## 2 Materials and Methods
### Experimental Design  
The micro-milling experiments were conducted in the Kern Evo five-axis vertical machining center. The cutting tools had a diameter of 800 \(\upmu\)m and a helix angle of 60 degrees. The workpiece material was a Ti-6 Al-4V alloy, the main dimensions of which are shown in Figure 6. In order to analyze and validate the power consumption model proposed above, the Fluke 1735 three-phase power logger was employed to record the power characteristics during the machining process, as shown in Figure 7.  
Due to the feed and spindle power consumption only being influenced by single factors in the non-machining stage, an experiment was designed to validate the proposed power consumption models, and the corresponding parameters are shown in Table 1.  
The material removal power is influenced by the combination of process parameters. In order to analyze the effects of the process parameters on the machining quality, production efficiency, and energy efficiency, an orthogonal experiment was designed, and the corresponding levels are shown in Table 2. Ignoring the interactions between process parameters, the experimental design was conducted based on the L16 Taguchi experimental table [30], as shown in Table 3. \begin{table}
\begin{tabular}{c c c} \hline \hline \(f\) (mm/min) & \(n\) (rpm) & \(a_{p}\) (\(\upmu\)m) \\ \hline
20, 120, 220, 320, and 420 & 0 & 0 \\ \hline
0 & 10,000, 15,000, 20,000, 25,000, 30,000, & 0 \\  & 35,000, 40,000, and 45,000 & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Process parameters for non-machining power measurement. Figure 6: Main dimensions of workpiece. Figure 7: Measurement of power consumption. To determine the model coefficients, a quadratic fitting was performed, and the trend of the power variation with the feed rate was obtained, as depicted in Figure 9.  
The result of the quadratic fitting is shown in Equation (23). \[P_{\text{feed-s}}=4.4\times 10^{-5}\cdot f^{2}+0.0038\cdot f+1.83 \tag{23}\]  
The variance (R2), adjusted variance (R2-adj), and prediction variance (R2-pre) of the proposed model all exceeded 90%, as shown in Table 4, which indicates that the modeling method presented in this study demonstrates high prediction accuracy. The variation trend of the spindle power at different speeds is shown in Figure 10. It can be observed that, compared with the feed motion, the spindle rotational motion consumes higher power. Therefore, in the process of energy consumption optimization, special attention should be given to the spindle power. \begin{table}
\begin{tabular}{c c c c c c} \hline  & **Feed Unit** & \multicolumn{4}{c}{**Spindle Unit**} \\ \hline
**R2** & **R2-pre** & **R2-adj** & **R2** & **R2-pre** & **R2-adj** \\ \hline
99.21\% & 94.42\% & 98.43\% & 99.92\% & 99.82\% & 98.89\% \\ \hline \end{tabular}
\end{table} 
Table 4: Non-machining power model prediction accuracy. Figure 10: Non-machining power at different spindle speeds. Figure 9: Variation in non-machining power with feed speed. The power consumption of the spindle demonstrates a well-fitted quadratic relationship with the rotational speed, as depicted in Figure 11. The fitting result is presented in Equation (24). The variance (R2), adjusted variance (R2-adj), and prediction variance (R2-pre) of the proposed fitting model all exceeded 98%, as shown in Table 4, which indicates that the proposed modeling method demonstrates good prediction accuracy. \[P_{\rm spindle-s}=2.37\times 10^{-7}\cdot n^{2}+0.00461\cdot n+1.3 \tag{24}\]  
To facilitate the fitting of the relationships between the process parameters and material removal power, Equation (14) was further manipulated into Equation (25). A linear regression approach can be employed to obtain the coefficients for each term.