A study on an FFT-based approach for fast estimation of pressure distribution in point EHL contacts of rough surfaces

An FFT-based approach for fast estimation of pressure distribution in point EHL contacts of rough surfaces is developed in order to reduce computing t ime, as full numerical deterministic models may require several days to ana lyze one case on a personal computer. As is known, any 3-dimensional surfac e rough ness can be decomposed into a series of sinusoidal waves with diffe rent wavelengths and orientation angles. Based on an assumption that each e lemental wave causes basically a sinusoidal pressure fluctuation with the s ame frequency and orientation angle, an EHL system model and an input/outpu t relationship are derived. Five constants in the relationship are determin ed through fitting numerical results from 50 selected cases. By means of Fa st Fourier Transform (FFT) the system model could give an estimated pressur e distribution for full film EHL or mixed lubrication within a few seconds. Sample cases show however; that, the estimated pressure is in agreement wi th full numerical solutions only for some selected rough surfaces. The esti mation error becomes quite significant for 3-D isotropic roughness. General ly the agreement may be fairly good for the pressure profiles in the direct ion perpendicular to the roughness ridges, but it is poor for those in the direction parallel to the ridges. It is believed that errors associated wit h the simplified model and curve fitting can possibly be reduced, brit thos e related to the inaccurate assumption on roughness/pressure correspondence are difficult to remove, which may leave a deficiency in the proposed appr oach. The authors believe that the results presented in this paper may prov ide useful information for other researchers who are interested in developi ng fast approaches for EHL and mixed lubrication.