This project is concerned with the efficient numerical solution of Elastohydrodynamic Lubrication problems - an important branch of tribology concerning the separation by a lubricant film of two bodies in relative motion under an applied load. Journal bearings, gear teeth and ball bearings are amongst the numerous examples. These, normally rigid bodies, deform elastically under the very high operating pressures (commonly up to 3 GPa). It is very important to be able to understand and predict the performance of lubricants under their often extreme working conditions in order to achieve efficiency (generally reduced friction) and durability of the machine components. These calculations are also used in the development of new lubricants with desired physical properties. Oil entrainment from left to right. The illustration above shows how the pressure varies across a typical circular contact. In the inflow region the pressure is very close to zero. This then rises sharply to approach the Hertian peak in the central region of the contact. There is commonly also a pressure spike (or ridge) seen near the outflow of the high pressure region. Finally, beyond the contact, air has become present in the film and hence the film is not continuous - the blue cavitation region. Accurate experimental measurements are difficult, and hence numerical simulation is increasingly employed. The Reynolds equation for the pressure distribution across the contact, must be solved together with an integral equation governing the deformation of the contacts. A conservation law for the applied load must also be satisfied. Use of a thermal model would require the energy equation to be solved as well. Finally, there are the equations governing the rheological model of the lubricant, which is not assumed to be incompressible, and provides many of the physical effects seen. Contact deformation The complex integro-differential nature of the governing equations means that standard PDE solution techniques tend to lead to prohibitively large numerical systems. More efficient multi-level techniques methods are therefore employed. A modified version of the standard Multigrid algorithm is used, and the use of Multi-level Multi Integration reduces the computational work of calculating the deformation of the contacts, dramatically. The deformation of the physical contacts is shown to the left. The undeformed geometry is taken to be that of a sphere. The red areas indicate the narrowest parts of the contact. The magenta represents the greater separation. The characteristic horseshoe shape of smallest film thickness is clearly visible. Again, oil entrainment is from left to right. Classical lubrication theory allows the reduction of 3D EHL problems to two space dimensions. Addition of non-Newtonian lubricant models implemented allow for effects from the third spatial direction to be included. These point contact cases are where we have done the majority of our work, but we also have working 1D line contact codes. Current research includes the use of adaptive meshing, and variable timestepping. Another area with great interest to industry, is that of surface roughness. Applying a small sequence of bumps and dimples across the geometry of the contact, results in a deformed geometry as show - with perspective - below left. The corresponding pressure plot is shown next to it. Geometry of a 'rough' contact. Pressure distribution across a 'rough' contact. These problems must be solved transiently, as the bumps will move through the domain as the contacts turn. In this case a frequency of 0.7s is used, and this cycle is shown in Quicktime movies of Surface Geometry and Pressure. We have also done work with real rough surfaces, but be warned that this page contains some very large images and may take a while to download.