Film thickness for different regimes of fluid-film lubrication

Mathematical formulas are presented which express the dimensionless minimum film thickness for the four lubrication regimes found in elliptical contacts: isoviscous-rigid regime; piezoviscous-rigid regime; isoviscous-elastic regime; and piezoviscous-elastic regime. The relative importance of pressure on elastic distortion and lubricant viscosity is the factor that distinguishes these regimes for a given conjunction geometry. In addition, these equations were used to develop maps of the lubrication regimes by plotting film thickness contours on a log-log grid of the dimensionless viscosity and elasticity parameters for three values of the ellipticity parameter. These results present a complete theoretical film thickness parameter solution for elliptical constants in the four lubrication regimes. The results are particularly useful in initial investigations of many practical lubrication problems involving elliptical conjunctions

Experimental investigations of elastohydrodynamic lubrication

Various experimental studies of elastohydrodynamic lubrication have been reviewed. The various types of machines used in these investigations, such as the disc, two and four ball, crossed-cylinders, and crossed-axes rolling disc machine, are described. The measurement of the most important parameters, such as film shape, film thickness, pressure, temperature, and traction, is considered. Determination of the film thickness is generally the most important of these effects since it dictates the extent to which the asperities on opposing surfaces can come into contact and thus has a direct bearing on wear and fatigue failure of the contacting surfaces. Several different techniques for measuring film thickness have been described, including electrical resistance, capacitance, X-ray, optical interferometry, laser beam diffraction, strain gage, and spring dynamometer methods. An attempt has been made to describe the basic concepts and limitations of each of these techniques. These various methods have been used by individual researchers, but there is no universally acceptable technique for measuring elastohydrodynamic film thickness. Capacitance methods have provided most of the reliable data for nominal line or rectangular conjunctions, but optical interferometry has proved to be the most effective procedure for elliptical contacts. Optical interferometry has the great advantage that it reveals not only the film thickness, but also details of the film shape over the complete area of the conjunction

Elastohydrodynamic lubrication theory

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 to 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

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

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

Design curves for optimizing stability of herringbone-grooved journal bearings

Curves span wide range of operating conditions, including: lubricant compressibility numbers from 0 to 80, bearing length-to-diameter ratios from 1/4 to 2, and either rotating or stationary grooved members

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

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

Elastohydrodynamics of elliptical contacts for materials of low elastic modulus

The influence of the ellipticity parameter k and the dimensionless speed U, load W, and materials G parameters on minimum film thickness for materials of low elastic modulus was investigated. The ellipticity parameter was varied from 1 (a ball-on-plane configuration) to 12 (a configuration approaching a line contact); U and W were each varied by one order of magnitude. Seventeen cases were used to generate the minimum- and central-film-thickness relations. The influence of lubricant starvation on minimum film thickness in starved elliptical, elastohydrodynamic configurations was also investigated for materials of low elastic modulus. Lubricant starvation was studied simply by moving the inlet boundary closer to the center of the conjunction in the numerical solutions. Contour plots of pressure and film thickness in and around the contact were presented for both fully flooded and starved lubrication conditions. It is evident from these figures that the inlet pressure contours become less circular and closer to the edge of the Hertzian contact zone and that the film thickness decreases substantially as the serverity of starvation increases. The results presented reveal the essential features of both fully flooded and starved, elliptical, elastohydrodynamic conjunctions for materials of low elastic modulus

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