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RESEARCH PAPERS

J. Tribol. 1988;110(2):193-200. doi:10.1115/1.3261583.

An unpressurized, elastomeric O-Ring seal inserted into a rectangular groove is analysed numerically and experimentally. The salient parameters characterizing the seal deformed geometry and stress field are investigated. The results gathered are confronted to those holding for a laterally unrestrained toroidal seal. Based on such a comparison, an analytical model is developed which accounts for the lateral restraining effects.

Topics: Seals , Stress , Geometry
Commentary by Dr. Valentin Fuster
J. Tribol. 1988;110(2):201-211. doi:10.1115/1.3261584.

The influence of varying slider temperature on the characteristics of a conical bearing with constant film thickness rotating with a uniform angular velocity is examined. The fluid is considered to be incompressible and the viscosity is assumed to vary exponentially with temperature. The governing system of coupled partial differential equations in conical coordinates is solved numerically using finite difference method to yield the various bearing characteristics. The results show that maintaining the slider at temperature lower than that of the pad causes an increase in the load capacity of the bearing.

Commentary by Dr. Valentin Fuster
J. Tribol. 1988;110(2):212-215. doi:10.1115/1.3261585.

Wear tests on the main bearings of 8.5 inch XHP 3 rock bits were performed, from which it is concluded that the way to improve the drilling effectiveness for the rock bits is to set drilling pressure and rotary speed properly, and to develop a new type of grease for rock bits which can bear a higher temperature than conventional grease. In addition, it is also shown that an inexpensive copper alloy can take the place of expensive Ag85Mn15 as an anti-wear material in the bearing, so that the production cost for the rock bits can be reduced.

Commentary by Dr. Valentin Fuster
J. Tribol. 1988;110(2):217-221. doi:10.1115/1.3261588.

The present paper discussed the critical depth, i.e., the depth at which the thermal tensile stress reaches a maximum, caused by the frictional excitation of a fast moving asperity. In the study, the critical depth was computed directly by maximizing the thermal tensile stress with respect to positions under the asperity inside the material. The relationship between critical depth and Peclet number for all materials in the two-dimensional formulation may be simplified to satisfy the exponential form

R(ηcr)2.275 = 20.4368.
Stellite III was chosen as the indicator material. Other parametric effects including mechanical properties and thermal properties were tested with materials having diverse property values. These tests confirmed that for the two-dimensional formulation, the Peclet number is the only one which dominates the critical depth.

Commentary by Dr. Valentin Fuster
J. Tribol. 1988;110(2):222-227. doi:10.1115/1.3261589.

This investigation considers the thermo-mechanical effects of an asperity traversing at a high speed over a semi-infinite medium with a thin, hard coated surface. The general analytical solution of the temperature field and the thermal stress state are obtained and expressed in Fourier transform space. The analysis emphasizes the heating effect of the friction force, which leads to the initiation of the thermo-mechanical cracking or “heat-checking,” in the coating layer, the substrate, or their interface. For hard coated layers, the initiation of a crack will occur either in the coating layer, the substrate or the interface depending on the relative properties of the coating and the substrate and their bonding strength.

Commentary by Dr. Valentin Fuster
J. Tribol. 1988;110(2):228-234. doi:10.1115/1.3261590.

This paper discusses the stability of a rigid rotor supported by double-row admission journal bearings with circular slot restrictors. In the theoretical analysis, the energy loss at the outlet of the slot is taken into account because the gas flow is subject to a rapid change in direction, and here, the energy loss coefficient is determined experimentally. It is found that a better agreement between the theoretical and experimental results for the threshold of instability can be obtained by considering the energy loss. Furthermore, in this paper, it is shown experimentally that an aerostatic journal bearing with circular slot restrictors has higher stiffness and higher stability than a conventional point source bearing with inherently compensated feeding holes.

Commentary by Dr. Valentin Fuster
J. Tribol. 1988;110(2):235-240. doi:10.1115/1.3261591.

The quasi-static sliding contact stress field due to a spherical indenter on an elastic half-space with a single layer is studied. The contact problem is solved using a least-squares iterative approach and the stress field in the layer and substrate is determined using the Papkovich-Neuber potentials. The resulting stresses are discussed for different values of the layer stiffness relative to the substrate and also for different values of the friction coefficient.

Commentary by Dr. Valentin Fuster
J. Tribol. 1988;110(2):241-246. doi:10.1115/1.3261592.

We propose an accurate numerical method to solve the classical line contact problem of elastohydrodynamic lubrication. The method incorporates a second order accurate discretization and a straightforward automatic local mesh refinement procedure. Using these elements, we remove discretization errors which have produced significant inaccuracies in previously published results, and we completely resolve the pressure spike which is shown to be smooth on a sufficiently small length scale.

Commentary by Dr. Valentin Fuster
J. Tribol. 1988;110(2):247-252. doi:10.1115/1.3261593.

Thermal simulation of complex mechanism performance is based on the simultaneous use of analytical methods for simple shaped moving parts and numerical techniques (Finite Element Method) of the others. The method presented called Hybrid method, uses these two techniques for 2-D and 3-D cases. A particular formulation of analytical results insures the compatibility with the Finite Element Method. Large CPU time savings are obtained when compared to a pure numerical analysis.

Commentary by Dr. Valentin Fuster
J. Tribol. 1988;110(2):253-261. doi:10.1115/1.3261594.

A generalized Reynolds-type lubrication equation valid for arbitrary Knudsen numbers, defined as the ratio of the molecular mean free path to the film thickness, is derived from a linearized Boltzmann equation by semi-numerically calculating the flow rates of fundamental flows in the lubrication film: Poiseuille flow, Couette flow, and thermal creep flow. Numerical analysis of the equation for high Knudsen numbers reveals three principal results. First, Burgdorfer’s modified Reynolds equation featuring the first-order velocity slip boundary condition overestimates load carrying capacities, while the approximation equation including both the first- and second-order velocity slip boundary condition underestimates them. Second, since the flow rate of the Couette flow, which is independent of Knudsen numbers, becomes dominant as the bearing number increases, all the lubrication equation results tend toward the same asymptotic value for an infinite bearing number. Third, a new kind of load carrying capacity caused by thermal creep flow occurs if temperature gradients at the boundaries exist in the flow direction.

Commentary by Dr. Valentin Fuster
J. Tribol. 1988;110(2):263-270. doi:10.1115/1.3261597.

The dynamic behavior of externally pressurized gas bearings is described by means of frequency response functions, from which dynamic stiffness and damping coefficients are derived. A numerical method is presented to calculate the frequency response function for plane circular thrust bearings with convergent gap geometry. A test procedure is described for measuring the frequency response function of an air film in order to verify computational, results. The comparison reveals a fairly good agreement between measured and calculated frequency responses. Finally, the effect of bearing parameters on the frequency response function of the air film is investigated.

Commentary by Dr. Valentin Fuster
J. Tribol. 1988;110(2):271-278. doi:10.1115/1.3261598.

A stability criterion is presented to evaluate instability phenomena in mechanical systems containing externally pressurized gas bearings. For this criterion, the gas bearing films and the supporting structure are characterized separately by means of frequency response functions. The overall system may be considered as a feedback-loop for which the Nyquist criterion will define stability limits. The analysis demonstrates the interaction between the dynamics of the supporting structure and the air gap. The stability criterion is generalized for systems containing more than one gas film. The stability criterion is verified experimentally.

Commentary by Dr. Valentin Fuster
J. Tribol. 1988;110(2):279-284. doi:10.1115/1.3261599.

The film thickness, pressure, and flow in elastohydrodynamically lubricated conjunctions were calculated for a line contact. The main focus of the study was to get a better understanding of why a pressure spike exists in elastohydrodynamically lubricated conjunctions. Various combinations of viscous or isoviscous and compressible or incompressible situations were studied for a wide range of loads. The basic parameters were pressure, pressure gradient, film shape, and flow. It was found that the major factor causing the pressure spike to occur was the viscosity.

Commentary by Dr. Valentin Fuster
J. Tribol. 1988;110(2):285-291. doi:10.1115/1.3261600.

Experiments are presented in which various combinations of two (almost) straight cylinders with circular cross-section are pressed together while their axes remain basically parallel. Results are compared with theoretical predictions from a half space model; from this half space model extended with adjustments for the finite dimensions of the cylinders in contact; and from an infinite cylinder model from literature. Frictional effects are not considered and the material is assumed to be linear-elastic. Agreement in the approach of the center lines of the cylinders under load is found to exist more or less between the experimental results and the theoretical predictions by the models. The behaviour of the models is discussed, and reasonable to good agreement is demonstrated for the extended half space model using an integral depth adjustment of 3/4 of the diameter of each cylinder in contact. A possible way to further improve this model is indicated.

Commentary by Dr. Valentin Fuster
J. Tribol. 1988;110(2):292-296. doi:10.1115/1.3261601.

This paper presents the results of a preliminary analysis of the branching behavior of a horizontal subsurface crack subjected to a moving compressive surface load. The purpose of the analysis is to provide some fundamental understanding concerning the behavior of subsurface contact fatigue cracks, including the onset of pitting or delamination. The analysis is approximate inasmuch as the traction-free boundary condition at the surface is only partially satisfied, and the history dependent effects arising from crack face friction are not included. The results show that mode I branching crack growth is possible even though the stress field is largely compressive. Nevertheless, based on a simple competing failure mode model the results indicate that within the limits of the analysis, nonbranching mode II growth is likely to be the dominant mode of propagation.

Commentary by Dr. Valentin Fuster
J. Tribol. 1988;110(2):298-303. doi:10.1115/1.3261604.

Finite element analysis techniques have been used to simulate braking friction in a large, heavy duty twin leading shoe brake. Temperature, lining wear and pressure distributions, and thermal distortions of the brake drum which are generated during high pressure brake applications from two different road speeds have been predicted and compared with experimental data. Two different types of brake lining, a conventional asbestos-based resin-bonded composite friction material and a heavy duty resin-bonded semi-metallic type of friction material have been studied in this way, and it is shown that observed in-stop and speed-related brake performance are strongly dependent upon the rate of frictional energy transformation at the lining/drum interface, which defines the development of interface transient temperatures. By relating the measured friction characteristic of the friction material to predicted lining friction surface temperatures good correlation between predicted and actual brake performance is demonstrated.

Commentary by Dr. Valentin Fuster
J. Tribol. 1988;110(2):306-311. doi:10.1115/1.3261608.

This paper discusses the temperature distribution and the stress state in the vicinity of a near-surface rectangular cavity. They occur when the solid is subjected to the Coulomb frictional loading of an asperity moving at moderately high speed. The finite difference method is employed to calculate both the temperature and stress fields. The energy balance method is applied at the corners of the rectangular cavity to resolve the problem of singularities in the temperature field there. The stress singularity at each corner is represented by a special element that is introduced representing the behavior of the known stress singularity at the corner and its surrounding vicinity. Results show that the thermal stress effect dominates the stress field and eventually leads to failure. When a defect, such as a cavity, exists, the stress state that determines the failure phenomenon is more severe and can be quantified depending on the location of the cavity. These results were determined through a numerical computation based on the material properties of Stellite III. However, the parametric effect of material variations including changes in both thermal and mechanical properties were also considered. The study of the cavity location also established the existence of a critical cavity location. This location is defined by the critical ligament thickness (thickness between the wear surface and the top edge of the cavity), at which the cavity-influenced thermal tensile stress reaches a maximum. This thickness is important to designers when cavities at coating/substrate interface are either unavoidable or are too expensive to control in fabrication.

Commentary by Dr. Valentin Fuster
J. Tribol. 1988;110(2):313-317. doi:10.1115/1.3261612.

This paper presents an analysis of a new noncontacting pumping seal. A hydrodynamic lubricating film is maintained due to Rayleigh-steps. If the low pressure side of the seal is filled with a fluid, the fluid can be pumped into the high pressure side by pumping grooves until the shaft speed reaches a limit value. The experimental results confirm the theoretical predictions for lubrication and sealing performance. Due to the high pumping ability in addition to the high stiffness of its hydrodynamic film, the seal can operate without wear and leakage for a high pressure fluid.

Commentary by Dr. Valentin Fuster
J. Tribol. 1988;110(2):320-326. doi:10.1115/1.3261619.

Nearly all magnetic bearings which have found use in modern technology are based on the attractive force between a magnet and a magnetic material. A distinct disadvantage is that such devices are inherently unstable and require active feedback for operation. In the present study an eddy current bearing is analyzed which uses repulsive forces to levitate a rotor, as in proposed advanced rail transportation systems. The journal bearing is considered to be a series of one-dimensional pads wrapped around a shaft. Maxwell’s equations are solved for the equivalent Cartesian geometry pad and rotor. This system is modeled as a sinusoidally varying surface current backed with an infinitely permeable (magnetic) pad which is separated from a conductive nonmagnetic rotor by a free gap. The magnetic forces are found to vary inversely with gap size, a necessary condition for stability. The behavior of an eddy current journal bearing is calculated and compared to that of fluid film bearings. Load, “friction” (which may also serve as propulsion), and attitude angle are determined as a function of eccentricity ratio, a slip parameter, clearance ratio and a number of pads. The approximate results presented may serve as guidelines for development work and subsequent analysis.

Commentary by Dr. Valentin Fuster
J. Tribol. 1988;110(2):327-334. doi:10.1115/1.3261623.

Wide thrust bearings operating in turbulent inertial flow regimes are studied. Isothermal and thermohydrodynamic performances of the bearing are analyzed. Integro-differential equations of motion, continuity, and energy equations are solved to yield pressure, mass-mean velocity, and temperature distributions. The effects of contraction ratio and film Reynolds number on the pressure field, load bearing capacity, flow rate and frictional resistance force of the bearing are examined. The effect of film temperature variation on the performance of bearing is studied and the result is compared with the isothermal case. It is observed that the viscous heating reduces the load bearing capacity to a significant extent. The effects of including the inertial terms are also considered. The results for inertial and noninertial cases are plotted and compared. It is shown that with the inclusion of the inertial terms the load bearing capacity somewhat increases. The results obtained are compared with the existing data and reasonable agreement is observed.

Commentary by Dr. Valentin Fuster
J. Tribol. 1988;110(2):335-341. doi:10.1115/1.3261624.

This paper is useful in analyzing the performance of finite-width-air bearings in the rarefied gas region, using a newly developed finite element method. The linearized Boltzmann equation was solved by numerical iteration and a pressure equation was obtained, coupled with a continuous equation. The finite element method was developed for solving the pressure equation. The results were compared with a two moment approximate solution for the Boltzmann equation, which corresponds to the conventional slip flow analysis developed by Burgdorfer. An analysis of tapered flat slider flying characteristics in the rarefied gas regime, e.g., when the inverse Knudsen number in the trailing edge = 1, showed that the present exact solution for the Boltzmann equation was different from the two moment approximate solution by more than 10 percent in load capacity value, when the dimensionless load was not so large as when it is used for actual slider design.

Commentary by Dr. Valentin Fuster
J. Tribol. 1988;110(2):342-346. doi:10.1115/1.3261627.

We have measured the separation and central pressure of a slightly concave axially symmetric pressurized bearing as a function of lubricant (air) mass flux and bearing load. We find that a mean face slope of 1.6 × 10−3 makes a dramatic difference in the behavior of the bearing, reducing the central pressure by more than a factor of two and eliminating the need for overpressures to start the system. We have also explored the behavior of the system analytically and find excellent agreement between theory and experiment.

Commentary by Dr. Valentin Fuster
J. Tribol. 1988;110(2):348-353. doi:10.1115/1.3261630.

The behavior of liquid droplets in O/W type emulsions flowing between a flat glass plate and a metal roller was observed by means of a microscope. The behavior of the droplets introduced into the EHL film was found to be related to the streamlines of the continuous water phase in the vicinity of the inlet zone. It was observed that the oil droplets which penetrated into the EHL zone formed an oily pool (an oily film zone) containing water droplets in the inlet zone close to the EHL zone. This oily pool was a W/O emulsion rich in oil caused by phase inversion. The effects of oil concentration, emulsifier content and rolling speed on the area of the oily pool were investigated, and it was found that the extent of the oily pool was influenced by the rolling speed as well as oil concentration. The EHD film thickness was measured by means of optical interferometry with use of two wavelengths, and the measured results were compared with the calculated ones employing the starvation theory of Wolveridge et al. and the empirical equation of Wymer and Cameron for the region of the oil pool. It was found that course droplets play an important role in film formation by causing the formation of the oily pool in the low speed range. In the high speed range, however, a fine O/W emulsion forms the film.

Commentary by Dr. Valentin Fuster
J. Tribol. 1988;110(2):354-359. doi:10.1115/1.3261631.

A new analysis procedure is presented which solves for the flow variables of an incompressible-flow annular pressure seal in which the rotor has a large static displacement from the centered position. The analysis begins with a set of governing equations based on a turbulent bulk-flow model and Moody’s friction equation. No simplification of these bulk-flow equations are required for the solution procedure. Perturbation of the flow variables yields a set of zeroth and first-order equations. The zeroth-order equations (which model the large static displacement) are integrated by means of an efficient new method which employs Fast Fourier Transforms. Further integration of the zeroth-order pressures yields the hydrodynamic reactive force. Predictions for the hydrodynamic forces from this analysis procedure are in excellent agreement with available experimental results.

Commentary by Dr. Valentin Fuster
J. Tribol. 1988;110(2):361-366. doi:10.1115/1.3261634.

In Part 1 of this paper, a new analysis procedure is presented which solves for the flow variables of an annular pressure seal in which the rotor has a large static displacement (eccentricity) from the centered position. This part of the paper (Part 2) incorporates the solutions from Part 1 to investigate the effect of eccentricity on the rotordynamic coefficients. The analysis begins with a set of governing equations based on a turbulent bulk-flow model and Moody’s friction factor equation. Perturbations of the flow variables yields a set of zeroth- and first-order equations. After integration of the zeroth-order equations by means of the method described in Part 1, the resulting zeroth-order flow variables are used as input in the solution of the first-order equations. Further integration of the first order pressures yields the eccentric rotordynamic coefficients. The results from this procedure compare very well with available experimental data, and are clearly more accurate than the predictions based on a Finite Element model.

Commentary by Dr. Valentin Fuster
J. Tribol. 1988;110(2):367-374. doi:10.1115/1.3261635.

Thermohydrodynamic theory is extended to include the effect of solid particles in hydrodynamically lubricated journal bearings. Appropriate governing equations and boundary conditions are derived for the fluid flow and heat transfer processes taking place in a finite journal bearing. A general computer program is developed to numerically solve the governing equations. Results are provided for biphase lubricants containing oil with molybdenum disulfide and polytetrafluoroethylene particles. The computational results are in good agreement with experimental findings. The results indicate that the bearing temperature field is affected significantly by the presence of particles in oil. Moreover, it is found that inclusion of particles in the lubricant results in a higher coefficient of friction in the mid-range of the Sommerfeld number compared to that of the clean oil.

Commentary by Dr. Valentin Fuster

DISCUSSIONS

ERRATA

TECHNICAL BRIEFS

J. Tribol. 1988;110(2):375-377. doi:10.1115/1.3261636.

The motion of an electrically conducting fluid film squeezed between two parallel disks in the presence of a magnetic field applied perpendicular to the disks is studied. Analytic solutions through use of a regular perturbation scheme are obtained. The results show that the electromagnetic forces increase the load carrying capacity considerably.

Commentary by Dr. Valentin Fuster
Commentary by Dr. Valentin Fuster
J. Tribol. 1988;110(2):380-382. doi:10.1115/1.3261638.
Abstract
Topics: Friction , Lubrication
Commentary by Dr. Valentin Fuster
Commentary by Dr. Valentin Fuster

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