Bernard J. Hamrock

Ball Bearing Lubrication (The Elastohydrodynamics of Elliptical Contacts)

The history of ball bearings is examined, taking into account rollers and the wheel in the early civilizations, the development of early forms of rolling-element bearings in the classical civilizations, the Middle Ages, the Industrial Revolution, the emergence of the precision ball bearing, scientific studies of contact mechanics and rolling friction, and the past fifty years. An introduction to ball bearings is presented, and aspects of ball bearing mechanics are explored. Basic characteristics of lubrication are considered along with lubrication equations, the lubrication of rigid ellipsoidal solids, and elastohydrodynamic lubrication theory. Attention is given to the theoretical results for fully flooded elliptical hydrodynamic contacts, the theoretical results for starved elliptical contacts, experimental investigations, the elastohydrodynamics of elliptical contacts for materials of low elastic modulus, the film thickness for different regimes of fluid-film lubrication, and applications.

Elastohydrodynamic Lubrication of Elliptical Contacts for Materials of Low Elastic Modulus I-Fully Flooded Conjunction

The study evaluates the effect of lubricant starvation on minimum film thickness in starved elliptical elastohydrodynamic conjunctions for materials of low elastic modulus. Lubricant starvation is studied simply by moving the inlet boundary closer to the center of the conjunction. A simple expression is presented for the dimensionless inlet boundary distance; this inlet boundary distance defines whether a fully flooded or a starved condition exists in the conjunction. A formula for the minimum film thickness under the starvation condition is derived. Contour plots of the pressure and film thickness in and around the contact are presented for both the fully flooded and starved lubrication conditions. It is shown that the inlet pressure contours become less circular and that the film thickness decreases substantially with increasing starvation severity.

Simplified solution for elliptical-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 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 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.

Fluid-Film Lubrication Regimes Revisited

Dimensionless film-thickness equations are provided for four fluid-film lubrication regimes found for nonconformal surfaces. Side-leakage effects are present in the equations. These regimes are isoviscous-rigid; piezoviscous-rigid, isoviscous-elastic, or soft EHL; and piezoviscous-elastic, or hard EHL. The influence or lack of influence of elastic and viscous effects is a factor that distinguishes these regimes. The film-thickness equation for the respected regimes come from earlier theoretical studies. Results are presented as a map of the lubrication regimes, with film thickness contours on a log-log grid of the viscosity and elasticity parameters for four values of the ellipticity parameter. Presented as a Society of Tribologlsts and Lubrication Engineers paper at the ASME/STLE Tribology Conference In Toronto, Ontario, Canada, October 8–10, 1990

Effect of geometry on hydrodynamic film thickness

The influence of geometry on the isothermal hydrodynamic film separating two rigid solids was investigated. Pressure-viscosity effects were not considered. 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 Kapitzas classical solution. However, the incorporation of Reynolds boundary conditions resulted in an additional geometry effect. Solutions using the parabolic film approximation are compared with those using the exact expression for the film in the analysis. Contour plots are shown that indicate in detail the pressure developed between the solids.

Elastohydrodynamic Lubrication of Line Contacts

A procedure for the numerical solution of the complete isothermal elastohydrodynamic lubrication problem for line contacts is outlined. This procedure calls for the simultaneous solution of the elasticity and Reynolds equations. In the elasticity analysis, the conjunction is divided into equal rectangular areas. It is assumed that a uniform pressure is applied over each area. In the numerical analysis of the Reynolds equation, the parameter π = QH3/2 is introduced in order to help the relaxation process. The analysis couples the elasticity and Reynolds equations, going from the inlet to the outlet without making any assumptions other than neglecting side leakage. By using the procedures outlined in the analysis, the influence of the dimensionless speed U, load W, and materials G parameters on minimum film thickness is investigated. Ten cases are used to generate the minimum-film-thickness relationship, ℏmin = 3.07 U0.71G0.57W−0.11. As was first discovered by Dowson and Higginson, the most dominant exponen...

A Complete Solution for Thermal-Elastohydrodynamic Lubrication of Line Contacts Using Circular Non-Newtonian Fluid Model

A complete solution is obtained for elastohydrodynamically lubricated conjunctions in line contacts considering the effects of temperature and the non-Newtonian characteristics of lubricants with limiting shear strength. The complete fast approach is used to solve the thermal Reynolds equation by using the complete circular non-Newtonian fluid model and considering both velocity and stress boundary conditions. The reason and the occasion to incorporate stress boundary conditions for the circular model are discussed

Effect of Surface Roughness on Pressure Spike and Film Constriction in Elastohydrodynamically Lubricated Line Contacts

In this paper a full numerical solution for the partial elastohydrodynamic lubrication in heavily loaded line contacts is obtained by using a Newton-Raphson iterative technique presented by Houpert and Hamrock (9). The results obtained from present work confirm the major conclusions by Path and Cheng (3), and by Zhu and Cheng (6), and demonstrate the effects of surface roughness on the pressure spike and the lubricant film constriction. Presented at the 44th Annual Meeting in Atlanta, Georgia May 1–4, 1989

Measurement of the Density of Base Fluids at Pressures to 2.20 GPa

The influence of pressure on the density of six base fluids is experimentally studied for a range of pressures from 0.422 to 2.20 GPa. An important parameter used to describe the results is the cha ...

Non-newtonian and thermal effects on film generation and traction reduction in EHL line contact conjunctions

The thermal circular non-Newtonian model accompanied with three specialized models was used to study the mechanisms of film generation and traction reduction in EHL line contact conjunctions. Results revealed that the film generation capability is mainly controlled by the inlet zone pressure buildup and the inlet zone piezothickening. The diffusion time effect enhances the thermal thinning that reduces this capability. On the other hand, the piezoviscosity and the shear rate in the central contact zone are the main traction generation factors whereas shear skidding and thermal skidding are the traction reduction mechanisms. Results also showed that neglecting either viscous heating or the combination of shear thinning and shear stress reduction in formulating an EHL simulator is inaccurate for many cases