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RESEARCH PAPERS

J. Tribol. 1988;110(3):387-393. doi:10.1115/1.3261640.

This paper presents a fast method for calculating the dynamic coefficients of the finite width journal bearings under quasi Reynolds boundary condition in which the trailing boundary line is given by a straight line and the continuity of bulk flow across this line is ensured. Calculated linear stiffness and damping coefficients agree well with the data of Lund and Thomsen [1]. The time required by this calculation with HITAC M682H is only 0.1–0.3 seconds (about 1/100 of the time required by the ordinary FDM), which suggests the possibility of real time journal bearing designs without using the database of the dynamic coefficients.

Commentary by Dr. Valentin Fuster
J. Tribol. 1988;110(3):394-401. doi:10.1115/1.3261641.

The behavior of zinc dithiophosphate (ZnDTP) is investigated for the antiwear properties in SiC-steel and Si3 N4 -steel sliding contact systems under boundary lubrication. Reaction products formed on the steel surfaces under the sliding contact differ in the chemical compositions and the thickness between these couples. These differences are specifically related to the physical properties of mating materials such as heat conductivity and friction coefficient. The reaction products are analyzed by SEM (scanning electron microscope), EPMA (electron probe microanalysis), AES (Auger electron spectroscope), and PAS (photoacoustic spectroscopy), and it is confirmed that iron phosphate for SiC-steel and iron phosphate and zinc sulfide (or some complex compound containing equal amounts of Zn and S in atomic ratio) for Si3 N4 -steel couple exist on the steel surface, respectively. An examination is conducted on steel-steel couple in comparison with ceramics-steel couples, and the atomic ratio (Zn:P:S) of the constituent elements of the reaction products coincides fairly with that of SiC-steel couple.

Commentary by Dr. Valentin Fuster
J. Tribol. 1988;110(3):402-407. doi:10.1115/1.3261642.

Recent advances in mathematical analysis of problems described by several small parameters equations are used to revisit the general roughness problem. In this paper, we put forward a new qualitative study of a thin film flow with a rapidly varying gap. Using an asymptotic analysis of the three-dimensional Stokes system we obtain a family of new generalized Reynolds equations. We are led to distinguish three different cases in which the periodic roughness wavelength is on the order of, greater or shorter than the mean thickness of the gap.

Commentary by Dr. Valentin Fuster
J. Tribol. 1988;110(3):408-413. doi:10.1115/1.3261643.

Crack propagation in a rotating inner raceway of a high-speed roller bearing is analyzed using the boundary integral method. The model consists of an edge plate under plane strain condition upon which varying Hertzian stress fields are superimposed. A multidomain boundary integral equation using quadratic elements was written to determine the stress intensity factors KI and KII at the crack tip for various roller positions. The multidomain formulation allows the two faces of the crack to be modeled in two different subregions making it possible to analyze crack closure when the roller is positioned on or close to the crack line. KI and KII stress intensity factors along any direction were computed. These calculations permit determination of crack growth direction along which the average KI times the alternating KI is maximum.

Commentary by Dr. Valentin Fuster
J. Tribol. 1988;110(3):414-420. doi:10.1115/1.3261644.

Our earlier work on the flow of a non-Newtonian fluid of the differential type in a journal bearing is extended here to include nonisothermal operations and temperature dependent viscosity. We show that for the type of lubricant investigated, even a slight departure from Newtonian behavior renders the bearing performance relatively insensitive to changes in lubricant temperature. But whether this change in lubricant behavior actually results in improved load capacity depends on the value and the sign of the material parameters.

Commentary by Dr. Valentin Fuster
J. Tribol. 1988;110(3):421-426. doi:10.1115/1.3261645.

The effect of longitudinal and transverse roughness on the elastohydrodynamic lubrication of circular contacts was investigated numerically for two different lubricating conditions. The influence of the amplitude and the wavelength of the roughness texture was also studied. The results are compared with predictions from the flow factor method.

Commentary by Dr. Valentin Fuster
J. Tribol. 1988;110(3):427-433. doi:10.1115/1.3261646.

The method of matched expansions is employed to analyze the steady state operation of a finite gas-lubricated flat sector bearing for the case where the ratio of radial to circumferential dimensions is small and the relevant bearing number, Λ, is moderate. This technique yields general expressions for the pressure distribution, load bearing capacity, power loss and center of pressure location that are valid for a significant and continuous range of bearing dimensions, orientations and operating conditions. Comparisons are made, where possible, with the existing results from the literature obtained by numerical methods.

Commentary by Dr. Valentin Fuster
J. Tribol. 1988;110(3):434-438. doi:10.1115/1.3261647.

The friction and wear characteristics of SiC whisker containing composite silicon nitride were studied. Silicon nitride powder which contains densification aids of Y2 O3 and La2 O3 was mixed with silicon carbide whiskers (10, 20, and 30 wt percent) and then hot-pressed at a temperature of 1800° C. Wear experiments were carried out with a ring on block type apparatus at the sliding conditions of the sliding speed of 314 mm/sec and the load of 5 N and experimental results showed that the SiC whisker had an evident effect to reduce the wear rate of silicon nitride blocks. Silicon carbide whiskers are not dispersed isotropically, but they are oriented to the direction which is perpendicular to the pressure of hot-press sintering. Therefore, wear characteristics of the composite ceramics are anisotropic. The effect of SiC whisker on wear rate of silicon nitride is larger for the surface which is perpendicular to the direction of pressure of hot-press sintering that than that for the surface which is parallel to the pressure. Although SiC whiskers have no evident effect on friction coefficient of silicon nitride at the above sliding condition, even small contents of SiC whiskers, such as 10 wt percent, reduce considerably the coefficient of friction and show similar frictional characteristics to that of monolithic silicon carbide at the lower sliding speed of 10 mm/min.

Commentary by Dr. Valentin Fuster
J. Tribol. 1988;110(3):439-447. doi:10.1115/1.3261648.

The flow field of a hydrodynamic journal bearing is calculated by the iterative solution of the system of Reynolds and energy equations. In the case of reverse flow at the film inlet, the temperature profile there can not be prescribed as a boundary condition but has to be determined from the flow in the film. This is achieved by a separate integration of the energy equation in the reverse flow area. The flow in the cavitation regions is approximated by a theoretical model leading to a form of the energy equation similar to that for pressure regions, thus enabling the integration of the energy equation over the whole film.

Commentary by Dr. Valentin Fuster
J. Tribol. 1988;110(3):448-455. doi:10.1115/1.3261649.

The present work deals with the investigations carried out on the various rolling element bearings after being operated under the influence of electric fields, and pure rolling friction on the roller bearing test machine. The significant magnetic flux density was detected on surfaces of the bearings lubricated with low-resistivity grease under the influence of electrical fields. No such phenomenon was observed either on bearings using high or low-resistivity greases under pure rolling friction or on bearings lubricated with high-resistivity grease under the influence of electrical fields. New bearing surfaces do not show significant magnetic flux density but it has been detected after long operation on different motor bearings, lubricated with low resistivity greases. The electroadhesion forces in the bearings using low-resistivity greases increase under the influence of electrical fields in contrast to those with high resistivity greases. Under pure rolling friction resistivity of greases do not affect the electroadhesion forces. The investigations reported in this paper along with the study of damaged/corrugated surfaces, and deterioration of the used greases [1, 2, 3], the leakage of current leading to failure of the noninsulated motor bearings can be established.

Commentary by Dr. Valentin Fuster
J. Tribol. 1988;110(3):456-461. doi:10.1115/1.3261650.

The general Reynolds equation for self-acting, finite length gas-lubricated journal bearings is solved using an interior collocation method. The method assumes an approximate solution to the governing differential equation in the form of a series of trial functions, wn , with n unknown coefficients. The coefficients are evaluated by substituting the assumed solution in the governing differential equation, and forcing the residual (error) at n collocation points in the computational domain to be zero. The effectiveness of the collocation method is demonstrated by using the technique for the static and dynamic analysis of a journal supported by a plane gas bearing. The results from the collocation method agree very well with those obtained from a finite difference technique. Periodic orbit plots for a single journal in a finite bearing are presented for various journal unbalances and speeds. The collocation method is shown to be an order of magnitude computationally faster than the finite difference method. The method can be extended to other bearing types such as slider, hydrostatic and tilting pad bearings.

Commentary by Dr. Valentin Fuster
J. Tribol. 1988;110(3):462-466. doi:10.1115/1.3261651.

A 1.2-kW, continuous wave, CO2 -gas laser was used to transformation harden or melt the surface of gray and ductile cast irons. Effects of surface-hardened layers on solid particle erosion showed that the erosion rate decreased with an increase in surface hardness and case depth. The order of matrix microstructures that increased the erosion rate were ledeburite, tempered martensite, and pearlite. These results were opposite to those observed in bulk-hardened alloys. Erosion mechanisms of brittle, gray iron included micromachining in the untreated condition and grain boundary cracking in the laser-treated condition. In contrast, erosion modes of ductile iron were plastic flow followed by cracking in the untreated condition and platelet formation and fatigue in the laser-treated conditions. The beneficial effects of surface hardening on erosion were examined and discussed.

Commentary by Dr. Valentin Fuster
J. Tribol. 1988;110(3):467-476. doi:10.1115/1.3261652.

Huge thrust bearings with centrally pivoted and tilted pads operating under heavy loads are analzyed using the (thermoelastohydrodynamic) TEHD-theory. The Reynolds equation, the energy equation of the oil film, and the heat conduction equation of the bearing, all are coupled with the deflection equation and solved simultaneously in order to determine the bearing characteristic values. The first three equations are transformed by means of finite difference method and the last equation is solved using the method of Ritz-Galerkin. Based on successive approximation method a new iterative scheme is presented to apply the heavy load incrementally which provides a successful convergence of the equation system. In order to find the equilibrium state of the pad, another iterative scheme based on a controlled change of the pad tilts is applied. The tilts are changed as a function of the offset of the hydrodynamic resultant force from the pivot location. It is proved that the new scheme is quite efficient in successful convergence of the equation system and in saving CPU time.

Commentary by Dr. Valentin Fuster
J. Tribol. 1988;110(3):477-485. doi:10.1115/1.3261653.

Based on the finite element method, the elastic contact problem of a layered semi-infinite solid compressed by a rigid surface is solved numerically. The case of a surface layer stiffer than the substrate is considered, and general solutions for the subsurface stress and deformation fields are presented for relatively thin, intermediate, and thick layers. Additionally, the stresses in a compressed homogeneous half-space having the substrate properties have been obtained for comparison. The significance of the layer thickness relative to the size of the half-contact width, the friction coefficient at the contact zone, and the stiffness of the layer are critically examined and the conditions under which the layer is beneficial are addressed. Furthermore, the mechanisms of microcrack initiation at the layer surface or interface, layer debonding, and onset of plastic flow in the layered solid are explained qualitatively, in light of the governing stresses, and the regimes of their prevalence are approximately determined.

Commentary by Dr. Valentin Fuster
J. Tribol. 1988;110(3):486-491. doi:10.1115/1.3261654.

In this paper the authors describe an experimental study to identify the damping laws associated with a squeeze-film vibration damper. This is achieved by using a nonlinear filtering algorithm to process displacement responses of the damper ring to synchronous excitation and thus to estimate the parameters in an nth-power velocity model. The experimental facility is described in detail and a representative selection of results is included. The identified models are validated through the prediction of damper-ring orbits and comparison with observed responses.

Commentary by Dr. Valentin Fuster
J. Tribol. 1988;110(3):492-498. doi:10.1115/1.3261655.

The complete stress field generated beneath an arbitrarily profiled axisymmetric indentor is found, both for normal indentation, and sliding. It is shown that a shallower profile than that of a sphere, i.e., one having a larger radius of curvature at the point of first contact, associated with a “flatter” pressure distribution, gives rise to a milder stress state, so that a heavier load may be sustained over a given contact disk without yielding.

Topics: Pressure , Stress , Disks
Commentary by Dr. Valentin Fuster
J. Tribol. 1988;110(3):499-502. doi:10.1115/1.3261656.

The load capacity, attitude angle, and lubricant flow rate are computed using a modified Reynolds equation combined with the modified Coyne-Elrod boundary conditions. It was found that the pressure is decreased and the rupture point is shifted further downstream as the Reynolds number is increased or the surface tension parameter is decreased. Under a light loading condition, and a low surface tension parameter, a continuous film is approached.

Commentary by Dr. Valentin Fuster
J. Tribol. 1988;110(3):503-507. doi:10.1115/1.3261657.

Minimum, central and average film thicknesses have been calculated for the isothermal E.H.L. point contact case, for a variety of load, rolling speed, and material parameters. The equations governing this problem were solved using a Multigrid method. This technique offers the possibility to work with a very fine grid, obtaining detailed and accurate solutions, at the cost of moderate cpu times and storage requirements, on medium size computers. Computations for low loads, requiring a large inlet zone, have been carried out using local grid refinements. The fluid in these calculations is assumed to be compressible and its viscosity-pressure behavior is described by either the Roelands equation, or the Barus equation. The ratio between the calculated minimum film thickness and the central value varied with the parameters governing the problem, but for low loads, a value of 3/4 was obtained. The film thickness behavior at these low loads can be accurately described in terms of the minimum film thickness. For higher loads, however, a description based on a film thickness, averaged over the Hertzian contact, is more appropriate to be compared with the asymptotic solution (Ertel, Grubin).

Commentary by Dr. Valentin Fuster
J. Tribol. 1988;110(3):508-515. doi:10.1115/1.3261660.

As is well known, ambient atmospheres can greatly affect the friction and wear behavior of metals sliding on each other, as well as the electric contact resistance between the metals. In order to better understand the mechanisms of those effects of ambient atmospheres, the coefficient of friction and the electric contact resistance have been studied for bundles of 50 micrometer thick copper wires, sliding on a polished copper surface in a specialized apparatus, called the hoop apparatus. The ambient gas was cycled between laboratory air and carbon dioxide, and between laboratory air and argon, respectively. The results indicate a reversible build-up and removal of surface films whose nature as well as speed of formation and removal depends on the gas present. Fiber bundles are used in order to eliminate the constriction resistance, so that the contact resistance is directly proportional to the specific film resistivity. The following properties were found to be affected by the ambient gases. (i) The average level of the contact resistance. (ii) The amplitude of the electric “noise.” (iii) The coefficient of friction. (iv) The difference between the static and the dynamic coefficients of friction in stick-slip motion. The results were found to be consistent with previous measurements in which the mechanism of forming wear particles was deduced from a wear chip analysis. Correspondingly they were interpreted in terms of the same wear model. This led to a further advance in the understanding of the interfacial processes accompanying sliding in this sample/substrate combination.

Commentary by Dr. Valentin Fuster
J. Tribol. 1988;110(3):517-524. doi:10.1115/1.3261663.

Fretting wear and fretting fatigue are governed by the rate of formation of materials (third-bodies) between the initial contact surfaces. Furthermore, the third-bodies must be maintained within the contact. The issue of the race between third-body formation and subsurface damage conditions the effect of fretting on fatigue. That race lasts for only a few hundred or at best a few thousand cycles. Effective third-bodies (or good anti-fretting lubricants) must adhere strongly to the rubbing surfaces, and be able to accommodate at least part of the relative displacement. Great care in the design of test equipment has to be exercised before definitive results on the effect of amplitude and frequency on either fretting fatigue or fretting wear can be obtained for a given contact condition, given materials and given environments.

Commentary by Dr. Valentin Fuster
J. Tribol. 1988;110(3):525-531. doi:10.1115/1.3261666.

Helium buffered floating-ring seals used in cryogenic turbopumps are sujbect to large temperature variations, shaft centrifugal growth, and dynamic shaft excursions. To prevent dangerous contact friction over a wide range of operating conditions generally requires liberal clearances with consequent high leakage. Reduction of helium consumption translates into lower space vehicle helium storage requirements and thus increased payload. A hydrostatic sectored floating-ring seal is described with self-adjusting clearance capabilities that enables the seal to operate with small clearances over the operating range to minimize leakage.

Commentary by Dr. Valentin Fuster
J. Tribol. 1988;110(3):533-538. doi:10.1115/1.3261670.

Measurements of instantaneous coefficients of friction and associated motions during start-up at a planar contact are presented for four different lubrication conditions. The various patterns of transient behavior are discussed. Difficulties in interpreting static friction coefficients during rapidly applied tangential loads are described in relation to the motion data. It is shown that a molybdenum disulphide grease yields a friction characteristic that is quite different from either dry or boundary lubricated conditions in the presence of liquid lubricants. Transition distances from a static or maximum initial friction to kinetic conditions are examined and found to be considerably longer than had been previously found for concentrated contacts. Some suggestions regarding future studies of unsteady friction behavior are made.

Commentary by Dr. Valentin Fuster
J. Tribol. 1988;110(3):539-545. doi:10.1115/1.3261673.

The effects of fluid inertia on the dynamic behavior of oil film journal bearings are theoretically investigated. The dynamic oil film forces considering the combined effects of turbulence and fluid inertia are analytically obtained under the short bearing assumption. Based on the linearized analysis, the whirl onset velocity for a balanced rigid rotor supported horizontally in the oil film journal bearings are determined initially in the case of the length-to-diameter ratio of λ = 0.5 for Reynolds numbers of Re = 2750, 4580, and 5500. Moreover, the nonlinear equations of motion for the rotor are solved by the improved Euler’s method, and the relations between the transient journal motion and the pressure distribution corresponding to the above Reynolds numbers are examined. It is found that the fluid inertia significantly affects the dynamic behavior of turbulent journal bearings under certain operating conditions.

Commentary by Dr. Valentin Fuster
J. Tribol. 1988;110(3):548-553. doi:10.1115/1.3261677.

This paper describes the results of an experimental and theoretical investigation of wear of steel under forced oscillations of applied load in boundary lubricated sliding contact. A special pin-on-disk type wear apparatus, which enabled continuous control of the dynamic loading parameters (mean load, amplitude and frequency of the load oscillations and sliding velocity), has been used in the experimental investigation. Wear rates and surface roughness were measured for various combinations of static and dynamic loading parameters. A wear equation which related wear to the parameters of dynamic loading has been derived. It has been shown both by experimental investigation and theoretical analysis that wear is an increasing function of the mean value of the applied load, amplitude of the load oscillation, and a ratio of the frequency of load oscillation to the sliding velocity.

Commentary by Dr. Valentin Fuster
J. Tribol. 1988;110(3):555-560. doi:10.1115/1.3261681.

This paper relates to the turbulent motion in the lubricant fluid film with centrifugal effects and the lubrication theory for thrust bearings operating in turbulent regime. Using Prandtl’s mixing-length theory, three-dimensional turbulent velocity distributions, including pressure gradients and centrifugal effects, are calculated, and the cross-coupling of nonplanar flow of the lubricant fluid film is discussed. From these results, turbulent lubrication equations with centrifugal effects are derived. Applying these lubrication equations to a sectorial inclined thrust bearing, the steady-state characteristics and the dynamic ones are calculated.

Commentary by Dr. Valentin Fuster
J. Tribol. 1988;110(3):563-571. doi:10.1115/1.3261685.

A nanoindenter apparatus is developed to measure the microhardness and microviscoelastic properties (in compression) of extremely thin films. In-situ indentation measurements are made by polarization interferometer by monitoring the absolute motions of the sample and indenter. A linear actuator provides the load, and the indenter load is inferred from the position of the indenter measured by the interferometer and the stiffness of the indenter parallel spring guide. A personal computer and associated electronics provide the control for load and penetration. These allow the instrument to determine microhardness and characterize microviscoelastic creep and relaxation properties. The linear actuator and the sample parallel spring guide are supported by an air bearing stage which is translated at a constant speed to conduct scratch tests for adhesion measurements. Based on the data reported in the paper, we find that microhardness and microviscoelastic properties at extremely low loads (or penetrations) are load (or penetration) dependent.

Commentary by Dr. Valentin Fuster
J. Tribol. 1988;110(3):572-577. doi:10.1115/1.3261688.

The design and analysis of pressure balanced seals are important to the designers and users of turbomachinery which require floating element seals. The design objective for compressor seals differs from that of the engineered pump seal but the common factor includes the ability to predict the dynamic response of the floating ring seal relative to the rotor shaft. Steady-state calculations can be used to study possible operating conditions for compressor designs, but they do not include accurate account of rotor shaft response and ring spin torque. In addition, engineered pump seal applications are such that the ring is expected to track shaft movement during start-up and shut-down transients when reduced pressures and leakage produce laminar flow sealing conditions. The analysis presented in this paper gives the designer the ability to evaluate seal ring dynamic transient response, including friction stick-slip on the axial sealing face and the ring spin torque interaction with the antirotation element. The analysis results presented in this paper were obtained from a personal computer program written specifically for seal transient analysis.

Commentary by Dr. Valentin Fuster

DISCUSSIONS

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

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