Rough contacts between actual engineering surfaces

New simple models of roughness description in contact mechanics for actual engineering surfaces are proposed in this work. The real profile is described by parabolas that simulate it by maintaining the constancy of some specific characteristics. Once the parabolas are determined, important parameters for contact mechanics studies can be evaluated as the radii of curvature of the asperities. The methods developed are applied to five profiles extracted from engineering surfaces with different roughness conditions. Comparisons are made based on roughness parameters evaluated for the measured profiles and for the simulated ones. The approach with the parabolas obtained with the least square approximation based on two reference lines gives usually the best results, but the method that provides the best approximation of each specific roughness parameter depends on the kind of profile. The models developed will be then compared by testing the real roughness profiles with some contact mechanics models in a related paper.