0

IN THIS ISSUE

### RESEARCH PAPERS

J. Tribol. 2005;128(1):1-9. doi:10.1115/1.1843134.

The element-free Galerkin-finite element (EFG-FE) coupling method, combined with the linear mathematical programming technique, is utilized to solve two-dimensional elasto-plastic contact problems. Two discretized models for an elastic cylinder contacting with a rigid plane are used to investigate the boundary effects in a contact problem when using the EFG-FE coupling method under symmetric conditions. The influences of the number of Gauss integration points and the size supporting the weight function in the meshless region on the contact pressure and stress distributions are studied and discussed by comparing the numerical results with the theoretical ones. Furthermore, the elasto-plastic contact problems of a smooth cylinder with a plane and a rough surface with a plane are analyzed by means of the EFG-FE method and different elasto-plasticity models.

Commentary by Dr. Valentin Fuster
J. Tribol. 2005;128(1):10-17. doi:10.1115/1.2125947.

Although in principle simple and neat results are obtained with the classical Greenwood-Williamson (GW) model (linearity of real contact area and conductance with load), the definition of asperity as local maxima of the surface leads to uncertain results for multiscale surfaces, as suspected already by Greenwood in a recent self-assessment of his theory [Greenwood, J. A., and Wu, J.J., 2001, “Surface roughness and contact: an apology  ,” Meccanica36(6), pp. 617–630]. Quoting the conclusions in the latter paper “The introduction by Greenwood and Williamson in 1966 of the definition of a ‘peak’ as a point higher than its neighbours on a profile sampled at a finite sampling interval was, in retrospect, a mistake, although it is possible that it was a necessary mistake”. Greenwood and Wu suggest that an alternative definition of asperity captures the mechanics of the contact more correctly, that of Aramaki-Majumbdar-Bhushan (AMB). Here, numerical experiments confirm that with a Weierstrass series fractal profile (taken as a 2D slice of a true fractal surface but then used to define a set of circular asperities), load and conductance for numerically measured asperities defined “à la Greenwood-Williamson” (3PP, 3-point peaks) differ significantly from the results obtained with the Aramaki-Majumbdar-Bhushan definition of asperity. The AMB definition, which is based on the bearing area intersection best parabola fitting, gives finite limits for all quantities and varies very little with small scale terms, and tends to coincide with the 3PP method only at unrealistically large fractal dimensions $D$, or at unrealistically large separations. However, it remains unclear how the AMB results compare with the proper treatment of the problem when interaction effects are fully taken into account.

Commentary by Dr. Valentin Fuster
J. Tribol. 2005;128(1):18-31. doi:10.1115/1.2114947.

Friction/stiction and wear are among the main issues in microelectromechanical systems (MEMS/NEMS) devices having contact interfaces. Relevant parameters, i.e., layers thickness, need to be optimized. The contact analyses of multilayered structure under both dry and wet conditions are necessary to optimize these parameters. This study presents a first attempt to perform three-dimensional contact analysis of multilayered solids with rough surfaces in both dry and wet conditions. The surface displacements and contact pressure distributions are obtained based on variational principle with fast Fourier transform scheme. The effective hardness is modeled and plays a role when the local displacement meets the maximum displacement criterion. Simulations are performed to obtain the contact pressures, fractional total contact area, fractional plastic contact area, surface/subsurface stresses. Relative meniscus forces are obtained with the presence of an ultrathin liquid film for different loads and layers properties. These contact statistics and meniscus forces are analyzed to study the effects of layer-to-substrate ratios of stiffness and hardness, and the layers thickness of rough, two-layered elastic/plastic solids. The methods to decrease friction/stiction and wear are investigated, and the optimum layer parameters are identified.

Commentary by Dr. Valentin Fuster
J. Tribol. 2005;128(1):32-39. doi:10.1115/1.2125907.

The thermal surface distortion of an anisotropic elastic half-plane is studied using the extended version of Stroh’s formalism. In general, the curvature of the surface depends both on the local heat flux into the half-plane and the local temperature variation along the surface. However, if the material is orthotropic, the curvature of the surface depends only on the local heat flux into the half-plane. As a direct application, the two-dimensional thermoelastic contact problem of an indenter sliding against an orthotropic half-plane is considered. Two cases, where the indenter has either a flat or a parabolic profile, are studied in detail. Comparisons with other available results in the literature show that the present method is correct and accurate.

Commentary by Dr. Valentin Fuster
J. Tribol. 2005;128(1):40-48. doi:10.1115/1.2114931.

An elastic adhesive contact model based on the element-free Galerkin-finite element (EFG-FE) coupling method is presented in this paper. The model is first validated though comparison to theoretical solutions. A numerical simulation of the adhesive contact between a microelastic cylinder and a rigid half-space is then conducted. The adhesive contact characteristics of three metals (Al, Cu, and Fe) are studied at different Tabor parameters. The relationships of the applied load and contact half-width of the adhesive contacts are analyzed. Contact pressures, stress contours and deformed profiles of different cylinder sizes and applied loads are illustrated and discussed. The results are compared to published solutions, and good agreements are observed.

Commentary by Dr. Valentin Fuster
J. Tribol. 2005;128(1):49-58. doi:10.1115/1.1843833.

Results of a combined theoretical and experimental investigation into the operation of thrust bearings with polytetrafluoroethylene (PTFE)-faced pads are reported. Bearing performance is analyzed in terms of temperature, power loss, oil film thickness and pressure. These parameters are first calculated using a THD model. The effect of PTFE facing on bearing thermal performance is then presented and discussed. A TEHD model is subsequently employed. Obtained TEHD results show that oil film thickness and temperature are strongly affected by the PTFE layer. Theoretical results are compared with measured temperature, oil film thickness, and pressure.

Commentary by Dr. Valentin Fuster
J. Tribol. 2005;128(1):59-66. doi:10.1115/1.1924575.

This paper presents a numerical two-dimensional model to study a rough thermal elastohydrodyanmic lubrication sliding contact locally and to calculate the stresses in multilayered solids. The model deterministically calculates the pressure and the surface temperature in solving simultaneously the equations that govern the lubrication and the thermoelasticity problem, respectively. The Reynolds equation and a parabolic profile for the temperature makes it possible to treat the lubrication part of the problem. The heat equation and the thermoelasticity equations in the solids are treated using a method based on the integral Fourier transform and solved with a fast Fourier transform algorithm.

Commentary by Dr. Valentin Fuster
J. Tribol. 2005;128(1):67-78. doi:10.1115/1.2125867.

The paper presents the results of a thermal analysis of a set of disk experiments carried out by Patching to investigate scuffing. The experiments used crowned steel disks at 76-mm centers with maximum Hertzian contact pressures of up to 1.7 GPa. Experimental measurements of contact friction were used as the basis for a thermal analysis of the disks and their associated support shafts. Temperatures measured by embedded thermocouples 3.2 mm below the running tracks of the disks were used to determine the heat partition between the faster and slower running disks in order to match the experimental with calculated temperatures. This partition was found to vary approximately as a function of the product of sliding speed and surface temperature difference. A transient (flash) temperature analysis of one of the experiments was also carried out. This shows large differences between the disk transient surface temperatures. These surface temperature distributions were compared with those obtained from corresponding elastohydrodynamic lubrication (EHL) analyses using two different non-Newtonian lubricant formulations. The EHL analyses show that the heat partition obtained depends on the form of non-Newtonian behavior assumed, and that to achieve the same partition as is evident in the experiment a limiting shear stress formulation is necessary. It is suggested that the combination of heat transfer and EHL analysis presented in the paper could be used as a sensitive tool for distinguishing between different non-Newtonian lubricant models under realistic engineering loads and with high sliding speeds.

Commentary by Dr. Valentin Fuster
J. Tribol. 2005;128(1):79-84. doi:10.1115/1.2125968.

Experiments and computer simulations have revealed some unusual results of elastohydrodynamic lubrication (EHL) associated with a high degree of thermally induced inhomogeneous shear across the lubricant film, or thermal shear localization. The results include the development of a sizable film dimple in the central EHL region and a dramatic reduction in EHL traction. In this study, a theoretical analysis is carried out to determine the conditions under which the thermal shear localization may develop in EHL films. For a Newtonian lubricant obeying the Barus law of viscosity, a dimensionless group-parameter is identified that fully governs the degree of the thermal inhomogeneous shear. Results are presented that show the critical range of values of this parameter corresponding to the onset of the shear localization. The analysis is also extended to lubricants with non-Newtonian behavior. Results suggest that the same dimensionless group-parameter may be used to measure the degree of the shear localization when the lubricant viscosity in the parameter is replaced by an effective viscosity that accounts for the non-Newtonian effect.

Commentary by Dr. Valentin Fuster
J. Tribol. 2005;128(1):85-95. doi:10.1115/1.2114932.

A comprehensive method of thermoelastohydrodynamic (TEHD) lubrication analysis for dynamically loaded journal bearings is presented. An algorithm for mass conserving cavitation is included, and the effect of viscosity variation with the temperature is taken into account. The Reynolds equation in the film is solved using the finite element (FE) discretization. Thermal distortions as well as the elastic deformation of the bearing surfaces are computed using the FE method. The temperature of the lubrication film is treated as a time-dependent three-dimensional variable with a parabolic variation with respect to the film thickness. In order to compute the temperature of the film and its surrounding solid surfaces, a new heat flux conservation algorithm is proposed. An important element in this analysis is the consideration of thermal boundary layers for solids. It is known that the thermal transients on the film-solid interfaces and the dynamic loading have the same period (one cycle). However, beyond the thermal boundary layers, the time scale for thermal transient in the journal and bushing are several orders of magnitude greater than those for the oil film. The Fourier series approximates the instantaneous temperature fields in the solid boundary layers. In this way, the mean heat flux that passes into the solid can be computed and a steady-state heat conduction equation can be used to obtain thermal fields inside the solids. Finally, solving the complex problem of big-end connecting-rod bearing TEHD lubrication proves the efficiency of the algorithm. Oil film temperatures are found to vary considerably over the time and space.

Commentary by Dr. Valentin Fuster
J. Tribol. 2004;128(1):96-102. doi:10.1115/1.2000264.

Measurements were made of the dynamic friction; wear volume and acoustic signal (AE) of several thermoplastics rubbing against smooth SAE-52100 steel. Polyoxymethylene, polyamide, poly(amide-imide), polypropylene, Poly(vinyl chloride), polytetrafluoroethylene, and polyethylene, were investigated using pin-on-disk configuration. Sliding speeds ranged from 0.05 to 0.45 m∕s, and normal loads from 40 to 160 N (2–8 MPa) for sliding distances varying from 4 to 20 km. Orthogonal experimental design and analysis method was used to develop wear equations expressing wear volume as function of the operating parameters. Consistent relations were also found between the integrated AE signal over time and the wear volume as well as the friction work.

Commentary by Dr. Valentin Fuster
J. Tribol. 2005;128(1):103-112. doi:10.1115/1.2000978.

Using a nonlinear model of a two disk brake system, coupled equations of motion are found for their frictional interaction. The mathematical formulation relates the tribological events at micron scale and the macroscopic scale vibration response of a two-disk brake system. This is accomplished by a viscoelastic account of interaction at the micron scale, its statistical quantification through the approximate analytical representation of the statistical expectation of contact force and the introduction of the contact force into the macroscale dynamics of the two-disk system. Steady-state analysis of the system establishes the relation between friction torque and speed and supports observed behavior of many mechanical systems with friction. It is shown that, as a result of coupling of the macrosystem’s dynamics and contact, there are combinations of parameters at the micro- and macroscale that yield negative slope in friction torque/sliding speed relation, a well known source of dynamic instability. This results in an effective negative damping that tends to decrease with decrease in the normal load and/or increase in structural damping of the system.

Commentary by Dr. Valentin Fuster
J. Tribol. 2005;128(1):113-121. doi:10.1115/1.2114930.

The effects of contact area and contact stress on friction and wear of polyethylene-metal articulation were evaluated using a bidirectional pin-on-disk apparatus. A doubling of the contact area under fixed loading conditions led to a 50% increase in the coefficient of friction and a doubling of the wear rate. There appeared to be a relationship between the increase in wear rate and the increase in the coefficient of friction. A model was developed to explain the mechanism by which engagement of asperities results in the increasing wear rate with increasing contact area despite the decreased stress.

Commentary by Dr. Valentin Fuster
J. Tribol. 2005;128(1):122-130. doi:10.1115/1.2000271.

The present work deals with the flow characteristics induced by a two-dimensional textured surface. The texture consists of identical and equally spaced rectangles with characteristic lengths at least one order of magnitude larger than the clearance of the thin film. Periodic boundary conditions enable the analysis of a single groove and the complete Navier–Stokes analysis is carried on for turbulent flow Reynolds numbers. The analysis is performed for shear driven flows (Couette), pressure driven flows (Poiseuille), and combined Couette–Poiseuille flows. First, the presence of inertial forces generated by the groove is emphasized by the momentum balance performed for the computational cell. The peculiar effect of the groove is also shown by the rotor and the stator shear stresses variations. Finally, it is shown that despite the presence of fluid inertia forces, cell-averaged rotor, and stator shear stresses obtained for pure Couette or Poiseuille flows can be added or subtracted to obtain with good accuracy the characteristics of combined shear and pressure driven flows.

Commentary by Dr. Valentin Fuster
J. Tribol. 2005;128(1):131-138. doi:10.1115/1.2125969.

A drag force reduction experiment is performed on polyoxyethylene (PEO) water solution using a rotary rheometer. Longitudinal, transverse, and isotropic grooves are notched on the rotor’s surface to investigate the effect of surface roughness patterns. The experiment results show that higher drag force is generated on the surface with transverse grooves compared with the drag force on a smooth surface, while lower drag force is generated on the surface with longitudinal grooves. The drag force on the surface with isotropic grooves is between them. Forces on the side wall of the grooves play important roles in drag force reduction. They are numerically analyzed based on the Navier-Stokes equation using the finite volume method. The viscous force on the groove’s bottom plane is far less than the force on the corresponding plane of the smooth surface, but the drag force on the groove’s surface is compensated either by the pressure drag on the side walls of the transverse groove or by the viscous force on the side walls of the longitudinal groove. The pressure drag on side wall of transverse groove is always higher than the viscous force on side wall of longitudinal groove. The numerical results cope with the experiment results that only the surface with longitudinal grooves can reduce the drag force.

Commentary by Dr. Valentin Fuster
J. Tribol. 2005;128(1):139-145. doi:10.1115/1.2033900.

This paper describes a numerical procedure for analyzing the dynamics of transient and steady state vibrations in a wavy thrust bearing. The major effects of the wavy geometry and the operating parameters on the dynamic characteristics of the bearing had been discussed in a previous paper; the present paper thus concentrates on examining the relationships between the development of the transient and steady state vibrations when operating conditions are parametrically varied. Special attention is given to the development of steady state vibrations from initial transients with comparisons and consequences to the overall system stability. Numerical based vibration signature analysis procedures are then used to identify and quantify the transient vibrations. The conclusions provide general indicators for designing wavy thrust bearings that are less susceptible to transients induced by external perturbations.

Commentary by Dr. Valentin Fuster
J. Tribol. 2005;128(1):146-154. doi:10.1115/1.2114929.

Direct lubrication tilting pad journal bearings (DLTPJ bearings) have rarely been applied to large-scale rotating machinery, such as turbines or generators, whose journal diameters are more than $500mm$. In this paper, static and dynamic characteristics of a $580mm$$(22.8in.)$ diameter DLTPJ bearing were studied experimentally using a full-scale bearing test rig. In the static test, distribution of metal temperature, oil film pressure, and bearing loss were measured in changing oil flow rate, with mean bearing pressure ranging up to $2.9MPa$. The maximum metal temperature of the DLTPJ bearing was compared to that of a conventional flood lubrication bearing, and it was confirmed that the direct lubrication could increase load capacity. In the dynamic test, spring and damping coefficients of oil film were obtained by exciting the bearing casing that was floated by air bellows. These data will be used for analysis and design of steam turbine rotors and their bearing systems. Also, vibration of pads was investigated because metal failure on upper pads due to vibration has been found in some actual machines. In order to generate oil film pressure on the surface of upper pads, a Rayleigh-step was machined there, and it was confirmed that vibration was reduced by the Rayleigh-step.

Commentary by Dr. Valentin Fuster
J. Tribol. 2005;128(1):155-167. doi:10.1115/1.2125887.

The paper describes an experimental technique combining optical interferometry and ultrasonic attenuation to measure the bulk modulus (compressibility) and film thickness profiles of oil and grease films entrapped between a stationary steel ball and a sapphire plate. Results are presented for lithium- and urea-based greases, and their base oils alone, at contact pressures up to and around 3 GPa, and are compared with some models and results from other studies, extrapolated to the higher pressures achieved here. Results show that the bulk modulus of a particular grease and its base oil are found to be similar, at a given pressure, and largely dependent on the base-oil properties, which is demonstrated to be what is expected with the concentration levels of fillers and solid lubricants present. However, the film shapes measured for the grease and its base oil can be quite different. This is seemingly due to the manner in which the lubricant samples “solidify”, due to the high pressures, and also to the way in which the edges of the squeeze-film entrapped fluid are sealed. This latter sealing effect seems to be assisted by secondary phases, particularly with greases where fillers and solid lubricants are present, creating a very effective sealed contact where the entrapped lubricant samples could be observed to remain stable for several hours.

Commentary by Dr. Valentin Fuster
J. Tribol. 2005;128(1):168-175. doi:10.1115/1.2114933.

This paper is devoted to a study of the enduring contact between granules of powder lubricants in an effort to better understand the flow characteristics of powder lubricants. Appropriate formulation of the governing equations is reported that can be used for prediction of the flow velocity, pseudo temperature, and volume fraction distribution of powders for a wide range of operating speeds. A set of parametric simulations and a limiting analytical solution is presented for predicting the behavior of a powder lubricant under low operating speeds when the enduring contact tends to dominate the kinetic regime. The limiting solution shows that below a certain sliding speed the volume fraction remains unchanged due to the effect of the enduring contact. It is also shown that below this limiting speed the enduring contact plays a major role and should not be neglected.

Commentary by Dr. Valentin Fuster
J. Tribol. 2005;128(1):176-180. doi:10.1115/1.2114967.

Lubrication by an extremely thin film has become very important in micromachines, magnetic recording disks, and so on. Molecularly thin perfluoropolyether (PFPE) films are considered a good lubricant for these micro devices. When the thickness of the PFPE film is thinned to several nanometers, it is possible to assume that the film consists of mobile and bonded molecules. In this paper, we investigated the role of these molecules from the viewpoint of the vibrational stability of the sliding ball with the disk surface. From experiments by the ball on disk type tribotester, it is found that both mobile and bonded molecules exist on the disk surface, the bouncing vibration of the sliding ball can be reduced wide load range. In the case where only mobile or only bonded molecules exists, there is little effect on the bouncing vibration.

Commentary by Dr. Valentin Fuster
J. Tribol. 2004;128(1):181-187. doi:10.1115/1.2000267.

Different compositions of bronze materials are used for sliding bearings in various applications including those involving oscillatory motion and moderate temperatures. The compatibility of new environmentally adapted synthetic esters with different contacting surface materials helps ensure good tribological performance. The present work deals with tribological studies on oscillatory journal bearings manufactured using three different compositions of bronze materials lubricated with EALs under boundary lubricated conditions. Under certain operating conditions, alloying constituents from the bronze-bearing material dissolute into the synthetic ester lubricant, thereby leading to the formation of a copper enriched bearing surface layer. Tin-bronze with synthetic ester lubricant showed more stable friction values and roughly ten times better wear results than harder aluminium- and manganese-bronze as well as outperforming the mineral oil under the same conditions.

Commentary by Dr. Valentin Fuster
J. Tribol. 2005;128(1):188-196. doi:10.1115/1.2125927.

A method is presented for predicting the occurrence of a hysteresis phenomenon, which is observed in experimental results dealing with the instability of rotor-bearing systems. The method is based on the Hopf bifurcation theory. It is shown that the existence of a hysteresis phenomenon is dependent upon the system’s operating parameters. To this end, the effect of oil viscosity on the hysteresis phenomenon and its implications on the rotor-bearing instability are investigated. The results of a series of experiments illustrating the effectiveness of the prediction of the hysteresis phenomenon using the Hopf bifurcation theory are also presented.

Commentary by Dr. Valentin Fuster
J. Tribol. 2005;128(1):197-202. doi:10.1115/1.2000269.

The mechanical spacing between the slider and the disk has to be reduced to less than 5 nm in order to achieve an areal density of $1Tbit∕in2$. Certain physical phenomena, such as those that can be caused by intermolecular and surface forces, which do not have a significant effect at higher flying heights, become more important at such low head-media separations. These forces are attractive for head-media separation as low as 0.5 nm, which causes a reduction in the mechanical spacing as compared to what would be the case without them. Single degree of freedom models have been used in the past to model these forces, and these models have predicted unstable flying in the sub-5-nm flying height range. Changes in the pitch and the roll angles were not accounted for in such models. A 3-DOF air bearing dynamic simulator model is used in this study to investigate the effect of the intermolecular forces on the static and dynamic performance of the air bearing sliders. It is seen that the intermolecular forces increase the level of flying height modulations at low flying heights, which in turn results in dynamic instability of the system similar to what has also been observed in experiments. The effect of initial vertical, pitch, and roll excitations on the static and dynamic flying characteristics of the slider in the presence of the intermolecular forces has also been investigated. A stiffness matrix is defined to characterize the stability in the vertical, pitch, and roll directions. The fly height diagrams are used to examine the multiple equilibriums that exist for low flying heights. Finally, a study was carried out to compare the performance of pico and femto designs based on the hysteresis observed during the touchdown-takeoff simulations.

Commentary by Dr. Valentin Fuster
J. Tribol. 2005;128(1):203-208. doi:10.1115/1.2000270.

Intermolecular and surface forces contribute significantly to the total forces acting on air bearing sliders for flying heights below 5 nm. Their contributions to the total force increase sharply with the reduction in flying height, and hence their existence can no longer be ignored in air bearing simulation for hard disk drives. Various experimentally observed dynamic instabilities can be explained by the inclusion of these forces in the model for low flying sliders. In this paper parametric studies are presented using a 3-DOF model to better understand the effect of the Hamaker constants, suspension pre load and pitch angle on the dynamic stability/instability of the sliders. A stiffness matrix is used to characterize the stability in the vertical, pitch, and roll directions. The fly height diagrams are used to examine the multiple equilibriums that exist for low flying heights. It has been found that the system instability increases as the magnitude of the van der Waals force increases. It has also been found that higher suspension pre load and higher pitch angles tend to stabilize the system.

Commentary by Dr. Valentin Fuster

### TECHNICAL BRIEFS

J. Tribol. 2005;128(1):209-212. doi:10.1115/1.2114948.

This study compares the flattening and indentation approaches for modeling single asperity contacts in order to reveal quantitatively their different behaviors in terms of the constitutive relationships for the contact parameters and deformation regimes. The comparison is performed with four empirical models recently developed for flattening and indentation based on the finite element method. In the elasto-plastic regime, the classic Hertz solution does not hold and, therefore, different mechanical behavior was obtained for flattening and indentation cases. Consequently, the contact condition and relative strength of mating surfaces should be considered when choosing between indentation or flattening models.

Commentary by Dr. Valentin Fuster
J. Tribol. 2005;128(1):213-217. doi:10.1115/1.2114949.

Statistical and fractal approaches for characterizing surface topography have been used widely in contact mechanics. In the present study, a comparison is conducted between contact mechanics results obtained with statistical and fractal approaches to characterize surface topography. Specifically, a three-dimensional fractal surface was generated and statistical surface parameters were extracted using different sampling resolutions. Contact mechanics simulations were performed using the simulated fractal surface and statistical surfaces represented by the extracted statistical surface parameters. Purely elastic contact (Hertz) is studied in order to eliminate any possible influence of the individual asperity mechanical response on the obtained results. Therefore, differences in the simulated contact area and load can be related solely to the different approach employed for surface characterization.

Commentary by Dr. Valentin Fuster
J. Tribol. 2005;128(1):218-220. doi:10.1115/1.2125967.

A high-pressure chamber is used to study lubricant compressibility when refrigeration oil is diluted by refrigerant. The tested lubricant in this work is a POE (polyol ester) oil, POE diluted with nonchlorinated (HFC) refrigerant R-134a, a naphthenic mineral oil, and the mineral oil diluted with the chlorinated (HCFC) refrigerant R-22. The high-pressure chamber experiments show that by adding 20 wt% of R-134a to the polyol ester oil, the stiffness of the lubricant increases by approximately 38 wt% at 1 GPa and is much higher than for R-22 and mineral oil.

Commentary by Dr. Valentin Fuster