# Stochastic Evaluation of Cutting Tool Load and Surface Quality during Milling of HPL
## 3 High-Pressure Laminate HPL Milling Results
### Evaluation of the Measurement of Forces and Moments during Milling  
An example of the time recording of the result of the measurement of the forces \(\mathrm{Fx}\), \(\mathrm{Fy}\), and \(\mathrm{Fz}\), and the moments \(\mathrm{Mx}\), \(\mathrm{My}\), and \(\mathrm{Mz}\) during machining (i.e., measurement 1; for successive machining, see Table 3) can be seen in Figure 6.  
The time record of the values shown in Figure 6 can be statistically evaluated, see Table 5, where  
\[\mathrm{F}=\sqrt{\mathrm{F}_{x}^{2}+\mathrm{F}_{y}^{2}+\mathrm{F}_{z}^{2}}\; \mathrm{and}\;\mathrm{M}=\sqrt{\mathrm{M}_{X}^{2}+\mathrm{M}_{Y}^{2}+\mathrm{ M}_{Z}^{2}} \tag{3}\]  
Figure 6: Time record of the result of the measurement of the forces \(\mathrm{Fx}\), \(\mathrm{Fy}\) and \(\mathrm{Fz}\) and the moments \(\mathrm{Mx}\), \(\mathrm{My}\) and \(\mathrm{Mz}\) during milling of the HPL (measurement 1; for down milling, see Table 3). All 36 measurements can also be evaluated in a similar way. The basic statistical evaluation of the resultant forces and moments for all measurements is given in Tables 6 and 7,  
Figure 8: Histogram of the force Fy when milling HPL material (measurement 1; for down milling, see Table 3). Figure 9: Histogram of the force Fz when milling HPL material (measurement 1; for down milling, see Table 3). where the evaluated median and maximum magnitudes of the resultant forces F and the resultant moments M during milling are given. \begin{table}
\begin{tabular}{c c c c c} \hline
**Measurement** & **F Median/N/** & **F Max/N/** & **M Median/N.m/** & **M Max/N.m/** \\ \hline  
\end{tabular}
\end{table} 
Table 6: Median and maximum values of the resulting forces and moments in down milling (measurements 1 to 16). \begin{table}
\begin{tabular}{c c c c c} \hline
**Measurement** & **F Median/N/** & **F Max/N/** & **M Median/N.m/** & **M Max/N.m/** \\ \hline
19 & 232.743 & 389.256 & 6.0585 & 30.065 \\ \hline
20 & 238.341 & 398.425 & 6.426 & 30.679 \\ \hline
21 & 240.161 & 396.847 & 6.155 & 30.905 \\ \hline
22 & 248.143 Even if the number of measurements is small, the data from Tables 6 and 7 can be interleaved (approximated) with a quadratic surface for initial observation of trends. The most appropriate approximation appears to be the function:  
\[f(\text{f},\,\text{a}_{\text{r}})=p_{00}+p_{10}\text{f}+p_{01}\text{a}_{\text{r} }+p_{11}\text{f}\,\text{a}_{\text{r}}+p_{02}\text{a}_{\text{r}}^{2} \tag{4}\]  
where \(p_{\text{ij}}\) (for \(\text{i}=0,\,1\) and \(\text{j}=0,\,1,\,2\)), are fitting constants. An example of the interleaving of these quadratic surfaces for median values of force F can be seen in Figure 10 (down milling) and in Figure 11 (up milling), which were obtained using sw Matlab 2022a in 'Surface fitting' toolbox [35]. From these measurement results, the global maxima of the resulting forces and moments for successive and up milling are evident. These maxima are shown in Table 8 and were obtained by evaluating the local maxima shown in Tables 5 and 6. The values in Table 8 provide new and valuable information on the actual dynamic loading of the cutting tool or workpiece during milling. It is clear from the above that up milling with the same cutting conditions results in higher force and moment loads than down milling with the same parameters. Figure 11: Fitting for median values of the resulting force F in up milling (measurements 17 to 32, see Table 7). Figure 10: Fitting for median values of the resulting force F in down milling (measurements 1 to 16, Table 6). \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Milling**} & \multicolumn{2}{c}{**F Max (Global Value)**} & \multicolumn{2}{c}{**M Max (Global Value)**} \\ \cline{2-5}  & **Value/N/** & **Measurement** & **Value/Nm/** & **Measurement** \\ \hline Down milling & 473.116 & 17 & 33.623 & 16 \\ \hline Up milling & 725.676 & 34 & 55.628 & 34 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Global maximum values of the resultant forces and moments for down milling and up milling (evaluation of measurements 1 to 36).