# An Accuracy-Efficiency-Power Consumption Hybrid Optimization Method for CNC Milling Process
## 4 Results and Discussions
### Power Consumption Analysis without Cutting Load  
According to the experiment scheme in the previous section, the experimental data can be divided into spindle and three servo motors. In the spindle experiments, six machining parameters were taken from 500 to 3000 rpm, with an increasing step every 500 rpm. The power consumption for each spindle speed parameter is shown in Figure 4. The experiment 1 to 3 and 4 to 6 were measured on different dates. It showed each power consumption value is very close to each other, around 0.00006 to 0.00009 kW. The power consumption does not significantly increase when the spindle speed increases. The reason is perhaps that the spindle is only in the idle state rather than the cutting state, so there is no cutting resistance, hence, increasing the spindle speed will not significantly affect the spindle power consumption. For X-axis servo motor, 13 combinations of feedrate were carried out from 200 mm/min until 6000 mm/min. The ommcinh feedrate was 200 mm/min and after 500 mm/min, the feedrate was increased every 500 mm/min up to 6000 mm/min. Figure 5 shows the resulting power consumption for different feedrates. The experiment was repeated three times, and the results were reproducible. However, only a few of data showed a difference of about 0.005 kW, even at the feedrate of 4500 mm/min, the maximum difference was 0.01 kW. As seen in Figure 5, the power consumption increase rate is about 0.00125 kW per 500 mm/min when the feedrate is 200 to1500 mm/min, but at feedrate of 2000 mm/min it reduces. When the feedrate is in the range of 2000 to 4000 mm/min, the power consumption trend is higher with an increase rate of about 0.0025 kW per 500 mm/min. However, at the feedrate of 4000 mm/min the power consumption is significantly reduced, but in the feedrate range of 4500 to 6000 mm/min the power consumption rises quickly with increasing \begin{table}
\begin{tabular}{c c c} \hline \hline
**Subject** & **Experiment 1** & **Experiment 2** \\ \hline Milling speed (m/min) & 30–60 & 30–60 \\ \hline Chip load (mm/t) & 0.12, 0.15, 0.18 & 0.12, 0.15, 0.18 \\ \hline Spindle speed (rpm) & 450–750 & 1000–2750 \\ \hline Feed rate (mm/min) & 192–540 & 480–1980 \\ \hline Width of Cut (mm) & 20 & 20 \\ \hline Depth of Cut (mm) & 4 & 4 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Machining parameters. value of 0.005 kW per 500 mm/min. The increasing trend is higher than the first two feedrate sections. It can be concluded that increasing feedrate will increase power consumption, but when the feedrate is 2000 mm/min and 4500 mm/min the power consumption is lower. Moreover, it recommends to use these two feedrates to obtain lower power consumption. Since the power consumption at the feedrate of 4500 mm/min is large, this data is excluded in the average calculation. Figure 6 shows the average calculation result, and each section regression equation can be obtained as follow:  
\[y=-0.0014x^{2}+0.0078x-0.0029 \tag{3}\]  
\[y=-0.0003x^{3}+0.0021x^{2}-0.0031x+0.0063 \tag{4}\]  
\[y=-0.0016x^{2}+0.0128x-0.0014 \tag{5}\]  
Figure 4: Relationship between spindle speed vs. power consumption w/o cutting load. Figure 5: Relationship between X-axis motor feedrate vs. power consumption w/o cutting load. For Y-axis servo motor, the parameter is similar to X-axis servo motor experiment, commencing at 200 mm/min and rising to 6000 mm/min with an increasing step of 500 mm/min. Figure 7 shows the relationship Y-axis motor upward direction with power consumption for different feedrates. It is seen the power consumption rate for feedrate range 200 to 1000 mm/min is about 0.0025 kW per 500 mm/min but smaller at a feedrate of 1500 mm/min. When the feedrate range is between 1500 and 2000 mm/min the power consumption increase rate is 0.005 kW per 500 mm/min, but a feedrate of 2500 to 3000 mm/min exhibits a decreasing trend. When the feedrate is between 3000 and 5500 mm/min the power consumption gradually increases from 0.008 kW up to 0.015 kW.