The oil film in a closing gap

This Thesis presents a solution to a problem of elasto-hydrodynamics of normal approach ie. the motion of two elastic circular cylinders approaching each other along the line joining their centres and separated by a viscous film. Elastic deformation of the cylinders is accounted for, and the viscosity of the separating film is taken to be a function of pressure and temperature. A numerical method of solution making the use of an electronic computer is devised, and the problem is solved assuming a constant load being applied to the cylinders. An investigation into the nature of the temperature rise in the oil film due to the motion showed that under certain circumstances this would be rather small, of the order of a few degrees centigrade. This makes the assumption of isothermal conditions in the lubricant film a reasonable approximation under these circumstances and the resulting simpler problem, where viscosity is regarded as a function of pressure alone)is given a more general numerical treatment. It is found that a very large pressure may be developed in the fluid film at a finite separation of the two cylinders. As the film thickness is further reduced,the value of the maximum pressure goes down and as the film thickness approaches zero, the pressure distribution seems to converge to the Hertsian dry contact form.
For a given load applied to the cylinders, the value of the maximum pressure reached seems to depend mainly upon the value of parameter xE, i.e. the product of the pressure coefficient of viscosity and the reduced Youngs modulus of the elastic system. It was found that the higher the value of xE, the higher the pressure would go for a given load under other-wise equal conditions. Furthermore, for a load high enough to produce sufficiently large pressures,a small increase in load will produce a large increase in maximum pressure. This gain is also dependent upon the parameter xE and is higher for increased values of xE. Finally, a series of experiments were performed in order to check some of the theoretical predictions made. These experiments consisted of letting a loaded steel ball normally approach the polished surface of various materials, the surface being covered by a lubricant film, and measuring up the plastic deformations produced in the surface. These tests showed clearly the influence of the lubricant in that in every case the depth of the impression with lubricant was significantly larger than the ones produced under Hertzian, dry contact impacts, under otherwise equal conditions. The experimental results also indicate a correlation between the value of the parameter xE and pressure developed in the lubricant film as predicted by theory.