ASME International

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.

Optical interferometry was used to study rough surfaces under lubricated point contact. Three dimensional “asperities” of chromium were sputtered onto a steel ball which was run against a smooth glass plate under both rolling and sliding. The experimental results were compared with the various published theories. The film thicknesses found in sliding are different from those observed in pure rolling, which are nearly equal to the theoretical values. Film thickness collapse occurred when the central film thickness/half asperity height ratio (λ ratio) reached a critical value.

An extension of the Hertz theory of impact to the oblique impact of elastic bodies with circular contact is outlined. The tangential compliance of the contact surface under the action of Coulomb friction is shown to have a significant effect on the rebound angles, if the local angle of incidence does not greatly exceed the angle of friction. Experiments are described in which the trajectory of a moving body is measured before and after impact with a fixed block of similar material. Results obtained using both steel and rubber show good agreement with the theoretical values.

The five-ball fatigue tester and full-scale rolling-element bearings were used to determine the effect of component hardness differences of SAE 52100 steel on bearing fatigue and load capacity. Maximum fatigue life and load capacity are achieved when the rolling elements of a bearing are one to two points (Rockwell C) harder than the races. There appears to be an interrelation among compressive residual stresses induced in the races during operation, differences in component hardness, and fatigue life. Differences in contact temperature and plastically deformed profile radii could not account for differences in fatigue life.

Dynamic simulations of the performance of a ball bearing are presented in terms of the general motion as obtained by integrating the differential equations of motion of the various bearing elements. It is shown that bearing misalignment significantly influences the ball/cage and race/cage interaction and, hence, the stability of cage motion. The increased radial to axial load ratios promote skidding which couples with the lubricant behavior to impose accelerations on the ball which ultimately influence the ball/cage interactions. Hence, the lubricant behavior and the large load variation on the balls play dominant roles not only in determining the extent of skidding but also in establishing the overall stability of the cage motion.

An analytical formulation for the generalized ball, cage, and race motion in a ball bearing is presented in terms of the classical differential equations of motion. Ball-race interaction is analyzed in detail and the resulting force and moment vectors are determined. The ball-cage and race-cage interactions are considered to be either hydrodynamic or metallic and a critical film thickness defines the transition between the two regimes. Simplified treatments for the drag and churning losses are also included to complete a rigorous analytical development for the real-time simulation of the dynamic performance of ball bearings.

The momentum equations are written for viscous fluids exhibiting magnetic stresses. The velocity profiles are deduced; then from continuity, a pressure differential equation, equivalent to Reynolds equation is obtained. This equation is discussed with emphasis on the case when magnetic stresses derive from a potential, also when the pyromagnetic coefficient vanishes. The boundary conditions for lubrication problems are then formulated. In particular, short bearings with ferromagnetic lubricants are considered. A numerical example yields the pressure diagrams at low and moderate eccentricity ratios and for different speeds. In conclusion, it is shown that ferromagnetic lubricants may improve substantially the performance of bearings operating under low loads and/or at low speeds. However, a correct variation of the magnetic field, toward the center of the lubricated area, is required. Under such conditions, the extent of the active area of the film is increased and bearing stiffness and stability are improved.

The purpose of this study on the turbulent lubricant film is: 1 To give a brief outline of a new theory called bulk-flow theory; 2 To investigate to what extent results of theories based on law of wall and mixing length concept agree with the newly developed theory; 3 To provide a theoretical basis for the design of bearings lubricated by fluids of low kinematic viscosity.