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TECHNICAL PAPERS

J. Tribol. 2002;124(4):653-667. doi:10.1115/1.1467920.

A three-dimensional elastic-plastic contact code based on semi-analytical method is presented and validated. The contact is solved within a Hertz framework. The reciprocal theorem with initial strains is then introduced, to express the surface geometry as a function of contact pressure and plastic strains. The irreversible nature of plasticity leads to an incremental formulation of the elastic-plastic contact problem, and an algorithm to solve this problem is set up. Closed form expression, which give residual stresses and surface displacements from plastic strains, are obtained by integration of the reciprocal theorem. The resolution of the elastic-plastic contact using the finite element (FE) method is discussed, and the semi-analytical code presented in this paper is validated by comparing results with experimental data from the nano-indentation test. Finally, the resolution of the rolling elastic-plastic contact is presented for smooth and dented surfaces and for a vertical or rolling loading. The main advantage of this code over classical FE codes is that the calculation time makes the transient analysis of three-dimensional contact problems affordable, including when a fine mesh is required.

Commentary by Dr. Valentin Fuster
J. Tribol. 2002;124(4):668-679. doi:10.1115/1.1467082.

Topographies of engineering surfaces normally have both random and periodic components, designated as surface roughness and waviness. True contacts between two such surfaces develop between the peaks, or asperities, on each surface. The waviness of the surfaces determines the spatial distribution of true contacts over the interface such that true contacts on wavy surfaces occur at and near the wave crests. This paper presents a computational method for analysis of contact between two rough wavy surfaces for which the nominal contact area may be arbitrarily large. The model used here combines local deflection of a contact point due only to the force acting on it with the non-local deflection of the same point due to forces at all other points of the surfaces. Using a three-stage loop similar to multi-level substructuring in finite element analysis and a nested iterative approach, the proposed method calculates the true contact area for a large number of asperity contacts, O(103). Results of calculations show how contact parameters change with external load and also demonstrate the validity of the method.

Commentary by Dr. Valentin Fuster
J. Tribol. 2002;124(4):680-688. doi:10.1115/1.1479698.

Complex crack networks are initiated in rails under Rolling Contact Fatigue. This paper attempts to model the RCF crack propagation with a particular emphasis on the branching conditions and the parameters that play a role on them. The numerical tool proposed rests on the combination of the author’s RCF model, Hourlier and Pineau’s criterion for the branch prediction and experimental data and the corresponding models for fatigue crack extension that are derived from a Joint European project. Parametric studies on the influence of (i) residual stresses, (ii) both interfacial crack and wheel/rail contact frictional effects, (iii) neighboring crack are conducted to reach a better understanding of the RC crack propagation behavior and more particularly the branch conditions, i.e., the length of the primary crack prior to branch formation and the branch direction.

Commentary by Dr. Valentin Fuster
J. Tribol. 2002;124(4):689-698. doi:10.1115/1.1491976.

A model was developed to study the elastohydrodynamics and contact mechanics of toroidal Continuously Variable Transmission (CVT) type contacts. The aim is to predict the fatigue life, traction and efficiency of such contacts with the intention of making optimizations based on design criteria and constraints. A generalized Reynolds equation was developed for isothermal, transient lubrication of elliptical rough contacts with mixed rolling, two-dimensional sliding, and spinning conditions, incorporating any non-Newtonian model, roughness asperity isothermal elastoplastic interactions, and a three-dimensional subsurface stress analysis. The output is in the form of film thickness and traction maps, including contact efficiency, three-dimensional stress fields, and, finally, the predicted fatigue lives of CVT contacts, based on the Ioannides-Harris life model. A parametric study reveals the effect of surface roughness, lubricant bulk temperature, contact ellipticity ratio, slide-roll ratio, and contact load on the fatigue life, traction and contact efficiency of CVTs, and allows for design optimizations based on a compromise between life, traction and efficiency.

Commentary by Dr. Valentin Fuster
J. Tribol. 2002;124(4):699-708. doi:10.1115/1.1491978.

Three-dimensional elastic-plastic rolling contact stress analysis was conducted incorporating elastic and plastic shakedown concepts. The Hertzian distribution was assumed for the normal surface contact load over a circular contact area. The tangential forces in both the rolling and lateral directions were considered and were assumed to be proportional to the Hertzian pressure. The elastic and plastic shakedown limits obtained for the three-dimensional contact problem revealed the role of both longitudinal and lateral shear traction on the shakedown results. An advanced cyclic plasticity model was implemented into a finite element code via the material subroutine. Finite element simulations were conducted to study the influences of the tangential surface forces in the two shear directions on residual stresses and residual strains. For all the cases simulated, the p0/k ratio (p0 is the maximum Hertzian pressure and k is the yield stress in shear) was 6.0. The Qx/P ratio, where Qx is the total tangential force on the contact surface in the rolling direction and P is the total normal surface pressure, ranged from 0 to 0.6. The Qy/P ratio (Qy is the total tangential force in the lateral direction) was either zero or 0.25. Residual stresses increase with increasing rolling passes but tend to stabilize. Residual strains also increase but the increase in residual strain per rolling pass (ratchetting rate) decays with rolling cycles. Residual stress levels can be as high as 2k when the Qx/P ratio is 0.6. Local accumulated shear strains can exceed 20 times the yield strain in shear after six rolling passes under extreme conditions. Comparisons of the two-dimensional and three-dimensional rolling contact results were provided to elucidate the differences in residual stresses and ratchetting strain predictions.

Commentary by Dr. Valentin Fuster
J. Tribol. 2002;124(4):709-715. doi:10.1115/1.1467087.

The behavior of the thermal elastohydrodynamic lubrication film in rough rolling/sliding line contacts at dynamic loads is investigated numerically. The lubricant is assumed to be a mixture of Newtonian and Ree-Eyring fluids. The results show that the maximum pressure in the contact region undergoes a noteworthy change with time due to dynamic loading and the effect of moving surface roughness. The variation of minimum film thickness and coefficient of friction with the composition of the lubricant is found to be dependent upon the reference viscosity ratio. The superposition of the effects of moving surface roughness and dynamic loading is shown to determine the behavior of time dependent film thickness and coefficient of friction.

Commentary by Dr. Valentin Fuster
J. Tribol. 2002;124(4):716-724. doi:10.1115/1.1472458.

A mathematical model is elaborated with analytical relations for transfer functions and for gas-film stiffness and damping coefficients for self-acting and externally pressurized gas journal bearings with four supply orifices positioned at the center plane for rotating shaft displacements near the bearing center. Averaging and corrective coefficients are elaborated. In this paper static and dynamic characteristics of self-acting gas bearings are investigated. Results derived using the developed mathematical model are compared with the results derived from numerical computations of a non-linear distributed parameter model of the gas bearings. The results obtained demonstrate that analytical data are in good agreement with the numerical data for wide range of parameters and the mathematical model developed makes the simple calculation of static and dynamic characteristics of self-acting gas bearings possible. Derived analytical relations for transfer functions and for gas-film coefficients of gas bearings provide an efficient means for designing rotor-bearing systems.

Commentary by Dr. Valentin Fuster
J. Tribol. 2002;124(4):725-735. doi:10.1115/1.1467632.

The paper considers the behavior of third bodies in dry contacts. A description of the mechanism operating in contacts is given and the influence of external parameters outlined. Both physicochemical and mechanical conditions greatly influence third body behavior. Depending on third-body composition, the external influence can be more or less dramatic. Due to difficulties with experimentation, numerical modeling is suggested as a complementary tool. Two approaches for such modeling are described, the continuum and the discrete approach. At present these models are at an early development stage (two-dimensional simulations), and great efforts should be made for their further development. While an experimental apparatus can study phenomena at only one scale; namely the nanometer with AFM, or the micron to millimeter with fretting machines, modeling is able to range from the microscopic properties (particle interactions like coefficient of restitution) to the macroscopic properties by integration or averaging (load capacity, friction coefficient).

Commentary by Dr. Valentin Fuster
J. Tribol. 2002;124(4):736-742. doi:10.1115/1.1484113.

A closed-form average lubrication equation for thin film grain flow with the effects of surface roughness is derived. This equation is based on Haff’s grain flow theory and also the flow factors proposed by Patir and Cheng. The flow factors, derived by the perturbation approach and coordinate transformation, are expressed in terms of surface characteristics (three characteristics for each surface: roughness orientation, Peklenik number and standard derivation) and particle size. Finally, the flow factors under different surface characteristics and particle size are discussed.

Commentary by Dr. Valentin Fuster
J. Tribol. 2002;124(4):743-754. doi:10.1115/1.1472459.

A numerical analysis of stiffness and damping coefficients for gas film face seals in three degrees of freedom is presented in this paper. By applying small perturbation approximation, the steady and perturbed Reynolds equations, taking account of both hydrodynamic and hydrostatic effects, are obtained and solved by finite element method. Several numerical samples, including externally pressurized annular thrust gas bearings and spiral groove thrust gas bearings, validate the model and numerical algorithm. The results show that the interactions between axial and angular perturbation are negligible. Hence, in the dynamic analysis of gas film face seals, the perturbation in three degrees of freedom can be simplified as two independent ones, an axial movement and an angular wobble around two orthogonal axes perpendicular to axial direction.

Commentary by Dr. Valentin Fuster
J. Tribol. 2002;124(4):755-761. doi:10.1115/1.1467635.

The gas film stiffness and damping properties for a spiral grooved mechanical face seal in a flexibly mounted stator configuration are computed using the step jump method and a novel direct numerical frequency response method. The seal model has three degrees of freedom, including axial displacement of the stator and two stator tilts about mutually perpendicular diametral axes. Results from both methods agree well with previously published results computed using the perturbation method, but the two new methods have the advantage of employing computer programs used in the direct numerical simulation of motion. Based on the linearized analysis, the two angular modes are proven to be coupled together and decoupled from the axial mode. Anomalies in the gas film properties tend to occur at large compressibility numbers. The step jump method requires less computing time than the direct frequency response method but at a sacrifice in accuracy at high excitation frequencies.

Commentary by Dr. Valentin Fuster
J. Tribol. 2002;124(4):762-770. doi:10.1115/1.1479699.

Two new air bearing slider designs are presented for storage densities greater than 100 Gb/in2 in hard disk drive (HDD) applications. Their dynamic frequencies and mode shapes are characterized, and they are used to study the flying height modulation (FHM) over wavy disks due to geometric effects as opposed to dynamic effects. It is found that low pitch designs experience large FHM at wavelengths on the order of the length of the sliders to one-eighth the length of the sliders due to a complex phase shift in the sliders trailing edge response as compared to the disk waviness. FHM due to disk waviness wavelengths from 2 mm to 0.16 mm was found to be a function of the sliders’ attitude (pitch angle) and the air bearing surface (ABS) geometry (pressure distribution over the ABS). The results presented suggest that the pitch should be greater than 100 μrad for the ABS designs presented and attention needs to be focused on the ABS design and disk morphology to avoid unacceptable FHM. An ABS design was introduced to reiterate the findings on geometric FHM showing an 83 percent decrease in geometric FHM. The FHM due to geometric effects of the slider designs studied in this paper could possibly be predicted by the disk morphology alone.

Commentary by Dr. Valentin Fuster
J. Tribol. 2002;124(4):771-774. doi:10.1115/1.1467613.

The influence of alumina and titanium carbide, components of magnetic recording sliders, on the carbon gasification reaction was investigated. Pure alumina and titanium carbide powders were each combined with graphite powder and subjected to thermogravimetric analysis (TGA). The molar ratio ranged from 0 to 20 mol percent; graphite powder was the balance. From the thermogravimetric analysis, the activation energy (Ea) of the reactions was determined. It was found that the activation energy for carbon gasification reduced slightly for increasing alumina mole percentage. Titanium carbide additions markedly increased the activation energy. This increase indicates a competitive oxidation reaction that forms titanium oxide, as confirmed by X-ray diffraction (XRD). As a result of these observations, titanium oxide was also mixed with graphite powders and analyzed by TGA. Titanium oxide has an activation energy behavior that becomes more complex with increasing mole percentage: the activation energy first increases and then decreases. These data are presented and the oxidation reaction is proposed.

Commentary by Dr. Valentin Fuster
J. Tribol. 2002;124(4):775-784. doi:10.1115/1.1467088.

An elastic-plastic contact analysis based on a finite element model and real surface topographies was performed to elucidate the evolution of deformation at the head-disk interface. The topographies of the head and disk surfaces were represented by an equivalent profile generated using a modified two-variable Weierstrass-Mandelbrot function, with fractal parameters determined from images of head and disk surfaces. A region of the equivalent rough surface profile was selected for analysis based on topography scale considerations and contact simulation results. The evolution of plasticity and the likelihood of cracking in the overcoat and the magnetic layer are interpreted in light of results for the subsurface von Mises equivalent stress, equivalent plastic strain, and maximum first principal stress. The finite element model provides insight into the elastic-plastic deformation behavior of the layered medium in terms of the thickness, mechanical properties, and residual stress in the carbon overcoat.

Commentary by Dr. Valentin Fuster
J. Tribol. 2002;124(4):785-793. doi:10.1115/1.1482117.

The Greenwood and Williamson microcontact model of rough surfaces is modified to include the presence of a surface layer which is stiffer and harder than the substrate. The axisymmetric contact between a rigid spherical asperity and an elastic layered halfspace is analyzed numerically and correction factors for the contact area, load and the maximum von Mises stress are approximated to a closed form by using curve fits of the numerical results. The correction factors for the contact area and load are applied to the GW model to reflect the effect of the finite layer thickness and the substrate material. The correction factor for the maximum von Mises stress is used to calculate the plasticity index for layered surfaces. Parametric calculation of the ratio of plastic contact area to real contact area is carried out for a TiN-coated steel surface. The modified GW model is compared with a more rigorous real surface model and the validity of the present model is discussed. When the layer thickness is sufficiently large, the influence of the soft substrate can be neglected. A simple criterion for realizing the contact free of the effect of the substrate is proposed.

Commentary by Dr. Valentin Fuster
J. Tribol. 2002;124(4):794-800. doi:10.1115/1.1456456.

This paper studies how temperature variations affect natural frequencies of rocking vibration of a rotating disk and spindle system through mathematical modeling and experimental measurements. Existing literature has shown that both radial bearing stiffness krr and natural frequency ω01B of one-nodal-diameter disk modes could substantially affect natural frequencies ω01U of rocking vibration. In this paper, a preliminary experiment first identifies that relaxation of bearing stiffness krr is the dominating factor to shift the natural frequency ω01U at elevated temperatures. In addition, the bearing relaxation primarily results from thermal mismatch between the bearing raceways and the rotating hub. Guided by the experimental results, a mathematical model is developed to determine how temperature variations affect bearing contact angles, bearing preloads, and subsequently the radial bearing stiffness krr. Based on the bearing stiffness krr and disk frequency ω01B at elevated temperatures, one can predict natural frequency ω01U of rocking vibration through the mathematical model by Shen and Ku (1997). Finally, ω01U of a rotating disk and spindle system are measured in a thermal chamber to validate the theoretical predictions.

Commentary by Dr. Valentin Fuster
J. Tribol. 2002;124(4):801-810. doi:10.1115/1.1484112.

The authors developed a computer simulator for in-contact head slider motion where a 3-DOF model of head-suspension assembly was introduced and effects of meniscus force between the slider and the disk were considered. The contact force between a contact pad and a disk surface was taken into account and the dynamic characteristics of an in-contact head slider were discussed from the viewpoints of both bouncing vibration and wear durability by not only 3-DOF head-suspension assembly model over a sinusoidal disk surface undulation but also 1-DOF head-suspension assembly model over a sinusoidal disk surface undulation. In addition to the critical frequency of bouncing, the critical frequency of pressure was introduced. As a result of 3-DOF simulation and 1-DOF analysis, it was found that there exists an optimum surface energy at which the stability of bouncing vibration and wear durability becomes highest under perfect contact condition. Furthermore, the behavior of the optimum point for several design parameters were made clear.

Commentary by Dr. Valentin Fuster
J. Tribol. 2002;124(4):811-814. doi:10.1115/1.1456090.

In this paper, a viscosity modification model is developed which can be applied to describe the thin film lubrication problems. The viscosity distribution along the direction normal to solid surface is approached by a function proposed in this paper. Based on the formula, lubricating problem of thin film lubrication (TFL) in isothermal and incompressible condition is solved and the outcome is compared to the experimental data. In thin film lubrication, according to the computation outcomes, the lubrication film thickness is much greater than that in elastohydrodynamic lubrication (EHL). When the velocity is adequately low (i.e., film thickness is thin enough), the pressure distribution in the contact area is close to Hertzian distribution in which the second ridge of pressure is not obvious enough. The film shape demonstrates the earlobe-like form in thin film lubrication, which is similar to EHL while the film is comparatively thicker. The transformation relationships between film thickness and loads, velocities or atmosphere viscosity in thin film lubrication differ from those in EHL so that the transition from thin film lubrication to EHL can be clearly seen.

Commentary by Dr. Valentin Fuster
J. Tribol. 2002;124(4):815-821. doi:10.1115/1.1430672.

The effect of axially-varying clearance on microfabricated gas journal bearings is explored. This variation commonly arises from difficulties inherent to etching deep, narrow channels. Two types of clearance variation commonly observed in etched bearings are investigated: taper and bow. Both shapes are shown to have a detrimental effect on load capacity and bearing stability compared to a cylindrical bearing with the minimum clearance. For the same variation magnitude, taper is shown to have a more serious effect, including complete closure of the stability corridor at low speed for some cases. Methods are suggested for estimating variable-clearance bearing performance using cylindrical bearing data.

Commentary by Dr. Valentin Fuster
J. Tribol. 2002;124(4):822-828. doi:10.1115/1.1494088.

Copper cylinder-on-silver plated copper cylinder wear tests in oscillating motion were carried out in oil. Time-dependent mild to severe wear transition was observed for a certain large load. The surface analyses and wear simulations were conducted and they revealed that the wear transition was attributable not to the wear-out of the silver plating, but to the increase of the contact pressure with increase of the number of oscillations, which was caused by the increase of sliding pair shape inconformity due to wear.

Commentary by Dr. Valentin Fuster
J. Tribol. 2002;124(4):829-833. doi:10.1115/1.1467085.

A method was developed to measure the wear of general engineering surfaces based on the roughness parameters of the worn surfaces. This method does not require any information of the initial surface. The surface height distribution is described using Johnson translatory system where the loss of surface height is attributed to wear. Experiments of engine running in were conducted to validate the method. The results show that the current method can determine wear comparable to surface roughness. The current approach simplifies the profilometrical wear measurement and extends such a measurement to non-Gaussian surfaces.

Commentary by Dr. Valentin Fuster
J. Tribol. 2002;124(4):834-839. doi:10.1115/1.1456088.

A carbon fabric composite of Polyetherimide (PEI) was fabricated and studied for fretting wear behavior along with neat PEI. The operating parameters were load, temperature, amplitude and frequency of fretting. It was observed that carbon fabric proved to be significantly beneficial for reducing friction and wear of PEI. The friction coefficient of PEI was quite high and independent of operating parameters. For the carbon fabric composites (CFC) it reduced from 0.3 to 0.18 with an increase in load. On the other hand it showed marginal increase (0.18 to 0.28) with increase in temperature from 25°C to 200°C. The wear rate of the composite, CFC showed little variation with increase in load and temperature. Amplitude and frequency also proved to be important influencing parameters. Microscopic studies proved useful for understanding wear mechanism.

Commentary by Dr. Valentin Fuster
J. Tribol. 2002;124(4):840-845. doi:10.1115/1.1454106.

Hot rolling tests were performed on low carbon steel strips with the objective of determining the coefficient of friction as a function of the process variables. The growth of the scale prior to rolling was controlled and the thickness of the layer of scale at the entry remained in the range of 20–100 μm, somewhat higher than in the finishing train of a hot strip mill. Roll separating forces, roll torques, the speed, the reduction and the entry temperature were monitored. The effective coefficient of friction was determined by using a one-dimensional model of the flat rolling process. The coefficient was chosen to allow matching the measured and calculated roll force and the roll torque. An empirical relation, connecting the coefficient of friction to process variables was obtained by non-linear regression analysis.

Commentary by Dr. Valentin Fuster
J. Tribol. 2002;124(4):846-851. doi:10.1115/1.1330732.

During some deep drawing operations liquid lubricants are used under the blankholder to reduce friction coefficients. Under the clamping action of the blankholder, lubricants will be squeezed out resulting in a changing film thickness after the initial application of the blankholder load. A relationship between kinetic friction coefficient values and the loading duration of the blankholder can be observed from analysis of results recorded during simulative testing. By using a numerical model to combine empirical measurements, friction coefficients during boundary lubrication, lubricant film thickness with sheet surface topography data, it can be shown that the coefficient of friction can reliably be predicted for a given loading duration.

Commentary by Dr. Valentin Fuster

TECHNICAL NOTES

J. Tribol. 2002;124(4):852-856. doi:10.1115/1.1467594.

A theoretical analysis is carried out in closed-form to quantitatively describe the pressing of an individual surface asperity into its elastic bulk when subjected to normal loads. To this end, a single asperity is simulated by a paraboloid of revolution of an arbitrary even power. The investigation is based on theory of elastic contact as originally developed by Shtaerman. It is shown that additional pressing of an individual asperity into the elastic bulk essentially depends upon four parameters: the elastic compression of its apex, the initial magnitude of the height of the asperity, a constant that characterizes the shape of the asperity peak, and the elastic properties of the materials involved in the contact. The analysis shows that the impression of the asperity into the elastic bulk increases for decreasing smoothness of the paraboloid. It will be demonstrated that the impression of the asperity into the elastic bulk, if both are made of the same material, typically reaches 50 percent of the value of elastic compression of the asperity peak.

Commentary by Dr. Valentin Fuster
J. Tribol. 2002;124(4):856-858. doi:10.1115/1.1467595.

The knowledge of the entraining velocity is necessary for the investigation of lubricated contacts. The entraining velocity is the average of the surface velocities of the two bodies in contact relative to the contact itself; its estimation can be actually not always immediate. In this work the general case of two pairing cylindrical surfaces in planar relative motion is analyzed from a kinematical point of view. Formulas for the evaluation of the entraining velocity are presented that are directly applicable to any case of connected members of a mechanism. The physical meaning of the terms of the proposed formulas is also briefly investigated from a lubrication point of view.

J. Tribol. 2002;124(4):858-863. doi:10.1115/1.1467639.

Willis,  R., 1828, “ On the Pressure Produced on a Flat Plate When Opposed to a Stream of Air Issuing From an Orifice on a Plane Surface,” Trans. Cambridge Philos. Soc., TCPSAE3, Part 1, pp. 121–140.tcpTCPSAE0371-5779Asawa,  Gridhari L., Pande,  Pramod K., and Godbole,  Pramond N. A., 1985, “ Radial Turbulent Flow Between Parallel Plates,” J. Hydraul. Eng., JHEND8111(4), pp. 695–712.9fnJHEND80733-9429Boyack,  B. E., and Rice,  W., 1970, “ An Integral Solution for the Laminar Radial Outflow of a Viscous Fluid Between Parallel Stationary Discs,” ASME J. Basic Eng., JBAEAI92(3), pp. 662–663.987JBAEAI0021-9223Ervin,  J. S., Suryanarayana,  N. V., and Ng,  Hon Chai, 1989, “ Radial Turbulent Flow of a Fluid Between Two Coaxial Discs,” ASME J. Fluids Eng., JFEGA4111, pp. 378–383.97kJFEGA40098-2202Gano,  R. F., Johnson,  A. G., and Malanoski,  S. B., 1988, “ Radial Flow Between Axisymmetric Nonparallel Plates of Small Slope,” ASME J. Tribol., JOTRE9110, pp. 343–347.jtiJOTRE90742-4787Geiger,  D., Fara,  H. D., and Street,  N., 1964, “ Steady Radial Flow Between Parallel Plates,” ASME J. Appl. Mech., JAMCAV31, pp. 354–356.97dJAMCAV0021-8936Lee,  Pai-Mow, and Lin,  Sui, 1985, “ Pressure Distribution for Radial Inflow Between Narrowly Spaced Discs,” ASME J. Fluids Eng., JFEGA4107, pp. 339–341.97kJFEGA40098-2202Li,  P. M., Mirza,  S. A., and Lin,  S., 1989, “ Pressure Distribution in Radial Flow Between Discs,” J. Eng. Mech., JENMDT115, pp. 210–215.979JENMDT0733-9399Moller,  P. S., 1963, “ Radial Flow Without Swirl Between Parallel Discs,” Aeronaut. Q., AEQUAY14, pp. 163–186.aeqAEQUAY0001-9259Moller, P. S., “A Radial Diffuser Using Incompressible Flow Between Narrowly Spaced Discs,” Paper No. 65-FE-12.Savage,  S. B., 1964, “ Laminar Radial Flow Between Parallel Plates,” ASME J. Appl. Mech., JAMCAV31, pp. 594–596.97dJAMCAV0021-8936Solovyov,  S. E., Volpert,  V. A., and Davtyan,  S. P., 1993, “ Radially Symmetric Flow of a Reacting Liquid With Changing Viscosity,” SIAM (Soc. Ind. Appl. Math.) J. Appl. Math., SMJMAP53, pp. 907–914.smjSMJMAP0036-1399Vatistas,  G. H., 1988, “ Radial Flow Between Two Closely Placed Flat Discs,” AIAA J., AIAJAH26, pp. 887–889.aiaAIAJAH0001-1452Vatistas,  G. H., 1990, “ Radial Inflow Within Two Flat Discs,” AIAA J., AIAJAH28, pp. 1308–1310.aiaAIAJAH0001-1452Walanetz,  L. F., 1956, “ A Suction Device Using Air Under Pressure,” ASME J. Appl. Mech., JAMCAV78, pp. 269–272.97dJAMCAV0021-8936Wilkes,  J. O., and Churchill,  S. W., 1966, “ The Finite Difference Computation of Natural Convection in a Rectangular Enclosure,” AIChE J., AICEAC12, pp. 161–170.aicAICEAC0001-1541Woolard,  H. W., 1957, “ A Theoretical Analysis of the Viscous Flow in a Narrowly Spaced Radial Diffuser,” ASME J. Appl. Mech., JAMCAV24, pp. 9–15.97dJAMCAV0021-8936

J. Tribol. 2002;124(4):863-865. doi:10.1115/1.1467640.

A novel technology to smooth the metal tab surfaces using a pulsed laser beam is applied to reduce the wear of the load/unload ramps used in disk drives that employ load/unload technology. The laser pulse length, pulse energy and the pulse repetition rate are so chosen that they cause the surface layer of the load/unload tab, approximately 2–3 um deep, to melt and refreeze quickly. As the surface layer melts, the surface tension of the melt removes most of the micro roughness and a smooth surface is obtained. The reduction in the micro surface roughness is confirmed by the AFM traces and a sharp decrease in the light scattered from the tab surface. In wear tests, such tabs show a remarkable improvement in the wear of the plastic load/unload ramps, allowing 5–10 × more load/unload cycles for a given amount of ramp wear.

J. Tribol. 2002;124(4):865-869. doi:10.1115/1.1467641.

The laminar squeeze flow of a viscous incompressible fluid between a flat circular disk and an axisymmetric curved disk of arbitrary shape is investigated theoretically using modified lubrication theory. The characteristics of squeeze film are investigated through inertia and curvature effects on the normal force exerted on the upper curved moving disk described by an exponential function for the sinusoidal squeeze motion. The constant force squeezing state is also examined. It has been observed that the load carrying capacity of the curved squeeze film is strongly influenced by the curvature and inertia effects.

J. Tribol. 2002;124(4):869-873. doi:10.1115/1.1479700.

A complete database for Couette flow rate (QC(D,α12),0.1≤α1,α2≤1.0,0.01≤D≤100, where D=inverse Knudsen number) for ultra-thin gas film lubrication problems is advanced. When the accommodation coefficients (AC) of the two lubricating surfaces are different 1≠α2), the Couette flow rate in the modified molecular gas film lubrication (MMGL) equation should be corrected. The linearized Boltzmann equation (under small Mach number conditions) is solved numerically for the case of non-symmetric molecular interactions 1≠α2). The Couette flow rate is then calculated, and the database is constructed. The present database can be easily implemented in the MMGL equation. In addition, the present database extends the previously published results for 0.1≤α1,α2≤0.7. The database for low ACs is valuable in the analysis and applications of MEMS devices (bushings of electrostatic micro motors, micro bearings, magnetic head/disk interfaces, etc.), and their future development.

J. Tribol. 2002;124(4):874-877. doi:10.1115/1.1482118.

In this work, the operating sensitivity of the hydrostatic thrust bearing with respect to pressure-induced deformations will be studied in a stationary setting. Using the classical lubrication equations for low Reynold’s number flow, closed-form expressions are generated for describing the pressure distribution, the flow rate, and the load carrying capacity of the bearing. These expressions are developed to consider deformations of the bearing that result in either concave or convex shapes relative to a flat thrust surface. The impact of both shapes is compared, and the sensitivity of the flow rate and the load carrying capacity of the bearing with respect to the magnitude of the deformation is discussed. In summary, it is shown that all deformations increase the flow rate of the bearing and that concave deformations increase the load carrying capacity while convex deformations decrease this same quantity relative to a non-deformed bearing condition.

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