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NASA NTRS1996

Forced Oscillations of Supported Drops

Oscillations of supported liquid drops are the subject of wide scientific interest, with applications in areas as diverse as liquid-liquid extraction, synthesis of ceramic powders, growing of pure crystals in low gravity, and measurement of dynamic surface tension. In this research, axisymmetric forced oscillations of arbitrary amplitude of viscous liquid drops of fixed volume which are pendant from or sessile on a rod with a fixed or moving contact line and surrounded by an inviscid ambient gas are induced by moving the rod in the vertical direction sinusiodally in time. In this paper, a preliminary report is made on the computational analysis of the oscillations of supported drops that have 'clean' interfaces and whose contact lines remain fixed throughout their motions. The relative importance of forcing to damping can be increased by either increasing the amplitude of rod motion A or Reynolds number Re. It is shown that as the ratio of forcing to damping rises, for drops starting from an initial rest state a sharp increase in deformation can occur when they are forced to oscillate in the vicinity of their resonance frequencies, indicating the incipience of hysteresis. However, it is also shown that the existence of a second stable limit cycle and the occurrence of hysteresis can be observed if the drop is subjected to a so-called frequency sweep, where the forcing frequency is first increased and then decreased over a suitable range. Because the change in drop deformation response is abrupt in the vicinity of the forcing frequencies where hysteresis occurs, it should be possible to exploit the phenomenon to accurately measure the viscosity and surface tension of the drop liquid.

Wilkes, Edward D.↗

NASA NTRS1996

Effect of Variable Gravity on Evaporation of Binary Fluids in a Capillary Pore Evaporator

The research project focuses on experimental investigation of the capillary-pumped evaporative heat transfer phenomenon. The objective is to examine whether the heat transfer and stability of a heated meniscus in a capillary pore can be enhanced by adding trace amounts of a non-volatile solute to a solvent and to understand the changes that occur. The experimental setup consists of a single pore evaporator connected to a reservoir which supplies liquid to the evaporator. In addition to the experiments of capillary-pumped evaporation, a parallel experimental study has been conducted to systematically investigate the effects of gravity as well as the effects of bulk composition on the heat transfer characteristics of evaporating binary thin films near the contact line region along an inclined heated surface. To investigate the buoyancy effects on evaporation along an inclined heated surface, the angle of inclination from a horizontal plane was varied fro 15 C to 90 C. An optimum concentration between 0.5% and 1% decane in pentane/decane solutions has been demonstrated at different angles of inclination. Improved heat transfer was found for the geometry with the smallest angle of inclination of 15 degrees. In addition, flow visualization has revealed that at low inclination angles effective heat transfer takes place primarily due to an extension of the thin film near the contact line. At these low inclination angles, the optimum concentration is associated with enhanced wetting characteristics and reduced thermocapillary stresses along the interface.

Girgis, Morris M.↗

NASA NTRS2015

Effect of Roller Geometry on Roller Bearing Load-Life Relation

Cylindrical roller bearings typically employ roller profile modification to equalize load distribution, minimize stress concentration at roller ends and allow for a small amount of misalignment. The 1947 Lundberg-Palmgren analysis reported an inverse fourth power relation between load and life for roller bearings with line contact. In 1952, Lundberg and Palmgren changed their load-life exponent to 10/3 for roller bearings, assuming mixed line and point contact. The effect of roller-crown profile was reanalyzed in this paper to determine the actual load-life relation for modified roller profiles. For uncrowned rollers (line contact), the load-life exponent is p = 4, in agreement with the 1947 Lundberg-Palmgren value but crowning reduces the value of the exponent, p. The lives of modern roller bearings made from vacuum-processed steels significantly exceed those predicted by the Lundberg-Palmgren theory. The Zaretsky rolling-element bearing life model of 1996 produces a load-life exponent of p = 5 for flat rollers, which is more consistent with test data. For the Zaretsky model with fully crowned rollers p = 4.3. For an aerospace profile and chamfered rollers, p = 4.6. Using the 1952 Lundberg-Palmgren value p = 10/3, the value incorporated in ANSI/ABMA and ISO bearing standards, can create significant life calculation errors for roller bearings.

Roller bearing↗

NASA NTRS1976

Simplified solution for point contact deformation between two elastic solids

A linear-regression by the method of least squares is made on the geometric variables that occur in the equation for point contact deformation. The ellipticity and the complete eliptic integrals of the first and second kind are expressed as a function of the x, y-plane principal radii. The ellipticity was varied from 1 (circular contact) to 10 (a configuration approaching line contact). These simplified equations enable one to calculate easily the point-contact deformation to within 3 percent without resorting to charts or numerical methods.

Brewe, D. E.↗

NASA NTRS1977

Simplified solution for elliptical-contact deformation between two elastic solids

A linear regression by the method of least squares is made on the geometric variables that occur in the equation for elliptical-contact deformation. The ellipticity and the complete elliptic integrals of the first and second kind are expressed as a function of the x,y-plane principal radii. The ellipticity was varied from 1 (circular contact) to 10 (a configuration approaching line contact). The procedure for solving these variables without the use of charts or a high-speed computer would be quite tedious. These simplified equations enable one to calculate easily the elliptical-contact deformation to within 3 percent accuracy without resorting to charts or numerical methods.

Brewe, D. E.↗

NASA NTRS1985

Fast approach for calculating film thicknesses and pressures in elastohydrodynamically lubricated contacts at high loads

The film thicknesses and pressures in elastohydrodynamically lubricated contacts have been calculated for a line contact by using an improved version of Okamura's approach. The new approach allows for lubricant compressibility, the use of Roelands' viscosity, a general mesh (nonconstant step), and accurate calculations of the elastic deformation. The new approach is described, and the effects on film thickness, pressure, and pressure spike of each of the improvements are discussed. Successful runs have been obtained at high pressure (to 4.8 GPa) with low CPU times.

Houpert, L. G.↗

NASA NTRS1986

Fast approach for calculating film thicknesses and pressures in elastohydrodynamically lubricated contacts at high loads

Houpert, L. G.↗

NASA NTRS1982

The motion of a drop in a rigid surface

The assumptions of a region of slip near a moving contact line (to remove the force singularity) and a constant contact angle are used to obtain the equation for the shape of a thin drop of liquid resting on a rigid plane. Three asymptotic expansions are matched together to obtain an expression for the rate at which the drop spreads. Some cases of sliding motion are also examined. Although the technique is presented here for thin drops only, it can also be applied to drops of arbitrary size.

Hocking, L. M.↗

NASA NTRS1994

Generation of gear tooth surfaces by application of CNC machines

This study will demonstrate the importance of application of computer numerically controlled (CNC) machines in generation of gear tooth surfaces with new topology. This topology decreases gear vibration and will extend the gear capacity and service life. A preliminary investigation by a tooth contact analysis (TCA) program has shown that gear tooth surfaces in line contact (for instance, involute helical gears with parallel axes, worm gear drives with cylindrical worms, etc.) are very sensitive to angular errors of misalignment that cause edge contact and an unfavorable shape of transmission errors and vibration. The new topology of gear tooth surfaces is based on the localization of bearing contact, and the synthesis of a predesigned parabolic function of transmission errors that is able to absorb a piecewise linear function of transmission errors caused by gear misalignment. The report will describe the following topics: description of kinematics of CNC machines with six degrees of freedom that can be applied for generation of gear tooth surfaces with new topology. A new method for grinding of gear tooth surfaces by a cone surface or surface of revolution based on application of CNC machines is described. This method provides an optimal approximation of the ground surface to the given one. This method is especially beneficial when undeveloped ruled surfaces are to be ground. Execution of motions of the CNC machine is also described. The solution to this problem can be applied as well for the transfer of machine tool settings from a conventional generator to the CNC machine. The developed theory required the derivation of a modified equation of meshing based on application of the concept of space curves, space curves represented on surfaces, geodesic curvature, surface torsion, etc. Condensed information on these topics of differential geometry is provided as well.

Litvin, F. L.↗

NASA NTRS1996

Wetting Hysteresis at the Molecular Scale

The motion of a fluid-fluid-solid contact line on a rough surface is well known to display hysteresis in the contact angle vs. velocity relationship. In order to understand the phenomenon at a fundamental microscopic level, we have conducted molecular dynamics computer simulations of a Wilhelmy plate experiment in which a solid surface is dipped into a liquid bath, and the force-velocity characteristics are measured. We directly observe a systematic variation of force and contact angle with velocity, which is single-valued for the case of an atomically smooth solid surface. In the microscopically rough case, however, we find (as intuitively expected) an open hysteresis loop. Further characterization of the interface dynamics is in progress.

Jin, Wei↗

NASA NTRS1982

A detailed treatment of two-dimensional, starved lubrication in the vicinity of two counter-rotating cylinders

The problem of starved lubrication in the inlet region for the case of line contact between two nondeforming, equal radii cylinders rotating in opposite directions with equal surface speeds is considered. The lubricant is assumed to be a constant density, isoviscous, Newtonian fluid. The usual approach, which involves the use of Reynolds equation everywhere, is not followed. Instead, the situation is restricted to one in which the lubricant enters the contact region in thin films which adhere to the cylinders. Using Reynolds equation only at the line of centers and a suitable thin film approximation far from that point, the intervening region is treated as a general creeping flow region. Solutions, incorporating complete free surface boundary conditions, are obtained numerically. The hitherto unobtained results due to this approach include the existence of a unique free surface location for a fixed set of operating conditions.

Medrow, R. A.↗

NASA NTRS1972

Optical interferometry study of film formation in lubrication of sliding and/or rolling contacts

Seventeen fluids of widely varying physical properties and molecular structure were chosen for study. Film thickness and traction were measured simultaneously in point contacts by interferometry, from which a new theory of traction was proposed. Film thickness was measured in line contacts by interferometry and electrical capacitance to establish correlation between these two methods. An interferometric method for the absolute determination of refractive index in the contact zone was developed and applied to point contact fluid entrapments. Electrical capacitance was used to study the thickness and properties of the soft surface film which sometimes forms near a metal-fluid interface.

Stejskal, E. O.↗

NASA NTRS1985

Surface roughness effects in elastohydrodynamic contacts

Surface roughness effects in full-film EHL contacts were studied. A flow factor modification to the Reynolds equation was applied to piezoviscous-elastic line contacts. Results for ensemble-averaged film shape, pressure distribution, and other mechanical quantities were obtained. Asperities elongated in the flow direction by a factor exceeding two decreased both film shape and pressure extrema at constant load; isotropic or transverse asperities increased these extrema. The largest effects are displayed by traction, which increased by over 5% for isotropic or transverse asperities and by slightly less for longitudinal roughness.

Tripp, J. H.↗

NASA NTRS1991

A system-approach to the elastohydrodynamic lubrication point-contact problem

The classical EHL (elastohydrodynamic lubrication) point contact problem is solved using a new system-approach, similar to that introduced by Houpert and Hamrock for the line-contact problem. Introducing a body-fitted coordinate system, the troublesome free-boundary is transformed to a fixed domain. The Newton-Raphson method can then be used to determine the pressure distribution and the cavitation boundary subject to the Reynolds boundary condition. This method provides an efficient and rigorous way of solving the EHL point contact problem with the aid of a supercomputer and a promising method to deal with the transient EHL point contact problem. A typical pressure distribution and film thickness profile are presented and the minimum film thicknesses are compared with the solution of Hamrock and Dowson. The details of the cavitation boundaries for various operating parameters are discussed.

Lim, Sang Gyu↗

NASA NTRS1992

A system-approach to the elastohydrodynamic lubrication point-contact problem

Lim, Sang G.↗

NASA NTRS1991

Local Synthesis and Tooth Contact Analysis of Face-Milled Spiral Bevel Gears

Computerized simulation of meshing and bearing contact for spiral bevel gears and hypoid gears is a significant achievement that could substantially improve the technology and the quality of the gears. An approach to the synthesis of face-milled spiral bevel gears and their tooth contact analysis is presented. The proposed approach is based on the following ideas: application of the principle of local synthesis that provides optimal conditions of meshing and contact at the mean contact point, M, and in the neighborhood of M; and application of relations between principle directions and curvatures for surfaces being in line contact or in point contact. The developed local synthesis of gears provides the following: (1) the required gear ratio at M; (2) a localized bearing contact with the desired direction of the tangent to the contact path on gear tooth surface and the desired length of the major axis of contact ellipse at M; (3) a predesigned parabolic function of a controlled level for transmission errors which enables absorption of linear functions of transmission errors caused by misalignment and reduces the level of vibrations. The proposed approach does not require either the tilt of the head-cutter for the process of generation or modified roll for the pinion generation. Improved conditions of meshing and contact of the gears can be achieved without the above mentioned parameters. A computer program for determination of basic machine-tool settings and tooth contact analysis for the designed gears is presented. The approach is illustrated with a numerical example.

Litvin, Faydor L.↗

NASA NTRS1982

Theoretical results for fully flooded, elliptical hydrodynamic contacts

The influence of the ellipticity parameter and the dimensionless speed, load, and materials parameters on minimum film thickness was investigated. The ellipticity parameter was varied from 1 (a ball-on-plate configuration) to 8 (a configuration approaching a line contact). The dimensionless speed parameter was varied over a range of nearly two orders of magnitude. Conditions corresponding to the use of solid materials of bronze, steel, and silicon nitride and lubricants of praffinic and naphthemic mineral oils were considered in obtaining the exponent in the dimensionless materials parameter. Thirty-four different cases were used in obtaining the minimum film thickness formula H min = 3.63U to the 0.68 power G to the 0.49 power W to the -0.073 power 1-e to the 0.68K power). A simplified expression for the ellipticity parameter was found where k = 1.03 (r(y)/r(x)) to the 0.64 power. Contour plots were also shown which indicate in detail the pressure spike and two side lobes in which the minimum film thickness occurs. These theoretical solutions of film thickness have all the essential features of the previously reported experimental observations based upon optical interferometry.

Hamrock, B. J.↗

NASA NTRS1976

Isothermal elastohydrodynamic lubrication of point contacts. III: Fully flooded results

The influence of the ellipticity parameter and the dimensionless speed U, load W, and material G parameters on minimum film thickness was investigated. The ellipticity parameter k was varied from 1 (a ball-on-plate configuration) to 8 (a configuration approaching a line contact). The dimensionless speed parameter was varied over a range of nearly two orders of magnitude. And the dimensionless load parameter was varied over a range of one order of magnitude. Conditions corresponding to the use of solid materials of bronze, steel, and silicon nitride and lubricants of paraffinic and naphthenic mineral oils were considered in obtaining the exponent on the dimensionless material parameter.

Hamrock, B. J.↗