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### Research Papers: Applications

J. Tribol. 2008;130(4):041101-041101-12. doi:10.1115/1.2958070.

In this paper, a shaft-bearing model is developed in order to investigate the rolling element vibrations for an angular contact ball bearing with and without defects. The shaft-bearing assembly is considered as a mass-spring system. The system shows a nonlinear characteristic under dynamic conditions. The equations of motion in radial and axial directions were obtained for shaft and rolling elements, and they were solved simultaneously with a computer simulation program. Additionally, the effect of localized defects on running surfaces (i.e., inner ring, outer ring, and ball) on the vibration of the balls is investigated. Vibration of rolling elements in the radial direction is analyzed in time and frequency domains. Characteristic defect frequencies and their components can be seen in the frequency spectra of rolling element vibrations. Comparison of the obtained results with similar studies available in literature showed reasonable qualitative agreement.

Commentary by Dr. Valentin Fuster
J. Tribol. 2008;130(4):041102-041102-9. doi:10.1115/1.2958079.

This research project aims to study the nonlinear dynamic behavior of a rigid rotor supported by hydrostatic squeeze film dampers (HSFDs). The investigated HSFD consists of four hydrostatic bearing flat pads fed by capillary restrictors. A nonlinear hydrostatic squeeze film damper model is developed, and the results are compared with those obtained using a linear approach. The effect of unbalance eccentricity on the vibration response and the transmitted force of the HSFD are investigated using the linear and nonlinear models. The results show good agreement between the linear and nonlinear methods when the unbalance force is small. However, as the unbalance forces become larger, the results obtained using the linear models cease to be representative of the real behavior of rotor dynamics and a nonlinear approach must be conducted. The effects of supply pressure, viscosity, pressure ratio, and rotational speed on the response and the force transmitted to the HSFD are investigated using a nonlinear approach.

Commentary by Dr. Valentin Fuster
J. Tribol. 2008;130(4):041103-041103-8. doi:10.1115/1.2959106.

A dynamic model for deep groove and angular contact ball bearings was developed to investigate the influence of race defects on the motions of bearing components (i.e., inner and outer races, cage, and balls). In order to determine the effects of dents on the bearing dynamics, a model was developed to determine the force-deflection relationship between an ellipsoid and a dented semi-infinite domain. The force-deflection relationship for dented surfaces was then incorporated in the bearing dynamic model by replacing the well-known Hertzian force-deflection relationship whenever a ball/dent interaction occurs. In this investigation, all bearing components have six degrees-of-freedom. Newton’s laws are used to determine the motions of all bearing elements, and an explicit fourth-order Runge–Kutta algorithm with a variable or constant step size was used to integrate the equations of motion. A model was used to study the effect of dent size, dent location, and inner race speed on bearing components. The results indicate that surface defects and irregularities like dent have a severe effect on bearing motion and forces. Furthermore, these effects are even more severe for high-speed applications. The results also demonstrate that a single dent can affect the forces and motion throughout the entire bearing and on all bearing components. However, the location of the dent dictates the magnitude of its influence on each bearing component.

Commentary by Dr. Valentin Fuster

### Research Papers: Biotribology

J. Tribol. 2008;130(4):041201-041201-7. doi:10.1115/1.2958076.

During normal breathing, the mesothelial surfaces of the lung and chest wall slide relative to one another. Experimentally, the shear stresses induced by such reciprocal sliding motion are very small, consistent with hydrodynamic lubrication, and relatively insensitive to sliding velocity, similar to Coulomb-type dry friction. Here we explore the possibility that shear-induced deformation of surface roughness in such tissues could result in bidirectional load-supporting behavior, in the absence of solid-solid contact, with shear stresses relatively insensitive to sliding velocity. We consider a lubrication problem with elastic blocks (including the rigid limit) over a planar surface sliding with velocity $U$, where the normal force is fixed (hence the channel thickness is a dependent variable). One block shape is continuous piecewise linear (V block) and the other continuous piecewise smoothly quadratic (Q block). The undeformed elastic blocks are spatially symmetric; their elastic deformation is simplified by taking it to be affine, with the degree of shape asymmetry linearly increasing with shear stress. We find that the V block exhibits nonzero Coulomb-type starting friction in both the rigid and the elastic case, and that the smooth Q block exhibits approximate Coulomb friction in the sense that the rate of change of shear force with $U$ is unbounded as $U→0$, shear force $∝U1∕2$ in the rigid asymmetric case and $∝U1∕3$ in the (symmetric when undeformed) elastic case. Shear-induced deformation of the elastic blocks results in load-supporting behavior for both directions of sliding. This mechanism could explain load-supporting behavior of deformable surfaces that are symmetrical when undeformed and may be the source of the weak velocity dependence of friction seen in the sliding of lubricated, but rough, surfaces of elastic media such as the visceral and parietal pleural surfaces of the lung and chest wall.

Commentary by Dr. Valentin Fuster

### Research Papers: Contact Mechanics

J. Tribol. 2008;130(4):041401-041401-13. doi:10.1115/1.2958073.

In chemical mechanical polishing (CMP), a rigid wafer is forced on a rough elastomeric polishing pad, while a slurry containing abrasive particles flows through the interface. One of the important factors that influence the material removal rate in CMP is the magnitude of contact force transmitted to the abrasive particles trapped at the contact interface. The total push-down force is distributed to the direct contact between the wafer and the pad, and to the three-body contact between the wafer, the pad, and the abrasive particles. The presence of the abrasive particles alters the asperity contact, which otherwise can be described by Hertz contact relationships. In this study, the effect of the interfacial particles on the single asperity contact is investigated. An approach used by Greenwood and Tripp (1967, “The Elastic Contact of Rough Spheres  ,” ASME J. Appl. Mech., 34, pp. 153–160) to study the contact of rough spheres is utilized since the presence of the particles provides a rough character to the contact. The results show that the contact behavior becomes non-Hertzian with decreasing contact force and increasing elastic modulus, particle size, and particle concentration. The role of the interfacial particles is to spread the contact over a larger area while lowering the maximum contact pressure at the center of contact predicted by Hertz contact. The conditions required to transfer the contact force on the particles effectively are also described.

Commentary by Dr. Valentin Fuster
J. Tribol. 2008;130(4):041402-041402-10. doi:10.1115/1.2959110.

A thermomechanical analysis of elasto-plastic bodies is a necessary step toward the understanding of tribological behaviors of machine components subjected to both mechanical loading and frictional heating. A three-dimensional thermoelastoplastic contact model for counterformal bodies has been developed, which takes into account steady state heat flux, temperature-dependent strain hardening behavior, and interaction of mechanical and thermal loads. The fast Fourier transform and conjugate gradient method are the underlying numerical algorithms used in this model. Sliding of a half-space over a stationary sphere is simulated with this model. The friction-induced heat is partitioned into two bodies based on surface temperature distributions. In the simulation, the sphere is considered to be fully thermoelastoplastic, while the half-space is treated to be thermoelastic. Simulation results include surface pressure, temperature rise, and subsurface stress and plastic strain fields. The paper also studies the influences of sliding speed and thermal softening on contact behaviors for sliding speed ranging three orders of magnitude.

Commentary by Dr. Valentin Fuster
J. Tribol. 2008;130(4):041403-041403-7. doi:10.1115/1.2960496.

Indents perturb the pressure and stress distribution and increase the failure risk of rolling element bearings. A numerical study of the pressure perturbation is proposed. An existing dry contact model is extended to account for the indent shoulder influence and the pressure collapse in deeper indents. Moreover, results for pure rolling lubricated contacts are presented. Finally, the ellipticity influence is studied for both dry and lubricated contacts.

Topics: Pressure
Commentary by Dr. Valentin Fuster

### Research Papers: Elastohydrodynamic Lubrication

J. Tribol. 2008;130(4):041501-041501-10. doi:10.1115/1.2958069.

Many elastohydrodynamically lubricated contacts in practical applications, e.g., in bearings, operate in the starved lubrication regime. As a result their performance is sensitive to variations of the lubricant layers present on the surfaces, which form the supply to the contact. Their shape is often determined by previous overrollings of the track and also by replenishment mechanisms and various migration effects. Variations of the layers induced in the direction of rolling lead to a time-varying lubricant supply to the contact. In this paper, by means of numerical simulations using a starved lubrication model, the film thickness modulations in the center of the contact induced by a harmonically varying inlet supply have been investigated. First, for a given load condition and layer wavelength, the effect of the nominal layer thickness (degree of starvation) and the layer variation amplitude is illustrated. Subsequently, using results for different load conditions, wavelengths, and degrees of starvation, it is shown that the response of the contact to such variations is determined by a nondimensional parameter, which represents the ratio of the entrainment length of the contact to the wavelength of the induced variation, and by the degree of starvation. A simple formula is presented for use in engineering predicting the ratio of the amplitude of the film modulations in the center of the contact to the amplitude of the layer variations in the inlet.

Commentary by Dr. Valentin Fuster
J. Tribol. 2008;130(4):041502-041502-12. doi:10.1115/1.2958078.

The influence of the transversely and/or longitudinally oriented surface waviness on the lubricating behavior in the rolling/sliding elliptic contact composed of two steel bodies and lubricated with a non-Newtonian lubricant was investigated theoretically with full numerical solution of the thermal elastohydrodynamic lubrication. The entrainment velocity was assumed to be along the minor axis of the Hertzian contact ellipse. The waviness of each surface was given by a sinusoidal function. The non-Newtonian flow of the lubricant was described by the Eyring model with a constant Eyring shear stress at the ambient pressure and temperature. The velocity of the faster surface was assumed to be four times as that of the slower surface in order not only to highlight the thermal and non-Newtonian effects, but also to ensure a cyclic solution when both surfaces were with transversely oriented waviness. Starting from a quasisteady solution, the cyclic time-dependent solution was achieved numerically time step by time step. The results show that the thermal and non-Newtonian effects can be enlarged significantly by the surface waviness, and the worst configuration of the surface topography is that both surfaces are with longitudinal waviness.

Commentary by Dr. Valentin Fuster
J. Tribol. 2008;130(4):041503-041503-16. doi:10.1115/1.2958077.

In this paper a computational fluid dynamics (CFD) approach for solving elastohydrodynamic lubrication using the freely available package OPENFOAM is introduced. The full Navier–Stokes equations are solved, which enables the entire flow domain to be modeled and all gradients inside the lubricated contact to be resolved. The phenomenon of cavitation is taken into account by employing a homogenous equilibrium cavitation model, which maintains a specified cavitation pressure inside the cavitating region. The energy equation used considers the effects of heat conduction and convection, viscous heating, and the heat of evaporation. The developed method has been applied to a series of cases of lubricated metal-on-metal line contact with an entrainment velocity of $uent=2.5m∕s$, viscosities $η0=[0.01,1]Pas$, and slide-to-roll ratios $SRR=[0,1,2]$ under both thermal and isothermal conditions. The isothermal results are compared to the Reynolds theory and most results agree very well. Only the high-viscosity pure rolling case shows small differences. The combined effects of temperature, pressure, and shear-thinning are studied for the thermal cases. A temperature-induced shear band occurs in the case of sliding combined with very large viscosity compared to the isothermal case, which results in significant pressure variations across the thickness of the film. The impact of temperature on the friction force is discussed, showing differences of up to $−88.5%$ compared to the isothermal case. The developed method is capable of giving new insights into the physics of elastohydrodynamic lubrication, especially in cases where the usual assumptions of the Reynolds theory break down.

Commentary by Dr. Valentin Fuster
J. Tribol. 2008;130(4):041504-041504-8. doi:10.1115/1.2959104.

The estimation or prediction of elastohydrodynamic lubrication (EHL) film thickness requires knowledge of the lubricant properties. Today, in many instances, the lubricant properties have been obtained from a measurement of the central film thickness and the assumption of a classical Newtonian film-thickness formula. This technique has the practical advantage of using an effective pressure-viscosity coefficient, which compensates for shear-thinning. We have shown by a perturbation analysis of limiting cases for fluid with Carreau rheology (represented by Newtonian and power fluid) and by a full EHL numerical solution for Carreau fluid that the practice of extrapolating from a laboratory scale measurement of film thickness to the film thickness of an operating contact may substantially overestimate the film thickness in the real machine if the machine scale is smaller and the lubricant is shear-thinning within the inlet zone. The intention here is to show that errors result from extrapolation of Newtonian formulas to different scale and not to provide advice regarding quantitative engineering calculations.

Commentary by Dr. Valentin Fuster
J. Tribol. 2008;130(4):041505-041505-13. doi:10.1115/1.2959111.

The combined influence of shear thinning and viscous heating on the behavior of film thickness and friction in elastohydrodynamic lubrication (EHL) rolling/sliding line contacts is investigated numerically. The constitutive equation put forward by Carreau is incorporated into the model to describe shear thinning. An extensive set of numerical simulations is presented. Comparison of the film thickness predictions with published experiments reveals good agreement, and it is shown that thermal effect plays an important role in the precise estimation of EHL film thickness and friction coefficient. Parametric simulations show that thermal effect in shear-thinning fluids is strongly affected by the power-law index used in the Carreau equation. Comparisons of prediction of the Newtonian fluid model are presented to quantify the degree to which it overestimates the film thickness.

Commentary by Dr. Valentin Fuster
J. Tribol. 2008;130(4):041506-041506-7. doi:10.1115/1.2959115.

An extensive set of full elastohydrodynamic lubrication point contact simulations has been used to develop correction factors to account for the effect of shear-thinning lubricant behavior on the central and minimum film thickness in circular contacts under pure rolling condition. The film thickness for a shear-thinning lubricant can be easily obtained by dividing the corresponding Newtonian film thickness by the appropriate correction factor. Comparisons of the film thickness values obtained using the correction factors have been matched with the published experimental results pertaining to shear-thinning lubricants with a variety of realistic flow and piezoviscous properties under a wide range of operating speed. The good agreement between them establishes the validity and versatility of the correction factors developed in this paper.

Commentary by Dr. Valentin Fuster
J. Tribol. 2008;130(4):041507-041507-10. doi:10.1115/1.2959119.

A running torque analysis was performed on axially loaded deep groove ball bearings lubricated with a polymer lubricant. The analysis included a Type I and a Type II bearing. The Type I bearing has a stamped steel riveted cage with its cavity packed with the polymer lubricant. The ball surface, except for the contact points of the ball and the raceways, was covered with the polymer lubricant. The Type II bearing had the polymer lubricant packed only on the riveted parts of the cage; the balls were not covered with the polymer lubricant. The analysis was applied to a 6206 deep groove ball bearing axially loaded in a range typical of preloads applied in actual application to this size bearing to establish bearing tare torque. The results were compared to an available database. The running torque formulas for deep groove ball bearings with polymer lubricant under axial load were proposed as the sums of the running torque caused by the shearing resistance of the mineral oil between the bearing rings and the polymer lubricant, the elastic hysteresis, the differential slip, the spinning friction of the balls, the elastohydrodynamic lubrication (EHL) viscous rolling resistance, and the friction between the balls and the polymer lubricant (or the cage). The effects of the sources of the running torque were investigated. In the case of the Type I bearing, the running torque caused by the friction between the balls and the polymer lubricant, the EHL viscous rolling resistance, and the shearing resistance of the mineral oil between the bearing rings and the polymer lubricant significantly affect the running torque. In the case of the Type II Bearing, the running torque caused by the EHL viscous rolling resistance and the shearing resistance of the mineral oil between the bearing rings and the polymer lubricant significantly affect the running torque. A reasonable correlation exists between the analysis and the database. However, the analysis needs to be further validated with bearing data from different size deep groove ball bearings run under varying loads and speeds.

Commentary by Dr. Valentin Fuster

### Research Papers: Friction & Wear

J. Tribol. 2008;130(4):041601-041601-7. doi:10.1115/1.2958080.

A probabilistic model based methodology has been applied to describe the relative rate of material loss from the steel surface subjected to simultaneous action of high temperature oxidation and mechanical erosion. Growth of the oxide scales is treated deterministically and erosion is described using an established probabilistic modeling methodology. Oxidation is described with a parabolic growth law to quantify the rate of growth of the oxide scales, namely, nickel, iron, and chromium, respectively. In consonance with the published model, erosion is treated using a probabilistic methodology as spatially random phenomena on the oxide surface. The model has been applied to predict the relative erosive loss of material as a function of time resulted as a consequence of influence oxidation on mechanical erosion in a synergetic manner.

Commentary by Dr. Valentin Fuster
J. Tribol. 2008;130(4):041602-041602-10. doi:10.1115/1.2959107.

Fatigue properties of powder metallurgy parts are affected mainly by the porosity fraction. Even though it has inferior mechanical and physical properties over the conventional materials, the application of powder metallurgy products in automotive fields is seen in recent trends. The rolling-sliding contact fatigue behavior of sintered and hardened steels has been investigated by performing experiments that represent practical sliding friction coefficient component prevailing in the medium- and heavy-duty bearings and gears. Introduction of sliding friction coefficient changes the typical failure pattern and wear rate of sintered and hardened steels. The sliding friction has been computed from available models and compared with the experimental data. The ratcheting strain has also been predicted for sintered and hardened steels for various contact pressures and sliding friction coefficients. The maximum value of this strain is responsible for surface crack initiation. The wear particle analysis is carried out for the sintered and hardened steels under rolling-sliding contact fatigue conditions. The ferrogram slides for pore free steel under the rolling-sliding contact fatigue conditions are also prepared to study the effect of porosity in wear mechanism. The characteristics of wear morphology and the size, shape, and concentration of worn particles for sintered and hardened steels are also analyzed for various rolling-sliding contact fatigue conditions.

Commentary by Dr. Valentin Fuster
J. Tribol. 2008;130(4):041603-041603-6. doi:10.1115/1.2959108.

Wear particles produced by vibratory cavitation erosion tests on 1017 carbon steels in water and oil-in-water (o∕w) emulsions were analyzed. Scanning electron microscope (SEM) images of wear particles were acquired, forming a database for further analysis. The particle morphology features were first clarified. Next, the size parameters (size, area, and perimeter) and shape factors (elongation and roundness) were determined for each test liquid, using image analysis software. The size parameters of the removed particles were higher in water than in o∕w emulsions. While the shape factors could not significantly discriminate between the particles produced in water and o∕w emulsions. The size distribution was in a wide range for water than that for o∕w emulsions. The cavitation erosion mechanism is fatigue failure for water and o∕w emulsions.

Commentary by Dr. Valentin Fuster
J. Tribol. 2008;130(4):041604-041604-9. doi:10.1115/1.2959114.

The aim of this study is to evaluate a methodology for modeling the influence of crystallographic grain orientation in sliding contacts. The simulations of translating interfering cylindrical asperities, using finite element analysis, were conducted using two different plasticity models for copper: a conventional isotropic, homogeneous $J2$ plasticity model and a continuum crystal plasticity model. Using crystal plasticity, the dependence of crystallographic orientation on plastic deformation and energy dissipation can be determined. The relative trends predicted using crystal plasticity are consistent with experiments that show friction depends on crystallographic orientation when plastic deformation is one of the primary energy dissipation mechanisms.

Commentary by Dr. Valentin Fuster
J. Tribol. 2008;130(4):041605-041605-7. doi:10.1115/1.2966388.

Carbon-fiber-reinforced paper-based friction material (CFRPF), as a new type of wet friction material for automatic transmission, was prepared by a paper-making process. The frictional response of CFRPF is highly complex under a set of dynamically variable operating conditions. To better understand the effect of operating factors (braking pressure, rotating speed, oil temperature, and oil flow rate) on friction stability of the material, tests were carried out using a single ingredient experiment and the Taguchi method. Experimental results show that the braking stability and the dynamic friction coefficient $(μd)$ decrease as braking pressure, rotating speed, oil temperature, and oil flow rate increase. The influence of braking pressure on $μd$ is largest among the four operating factors. $μd$ declines gradually during the first 3000 repeated braking cycles and changes very little subsequently due to the surface topography change in friction material.

Commentary by Dr. Valentin Fuster

### Research Papers: Lubricants

J. Tribol. 2008;130(4):041801-041801-6. doi:10.1115/1.2908913.

The present investigation analyzes a green, petroleum-free lubricant that is produced by mixing two environmentally benign components—canola oil and boric acid powder. To study the influence of boric acid particle size and solid volume fraction on the proposed lubricant performance, pin-on-disk experiments were conducted with spherical copper pins (radius $6.5mm$) and aluminum disks $(Ra=1.35μm)$. Friction coefficient measurements were taken at more than 20 distinct operating conditions while varying the lubrication condition (unlubricated, boric acid, canola oil, boric acid/canola oil mixture), boric acid volume fraction, and boric acid particle size. Based on the experiments, it was determined that a solid volume fraction of 7% with $350–700μm$ particles was the optimum green particulate lubricant candidate for minimizing the friction at the conditions tested. This work also uncovered an inverse relationship between the friction coefficient and boric acid particle size (in canola oil at 7% solid fraction). Micrographs of the pin and disk wear track were analyzed to study this frictional behavior of the interface materials. Additionally, rheological tests were conducted to measure the viscosity of the canola oil and boric acid powder mixture as a function of particle size, and it was found that the viscosity increased with particle size over the size range tested. Finally, the results indicated that the boric acid-canola oil lubricant mixture demonstrated excellent potential for use as lubricants in industrial applications such as sheet metal forming.

Commentary by Dr. Valentin Fuster
J. Tribol. 2008;130(4):041802-041802-7. doi:10.1115/1.2959116.

Quantitative calculations of film thickness and friction in elastohydrodynamic lubrication will require that the low-shear viscosity, $μ$, be described with far greater accuracy than it is today. The free volume model has the advantage, over those currently used, of reproducing all of the trends that were known $80years$ ago, although not necessarily to experimental accuracy. A scaling parameter, $φ∝TVγ$, based on the repulsive intermolecular potential having exponent $−3γ$ allows the viscosity to be written as a function of temperature, $T$, and volume, $V$, only, as $μ=F(φ)$. The appropriate function for lubricants appears to be a Vogel-like form, $μ∝exp(BFφ∞∕(φ−φ∞))$. Parameters are presented here for seven liquids. When the dynamic crossover is present, two such functions are required. A low molecular weight dimethyl silicone having high compressibility is an exception.

Commentary by Dr. Valentin Fuster

### Research Papers: Magnetic Storage

J. Tribol. 2008;130(4):041901-041901-6. doi:10.1115/1.2958075.

Thermomechanical actuation (TMA) at the transducer region of the air bearing surface (ABS) protrudes from the transducer toward the recording media. This actuation induces a change in the air bearing pressure and a concomitant lift of the slider. The actual actuation in flying height divided by the TMA protrusion, defined as the TMA efficiency, is intimately coupled to the ABS design. After introducing an expression describing the changes in the air bearing forces due to the TMA protrusion, three approaches are proposed that facilitate the optimization of the ABS design for improving the TMA efficiency. These approaches include (a) reducing the air bearing pressure, (b) reducing the size of the TMA affected area, and (c) decoupling the peak air bearing pressure area from the TMA affected area. To illustrate these approaches, several ABS designs are evaluated by comparing their TMA efficiencies.

Commentary by Dr. Valentin Fuster
J. Tribol. 2008;130(4):041902-041902-10. doi:10.1115/1.2966386.

The current effort was motivated by the increasing appearance of data storage devices in small portable and mobile product formats and the need for these devices to deliver high storage capacity, low power requirements, and increased ruggedness. In order to address these requirements, this work considered the storage device to utilize a 1 in. titanium foil disk and a pair of opposed femtosized zero-load recording head sliders with asymmetrically configured air bearing surfaces. A titanium foil disk, due to its reduced thickness and relatively low mass density, requires less operational energy than a hard disk while providing storage densities and data transfer rates typical of a hard disk. The zero-load sliders were chosen in order to make negligible the air bearing interface normal force acting on the disk surface that can lead to high speed disk instability. The asymmetry of the slider air bearing surfaces, together with the disk dynamic flexibility, greatly improves the ability of the slider-disk interface to absorb substantial mechanical shock and other dynamic effects without the associated contact and impact typically observed with a hard disk. The current project evaluated the characteristics of this slider-disk air bearing interface for both static and unsteady operating conditions. Time dependent studies included a numerical simulation of the dynamic load process and the response to mechanical shock. A comparison with the performance of a hard disk interface was also included.

Commentary by Dr. Valentin Fuster

### Research Papers: Other (Seals, Manufacturing)

J. Tribol. 2008;130(4):042201-042201-11. doi:10.1115/1.2959109.

Fatigue lives of rolling element bearings exhibit a wide scatter due to the statistical nature of the rolling contact fatigue failure process. Empirical life models that account for this dispersion do not provide insights into the physical mechanisms that lead to this scatter. One of the primary reasons for dispersion in lives is the stochastic nature of the bearing material. Here, a damage mechanics based fatigue model is introduced in conjunction with the idea of discrete material representation that takes the effect of material microstructure explicitly into account. Two sources of material randomness are considered: (1) the topological randomness due to geometric variability in the material microstructure and (2) the material property randomness due to nonuniform distribution of properties throughout the material. The effect of these variations on the subsurface stress fields in rolling element line contacts is studied. The damage model, which incorporates cyclic damage accumulation and progressive degradation of material properties with rolling contact cycling, is used to study the mechanisms of subsurface initiated spalling in bearing contacts. Crack initiation as well as propagation stages are modeled using damaged material zones in a unified framework. The spalling phenomenon is found to occur through microcrack initiation below the surface where multiple microcracks coalesce and subsequent cracks propagate to the surface. The computed crack trajectories and spall profiles are found to be consistent with experimental observations. The microcrack initiation phase is found to be only a small fraction of the total spalling life and the scatter in total life is primarily governed by the scatter in the propagation phase of the cracks through the microstructure. Spalling lives are found to follow a three-parameter Weibull distribution more closely compared to the conventionally used two-parameter Weibull distribution. The Weibull slopes obtained are within experimentally observed values for bearing steels. Spalling lives are found to follow an inverse power law relationship with respect to the contact pressure with a stress-life exponent of 9.35.

Commentary by Dr. Valentin Fuster

### Research Papers: Tribochemistry & Tribofilms

J. Tribol. 2008;130(4):042301-042301-6. doi:10.1115/1.2958071.

Fundamentals of tribofilm formation and their properties were studied. In order to understand the effects of lubricants on tribofilms, four base oils were investigated. Lubricants include castor oil, polyethylene glycol, mineral oil, and margarine. These oils were chosen based on their molecular structure, polarity, utility, and biodegradability. Experiments were conducted using a ball-on-disk tribometer to form tribofilms. Surface characterization was carried out using a stylus profilometer, a scanning electron microscope, and a transmission electron microscope. Results showed that oils with high polarity such as castor oil enhanced the formation of a transfer layer on the steel surface, whereas nonpolar oils such as mineral oil failed to do so. Oils with high polarity act as effective base oils to prevent metal hardening and bond debris particles to the metal surface. Oils with nonpolar components, on the other hand, generate abrasive nanoparticles during rubbing. Experiments with margarine at elevated temperature resulted in the formation of a hard and thick tribofilm. An adsorption model is illustrated to highlight the effects of lubricant molecules.

Commentary by Dr. Valentin Fuster
J. Tribol. 2008;130(4):042302-042302-12. doi:10.1115/1.2961808.

In recent years, the optimized use of low friction nonferrous coatings under boundary lubrication conditions has become a challenge to meet the demands of improved fuel economy in automotive applications. This study presents the tribological performance of chromium nitride (CrN) coating using conventional friction modifier (moly dimer) and/or antiwear additive (zinc dialkyl dithiophosphate (ZDDP)) containing lubricants in a pin-on-plate tribometer. Using surface analysis techniques such as the atomic force microscope (AFM) and X-ray photoelectron spectroscopy (XPS), both topographical and chemical analyses of tribofilms were performed. This paper shows that ZDDP and moly dimer both give a positive effect for both low friction and antiwear performance in CrN/cast iron system. Both AFM and XPS analyses give evidence of the formation of ZDDP and moly dimer derived tribofilms on the CrN coating and thus support friction and wear results.

Commentary by Dr. Valentin Fuster

### Technical Briefs

J. Tribol. 2008;130(4):044501-044501-3. doi:10.1115/1.2958074.

The Hertzian contact theory is approximated according to a concept by Tanaka (2001, “A New Calculation Method of Hertz Elliptical Contact Pressure  ,” ASME J. Tribol., 123, pp. 887–889) yielding simple analytical expressions for the elliptical semi-axes, the maximum contact pressure, the mutual approach and the contact spring constant. Several configurations are compared using the exact Hertz theory and the current approximation. The results agree within technical accuracy.

Commentary by Dr. Valentin Fuster
J. Tribol. 2008;130(4):044502-044502-6. doi:10.1115/1.2958081.

An axisymmetrical hemispherical asperity in contact with a rigid flat is modeled for an elastic perfectly plastic material. The present analysis extends the work (sphere in contact with a flat plate) of Kogut–Etsion Model and Jackson–Green Model and addresses some aspects uncovered in the above models. This paper shows the critical values in the dimensionless interference ratios $(ω∕ωc)$ for the evolution of the elastic core and the plastic region within the asperity for different $Y∕E$ ratios. The present analysis also covers higher interference ratios, and the results are applied to show the difference in the calculation of real contact area for the entire surface with other existing models. The statistical model developed to calculate the real contact area and the contact load for the entire surfaces based on the finite element method (FEM) single asperity model with the elastic perfectly plastic assumption depends on the $Y∕E$ ratio of the material.

Commentary by Dr. Valentin Fuster