The application of multilevel multi-integration to the calculation of the elastic deformation integrals and the use of an alternative relaxation process in the multilevel solution of the governing equations have resulted in an algorithm solving the EHL line contact problem in O(n ln n) operations, also for highly loaded situations. The reduction in computing time thus obtained was used to solve the problem using large numbers of nodal points and to study the pressure spike. The presented algorithm will enable fast and accurate solution of surface roughness and transient problems.

Film thickness and pressure profiles have been calculated for line contacts at moderate and high loads, using a Multigrid method. Influence of the compressibility of the lubricant on the minimum film thickness and on the pressure spike has been examined. The required computing time is an order of magnitude less than when using the previous methods.

The effect of longitudinal and transverse roughness on the elastohydrodynamic lubrication of circular contacts was investigated numerically for two different lubricating conditions. The influence of the amplitude and the wavelength of the roughness texture was also studied. The results are compared with predictions from the flow factor method.

Surface Roughness Effects in an EHL Line ContactIn this paper the influence of surface roughness on the pressure profile and film thickness in a steady state EHL line contact is investigated using input from an actually measured roughness profile in the calculations. Pressure profiles and film shapes for different load conditions are shown. The presented results strongly indicate that in the steady state situation considered here a significant deformation of the roughness profile occurs. As a result the often used A parameter being the ratio of film thickness and standard deviation of the roughness (h/a) with a based on the undeformed roughness profile may give misleading information as far as the effect of the roughness on pressure and film shape is concerned.

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Detailed and accurate film thickness and pressure profiles have been calculated for point contacts at moderate and high loads, using a multigrid method. The influence of the compressibility of the lubricant and of the number of nodal points on the calculated minimum film thickness and maximum spike pressure have been examined. The required computing time is two orders of magnitude less, compared with the calculations using “classical” iterative methods.

This paper describes a fast numerical solver for the elastohydrodynamically lubricated circular contact problem. As a result of the application of multigrid techniques the algorithm is of very low complexity, ie. O(n In n), where n is the number of nodes on the grid. Consequently, it enables the solution of the problem using large numbers of nodes (O(10')) on a small-capacity computer, as is demonstrated by the results presented for an example load situation.

In this paper a Multigrid extension of a stationary solver is outlined for the EHL solution of a line contact under transient conditions. The solver is applied to calculate pressure and film thickness profiles at each time step when an indentation is moving through the contact, which results in an asymmetric pressure profile. The time-dependent results are compared with the stationary solutions. The pressure as a function of time is presented as well as the integrated pressure (over time) as a function of the spatial coordinate. These time-dependent pressures are used to compute the sub-surface stress field, which shows higher stresses below the trailing edge of the indentation. Therefore the risk of fatigue is higher below the trailing edge of the indentation, as is experimentally observed. The transient pressures can be used for a fundamental study of the emitted frequency spectrum of rolling bearings, as used in condition monitoring.