# Hybrid Optimization Method for Correcting Synchronization Errors in Tapping Center Machines
## 4 Experimental Planning and Methods  
Drilling and tapping processes are used in the manufacturing processes for diverse products ranging from cylinder engines in the automobile industry to mobile phone molds in the consumer electronics industry. Since the manufacture of these products often requires numerous drilling and tapping procedures, determining the parameter combination that provides the best tapping accuracy is needed to achieve high product quality in the post-process. This study's objective was to find the parameter combination that minimizes rigid tapping synchronization error without increasing manufacturing time. Figure 2 shows that the experiments were performed in an NDV series machine tool (Yeong-Chin machinery industries Co. Ltd., Taichung, Taiwan) with a FANUC 31 iMA controller. The material used for the through-hole processing experiments was polymethyl methacrylate (PMMA) due to its high plasticity, high hardness, and low brittleness. The PMMA was considered an excellent experimental material because it enabled observation of broken or irregular cutters' effects. Therefore, even a significant synchronization error would be unlikely to damage the tapping tool in the tapping axis. The phenomena of stripped thread or thread damage can still be observed in PMMA. An M6 \(\times\) 1 tapping tool was used in the experiments. The cutting conditions were as follows. Spindle speed, tapping axis feed rate, and tapping depth were set to 3000 RPM, 3000 mm/min, and 50 mm, respectively. The experiment was performed five times at these settings. Figure 3 shows the processing path. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \(L_{9}(3^{4})\) & **1** & **2** & **3** & **4** \\ \hline
2 & 1 & 2 & 2 & 2 \\
4 & 2 & 1 & 2 & 3 \\
5 & 2 & 2 & 3 & 1 \\
6 & 2 & 3 & 1 & 2 \\
7 & 3 & 1 & 3 & 2 \\
8 & 3 & 2 & 1 & 3 \\
9 & 3 & 3 & 2 & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The \(L_{9}(3^{4})\) orthogonal array. The experimental input was the factor that affected synchronization error, and the output was synchronization error. Input factors were factors that affected synchronization error, including feedforward speed coefficient (\(x_{1}\), unit: 0.01%), rigid tapping speed loop proportional gain (\(x_{2}\), unit: As), motor excitation delay time (\(x_{3}\), unit: microsecond), rigid tapping speed loop integral gain (\(x_{4}\), unit: microsecond)), feed position coefficient (\(x_{5}\), unit: 0.01%) and tapping axis position gain (\(x_{6}\), unit: 0.01s-1) [54; 55; 56; 57]. These parameters were set on the FANUC controller system. Figure 4 shows the experimental procedure. The uniform distribution characteristic of UD made each experimental combination meaningful, which substantially reduced the required number of experiments. Table 3 shows the \(U\)\({}^{*}\)\({}_{28}\) (288) uniform layout selected for this study's experiments. First, input factors were entered in the \(U\)\({}^{*}\)\({}_{28}\) uniform layout. Figure 3: Diagram of rigid tapping path relationship. Figure 2: Tapping center machine (YCM NDV102A) used for the experiments in this study. Synchronization error was the quality characteristic, and the response value was obtained by the-smaller-the-better characteristic. Table 4 is the table for selecting column numbers according to the experiment number. Table 4 shows that columns 1-7 were used to construct the \(U\)\({}^{*}\)\({}_{28}\) (286) uniform layout, and Table 5 shows the resulting layout. Table 6 shows the 28 levels for each factor. A CCD electronic image microscope was used to observe the results (thread pitch and workpiece shape) of the tapping experiments performed using the factor combinations in Tables 5 and 6. Table 7 displays the experimental results.