# Hybrid Optimization Method for Correcting Synchronization Errors in Tapping Center Machines
## 2 Problem Description  
Machining internal threads is an essential process in mechanical parts manufacturing in various industries. For example, numerous internally threaded holes are required to manufacture printed circuit boards (PCBs) in the computer, communications, and consumer-electronics (3C) electronics industry and manufacture mobile phone cases in the mold industry. Holes are typically threaded in a late stage of the manufacturing process. Poorly threaded holes can severely diminish the manufactured part's quality and performance; therefore, manufacturers require a fast and reliable method for tapping internally threaded holes.  
Tapping can be classified as floating or rigid. Each method uses a different tool clamping device, so each method has different synchronization requirements for the spindle and the tapping axis. Floating tapping was developed to solve the problem of synchronization between the spindle and the tapping axis. In floating tapping, the tap-ping tool is clamped in an elastic chuck. The advantage of floating tapping is that tapping can be achieved without complex control theory. The disadvantage, however, is that an excessively high tapping speed causes severe vibration resulting in imprecise tapping and/or disordered or broken teeth. In rigid tapping, a tap collet is typically used to clamp the tapping tool, which provides more precise teeth and enables a more efficient tapping speed than floating tapping. Rigid tapping is also much faster than floating tap-ping. However, synchronization between the spindle and the tapping axis must be exact. Even a slight difference can cause a breakage of the tool. Therefore, accurate synchronization of the spindle and tapping axis is essential. Most research in rigid tap-ping control has focused on minimizing the synchronization error between the tapping axis movement and the spindle to obtain internal threads with high quality and accuracy.  
To obtain the required screw pitch specifications in a rigid tapping process, the tapping axis and the spindle must be adjusted to meet the required combination of spindle speed and feed rate of the tapping axis. The relationships can be formulated as in Equation (1)  
\[P=F/S \tag{1}\]  
where \(P\) is the thread pitch (unit: mm), \(F\) is the feed rate of the tapping axis (unit: mm/min), and \(S\) is the spindle speed (RPM).  
In a rigid tapping procedure, the spindle speed and tapping axis feed rate must maintain a certain proportional relationship according to the required pitch specifications. Because pitch \(P\) depends on the scale of spindle speed and feed rate of the feed axis, if spindle speed and feed rate of feed axis do not match, it causes synchronization error which is too large and pitch \(P\), not precision. Therefore, the controller has a command-type compensation architecture, and the controller simultaneously commands the spindle and the tapping axis and compensates for positioning errors.  
Additionally, the FANUC 31 iMA controller used in this experiment is that the control method in which the tapping axis follows the spindle identifies synchronization errors between the spindle and the tapping axis. Figure 1 shows that synchronization error is an essential indicator in rigid tapping because it affects internal threads' shape and precision.