Engineering topics

Hamrock, B. J.

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

At least 55 records · Page 3

NASA NTRS1982

Lubrication of rigid ellipsida solids

The influence of geometry on the isothermal hydrodynamic film separating two rigid solids was investigated. 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' classical solution. However, the incorporation of Reynolds boundary conditions resulted in an additional geometry effect. Solutions using the parabolic film approximation are compared by using the exact expression for the film in the analysis. Contour plots are known that indicate in detail the pressure developed between the solids.

Hamrock, B. J.↗

NASA NTRS1982

Geometry and starvation effects in hydrodynamic lubrication

Numerical methods were used to determine the effects of lubricant starvation on the minimum film thickness under conditions of a hydrodynamic point contact. Starvation was effected by varying the fluid inlet level. The Reynolds boundary conditions were applied at the cavitation boundary and zero pressure was stipulated at the meniscus or inlet boundary. A minimum-film-thickness equation as a function of both the ratio of dimensionless load to dimensionless speed and inlet supply level was determined. By comparing the film generated under the starved inlet condition with the film generated from the fully flooded inlet, an expression for the film reduction factor was obtained. Based on this factor a starvation threshold was defined as well as a critically starved inlet. The changes in the inlet pressure buildup due to changing the available lubricant supply are presented in the form of three dimensional isometric plots and also in the form of contour plots.

Brewe, D. E.↗

NASA NTRS1982

High-speed motion picture camera experiments of cavitation in dynamically loaded journal bearings

A high-speed camera was used to investigate cavitation in dynamically loaded journal bearings. The length-diameter ratio of the bearing, the speeds of the shaft and bearing, the surface material of the shaft, and the static and dynamic eccentricity of the bearing were varied. The results reveal not only the appearance of gas cavitation, but also the development of previously unsuspected vapor cavitation. It was found that gas cavitation increases with time until, after many hundreds of pressure cycles, there is a constant amount of gas kept in the cavitation zone of the bearing. The gas can have pressures of many times the atmospheric pressure. Vapor cavitation bubbles, on the other hand, collapse at pressures lower than the atmospheric pressure and cannot be transported through a high-pressure zone, nor does the amount of vapor cavitation in a bearing increase with time. Analysis is given to support the experimental findings for both gas and vapor cavitation.

Jacobson, B. O.↗

NASA NTRS1982

Film shape calculations on supercomputers

Both scalar and vector operations are described to demonstrate usefulness of supercomputers (computers with peak computing speeds exceeding 100 million operative per second) in solving tribological problems. A simple kernel of the film shape calculations in an elastohydrodynamic lubricated rectangular contact is presented and the relevant equations are described. Both scalar and vector versions of the film shape code are presented. The run times of the two types of code indicate that over a 50-to-1 speedup of scalar to vector computational time for vector lengths typically used in elastohydrodynamic lubrication analysis is obtained.

Hamrock, B. J.↗

NASA NTRS1982

Numerical methods and computers used in elastohydrodynamic lubrication

Some of the methods of obtaining approximate numerical solutions to boundary value problems that arise in elastohydrodynamic lubrication are reviewed. The highlights of four general approaches (direct, inverse, quasi-inverse, and Newton-Raphson) are sketched. Advantages and disadvantages of these approaches are presented along with a flow chart showing some of the details of each. The basic question of numerical stability of the elastohydrodynamic lubrication solutions, especially in the pressure spike region, is considered. Computers used to solve this important class of lubrication problems are briefly described, with emphasis on supercomputers.

Hamrock, B. J.↗

NASA NTRS1981

Basic lubrication equations

Lubricants, usually Newtonian fluids, are assumed to experience laminar flow. The basic equations used to describe the flow are the Navier-Stokes equation of motion. The study of hydrodynamic lubrication is, from a mathematical standpoint, the application of a reduced form of these Navier-Stokes equations in association with the continuity equation. The Reynolds equation can also be derived from first principles, provided of course that the same basic assumptions are adopted in each case. Both methods are used in deriving the Reynolds equation, and the assumptions inherent in reducing the Navier-Stokes equations are specified. Because the Reynolds equation contains viscosity and density terms and these properties depend on temperature and pressure, it is often necessary to couple the Reynolds with energy equation. The lubricant properties and the energy equation are presented. Film thickness, a parameter of the Reynolds equation, is a function of the elastic behavior of the bearing surface. The governing elasticity equation is therefore presented.

Hamrock, B. J.↗

NASA NTRS1981

Effect of surface roughness on elastohydrodynamic line contact

A numerical solution of an elastohydrodynamic lubrication (EHL) contact between two long rough surface cylinders is obtained. A simultaneous solution of an elasticity equation and the Reynolds equation for two partially lubricated rough surfaces is used to obtain a theoretical solution of pressure distribution, elastohydrodynamic load and film thicknesses for given speeds. A theoretical solution is also found for lubricants with pressure dependent viscosity, material properties of cylinders, and surface roughness parameters. Elastic deformation is found from hydrodynamic and contact pressure using plane strain analysis, and results indicate that for a constant central film thickness, increasing the surface roughness decreases the EHL load and there is little variation in minimum film thicknesses as the surface roughness is increased.

Majumdar, B. C.↗

NASA NTRS1981

Analysis of starvation effects on hydrodynamic lubrication in nonconforming contacts

The effects of lubricant starvation on minimum film thickness, under conditions of a hydrodynamic point contact, are determined by numerical methods where: (1) starvation is effected by varying the fluid inlet level; (2) the Reynolds boundary conditions are applied at the cavitation boundary; and (3) zero pressure is stipulated at the meniscus or inlet boundary. Seventy-four cases were used to numerically determine a minimum-film-thickness equation, as a function of the ratio of dimensionless load to dimensionless speed for varying degrees of starvation. A film reduction factor was in turn determined as a function of the fluid inlet level, and a starved, fully-flooded boundary was defined along with an expression determining the onset of starvation. It is found that as the degree of starvation increases, the minimum film thickness decreases gradually until the fluid inlet becomes critical. The changes in the inlet pressure buildup due to changing the available lubricant supply are presented in the form of three-dimensional isometric plots.

Brewe, D. E.↗

NASA NTRS1981

Simplified solution for stresses and deformations

A shortcut is presented to the classical Hertzian solution for local stress and deformation of two elastic bodies in contact, which employs simplified forms for the ellipticity and for the complete elliptic integrals of the first and second kinds as a function of the geometry. Unlike previously proposed simplified formulas whose range of applicability was limited to ellipticities equal to, or greater than one, the present method extends the range of validity to include ellipticities less than one; in which the semimajor axis in the elliptical contact lies in a direction parallel to the rolling, rather than being perpendicular, as in previous studies. An auxiliary shear stress parameter is also expressed in simplified form as a function of the geometry, permitting a shortcut calculation to be made for the location and magnitude of the maximum subsurface shear stress.

Hamrock, B. J.↗

NASA NTRS1981

Lubrication background

Surface topography, including the various physical methods of measuring surfaces, and the various lubrication regimes (hydrodynamic, elastohydrodynamic, boundary, and mixed) are discussed. The historical development of elastohydrodynamic lubrication is outlined. The major accomplishments in four periods, the pre-1950's, the 1950's, the 1960's, and the 1970's are presented.

Hamrock, B. J.↗

NASA NTRS1981

Lubrication fundamentals

A lubricant is any substance that is used to reduce friction and wear and to provide smooth running and a satisfactory life for machine components. Lubrication fundamentals are discussed and the various lubrication mechanisms are defined. These include: hydrodynamic, elastohydrodynamic, mixed, boundary, and extreme pressure. Before the various lubrication mechanisms are presented, it is desirable to define conformal and nonconformal surfaces.

Hamrock, B. J.↗

NASA NTRS1981

History of ball bearings

The familiar precision rolling-element bearings of the twentieth century are products of exacting technology and sophisticated science. Their very effectiveness and basic simplicity of form may discourage further interest in their history and development. Yet the full story covers a large portion of recorded history and surprising evidence of an early recognition of the advantages of rolling motion over sliding action and progress toward the development of rolling-element bearings. The development of rolling-element bearings is followed from the earliest civilizations to the end of the eighteenth century. The influence of general technological developments, particularly those concerned with the movement of large building blocks, road transportation, instruments, water-raising equipment, and windmills are discussed, together with the emergence of studies of the nature of rolling friction and the impact of economic factors. By 1800 the essential features of ball and rolling-element bearings had emerged and it only remained for precision manufacture and mass production to confirm the value of these fascinating machine elements.

Dowson, D.↗

NASA NTRS1981

Introduction to ball bearings

The purpose of a ball bearing is to provide a relative positioning and rotational freedom while transmitting a load between two structures, usually a shaft and a housing. For high rotational speeds (e.g., in gyroscope ball bearings) the purpose can be expanded to include rotational freedom with practically no wear in the bearing. This condition can be achieved by separating the bearing parts with a coherent film of fluid known as an elastohydrodynamic film. This film can be maintained not only when the bearing carries the load on a shaft, but also when the bearing is preloaded to position the shaft to within micro- or nano-inch accuracy and stability. Background information on ball bearings is provided, different types of ball bearings and their geometry and kinematics are defined, bearing materials, manufacturing processes, and separators are discussed. It is assumed, for the purposes of analysis, that the bearing carries no load.

Hamrock, B. J.↗

NASA NTRS1981

Elastohydrodynamic lubrication of elliptical contacts

The determination of the minimum film thickness within contact is considered for both fully flooded and starved conditions. A fully flooded conjunction is one in which the film thickness is not significantly changed when the amount of lubricant is increased. The fully flooded 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. These results are applied to materials of high elastic modulus (hard EHL), such as metal, and to materials of low elastic modulus(soft EHL), such as rubber. In addition to the film thickness equations that are developed, contour plots of pressure and film thickness are given which show the essential features of elastohydrodynamically lubricated conjunctions. The crescent shaped region of minimum film thickness, with its side lobes in which the separation between the solids is a minimum, clearly emerges in the numerical solutions. In addition to the 3 presented for the fully flooded results, 15 more cases are used for hard EHL contacts and 18 cases are used for soft EHL contacts in a theoretical study of the influence of lubricant starvation on film thickness and pressure. From the starved results for both hard and soft EHL contacts, a simple and important dimensionless inlet boundary distance is specified. This inlet boundary distance defines whether a fully flooded or a starved condition exists in the contact. Contour plots of pressure and film thickness in and around the contact are shown for conditions.

Hamrock, B. J.↗

NASA NTRS1981

Effect of Surface Roughness on Hydrodynamic Bearings

A theoretical analysis on the performance of hydrodynamic oil bearings is made considering surface roughness effect. The hydrodynamic as well as asperity contact load is found. The contact pressure was calculated with the assumption that the surface height distribution was Gaussian. The average Reynolds equation of partially lubricated surface was used to calculate hydrodynamic load. An analytical expression for average gap was found and was introduced to modify the average Reynolds equation. The resulting boundary value problem was then solved numerically by finite difference methods using the method of successive over relaxation. The pressure distribution and hydrodynamic load capacity of plane slider and journal bearings were calculated for various design data. The effects of attitude and roughness of surface on the bearing performance were shown. The results are compared with similar available solution of rough surface bearings. It is shown that: (1) the contribution of contact load is not significant; and (2) the hydrodynamic and contact load increase with surface roughness.

Majumdar, B. C.↗

NASA NTRS1981

Surface roughness effect on finite oil journal bearings

A theoretical study of the performance of finite oil journal bearings is made, considering the surface roughness effect. The total load supporting ability under such a condition derives from the hydrodynamic as well as asperity contact pressure. These two components of load are calculated separately. The average Reynolds equation for partially lubricated surfaces is used to evaluate hydrodynamic pressure. An analytical expression for average film thickness is obtained and introduced to modify the average Reynolds equation. The resulting differential equation is then solved numerically by finite difference methods for mean hydrodynamic pressure, which in turn gives the hydrodynamic load. Assuming the surface height distribution as Gaussian, the asperity contact pressure is found. The effect of surface roughness parameter, surface pattern, eccentricity ratio, and length to diameter ratio on hydrodynamic load and on side leakage is investigated. It is shown that hydrodynamic load increases with increasing surface roughness when both journal and bearing surfaces have identical roughness structures or when the journal only has a rough surface. The trend of hydrodynamic load is reversed if the journal surface is smooth and the bearing surface is rough.

Majumdar, B. C.↗

NASA NTRS1981

Simplified solution for stresses and deformation

Conventional contact deformation analysis for ball bearings, gears, and cams involves tedious iterative procedures or the use of design charts. A simplified approach that makes the elastic deformation at the center of contact easy to calculate was previously reported. The range of validity in which these equations can be used is extended. A simplified approach to the calculation of the location and magnitude of subsurface stresses developed in machine element applications is included.

Hamrock, B. J.↗

NASA NTRS1981

Analysis of starvation effects on hydrodynamic lubrication in nonconforming contacts

Numerical methods were used to determine the effects of lubricant starvation on the minimum film thickness under conditions of a hydrodynamic point contact. Starvation was effected by varying the fluid inlet level. The Reynolds boundary conditions were applied at the cavitation boundary and zero pressure was stipulated at the meniscus or inlet boundary. A minimum-fill-thickness equation as a function of both the ratio of dimensionless load to dimensionless speed and inlet supply level was determined. By comparing the film generated under the starved inlet condition with the film generated from the fully flooded inlet, an expression for the film reduction factor was obtained. Based on this factor a starvation threshold was defined as well as a critically starved inlet. The changes in the inlet pressure buildup due to changing the available lubricant supply are presented in the form of three dimensional isometric plots and also in the form of contour plots.

Brewe, D. E.↗