# Hybrid Optimization Method for Correcting Synchronization Errors in Tapping Center Machines
###### Abstract  
A hybrid method is proposed for optimizing rigid tapping parameters and reducing synchronization errors in Computer Numerical Control (CNC) machines. The proposed method integrates uniform design (UD), regression analysis, Taguchi method, and fractional-order particle swarm optimizer (FPSO) to optimize rigid tapping parameters. Rigid tapping parameters were laid out in a 28-level uniform layout for the experiments in this study. Since the UD method provided a layout with uniform dispersion in the experimental space, the UD method's uniform layout provided iconic experimental points. Next, the 28-level uniform layout results and regression analysis results were used to obtain significant parameters and a regression function. To obtain the parameter values from the regression function, FPSO was selected because its diversity and algorithmic effectiveness are enhanced compared with PSO. The experimental results indicated that the proposed method could obtain suitable parameter values. The best parameter combination in FPSO yielded the best results in comparisons of the non-systematic method. Next, the best parameter combination was used to optimize actual CNC machining tools during the factory commissioning process. From the commissioning process perspective, the proposed method rapidly and accurately minimizes synchronization error from 23 pulses to 18 pulses and processing time from 20.8 s to 20 s. In conclusion, the proposed method reduced the time needed to tune factory parameters for CNC machining tools and increased machining precision and decreased synchronization errors. t 11 March 2021 8 April 2021 12 April 2  
accuracy. [PERSON] et al. [2] proposed \"learning automata,\" an automatic parameter adjustment method for improving parameter convergence and improving efficiency in adjusting control parameters. To optimize the synchronous motion between the spindle and the tap-ping axis, [PERSON] et al. [3] proposed several linear and nonlinear control design techniques for improving control performance and synchronization, including (1) Cross-coupling control, (2) Nonlinear friction compensation, and (3) Interference observation. Servo gain was optimized by the command control method. The authors achieved synchronization accuracy within 10 ums at a spindle speed of 6000 rpm by applying these techniques. [PERSON] et al. [4] used a fuzzy adaptive proportional-integral-derivative (PID) controller to control Computer Numerical Control (CNC) machine tools used in rigid tapping. The proposed control method can be performed without establishing a controlled object, and the online PID controllable parameters are automatically adjusted by the fuzzy inference method. In another study, [PERSON] et al. [5] proposed a cross-coupled controller for accurately synchronizing the motion of a servo system driven by dual motors. The proposed cross-coupled controller compensates for differential positioning errors between dual servo drives by modifying reference positions and speed commands. [PERSON] et al. [6] performed experiments to compare the effectiveness of eliminating positioning and contour errors. The authors also proposed an adjustment method based on a mathematical model and evaluated its performance in reducing positioning and contour errors in CNC machine tools. [PERSON] et al. [7] proposed an iterative learning control (ILC) algorithm for reducing synchronization error in rigid tapping. In recent years, additive manufacturing (AM) technology has been proposed to be suitable for manufacturing critical components. Additive manufacturing is completely different from traditional subtractive processing. In contrast, additive manufacturing uses polymer, metal, or ceramic material spray stacking to construct a 3D shapes method that can quickly and flexibly produce a small number of diverse products, significantly reducing the time from the design stage to mass production of the products and considerably improving the utilization rate of materials [8; 9; 10; 11; 12].