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Hamrock, B. J.

Publications and source records attributed to Hamrock, B. J..

At least 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
NASA NTRS1981

Ball bearing lubrication: The elastohydrodynamics of elliptical contacts

The history of ball bearings is examined, taking into account rollers and the wheel in the early civilizations, the development of early forms of rolling-element bearings in the classical civilizations, the Middle Ages, the Industrial Revolution, the emergence of the precision ball bearing, scientific studies of contact mechanics and rolling friction, and the past fifty years. An introduction to ball bearings is presented, and aspects of ball bearing mechanics are explored. Basic characteristics of lubrication are considered along with lubrication equations, the lubrication of rigid ellipsoidal solids, and elastohydrodynamic lubrication theory. Attention is given to the theoretical results for fully flooded elliptical hydrodynamic contacts, the theoretical results for starved elliptical contacts, experimental investigations, the elastohydrodynamics of elliptical contacts for materials of low elastic modulus, the film thickness for different regimes of fluid-film lubrication, and applications.

Hamrock, B. J.↗
NASA NTRS1980

Stresses and deformations in elliptical contacts

Topics presented deal with defining conformal and nonconformal surfaces, curvature sum and difference, and surface and subsurface stresses in elliptical contacts. Load-deflection relationships for nonconformal contacts are developed. The deformation within the contact is, among other things, a function of the ellipticity parameter and elliptic integrals of the first and second kinds. Simplified expressions that allow quick calculations of the deformation to be made simply from a knowledge of the applied load, the material properties, and the geometry of the contacting elements are presented.

Hamrock, B. J.↗
NASA NTRS1980

Fully flooded elastohydrodynamic lubricated elliptical contacts

Emphasis is on fully flooded, elastohydrodynamic lubricated, elliptical contacts. A fully flooded conjunction is one in which the film thickness is not significantly changed when the amount of lubricant is increased. A brief description of the relevant equations used in the elastohydrodynamic lubrication of elliptical contacts is given. The most important practical aspect of the elastohydrodynamic theory is the determination of the minimum film thickness within the contact. The maintenance of a fluid film of adequate magnitude is an essential feature of the correct operation of lubricated machine elements. The results presented show the influence of contact geometry on minimum film thickness as expressed by the ellipticity parameter and the dimensionless speed, load, and materials parameters. Film thickness equations are developed for materials of high elastic modulus, such as metal, and for materials of low elastic modulus, such as rubber. In addition to the film thickness equations that are developed, plots of pressure and film thickness are presented. These theoretical solutions for film thickness have all the essential features of previously reported experimental observations based on optical interferometry. Correlation between theory and experiments is also presented.

Hamrock, B. J.↗
NASA NTRS1980

Starved elastohydrodynamic lubricated elliptical contacts

A theoretical study of the influence of lubricant starvation on film thickness and pressure in hard and soft elliptical elastohydrodynamic contacts is presented. From the results for both hard and soft EHL contacts a simple and important dimensionless inlet boundary distance is specified. This inlet boundary defines whether a fully flooded or a starved condition exists in the contact. Furthermore it is found that the film thickness for a starved condition could be written in dimensionless terms as a function of the inlet distance parameter and the film thickness for a fully flooded condition. Contour plots of pressure and film thickness in and around the contact are shown for fully flooded and starved conditions. The theoretical findings are compared directly with results obtained experimentally.

Hamrock, B. J.↗
NASA NTRS1980

Film thickness for different regimes of fluid-film lubrication

Film thickness equations are provided for four fluid-film lubrication regimes found in elliptical contacts. These regimes are isoviscous-rigid; viscous-rigid; elastohydrodynamic lubrication of low-elastic-modulus materials (soft EHL), or isoviscous-elastic; and elastohydrodynamic lubrication of high-elastic-modulus materials (hard EHL), or viscous-elastic. The influence or lack of influence of elastic and viscous effects is the factor that distinguishes these regimes. The results are presented as a map of the lubrication regimes, with film thickness contours on a log-log grid of the viscosity and elasticity for three values of the ellipticity parameter.

Hamrock, B. J.↗
NASA NTRS1978

Minimum film thickness in elliptical contacts for different regimes of fluid-film lubrication

The film-parameter equations are provided for four fluid-film lubrication regimes found in elliptical contacts. These regimes are isoviscous-rigid; viscous-rigid; elastohydrodynamic of low-elastic-modulus materials, or isoviscous-elastic; and elastohydrodynamic, or viscous-elastic. The influence or lack of influence of elastic and viscous effects is the factor that distinguishes these regimes. The film-parameter equations for the respective regimes come from earlier theoretical studies by the authors on elastohydrodynamic and hydrodynamic lubrication of elliptical conjunctions. These equations are restated and the results are presented as a map of the lubrication regimes, with film-thickness contours on a log-log grid of the viscosity and elasticity parameters for five values of the ellipticity parameter. The results present a complete theoretical film-parameter solution for elliptical contacts in the four lubrication regimes.

Hamrock, B. J.↗
NASA NTRS1978

Elastohydrodynamic lubrication of elliptical contacts for materials of low elastic modulus. II - Starved conjunction

The study evaluates the effect of lubricant starvation on minimum film thickness in starved elliptical elastohydrodynamic conjunctions for materials of low elastic modulus. Lubricant starvation is studied simply by moving the inlet boundary closer to the center of the conjunction. A simple expression is presented for the dimensionless inlet boundary distance; this inlet boundary distance defines whether a fully flooded or a starved condition exists in the conjunction. A formula for the minimum film thickness under the starvation condition is derived. Contour plots of the pressure and film thickness in and around the contact are presented for both the fully flooded and starved lubrication conditions. It is shown that the inlet pressure contours become less circular and that the film thickness decreases substantially with increasing starvation severity.

Hamrock, B. J.↗
NASA NTRS1978

Effect of geometry on hydrodynamic film thickness

The influence of geometry on the isothermal hydrodynamic film separating two rigid solids was investigated. Pressure-viscosity effects were not considered. The minimum film thickness is derived for fully flooded conjunctions by using the Reynolds boundary conditions. It was found that the minimum film thickness had the same speed, viscosity, and load dependence as Kapitza's classical solution. However, the incorporation of Reynolds boundary conditions resulted in an additional geometry effect. Solutions using the parabolic film approximation are compared with those using the exact expression for the film in the analysis. Contour plots are shown that indicate in detail the pressure developed between the solids.

Brewe, D. E.↗
NASA NTRS1978

Effect of geometry on hydrodynamic film thickness

The influence of geometry on the isothermal hydrodynamic film separating two rigid solids was investigated. Pressure-viscosity effects were not considered. The minimum film thickness is derived for fully flooded conjunctions by using the Reynolds conditions. It was found that the minimum film thickness had the same speed, viscosity, and load dependence as Kapitza's classical solution. However, the incorporation of Reynolds boundary conditions resulted in an additional geometry effect. Solutions using the parabolic film approximation are compared with those using the exact expression for the film in the analysis. Contour plots are shown that indicate in detail the pressure developed between the solids.

Brewe, D. E.↗
NASA NTRS1978

Elastohydrodynamic lubrication of elliptical contacts for materials of low elastic modulus. 2: Starved conjunction

Lubricant starvation effects on minimum film thickness for low-elastic modulus materials are studied by moving the inlet boundary closer to the contact center. Contour plots of the pressure and film thickness in and around the contact were obtained for fully flooded and starved lubrication conditions. These contour plots show that the inlet pressure contours become less circular and that the film thickness decreases substantially as the severity of starvation increases.

Hamrock, B. J.↗
NASA NTRS1978

Additional aspects of elastohydrodynamic lubrication

An up-to-date review of the varying aspects of elastohydrodynamic lubrication is presented.. Some recent work on elastohydrodynamic lubrication of materials of low elastic modulus as well as on hydrodynamic lubrication is included. Both these topics are applicable for contacts with any ellipticity parameter (ranging from a circular contact to a line contact).

Hamrock, B. J.↗
NASA NTRS1978

Additional aspects of elastohydrodynamic lubrication

Elastohydrodynamic lubrication (EHL) for materials of low elastic modulus is considered. Engineering applications in which EHL is important for low-elastic-modulus materials include seals, human joints, tires, and elastomeric-material machine elements. Theoretical solutions of the problem of fully flooded line contacts in the case of low-elastic-materials are discussed. The equation regarding dimensionless minimum film thickness for fully flooded elliptical contacts for low elastic modulus is compared with the corresponding equation for materials of high elastic modulus. The powers of the dimensionless speed parameter U are quite similar in both equations, but the power of the dimensionless load parameter W is much more significant for low-elastic-modulus materials. Attention is given to aspects of dimensionless grouping, the isoviscous rigid regime, the viscous rigid regime, the isoviscous elastic regime, and the viscous elastic regime.

Hamrock, B. J.↗
NASA NTRS1978

Simplified contact analysis

A simple and straightforward method for calculating the elastic deformation at the center of contact between two solids with different radii of curvature is proposed instead of the conventional contact deformation analysis for ball bearings, gears, and cams, which usually involves tedious iterative procedures or the use of design charts. Ellipticity of the contact is approximated from a least-squares power fit. Simplified expressions are derived which allow rapid calculation of deformation from the material properties and geometry of the contacting elements.

Brewe, D. E.↗
NASA NTRS1978

Determining minimum lubrication film for machine parts

Formula predicts minimum film thickness required for fully-flooded ball bearings, gears, and cams. Formula is result of study to determine complete theoretical solution of isothermal elasto-hydrodynamic lubrication of fully-flooded elliptical contacts.

Hamrock, B. J.↗
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.↗