# Energy Consumption Model for Drilling Processes Based on Cutting Force
## 3 Energy Consumption Model Calibration Experiments
### Energy Consumption Model Calibration  
The \(P_{total}\) was equal to \(P_{idle}\) when the machine was in the non-cutting state. In the non-cutting state, the PW3360 was used to collect the total power (\(P_{total}\)) at different spindle speeds, and the \(P_{idle}\) at different spindle speeds was obtained. Then, the relationship between \(P_{idle}\) and the spindle speed could be established. Figure 4 shows the experimental data and the numerically fitted curve which clearly resembles a quadratic relationship. Explicitly, the experimental data in Figure 4 shows that the idle power (\(P_{idle}\)) can be expressed as:  
\[P_{idle} = 0.0003n^{2}+0.0524n+1221 \tag{13}\] \begin{table}
\begin{tabular}{c c c c c} \hline \hline \(n\) (rpm) & & \multicolumn{3}{c}{\(c\) (mm/r)} \\ \hline
400 & 0.08 & 0.11 & 0.14 & 0.17 \\
550 & 0.08 & 0.11 & 0.14 & 0.17 \\
700 & 0.08 & 0.11 & 0.14 & 0.17 \\
850 & 0.08 & 0.11 & 0.14 & 0.17 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Cutting parameters for Experiment I.  
Figure 4: The idle power at different spindle speed. Figure 3: The experimental setup: (**a**) force and (**b**) power signal processing and collection. Reliable cutting force coefficients must be obtained before \(P_{cutting}\) is calculated according to Equation (3a-c) which can be calculated using the proposed force experiments [28]. According to Equation (10), it is only necessary to calibrate the cutting force coefficients in the tangential and the z directions. According to the experimental data, the cutting force coefficient can be obtained as:  
\[\mathbf{K}=[K_{tc}\quad K_{te}\quad K_{zc}\quad K_{zc}]^{T}=[4196.8\quad 202.6\quad 5395.7 \quad 339.2]^{T}\]  
Figure 5 shows the comparison of the predicted cutting force and experimental cutting force, which were calculated using the obtained cutting force coefficient under several different processing parameters. The results show that the error between the predicted cutting force and experimental cutting force was acceptable, and that the obtained cutting force coefficients were reliable. Table 2 lists the data from Experiment-I. The \(P_{total}\) is the measured data obtained by the power recorder. The \(P_{tilde}\) was calculated by Equation (13). The \(P_{cutting}\) was calculated by the Equation (10). Figure 5: Comparison of predicted and experimental values of cutting force under different cutting conditions: (**a**) \(n=400\) rpm, \(f=32\) mm/min; (**b**) \(n=550\) rpm, \(f=60\) mm/min; (**c**) \(n=700\) rpm, \(f=98\)mm/min; (**d**) \(n=850\) rpm, \(f=144\) mm/min. Based on these results, the auxiliary power, \(P_{\textit{auxiliary}}\), can then be calculated from Equation (11a) as shown in Figure 6.  
It can be seen from the experimental data that under the current processing parameters, the linear relationship used to describe the relationship between \(P_{\textit{auxiliary}}\) and \(P_{\textit{cutting}}\) had reached high accuracy, so that in order to simplify the calculation process, the equation for calculating \(P_{\textit{auxiliary}}\) can be obtained by Equation (11a):  
\[P_{\textit{auxiliary}}\ =\ 0.1336P_{\textit{cutting}} \tag{14}\]  
Finally, the \(P_{\textit{total}}\) was expressed as the equation for \(P_{\textit{idle}}\) and \(P_{\textit{cutting}}\), where both \(P_{\textit{idle}}\) and \(P_{\textit{cutting}}\) can be calculated by Equations (13) and (10), the \(P_{\textit{total}}\) can be expressed as:  
\[P_{\textit{total}}\ =\ P_{\textit{idle}}+1.1336P_{\textit{cutting}} \tag{15}\]  
In summary, in order to more clearly show the calculation process of the energy consumption model, the energy consumption calculation process of the drilling process can be described by the following flowchart (Figure 7):