## 4 Discussion
The center of each concentrated link region is approximately eight teeth number next to each other, which correlates with the result in the pixel plot where the center of each high correlation coefficient region is approximately eight teeth number next to the center of the high correlation coefficient region next to it. When the network images with a coefficient range of \(0.75\leq r_{j,k}\leq 1.0\) were plotted on the illustration of gear used in this study, it became apparent that the injection molding  
Figure 11: Comparison of left helix deviation curves of high and low correlation coefficient regions in the pixel plot: (**a**) Left helix deviation curves of tooth number 3 rd–6 th; (**b**) Left helix deviation curves of tooth number 7 th–10 th. Figure 12: Comparison of right helix deviation curves of high and low correlation coefficient regions in the pixel plot: (**a**) Right helix deviation curves of tooth number 1 st–3 rd; (**b**) Right helix deviation curves of tooth number 4 th–7 th. gate has a significant impact on the result of our studies. In plastic injection molding, the gate is the point where molten plastic is injected into the mold during the process. The gate's position plays a pivotal role in the mold design and directly impacts the quality of the molded product. The position of the gate determines the flow of plastic into the mold cavity, and a poorly positioned gate can cause common defects such as shrinkage and weld lines. However, by adjusting the gate position, it is possible to control these defects and enhance the final product's quality significantly [16; 17]. Therefore, identifying the optimal gate position is crucial for attaining optimal injection molding outcomes. In the case of injection-molded gear used in this study, there are six gate marks on the surface of the gear. The injection molding gate mark of the gear used in this study is shown in Figure 13a, and Figure 13b shows the gate mark observed with an electronic microscope. These gate marks are located at the position of tooth numbers 7 th, 15 th, 23 rd, 31 st, 39 th, and 47 th, where the location of each gate mark is eight teeth apart from each other. The concentrated link spots are formed at the region between the gate mark and the weld line. The gate marks are marked with a grey circular ring on the gear illustration and the weld lines are marked with dotted lines in Figure 14. In the case of left helix deviation shown in Figure 14a, the concentrated link spots, highlighted by the large blue circles, were formed on the left side of the gate mark, whereas in the case of right helix deviation shown in Figure 14b, the concentrated link spots were formed on the right side of the gate mark. In the plastic injection molding process, fountain flow occurs when the material at the flow front is pushed forward and channeled out of the injection molding gate. During the mold filling process, the material is injected into an empty melt flow channel fountains to the channel walls. The fountain flow creates similar left helix deviations at the left side of the gate mark to the weld line to its left, and similar right helix deviations at the right side of the gate mark to the weld line to its right. Since the temperature of the molten material decreases as it moves through the mold, the temperature of each tooth during injection molding changes depending on its position from the gate. This temperature distribution causes differences in material shrinkage behavior during the cooling process, which is thought to influence the shape of the tooth flank. However, the effect of changes in manufacturing conditions during injection molding on the tooth flank was not investigated in this study. Future investigation is necessary to evaluate the effect of temperature distribution in the material during injection molding. Figure 13: Gate mark of injection-molded plastic gear used in this study: (**a**) Gate mark of gear; (**b**) Gate mark observed with electronic microscope.