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### Applications

J. Tribol. 2012;134(3):031101-031101-15. doi:10.1115/1.4006176.

Catcher bearings (CB) are an essential component for rotating machine with active magnetic bearings (AMBs) suspensions. The CB’s role is to protect the magnetic bearing and other close clearance component in the event of an AMB failure. The contact load, the Hertzian stress, and the sub/surface shear stress between rotor, races, and balls are calculated, using a nonlinear ball bearing model with thermal growth, during the rotor drop event. Fatigue life of the CB in terms of the number of drop occurrences prior to failure is calculated by applying the Rainflow Counting Algorithm to the sub/surface shear stress-time history. Numerical simulations including high fidelity bearing models and a Timoshenko beam finite element rotor model show that CB life is dramatically reduced when high-speed backward whirl occurs. The life of the CB is seen to be extended by reducing the CB clearances, by applying static side-loads to the rotor during the drop occurrence, by reducing the drop speed, by reducing the support stiffness and increasing the support damping and by reducing the rotor (journal)—bearing contact friction.

Commentary by Dr. Valentin Fuster
J. Tribol. 2012;134(3):031102-031102-11. doi:10.1115/1.4005892.

Oil-free turbochargers (TCs) will increase the power and efficiency of internal combustion engines, both sparking ignition and compression ignition, without engine oil lubricant feeding or scheduled maintenance. Using gas foil bearings (GFBs) in passenger vehicle TCs enables compact, lightweight, oil-free systems, along with accurate shaft motion. This paper presents extensive test measurements on GFBs for oil-free TCs, including static load-deflection measurements of test GFBs, rotordynamic performance measurements of a compressed air driven oil-free TC unit supported on test GFBs, and bench test measurements of the oil-free TC driven by a passenger vehicle diesel engine. Two configurations of GFBs, one original and the other modified with three shims, are subjected to a series of experimental tests. For the shimmed GFB, three metal shims are inserted under the bump-strip layers, in contact with the bearing housing. The installation of shims creates mechanical preloads that enhance a hydrodynamic wedge in the assembly radial clearance to generate more film pressure. Simple static load-deflection tests estimate the assembly radial clearance of the shimmed GFB, which is smaller than that of the original GFB. Model predictions agree well with test data. The discrepancy between the model predictions and test data is attributed to fabrication inaccuracy in the top foil and bump strip layers. Test GFBs are installed into a TC test rig driven by compressed air for rotordynamic performance measurements. The test TC rotor, 335 g in weight and 117 mm long, is coated with a commercially available, wear-resistant solid lubricant, Amorphous M, to prevent severe wear during start-up and shutdown in the absence of an air film. A pair of optical proximity probes positioned orthogonally at the compressor end record lateral rotor motions. Rotordynamic test results show that the shimmed GFB significantly diminishes the large amplitude of subsynchronous rotor motions arising in the unmodified GFB. Predicted synchronous rotor amplitudes and rigid body mode natural frequencies agree reasonably well with recorded test data. Finally, the oil-free TC is installed into a passenger vehicle diesel engine test bench. The TC rotor speed is controlled by the vehicle engine. Speed-up tests show dominant synchronous motion (1X) of the rotor. Whirl frequencies of the relatively small subsynchronous motions are associated with the rigid body natural mode of the TC rotor-GFB system as well as (forced) excitation from the four-cylinder diesel engine. The bench test measurements demonstrate a significant reduction in the amplitude of subsynchronous motions for the shimmed GFB, thus verifying the preliminary test results in the TC test rig driven by compressed air.

Commentary by Dr. Valentin Fuster

### Contact Mechanics

J. Tribol. 2012;134(3):031401-031401-8. doi:10.1115/1.4006747.

A contact model using semi-analytical methods, relying on elementary analytical solutions, has been developed. It is based on numerical techniques adapted to contact mechanics, with strong potential for inelastic, inhomogeneous or anisotropic materials. Recent developments aim to quantify displacements and stresses of an anisotropic material contacting both an isotropic or anisotropic material. The influence of symmetry axes on the contact solution will be more specifically analyzed.

Commentary by Dr. Valentin Fuster
J. Tribol. 2012;134(3):031402-031402-6. doi:10.1115/1.4006924.

Based on the Greenwood and Williamson theory, an assumption about the contact-area size of asperities on rough surfaces is proposed under the premise that the height of these asperities on rough surfaces is a Gaussian distribution. A formula has been derived to measure the number of asperities on 2D surfaces. The contact stiffness on a unit length of a 1D outline and that on a unit area of 2D surfaces are presented based on a formula for determining the number of asperities. The relationship between macro parameters, such as contact stiffness and micro parameters on the joint surface, is established.

Commentary by Dr. Valentin Fuster

### Elastohydrodynamic Lubrication

J. Tribol. 2012;134(3):031501-031501-8. doi:10.1115/1.4006917.

A numerical model to predict static friction for metallic point contacts was developed and validated by comparison to experimental measurements using a specially designed test rig. Key aspects of the numerical model were the incorporation of a digitized real rough surface profile, application of discrete convolution fast Fourier transform (DC-FFT) to predict local asperity interference, and modification of the yield strength to capture the effect of cold hardening. It was found that these model features are critically important to quantitative prediction of static friction. The model significantly underestimated the static friction coefficient if randomly generated surfaces having statistical parameters the same as the measured rough surface were used; digitized real rough surfaces enabled accurate predictions. Further, the model was able to describe the static friction of worn surfaces after cold hardening was introduced through modification of material yield strength. This work illustrates the importance of incorporating the surface features and the change of those features with wear to accurately and reliably predict static friction.

Commentary by Dr. Valentin Fuster
J. Tribol. 2012;134(3):031502-031502-8. doi:10.1115/1.4006860.

The coupled extended Reynolds (which includes the effects of Navier-slip and flow rheology), elasticity deformation, and the load equilibrium (under a constant load condition) equations are solved simultaneously for the EHL problems. Results show that as the slip length increases or the flow index decreases, the film thickness decreases, the central pressure increases, the pressure spike decreases, the maximum pressure switches from the pressure spike to the central pressure, and the film shape and pressure profiles moves gradually toward the outlet. A proper combination of flow rheology and slip length could fulfill some preferred EHL conditions.

Commentary by Dr. Valentin Fuster

### Friction & Wear

J. Tribol. 2012;134(3):031601-031601-11. doi:10.1115/1.4004877.

The coefficient of friction (CoF) is a very important factor for designing, operating, and maintaining the wheel-rail system. In the real world, accurate estimation of the CoF at the wheel-rail interface is difficult due to the effects of various uncertain parameters, e.g., wheel and rail materials, rail roughness, contact patch size, and so on. In this study, a stochastic analysis using polynomial chaos (poly-chaos) theory is performed with the newly developed 3D dry CoF model at the wheel-rail contact. The wheel-rail system is modeled as a mass-spring-damper system. Stochastic analyses with one uncertainty, combinations of two uncertainties, and a combination of three uncertainties are performed. The probability density function (PDF) results for stick CoF, slip CoF, and combined (total) CoF are presented. The stochastic analysis results show that the total CoF PDF before 1 s is dominantly affected by the stick phenomenon, whereas the slip dominantly influences the total CoF PDF after 1 s. The CoF PDFs obtained from simulations with combinations of two and three uncertain parameters have wider PDF ranges than those obtained for only one uncertain parameter. The current work demonstrates that the CoF is strongly affected by the stochastic variation of dynamic parameters. Thus, the PDF distribution of the CoF could play a very important role in the design of the wheel-rail system.

Commentary by Dr. Valentin Fuster

### Hydrodynamic Lubrication

J. Tribol. 2012;134(3):031701-031701-7. doi:10.1115/1.4006702.

Cavitation phenomenon in lubricants significantly influences the performance of associated machinery. In this paper, the cavitation mechanism of an oil-film bearing is attributed to gaseous cavitation, and a new gaseous cavitation model based on air solubility in the lubricant is presented. The model is validated using the Reynolds equation algorithm for fixed-geometry oil-film journal bearing, and the predicted results at different eccentricity ratios show good agreement with published data. The analyses show that gaseous mechanism can explain the cavitation phenomena that occur in the bearing except for very heavy load cases. In particular, this new model is compatible with the Jakobsson–Floberg–Olsson condition. Therefore, the new model has an explicit physical meaning, can produce good results, can identify whether vaporous cavitation occurs, and more importantly, can provide a novel means of developing cavitation models for low-vapor-pressure lubricants.

Commentary by Dr. Valentin Fuster
J. Tribol. 2012;134(3):031702-031702-9. doi:10.1115/1.4006511.

The potential use of laser surface texturing (LST) in hydrodynamic journal bearings is examined theoretically. The regular surface texture has the form of micro-dimples with preselected diameter, depth, and area density. It can be applied to only a certain portion of the bearing perimeter (partial LST) or the full bearing perimeter (full LST). The effect of such a texture on load capacity and on the attitude angle of the journal bearing is investigated in the present work. The optimum parameters of the dimples and favorable LST mode for maximum load capacity have been found.

Commentary by Dr. Valentin Fuster
J. Tribol. 2012;134(3):031703-031703-16. doi:10.1115/1.4006615.

Steady-state smooth surface hydrodynamic lubrications of a pocketed pad bearing, an angularly grooved thrust bearing, and a plain journal bearing are simulated with the mass-conservation model proposed by Payvar and Salant. Three different finite difference schemes, i.e., the harmonic mean scheme, arithmetic mean scheme, and middle point scheme, of the interfacial diffusion coefficients for the Poiseuille terms are investigated by using a uniform and nonuniform set of meshes. The research suggests that for the problems with continuous film thickness and pressure distributions, the results obtained with these numerical schemes generally well agree with those found in the literatures. However, if the film thickness is discontinuous while the pressure is continuous, there may be an obvious deviation. Compared with both the analytical solution and other two schemes, the harmonic mean scheme may overestimate or underestimate the pressure. In order to overcome this problem artificial nodes should be inserted along the wall of the bearings where discontinuous film thickness appears. Moreover, the computation efficiency of the three solvers, i.e., the direct solver, the line-by-line the tridiagonal matrix algorithm (TDMA) solver, and the global successive over-relaxation (SOR) solver, are investigated. The results indicate that the direct solver has the best computational efficiency for a small-scale lubrication problem (around 40 thousand nodes). TDMA solver is more robust and requires the least storage, but the SOR solver may work faster than TDMA solver for thrust bearing lubrication problems. Numerical simulations of a group of grooved thrust bearings were conducted for the cases of different outer and inner radii, groove depth and width, velocity, viscosity, and reference film thickness. A curve fitting formula has been obtained from the numerical results to express the correlation of load, maximum pressure, and friction of an angularly grooved thrust bearing in lubrication.

Commentary by Dr. Valentin Fuster
J. Tribol. 2012;134(3):031704-031704-8. doi:10.1115/1.4006928.

This paper extends the theory originally developed by Tichy (Tichy and Bou-Said, 1991, Hydrodynamic Lubrication and Bearing Behavior With Impulsive Loads,” STLE Tribol. Trans. 34 , pp. 505–512) for impulsive loads to high reduced Reynolds number lubrication. The incompressible continuity equation and Navier-Stokes equations, including inertia terms, are simplified using an averaged velocity approach to obtain an extended form of short bearing Reynolds equation which applies to both laminar and turbulent flows. A full kinematic analysis of the short journal bearing is developed. Pressure profiles and linearized stiffness, damping and mass coefficients are calculated for different operating conditions. A time transient solution is developed. The change in the rotor displacements when subjected to unbalance forces is explored. Several comparisons between conventional Reynolds equation solutions and the extended Reynolds number form with temporal inertia effects are presented and discussed. In the specific cases considered in this paper, the primary conclusion is that the turbulence effects are significantly more important than inertia effects.

Commentary by Dr. Valentin Fuster
J. Tribol. 2012;134(3):031705-031705-13. doi:10.1115/1.4006408.

Low clearance gas bearing applications require an understanding of surface roughness effects at increased levels of Knudsen number. Because very little information has been reported on the relative air-bearing influence of roughness location, this paper is focused on a comparison of the effects of moving and stationary striated surface roughness under high Knudsen number conditions. First, an appropriate lubrication equation will be derived based on multiple-scale analysis that extends the work of White (2010, “A Gas Lubrication Equation for High Knudsen Number Flows and Striated Rough Surfaces,” ASME J. Tribol., 132 , p. 021701). The resulting roughness averaged equation, applicable for both moving and stationary roughness over a wide range of Knudsen numbers, allows an arbitrary striated roughness orientation with regard to both (1) the direction of surface translation and (2) the bearing coordinates. Next, the derived lubrication equation is used to analyze and compare the influences produced by a stepped transverse roughness pattern located on the moving and the stationary bearing surface of a wedge bearing geometry of variable inclination. Computed results are obtained for both incompressible and compressible lubricants, but with an emphasis on high Knudsen number flow. Significant differences in air-bearing performance are found to occur for moving versus stationary roughness.

Commentary by Dr. Valentin Fuster
J. Tribol. 2012;134(3):031706-031706-9. doi:10.1115/1.4006021.

Magnetorheological (MR) fluids are fluids whose properties vary in response to an applied magnetic field. Such fluids are typically composed of microscopic iron particles ($~1-20μm$ diameter, $20-40%$ by volume) suspended in a carrier fluid such as mineral oil or water. MR fluids are increasingly proposed for use in various mechanical system applications, many of which fall in the domain of tribology, such as smart dampers and clutches, prosthetic articulations, and controllable polishing fluids. The goal of this study is to present an overview of the topic to the tribology audience, and to develop an MR fluid model from the microscopic point of view using the discrete element method (DEM), with a long range objective to better optimize and understand MR fluid behavior in such tribological applications. As in most DEM studies, inter-particle forces are determined by a force-displacement law and trajectories are calculated using Newton’s second law. In this study, particle magnetization and magnetic interactions between particles have been added to the discrete element code. The global behavior of the MR fluid can be analyzed by examining the time evolution of the ensemble of particles. Microscopically, the known behavior is observed: particles align themselves with the external magnetic field. Macroscopically, averaging over a number of particles and a significant time interval, effective viscosity increases significantly when an external magnetic field is applied. These preliminary results would appear to establish that the DEM is a promising method to study MR fluids at the microscopic and macroscopic scales as an aid to tribological design.

Commentary by Dr. Valentin Fuster

### Lubricants

J. Tribol. 2012;134(3):031801-031801-13. doi:10.1115/1.4006634.

In the present study, two commercial greases with different rheological properties were subjected to four-ball tests to identify their performance in anti-wear and anti-scuffing. A wear test machine equipped with a data acquisition system was used to collect and analyze the experimental data of electrical contact resistance (ECR) and friction torque (Tf ). Fractal theory was used to deal with the signals of the above two parameters simultaneously. The fractal dimension (Ds ) and topothesy (G) of the signals were used to establish their magnitude in relation to the tribological parameters, such as worn surface roughness and friction coefficients. The variations in the fractal parameters can be used to determine the possibility of surface scuffing under the given operating conditions. The frictional energy required for surface scuffing decreases with increasing normal load. Worn surface roughness (Ra ) that varies with test time depends strongly on the amount of oxide residual on the worn surface. If the oxide amount increases with time, the surface roughness decreases, which increases the fractal dimension and topothesy of ECR. For grease, the time starting the net growth of oxides is thus the governing factor for variations in worn surface roughness. The fractal dimension of friction coefficients varied in a narrow range regardless of scuffing. However, scuffing in the wear process affected the topothesy of the friction coefficient. The fractal analysis of friction coefficients is an efficient method for determining the possibility of scuffing that arises at contact surfaces during the wear testing processes.

Commentary by Dr. Valentin Fuster
J. Tribol. 2012;134(3):031802-031802-8. doi:10.1115/1.4006925.

Commentary by Dr. Valentin Fuster

### Magnetic Storage

J. Tribol. 2012;134(3):031901-031901-8. doi:10.1115/1.4006134.

An unstructured triangular mesh is successfully applied to the static simulations of air bearing sliders due to its flexibility, accuracy and mesh efficiency in capturing various complex rails and recess wall regions of air bearing surface, as well as fast simulation speed. This paper introduces a new implicit algorithm with second order time accuracy for the time-dependent simulations of the slider dynamics and available for the unstructured triangular mesh. The new algorithm is specially developed for the finite volume method. Since the algorithm has second order time accuracy, it provides the flexibility of applying various time steps while guaranteeing the numerical accuracy and convergence. Moreover, the unstructured triangular mesh is highly efficient and fewer nodes are used. Finally, due to the small variation of flying attitude between two neighboring time steps, it is especially efficient for iteration methods which are used in the finite volume method. As a result, the algorithm shows very fast speed in time-dependent dynamic simulations. Simulation studies are conducted on the flying dynamics of a thermal flying-height control slider after external excitations. The simulation results are compared with the simulation results obtained by the rectangular mesh based on the finite element method. It is observed that the simulation results are well correlated. The fast Fourier transform is also employed to analyze the air bearing frequencies. It is indicated that the new algorithm is of high efficiency and importance for time-dependent dynamic simulations.

Commentary by Dr. Valentin Fuster

### Mixed and Boundary Lubrication

J. Tribol. 2012;134(3):032101-032101-5. doi:10.1115/1.4006782.

The contact model for rough surfaces with power-law axisymmetric asperities in the presence of adhesion is developed. The extended JKR adhesive contact model for power-law axisymmetric asperities, denoted as JKR-n, developed by Zheng and Yu (2007,“Using the Dugdale Approximation to Match a Specific Interaction in the Adhesive Contact of Elastic Objects,” J. Colloid Interface Sci., 310 , pp. 27–34) is utilized to investigate the adhesive contact of rough surfaces. The JKR-n adhesive contact model generalizes the most adopted JKR model for spherical objects of n = 2. This work compares the effect of surface roughness on the adhesion force for rough surfaces with various power-law axisymmetric asperities. It is found that shapes of the asperities influence the pull-off forces greatly during the separation of rough surfaces. A general adhesion parameter that includes the shape index of asperities is proposed, and it can be used to characterize the adhesion performance of rough surfaces.

Commentary by Dr. Valentin Fuster

### Tribochemistry & Tribofilms

J. Tribol. 2012;134(3):032301-032301-8. doi:10.1115/1.4006581.

Poly-α-olefin (PAO) is an important synthetic fluid in the field of industry lubricants. To improve the tribological properties of PAO, a Schiff base copper complex was added to the lubricants. The tribological properties of steel and steel lubricated with PAO and PAOs containing a Schiff base copper complex were studied. The friction and wear properties of steel and steel lubricated with PAO and PAOs containing a Schiff base copper complex were evaluated using a SST-ST pin-disc tester. The sliding friction was measured using lubricants with or without a Schiff base copper complex and analyzed using surface analysis techniques including scanning electron microscopy, Fourier transform infrared spectroscopy, and confocal white light microscopy. A UMT-2 universal tribometer was also used to study the tribological properties of modifying PAO containing the Schiff base copper complex. The Schiff base copper complex structure was found to assist in the formation of a stronger tribofilm; more than the tribofilm prepared by lubricating only with PAO and this is crucial in obtaining a low and stable coefficient of friction. A lower stable friction coefficient and wear was found for the steel/steel surface contact when using the PAOs containing the Schiff base copper complex compared to the samples lubricated with the PAO without additives. The excellent tribological performance of the PAOs containing the Schiff base copper complex is attributed to the formation of a useful tribofilm with organic and inorganic groups on the sliding surface.

Commentary by Dr. Valentin Fuster

### Technical Briefs

J. Tribol. 2012;134(3):034501-034501-5. doi:10.1115/1.4005647.

The magnetic tape industry applies a mixture of stearic acid/butylstearate as a lubricant mixture in their formulation. This lubricant system has several disadvantageous points since it enhances corrosion to the GMR head, due to the existence of the stearic acid free carboxylic group; also, it is not chemically bonded to the tape surface and can freely leave the tape surface in time, leading to inferior winding/unwinding performance of the tape. In this work, we pursue our challenging task for finding a better lubricant(s) to resolve the problems with the current commercial lubricant system. We also continue working with the hypothesized model test sample which imitates the features for the real magnetic tape surface. The goal of this series of work is to correlate between the chemical structures for the miscellaneous lubricants and their micro-tribological behavior at the interface between the sample and reference guide surfaces.

Commentary by Dr. Valentin Fuster

### Discussions

J. Tribol. 2012;134(3):035501-035501-1. doi:10.1115/1.4006579.
FREE TO VIEW

The authors present an interesting thermodynamic interpretation of the Archard wear coefficient. However, their interpretation is confined to the steady state. The purpose of this discussion is, first, to extend the domain of the authors’ derivation to the entire regime of rubbing (running-in to steady state), and, second, to point out a possible thermodynamic functional interpretation of wear rate resulting from the current derivation. The starting point is to represent the hardness of the material as a linear function of the melting temperature Tm , viz: Display Formula

$H(T)=Ho[Tm-TTm]=Ho[T′Tm]$
(1)
Where T′ is the difference between the melting temperature and the temperature rise above ambient, T. Here T′ represents a degradation metric that indicates how close the material is to reach the energy barrier needed to degrade the volume active in rubbing from a solid to a liquid state. Substituting Eq. 1 in Eq. (A4) of the authors’ work, and following the authors’ method, we obtain: Display Formula
$K=wo[μH(T)TSo+μ(l.N)To/T′]$
(2)
The term To in Eq. 2 represents the time rate of change in the temperature rise above ambient. This quantity is a vanishing function in time, and at steady state, the temperature reaches a constant value that does not depend on time, i.e.,
$To{=0 steady state< 0 running-in$
Equation 2 expresses a ratio between two fundamental quantities: the energy barrier to be overcome for complete degradation of the solid state of the active volume, and the net heat transferred away from that volume. The net heat transfer is the balance of the heat transfer (TSo ) and the maximum possible amount of work extracted due to the temperature difference between the various parts of the active volume (i.e., the term μlNTo / T′). This later quantity may be considered as leakage from the heat flux transferred out of the active volume. It is of maximum value at the start of running-in and zero at steady state. At steady state, considering the contact is under constant pressure, the heat transfer will equal the enthalpy of the active volume. Thus, Display Formula
$K=wo[μH(T)E]$
(3)
K in this formulation is interpreted as the ratio of the total energy needed to degrade the wear volume to the enthalpy of the active volume. Noting that To decreases during running-in, Eq. 2 may be recast in terms of the first law, viz: Display Formula
$wo=K[Q-w′u]≡KΔuu$
(4)
with u being the internal energy per unit volume.

Commentary by Dr. Valentin Fuster

### Closures

J. Tribol. 2012;134(3):036001-036001-1. doi:10.1115/1.4006578.
FREE TO VIEW

We thank Dr. Abdel-Aal for his interest in our paper and for providing an interesting discussion. The premise of this discussion is to further develop the entropy concept to account for the running-in (transient) period. The idea is to consider the variation of hardness as a function of temperature.

Commentary by Dr. Valentin Fuster