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RESEARCH PAPERS

J. of Lubrication Tech. 1974;96(3):305-313. doi:10.1115/1.3451948.

An analytical method developed for determining the bore wear pattern for a reciprocating piston engine over a complete running cycle is presented. The method includes the considerations of the hydrodynamic lubrication theory between the ring and the cylinder bore wall, piston ring geometric and elastic characteristics, blowby through the piston ring pack, minimum film thickness permitting film lubrication, piston side thrust load and Archard’s wear relation. Since the method is general, it also can be applied to other reciprocating piston devices, such as gas compressor, Rankine cycle engine or Stirling engine. Wear factor data, however, must be available in order to make quantitative predictions of wear. The verification of the present theory is given in a subsequent paper (Part II) which shows good agreement between the predicted bore wear curves and measured ones for actual engines.

Commentary by Dr. Valentin Fuster
J. of Lubrication Tech. 1974;96(3):315-320. doi:10.1115/1.3451951.

The thermohydrodynamic (THD) performance of finite slider bearings is studied under nonsteady-state conditions. The fluid film energy, momentum and continuity equations are coupled to the heat conduction equation for the bearing solids and the mathematical system is solved numerically to yield the fluid film temperature-time and load capacity-time histories. The effect of isothermal and adiabatic conditions at the fluid-solid interface is presented. The bearing transient response to constant and time-dependent runner speeds is also discussed.

Commentary by Dr. Valentin Fuster
J. of Lubrication Tech. 1974;96(3):322-328. doi:10.1115/1.3451955.

The effect of varying the ratio of slider to pad temperature boundary conditions and the influence of varying inlet to outlet ratio of a plane infinitely wide slider bearing is examined. The lubricant is assumed to be incompressible and the variation of viscosity with temperature is taken into account. The nondimensionalized governing equations, transformed in terms of the stream function, are solved numerically. The results show that maintaining a lower slider temperature to pad temperature ratio causes an increase in the load carrying capacity of the bearing. A means of which advantage could be taken of this effect in the design of thrust bearings is suggested.

Commentary by Dr. Valentin Fuster
J. of Lubrication Tech. 1974;96(3):329-336. doi:10.1115/1.3451958.

A circular thrust bearing with inherently compensated feedholes evenly distributed around an interior radius is analyzed. The feedhole boundary between the central disk region and exterior annular region is modeled as a line source. A periodic load disturbance is imposed on the bearing, and the dynamic pressure distribution is determined by small perturbations of the Reynolds equation. The solution is given in terms of Kelvin functions. Design curves are presented for the stiffness and damping as a function of squeeze number, external pressure, restrictor coefficient and feedhole location.

Commentary by Dr. Valentin Fuster
J. of Lubrication Tech. 1974;96(3):337-345. doi:10.1115/1.3451961.

A spiral groove journal bearing has two significant advantages, compared with a plain journal bearing. These are the self-sealing capabilities and the favorable stability properties of the bearing under no-load or light-load conditions. Under eccentric operating conditions the axial width of the liquid film in such a bearing varies in the circumferential direction. The shape of the gas-to-liquid interface and its effect on load capacity and stability are investigated both theoretically and experimentally. It appears that there is a considerable difference in the shape of the gas-to-liquid interface, depending on whether it is the housing or the shaft that has spiral grooves, or more generally, on whether the load vector is rotating with respect to the grooves or not. It has further been found that the free boundary has an unfavorable effect on the stability of unloaded spiral groove journal bearing. A deep groove in the circumferential direction, close to the gas-to-liquid interface, can practically cancel this unfavorable effect.

Commentary by Dr. Valentin Fuster
J. of Lubrication Tech. 1974;96(3):346-353. doi:10.1115/1.3451962.

The Reynolds condition is shown to correctly describe the film termination in hydrodynamic porous journal bearings. A practical and accurate numerical method for calculating bearing performance is developed, which permits the use of realistic boundary conditions, including the Reynolds condition. It also accounts for slip at the film-bearing interface by means of Darcy’s law. Results show that performance predicted on the basis of the Reynolds condition is closely approximated when the Gumbel and Everting condition is used, but that the Sommerfeld condition yields a substantial difference. For practical bearings, it is found that (a) slip at the interface is negligible, (b) the “thin wall” assumption is valid, (c) sealing the axial ends of the bearing produces only a small increase in load capacity, and (d) axial flow in the film is significant.

Commentary by Dr. Valentin Fuster
J. of Lubrication Tech. 1974;96(3):354-360. doi:10.1115/1.3451963.

An analytical solution is presented to predict the performance of an externally pressurized porous gas thrust bearing. When the wall thickness of the pad is small compared to its radius, the expressions for the bearing characteristics can be given in a closed form. The bearing number Λ—a dimensionless design variable—can adequately describe the performance of the bearing. The load capacity and mass flow rate progressively increase with the bearing number; the static stiffness increases with the bearing number up to Λ ∼ 4.0 and then gradually decreases. The decisive influence of permeability of the pad material in controlling the performance of the bearing is discussed and the interesting behaviour of the static stiffness as the film thickness is reduced is pointed out. It is found that there is near perfect agreement between the predicted performance of the bearing and the one experimentally evaluated. The characteristics are plotted over a wide range for the bearing number (.01 ≤ Λ ≤ 2500) in such a way that the information is of direct use to designers and applications engineers. Also, the results are given in tabular form to facilitate interpolation of the values as required.

Commentary by Dr. Valentin Fuster
J. of Lubrication Tech. 1974;96(3):361-364. doi:10.1115/1.3451964.

The dynamic behavior of squeeze film in a narrow porous journal bearing under a cyclic load is analyzed. A thin-walled bearing with a nonrotating journal is considered and a closed form expression for the pressure distribution is derived. The locus of the journal center is found by numerical methods and it is established with an example that actual contact between the journal and bearing can be avoided by appropriate design of the bearing. Consequently, it is proved that pure squeeze films have a load capacity only under cyclic loads. The analysis also reveals that the permeability of the bearing material and the wall thickness of the bearing influence significantly the operating eccentricity ratio.

Commentary by Dr. Valentin Fuster
J. of Lubrication Tech. 1974;96(3):365-369. doi:10.1115/1.3451965.

Exact solutions for a class of incompressible spiral-grooved viscous pumps were obtained by solving the dynamic perturbation equations based on the governing equations of the well-known narrow groove theory. The resulting closed-form analytical expressions contain two integration constants which can be determined by appropriate boundary conditions pertinent to a specific application and design. A flat thrust bearing was chosen to illustrate the application of these results. The load-carrying capacity calculated from present theory was compared with those obtained by other investigator [2]. The agreement is extremely good. No attempt was made to generate design charts for various designs since the resulting expressions obtained in this work can be used quite easily in a straightforward fashion.

Commentary by Dr. Valentin Fuster
J. of Lubrication Tech. 1974;96(3):370-375. doi:10.1115/1.3451966.

A simple theoretical model of a bearing and measured traction curves are used to explain the different types of experimentally observed cage behavior which result from different lubricants. Traction curves with a pronounced peak are shown to produce unstable cage slip behavior, although bearings can operate steadily in the high slip region. The instability occurred in tests with a high traction fluid but not with ester-type gas turbine lubricants. A bench-top roller bearing rig of the type used in these experiments provides an effective method of assessing the tractive properties of lubricants, using a 25-ml sample.

Commentary by Dr. Valentin Fuster
J. of Lubrication Tech. 1974;96(3):376-380. doi:10.1115/1.3451967.

The stress field generated in an elastic layer by normally loaded, periodically spaced circular contacts is analyzed. It is intended that this model represent a pair of rough, plated contact surfaces whose plating is much more compliant than the substrate material. The effect of plating thickness and spacing of load-bearing asperities upon the state of stress within the layer is studied. It is shown that there exist values of layer thickness and contact-spot spacing such that the octahedral shear stress within the layer is maximized. Further, for very thin layers, the maximum octahedral shear occurs at the surface of the layer as in tangentially loaded contacts.

Commentary by Dr. Valentin Fuster
J. of Lubrication Tech. 1974;96(3):381-389. doi:10.1115/1.3451968.

The fluid film lubrication equations for externally pressurized bearings are solved for steady-state performance and spring and damping coefficients using finite differences and a variable grid bearing model. Turbulence is included as local effective viscosities. Entrance inertia effects are included at the recess edges and are seen to be a significant factor for flow estimates. Performance data is developed for a six-pocket bearing of L/D = 0.75. Experimental verification was obtained for load capacity, flow, and dynamic coefficients, using a two-bearing dynamic test rig and water at speeds from 0 to 4000 rpm. Axial flow of Reynolds numbers range from 22,000 to 125,000.

Commentary by Dr. Valentin Fuster
J. of Lubrication Tech. 1974;96(3):391-397. doi:10.1115/1.3451972.

A survey of the literature suggests that a stress-life exponent of approximately 12 is typical of vacuum-processed steels for ball bearings rather than the exponent of 9 which has been generally accepted by the bearing industry and bearing users. Tests run with vacuum-degassed AISI 52100 balls in the five-ball fatigue tester at four maximum Hertz stress levels in the range from 650000 to 875000 psi showed good agreement with the literature. However, tests run with consumable-electrode vacuum melted AISI M-50 steel angular-contact ball bearings at 500 deg F at three thrust loads did not show significant deviation from the accepted ninth power stress-life relation.

Commentary by Dr. Valentin Fuster
J. of Lubrication Tech. 1974;96(3):398-406. doi:10.1115/1.3451975.

Local variations in asperity dimensions (rippling) of elastohydrodynamic (EHD) pressure are calculated using Christensen’s stochastic model of the hydrodynamics of heavily loaded two-dimensional contacts between rough surfaces. Pressure ripple amplitudes of the order of the maximum Hertz pressure, i.e., well in excess of 105 psi (69.107 N/m2 ) are predicted at the inlet perimeter of the EHD contact plateau and at the upstream slope of the exit constriction for heavily loaded contacts, if the plateau film thickness to rms roughness ratio is h/σ = 2. Pressure ripple amplitudes in excess of 104 psi (69.106 N/m2 ) are probable even for the thick film condition h/σ = 10. Sliding traction rippling is calculated for small slide/roll velocity ratios in the same type of contact, and ripple amplitudes in excess of the mean value of the traction are predicted in the high pressure EHD plateau region of the contact for h/σ = 3. The predicted traction ripple amplitude exceeds 30 percent of the mean traction, even for h/σ = 6. Rippling increases the average traction over that for smooth surfaces. Both the pressure and traction rippling may contribute to surface plastic flow and fatigue.

Commentary by Dr. Valentin Fuster
J. of Lubrication Tech. 1974;96(3):410-417. doi:10.1115/1.3451980.

The viscosity-pressure-temperature behavior of a series of 14 siloxane polymers is reported. The series of fluids includes a range of degree of polymerization and of size and nature of side radicals. The variations span the range of siloxane fluids currently available and considered as possible lubricants. The major conclusion is that the pressure viscosity coefficient considered important to elastohydrodynamic lubrication is only influenced by changing the nature of the side radical and not by the degree of polymerization or the size of alkyl side groups on the siloxane chain.

Commentary by Dr. Valentin Fuster
J. of Lubrication Tech. 1974;96(3):418-422. doi:10.1115/1.3451984.

A critical examination is made of the concept that gear scoring occurs when the EHD film thickness is less than several times the combined surface roughness. The well known experimental data of Borsoff, Borsoff and Godet, and Ku and Baber is analyzed using advanced EHD computational techniques. The study finds: (a) Gear scoring occurs under fully boundary-lubricated conditions and not even close to the breakdown of the EHD film. (b) Isothermal calculations of minimum EHD film thickness are in error both in magnitude and in trend with failure velocity. An analysis which takes thermal effects into account must be used. (c) Pitch point EHD film thickness does not reliably represent minimum EHD film thickness and therefore cannot be substituted for it. (d) The peak Hertz contact stress in a gear mesh may be significantly understated if calculated only at the pitch point.

Commentary by Dr. Valentin Fuster
J. of Lubrication Tech. 1974;96(3):426-430. doi:10.1115/1.3451989.
Commentary by Dr. Valentin Fuster
J. of Lubrication Tech. 1974;96(3):432-435. doi:10.1115/1.3451993.

Analysis of the dynamic behavior of planar foil bearings is presented for the case when both self acting and external pressurization effects are present. From it, responses to arbitrary disturbances or initial conditions may be deduced. Graphical examples for the film response to step reduction in tension and to a moving pressurization source are shown.

Commentary by Dr. Valentin Fuster
J. of Lubrication Tech. 1974;96(3):437-442. doi:10.1115/1.3451996.

Forty-millimeter-bore ball bearings with lead and lead-alloy-coated retainers were operated in liquid hydrogen at 30000 rpm under a thrust load of 1780 Newtons (400 lb). Bearing lives were compared using different (1) lead- and lead-alloy coatings, (2) coating thicknesses, (3) substrate materials, (4) retainer locating surfaces, and (5) plating techniques. Longer bearing run times were achieved using retainers with a lead-tin-copper alloy coating electroplated onto a leaded-bronze material (22.5 hr) and an aluminum-bronze alloy (19.3 hr). Thirty percent of the bearings tested achieved the desired objective of 10 hours. All of the lead-alloy coated retainers exceeded this objective. A coating thickness of at least 36 microns (0.0014 in.) was used for all bearings exceeding the 10-hour goal.

Commentary by Dr. Valentin Fuster
J. of Lubrication Tech. 1974;96(3):443-448. doi:10.1115/1.3451999.

The performance characteristics of viscoseals are analyzed including the effects of convective inertia and the groove side wall. For the geometries studied, the present theory correlates the experimental data for the sealing and friction coefficient better than previous theories. The sealing coefficient is found to be dependent on the Reynolds number and groove width-to-depth aspect ratio. Leakage and critical Reynolds numbers are also discussed.

Commentary by Dr. Valentin Fuster
J. of Lubrication Tech. 1974;96(3):449-454. doi:10.1115/1.3452000.

A new model of the fluid-filled articular cartilage in human joints is introduced. It is a composite which can imbibe and exudate across the surface and offers resistance in tension and compression, while preserving the essential nonlinearity. The model makes tractable transient static or moving contact problems whose solutions are paramount in the study of failure criteria associated with arthritic conditions. In two examples, indentation—time characteristics and friction coefficient, based on deformation theory, are found and they agree with measured values. Moreover, a third example illustrates the mutual inclusiveness of the two leading theories: the weeping and boosted lubrication theories.

Commentary by Dr. Valentin Fuster
J. of Lubrication Tech. 1974;96(3):455-461. doi:10.1115/1.3452001.

Wear life analysis methods are set forth for mechanical components subjected to a large number of repeated compound impacts (normal impact coupled with relative sliding). The wear mechanism in the elastic stress range is surface fatigue, and wear life is strongly contact-stress dependent. Several typical impact problems are discussed in conjunction with analytical and experimental solution methods. A general impact wear formulation is presented for two elastically restrained bodies. The role of lubrication is discussed. Some charts and diagrams are given to aid quantitative treatment.

Commentary by Dr. Valentin Fuster
J. of Lubrication Tech. 1974;96(3):464-469. doi:10.1115/1.3452005.

Techniques using the infrared radiation emitted by a sliding EHD point contact to measure oil film and surface temperature are discussed. Temperature distributions in the EHD contact are presented for a naphthenic mineral oil at 1.04 × 109 N/m2 (150,000 psi) Hertz pressure and several sliding velocities. Film temperatures as high as 360 C are reported at locations near the points of minimum film thickness in the contact side lobes.

Commentary by Dr. Valentin Fuster
J. of Lubrication Tech. 1974;96(3):472-479. doi:10.1115/1.3452011.

An empirical elastohydrodynamic (EHD) film thickness formula for predicting the minimum film thickness occurring within heavily loaded contacts (maximum Hertz stresses above 1.04 × 109 N/m2 (150,000 psi)) was developed. The formula was based upon X-ray film thickness measurements made with synthetic paraffinic, fluorocarbon, Type II ester and polyphenyl ether fluids covering a wide range of test conditions. Comparisons were made between predictions from an isothermal EHD theory and the test data. The deduced relationship was found to adequately reflect the high-load dependence exhibited by the measured data. The effects of contact geometry, material and lubricant properties on the form of the empirical model are also discussed.

Commentary by Dr. Valentin Fuster
J. of Lubrication Tech. 1974;96(3):482-487. doi:10.1115/1.3452015.

Available mathematical analyses have been applied to develop a reliable method for treating experimental results from ring compression tests with and without bulge formation to obtain quantitative evaluation of constant and varying friction factors, m, and stress-strain curves of the test material. Ring compression tests were made at room temperature on dry and lubricated rings of aluminum, copper, and 1018 steel with 6:3:2 and 6:2:1 (outside diameter:inside diameter:height) nominal dimensions. Neutral radii of the rings at each test height during compression were determined mathematically from measurements of ring dimensions. Substitution of calculated neutral radii and measured ring dimensions into mathematical equations provided quantitative values of the friction factor, m, at each height after compression. Load measurements, made during compression tests, were utilized for verifying the validity of the method.

Commentary by Dr. Valentin Fuster
J. of Lubrication Tech. 1974;96(3):489-496. doi:10.1115/1.3452020.

The Reynolds equation, for short journal bearings, is treated with a new approach to the boundary condition at the beginning of the lubricating film. The nondimensional hydrodynamic side leakage and other performance characteristics of the bearing are shown to be a function not only of Sommerfeld number and width over diameter ratio but also of another parameter which depends on the starting condition at the film inlet. The results obtained by other investigators till now are shown to be only a limiting case of the more general analysis given here. This work is the first part of a larger work embracing the analysis of finite bearings.

Commentary by Dr. Valentin Fuster
J. of Lubrication Tech. 1974;96(3):497-505. doi:10.1115/1.3452024.

This paper describes an investigation of the sliding contact problem encountered in high-energy disk brakes. The analysis includes a simulation modeling, using the finite element method, of the thermoelastic instabilities that cause transient changes in contact to occur on the friction surface. In order to include the effect of wear of the concentrated contacts on the friction surface, a wear criterion is proposed that results in prediction of wear rates for disk brakes that are quite close to experimentally determined wear rates. The thermal analysis shows that the transient temperature distribution in a disk brake can be determined more accurately by use of this thermomechanical analysis than by a more conventional analysis that assumes constant contact conditions. It is also shown that lower, more desirable, temperatures in disk brakes can be attained by increasing the volume, the thermal conductivity, and especially, the heat capacity of the brake components.

Commentary by Dr. Valentin Fuster
J. of Lubrication Tech. 1974;96(3):508-514. doi:10.1115/1.3452030.

A technique for observing two-dimensional variations of pressures using a Manganin pressure transducer is presented. Comparisons are made between pressure predictions using a straightforward analytical tool for pressure analysis and experimental observations. These comparisons are made for the case of a roller with a cylindrical central region with a dub-off edge radius in both aligned as well as misaligned contact with a flat cylinder. Reasonable agreement is shown between theory and experiment. In addition, the theory has been found to be capable of isolating stress risers such as occur at sharp curvature changes between bodies in contact.

Commentary by Dr. Valentin Fuster
J. of Lubrication Tech. 1974;96(3):515-524. doi:10.1115/1.3452031.

A parametric study was performed with 120-mm bore angular-contact ball bearings under varying thrust loads, bearing and lubricant temperatures, and cooling and lubricant flow rates. Contact angles were nominally 20 and 24 deg with bearing speeds to 3 million DN. Endurance tests were run at 3 million DN and a temperature of 492 K (425 deg F) with 10 bearings having a nominal 24-deg contact angle at a thrust load of 22241 N (5000 lb). Bearing operating temperature, differences in temperatures between the inner and outer races, and bearing power consumption can be tuned to any desirable operating requirement by varying 4 parameters. These parameters are outer-race cooling, inner-race cooling, lubricant flow to the inner race, and oil inlet temperature. Preliminary endurance tests at 3 million DN and 492 K (425 deg F) indicate that long-term bearing operation can be achieved with a high degree of reliability.

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
J. of Lubrication Tech. 1974;96(3):461-462. doi:10.1115/1.3452002.
FREE TO VIEW
Abstract
Topics: Wear , Design
Commentary by Dr. Valentin Fuster
J. of Lubrication Tech. 1974;96(3):462-463. doi:10.1115/1.3452003.
FREE TO VIEW
Abstract
Topics: Wear , Design
J. of Lubrication Tech. 1974;96(3):463. doi:10.1115/1.3452004.
FREE TO VIEW
Abstract
Topics: Design

TECHNICAL BRIEFS

J. of Lubrication Tech. 1974;96(3):525-526. doi:10.1115/1.3452034.
Abstract
Topics: Vacuum , Bearings
Commentary by Dr. Valentin Fuster

BOOK REVIEWS

J. of Lubrication Tech. 1974;96(3):527. doi:10.1115/1.3452035.
FREE TO VIEW
Abstract
Commentary by Dr. Valentin Fuster

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