## 3 Experimental Procedure and Analysis Process  
### Experimental Designs  
To establish the data-driven model, an automated acquisition system (AAS) was developed. The AAS uses the Fuji Automatic Numerical Control (FANUC) Open CNC API Specifications library (FOCAS) to capture the position command and position feedback. The tracking error and contour error can be computed accordingly. The vibration signal measured by a three-axis accelerometer (PCB 356A32 was made by PCB Piezotronics, Depew, NY, USA) is captured using National Instrument (NI) devices (NI-9234). To ensure the AAS could acquire data without operators, the library provided by NI ANSI C support was used together with the FOCAS library. The human-machine interface (HMI) program is presented in Figure 4. The program includes functions to connect the CNC controller and NI device and to execute experiments sequentially by using a designed script file that can change the values of five interpolator parameters and the total acquisition time. Here, the sampling rate for the CNC was 1000 Hz, and that for the NI-9234 was 2048 Hz.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Para.** & **Contour Errors** & **Machining Time** & **Corner Vibrations** \\ \hline \(A_{max}\) & \(\blacktriangle\) Increase & \(\blacktriangle\) Decrease & \(\blacktriangle\) Increase \\ \hline \(T_{a}\) & \(\blacktriangle\) Increase & \(\blacktriangle\) Increase & \(\blacktriangle\) Decrease \\ \hline \(T2\) & \(\blacktriangle\) Decrease & \(\blacktriangle\) Increase & \(\blacktriangle\) Decrease \\ \hline \(V_{c}\) & \(\blacktriangle\) Increase & \(\blacktriangle\) Decrease & \(\blacktriangle\) Increase \\ \hline \(V_{max}\) & \(\blacktriangle\) Increase & \(\blacktriangle\) Decrease & \(\blacktriangle\) Increase \\ \hline \end{tabular}
\end{table}
Table 1: Trends in machine performance as the interpolation parameters change.  
Figure 3: (**a**) Velocity profiles in the Acc/Dec after interpolation (ADAI). (**b**) Velocity profiles out of the ADAI [25].  
The experiments were conducted on a three-axis horizontal milling machine (Tongtai HA-500 II was manufactured by Tongtai Machine and Tool Co., LTD., R.O.C., Kaohsiung City, Taiwan), with the three-axis accelerometer (PCB 356A32) installed on the spindle housing, as shown in Figure 5.  
To investigate the dynamic responses for setting various interpolation parameters, a FFD was adopted in this study. The design of the interpolation parameters is presented in Table 2; the values of the parameters were selected according to the various machining conditions. Each parameter, namely, \(A_{max}\), \(T_{a}\), \(T_{2}\), \(V_{c}\), and \(f_{max}\), was set to four different levels. In total, 1024 experiments were conducted for the FFD, and the designed parameter ranges were applied to various machining processes.  
Figure 4: Human-machine interface (HMI) of the automated acquisition system.  
Figure 5: Experimental machine and accelerometer setup.  
The 1024 experiments for the given trajectory discussed in Section 3 required 9 h to complete. However, the AAS could command the machine to conduct the designed trajectory and capture the data automatically without pressing the cycle-start button. Compared with the TED, the FFD obtained an enhanced ANN model; this finding is described in Section 4.2.