Modelling of the Roughness Profile by Means of the Autoregressive Type Stochastic Processes

Abstract

The 2D roughness profile resulting from the standard measurement using a mechanical profilometer is usually the basic examination of a machined surface. Obtained results, usually in the form of the statistical parameters’ set are used for the surface machining evaluation as well as the forecast of the tribological behavior of the surface. The second mentioned purpose demands a particularly well suited mathematical model to accomplish a quantitative evaluation of the tribological parameters. In this paper a specific method is presented for this modelling based on the stochastic processes. In these processes the amplitude distribution has been modelled with the application of different probabilities densities and the spatial behavior has been modelled with application of the autoregressive process idea. The autoregressive capabilities of the model have also been proved by means of spectral analysis. The obtained results show that some probability densities of the used processes are highly related with the statistical roughness parameters, especially skewness and kurtosis. This in turn gives a good basis to forecast the tribological properties of the examined surface, including its directional characteristics. The numerical results have been compared with the experimental surfaces roughness measurements, showing good compatibility with the forecasted tribological parameters.