Abstract
The application of the spectral representation method in generating Gaussian and non-Gaussian fractal rough surfaces is studied in this work. The characteristics of fractal rough surfaces simulated by the spectral representation method and the conventional Fast Fourier transform filtering method are compared. Furthermore, the fractal rough surfaces simulated by these two methods are compared in the simulation of contact and lubrication problems. Next, the influence of low and high cutoff frequencies on the normality of the simulated Gaussian fractal rough surfaces is investigated with roll-off power spectral density and single power-law power spectral density. Finally, a simple approximation method to generate non-Gaussian fractal rough surfaces is proposed by combining the spectral representation method and the Johnson translator system. Based on the simulation results, the current work gives recommendations on using the spectral representation method and the Fast Fourier transform filtering method to generate fractal surfaces and suggestions on selecting the low cutoff frequency of the power-law power spectral density. Furthermore, the results show that the proposed approximation method can be a choice to generate non-Gaussian fractal surfaces when the accuracy requirements are not high. The MATLAB codes for generating Gaussian and non-Gaussian fractal rough surfaces are provided.
Highlights
Many rough surfaces are nearly self-affine fractal within a wide range of scales, such as road surfaces, surfaces produced by fracture, and sandblasted surfaces.[1]
Surfaces generated by the fast Fourier transform (FFT) filtering method and spectral representation method (SRM)
Gaussian fractal rough surfaces with a grid size of 2048 × 2048 were generated by the FFT filtering method and SRM
Summary
Many rough surfaces are nearly self-affine fractal within a wide range of scales, such as road surfaces, surfaces produced by fracture, and sandblasted surfaces.[1]. Gaussian fractal rough surfaces with a grid size of 2048 × 2048 were generated by the FFT filtering method and SRM. For each group of φkl, the roughness parameters of the 1000 simulated surfaces with randomized Bkl values were averaged, and the corresponding SDs were plotted to show the uncertainties.
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