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IN THIS ISSUE


RESEARCH PAPERS

J. Tribol. 1998;120(4):645-651. doi:10.1115/1.2833761.

A thermal model for magnetic field assisted polishing of ceramic balls/rollers is presented. The heat source at the area of contact between the balls and the abrasives where material removal takes place is approximated to a disk. The disk heat source is considered as a combination of a series of concentric circular ring heat sources with different radii. Each ring in turn is considered as a combination of a series of infinitely small arc segments and each arc segment as a point heat source. Jaeger’s classical moving heat source theory (Jaeger, 1942; Carslaw and Jaeger, 1959) is used in the development of the model, starting from an instantaneous point heat source, to obtain the general solution (transient and steady-state) of the moving circular ring heat source problem and finally the moving disc heat source problem. Due to the formation of fine scratches during polishing (on the order of a few micrometers long), the conditions are found to be largely transient in nature. Calculation of the minimum flash temperatures and minimum flash times during polishing enables the determination if adequate temperatures can be generated for chemo-mechanical polishing or not. This model is applied in Part II for magnetic float polishing (MFP) of ceramic balls and in Part III for magnetic abrasive finishing (MAF) of ceramic rollers.

Commentary by Dr. Valentin Fuster
J. Tribol. 1998;120(4):652-659. doi:10.1115/1.2833762.

The thermal model developed in Part I of this three-part series is applied in this paper to magnetic float polishing (MFP) of ceramic (Si3 N4 ) balls. Using this method, the flash temperatures, flash times, and temperature distribution at the interface between the balls and the shaft of the MFP apparatus are calculated. Examination of the polished surfaces (scratch lengths) of the balls showed that the length of most scratches during the final stage of polishing is <20 μm and most are formed under transient conditions. But because of the small area of contact and low load encountered in MFP, the results of the calculations under these conditions were found to be very close to the quasi-steady-state conditions. However, it is not possible to know a priori if the conditions are transient or quasi-steady state unless solutions are available for each case. The use of the general solution developed in Part I enables this determination. The minimum flash temperatures and minimum flash times that occur during polishing ensure the determination if adequate temperatures are generated for chemo-mechanical polishing to take place. Of course, the lengths of the scratches would be much longer and the corresponding flash duration longer during the semifinishing operation than during flnishing. The combined temperature and flash duration would determine the extent of chemo-mechanical action under these conditions. The flash temperatures and flash times required for chemo-mechanical action can be used as a basis for the optimization of polishing conditions in MFP.

Commentary by Dr. Valentin Fuster
J. Tribol. 1998;120(4):660-667. doi:10.1115/1.2833763.

Conditions during finishing of advanced ceramics by magnetic abrasive finishing (MAF) processes are found to be, by and large, transient. Consequently, the available quasi-steady-state solutions for the moving heat sources are not directly applicable for this case. Hence, the general solution for a moving disk heat source, developed in Part I of this three-part series, is applied to determine the minimum flash temperatures and flash times generated at the contact points between the workmaterial (Si3 N4 roller) and the abrasive (Cr2 O3 )). Since chemo-mechanical action between the abrasive—the workmaterial—the environment depends on both the thermodynamics and kinetics of the process, it is important to determine the flash temperatures as well as flash times during polishing. These were determined as a function of the polishing pressure and the rotational speed of the work material in this investigation. Thermodynamic considerations (not covered in this paper) indicate that even the minimum flash temperatures generated under the conditions of lower pressure, lower sliding velocity, and transient state would be adequate to initiate chemo-mechanical action, and experimental results confirmed the formation of chemo-mechanical reaction products during polishing (Bhagavatula and Komanduri, 1996).

Commentary by Dr. Valentin Fuster
J. Tribol. 1998;120(4):668-676. doi:10.1115/1.2833764.

Coatings are increasingly used to improve the mechanical and tribological behavior of surfaces. It is necessary to develop models to guide the initial choice of coating/substrate combinations that can withstand the applied loads. A three-dimensional model of an elastic multilayered body, loaded both normally and tangentially against an elliptical rigid body (partial sliding, rolling/sliding conditions), is presented here. This model is based on linear elasticity theory, integral transforms, Fast Fourier Transform, and unilateral contact analysis with friction. Normal and tangential contact conditions between the two bodies are first determined and then used to calculate the multilayered body stress field. One application is given here: The influence of the mechanical properties of coating and substrate, as well as coating thickness, is studied on contact conditions, internal stresses, and potential failure mechanisms.

Commentary by Dr. Valentin Fuster
J. Tribol. 1998;120(4):677-684. doi:10.1115/1.2833765.

Two nonrotating elastic half-planes in quasi-static contact without coupling of the normal and tangential surface stresses are analyzed in this paper. It is proved that the tangential traction under constant normal forces and increasing tangential forces is equal to the difference between the actual normal pressure and the pressure for a smaller contact area, multiplied by the coefficient of friction. Every stick area corresponds to a contact area (or a configuration of multiple contact areas) that is smaller than the present contact area. In the same way as the contact area develops with increasing pressure, the stick area recedes with increasing tangential traction. General loading scenarios are solved by superposition of oblique increments under constant angles. As an example, this principle is applied to a rigid surface of the form Ak xk , in contact on 0 ≤ x ≤ a and with a corner at x = 0, indenting an elastic half-plane.

Commentary by Dr. Valentin Fuster
J. Tribol. 1998;120(4):685-694. doi:10.1115/1.2833766.

An approximate but economical approach to the non-Newtonian thermal elastohydrodynamic (EHD) lubrication in heavily loaded elliptical contacts (p0 ≥ 1 GPa) has been developed by the author. From an empirically corrected Hertzian pressure distribution, the rheology, generalized momentum, and energy equations were solved to obtain the shear stress, velocity, and temperature distributions in the film. The computerized model, incorporating a number of fluid rheological laws, has been used to examine the influences of the non-Newtonian behavior of lubricants on the temperature, film thickness, and traction in the EHD contact. In this paper, the numerical formulation and computation scheme are briefly described. Then a comparison between the results obtained with some well known rheological laws is presented. The results show that the non-Newtonian characteristic of lubricants has a significant effect on the temperature and traction for lower sliding speeds, but it has a modest influence on the film thickness. By comparison with experiment, Bair and Winer’s fluid model appears to be quite realistic.

Commentary by Dr. Valentin Fuster
J. Tribol. 1998;120(4):695-704. doi:10.1115/1.2833767.

The column continuity equation is used in formulating a modified Reynolds equation for elastohydrodynamic lubrication of elliptical contacts. A finite element method (FEM), here the Galerkin weighting method with isoparametric Q9 elements, is used to discretize the weak form of the Reynolds equation. In addition to the nodal pressures and the offset film thickness, the locations of the two-dimensional irregular free boundary are explicitly solved for by simultaneously forcing the essential and the natural Reynolds boundary conditions. Newton-Raphson’s iterations with a user-friendly yet efficient meshless scheme (i.e., automatic meshing-remeshing) are finally applied to solve these equations. A decoupled circular non-Newtonian fluid model is adapted in a way to illustrate the implementation of this new solution method. Extensive results will be given in Part II.

Commentary by Dr. Valentin Fuster
J. Tribol. 1998;120(4):705-709. doi:10.1115/1.2833768.

Due to technological pressures the lubricant film thickness in EHD contacts has decreased over the years and will continue to do so for the foreseeable future. On the other hand, financial constraints cause the surface roughness in these contacts to decrease very slowly, or might even cause an increase. As a result, the ratio of film thickness to composite roughness will continue to decrease. The question that remains to be answered is to what extent this decrease will affect the contact performance. A third development makes this question even more acute, the request of increased reliability. As a consequence, the problem of the detailed understanding of the elastohydrodynamic lubrication with rough surfaces is as urgent as ever. Recent work has shown that the features inside the contact deform, and that the level of deformation is a function of the wavelength of the feature and the contact operating conditions, including slip. This last aspect of the problem, which has not been addressed previously, forms the central topic of the current paper. Instead of studying the deformation of a real roughness profile, the deformation of its sinusoidal Fourier components is investigated.

Commentary by Dr. Valentin Fuster
J. Tribol. 1998;120(4):710-715. doi:10.1115/1.2833769.

A new boundary-element method is presented for the rapid and accurate solution of viscous-flow boundary-value problems in which the inherent geometry has a high aspect ratio, R ≫ 1, As such, the method is particularly suited to the investigation of steady flow within thin-gap bearings of arbitrary geometry, in which the spatial dimension in one direction is an order of magnitude greater than that in a perpendicular direction. Our theory predicts that the new method is O (R 2 ) times faster than, and requires O (R −1 ) the storage of, existing boundary-element techniques with equivalent computational mesh resolution. The new method is applied to the test problem of steady 2-D viscous flow within an exponential-profile slider bearing, and results obtained provide convincing evidence to support the theory in that, as R → ∞, the thin-film solution is recovered. The new method, which brings problems which were hitherto computationally restrictive within reach of modest computational platforms, is intended to provide the basis of a fast and accurate solver which can incorporate random surface roughness.

Commentary by Dr. Valentin Fuster
J. Tribol. 1998;120(4):716-723. doi:10.1115/1.2833770.

A new friction testing method based on combined forward conical can-backward straight can extrusion is proposed in order to evaluate friction characteristics in severe metal forming operations. By this method the friction coefficient along the conical punch surface is determined knowing the friction coefficient along the die wall. The latter is determined by a combined forward and backward can extrusion of straight cans. Calibration curves determining the relationship between punch travel, can heights, and friction coefficient for the two tests are calculated based on a rigid-plastic FEM analysis. Experimental friction tests are carried out in a mechanical press with aluminium alloy A6061 as the workpiece material and different kinds of lubricants. They confirm that the theoretical analysis results in reasonable values for the friction coefficient.

Commentary by Dr. Valentin Fuster
J. Tribol. 1998;120(4):724-728. doi:10.1115/1.2833771.

A series of experiments was carried out using a rolling-type tribometer to investigate the frictional dependence on the average velocity of the lubricant V at the contact zone inlet and the relative sliding velocity ΔV between the roll and workpiece during deformation. Experiments using mild steel strips with a dull surface of 0.63 fxm Ra showed that the friction coefficient decreases with increasing forming velocity, especially at high forming velocity. This variation in the friction coefficient may be due to the increase in ΔV derived from the increase of the forming velocity, because the friction coefficient decreases with increasing ΔV but varies little with increasing V. It was also confirmed that an increase of ΔV or a decrease in V promotes flattening of the workpiece asperities.

Commentary by Dr. Valentin Fuster
J. Tribol. 1998;120(4):729-736. doi:10.1115/1.2833772.

The effects of frequency on the fretting conditions in a glass/PMMA contact have been investigated using experimental analysis and numerical simulations. For partial slip conditions, the changes in the shape of the fretting cycles giving the tangential load as a function of the imposed displacement have been interpreted on the basis of changes in the dynamic modulus of the PMMA as a function of frequency. Using the numerical simulations, the values of the PMMA’s modulus at the various frequencies were determined from the analysis of the fretting cycles. For gross slip conditions, the emphasis was placed on the determination of the range of velocity associated with stick-slip processes. This information has been summarized in a fretting map giving the initial fretting condition as a function of normal load, displacement amplitude, and frequency.

Commentary by Dr. Valentin Fuster
J. Tribol. 1998;120(4):737-743. doi:10.1115/1.2833773.

This paper concerns an experimental investigation of fretting behavior using grease lubrication for ball (ball bearing steel) -flat (low alloyed steel) contact. The influences of the imposed displacement amplitude, contact geometry, pressure, and frequency are emphasized. In order to better understand the effect of grease lubrication at the interface, a glass counterface was used to visualize the contact; sliding tests were used to identify the effect of a large displacement amplitude. Dynamic loading analysis, in combination with subsequent metallographic examinations, have shown that fretting damage depends strongly upon fretting conditions and upon grease durability. Lubrication conditions and palliative effect in fretting are discussed. Results have shown an important effect of normal force, displacement amplitude, and frequency of motion on the lubricating effect of grease. The separation of grease into two phases in the contact during friction, creating bubbles, appears to be an important phenomenon.

Commentary by Dr. Valentin Fuster
J. Tribol. 1998;120(4):744-749. doi:10.1115/1.2833774.

Real fretting fatigue cycles often involve complex loading where the fretting force may vary with a different phase or frequency to the other loads on the components. Analysis of the contact tractions in such cases can be difficult. Here we present a quadratic programming technique which enables the shear tractions to be determined in a relatively straightforward manner. A number of sample load histories are investigated and it is shown that the shear traction cycle rapidly shakes down to a steady state. Further, the results are relatively insensitive to the manner in which loading is commenced.

Commentary by Dr. Valentin Fuster
J. Tribol. 1998;120(4):750-757. doi:10.1115/1.2833775.

In this study, the characteristics of ultra-thin gas films are analyzed asymptotically for infinite squeeze number using the molecular gas film lubrication equation with coupled roughness and rarefaction effects taken into consideration. The governing equation of the internal region was obtained by a time averaged technique, and the boundary conditions were obtained numerically from the matching conditions near the boundaries. Two new functions, H and H−1 were proposed for deriving the matching equation near the boundary. Finally, the characteristics of squeeze film bearings with infinite width were analyzed for various roughness parameters (Peklenik number, standard deviations of the composite roughness, and roughness orientation angles), rarefaction parameter (Knudsen number), and operation conditions (excursion ratio).

Commentary by Dr. Valentin Fuster
J. Tribol. 1998;120(4):758-764. doi:10.1115/1.2833776.

The technique of High-Resolution Modeling of Thin Films is combined with a two-scale analysis to formulate the Compressible Narrow Groove Analysis. The data bank of Fukui and Kaneko (1990) is emulated in the form of an empirical formula to treat the state of arbitrary rarefaction of the gas film. Due to its transcendental character, the compressible fine-scale solution is treated on the fly as a part of the global-scale computation. Derivations for the Compressible Narrow Groove Analysis are presented here. In a companion paper (Pan, 1998), the Compressible Narrow Groove Analysis is used to compute the pressure field of a spherical device operating in both the pressurizing and evacuating modes.

Commentary by Dr. Valentin Fuster
J. Tribol. 1998;120(4):765-771. doi:10.1115/1.2833777.

Compressible Narrow Groove Analysis, as derived in a companion paper (Pan, 1998), is a model implementation of Thin Film High-Resolution Modeling for gas films. This paper describes the numerical procedure to compute the pressure field in a centered spherical device, which has general design features originally intended for a high performance gas bearing gyroscope (Keating and Pan, 1968). The number of groove patterns is varied to bring out the significance of the local compressibility number. Increased local compressibility, associated with reduced number of groove patterns, causes successive degradation of the pressurization capacity until it is entirely suppressed at 32 groove patterns. Further study is made with reversed rotation to create a high vacuum state in the gas film concurrent with a large compressibility number. The evacuation operation (with reversed rotation) is relatively insensitive to the number of groove patterns, but is highly dependent on the accommodation coefficient. Experience in preparing these examples lends evidence to the robustness of Thin Film High-Resolution Modeling. Trouble free iterative computations are routinely performed for the local Knudsen number in excess of 109 and the effective local compressibility number larger than 100.

Commentary by Dr. Valentin Fuster
J. Tribol. 1998;120(4):772-780. doi:10.1115/1.2833778.

In this paper, the relations expressing the effects of surface roughness and homogeneous mixture (the mixture of power-law fluid inserted into a Newtonian fluid) on the roughness-induced flow factors are derived. A coordinate transformation is utilized to simplify the derivation. By using the perturbation approach incorporated with Green function technique, the flow factors and shear stress factors are derived and expressed as functions of the volume fraction of the power-law fluid in the mixture (υ p ), the viscosity ratio of the power-law fluid to that of the Newtonian fluid (N or μp *), the flow behavior index of the power-law fluid (η), the Peklenik numbers (γi ) and the standard deviations (σl ) of each surface. A form of the average Reynolds equation is then obtained. It is shown that a number of currently available models are special cases of the theory presented here. Finally, the performance of a journal bearing is discussed.

Commentary by Dr. Valentin Fuster
J. Tribol. 1998;120(4):781-788. doi:10.1115/1.2833779.

In statically indeterminate rotor bearings systems, where the rotor is supported by one or more hydrodynamic bearings, the reactions at each hydrodynamic bearing, and hence its stiffness and damping properties depend not only on the bearing type, the operating conditions and the bearing dimensions but also on the relative lateral alignment between the journal and the bearing housing; the alignment, therefore, has a significant influence on the system stability and unbalance response. Additional complications arise if nonsymmetric bearing types such as elliptic or tilting pad bearings are present. An iterative procedure is outlined which enables the bearing reactions to be determined at any speed, thereby enabling even large systems such as turbomachinery to be rapidly analyzed in conjunction with existing linear rotor bearing vibration analysis software. Sample numerical examples show how misalignment and bearing type can affect the natural frequencies, the stability threshold, and the unbalance response of such statically indeterminate systems.

Commentary by Dr. Valentin Fuster
J. Tribol. 1998;120(4):789-794. doi:10.1115/1.2833780.

A theoretical analysis is presented of heat partition and surface temperatures for the grinding of hardened steel with both aluminum oxide and CBN wheels. The numerical predictions of the model are shown to agree with experimental results available in the literature. It is found that heat partition varies over a wide range depending on grinding conditions. Also, heat partition is a strong function of position inside the grinding zone. The presence of the fluid inside the grinding zone can reduce the heat flux into the workpiece and the workpiece temperature significantly. For typical grinding of steel with CBN wheels, or creep feed grinding of steel with aluminum oxide or CBN wheels, it is possible to keep the fluid active and therefore to reduce thermal damage. However, the analysis suggests that the fluid may not be effective inside the grinding zone, in the conventional grinding of steel with aluminum oxide, due to boiling.

Commentary by Dr. Valentin Fuster
J. Tribol. 1998;120(4):795-799. doi:10.1115/1.2833781.

Cathodic arc deposition forms ultra-thin amorphous hard carbon films of high sp3 content, high hardness, and low coefficient of friction. These properties make it of great interest for head/disk interface application, in particular for contact recording. In many cases, the tribological properties of the head disk interface could be improved by factors up to ten by applying cathodic arc overcoats to the slider or disk surface. This paper reviews the results of cathodic arc ultra-thin (2–10 nm) carbon overcoats for head/disk interface tribological applications.

Commentary by Dr. Valentin Fuster
J. Tribol. 1998;120(4):800-807. doi:10.1115/1.2833782.

This three part paper presents the experiment and numerical analysis of the friction of a thin-film rigid disk with circumferential surface texture. In Part III, we examine the friction of a disk on the unworn virgin and worn tracks at various relative humidities. The real contact areas and pressures on both tracks are estimated using the Hertz contact model of two-dimensional asperities in Part I and related to the frictional coefficients on the basis of the meniscus model in Part II. The analysis yields that the effect of meniscus is predominant in the flat contact situation, particularly on the worn track at high humidity, while the effect is negligible in the taper/flat edge contact situation on both the tracks even at high humidity.

Commentary by Dr. Valentin Fuster
J. Tribol. 1998;120(4):808-813. doi:10.1115/1.2833783.

High adhesion is often encountered at contact interfaces of miniaturized devices, known as microelectromechanical systems, due to the development of capillary, electrostatic, and van der Waals attractive forces. In addition, deformation of contacting asperities on opposing surfaces produces a repulsive interfacial force. Permanent surface adhesion (referred to as stiction) occurs when the total interfacial force is attractive and exceeds the micromachine restoring force. In the present study, a three-dimensional fractal topography description is incorporated into an elastic-plastic contact mechanics analysis of asperity deformation. Simulation results revealing the contribution of capillary, electrostatic, van der Waals, and asperity deformation forces to the total interfacial force are presented for silicon/silicon and aluminum/aluminum material systems and different mean surface separation distances. Results demonstrate a pronounced effect of surface roughness on the micromachine critical stiffness required to overcome interfacial adhesion.

Commentary by Dr. Valentin Fuster
J. Tribol. 1998;120(4):814-819. doi:10.1115/1.2833784.

A combination of finite element analysis (FEA) calculations and resonant frequency measurements are applied for determining normal and lateral spring constants of microfabricated ceramic/gold cantilevers for friction force microscopes. The cantilever Si3 N4 and Au layers are combined analytically into an equivalent single composite layer. Bending and torsion behavior of the cantilever under typical operating forces are determined through FEA. Effective Young’s modulus for the composite Si3 N4 -Au beam from 172 to 185 GPa is determined through assimilation of FEA and fundamental resonant frequency measurements. Several current analytical solutions are compared to the full FEA evaluation. A new analytical expression is derived for obtaining the ratio of lateral to normal spring constants and thereby evaluation of absolute values of friction coefficients. Calibration plots are presented for assessment of both vertical and torsion spring constants of bicomponent cantilevers by measuring their resonant frequencies and thickness of gold overlay.

Commentary by Dr. Valentin Fuster
J. Tribol. 1998;120(4):820-828. doi:10.1115/1.2833785.

Titanium nitride films were deposited by the methods of ion beam enhanced deposition (IBED), plasma chemical vapor deposition (PCVD) and ion plating (IP). X-ray diffraction analysis was employed to determine the internal stress state of TiN film and 52100 steel substrate at both sides of the interface. The effect of stress state on their bonding strength and tribological behavior was analyzed systematically, their wear and failure mechanisms were discussed in detail as well.

Commentary by Dr. Valentin Fuster
J. Tribol. 1998;120(4):829-834. doi:10.1115/1.2833786.

Scuffing failure phenomenon in sliding lubricated contacts is studied experimentally in this work. Factors influencing the scuffing resistance of rough surfaces, including contact temperature, surface pitting, specific film thickness, and frictional heating, are investigated. A new criterion (the TFPI criterion) that takes into account the effect of oil in surface roughness valleys, microcontact characteristics, and the protective film formation mechanism is proposed to predict onset of scuffing failure. Good agreement is found between experimental scuffing data and predicted failure criterion. The results show that the modified TFPI value can be considered as a performance parameter that represents the scuffing failure resistance capacity and the effectiveness of the running-in process. A low modified TFPI value has a high scuffing resistance in lubricated systems.

Commentary by Dr. Valentin Fuster
J. Tribol. 1998;120(4):835-842. doi:10.1115/1.2833787.

The rotational speed requirements of high speed spindles led to the development of angular contact hybrid bearings with ceramic balls and PVD coated steel races. The present paper describes the determination and verification of critical coating fatigue stresses as well as their application in coating fatigue calculations of hybrid bearing steel races. The fatigue limits of low temperature deposited PVD coatings were determined by the application of the impact test and its FEM simulation and validated through their successful application to the prediction of coating life in rolling contact fatigue tests of coated specimens. Furthermore, a computer program that performs the quasi-static simulation of bearing operation yields the necessary kinematic and dynamic parameters for a FEM simulation of the stress field occurring in coated rings. For the investigated bearings, an adequate fatigue performance of their coated races was computationally exhibited. The PVD coated hybrid bearings illustrated the predicted behavior in long duration tests, conducted in full scale test rigs.

Commentary by Dr. Valentin Fuster

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