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REPORTS

J. of Lubrication Tech. 1976;98(3):353-356. doi:10.1115/1.3452850.
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Abstract
Topics: Lubrication
Commentary by Dr. Valentin Fuster

RESEARCH PAPERS

J. of Lubrication Tech. 1976;98(3):357-361. doi:10.1115/1.3452851.

The elastohydrodynamic lubrication of two rollers in combined rolling and sliding is considered. A simple rheological model to predict the traction is presented. The model is based upon an exponential pressure dependent viscosity at low pressures and a linear shear stress/pressure relationship at high pressures. The slope of the latter is assumed to be a function of the rolling and sliding velocities. The model is used to analyze the traction data of two recently published experimental investigations of other authors and good agreement is achieved in most cases. The model should be of considerable use to designers in the preliminary analysis of rolling contact systems in combined rolling and sliding.

Commentary by Dr. Valentin Fuster
J. of Lubrication Tech. 1976;98(3):362-365. doi:10.1115/1.3452854.

An existing shear stress theory and lubricant rheological model were studied and evaluated by applying them to traction prediction in a sliding elastohydrodynamic point contact. Numerical calculations, using measured film thickness and surface temperature data, were compared with measured tractions under several conditions of normal load and sliding speed. In addition, the theory was used to study the effect on the traction of variations in the lubricant material properties.

Commentary by Dr. Valentin Fuster
J. of Lubrication Tech. 1976;98(3):367-372. doi:10.1115/1.3452858.

An inlet zone analysis is presented for the elastohydrodynamic lubrication of heavily loaded contacts of layered elastic solids under isothermal and isoviscous conditions. An elastic layer of incompressible elastomeric material (with Poisson’s ratio, ν = 0.50) bonded to a rigid substrate is considered. Numerical results are presented in dimensionless form to describe the variation of nominal film thickness over a wide range of loads, layer thicknesses, and other operating variables.

Commentary by Dr. Valentin Fuster
J. of Lubrication Tech. 1976;98(3):375-381. doi:10.1115/1.3452861.

A numerical solution of the isothermal elastohydrodynamic problem for point contacts has been presented which reproduces all the essential features of the previously reported experimental observations based upon optical interferometry. In particular, the two “side lobes” in which minimum film thickness regions occur are shown to emerge in the theoretical solutions. The influence of the ellipticity parameter upon solutions to the point contact problem has been explored in the present paper. The ellipticity parameter (k) was varied from one (a ball on a plate) to eight (a configuration approaching line contact), and it has been shown that the minimum film thicknesses can be related to the well known line contact solutions by remarkably simple expressions involving either (k) or the effective radius of curvature ratio (Ry /Rx ).

Commentary by Dr. Valentin Fuster
J. of Lubrication Tech. 1976;98(3):384-392. doi:10.1115/1.3452865.

In this second part of a two-part paper, experimental fatigue life data on ball bearings operated under different lubrication conditions are correlated to surface damage densities of life tested ball bearing inner rings, as determined by scanning electron microscopy. In Part I [16], five cases of a mathematical model for the prediction of fatigue life in contaminated bearings were presented. These models are fitted to the experimental data given in the present Part II. The correlation coefficient of experimental L10 life with model Case II predictions, based on observed defect densities, is of the order of 0.99 and highly significant for most test groups. One grease lubricated group requires fitting by model Case III. Predicted life dispersion exponents are too high compared to experiment. General data on lubricant contaminant densities show a sufficiency of particles to cause the observed surface damage, but tend to overpredict damage on the basis of the simple particle transport model used. The principal usefulness of the model in its present form is as a tool for the interpretation of the influence on fatigue life of surface damage acquired in service.

Commentary by Dr. Valentin Fuster
J. of Lubrication Tech. 1976;98(3):401-407. doi:10.1115/1.3452869.

This paper contains an analysis of a class of elastohydrodynamic squeeze film problems. A true transient analysis is presented. Thick films bounded by a finite rigid plate and a compliant half-space are considered. The effect of different approach constraints is explored, among these being constant and time varying load and constant and time varying center point pressure. The effect of different material models is also considered.

Commentary by Dr. Valentin Fuster
J. of Lubrication Tech. 1976;98(3):409-411. doi:10.1115/1.3452872.

The momentum and energy integral methods are used to study the effect of inertia on the behavior of a non-Newtonian (Power Law) squeeze film. It is shown that the inertia correction in the load capacity is more significant for pseudoplastic fluids, n < 1. For a Newtonian fluid, n = 1, the expressions obtained by using the energy integral method yield results identical to those obtained from a first-order iteration, and which are in good agreement with available experiments.

Commentary by Dr. Valentin Fuster
J. of Lubrication Tech. 1976;98(3):412-417. doi:10.1115/1.3452873.

The Reynolds equation for the general case of dynamic loading is derived for fluid suspensions, using the micropolar fluid theory. Detailed consideration is given to the dynamic behavior of squeeze films in journal bearings under a fluctuating load with no journal rotation. The characteristics of an infinitely long journal bearing under a cyclic sinusoidal load are shown in curve form, so as to elaborate the micropolar effects.

Commentary by Dr. Valentin Fuster
J. of Lubrication Tech. 1976;98(3):418-425. doi:10.1115/1.3452874.

Tests were conducted at 350 K (170° F) with three groups of 8.9 cm (3.5 in.) pitch diameter spur gears made of vacuum-induction melted (VIM), vacuum-arc remelted (VAR), AISI M-50 steel and one group of vacuum-arc remelted (VAR) AISI 9310 steel. The pitting fatigue life of the standard forged and ausforged gears was approximately five times that of the VAR AISI 9310 gears and ten times that of the bending fatigue life of the standard machined VIM-VAR AISI M-50 gears run under identical conditions. There was a slight decrease in the 10-percent life of the ausforged gears from that for the standard forged gears. However, the difference is not statistically significant. The standard machined gears failed primarily by gear tooth fracture while the forged and ausforged VIM-VAR AISI M-50 and the VAR AISI 9310 gears failed primarily by surface pitting fatigue. The ausforged gears had a slightly greater tendency to fail by tooth fracture than the standard forged gears.

Commentary by Dr. Valentin Fuster
J. of Lubrication Tech. 1976;98(3):426-431. doi:10.1115/1.3452877.

An analytical model for the hydrodynamic lubrication of high speed strip rolling is developed. The model includes the effect of thermal loading due to back flow and slip on the film formation process. The work zone analysis takes account of thermal effects on film thickness and friction. The influence of geometry, speed and lubricant and work-piece properties on the forward slip, roll load and torque are described in detail and compared with previously published experimental data.

Commentary by Dr. Valentin Fuster
J. of Lubrication Tech. 1976;98(3):433-440. doi:10.1115/1.3452883.

The notion of a “plug” bearing taken up in this work refers to bodies moving within tight circular conduits. Our interest lies in the hydrodynamic film generated in the narrow interspace between body and wall under conditions of an incompressible fluid and unequal boundary pressures. For generality rotation as well as translation is considered. Performance characteristics are given for nontilting frustums, both diverging and converging in the direction of motion. It is shown that for a given body shape the amount of leakage past the plug is the same regardless of its orientation. However, with geometries whose film increases in the direction of plug velocity there is a wide range of operating conditions when the resultant force is such as to drive the body against the wall of the conduit; over the same range, shapes which produce films decreasing in the direction of motion yield a floating force.

Commentary by Dr. Valentin Fuster
J. of Lubrication Tech. 1976;98(3):441-445. doi:10.1115/1.3452884.

A new concept of a journal bearing is developed which prevents side leakage of the lubricant, thus eliminating the need for sealing and collecting this leakage. The cooling of the bearing is accomplished by the prevailing circumferential flow. An analysis is performed and solutions are given for the bearing geometries and inlet pressures required to achieve the above purpose.

Commentary by Dr. Valentin Fuster
J. of Lubrication Tech. 1976;98(3):446-452. doi:10.1115/1.3452885.

The method of matched asymptotic expansions is used to develop an asymptotic expression for the pressure for large bearing numbers for the case of an infinite slider bearing with a general film thickness that has a discontinuous slope at a point. It is shown that, in addition to the boundary layer of the pressure at the trailing edge, there is also a boundary layer in the derivative of the pressure at the point of discontinuity. The corresponding load formula is also derived. The special cases of the taper-flat and taper-taper slider bearings are discussed.

Commentary by Dr. Valentin Fuster
J. of Lubrication Tech. 1976;98(3):453-462. doi:10.1115/1.3452886.

The general governing equations for finite porous journal bearings with compressible lubricants and slip-flow are derived. A mass content rule is developed for infinitely long porous bearings; an exact solution is established for a gas-lubricated porous bearing with very large bearing number consistent with the mass content rule. An analytic-numerical technique which takes advantage of the linearity of the pressure equation in the porous medium is developed to solve the problem for finite values of compressibility. The results approach those for the solid bearing case as the defined poro-slip parameter β becomes very large.

Commentary by Dr. Valentin Fuster
J. of Lubrication Tech. 1976;98(3):463-469. doi:10.1115/1.3452889.

This paper describes the development of a computer program used to analyze completely the motion of a ball in a high-speed, thrust-loaded ball bearing. Particular emphasis is paid to the role of the lubricant in governing the forces and moments acting on each ball. Expressions for these forces due to the rolling and sliding of the ball are derived in the light of the latest fluid models, and estimates are also made of the cage forces applicable in this specific situation. It is found that only when lubricant viscoelastic behavior is considered do the theoretical predictions agree with existing experimental evidence.

Commentary by Dr. Valentin Fuster
J. of Lubrication Tech. 1976;98(3):472-475. doi:10.1115/1.3452893.

Spherically hollow balls of 21.7, 50.0 and 56.5 percent mass reduction have been operated in ball bearings and in a 5-ball fatigue tester with differing outcomes. Available theoretical and experimental treatments of stresses in spherically hollow balls are reviewed and compared. Bending stresses are estimated for these spherically hollow balls to better understand the differences in ball bearing and fatigue test experience.

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

TECHNICAL FORUM

Commentary by Dr. Valentin Fuster

TECHNICAL BRIEFS

J. of Lubrication Tech. 1976;98(3):476-478. doi:10.1115/1.3452896.

A model for the variation of lubricant viscosity in a concentrated contact and a graphical method for determining the reduction of effective viscosity of a lubricant due to insufficient time in the contact zone has been presented in [1]. Design equations are now developed for the effective viscosity which are more convenient for use in numerical procedures.

Commentary by Dr. Valentin Fuster

BOOK REVIEWS

J. of Lubrication Tech. 1976;98(3):479. doi:10.1115/1.3452897.
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Abstract
Commentary by Dr. Valentin Fuster
J. of Lubrication Tech. 1976;98(3):479-480. doi:10.1115/1.3452898.
FREE TO VIEW
Abstract
Commentary by Dr. Valentin Fuster

AWARDS

J. of Lubrication Tech. 1976;98(3):480. doi:10.1115/1.3452899.
FREE TO VIEW
Abstract
Commentary by Dr. Valentin Fuster

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