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IN THIS ISSUE

### TECHNICAL PAPERS

J. Tribol. 2007;129(4):705-711. doi:10.1115/1.2768068.

In porous resistances, Darcy’s law provides a good approximation of mass flow rate when the differences between upstream and downstream pressures are sufficiently small. In this range, the mass flow rates are proportional to the porous resistance’s permeability. For gas bearings, the pressure difference is normally higher, and it is known experimentally that the mass flow rates are lower than would result from Darcy’s law. Forchheimer’s law adds an inertial term to Darcy’s law and, when an appropriate coefficient is selected for this term, provides a good approximation of flow rates for the same applications even with the highest pressure differences. This paper presents an experimental and theoretical investigation of porous resistances used in gas bearing and thrust pad supply systems. The porous resistances considered in the investigation were made by sintering bronze powders with different grain sizes to produce cylindrical inserts that can be installed in bearing supply devices. The paper describes the test setup and experimental results obtained for: (i) mass flow rate through single porous resistances at different upstream and downstream pressures and (ii) mass flow rate and pressure distribution on a pneumatic pad featuring the same porous resistances. The theoretical permeability of the chosen porous resistances was calculated, and the results from setup (i) were then used to obtain experimental permeability and to determine the inertial coefficients. The results, which are expressed as a function of the Reynolds number, confirmed the validity of using Forchheimer’s law. The mass flow rates from setup (ii) were compared to those from setup (i) at the same pressure differentials across the resistance.

Commentary by Dr. Valentin Fuster
J. Tribol. 2007;129(4):712-719. doi:10.1115/1.2768069.

A simulation method in which grooves are virtually distributed on the slider air bearing instead of on the grooved medium surface has been developed and used to investigate the performance of sliders flying over the surface of a discrete-track medium. The simulated flying height loss due to a discrete-track medium coincides well with the measured data, whereas the average-estimation method overestimates flying height loss. Among the characteristics of a slider flying over the surface of a discrete-track medium that were studied are the flying attitude, the effect of groove parameters on flying profile, and the flying height losses due to manufacturing variation and altitude. The results indicate that when a slider is flying over the surface of a discrete-track medium, it will have a higher $3σ$ of flying height, be more sensitive to altitude, and will have a greater flying height loss.

Commentary by Dr. Valentin Fuster
J. Tribol. 2007;129(4):720-728. doi:10.1115/1.2768070.

Spring constants and damping coefficients of a thin lubricant bridge of a perfluoropolyether (PFPE) lubricant intervening between a diamond probe tip and a diamond-like carbon (DLC) surface of a magnetic disk are identified through regression analysis of tip damping vibration. PFPE lubricants with functional end groups were used to form a lubricant bridge between the DLC surface and a probe tip with a notably small curvature radius of $0.1μm$. The tip was both retracted from and extended toward the disk surface at four different progressive distances to attain varied elongation of the bridge. It was also vibrated at each step to provide damping waveforms. By applying regression analysis to the observed waveforms, the spring constant and the damping coefficient of the lubricant bridge were identified within an elongation range from $50nm$ to $800nm$. Spring constant of the lubricant bridge $kb$ had a negative value varying from $−0.15N∕m$ to $−0.1N∕m$. The damping value expressed in the form of frequency-multiplied damping $cb×ω$ ranged from $0.02N∕m$ to $0.06N∕m$. Note that both the absolute value of spring constant $∣kb∣$ and frequency-multiplied damping $cb×ω$ exhibited U-shaped variation with lubricant bridge elongation; that is, those values decrease with bridge elongation and they begin to increase after reaching the minimum. The variation in the spring constant was found to be in good accordance with the quasi-static stiffness of the lubricant bridge, and variation in the damping coefficient was explained by energy loss arising in the vibrating lubricant bridge.

Commentary by Dr. Valentin Fuster
J. Tribol. 2007;129(4):729-734. doi:10.1115/1.2768071.

With ever increasing areal density, interactions of particles with a head-disk interface become an ever more important factor impacting the drive reliability. Although particles trapped between the head and the disk could induce mechanical damage to the media resulting in permanent loss of data, data loss has also been observed without any obvious signs of physical damage to the media. We devised a component-level test to study this mode of data erasure on both glass and aluminium media. Our data indicate that the frictional heating associated with contact force between the particle and the disk could lead to permanent loss of data. In addition, we performed investigations to study the impact of air bearing design features, load/unload mechanism, and particle number density on the head disk interface.

Commentary by Dr. Valentin Fuster
J. Tribol. 2007;129(4):735-742. doi:10.1115/1.2768072.

The apparent contact area of curved rough surfaces can be larger than that predicted by the Hertz theory due to asperity interaction outside the Hertzian region. In the present study, simple theoretical formulas for the contact semi-width and radius for Gaussian and truncated Gaussian height distributions were derived, and a numerical contact model was developed based on a general power-law relationship between the local apparent pressure and real-to-apparent contact ratio. Numerical results of the contact semi-width agree well with the prediction of the formula. The apparent contact region becomes increasingly larger than the Hertzian region as a dimensionless roughness parameter increases or as a dimensionless load parameter decreases. The ratio of the contact semi-width to the Hertzian semi-width and the apparent pressure distribution are completely determined by a dimensionless contact parameter and the dimensionless roughness parameter, which are both independent of the instrument resolution, thus providing a long awaited solution to the problem of instrument dependency in a traditional theory. An application to fractal-regular surfaces indicates that the influence of the fractal dimension on the contact behavior is due to its effects on both the area-load coefficient and the load exponent.

Commentary by Dr. Valentin Fuster
J. Tribol. 2007;129(4):743-753. doi:10.1115/1.2768073.

This study investigates the effects of asperity interactions on the mean surface separation and real contact area of rough surfaces containing elliptical asperities with Gaussian and non-Gaussian height distributions. The elastic-plastic contact behavior of surfaces with elliptical asperities with both single-mode and bimodal height distributions are studied. The results indicate that the effects of asperity interactions become more pronounced as the effective radius ratio of the asperities increases. The findings also reveal that the real contact load, the real contact area, and the surface contact mode observed for elliptical asperities are significantly different from those noted for spherical asperities. Furthermore, it is found that the form of the non-Gaussian height distribution has a significant effect on the contact mode of rough surfaces. Specifically, the contact mode of surfaces with a negatively skewed height distribution is found to be more elastic than that of surfaces with a Gaussian height distribution.

Commentary by Dr. Valentin Fuster
J. Tribol. 2007;129(4):754-760. doi:10.1115/1.2768074.

An experimental study was conducted to measure the static friction coefficient under constant normal load and different interface conditions. These include surface roughness, dwell time, displacement rate, as well as the presence of traces of lubricant and wear debris at the interface. The static friction apparatus includes accurate measurement of friction, normal and lateral forces at the interface (using a high dynamic bandwidth piezoelectric force transducer), as well as precise motion control and measurement of the sliding mass. The experimental results show that dry surfaces are more dependent on the displacement rate prior to sliding inception compared to boundary lubricated surfaces in terms of static friction coefficient. Also, the presence of wear debris, boundary lubrication, and rougher surfaces decrease the static friction coefficient significantly compared to dry smooth surfaces. The experimental measurements under dry unlubricated conditions were subsequently compared to an improved elastic-plastic static friction model, and it was found that the model captures the experimental measurements of dry surfaces well in terms of the surface roughness.

Commentary by Dr. Valentin Fuster
J. Tribol. 2007;129(4):761-771. doi:10.1115/1.2768076.

A three-dimensional numerical model based on a semianalytical method in the framework of small strains and small displacements is presented for solving an elastic-plastic contact with surface traction. A Coulomb’s law is assumed for the friction, as commonly used for sliding contacts. The effects of the contact pressure distribution and residual strain on the geometry of the contacting surfaces are derived from Betti’s reciprocal theorem with initial strain. The main advantage of this approach over the classical finite element method (FEM) is the computing time, which is reduced by several orders of magnitude. The contact problem, which is one of the most time-consuming procedures in the elastic-plastic algorithm, is obtained using a method based on the variational principle and accelerated by means of the discrete convolution fast Fourier transform (FFT) and conjugate gradient methods. The FFT technique is also involved in the calculation of internal strains and stresses. A return-mapping algorithm with an elastic predictor∕plastic corrector scheme and a von Mises criterion is used in the plasticity loop. The model is first validated by comparison with results obtained by the FEM. The effect of the friction coefficient on the contact pressure distribution, subsurface stress field, and residual strains is also presented and discussed.

Commentary by Dr. Valentin Fuster
J. Tribol. 2007;129(4):772-782. doi:10.1115/1.2768077.

The determination of the elastoplastic deformation regime arising at the microcontact of a deformable ellipsoid and a rigid smooth flat was the main purpose of this study. One-eighth of an ellipsoid and a flat plate were taken as the contact bodies in the finite element analysis, and a mesh scheme of multisize elements was applied. Two observed phenomena regarding the contact pressures and the equivalent von Mises stresses formed at the contact area are given in order to identify the inception of the fully plastic deformation regime of an ellipsoid with an ellipticity $ke$. If the ellipticity $(k)$ of an elliptical contact area is defined as the length ratio of the minor axis to the major axis, it is asymptotic to the $ke$ value when the interference is sufficiently increased, irrespective of the $ke$ value. The dimensionless interference regime associated with the elastoplastic deformation regime is narrowed by increasing the ellipticity of the ellipsoid $(ke)$. Significant differences in the microcontact parameters such as the contact pressure, the contact area, and the contact load were found to be a function of the interference and the $ke$ parameter of an ellipsoid. The interferences corresponding to the inceptions of the elastoplastic and fully plastic deformation regimes are both increased if the $ke$ value is lowered. The interference, the contact area, and the contact load predicted by the present model for the behavior demonstrated at the inception of the elastoplastic deformation regime are lower than those obtained from the Horng model (Horng, J. H., 1998, “An Elliptical Elastic-Plastic Asperity Microcontact Model for Rough Surfaces  ,” ASME J. Tribol., 120, pp. 82–88) and the Jeng-Wang model (Jeng, Y. R., and Wang, P. Y., 2003, “An Elliptical Microcontact Model Considering Elastic, Elastoplastic, and Plastic Deformation  ,” ASME J. Tribol., 125, pp. 232–240). Big differences in the results of the average contact pressure, the contact area, and the contact load among the above microcontact models are discussed. The discrepancies are also explained from the developments of these models and boundary conditions set for the elastoplastic deformation regime.

Commentary by Dr. Valentin Fuster
J. Tribol. 2007;129(4):783-790. doi:10.1115/1.2772322.

Commentary by Dr. Valentin Fuster
J. Tribol. 2007;129(4):791-800. doi:10.1115/1.2768078.

The paper presents a numerical analysis of the rolling contact between an elastic ellipsoid and an elastic-plastic flat. Numerical simulations have been performed with the help of a contact solver called Plast-Kid®, with an algorithm based on an integral formulation or semi-analytical method. The application of both the conjugate gradient method and the discrete convolution and fast Fourier transform technique allows keeping the computing time reasonable when performing transient 3D simulations while solving the contact problem and calculating the subsurface stress and strain states. The effects of the ellipticity ratio $k$—ranging from 1 to 16—and of the normal load—from 4.2 GPa to 8 GPa—are investigated. The reference simulation corresponds to the rolling of a ceramic ball on a steel plate made of an AISI 52100 bearing steel under a load of 5.7 GPa. The results that are presented are, first, the permanent deformation of the surface and, second, the contact pressure distribution, the von Mises stress field, the hydrostatic pressure, and the equivalent plastic strain state within the elastic-plastic body. A comparison with an experimental surface deformation profile is also given to validate the theoretical background and the numerical procedure.

Commentary by Dr. Valentin Fuster
J. Tribol. 2007;129(4):801-808. doi:10.1115/1.2768079.

An analysis of double arched ball bearing, which considers centrifugal forces and gyroscopic effects, is performed. Based on operating conditions of a five DOF inner ring and Coulomb friction model, the conventional bearing theory is extended from two to three or four-contact points. The commonly used control criterion of ball bearing by the inner or outer raceway is debatable and is known to fit with difficulty with experimental data. In addition, when more than two-contact points are involved, it becomes obsolete. The paper presents a mathematical model to describe the complex ball bearing internal kinematics under the effect of the external working conditions. Lubricant thickness is taken into account in geometrical equations and the nonlinear system of this quasistatic model is solved by a Newton-Raphson method. The model is first validated through comparisons with published data for conventional or single arched ball bearings. Results are also compared to those provided by the commercial software RBL4 . The analysis of a double arched ball bearing is finally performed and the complex motion of the ball highlighted.

Commentary by Dr. Valentin Fuster
J. Tribol. 2007;129(4):809-817. doi:10.1115/1.2768081.

The objective of the present work is to investigate experimentally and numerically the influences of surface roughness, produced by typical machining processes, on friction performances in lubricated-point contacts. Prior to the full experimental investigation, a series of tests had been conducted to examine the experimental errors, resulting from repeated tests on the same specimen but at different tracks, with different amounts of lubricant supply, or after the sample reinstallation. Then, the effects of amplitude and texture of surface roughness on friction behavior are investigated in rotational and reciprocal-mode tests, respectively. The measured friction, averaged over the repeated tests and plotted as a function of sliding speed, shows Stribeck-type curves, which manifest the transition from full-film, mixed, to boundary lubrication. Results show that the roughness amplitude imposes a strong influence on the magnificence of friction and the route of lubrication transition. It is also observed that transverse roughness would give rise to a smaller friction coefficient than the longitudinal one under the same operating conditions. Moreover, the deterministic numerical solution of mixed lubrication has been extended to evaluate friction between rough surfaces over a wide range of lubrication regimes. The numerical simulation results are compared and agree very well with experiments.

Commentary by Dr. Valentin Fuster
J. Tribol. 2007;129(4):818-828. doi:10.1115/1.2768082.

Annular components are used widely in engineering systems and include bearing bushes and races, which may be exposed to extreme operating conditions. A method to establish the localized transient thermoelastic deformation of a homogeneous two-dimensional annular component is developed. The analysis is based on solving the thermoelasticity equations using a state space formulation for the Fourier components of the radial and tangential displacements. Two boundary conditions are considered, namely, rigid and resiliently mounted outer boundaries, both associated with stress free inner boundary conditions. The thermoelastic solution is then demonstrated for a transient temperature distribution induced by inner boundary frictional heating due to rotor contact, which is derived from a dynamic Hertzian pressure distribution. The application is to a relatively short auxiliary bearing for which a state of plane stress is appropriate. However, the thermoelastic analysis is generalized to cover cases of plane strain and plane stress.

Commentary by Dr. Valentin Fuster
J. Tribol. 2007;129(4):829-835. doi:10.1115/1.2768083.

This paper presents an overview of a discrete element method approach to dry friction in the presence of a third body. Three dimensional computer simulations have been carried out to show the influence of the third body properties (and more specifically their adhesion) on friction coefficient and profiles of dissipated power. Simple interaction laws and a cohesive contact are set up to uncouple the key parameters governing the contact rheology. The model is validated through a global energy balance. As it is shown that dynamic friction coefficient can be explained only in terms of local energy dissipation, this work also emphasizes the fact that mechanism effects and third body rheology have important consequences on the energy generation and dissipation field. Therefore, asymmetries can arise and the surface temperature of first bodies can be significantly different even for the same global friction coefficient value. Such investigations highlight the fact that friction coefficient cannot be considered in the same way at the mechanism scale as at the contact scale where the third body plays a non-negligible role, although it has been neglected for years in thermal approaches to study of surfaces in contact.

Commentary by Dr. Valentin Fuster
J. Tribol. 2007;129(4):836-840. doi:10.1115/1.2768084.

Effects of the piezoelectricity of polyvinylidene fluoride (PVDF) on sliding friction against itself are investigated in this research. The piezoelectricity is the response of a piezoelectric material, such as PVDF, to an applied electrical voltage in terms of stress or physical dimension. Such a response is found to influence the sliding-frictional behavior. This research is beneficial in terms of understanding fundamental friction. The applications of this research are in wide areas, such as the design of a microgripper used for surgeries, microassembly, and micromanipulation.

Commentary by Dr. Valentin Fuster
J. Tribol. 2007;129(4):841-850. doi:10.1115/1.2768086.

A numerical modeling of thermoelastohydrodynamic mechanical face seal behavior is presented. The model is an axisymmetric one and it is confined to high pressure compressible flow. It takes into account the behavior of a real gas and includes thermal and inertia effects, as well as a choked flow condition. In addition, heat transfer between the fluid film and the seal faces is computed, as are the elastic and thermal distortions of the rings. In the first part of this paper, the influence of the coning angle on mechanical face seal characteristics is studied. In the second part, the influence of the solid distortions is analyzed. It is shown that face distortions strongly modify both the gap geometry and the mechanical face seal’s performance. The mechanical distortions lead to a converging gap, while the gas expansion, by cooling the fluid, creates a diverging gap.

Commentary by Dr. Valentin Fuster
J. Tribol. 2007;129(4):851-859. doi:10.1115/1.2768087.

A numerical analysis is conducted to investigate the elastohydrodynamic effect of deterministic microasperities on the shaft of a lip seal. Various geometries of microasperities (triangular, square, hexagonal, and circular) are put into a $100×100μm2$ unit cell and are investigated using Reynolds equation. For each shape, the area fraction of the microasperity is varied between 0.2 and 0.8, and the asperity height is varied between $0.3μm$ and $5μm$. The calculation for load capacity and friction coefficient indicates that there are values for asperity height, where the load capacity and friction coefficient are optimized. These optimum heights were reached at $1–3μm$. Although the lip seal surface is considered to be smooth, reverse pumping can still be obtained using an oriented triangular design. The Couette flow rate for this asperity showed lubricant is reverted back toward the seal side 2.6 times more than using a conventional lip seal. The addition of microasperities to the shaft surface shows significant improvement in lubrication characteristics for the lip seal in the form of a simultaneous reduction in friction coefficient and increase in the reverse pumping rate.

Commentary by Dr. Valentin Fuster
J. Tribol. 2007;129(4):860-867. doi:10.1115/1.2769732.

This paper presents experimental results correlating acoustic emission (AE) activity and the specific film thickness $(λ)$ for operational spur gears. This relationship was established by spraying liquid nitrogen onto a rotating gear wheel, thereby reducing its operating temperature and controlling the specific film thickness for a range of load and speed conditions. It is concluded that the level of AE activity is dependent on the specific film thickness and the source of AE during meshing is predominately due to asperity contact. Furthermore, measurements of AE activity may offer an opportunity to quantify the level of asperity contact for meshing gears under a range of operating conditions.

Commentary by Dr. Valentin Fuster
J. Tribol. 2007;129(4):868-875. doi:10.1115/1.2768088.

In this paper, we analyze the impact of the cavitation model on the numerical assessment of lubricated journal bearings. We compare results using the classical Reynolds model and the so-called $p-θ$ model proposed by Elrod and Adams [1974, “A Computer Program for Cavitation and Saturation Problems  ,” Proceedings of the First LEEDS-LYON Symposium on Cavitation and Related Phenomena in Lubrication, Leeds, UK] to fix the lack of mass conservation of Reynolds’ model. Both models are known to give quite similar predictions of load-carrying capacity and friction torque in nonstarved conditions, making Reynolds’ model the preferred model for its better numerical behavior. Here, we report on numerical comparisons of both models in the presence of microtextured bearing surfaces. We show that in the microtextured situation, Reynolds’ model largely underestimates the cavitated area, leading to inaccuracies in the estimation of several variables, such as the friction torque. This dictates that only mass-conserving models should be used when dealing with microtextured bearings.

Commentary by Dr. Valentin Fuster
J. Tribol. 2007;129(4):876-886. doi:10.1115/1.2768089.

The aim of this paper is to present a numerical model to compute laminar, turbulent, and transitional incompressible fluid flows in thin lubricant films where inertia effects cannot be neglected. For this purpose, an averaged inertia method is used. A numerical scheme based on the finite element method is presented to solve simultaneously the momentum and continuity equations. The numerical model is then validated by confronting it with previously published analytical, experimental, and numerical results. Particular attention is devoted to analyzing the numerical conservation of mass and momentum. The influence of mesh size on numerical precision is also analyzed. Finally, the model is applied to a misaligned hydrostatic seal. These seals operate with a substantial leakage flow, where nonlaminar phenomena occur. The influence of inertia and misalignment of the faces on the seal behavior is analyzed through a comparison with an inertialess solution. Significant differences are observed for high values of the tilt angle when the flow is nonlaminar. Inertia effects increase when the flow is laminar.

Commentary by Dr. Valentin Fuster
J. Tribol. 2007;129(4):887-894. doi:10.1115/1.2768977.

There is direct interaction between crankshaft and bearing in an internal combustion engine. The effect of lubrication status of bearing was not considered in the present calculation of crankshaft strength. A given oil film pressure distribution of bearing was generally used as load acted on journal. In this paper, a crankshaft-bearing system was taken as the study object. On the basis of lubrication analysis of misaligned bearing caused by crankshaft deformation, the stress and strength of-crankshaft were calculated using analytical oil film pressure of bearing as the load boundary condition. Crankshaft deformation and bearing load were calculated by whole crankshaft beam-element method. The lubrication of crankshaft bearing was analyzed by the kinetics method. Crankshaft stress was calculated by the finite-element method. The results show that when the effect of crankshaft deformation under load is considered, the offset distribution of oil film pressure of bearing appears and the highest oil film pressure increases remarkably, which result in the stresses of local area on fillet surface of crankshaft journal increase obviously and the safety factor of crankshaft decreases.

Commentary by Dr. Valentin Fuster
J. Tribol. 2007;129(4):895-903. doi:10.1115/1.2768609.

This is Part I of a two-part series of papers describing the effects of high-pressure injection pockets on the operating conditions of tilting-pad thrust bearings. In Part I a numerical model based on the Reynolds equation is developed extending the three-dimensional thermoelastohydrodynamic (TEHD) analysis of tilting-pad thrust bearings to include the effects of high-pressure injection and recesses in the bearing pads. The model is applied to the analysis of an existing bearing of large dimensions and the influence of the pocket is analyzed. In the analysis, the high-pressure oil injection used for hydrostatic jacking is turned off (i.e., only the effect of the pocket is studied). It is shown that a shallow pocket positively influences the performance of the bearing because it has characteristics similar to those of a Rayleigh-step bearing. In Part II of the paper (Heinrichson, N., Fuerst, A., and Santos, I. F., 2007, ASME J. Tribol., 129(4), pp. 904–912) measurements of pressure profiles and oil film thickness for a test-pad are compared to theoretical results. The analysis of Part II deals both with flow situations, where the high-pressure injection is turned off, as well as with situations where it is turned on for hydrostatic jacking.

Commentary by Dr. Valentin Fuster
J. Tribol. 2007;129(4):904-912. doi:10.1115/1.2768610.

This is Part II of a two-part series of papers describing the effects of high-pressure injection pockets on the operating conditions of tilting-pad thrust bearings. The paper has two main objectives. One is an experimental investigation of the influence of an oil injection pocket on the pressure distribution and oil film thickness. Two situations are analyzed: (i) when the high-pressure oil injection is turned off and (ii) when the high-pressure injection is turned on. The other objective is to validate a numerical model with respect to its ability to predict the influence of such a pocket (with and without oil injection) on the pressure distribution and oil film thickness. Measurements of the distribution of pressure and oil film thickness are presented for tilting-pad thrust bearing pads of $∼100cm2$ surface area. Two pads are measured in a laboratory test rig at loads of $∼1.5MPa$ and $∼4.0MPa$ and velocities of up to $33m∕s$. One pad has a plain surface. The other pad has a conical injection pocket at the pivot point and a leading-edge taper. The measurements are compared to theoretical values obtained using a three-dimensional thermoelastohydrodynamic (TEHD) numerical model. At the low load, the theoretical pressure distribution corresponds well with the measured values for both pads, although the influence of the pocket is slightly underestimated. At the high load, large discrepancies exist for the pad with an injection pocket. It is argued that the discrepancies are due mainly to geometric inaccuracies of the collar surface, although they may to some extent be due to the simplifications employed in a Reynolds equation description of the pocket flow. The measured and theoretical values of oil film thickness compare well at low loads and velocities. At high loads and velocities, discrepancies grow to up to 25%. This is due to the accuracy of the measurements. When using hydrostatic jacking the model predicts the start-up behavior well.

Commentary by Dr. Valentin Fuster
J. Tribol. 2007;129(4):913-919. doi:10.1115/1.2768612.

The tribological properties of $MoS2$ microsized spheres $(MS-MoS2)$ with diameter of $0.5–3μm$ modified by self-prepared surfactant quaternary ammonium salt of 2-undecyl-1-dithioureido-ethyl-imidazoline (SUDEI) as an additive in base oil 500 SN were investigated and compared with those of commercial colloidal $MoS2$$(CC-MoS2)$ on a four-ball tester and an Optimol SRV oscillating friction and wear tester in a ball-on-disk contact configuration. The worn surfaces of the bottom flat disk were examined with scanning electron microscopy and X-ray photoelectron spectroscopy. It was found that the $MoS2$ microsized spheres product was a much better extreme-pressure additive and antiwear and friction-reduction additive in 500 SN than commercial colloidal $MoS2$$(CC-MoS2)$. Under the appropriate concentration of 0.1% and 0.25% for $MS-MoS2$ and $CC-MoS2$ and the load of $400N$, the friction coefficient of $MS-MoS2$/oil and $CC-MoS2$/oil decreased about 25.0% and 12.5% and the wear volume loss decreased about 50.4% and 12.9% compared with the pure base stock. The boundary lubrication mechanism could be deduced as the effective chemical adsorption film formed by the long chain alkyl $(C11H23)$ and active elements (S and N) in the surfactant SUDEI and tribochemical reaction film composed of the tribochemical reaction products.

Commentary by Dr. Valentin Fuster
J. Tribol. 2007;129(4):920-922. doi:10.1115/1.2768611.

The development of new types of high-pressure plastic lubricants using natural minerals is of much importance. The effects of surfactant proportion and the structure of the nanoparticle thickener surface on the tribological properties of the bentonite-based grease were studied. The plastic lubricants that provide the best anti-friction and anti-wear properties were revealed to be the one that is modified by quaternary amine and urotropine-type ammonium salts. The surface ratio of bentonite particles modified by quaternary ammonium salts, which results in composite with the best tribological properties, was also revealed.

Commentary by Dr. Valentin Fuster
J. Tribol. 2007;129(4):923-932. doi:10.1115/1.2768613.

An experimental investigation of the friction and lift characteristics of granular lubrication is presented. Experiments are carried out to demonstrate the vertical displacement (lift) observed in an annular shear cell apparatus. Results are presented for the friction coefficient as a function of the rotational speed and the applied load for several surface roughness combinations. Simulations of the kinetic theory for the granular material are performed and compared to the experimental results. The experiments provide an evidence for the formation of granular lift between two disks undergoing sliding motion.

Commentary by Dr. Valentin Fuster
J. Tribol. 2007;129(4):933-941. doi:10.1115/1.2768614.

Chemical mechanical polishing (CMP) is a manufacturing process in which a wafer surface is polished by pressing it against a rotating pad that is flooded with slurry. The slurry itself is a fluid containing abrasive particles. Past experimentation has shown that the distribution of suspended particles in the slurry is significantly related to the distribution of material removal on the wafer during CMP. Therefore, this study involves the development and simulation of a model that predicts the kinematics and trajectory of the abrasive particles. The simulation results compare well to data from shear cell experiments data conducted by other researchers.

Commentary by Dr. Valentin Fuster
J. Tribol. 2007;129(4):942-951. doi:10.1115/1.2768615.

Flat faces of steel pins were slid on an eutectic aluminium silicon alloy under lubricated condition in the $1–100MPa$ mean contact pressure range and $0.2m∕s$ sliding speed. Two transition in wear rate were observed, at $10MPa$ and $70MPa$. The wear rate in the $1–10MPa$ regime was found to be very small and within the measuring instrument resolution and also insensitive to contact pressure. The regime is designated ultramild wear. Lack of plastic flow, minimal fragmentation of silicon particles, and the presence of undistorted voids on the fractured and unfractured silicon particles in the subsurface suggest that the state of stress in the near surface region is elastic. Contact mechanical calculations demonstrate that at contact pressures $<13.7MPa$, the system is likely to shakedown to an elastic state.

Commentary by Dr. Valentin Fuster

### TECHNICAL BRIEFS

J. Tribol. 2007;129(4):952-956. doi:10.1115/1.2768617.

A fractal dimension and a fractal roughness parameter are usually used to characterize a fractal surface. For a fractal-regular surface, a fractal domain length is also included. Such a formulation is based on an approximation using a constant value of the fractal scaling parameter that represents the ratio of the spatial frequencies of adjacent harmonic components in the Weierstrass–Mandelbrot (W-M) function. Although there were some reasons for assuming a constant value of 1.5 for the fractal scaling parameter, it is still left more or less arbitrary to adopt this assumption in fractal modeling of solid contact. In the present study, the fractal scaling parameter was treated as a variable rather than a constant by using a form of the W-M function with randomized phases based on a random walk formulation. A simple numerical scheme with clear graphical interpretation was developed to determine the value of the fractal scaling parameter. The fractal dimension, fractal roughness parameter, and fractal scaling parameter were all recovered with reasonable accuracy from numerically generated surface profiles.

Commentary by Dr. Valentin Fuster
J. Tribol. 2007;129(4):957-962. doi:10.1115/1.2768618.

In this paper, a theoretical and experimental investigation is presented to study the contact behavior of the plastic contact of deterministic rough surfaces. Analyses exclude bulk deformation of the rough surface and concentrate to the contact on asperity level. Surface asperities are modeled by an array of elliptic paraboloids where the unit event of a single contact is analyzed using an elastic-plastic elliptical contact model. A new method to determine the surface topography change due to plastic deformation is presented. Results show that the theoretical model developed predicts the contact area and the deformed geometry of the rough surface very well.

Commentary by Dr. Valentin Fuster
J. Tribol. 2007;129(4):963-967. doi:10.1115/1.2768619.

A discrete probability distribution function is used to represent the squared transverse roughness effect in a modified Reynolds equation, and the Reynolds equation is used to calculate the hydrodynamic lubrication in a slider-disk interface compared to the CFD method. When the roughness height is below 1% of the film thickness, the results acquired by the two methods are the same and the surface roughness does not show obvious effect on the lubrication results compared to that on the smooth surface. The load capacity and friction force increase as the roughness height increases when the roughness height exceeds 1% of the film thickness. Moreover, the forces acquired by Reynolds equations are smaller than those acquired by CFD, and the difference between them exceeds 10% when the roughness height is higher than 10% of the film thickness. Sidewall effect is considered to be the main reason for the difference, and the Reynolds equation is believed not suitable for calculating the effect of the squared transverse roughness in the hydrodynamic lubrication.

Commentary by Dr. Valentin Fuster