Engineering topics

Hamrock, B. J.

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

At least 91 records · Page 5

NASA NTRS1977

Elastohydrodynamic lubrication of elliptical contacts for materials of low elastic modulus. I - Fully flooded conjunction

A complete numerical solution is presented to the problem of isothermal elastohydrodynamic lubrication of elliptical contacts for low-elastic-modulus materials operating under fully loaded conditions. No assumption is made for the pressure or film thickness within the contact, and compressibility and viscous effects are taken into account. Because of the dimensionless representation of the coordinates, the actual Hertzian contact ellipse becomes a circle regardless of the value of the ellipticity parameter. A minimum-film-thickness relation and a central-film-thickness relation are derived from examining 17 different cases. Contour plots for detailed illustration of the pressure distribution and film thickness in the conjunction are provided.

Hamrock, B. J.↗

NASA NTRS1977

Elastohydrodynamic lubrication of elliptical contacts for materials of low elastic modulus. 1: Fully flooded conjunction

Elastohydrodynamic lubrication concepts of conjunctions of elliptical form are applied to materials of low elastic modulus. The influence of the ellipticity parameter and the dimensionless speed, load, and material parameters on minimum film thickness for these materials has been investigated. The ellipticity parameter was varied from a ball on plate configuration to a configuration approaching a line contact. The dimensionless speed and load parameters were varied by 1 order of magnitude. Seventeen different cases were used to generate minimum and central film thickness relations. Contour plots are presented that illustrate the pressure distribution and film thickness in the conjunction.

Hamrock, B. J.↗

NASA NTRS1977

Optimum step design for centering of pistons moving in an incompressible fluid

Hydrodynamic effects are analyzed for a stepped piston moving within a tight clearance tube filled with an incompressible fluid. Together with the hydrostatic effects that were analyzed in an earlier paper, a complete solution is obtained and an optimum step design for centering of the piston is suggested. The axial speed resulting from an axial driving force is calculated, and some experimental results for pistons falling in a water filled tube are presented.

Etsion, I.↗

NASA NTRS1976

Optimum step design for centering of pistons moving in an incompressible fluid

Hydrodynamic effects are analyzed for a stepped piston moving within a tight clearance tube filled with an incompressible fluid. Hydrostatic effects are analyzed and a complete solution is obtained and an optimum step design for centering of the piston is suggested. The axial speed resulting from an axial driving force is calculated, and some experimental results for pistons falling in a water-filled tube are presented.

Etsion, I.↗

NASA NTRS1976

Isothermal elastohydrodynamic lubrication of point contacts. 4: Starvation results

The influence of lubricant starvation on minimum film thickness was investigated by moving the inlet boundary closer to the contact center. The following expression was derived for the dimensionless inlet distance at the boundary between the fully flooded and starved conditions: m* = 1 + 3.06 ((R/b)(R/b)H) to the power 0.58, where R is the effective radius of curvature, b is the semiminor axis of the contact ellipse, and H is the central film thickness for fully flooded conditions. A corresponding expression was also given based on the minimum film thickness for fully flooded conditions. Therefore, for m m*, starvation occurs and, for m m*, a fully flooded condition exists. Two other expressions were also derived for the central and minimum film thicknesses for a starved condition. Contour plots of the pressure and the film thickness in and around the contact are shown for the fully flooded and starved lubricating conditions, from which the film thickness was observed to decrease substantially as starvation increases.

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.↗

NASA NTRS1976

Performance of 75-millimeter bore arched outer-race ball bearings

An investigation was performed to determine the operating characteristics of 75-mm bore, arched outer-race bearings, and to compare the data with those for a similar, but conventional, deep groove ball bearing. Further, results of an analytical study, made using a computer program developed previously, were compared with the experimental data. Bearings were tested up to 28,000 rpm shaft speed with a load of 2,200 N (500 lb). The amount of arching was 0.13, 0.25, and 0.51 mm (0.005, 0.010, and 0.020 in). All bearings operated satisfactorily. The outer-race temperatures and the torques, however, were consistently higher for the arched bearings than for the conventional bearings

Coe, H. H.↗

NASA NTRS1976

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

Procedures outlined by the authors in an earlier publication (1976) on theoretical formulation for isothermal elastohydrodynamic lubrication of point contacts are used to assess the influence of the ellipticity parameter and the dimensionless speed, load, and material parameters on minimum film thickness. Conditions equivalent to using solid materials of bronze, steel, and silicon nitride, and lubricants of paraffinic and naphthenic mineral oils are considered in obtaining the exponent on the dimensionless material parameter. Thirty-four different cases are used to generate the fully flooded film thickness formula. A fully flooded condition is said to exist when the inlet distance of the conjunction ceases to influence in any significant way the minimum film thickness. Contour plots are also shown that indicate in detail the pressure spike and two side lobes in which the minimum film thickness occurs.

Hamrock, B. J.↗

NASA NTRS1976

Isothermal elastohydrodynamic lubrication of point contacts. IV - Starvation results

Previously developed basic theory for isothermal elastohydrodynamic lubrication of point contacts is used to study the effect of lubricant starvation on pressure and film thickness within the conjunction. A simple expression for the dimensionless inlet boundary distance is derived. This inlet boundary distance defines whether a fully flooded or a starved condition exists in the contact. Simple expressions for the minimum and central film thickness under starvation condition are presented. Contour plots of pressure and film thickness in and around the contact are shown in order to gain a better insight into what occurs in going from fully flooded to lubricant starvation condition. Theoretical predictions are compared with earlier results.

Hamrock, B. J.↗

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 NTRS1976

Elastohydrodynamic lubrication of point contacts

A procedure for the numerical solution of the complete, isothermal, elastohydrodynamic lubrication problem for point contacts is given. This procedure calls for the simultaneous solution of the elasticity and Reynolds equations. By using this theory the influence of the ellipticity parameter and the dimensionless speed, load, and material parameters on the minimum and central film thicknesses was investigated. Thirty-four different cases were used in obtaining the fully flooded minimum- and central-film-thickness formulas. Lubricant starvation was also studied. From the results it was possible to express the minimum film thickness for a starved condition in terms of the minimum film thickness for a fully flooded condition, the speed parameter, and the inlet distance. Fifteen additional cases plus three fully flooded cases were used in obtaining this formula. Contour plots of pressure and film thickness in and around the contact have been presented for both fully flooded and starved lubrication conditions.

Hamrock, B. J.↗

NASA NTRS1976

Isothermal elastohydrodynamic lubrication of point contacts. 2: Ellipticity parameter results

A numerical solution of the isothermal elastohydrodynamic problem for point contacts is presented which reproduces all the essential features of experimental observations based upon optical interferometry. In particular, the two side lobes, in which minimum film thickness regions occur, emerge in the theoretical solutions. The influence of the ellipticity parameter on solutions to the point contact problem is explored. The ellipticity parameter k was varied from 1 (a ball on a plate) to 8 (a configuration approaching line contact). It is shown that the minimum film thickness can be related to the well known line contact solutions by a remarkably simple expression involving either k or the effective radius of curvature ratio R sub y/R sub x.

Hamrock, B. J.↗

NASA NTRS1976

Performance of 75 millimeter-bore arched outer-race ball bearings

An investigation was performed to determine the operating characteristics of 75-mm bore, arched outer-race bearings, and to compare the data with those for a similar, but conventional, deep groove ball bearing. Further, results of an analytical study, made using a computer program developed previously, were compared with the experimental data. Bearings were tested up to 28,000 rpm shaft speed with a load of 2200 N (500 lb). The amount of arching was 0.13, 0.25, and 0.51 mm (.005, .010, and .020 in.). All bearings operated satisfactorily. The outer-race temperatures and the torques, however, were consistently higher for the arched bearings than for the conventional bearing.

Coe, H. H.↗

NASA NTRS1975

Isothermal elastohydrodynamic lubrication of point contacts. II - Ellipticity parameter results

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 both the central and 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).

Hamrock, B. J.↗

NASA NTRS1975

Isothermal elastohydrodynamic lubrication of point contacts. I - Theoretical formulation

The analysis of an isothermal elastohydrodynamic lubrication (EHL) point contact was evaluated numerically. This required the simultaneous solution of the elasticity and Reynolds equations. In the elasticity analysis the contact zone is divided into equal rectangular areas and it is assumed that a uniform pressure is applied over each element. In the numerical analysis of the Reynolds' equation a phi analysis where phi is equal to the pressure times the film thickness to the 3/2 power is used to help the relaxation process. The EHL point contact analysis is applicable for the entire range of elliptical parameters and is valid for any combination of rolling and sliding within the contact.

Hamrock, B. J.↗

NASA NTRS1975

Isothermal elastohydrodynamic lubrication of point contacts. 1: Theoretical formulation

The isothermal elastohydrodynamic lubrication (EHL) of a point contact was analyzed numerically by simultaneously solving the elasticity and Reynolds equations. In the elasticity analysis the contact zone was divided into equal rectangular areas, and it was assumed that a uniform pressure was applied over each area. In the numerical analysis of the Reynolds equation, a phi analysis (where phi is equal to the pressure times the film thickness of the 3/2 power) was used to help the relaxation process. The EHL point contact analysis is applicable for the entire range of elliptical parameters and is valid for any combination of rolling and sliding within the contact.

Hamrock, B. J.↗

NASA NTRS1975

Numerical evaluation of the surface deformation of elastic solids subjected to a Hertzian contact stress

The elastic deformation of two ellipsoidal solids in contact and subjected to a Hertzian stress distribution has been evaluated numerically as part of a general study of the elastic deformation of such solids in elastohydrodynamic contacts. In the analysis the contact zone is divided into equal rectangular areas and it is assumed that a uniform pressure is applied over each rectangular area. A study has been made of the influence on the size of the rectangular area upon accuracy. The results also indicate how far from the center of the contact one needs to go before elastic deformation becomes insignificant.

Dowson, D.↗

NASA NTRS1975

Numerical evaluation of the surface deformation of elastic solids subjected to a Hertzian contact stress

The elastic deformation of two ellipsoidal solids in contact and subjected to a Hertzian stress distribution was evaluated numerically as part of a general study of the elastic deformation of such solids in elastohydrodynamic contacts. In the analysis the contact zone is divided into equal rectangular areas and it is assumed that a uniform pressure is applied over each rectangular area. A study was made of the influence on the size of the rectangular area upon accuracy. The results also indicate how far from the center of the contact one needs to go before elastic deformation becomes insignificant.

Dowson, D.↗