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RESEARCH PAPERS

J. Basic Eng. 1965;87(3):537-546. doi:10.1115/1.3650602.

An approach is presented for simplified analytical, graphical, and numerical solutions to extremely general problems of dynamically loaded bearings. A series of examples illustrates the application of the method to problems of varying complexity.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1965;87(3):547-555. doi:10.1115/1.3650603.

A generalized analysis for spiral-grooved thrust bearings is presented. The effects of local radius are considered. For the same grooving geometry and the same inside-to-outside radius ratio, the inflow design is shown to be superior in both stiffness and load capacity. The analysis also treats a relative, transverse, oscillatory motion of the bearing surfaces. Both the magnitude and phase angle (in the temporal sense) of the bearing reaction are dependent on the frequency of the motion. The results for the oscillating motion reveal the possibility of a self-excited, rotor-bearing instability. The criterion for determining the onset of this type of instability is given.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1965;87(3):559-567. doi:10.1115/1.3650606.

Use of Ausman’s linearized, PH method to determine the threshold of half frequency whirl for a rigid rotor in self-acting cylindrical journal bearings is extended to include finite length effects. Rotating polar coordinates are used to derive the governing equation. Results obtained are generally consistent with several previous works in wide ranges of all parameters. This method is judged to give conservative results and is suitable for studying dynamic problems of more complicated systems.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1965;87(3):568-576. doi:10.1115/1.3650607.

A differential equation is obtained for the smoothed “overall” pressure distribution around a herringbone-grooved, gas-lubricated journal bearing operating with a variable film thickness. The equation is based on the limiting case of an idealized bearing for which the number of grooves approaches an infinite number. A numerical solution to the differential equation is obtained valid for small eccentricities. This solution includes the case where the journal is undergoing steady circular whirl. In addition to the usual plain bearing parameters L/D, Λ, and whirl speed ratio ω3 /(ω1 + ω2 ), the behavior of a grooved bearing also depends on four additional parameters: The groove angle β, the relative groove width α, the relative groove depth H0 , and a compressibility number, Λs , which is based on the relative speed between the grooved and smooth members of the bearing. Results are presented showing bearing radial force and attitude angle as functions of β, α, H0 , Λs , Λ, and whirl speed ratio.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1965;87(3):579-587. doi:10.1115/1.3650611.

Paper starts with a study of static stability response of gas-lubricated bearing, followed by a general small perturbations theory of the dynamic stability of journal bearings. Then the pressure equation for bearings subjected to variable forces and velocities is analyzed, by pointing out the existence of a limiting solution which can occur both for high speeds or for high frequency of the bearing eccentricity. At the same time the squeeze effect can be strongly altered by the lubricant compressibility so that, for motions with high tangential speeds or with high frequencies, the pressures depend only on the thickness h and not on the derivative with respect to time ḣ as is the case of incompressible films. Finally, the analysis of the stability conditions reveals that bearings operating at low numbers H are unstable according to the small perturbations theory. The same situation occurs to the bearings operating with small eccentricity ratios, for any number H. The frequency of undamped oscillations is proportional to the shaft angular speed ω for low numbers H but tends to a bounded value ω0 * for high number H. Quasi-resonant conditions may also occur when the number H is increasing, a fact which allows the deduction of a simple half-empirical stability condition.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1965;87(3):589-598. doi:10.1115/1.3650614.

Linearized steady-state time-dependent solutions to the equations of journal motion are obtained for sinusoidally time-varying radial loads by utilizing the “linearized ph” technique to approximate lubricant pressure forces. An exemplary check for vibration at half-rotor frequency shows that the nonlinear terms can be neglected provided the total eccentricity ratio (static plus dynamic) remains less than one half. A typical journal-bearing frequency response exhibits two distinct types of resonances: One at half-rotor frequency and another at a frequency given by K/M, where K is the effective spring constant due to the bulk modulus of the gas lubricant and M is the mass of the supported rotor. As the static eccentricity ratio ∊0 increases, the amplitude of the half-rotor frequency resonance decreases drastically, but the amplitude of the K/M resonance increases slightly. Rotating load response can be synthesized by superimposing the responses to two 90 deg out-of-phase radial loads acting along perpendicular axes. The resulting response is a nearly circular ellipse centered about the static equilibrium position.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1965;87(3):604-612. doi:10.1115/1.3650617.

Space-simulator bearings of the externally pressurized gas-lubricated type must meet a number of unusually stringent requirements. Of primary importance is that they contribute as nearly as possible zero error torque to the supported simulator structure, and that changes in this torque as the structure is rotated as desired about all three axes be extremely small. The bearing must be stable and free of vibration under all conditions; and in the more sophisticated simulators, the bearing must sustain lateral as well as vertical loads with close control of film thickness. Low-error torque requires first of all that the rotatable sphere be both geometrically perfect and flawless of surface. Errors in the bearing causing roll and pitch torques can be balanced out by the table balance weights; but azimuth torques cannot be counterbalanced. They are minimized by appropriate bearing design which places the gas-flow lines in planes passing through the azimuth axis. Bearing-design parameters and equations are established. A detailed computer analysis explains why these bearings cannot be operated below a certain minimum film thickness. Error torques resulting from flaws or scratches in the bearing and sphere surfaces are analyzed and found to increase with film thickness. Bearing-error torque is found to increase as the square of the load.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1965;87(3):613-620. doi:10.1115/1.3650618.

The externally pressurized circular thrust gas bearing with porous bearing surface is analysed here theoretically. The authors use “permeability coefficient” which identifies the characteristic of porous media, and introduce the concepts of the “equivalent clearance” and the “effective restricting thickness” of the porous layer so that the flow through the porous material can be analyzed in both axial and radial directions, and the flow in the porous material and the bearing clearance may be considered as two parallel flows connected with each other. The analysis coincided qualitatively as well as quantitatively with the results of the experiments concerning the pressure distribution and the load capacity.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1965;87(3):622-630. doi:10.1115/1.3650621.

In this paper, an analytical solution is obtained and discussed for externally pressurized porous gas-bearings from a theoretical standpoint in which the flowing condition in bearing clearance is taken into consideration as a boundary value of the three-dimensional flow in porous media. This approach makes it possible to investigate the characteristics of various bearing configurations with consideration of anisotropy of porous material. And it is assumed that the flow in bearing clearance is laminar and fully viscous while the flow in porous media is characterized by Darcy’s law. The theoretical results are found to give more reasonable prediction of porous gas-bearing performance than those in the previous paper [1].

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1965;87(3):631-638. doi:10.1115/1.3650622.

The effects of introducing a small amount of lubricant under pressure into a self-acting foil bearing film are investigated. Foil shape and pressure distribution under the foil are obtained by combining the equilibrium equation with the Reynolds’ equation and solving the resulting equation. The results show that the effect of even small external pressurization in a self-acting foil bearing is very important.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1965;87(3):641-651. doi:10.1115/1.3650625.

The flash-temperature theory plays an important part in the attempt to explain the scoring phenomenon of gears. Purpose of the investigations was to measure the surface temperatures of meshing gears. Results are presented as to the following influences on the surface temperatures: Tooth profile, loading, pitch-line velocity, surface roughness, synthetic lubricant and face width. The results are compared with the flash-temperature equation according to Blok.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1965;87(3):655-663. doi:10.1115/1.3650629.

In this paper the oil film separating the mating surfaces of involute spur gears operating under hydrodynamic lubrication conditions is analyzed. This analysis surpasses previous analyses in as much as the actual motion of the involute profiles (rolling, sliding, and squeezing motion) and the total number of teeth engaged at any one time are considered. Expressions are derived for the pressure distribution, shear stress, and power loss in the oil film at any phase of tooth engagement. A method is developed by which these expressions can be applied to determine the film thickness at any instant and the power loss for a given load, speed, and lubricant viscosity.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1965;87(3):666-672. doi:10.1115/1.3650635.

The analysis of the mechanism of air leakage through the interstices between metal surfaces in contact or of the mechanism of thermal resistance between them is dependent on the average clearance between opposite surfaces or on the distribution of the real contact area; i.e., the mechanism of contact. Assuming that the distribution curve obtained from the profile curve of the surface has a normal distribution, the relation between the applied load and the average clearance or the penetrating depth, i.e., the distance through which the one surface moves into the other surface, is obtained theoretically. A comparison of calculated values based on this theory with experimental data shows good agreement.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1965;87(3):675-682. doi:10.1115/1.3650640.

The “law of wall” for turbulent shear flows has been adapted to analyze turbulent lubrication. This new approach takes into account many well-established facts concerning turbulent shear flows. Isotropy of turbulent momentum transport (eddy viscosity) is assumed in treating nonplanar mean flows. A linearized version of the governing differential equation is established. Sample results agree well with available experimental data.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1965;87(3):689-693. doi:10.1115/1.3650644.

The extension of Newton’s shearing law is aimed at the tensions being expressed by means of a general type equation. The case of the Bingham type media is considered and the components of the tensions tensor for homogeneous isotropic bodies are obtained in an orthogonal system of coordinates. The notion of viscosity is also extended by the introduction of viscosities of any order n, having the dimensions (M/L)Tn−2 . The equation of motion upon any direction xi is then derived, extending thus the Navier-Stokes equations. Further the particular cases of incompressible fluids and steady motions are considered. Applications to simple cases are performed: The motion in tubes, coaxial cylinders, or between solid parallel surfaces. These applications lead, as particular forms of the general formulas obtained, to result in good agreement with those found by other authors (Paslay and Slibar, Milne, and so on). The flow between parallel plates is studied too, for different shearing laws. Finally, a more general form of the shearing stresses is considered and by the proposed generalization, the possibility of a direct unitary study of various continuous bodies of a great practical importance is obtained.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1965;87(3):695-704. doi:10.1115/1.3650647.

A nummerical solution to the coupled Reynolds, elasticity, and energy equations for the pressure, temperature, and film thickness between two heavily loaded rolling and sliding cylinders is obtained. The analysis of the energy equation is based on a mean viscosity across the film. Results for a thermal case with a slip ratio of 0.25 as well as an isothermal solution are presented. Pressure peak is found near the exit of the film for cases with or without thermal effects and the influence of the temperature on the film thickness is moderate.

Commentary by Dr. Valentin Fuster
Commentary by Dr. Valentin Fuster
J. Basic Eng. 1965;87(3):713-723. doi:10.1115/1.3650657.

If nonrotating rolling bearings are exposed to vibration then the raceways especially in roller bearings can be damaged in a short time. False brinelling in bearings is caused by fretting corrosion. All research in this area therefore belongs to the field of fretting corrosion. Owing to the alternating elastic deformation in the contact area between the rolling elements and the raceway as well as to the shearing strength being exceeded in the microcontact area, surface particles are abraded, which become immediately oxidized. The kind and the extent of damage primarily depend on the static load of the bearings. The resistance to false brinelling can be increased by means of lubricants and surface treatments. It is possible to give limits for the admissible flute characteristics. In cases of already known vibration characteristics the time of the bearing failure can be mathematically predetermined.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1965;87(3):724-728. doi:10.1115/1.3650660.

The energy required to roll a sphere in a cylindrical groove is shown to be partly a hysteresis loss and partly a microslip loss. Data for three different sphere-groove combinations are separated into the two types of losses by comparison with data for toroid-plane rolling combinations chosen to give identical stress fields. The microslip loss is accounted for by the Palmgren-Heathcote equation assuming a coefficient of sliding friction of 0.073. Once the microslip torque is subtracted from the total rolling torque, the remaining torque turns out to be proportional to the load and independent of the geometry of the rolling elements, which includes various diameter spheres in addition to the combinations mentioned previously.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1965;87(3):729-734. doi:10.1115/1.3650661.

A solution of the normal displacement of the elastic half-space under an arbitrarily distributed fast-moving heat source of constant velocity within the two-dimensional quasi-static, uncoupled thermoelasticity theory is presented. The surface of the half-space is allowed to dissipate heat by convection. Moreover, an example associated with the problem of elastohydrodynamics is given.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1965;87(3):735-739. doi:10.1115/1.3650662.

Experimental work was carried out on the boundary lubrication of a copper-copper couple with pure cetane, palmitic acid solution of cetane, and some other organic materials. The purpose was to get information about α and μlube , which appear in the friction equation:

μ = αμsolid + (1 − α)μlube,
by using two different kinds of copper surface, a clean surface, and an oxidized surface. α was found to be small with palmitic acid solution, and the estimated shear strength of palmitic acid was high under the examined condition. α and μlube seemed to be properties which are independent of each other. α is closely related to the attraction force between the lubricant and the substrate, whereas μlube is related to the complexity of molecular structure of the lubricant. A comparison was made of bulk-liquid and thin-film lubrication. μlube was smaller in thin-film lubrication than it was in bulk-liquid lubrication. This suggests that the frictional resistance may be partly contributed by liquid in the edge space around the real contact.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1965;87(3):741-745. doi:10.1115/1.3650666.

This paper, a further development of our earlier investigations of heavy boundary friction duties of steel in mineral oils, presents the results of a study of the antifriction, antiwear (and EP) properties of low-molecular individual hydrocarbons. The dependence of the lubricating action of low-molecular hydrocarbons on their nature and on the oxidative activity of the gas phase is such that it improves greatly with the intensity of oxidation in the friction zone. The effectiveness of higher fatty acids as lubricitors under heavy friction duties depends on the oxidative activity of the gas phase and the tendency of the hydrocarbons to oxidize. During a study of the boundary friction of steel in mineral oils in the air and in vacuum with sliding speeds varying over a 108 -fold range, it was established that under constant load and temperature both increasing and decreasing the sliding speed may result in seizure. Hot seizure occurs in the former case, cold seizure in the latter.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1965;87(3):747-752. doi:10.1115/1.3650669.

The antiwear and antifriction (lubricating) properties of polyorganosiloxanes of various kinds and of their mixtures with hydrocarbons are studied. It is shown that in mixtures with hydrocarbons, polyorganosiloxanes may display a high activity under boundary friction. The conditions under which this activity is brought out are determined. A change in the oxidative activity of the gas phase acts on the lubricity of polyorganosiloxanes in the same direction as on that of mineral oils; this action is weaker as the stability of the polyorganosiloxanes to thermal oxidation increases. Additives highly active in preventing steel seizure in hydrocarbon lubricants are either utterly inactive in polyorganosiloxanes (polymethylphenylsiloxanes) or are much weaker (polyethylsiloxanes). A hypothesis is suggested, attributing this to the difficulty in polyorganosiloxanes of processes occurring which involve chain reactions initiated by free radicals. The mechanism of action of E.P. additives in lubricating media is discussed.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1965;87(3):754-759. doi:10.1115/1.3650672.

The temperatures on the rubbing surfaces were calculated (just before seizure) for the row tests of different mineral oils (without EP additives), which were carried out by different authors on several testing machines (four-ball machines, crossed-cylinder machine and disk machine) with different sliding speeds. These temperatures for certain oil-metal combinations, evaluated by means of the theoretical formulas (developed by Blok and Jaeger) practically coincide with the values of the critical temperatures of the same oils, obtained by the author directly from experiments with KT-2 four-ball machine (very low)—sliding speed, high contact load, and external heating of the oil and specimens). The influence of the plastic deformation at the area of contact on the value of the critical temperatures for some oil-metal combinations is shown.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1965;87(3):761-767. doi:10.1115/1.3650676.

A radiochemical analysis has been made of the EP film formed on the surfaces of the tappets of an engine lubricated with an oil containing triphenyl phosphate, labeled with phosphorus –32, as the EP additive. The results do not support the widely held view that phosphate esters owe their effectiveness as EP additives to the formation of phosphide eutectics of low melting point on metal surfaces. The results indicate the presence of metal phosphates and metal organophosphates formed from acid-phosphate intermediates derived from the ester. These findings, together with the results of subsequent rig tests, suggest that the effectiveness of neutral organic phosphates as EP additives depends on the ease with which they hydrolyze on the metal surface to form acid phosphates; the more readily the ester hydrolyzes the better its performance.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1965;87(3):771-776. doi:10.1115/1.3650682.
Abstract
Topics: Friction
Commentary by Dr. Valentin Fuster
J. Basic Eng. 1965;87(3):778-780. doi:10.1115/1.3650685.

The effect of a nonuniform applied magnetic field on the operation of a parallel plate slider bearing is investigated analytically. It is found that the optimum magnetic field profile is a step function. This profile increases the load-carrying capacity while decreasing the friction factor. Results indicate that the nonuniform applied magnetic field is definitely superior to the uniform applied magnetic field.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1965;87(3):781-784. doi:10.1115/1.3650686.

When the bearing is running, its clearance is no longer equal to the initial one, as a result of the thermal regime and load. This paper presents a calculation method which takes into consideration the temperature distribution in the bearing, the load, and the elastic properties of the materials. The deduced calculus relations allow to establish the correction of the initial radial clearance in order to obtain the designed clearance when the bearing is running.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1965;87(3):785-790. doi:10.1115/1.3650690.

This paper contains exhaustive analytical data on factors contributing to wear. The wear of a deformed body interacting with an absolutely rigid rough solid is considered. It is believed that wear results from the deformation of a body due to geometrical and mechanical factors and due to the adhesion bonds thereof. Three types of wear are considered: By elastic deformation, by plastic deformation, and by microcutting. The suggested criteria allow us to determine conditions which cause these types of wear to appear. It is shown that the rate of wear, i.e., the ratio of height of the worn layer to the distance of sliding at elastic contact depends on the elasticity modulus, roughness, friction coefficient, nominal pressure, rupture stress of material, and on the power exponent of fatigue curve; at plastic contact it depends on roughness, nominal pressure, hardness, destroying deformation, and friction coefficient; at microcutting—on roughness, nominal pressure, and hardness; wear at microcutting is independent of friction coefficient. The formulas deduced are borne out by experiments. These formulas may be readily modified for the case of two rough surfaces.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1965;87(3):791-804. doi:10.1115/1.3650691.

In this review the developments in the fields of lubricants, friction, and bearing materials have been summarized by various authorities in each particular field. The review covers the period from June to December, 1963. The developments in bearings and gears will be published at a later date. Much of the published work is concerned with high temperature and vacuum conditions. However, it is of interest to note the large increase in the published work in solid lubricants over that of previous years.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1965;87(3):805-809. doi:10.1115/1.3650692.

A theoretical analysis is given for squeeze film bearings which use an electrically conducting fluid, such as a liquid metal, as the lubricant and which are in the presence of a magnetic field. Electrical energy is added to the film by an exterior source. By considering infinitely long rectangular plates, the fluid film thickness is determined as a function of time, with the applied magnetic and electric fields as parameters. It is shown that the squeeze action is altered significantly when the electric field is symmetrical about the center of the bearing, and results are presented for various values of the Hartmann number.

Commentary by Dr. Valentin Fuster

DISCUSSIONS

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

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