure in a viscous fluid film confined between two solid surfaces with a relative sliding/rolling motion. For hundreds of years, the classical lubrication mechanics has been based on the frame of the Reynolds theory with no slip assumption. Recent studies show that a large boundary slip occurs on an ultrahydrophobic surface, which results in a very small friction drag. Unfortunately, such a slip surface also produces a small hydrodynamic pressure in a fluid film between two solid surfaces. This paper studies the lubrication behavior of infinite width slider bearings involving a mixed slip surface (MSS). The results of the study indicate that any geometrical wedges (gaps), i.e., a convergent wedge, a parallel gap, and even a divergent wedge, can generate hydrodynamic pressure in an infinite slider bearing with a mixed slip surface. It is found that with an MSS, the maximum fluid load support capacity occurs at a slightly divergent wedge (roughly parallel sliding gap) for an infinite width slider bearing, but not at a converging gap as what the classical Reynolds theory predicts. Surface optimization of a parallel sliding gap with a slip surface can double the hydrodynamic load support and reduce the friction drag by half of what the Reynolds theory predicts for an optimal wedge of a traditional slider bearing.

Commentary by Dr. Valentin Fuster
J. Tribol. 2006;128(4):908-914. doi:10.1115/1.2345420.

This paper proves that a generalized Hertz pressure (the product of Hertz square root and an even polynomial of degree $2n$ with respect to coordinates) applied over elastic half-space boundary generates a polynomial normal displacement of degree $2n+2$. Polynomial surface coefficients are combinations of elliptical integrals. The equation of rigid punch surface generating this pressure is derived, as well as the conditions in which an elliptical contact occurs. For second order surfaces, $n=0$, these results yield all Hertz formulas, whereas new formulas are derived for contact parameters between fourth, sixth, and eight order surfaces.

Commentary by Dr. Valentin Fuster
J. Tribol. 2006;128(4):915-917. doi:10.1115/1.2345421.

Surface deformations measured by laser profilometry in a contact model metal punch-sapphire window yield pressure distribution if the contact area is known. This paper advances a new method to assess this area by reflectivity. The contact model possesses higher reflectivity outside the contact area than inside, the step evidencing contact contour. A correction for interference effects is derived. Experimental results on circular Hertz contacts agree well with theoretical predictions.

Commentary by Dr. Valentin Fuster