The solution of the point contact elasto-hydrodynamic problem

Abstract

A numerical solution method is described for the determination of oil film shape and film pressure in the lubricated contact between an elastic sphere rolling on an elastic plane. Steady loading and an isothermal film are assumed. The Reynolds equation (governing film pressure) and the elasticity equation (governing deformation) are solved simultaneously for a lubricant with the pressure-viscosity characteristic η = η 0 e αp treatment of the elasticity equation is described such that the deformation matrix is sufficiently compact. To give generality to the solution a set of results was subjected to multiple regression, which indicated that the influence of load on film thickness was very small. The regression results compare well with published data. The effect of restricting the amount of lubricant to the contact was also studied. The computed film shapes under such ‘starved’ conditions were found to be very close to those found by optical interferometry.

Efficiency and Durability Predictions of High Performance Racing Transmissions

“…[2] produced a series of computed solutions over a wide range of speeds, loads and material properties and derived regression equations expressed in terms of three non-dimensional groups to predict minimum film thickness for line contact configuration, such as a rigid roller against a semi-infinite elastic solid. In the 1960s, Archard and Cowking [3] and Ranger et al [4] produced full numerical solutions of the 2D EHL problem for point contact. Hamrock and Dowson [5] extended these to the elliptical contact footprint geometry.…”

Numerical Analysis of the Oil-Supply Condition in Isothermal Elastohydrodynamic Lubrication of Finite Line Contacts

“…This distance was used as the parameter governing the condition of starvation. Theoretical models for point contact-starved lubrication were investigated by Ranger et al [4] and Hamrock and Dowson [5], they used small inlet region boundaries to simulate the effect of the reduced pressure generation compared with a fully flooded contact. Based on the study of Elrod [6] and Chevalier et al [7,8] presented a steady-state solution for circular EHL contact with the multilevel method that facilitated the simulation of starvation/cavitation problems as a free boundary problem.…”

Discussion: “Film Thickness Calculations in Elastohydrodynamically Lubricated Circular Contacts, Using a Multigrid Method” (Lubrecht, A. A., Venner, C. H., ten Napel, W. E., and Bosma, R., 1988, ASME J. Tribol., 110, pp. 503–507)

“…Chittenden 1 The calculations described in this paper provide yet another example of the considerable benefit which may be gained by the use of multi-level techniques over more traditional methods. A few points come to mind concerning the numerical methods employed.…”