## 2 Materials and Methods
### Roughness Measurement  
The surface morphology of the beech samples was measured with MarSurf XT20 equipment manufactured by MAHR Gottingen GMBH, Gottingen, Germany (Figure 4a). It used an MFW 250 scanning head with a tracing arm in the range of \(\pm\)750 \(\upmu\)m, and a stylus with 2 \(\upmu\)m tip radius and 90\({}^{\circ}\) tip angle, as shown in Figure 4b. Figure 3: Sample cross-section with four zones of linear measurement. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Tool Rotation** & \multirow{2}{*}{**Feed Rate v\({}_{\text{f}}\) (m/min)**} & \multirow{2}{*}{**Measured Point**} & \multirow{2}{*}{**Profile Depth**} & \multirow{2}{*}{**Cutting Speed v\({}_{\text{c}}\) (m/s)**} & \multirow{2}{*}{**Feed per tooth f\({}_{\text{z}}\) (mm/Tooth)**} \\ \cline{5-8}
**n\({}_{1}\)** & & & & & & & **(mm/Tooth)** \\ \cline{5-8}
**n\({}_{2}\)** & & & & & & & & \\ \cline{5-8}
**n\({}_{1}\)** & 3308 & \(\frac{\text{v}_{\text{f}}}{\text{v  
For measuring the beech milled profiles, only the straight zones were considered, as marked by red arrows in Figure 3. The depth for the marked points were 2 mm for point 1, 8 mm for point 2, 16 mm for point 3, and 10 mm for point 4. This decision was drawn from the requirement that the stylus remains normal in relation to the processed surface. Further studies will take into consideration the possibility of measuring round profiles as well, by using adequate supports. Four profiles, 30 mm long, were measured from the numbered zones (Figure 3) along the milling direction with a speed of 0.5 mm/s, a scanning force of 0.7 mN, and a resolution of 5 um. This meant 4 profiles were taken from each sample. In case of the first set of samples, there were 12 profiles for one parameters combination. For all 4 parameter combinations (ex. \(\mathrm{n_{1}-v_{\mathrm{f1}}}\); \(\mathrm{n_{1}-v_{\mathrm{f2}}}\); etc. ), the total number of measurements reached 48. Similarly, for the second set of samples, there were 32 measurements. Data acquired were further processed with MARWIN XR20 software provided together with the measuring equipment. Data evaluation began with removing any unwanted form errors, followed by a procedure of filtering with a robust Gaussian regression filter, contained in ISO/TS 16610-31 [25]. This filter was tested and it was recommended for wood surfaces because it reduces the distortions associated with deep grouped valleys in the profiles and it is more reliable in comparison with a simple Gaussian filter, common in most measuring instruments [9; 29; 30; 31; 32]. In this way, the measured data were separated by filtering the wavelengths of irregularities in waviness profiles and roughness profiles, corresponding to W parameters for the longest wavelengths, while R parameters evaluated the shortest wavelengths. The cut-off length used for filtering was 2.5 mm, recommended for wood surfaces [30; 32]. After filtering, a number of useful parameters were calculated, such as Ra (arithmetic mean deviation of the roughness profile), Rv (the largest absolute profile valley depth), Rsk (skewness of the profile), and Wa (arithmetic mean deviation of the waviness profile) according to ISO 4287 [23]. In addition, Rk (the core roughness depth), Rpk (the reduced peak height), Rvk (the reduced valley depth), A1 (peak area in \(\mathrm{\SIUnitSymbolMicro m}^{2}/\mathrm{mm}\)), and A2 (valley area in \(\mathrm{\SIUnitSymbolMicro m}^{2}/\mathrm{mm}\)) were employed according to ISO 13565-2 [24]. The parameters from ISO 13565-2 [24] are particularly useful to characterize the stratified structure of a processed surface. Compared with other parameters, Rk depends the least on the wood anatomical structure and measures the height of the core roughness, the region defined by the highest concentration of data points in a measured profile, which excludes isolated peaks and valleys. For a milling process, it can be an approximation of the tool marks left on wood.