## 4 Discussion  
The present study demonstrates that visualizing the network between helix deviations of an injection-molded plastic gear enables the extraction and visualization of the periodicity left on the gear tooth flank during the gear manufacturing process. To ensure the accurate analysis and extraction of the periodicity left on the gear tooth flank during the injection molding process, the DC and slope components were eliminated to eliminate unnecessary weight that would affect the accuracy of the analysis result. Gaussian filter was not adopted in this study as the extraction of the waviness component would eliminate the periodicity left on the tooth flank of an injection-molded plastic gear. Furthermore, with the visualization of the pixel plot, the relative relationship between each gear tooth can be recognized easily. When the pixel plots of left and right helix deviation of the injection-molded plastic gear were generated, a grid pattern was formed in the network of the left helix deviation shown in Figure 8a, whereas in the case of the network of right helix deviation shown in Figure 8b, a houndstooth pattern was formed. By comparing the pixel plot of a specific tooth number across the pixel plot vertically or horizontally, the information on the correlation coefficient of the specific tooth with all other 47 th teeth could be obtained. For instance, in the case of the pixel plot of left helix deviation, tooth numbers 7 th to 10 th were filled with bluish pixels when observed across the plot. This implies that the helix deviations of tooth numbers 7 th to 10 th exhibit a lower correlation coefficient, meaning that the helix deviations are dissimilar when compared to other teeth. Figure 11a and Figure 11b show the left helix deviation curves of tooth number 3 rd-6 th and 7 th-10 th, respectively. When the helix deviation curves of tooth number 7 th-10 th are compared to the helix deviation curves of tooth number 3 rd-6 th, which largely possess pixels filled with yellowish color when observed across the plot, it is apparent that the curves have a different distinctive shape. In the case of tooth number 3 rd-6 th, the helix deviation curves possess convex shape curves, with a slight dent at evaluation length 1.8 mm, whereas in the case of tooth number 7 th-10 th, the helix deviation curves possess M-shaped curves, where the dent of the curves occurred at evaluation length 2.5 mm. In the case of pixel plot of right helix deviation, when the pixels of tooth number 1 st-3 rd are observed horizontally across the plot, pixels filled with yellowish color and bluish color alternated and occurred next to each other, where the yellowish pixels formed first from the left. On the contrary, for tooth number 4 th-7 th, pixels filled with yellowish and bluish color can be observed across the plot, where the bluish pixels formed first from the left. Figure 12a and Figure 12b show the right helix deviation curves of tooth numbers 1 st-3 rd and 4 th-7 th, respectively. When the helix deviation curves of tooth number 1 st-3 rd are compared to tooth number 4 th-7 th, helix deviation curves in both cases possess m-shaped curves, where the valley of the curves occurred at evaluation length 2.5 mm. However, the minima of the valley of the curves in tooth number 4 th-7 th has a smaller value of helix deviation compared to the valley in the case of tooth number 1 st-3 rd. The network of the helix deviations was then output in the form of a network image to investigate the relative relationship between each gear tooth when the correlation coefficient is at a fixed range. In this study, the range was set to \(-0.5\)-\(1.0\) with an interval of \(0.25\). When the network of left and right helix deviation was output in the form of network images as shown in Figures 9 and 10, a network pattern with a hexagon shape and six spots of concentrated link spots were formed within the correlation coefficient range of \(0.75\leq r_{j,k}\leq 1.0\). Moreover, these concentrated link spots occurred at the same span.