## 2 Materials and Methods
### Tool Wear Measurement and Tool Life Estimation  
The measurement of circular saw blades' wear was carried out after industrial tool life tests, using a workshop (optical) microscope Mitutoyo TM-510 (Mitutoyo Corporation, Kawasaki, Japan). The oblique teeth of circular saws were selected for the wear tests, because of the set of four geometries (straight tooth, oblique to the left, oblique to the right and trapezoidal tooth), the oblique teeth were worn the most. From a metrological point of view, what is greater should be measured, because it is easier and with a smaller relative error to assess the wear. There were 40 oblique teeth on each of the circular saws. Figure 6 shows what direct tool wear indicator was measured. Retraction of the cutting edge was measured on the bisector of blade angle (Figure 6). The teeth of new (non-cutting) circular saws were used to determine the base value of the direct wear indicator. The value of actual wear was calculated as follows  
\[Z_{i}=W_{zi}-\overline{W}_{z0}\ (\mathrm{mm}) \tag{1}\]  
where:  
\(Z_{i}\)--actual wear of a given tooth in (mm),  
\(W_{zi}\)--measured wear of a given tooth in (mm),  
\(\overline{W}_{z0}\)--average value of the measured base indicator of new saw teeth in (mm). The wear of one circular saw blade was obtained by averaging 40 values of actual wear of teeth for that saw (\(\overline{Z}_{i}\) indicator). Such calculations were made for all six tools. Figure 5: Schemes of cross-section door frame’s components: (**a**) PS-type door frame, (**b**) component, (**a**,**c**) component E160 type, (**d**) oblique cut of the door frame. The average wear of circular saw teeth is not this tool's life. In order to determine the tool's life, it is necessary to estimate the total cutting length (total feed length) until the value of blunting criterion (tool life criterion), that is the value of the direct wear indicator, from which tool is blunted and not suitable for further machining. In continuous operation of the industrial plant and during the experiment, circular saw blades were replaced based on the assessment of the quality of machining edges by an operator of the machine tool. In tool life tests it is such an unreliable indicator (it depends not only on tool wear, but also on the condition of the machine tool, operator's subjective assessment, material quality, etc.) that it was necessary to calculate the tool's life based on measured tool wear and total cutting length performed. Tool life was therefore determined using the point estimation and linear least squares method as the most widely used analytical method of straight line fitting. Name of the method results from the fact that we are looking for a line with such parameters that the sum of the squared differences of experimental values \(y_{i}\) calculated from the equation of the line \(ax_{i}+b\) is as small as possible (Equation (2)). \[M(a,b)=\sum_{i=1}^{n}\left[y_{i}-(ax_{i}+b)\right]^{2}=\text{min} \tag{2}\]  
The differences \(r_{i}=y_{i}-(ax_{i}+b)\) are called residuals. The essence of the linear least squares method is to minimize the sum of squares of residuals. The adopted linear model is true for the second wear phase (steady-state wear region) on the classic wear curve (Lorenz wear curve--Figure 7). To determine the linear wear functions of non-treated and ion-implanted circular saw blades, the measured values of direct wear indicators and the total cutting length in industrial tool life tests were used. In calculations of tool life, the limit value of the direct wear indicator was assumed to be 0.5 mm as the blunting criterion (tool life criterion). Thus, the measure of tool life was the estimated total cutting length up to 0.5 mm criterion.