# Hybrid Optimization Method for Correcting Synchronization Errors in Tapping Center Machines
## 5 Conclusions  
The proposed hybrid method for optimizing synchronization in rigid tapping was verified in an actual thread cutting process. Errors in synchronization of the spindle and the tapping axis were captured, and parameter values were adjusted for optimal synchronization. Rigid tapping is easily performed when the CNC machine tool used for spiral tapping is operated at the expected speed and feed rate. However, high synchronization of motion is required to achieve a high-quality tap and avoid damage to the tapping tool and the workpiece. Therefore, the UD method proposed in this study integrated regression analysis, FPSO, and the Taguchi method to optimize rigid tapping parameters and obtained excellent tapping results. For parameters \(x_{2}\), \(x_{3}\), \(x_{4}\), \(x_{5}\), \(x_{6}\), the optimal combination of values was 55, 355, 260, 7900, and 9900, respectively. This combination reduced synchronization error from 23 pulses under the original parameters to 18 pulses, which was a 22% improvement in accuracy. The optimized combination also reduced processing time from 20,880 ms to 20,033 ms. The method proposed in this study improves machining accuracy by determining the critical factors in rigid tapping synchronization error and the optimal values for the key factors. Additionally, the proposed method reduces the potential for damage to the workpiece during a tapping procedure and reduces the time required for parameter commissioning. The four main findings of the experiments were as follows:  
1. The proportional gain and integral gain of the spindle can be adjusted to increase its rigidity during rigid tapping. 2. Adjusting the position gain of the tapping axis and the feedforward coefficient can substantially decrease synchronization errors. Figures 7 and 8 show how to position \begin{table}
\begin{tabular}{c c c c} \hline \hline
**No.** & **Before Commissioning** & **After Commissioning** \\ \hline
1 & & difference & difference \\
2 & & difference & difference \\
3 & & difference & difference \\
4 & & difference & 1.06 \\
5 & & difference & difference \\
6 & & difference & 1.04 \\
7 & & difference & 1.04 \\
8 & & difference & 1.04 \\
**Average** & **0.972** & **Average** & **1.048** \\ \hline \hline \end{tabular}
\end{table} 
Table 14: Difference between outer diameter (D1) and inner diameter (D2) before and after commissioning. gain affects synchronization error and torque command. When position gain is significant, synchronization error is small, but current increases. Notably, the present value during air cut commissioning should not exceed 70-80%, and a reserve margin should be set to avoid overheating or overloading the motor during actual cutting. Air cut commissioning means dry run commissioning. Figures 9 and 10 compare the effects of different feedforward coefficients on torque command. 3. Adjusting the time required for motor excitation and stabilization can reduce errors at the start of rigid tapping. 4. Reducing the \(z\)-axis following error, the synchronization error of rigid tapping can get better performance. After a synchronization error, reducing the \(z\)-axis following error and commissioning proportional gain, integral gain, and position gain can improve rigid tapping precision. **Author Contributions:** Formal analysis, [PERSON]-Y.C. and [PERSON]-Y.Y. ; funding acquisition, [PERSON]-Y.Y. and [PERSON]; methodology, [PERSON]-[PERSON] and [PERSON]-[PERSON]; software, [PERSON]-Y.C. and [PERSON]-Y.Y. ; supervision, [PERSON]-[PERSON] and [PERSON]-[PERSON]; validation, [PERSON]-Y.C. and [PERSON]-Y.Y. ; writing--original draft, [PERSON]-Y.C. and P.-Y.Y. ; writing--review and editing, [PERSON]-[PERSON] and [PERSON]. All authors have read and agreed to the published version of the manuscript. **Funding:** This research was funded in part by the Ministry of Science and Technology, Taiwan, R.O.C., grant numbers MOST 107-2221-E-992-086-MY3, and MOST 109-2222-E-035-002. And the APC was funded by MOST 107-2221-E-992-086-MY3. **Institutional Review Board Statement:** Not applicable.