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### Research Papers: Applications

J. Tribol. 2009;131(2):021101-021101-12. doi:10.1115/1.3063809.

Commentary by Dr. Valentin Fuster
J. Tribol. 2009;131(2):021102-021102-11. doi:10.1115/1.3063817.

A model for deep-groove and angular-contact ball bearings was developed to investigate the influence of a flexible cage on bearing dynamics. The cage model introduces flexibility by representing the cage as an ensemble of discrete elements that allow deformation of the fibers connecting the elements. A finite element model of the cage was developed to establish the relationships between the nominal cage properties and those used in the flexible discrete element model. In this investigation, the raceways and balls have six degrees of freedom. The discrete elements comprising the cage each have three degrees of freedom in a cage reference frame. The cage reference frame has five degrees of freedom, enabling three-dimensional motion of the cage ensemble. Newton’s laws are used to determine the accelerations of the bearing components, and a fourth-order Runge–Kutta algorithm with constant step size is used to integrate their equations of motion. Comparing results from the dynamic bearing model with flexible and rigid cages reveals the effects of cage flexibility on bearing performance. The cage experiences nearly the same motion and angular velocity in the loading conditions investigated regardless of the cage type. However, a significant reduction in ball-cage pocket forces occurs as a result of modeling the cage as a flexible body. Inclusion of cage flexibility in the model also reduces the time required for the bearing to reach steady-state operation.

Commentary by Dr. Valentin Fuster
J. Tribol. 2009;131(2):021103-021103-9. doi:10.1115/1.3070583.

This paper presents a theoretical study of the performance characteristics of a constant flow valve compensated multirecess hydrostatic journal bearings operating with micropolar lubricant. The finite element method and iterative procedure have been used to solve the modified Reynolds equation governing the micropolar lubricant flow in the bearing. The performance characteristics are presented for a wide range of nondimensional load, lubricant flow, and micropolar parameters. It has been observed that the micropolar parameters significantly influence the performance characteristics of the bearing.

Commentary by Dr. Valentin Fuster

### Research Papers: Coatings & Solid Lubricants

J. Tribol. 2009;131(2):021301-021301-11. doi:10.1115/1.3085941.

This paper experimentally investigates the effect of coating thickness on the thread, bearing friction coefficients, and torque-tension relationship in threaded fasteners, as well as an investigation into the effect of coating thickness on surface roughness properties. The torque-tension relationship is highly sensitive to frictional changes. Two different coating thicknesses are investigated using two bolt thread pitch; test data are collected for a preselected level of bolt tension. The experimental setup collects real-time data on the tightening torque, bolt tension, and the corresponding reaction torque. Test data are used for calculating the thread and bearing friction coefficients, as well as the overall torque-tension relationship for two different coating thicknesses. The study would provide an insight into the variation in the torque-tension relationship, which is a key factor that significantly affect the reliability and safety of bolted assemblies in many mechanical and structural applications.

Commentary by Dr. Valentin Fuster

### Research Papers: Contact Mechanics

J. Tribol. 2009;131(2):021401-021401-8. doi:10.1115/1.3063697.

The interfacial contact pressure and shear traction distributions are found for a sphere pressed onto an elastically similar half-space whose surface is populated by a uniform array of spherical asperities, when the normal load is constant and an oscillatory shear, less than that needed to cause sliding, is imposed. Details of the load history suffered by asperities in an outer sliding annulus and an inner disk, where they experience partial slip, are found, together with the effects of the roughness on the overall tangential compliance and the frictional energy losses. It is shown that for the example combination of parameters chosen, under light shear loads, the rough contact absorbs less energy than a smooth one subject to the same loading history, but that for larger shearing forces the reverse is true.

Commentary by Dr. Valentin Fuster
J. Tribol. 2009;131(2):021402-021402-8. doi:10.1115/1.3063814.

The relative motion between two surfaces under a normal load is impeded by friction. Interfacial junctions are formed between surfaces of asperities, and sliding inception occurs when shear tractions in the entire contact area reach the shear strength of the weaker material and junctions are about to be separated. Such a process is known as a static friction mechanism. The numerical contact model of dissimilar materials developed by the authors is extended to evaluate the maximum tangential force (in terms of the static friction coefficient) that can be sustained by a rough surface contact. This model is based on the Boussinesq–Cerruti integral equations, which relate surface tractions to displacements. The materials are assumed to respond elastic perfectly plastically for simplicity, and the localized hardness and shear strength are set as the upper limits of contact pressure and shear traction, respectively. Comparisons of the numerical analysis results with published experimental data provide a validation of this model. Static friction coefficients are predicted for various material pairs in contact first, and then the behaviors of static friction involving rough surfaces are extensively investigated.

Commentary by Dr. Valentin Fuster
J. Tribol. 2009;131(2):021403-021403-10. doi:10.1115/1.3075857.

The friction coefficient $(μ)$ of a contact surface with elliptical asperities is examined at various values of the plasticity index $(ψ)$, the effective radius ratio $(γ)$, the shear-strength-pressure proportionality constant $(c)$, and the dimensionless limiting interfacial shear strength $(τ¯m)$. The results demonstrate that the friction coefficient of the contact system increases with an increasing value of $γ$ but decreases with an increasing value of $ψ$. Furthermore, it is shown that Amonton’s law is applicable for contact systems with either a low $ψ$ and a high $τ¯m$ or a high $ψ$ and a low $τ¯m$. Analyzing the ratio of the nonelastic contact area, it is found that the asperities of a surface characterized by a large $γ$ generally deform elastically at all values of the plasticity index, while those of a surface with a larger $c$ deform plastically, particularly for surfaces with higher values of $τ¯m$ and $ψ$. Finally, an inspection of the critical dimensionless real contact area shows that the contact mode of the surface is determined primarily by the value of the effective radius ratio.

Commentary by Dr. Valentin Fuster
J. Tribol. 2009;131(2):021404-021404-10. doi:10.1115/1.3075866.

A model for elastic-plastic spherical contact of rough surfaces under combined normal and tangential loadings, with full stick contact condition, is presented. The model allows evaluation of the effect of surface roughness on the real contact area, static friction and junction growth under small normal loads. It is shown that as the normal load approaches a certain threshold value, which depends on the plasticity index, the results of the present rough surface model approach these of previous corresponding models for smooth sphere and a rigid flat. At normal load values below the threshold load, the correlation of the present results and published experimental results is much better in comparison with the results of the smooth surface models.

Commentary by Dr. Valentin Fuster
J. Tribol. 2009;131(2):021405-021405-11. doi:10.1115/1.3078772.

The contact problem for an elastic body indenting a similar half-space resulting in multiple contacts is important for various applications. In this paper an exact fast numerical method based on singular integral equations is developed to solve the normal contact (including applied moments), partial slip, and shear-reversal problems for such contacts. The contact patches are considered to be fully interacting, with no simplifying assumptions. A contact algorithm to automatically generate trial values based on an analysis of the profile and to subsequently guide the solver toward convergence is detailed. Some applications are discussed, including regular rough cylinders and a regularly rough flat punch with rounded edges. The examples involve between 3 and 29 contacts. The partial slip problems include demonstration of cases with multiple stick zones in some contact patches and complete sliding in others.

Commentary by Dr. Valentin Fuster
J. Tribol. 2009;131(2):021406-021406-10. doi:10.1115/1.3084214.

Sliding electrical contacts are found in many electromechanical devices, such as relays, switches, and resistance spot welding. Temperature rise due to sliding friction and electrical current may be the major source of sliding electrical contact deterioration. This paper reports the development of a three-dimensional thermo-elasto-plastic contact model of counterformal bodies, which takes into account transient heat flux, temperature-dependent strain hardening behavior, and a realistic heat partition between surfaces. Transient contact simulations induce a significant increase in computational burden. The discrete convolution and fast Fourier transform and the conjugate gradient method are utilized to improve the computation efficiency. The present model is used to study the case of a half-space sliding over a stationary sphere, and both are made of 7075 aluminum alloy; the contact resistance is considered mainly due to the surface oxide film. The simulation results indicate that the transient contact model is able to capture the history of plastic deformation accumulation and the material melting inception.

Commentary by Dr. Valentin Fuster
J. Tribol. 2009;131(2):021407-021407-10. doi:10.1115/1.3081978.

A set of finite element simulations was performed to analyze the creep behavior of an elastic–perfectly plastic hemisphere in contact with a rigid flat. This study focuses on the time-dependent stress relaxation of a fully plastic asperity. Assuming a Garofalo (hyperbolic sine) type material creep law, the asperity shows two distinct phases of relaxation. In the first phase, the asperity creeps with an accelerated creep rate and shows a contact area increase similar to that of a cylindrical geometry. In the second phase, no contact area change can be measured and the asperity creeps with a slower rate. Empirical evolution laws for the asperity creep behavior are presented, analyzing the influence of both material and geometrical parameters. The results are interpreted in terms of transient friction.

Commentary by Dr. Valentin Fuster
J. Tribol. 2009;131(2):021408-021408-8. doi:10.1115/1.3084237.

Line contact problems, such as those seen in spur gears and cam-roller follower systems, are often simplified with the plane-strain assumption and thus modeled by two-dimensional equations. However, in order to address the effects of roughness and textured surfaces, three-dimensional modeling is necessary. The challenge arises when the contact domain is several orders of magnitude greater than the grid size needed to properly describe the surface roughness or texture. Considering the surface geometry of a so-called “line contact,” the contact domain is nonperiodic in contact width direction, but it can be treated as periodic in the contact length direction–semiperiodic line contact problem. Thus, only a section of the entire contact domain is used as the computational domain with a much-reduced size. Based on an in-depth investigation of available algorithms, $DC-FFTS$ and DC-CC-FFT algorithms are proposed. The $DC-FFTS$ algorithm is a modified discrete convolution and fast Fourier transform algorithm with superposition of influence coefficients. The DC-CC-FFT algorithm is a hybrid fast Fourier transform based algorithm, which combines the discrete convolution–FFT and the continuous convolution–FFT methods. The proposed algorithms are used to solve three-dimensional displacement, contact pressure, and stresses for line contact problems. The results are compared with the other available algorithms from literature. The accuracy and efficiency of different algorithms are discussed.

Commentary by Dr. Valentin Fuster
J. Tribol. 2009;131(2):021409-021409-6. doi:10.1115/1.3085944.

Elastic-plastic contact of a smooth sphere and a half-space with a real machined surface is simulated using an integration-based multilevel contact model. The total surface deflection is composed of bulk and asperity deformations. They are calculated at the global and the asperity level, respectively, which are connected through the asperity-supporting load. With this new model, the accurate contact area and contact pressure under a given load are quickly predicted using a relatively coarse grid system. The calculated load-area curve shows good agreement with the experimental data. Finally, the effects of the surface topography, including roughness and the asperity radius, upon the real contact area are analyzed.

Commentary by Dr. Valentin Fuster
J. Tribol. 2009;131(2):021410-021410-8. doi:10.1115/1.3089217.

The asperity contact regions in static contact are subjected to very high stress. Deformation is plastic and the material can suffer localized creep that is not usually observed at conventional stress levels. Creep of the asperity contacts causes an increase in contact area and hence an increase in the adhesive component of friction. The strains are so small compared with the bulk deflections that they are hard to measure by displacement of strain transducers. However, one measurement approach is to use the reflection of an ultrasonic pulse since this depends only on the interface behavior, specifically its stiffness. In this study, ultrasound was used to investigate the increase in interfacial stiffness with time. A power law relationship between stiffness and hold time was observed for both steel and aluminum surfaces pressed together. An analytical model that assumes a simple geometry for the contact has been developed. A single asperity was considered to determine the geometry of the whole interface by superposition. The stiffness predicted by the model was compared with experimental data and was used to determine the creep rate exponent for the material.

Commentary by Dr. Valentin Fuster

### Research Papers: Elastohydrodynamic Lubrication

J. Tribol. 2009;131(2):021501-021501-10. doi:10.1115/1.3063820.

A numerical soft elastohydrodynamic lubrication model of a reciprocating hydraulic seal has been used to simulate the performance of a U-cup seal and a step seal in a conventional actuator. The model consists of coupled steady state fluid mechanics, deformation mechanics, contact mechanics, and thermal analyses, with an iterative computational procedure. The results indicate that for a given seal roughness and stroke length there is a critical rod speed above which the seal will not leak. The critical speed is dependent on both seal roughness and sealed pressure.

Commentary by Dr. Valentin Fuster
J. Tribol. 2009;131(2):021502-021502-8. doi:10.1115/1.3070582.

This paper presents numerical quasistatic simulation results of the air entrainment phenomenon between a web and a spirally grooved roller. The numerical results show that during one complete rotation of the spirally grooved roller, the traction coefficient between the web and the roller changes with time due to the changing shape of the groove in the contact region, and the average traction coefficient of the circumferentially grooved roller is higher than that of the spirally grooved roller. Using a laser sensor, web deflection is measured and compared with the numerical results at the inlet. Furthermore, a smoke wire experiment shows a clear view of the air entrainment phenomenon at the entrance, between the web and the roller.

Commentary by Dr. Valentin Fuster
J. Tribol. 2009;131(2):021503-021503-7. doi:10.1115/1.3071973.

This paper presents a nonlinear theoretical model to study the effect of laser surface texturing on the tribological performance in soft elastohydrodynamic lubrication. Both geometrical and physical nonlinearities of the elastomer are considered by using a logarithmic strain and the Mooney–Rivlin constitutive law, respectively. The results of the present nonlinear model are compared with a previous linear one over a wide range of operating conditions. It is found that the simpler linear elasticity model predicts results that are only slightly different from these predicted by the more accurate nonlinear one. Hence, the linear elasticity model can be practically considered valid over the entire range of operating conditions.

Commentary by Dr. Valentin Fuster

### Research Papers: Friction & Wear

J. Tribol. 2009;131(2):021601-021601-14. doi:10.1115/1.3071976.

A method for treating the thermomechanical interaction of bodies that undergo relative oscillatory motion is developed. The approach utilizes a combination of the transfer matrix and the finite element methods. The thermomechanical coupling process between the contacting bodies involves a transient solution scheme where the frictional heat is automatically partitioned between the contacting surfaces. The coupling between thermal and mechanical interactions is treated iteratively. An application of the proposed model in the study of thermomechanical behavior of journal bearings with oscillatory motion undergoing thermally induced seizure is presented. The results of a wide range of operating parameters are presented. The significance of applied load, contact clearance, friction coefficient, oscillation parameters, convective heat transfer, and variable load direction condition in the thermally induced seizure is discussed in light of the numerical results.

Commentary by Dr. Valentin Fuster

### Research Papers: Hydrodynamic Lubrication

J. Tribol. 2009;131(2):021701-021701-7. doi:10.1115/1.3070580.

Commentary by Dr. Valentin Fuster
J. Tribol. 2009;131(2):021702-021702-9. doi:10.1115/1.3070579.

The applications of foil air bearings have been extended for use in a wide range of turbomachineries with high speed and high temperature. Lubricant temperature becomes an important factor in the performance of foil air bearings, especially at high rotational speeds and high loads or at high ambient temperature. This study presents a thermohydrodynamic (THD) analysis of multiwound foil bearing, in which the Reynolds’ equation is solved with gas viscosity as a function of temperature that is obtained from the energy equation. Lobatto point quadrature is utilized to accelerate the iteration process with a sparse mesh across film thickness. A finite element model of the foil is used to describe the foil elasticity. An iterative procedure is performed between the Reynolds equation, the foil elastic deflection equation, and the energy equation until convergence is achieved. A three-dimensional temperature prediction of air film is presented, and a comparison of THD to isothermal results is made to emphasize the importance of thermal effects. Finally, published experimental data are used to validate this numerical solution.

Commentary by Dr. Valentin Fuster
J. Tribol. 2009;131(2):021703-021703-8. doi:10.1115/1.2961919.

Over the years, the deterministic elastohydrodynamic lubrication (EHL) approach has been widely used. This technique is very powerful in capturing details of asperity deformation and interaction. The probabilistic EHL methodology is still used when the main interest of the engineer is directed toward computations of bulk properties. During recent years, the results of many deterministic analyses have been published. The reduction of the waviness amplitude in EHL contacts under rolling-sliding was systematically studied and it was shown that the amplitude reduction is completely described by a single parameter that includes relative wavelength and the operating conditions. This approach, usually referred to as the amplitude reduction technique, has opened the way for developing improved probabilistic EHL models by incorporating the effects of fluid-induced roughness deformation, which is calculated using the fast fourier transform. In this paper we provide a review of the latest developments in the amplitude reduction technique and we present a probabilistic EHL algorithm for the computation of the load supported by the fluid, the elastically deformed asperities and the plastically deformed asperities, in a mixed EHL contact with either isotropic on nonisotropic roughness. The fluid-induced roughness deformation is incorporated into the probabilistic model via the use of the amplitude reduction technique.

Commentary by Dr. Valentin Fuster

### Research Papers: Lubricants

J. Tribol. 2009;131(2):021801-021801-5. doi:10.1115/1.3075870.

In progress of anti-shock characteristics of small size precision equipment, a miniaturized damper is required to have better damping characteristics. However, damping efficiency becomes less as damper size decreases, and so for compensation of its defect, a porous elastic sheet damper with a magnetic fluid is proposed. An analytical estimation of this sheet damper is presented to investigate variation of damping characteristics with intensity and direction of a magnetic field and to give effects of porosity of porous sheets on damping characteristics.

Commentary by Dr. Valentin Fuster

### Research Papers: Magnetic Storage

J. Tribol. 2009;131(2):021901-021901-5. doi:10.1115/1.3063696.

To quantitatively predict the static and dynamic characteristics of a flying head slider on a patterned disk surface, the “mixed averaging method” has been successfully applied to the molecular gas lubrication problem incurred by groove-shaped textures formed over the lubricating surface. First, formulation of the alternative direction implicit method using a “mixed averaged” film thickness was derived and implemented as a numerical simulation system. To analyze several types of surface patterns including their mixture patterns, the mixing ratio for the pressure flow and the shear flow were tabulated and interpolated at every mesh point, and then the spacing variations of typical sliders on a discrete track recording medium were demonstrated.

Commentary by Dr. Valentin Fuster
J. Tribol. 2009;131(2):021902-021902-9. doi:10.1115/1.3063808.

A five-degree-of-freedom model was developed for the analysis of the off-track motion of the magnetic head slider in a hard disk drive. The air bearing was integrated into the dynamic system by combining its stiffness and damping matrices with those of the suspension. Simulation was conducted for the slider in intermittent contact with circumferentially located bumps on a rotating magnetic disk. For a single bump, the excitation to the transverse displacement of the slider is close to that of an impulse. However, for multiple bumps in a sequence, the excitation gives an effect similar to that of a step force function. The maximum transverse displacement increases almost linearly with both the coefficient of friction and the skew angle. The average contact force is determined by the maximum contact force, the contact time ratio, and the shape factor of the contact force, which change with the bump spacing and the rotational speed of the disk. The steady-state transverse displacement is related to the average contact force. As the bump spacing decreases, the average contact force increases, resulting in a greater transverse displacement. Based on the system dynamic characteristics alone, changing the rotational speed of the disk has only a small impact on the average contact force and, thus, on the transverse displacement. At zero skew angle with the bump path close to a rear pad edge, significant transverse motion occurs because of the excited roll mode and the coupling between the roll angle and the transverse displacement. The off-track motion of the slider is dominated by the rotational mode of the actuator arm and the sway mode of the suspension, as verified by comparing the results of the transverse displacement from the 5DOF model to that from a 2DOF model of the transverse motions of the actuator arm and suspension. The effects of the roll angle on the transverse displacement through coupling were found to be responsible for the difference in the transverse displacements obtained from the two models.

Commentary by Dr. Valentin Fuster
J. Tribol. 2009;131(2):021903-021903-9. doi:10.1115/1.3078770.

With the increased use of hard disk drives (HDDs) in mobile and consumer applications combined with the requirement of higher areal density, there is enhanced focus on reducing head disk spacing, and consequently there is higher susceptibility of slider/disk impact damage during HDD operation. To investigate this impact process, a dynamic elastic-plastic finite element model of a sphere (representing a slider corner) obliquely impacting a thin-film disk was created to study the effect of the slider corner radius and the impact velocity on critical contact parameters. To characterize the energy losses due to the operational shock impact damage, the coefficient of restitution for oblique elastic-plastic impact was studied using the finite element model. A modification to an existing physics-based elastic-plastic oblique impact coefficient of restitution model was proposed to accurately predict the energy losses for a rigid sphere impacting a half-space. The analytical model results compared favorably to the finite element results for the range from low impact angles (primarily normal impacts) to high impact angles (primarily tangential impacts).

Commentary by Dr. Valentin Fuster

### Research Papers: Micro-Nano Tribology

J. Tribol. 2009;131(2):022001-022001-10. doi:10.1115/1.3063812.

The nanoscale contacts, which play a key role in nanotechnology and micro-/nanoelectromechanical systems, are fundamentally important for a wide range of problems including adhesion, contact formation, friction and wear, etc. Because continuum contact mechanics has limitations when it is applied at length of nanoscale, molecular dynamics (MD) simulations, which can investigate internal physical mechanisms of nanostructures by atomic motions in detail, become one of the most promising approaches for investigating mechanical behaviors of contacts in nanoscale. First, contacts between rigid cylindrical probes with different radii and an elastic half-space substrate are studied by using MD simulations with the assistance of the classical Lennard-Jones potential. For contacts without adhesion, the relationship between the applied force and the contact half-width is analyzed. The von Mises stress distributions are then discussed. For contacts with adhesion, the phenomena of the jump-to-contact, the break-off contact, and the hysteresis are observed. The pressure distributions and the von Mises stress contours in the contact region agree with the existing solutions. Second, the effects of the surface topography on adhesive contacts are studied by using MD simulations with the embedded atom method potential. The adhesive contact mechanical characteristic of a series of asperities with different shapes, different sizes, and different numbers on contacting surfaces are discovered and compared. The results show that the surface topography is one of the major factors, which may influence the contact behaviors between the interfaces of nanoscale components.

Commentary by Dr. Valentin Fuster

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

J. Tribol. 2009;131(2):022201-022201-11. doi:10.1115/1.3085943.

A physics-based fluid mechanics model is proposed to predict spin power losses of gear pairs due to oil churning and windage. While the model is intended to simulate oil churning losses in dip-lubricated conditions, certain components of it apply to air windage losses as well. The total spin power loss is defined as the sum of (i) power losses associated with the interactions of individual gears with the fluid, and (ii) power losses due to pumping of the oil at the gear mesh. The power losses in the first group are modeled through individual formulations for drag forces induced by the fluid on a rotating gear body along its periphery and faces, as well as for eddies formed in the cavities between adjacent teeth. Gear mesh pumping losses will be predicted analytically as the power loss due to squeezing of the lubricant, as a consequence of volume contraction of the mesh space between mating gears as they rotate. The model is applied to a unity-ratio spur gear pair to quantify the individual contributions of each power loss component to the total spin power loss. The influence of operating conditions, gear geometry parameters, and lubricant properties on spin power loss are also quantified at the end. A companion paper (Seetharaman, 2009, “Oil Churning Power Losses of a Gear Pair: Experiments and Model Validation  ,” ASME J. Tribol., 131, p. 022202) provides comparisons to experiments for validation of the proposed model.

Commentary by Dr. Valentin Fuster
J. Tribol. 2009;131(2):022202-022202-10. doi:10.1115/1.3085942.

This paper presents the results of an experimental study on load-independent (spin) power losses of spur gear pairs operating under dip-lubricated conditions. The experiments were performed over a wide range of operating speed, temperature, oil levels, and key gear design parameters to quantify their influence on spin power losses. The measurements indicate that the static oil level, rotational speed, and face width of gears have a significant impact on spin power losses compared with other parameters such as oil temperature, gear module, and the direction of gear rotation. A physics-based gear pair spin power loss formulation that was proposed in a companion paper (Seetharaman and Kahraman, 2009, “Load-Independent Spin Power Losses of a Spur Gear Pair: Model Formulation,” ASME J. Tribol., 131, p. 022201) was used to simulate these experiments. Direct comparisons between the model predictions and measurements are provided at the end to demonstrate that the model is capable of predicting the measured spin power loss values as well as the measured parameter sensitivities reasonably well.

Topics: Particle spin , Gears
Commentary by Dr. Valentin Fuster
J. Tribol. 2009;131(2):022203-022203-15. doi:10.1115/1.3063818.

Microlevel material failure has been recognized as one of the main modes of failure for rolling contact fatigue (RCF) of bearing. Therefore, microlevel features of materials will be of significant importance to RCF investigation. At the microlevel, materials consist of randomly shaped and sized grains, which cannot be properly analyzed using the classical and commercially available finite element method. Hence, in this investigation, a Voronoi finite element method (VFEM) was developed to simulate the microstructure of bearing materials. The VFEM was then used to investigate the effects of microstructure randomness on rolling contact fatigue. Here two different types of randomness are considered: (i) randomness in the microstructure due to random shapes and sizes of the material grains, and (ii) the randomness in the material properties considering a normally (Gaussian) distributed elastic modulus. In this investigation, in order to determine the fatigue life, the model proposed by Raje (“A Numerical Model for Life Scatter in Rolling Element Bearings,” ASME J. Tribol., 130, pp. 011011-1–011011-10), which is based on the Lundberg–Palmgren theory (“Dynamic Capacity of Rolling Bearings,” Acta Polytech. Scand., Mech. Eng. Ser., 1(3), pp. 7–53), is used. This model relates fatigue life to a critical stress quantity and its corresponding depth, but instead of explicitly assuming a Weibull distribution of fatigue lives, the life distribution is obtained as an outcome of numerical simulations. We consider the maximum range of orthogonal shear stress and the maximum shear stress as the critical stress quantities. Forty domains are considered to study the effects of microstructure on the fatigue life of bearings. It is observed that the Weibull slope calculated for the obtained fatigue lives is in good agreement with previous experimental studies and analytical results. Introduction of inhomogeneous elastic modulus and initial flaws within the material domain increases the average critical stresses and decreases the Weibull slope.

Commentary by Dr. Valentin Fuster

### Technical Briefs

J. Tribol. 2009;131(2):024501-024501-4. doi:10.1115/1.3063819.

This work is intended to evaluate a cavitation model based on the complete Rayleigh–Plesset (RP) equation for use in squeeze film damper calculations. The RP equation governs the variation in the radius of the cavitation bubbles at rest, surrounded by an infinite incompressible fluid and subjected to an external pressure. This equation is obtained from the momentum equation and it takes into account the ensemble of the phenomena related to the dynamics of the bubbles (surface tension, damping, and inertia). All the terms in the RP equation will be taken into account in the present work plus a dilatation viscosity introduced by Someya in 2003. Numerical results will be compared with experimental data obtained by Adiletta and Pietra in 2006. The results underline the influence of the effects contained in the RP equation on the pressure field.

Commentary by Dr. Valentin Fuster
J. Tribol. 2009;131(2):024502-024502-3. doi:10.1115/1.2958072.

The normal contact of a frictionless elastic coated cylinder indented by a flat rigid surface is solved using a Michell–Fourier series expansion, which satisfies the mixed boundary value problem resulting from partial contact. The boundary conditions are chosen such that the elastic layer rests on the cylindrical substrate. When the contact region is small compared to the radius of curvature of the coated cylinder, semi-analytical solutions are obtained by exploiting dual series equation techniques. The stresses on the surface are evaluated for plane strain. The results may have application to coated cylindrical structures, bimaterial inclusions, or pin-joint contact.

Commentary by Dr. Valentin Fuster
J. Tribol. 2009;131(2):024503-024503-5. doi:10.1115/1.3075859.

The concept of load sharing between asperities and fluid film is applied in conjunction with lubricated sliding wear formulation proposed by Wu and Cheng (1991, “A Sliding Wear Model for Partial-EHL Contacts,” ASME J. Tribol., 113, pp. 134–141; 1993, “Sliding Wear Calculation in Spur Gears,” ASME J. Tribol., 115, pp. 493–500) to predict the steady state adhesive wear in gears. Thermal effects are included using a simplified thermoelastohydrodynamic analysis. The prediction of the model is verified by comparing simulation results with published experimental data pertinent to steady state wear rate. The main advantages of this method are the accuracy and the remarkable computational efficiency. The results of parametric simulation study are presented to investigate the effect of speed and surface roughness on a portion of load carried by asperities and wear rate.

Commentary by Dr. Valentin Fuster
J. Tribol. 2009;131(2):024504-024504-5. doi:10.1115/1.3084213.

The strong stiction of adjacent surfaces with meniscus is a major design concern in the devices with a microsized interface. The present research concerns the elastic adhesion of rough fractal surfaces in the presence of a thin liquid film. A rough fractal surface is characterized with a two-variable Weierstrass–Mandelbrot fractal function. The microcontact model of the single asperity is established in terms of the fractal parameters. The adhesion model from meniscus is developed with the Dugdale approximation of the Laplace pressure to consider the adhesive interaction within/outside the contact area. Then the Maugis–Dugdale model and its extension are used to solve the elastic adhesive interaction for the two approaching fractal surfaces by incorporating the fractal surface model. Simulations of the external force versus the interface stiffness, surface roughness, and relative humidity are performed, respectively. The simulation results show that the interface stiffness, surface topography, and relative humidity can heavily influence the interface adhesion of rough surfaces with meniscus.

Commentary by Dr. Valentin Fuster