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RESEARCH PAPERS

J. Tribol. 1989;111(3):401-405. doi:10.1115/1.3261938.

Friction experiments were conducted with a reciprocating friction test apparatus to determine the effect of humidity and oxide films on the friction characteristics of ceramics slid against pure metals. The friction coefficients of silicon carbide were not affected very much by varying humidity or metals. On the other hand, the friction coefficients of nitride were affected by both humidity and the type of metal. Some of these metals showed high friction coefficients in high humid air. Preexisting thick oxide layers, which had formed on metal surfaces before sliding, caused an increase in the friction coefficients in an environment of 50 percent relative humidity (RH) air. The friction coefficients of silicon nitride to metal contacts were strongly affected by the oxidation of the metal surfaces, and those in 90 percent RH air correlated well with the Gibbs free energy of formation of the lowest metal oxide.

Commentary by Dr. Valentin Fuster
J. Tribol. 1989;111(3):406-412. doi:10.1115/1.3261939.

This paper describes a study on the performance characteristics of sector-shaped, high-speed thrust bearings subjected to the effects of both turbulence and fluid inertia forces. The basic lubrication equations are derived by integrating the momentum and continuity equations in the polar coordinates including the full inertia terms throughout the film thickness; and a numerical calculation technique combining the control volume integration and the Newton-Raphson linearization method is applied to solve the equations. The static characteristics such as the load carrying capacity and the pressure center are calculated for various values of pad extent angle and inner-to-outer radius ratio of a pad. The theoretical results of the load carrying capacity are compared with the experimental results. It was found that the fluid inertia forces have significant effects on the static characteristics of the bearings. Good agreement was obtained between theoretical and experimental results.

Commentary by Dr. Valentin Fuster
J. Tribol. 1989;111(3):413-417. doi:10.1115/1.3261940.

The transient elastohydrodynamic lubrication (EHL) process of cam-tappet pair in I. C. engine is analyzed with a full numerical method. The variations of pressure distribution and film profile as a function of rotation angle of cam shaft provide useful information in evaluating lubrication conditions as well as analyzing failures of contacting surfaces. Results show that the segment in cam contour from φ = 30 to φ = 110 deg is a difficult lubrication range, and surface failure may occur first in this range. This statement was confirmed by preliminary exprimental work conducted in a testing rig.

Commentary by Dr. Valentin Fuster
J. Tribol. 1989;111(3):418-425. doi:10.1115/1.3261941.

This paper is an attempt to provide an estimation of dynamic gear tooth loading due to coupled torsional-lateral vibrations in a geared rotor-hydrodynamic bearing system. The effects of mass unbalance and geometrical eccentricity of the pinion and the combined effects of manufacturing errors and profile modifications of gear teeth have been considered. Gear mesh compliance and damping at gear teeth are also included in the analysis. Journal lateral motions in the oil film spaces of hydrodynamic bearings are shown to be associated with variations in the angular velocity ratio of meshing gears and with dynamic loading of gear teeth. The journal center is observed to trace trajectories of limited amplitudes under stable operating conditions.

Commentary by Dr. Valentin Fuster
J. Tribol. 1989;111(3):426-429. doi:10.1115/1.3261942.

A computer program for calculating dynamic coefficients of journal bearings is necessary in designing fluid film journal bearings and an accuracy of the program is sometimes checked by the relation that the cross terms of linear damping coefficients of journal bearings are equal to each other, namely “Cxy = Cyx ”. However, the condition for this relation has not been clear. This paper shows that the relation “Cxy = Cyx ” holds in any type of finite width journal bearing when these are calculated under the following condition: (I) The governing Reynolds equation is linear in pressure or regarded as linear in numerical calculations; (II) Film thickness is given by h = c (1 + κcosθ); and (III) Boundary condition is homogeneous such as p=0 or dp/dn=0, where n denotes a normal to the boundary.

Commentary by Dr. Valentin Fuster
J. Tribol. 1989;111(3):430-439. doi:10.1115/1.3261943.

The elastic-plastic contact problem of a layered half-space indented by a rigid surface is solved with the finite element method. The case of a layer stiffer and harder than the substrate is analyzed and solutions for the contact pressure, subsurface stresses and strains, and location, shape, and growth of the plastic zone are presented for various layer thicknesses and indentation depths. Finite element results for a halfspace having the substrate properties are also given for comparison purposes. Differences between the elastic and elastic-plastic solutions are discussed and the significance of critical parameters such as the layer thickness, mechanical properties of layer and substrate materials, indentation depth, and interfacial friction on the threshold of plasticity, contact pressure distribution, and growth of the plastic zone are examined. Additionally, the mechanisms of layer decohesion and subsurface crack initiation are interpreted in light of the results obtained in this study.

Commentary by Dr. Valentin Fuster
J. Tribol. 1989;111(3):440-444. doi:10.1115/1.3261944.

A theoretical study of the effectiveness of solid particles dispersed in oil in the elastohydrodynamic line contact is presented. The analysis includes the variation of the viscosity and density of the lubricant as a function of pressure. The deformation of solid particles and that of the bounding surfaces are taken into consideration. Results are presented for the variation of the film thickness and the load carrying capacity as a function of the particle size, concentration, and properties of various types of particles.

Commentary by Dr. Valentin Fuster
J. Tribol. 1989;111(3):445-451. doi:10.1115/1.3261945.

Given the contact region between two bodies, the normal pressure distribution over the contact region, and the coefficient of friction, we seek to find all combinations of tangential forces and twisting moment (about the normal to the contact surface) for which fully developed sliding impends. As part of the solution we must determine the distribution of the surface tractions (shear stresses) and the location of the instantaneous center (IC) of the impending motion. New closed form solutions of the stated problem are found for circular contact patches with pressure distributions corresponding to (a): a flat stamp; and (b): elastic spheroids with Hertzian pressure distributions. For contact regions other than circular, no closed form solutions are known. We have developed numerical procedures to solve for arbitrary contact patches, with arbitrary distributions of normal pressure, and present carpet plots of tangential force components (Fx , Fy ) and IC coordinates for the following cases: flat ellipsoidal stamps; ellipsoidal indenters (Hertzian pressure); and a non-Hertzian, nonelliptical contact of a rail and wheel. Level curves of twisting moment Mz versus tangential force components are provided. Given any two of the three quantities (Fx , Fy , Mz ), the algorithms and the plots in this paper make it possible and convenient to find the remaining force or moment which will cause gross sliding to impend, for virtually arbitrary contact regions and arbitrary pressure distributions.

Commentary by Dr. Valentin Fuster
J. Tribol. 1989;111(3):452-458. doi:10.1115/1.3261946.

The analysis of real area of contact for particulate and thin-film rigid disks is presented. The mechanical properties (hardness and modulus) of the disk structure are measured by a nanoindentation apparatus and the surface texture is measured by a three-dimensional noncontact optical profiler. For typical rigid disks selected for this study, we find that most contacts are elastic; the same observation was made by Bhushan (1984) for flexible media. In the case of elastic contacts, the real area of contact is governed by the effective elastic modulus of the disk structure and its surface summit distribution. Typical values for the fractional real area of contact, number of contacts per unit area, mean asperity diameter, and mean real pressure for a thin-film disk are calculated to be of the order of 5 × 10−5 , 20/mm2 , 1μm, and 200 MPa, respectively.

Commentary by Dr. Valentin Fuster
J. Tribol. 1989;111(3):459-467. doi:10.1115/1.3261947.

With recent developments in N. C. manufacturing processes it is relatively straightforward to produce a journal bearing with spherical surfaces. Such a bearing offers two main advantages over a conventional bearing: it can tolerate much larger misalignment and it can resist axial forces. In this paper, the steady state performance of a spherical journal bearing is studied by using a finite bearing theory. The dynamic characteristics of the bearing are represented by eight displacement and velocity force coefficients and the boundary of bearing stability is determined. The effect of superlaminar flow upon the bearing performance is also studied, and typical bearing design charts are provided. In comparison, the behavior of the spherical journal bearing is found to be similar to that of an equivalent cylindrical bearing.

Commentary by Dr. Valentin Fuster
J. Tribol. 1989;111(3):468-474. doi:10.1115/1.3261948.

A wear model which permits the wear rate to be dependent on time is introduced to study the dynamic wear behavior observed in practice. In this model, it is postulated that the wear rate is proportional to a forcing term, I, which is contributed by the stress field induced by the frictional force at the asperity contacts; and inversely proportional to a wear resisting term, S, which is related to the material antiwear strength near the surface. One of the important characteristics of the dynamic wear model is that both I and S are now time dependent or wear dependent because when wear progresses the material strength at various layers would change and the stress field would also change as a result of the change of surface topography. Using this dynamic wear model, it is shown that the commonly observed running-in, steady-state, or accelerated wear phenomena can be explained.

Commentary by Dr. Valentin Fuster
J. Tribol. 1989;111(3):475-479. doi:10.1115/1.3261949.

Very general relations are derived in compact form for fluid-film lubrication with variable material properties. Rigorous consideration of mechanical work leads to simple (and apparently novel) power dissipation formulas, one of which is particularly appropriate for finite element calculations. Comparison is made to previous results for the particular example of a flooded journal bearing.

Commentary by Dr. Valentin Fuster
J. Tribol. 1989;111(3):484-490. doi:10.1115/1.3261955.

A new type herringbone grooved journal bearing, which produces an oil film bearing pressure with a shaft or bearing rotation in either direction, is proposed in this paper. A numerical analysis of the bearing parameters using the narrow groove theory and the Gümbel condition confirmed that the load capacity of this bearing and the radial load component (related to stability) do not differ greatly from those of a conventional bearing. The values of the bearing parameters which give maximum load capacity, and the values of the load capacity and its direction angle are also determined numerically for the case of either grooved member or smooth member rotation.

Commentary by Dr. Valentin Fuster
J. Tribol. 1989;111(3):491-494. doi:10.1115/1.3261956.

An analytical model of friction under combined linear sliding and spin of the contact area is presented. It is shown that the model, although based on simplifying assumptions, predicts reasonably well the characteristic features of the friction process.

Commentary by Dr. Valentin Fuster
J. Tribol. 1989;111(3):495-503. doi:10.1115/1.3261957.

The average film thickness theory is extended to gas lubrication possessing surface roughness in the slip flow regime. A simplified averaged Reynolds equation is derived and its applicability is confirmed through comparing with experiments. This averaging equation makes use of the mixed average film thickness defined as Have m = αHm + (1 − α)Hmˆ, where m = 1, 2 and 3; α indicates the mixing ratio; and H̄ and Ĥ denote the arithmetically and harmonically averaged film thicknesses. The experiments were performed using computer flying heads having precisely photolithography-fabricated longitudinal, transverse or checkered pattern roughnesses under submicron spacing conditions. From the excellent agreement obtained between the calculated and experimental results, it can be concluded that the assumption that velocity slippage occurs along the surface even if roughnes is present is justified, and that the approximate method is applicable for determining the surface roughness effects in the slip flow regime.

Commentary by Dr. Valentin Fuster
J. Tribol. 1989;111(3):504-509. doi:10.1115/1.3261958.

The tribological properties of titanium in sliding contact with single crystal Al2 O3 were studied to investigate wear mechanism associated with tribo-chemical reaction due to friction heating. Oxidational wear was observed. A theoretical approach to predict the wear rate of titanium was also studied.

Commentary by Dr. Valentin Fuster
J. Tribol. 1989;111(3):510-517. doi:10.1115/1.3261959.

This paper deals with the analysis of thrust bearings with tilted circular pads running under thermohydrodynamic conditions. During operation, a considerable quantity of air/gas bubbles is dispersed inside the lubricating oil and build a compressible medium. The important lubricant properties, namely viscosity and density are altered substantially due to bubble presence as well as temperature rise. The influence of the centrifugal forces become significant as the speed and load become higher. Such type of bearings has been herein investigated taking into account both influencing phenomena. The geometric and loading parameters are varied to show the combined effect on the bearing characteristic values. The governing equations of the THD theory are solved numerically using the finite difference method. The surface tension of bubbles and the change of bubble content with temperature and pressure are included in the governing equations as are the centrifugal forces.

Commentary by Dr. Valentin Fuster
J. Tribol. 1989;111(3):518-524. doi:10.1115/1.3261960.

The unbonded frictionless receding contact problem of a symmetrically loaded thin rectangular plate resting on an elastic layer is solved in this paper. The contact is assumed to be tensionless. The problem is transformed into the solution of three coupled two-dimensional singular integral equations. The possible contact pressure singularities along the plate edges and at the corners are treated using adaptive discretization. The contact regions are found iteratively since the problem is nonlinear. Contact regions and numerical values of displacements and contact pressures are presented to illustrate the influences of uplift, layer depth, aspect ratio, stiffness ratio, Poisson’s ratio, and other quantities.

Commentary by Dr. Valentin Fuster
J. Tribol. 1989;111(3):525-531. doi:10.1115/1.3261961.

The uncertainty in calculated results of the flow factors greatly limits the application of the average flow model [1] which otherwise is an approach with broad prospects for studying the lubrication behavior of rough surfaces. The effects of boundary conditions, grid systems, and surface statistics on the flow factors are discussed in the paper, and the reason why the calculated results for the flow factors obtained by different researchers widely differ from each other is revealed. The research shows that ∂p /∂y over the micro-bearing has an effect on the calculated value of flow factors; the influence of the sideflow arises from the simulation approach itself, in which a micro-bearing is used for determining flow factors; the grid systems and the procedure to generate random surfaces may change the statistics of the surfaces used in calculation and affect the results thereby.

Commentary by Dr. Valentin Fuster
J. Tribol. 1989;111(3):532-537. doi:10.1115/1.3261962.

A critical condition for seizure initiation has been investigated under a relatively low extrusion speed using an extrusion-type friction testing machine. To examine the effects of lubricant oil film thickness on seizure initiation, the oil film thicknesses at the tool-workpiece interface were estimated theoretically, and paraffinic mineral oils with three grades of viscosity were tested with various thicknesses of oil film applied, using commercially pure aluminium as the workpiece. The seizure phenomenon was always near the die exit. The lower the viscosity grade of oil used and the thinner the oil film applied, the shorter the critical punch stroke for seizure initiation became. Consequently, it has been clarified that the critical oil film thickness for seizure initiation was about 0.2 μm.

Commentary by Dr. Valentin Fuster
J. Tribol. 1989;111(3):538-544. doi:10.1115/1.3261963.

Hard coatings are more and more used to improve the mechanical and tribological behavior of surfaces. Thermomechanical cracking can occur in these coatings when they slide under heavy loads. We present a two-dimensional model of a finite thickness layered medium submitted to a moving heat source. The analytical solution of the temperature and thermoelastic stress fields is obtained using Fourier transforms. The behavior of each layer is described by transfer-matrices and a relation between the displacement- and stress-vectors is given. The originality of the study is the use of a Fast Fourier Transform algorithm. With this method, calculation time is reduced, no singularity problems are met in the inverse transform and each parameter (especially the thickness of the layers) can be studied over a wide range.

Commentary by Dr. Valentin Fuster
J. Tribol. 1989;111(3):545-552. doi:10.1115/1.3261964.

The compressible flow in a seal can be described by the Navier-Stokes equations in connection with a turbulence model (k–ε model) and an energy equation. By introducing a perturbation analysis in these differential equations we obtain zeroth order equations for the centered position and first order equations for small motions of the shaft about the centered position. These equations are solved by a finite difference technique. The zeroth order equations describe the leakage flow. Integrating the pressure solution of the first order equations yields the fluid forces and the rotordynamic coefficients, respectively.

Commentary by Dr. Valentin Fuster

DISCUSSIONS

Commentary by Dr. Valentin Fuster
Commentary by Dr. Valentin Fuster

TECHNICAL BRIEFS

J. Tribol. 1989;111(3):553-555. doi:10.1115/1.3261965.
Abstract
Topics: Gas bearings
Commentary by Dr. Valentin Fuster
J. Tribol. 1989;111(3):555-556. doi:10.1115/1.3261966.
Abstract
Commentary by Dr. Valentin Fuster
Commentary by Dr. Valentin Fuster

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