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 = η₀e^αptreatment 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.