This thesis deals with a new numerical analysis of the three-dimensional elastohydrodynamic lubrication (EHL) problems such as elliptical contact problem and the EHL of axially profiled cylindrical roller. The problem is systematically analyzed using finite difference method and the Newton-Raphson method. Nonuniform grid system is adopted to reduce the number of grid points and to investigate accurate behavior of pressure profiles and film shapes.
The results of elliptical contact problem show that the present numerical procedure is fully systematic and convergence is good compared with previously reported numerical methods, and more accurate and physically reasonable results can be obtained with relatively small number of grid points. It is also proved that Hamrock and Dowson's formulas to estimate film thickness are quite accurate.
A complete solution is presented to the HEL of an axially profiled cylindrical roller which is rolling over a flat plane. Contour plots of film thickness give a good agreement with the experimental data in literatures which were obtained by means of optical interferometry. Near the position where the profiling starts, the EHL behavior is highly different from that of infinite solution. The maximum pressure an the minimum film thickness always occur at that region and these are highly dependent upon the local geometry there. Variations of the minimum film thickness with dimensionless parameters show considerably different behavior from those of infinite solution.
For two different types of profiles which have nearly similar elastostatic pressure distribution, the EHL results show large differences. Especially the difference in film shape is larger than that of pressure distribution. Therefore, the magnitude of the minimum film thickness should be major criteria to design the axial profile of the roller. A new design procedure is presented which take into account the minimum film thickness as well as the pressure distribution. Present numerical scheme can be used generally in the analysis of three-dimensional EHL problem.
