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Utilizing the theory developed by the authors in an earlier publication, the influence of the ellipticity parameter, the dimensionless speed, load, and material parameters on minimum film thickness was investigated. The ellipticity parameter was varied from one (a ball on a plate configuration) to eight (a configuration approaching a line contact). The dimensionless speed parameter was varied over a range of nearly two orders of magnitude. 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 in the dimensionless material parameter. Thirty-four different cases were used in obtaining the minimum film thickness formula given below as H¯min=3.63U0.68G0.49W−0.073(1−e−0.68k) A simplified expression for the ellipticity parameter was found where k=1.03RyRx0.64 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.

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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.

Our earlier studies of elastohydrodynamic lubrication of conjunctions of elliptical form are applied to the particular and interesting situation exhibited by materials of low elastic modulus. By modifying the procedures we outlined in an earlier publication, the influence of the ellipticity parameter k and the dimensionless speed U, load W, and material G parameters on minimum film thickness for these materials has been investigated. The ellipticity parameter was varied from 1 (a ball-on-plate configuration) to 12 (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 the following minimum- and central-film-thickness relations: H˜min=7.43(1−0.85e−0.31k)U0.65W−0.21H˜c=7.32(1−0.72e−0.28k)U0.64W−0.22 Contour plots are presented that illustrate in detail the pressure distribution and film thickness in the conjunction.

Utilizing the theory and numerical procedure developed by the authors in an earlier publication the influence of lubricant starvation on minimum film thickness was investigated. This study of lubricant starvation was performed simply by moving the inlet boundary closer to the contact center. From the results it was found that for the range of conditions considered the value of dimensionless inlet distance at the boundary between fully flooded and starved conditions (m*) can be expressed simply as m*=1+3.06Rxb2Hc,F0.58 or m*=1+3.34Rxb2Hmin,F0.56 that is, for a dimensionless inlet distance (m) less than m*, starvation occurs, and for m ≥ m*, a fully flooded condition exists. Furthermore, it has been possible to express the central and minimum film thickness for a starved condition as Hc,S=Hc,Fm−1m*−10.29Hmin,S=Hmin,Fm−1m*−10.25 Contour plots of the pressure and film thickness in and around the contact are shown for the fully flooded and starved lubricant condition. From these contour plots it was observed that the pressure spike becomes suppressed and the film thickness decreases substantially as starvation increases.

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 for 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.

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 deformations. 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.