# A Study on Improving the Machining Performance of Scrolls
## 5 Experimental Results and Discussion
### Tests of Adaptive Feed Rate Planning  
To verify the effects of the adaptive feed rate planning on the promotion of machining efficiency and the consistency of machining quality, we conducted experimental tests on the rough machining processes of scrolls (Video S1: Scroll machining processes). In these experiments, the cutter was a Starpoint S2009, the specifications of which are shown in Table 1. As shown in Figure 7, a tool holder embedded with sensors was used to measure the tension, bending moment, and torque. Table 2 shows the specifications of the tool holder, which was based on a BT-40. As the data transmission frequency was 2.45 GHz, the sampling rate reached up to 1.8 kHz, and the spindle speed was 6000 rpm. This was sufficient for experiments on the estimation of the dynamic performance. Utilizing Equations (1) and (2), Figure 8 shows the simulation results for the cutting area per cutter tooth, which were calculated with a spindle speed of 6000 rpm and a feed rate of 800 mm/min. Based on the adaptive feed rate planning method (i.e., Equation (3)), we were able to simulate adjustable feed rates with different cutting areas per cutter tooth \(A_{z}\), such as 0.4, 0.5, and 0.6 mm\({}^{2}\). The simulated results are depicted in Figure 9. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Tooth Diameter (mm)** & **Tooth Length (mm)** & **Cutter Length (mm)** & **Handle Diameter (mm)** \\ \hline
100 & & & \\ \hline
2 & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Specifications of the Starpoint S2009 cutter. \begin{table}
\begin{tabular}{c c c} \hline \hline Signal Reception & Wireless 2.45 GHz \\ \hline Sampling Rate & 1800 Hz \\ \hline \multirow{3}{*}{Measuring Range} & Tension & \(\pm\)37.2 kN \\ \cline{2-3}  & Bending Moment & \(\pm\)462.6 Nm \\ \cline{2-3}  & Torque & \(\pm\)584.0 Nm \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Specifications of the tool holder. Figure 7: Tool holder embedded with sensors (Spike® from Pro-micron GmbH). To compare the different effects of the machining processes without and with adaptive feed rate planning, Table 3 lists the experimental results. They include the maximum bending moment, the machining time, and the material removal rate and different cutting areas per cutter tooth \(A_{z}\) and feed rate limits from 700 to 1200 mm/min were employed. These experiments were implemented with a cutting depth of 2 mm and a stretched length of 55 mm for the cutter stretching out of the holder. The bending moment was used to evaluate the instantaneous cutting load since it is linearly proportional to the tool force for a cutter with a fixed stretched length. Utilizing the experimental results obtained without adaptive feed rate planning, Figure 10 illustrates as an example the bending moment with a constant feed rate of 800 mm/min, the variation in which is approximately similar and depends on that of the cutting area shown in Figure 8. In Figure 10, period A is the region with the highest bending moment since the slot-milling processes occur in this period. We utilized adaptive feed rate planning to decrease the feed rate of the machining in period A and then to reduce the cutting loads and stabilize the machining quality during the rough machining processes. Period B represents the region with the lower bending moment because the side-milling processes occur in this period. We also used the adjustment provided by the adaptive feed rate planning to increase the feed rate of the machining according to the calculation of the cutting area and, thus, enhanced the material removal rate and the machining efficiency. Figure 8: Cutting area per cutter tooth in the rough machining process. Figure 9: Variation in feed rate for different cutting areas per cutter tooth. Based on the results shown in Table 3, Figures 11 and 12 depict the schematic relationship between the maximum bending moments, material removal rates, and feed rate limits without and with adaptive feed rate planning, respectively.