## 3 Machining and Measurement Conditions
### Tool Wear Modeling and Calibration  
The research on tool wear and tool life, to develop a model and calibrate tool wear, involved a series of passes in a multi-axis milling process with a torus milling cutter, whose axis was deflected with respect to the normal vector of the machined surface in the feed direction by the inclination angle parameter \(\delta\) (see Figure 1). The experimental tests were carried out in two main stages. Flood cooling was used in all cutting tests. The cutting conditions were chosen on the basis of our own preliminary research and works [10; 11; 13; 40]. The ambient temperature was 21\({}^{\circ}\). In the first stage, by carrying out machinability tests, data were obtained to develop a wear model using a non-linear estimation method. Cutting tests were carried out under HSM (High-Speed Machining). A constant cutting speed of \(v_{c}=140\,\mathrm{m/min}\) was determined at the principal diameter of the torus \(D_{PRIN}\) (see Figure 5). The inclination angle was determined to be constant throughout the machining and was \(\delta=1.10946^{\circ}\). This angle ensured that the surface machining process was carried out with the greatest efficiency. Consequently, the real cutting speed \(v_{c}\) at the \(CP_{i}\) contact point of the shaping of the machined surface was 71 m/min. In addition, two criteria were used as follows: uniformly distributed roughness \(Rth=R_{thref}\) (i.e., the theoretical roughness has the same value in the feed direction as in the direction perpendicular to it), and a wear limit criterion of \(VB_{Blim}=0.2\) mm was adopted. The machining parameters for this stage are shown in Table 1. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{\begin{tabular}{c} **Inclination** \\ **Angle** \\ \(\delta\) [\({}^{\circ}\)] \\ \end{tabular} } & \begin{tabular}{c} **Work Angle** \\ **of Cutting** \\ **Blade** \\ \(\psi_{r,rel}\) [\({}^{\circ}\)] \\ \end{tabular} & \begin{tabular}{c} **Distance** \\ **Between** \\ **Blade** \\ \(\psi_{r,rel}\) [\({}^{\circ}\)] \\ \end{tabular} & \begin{tabular}{c} **Axial Depth** \\ **of Cut** \\ **Topaths** \\ \(\psi_{r}\) [mm] \\ \end{tabular} & \begin{tabular}{c} **Feed per** \\ **of Cut** \\ **\(a_{p}\) [mm]** \\ \end{tabular} & \begin{tabular}{c} **Cutting** \\ **Speed** \\ **(at p. \(CP_{i}\))** \\ \(v_{c}\) [m/min] \\ \end{tabular} & \
\begin{tabular}{c} **Criterion** \\ **Rth = R_thref_ \\ **[mm]** \\ \end{tabular} &
\begin{tabular}{c} **Criterion** \\ **\(VB_{Blim}\) [mm]** \\ \end{tabular} \\ \hline \(1.10946\) & 23.4411 & 1.6 & 0.3 & 0.1549 & 71 & 0.0015 & 0.2 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Cutting conditions for the first stage of the research. Figure 8: Experimental test bench (1. Machining tool, 2. Torus milling cutter, 3. Workpiece, 4. Dino-Lite 7000 CE series digital workshop microscope). In order to obtain more accurate test results, the second stage of the model tests, i.e., wear calibration, was carried out. A relationship was established between the maximum allowable cutting time (MACT) at the \(CP_{i}\) contact point of the cutter and its axial distance from the TCP vertex. The relationship was established with constant machining parameters (spindle speed and feed rate) in relation to a fixed tool wear threshold, \(VB_{Blim}=0.2\) mm. For the calibration test, the method described by [PERSON] [40] was adopted, and Figure 7 shows a simple test setup; by continuously machining at a constant angle \(\delta\) until tool wear reached a threshold of 0.2 mm, MACT was obtained for a cutter axis orientation of 1.10946\({}^{\circ}\). The machining parameters for the calibration test are shown in Table 2. Each of the machinability and calibration tests was repeated three times, after which the average was calculated. On the basis of the data thus obtained, a tool life model was determined. Tool wear values are similar for the same milling parameters. In each iteration, measurements were carried out at the same fixed points on the time axis.