# Roughness Evaluation of Burnished Topography with a Precise Definition of the S-L Surface
## 2 Materials and Methods
### Introduction to the Applied Methods
Modification of the spectrum method [79], the singular spectrum analysis (SSA), can be used for enhanced surface roughness monitoring of vibration signals generated in workpiece-cutting tool interaction in CNC finish turning operations [80]. The surface roughness spectrum can be analysed by the fast Fourier transform (FFT) method to identify how different wavelengths of roughness behave [81]. However, the limitation of the traditional FFT spectrum method must be mentioned, that is, is to describe the frequency characteristics in the entire time domain, which is limited in many studies [82]. Some experimental results with PSD application have indicated that the profile of the tool marks is distorted by the effect of swelling of the materials being cut when the diamond turning of single crystals was considered [83]. The application of PSD makes AFM a powerful tool that provides quantitative information not only on the height deviation of the roughness profile, but the spatial extent of the height variations in the roughness profile [84]. Nevertheless, the PSD has been found to be an appropriate method to also improve the definition of high-frequency measurement errors from the results of surface topography measurements [34]. A comprehensive analysis of the surface roughness can be markedly improved through the application of the texture direction (TD) graphs. It was demonstrated that the method of surface roughness measurement, especially based on the overlap degree of the colour image, had relatively high accuracy and a relatively wide measurement range and can be robust to the brightness of the light source and to the texture direction [85]. A three-dimensional roughness measurement method based on mathematical morphology can ignore surface directionality, and as such, applies to directional and non-directional surfaces [86]. Generally, the texture direction, simultaneously represented by the Std parameter, also plays an important role in determining the frictional behaviour of the surfaces [87]. The validation of the method for areal form removal, defined as the L-surface, analysis of the isometric view of a surface, can be especially valuable but only for an experienced user. In Figure 2, the surface (left column) after areal form removal by application of regular methods is presented. From this analysis, the usage of the polynomial of the second degree seems to be the best solution as some form components were found (not entirely removed) for other methods. The distortion of dimples increased when digital filters (GRF, RGRF, SF) were applied to cylindrical surfaces containing deep and wide dimples (Figure 3). The ex-aggregation was especially visible when oil reservoirs were located near/on the edge of the analysed detail. Least-square fitting methods (LSFC and POLY2) could provide more suitable results, nevertheless, fitting of the cylindrical element (LSFC) caused that form to not be eliminated entirely (Figure 3a). Reduction in errors in the definition of the S-surface could be received when analysing the noise surface (NS) properties, which were comprehensively studied and widely defined in [34]. In Figure 4, the S-L surfaces were obtained by the application of various methods. A properly defined L-surface (Figure 4d) was not valuable in the S-L surface description when an S-surface (Figure 4g) was calculated erroneously. On the other hand, the proper S-surface (Figure 4i) was useless in the S-L surface characterisation if the L-surface (Figure 4f) was falsely estimated. Both surfaces must be determined precisely. Figure 2: Contour map plots of the surface after the areal form removal (left column), reference planes (middle), and ISO 25178 parameters (right column), received from a plateau-honed cylinder liner surface with oil pockets created by burnishing techniques, after the application of LSFC (**a**–**c**), POLY2 (**d**–**f**), POLY6 (**g**–**i**), RGRF (**j**–**l**), and SF (**m**–**o**), cutoff = 0.8 mm.