## 6 Conclusions  
During thread milling operations, the helical contour motion accuracy of feed drive axes is critical because it can significantly affect the accuracy of manufactured threads. The contour control design can improve the contour motion accuracy of feed drive axes; however, the motion dynamics and friction disturbance of each feed drive axis and the cutting force in thread milling operations significantly affect the helical contour motion accuracy of feed drive axes. Although the ILCC can reduce contour errors while feed drive axes perform repeated motions, recording and processing large amounts of data increase the memory usage and the computational burden on the motion control system. Moreover, during the ILCC convergence, producing multiple defective products can lead to wasted materials while increasing manufacturing costs. Because the helical path is composed of multiple pitch cycles, and feed drive axes are generally influenced similarly by motion dynamics and external disturbances such as the friction disturbance and cutting force during the motions of pitch cycles, the PCB-ILCC is developed to apply the contour error in the previous pitch cycle motion to modify the position command of the current pitch cycle motion so as to not only improve the contour motion accuracy of the feed drive axes while performing a helical path but also deal with the control  
Figure 14: Control performance comparison in machine tool thread milling experiment. Figure 13: Contour error variations in machine tool thread milling experiment. system problem and thread manufacturing problem induced by applying the ILCC to thread milling operations. To realize the PCB-ILCC, the CEV estimation method must not excessively increase the computational burden, and the ILCC must be easy to implement; in addition, the PMSM driving control must mitigate the adverse influence of motion dynamics and external disturbances acting on the feed drive axes. Therefore, the PCB-ILCC estimated the CEV by referring to the interpolated positions on the helical path, designed the ILCC using a cycle learning method, and designed the PMSM driving control using the robust control method that integrates friction compensation and dynamics compensation. The motion control experiments performed on a testbench validated that the robust PMSM driving control method developed in this study can significantly reduce contour errors compared with the extensively used proportional-proportional-integral control. As proportional-proportional-integral control is susceptible to the influence of PMSM motion dynamics and external disturbances, the contour errors vary considerably. Compared with proportional-proportional-integral control, the PCB-ILCC integrated with the PMSM driving control has robust control results and small contour errors owing to the compensation of PMSM motion dynamics and friction disturbances and the robust performance of PMSM motions. Compared with the extensively used proportional-proportional-integral control, the PCB-ILCC achieves a rate of reduction in the contour errors of over 90%. Moreover, compared with the robust PMSM driving control, the PCB-ILCC can further reduce the contour errors with a rate of reduction of over 40%. Thread milling experiments performed on a five-axis CNC machining center showed that even though the feed drive axes were adversely influenced by the motion dynamics and external disturbances, including the friction disturbance and cutting force, the PCB-ILCC achieved a significant contour error reduction because of the cycle learning method developed in this study. The reduction rate of contour errors when applying the PCB-ILCC reached 80% in thread milling operations compared to proportional-proportional-integral control. Thus, the experimental results validated that the PCB-ILCC can be applied to thread milling operations, effectively improving the helical contour motion accuracy of the feed drive axes. The PCB-ILCC presented in this paper exhibited improved contour motion accuracy for helical contour motions.