## 4 Analysis of Electromagnetic Weft Insertion Characteristics
### Simulation Analysis
In terms of electromagnetic force, the range of electromagnetic force of 30 mm segmented coils is 1200-1500 N, with an average force of 1400 N; and the electromagnetic force of 15 mm segmented coils ranges from 1400 to 1800 N, with an average force of 1600 N. The design principle of the segment  
Figure 10: The electromagnetic force of the 45 mm continuous acceleration coil. In the steady state, the electromagnetic force of the three different lengths of segmented coils is shown in Figure 14. The electromagnetic force increases continuously from the starting point and decreases near the end of the coil. The electromagnetic force of the 15 mm combined coil shows a downward trend after the moving distance of 15 mm, because the thickness of the yokes of the two adjacent coils reaches 4 mm, and each coil had a yoke length of 2 mm in the axial direction. The reason for the small coil length, the increased difficulty of the production process, and the influence on control requirements and electromagnetic force cannot be ignored. The electromagnetic force of the 30 mm and 45 mm combined coils reaches its peak at about 20 mm and 40 mm, and the electromagnetic force begins to decrease. This is consistent with the peak electromagnetic force of the single-stage 90 mm coil at 75-85 mm. The peak electromagnetic force of the 30 mm combined coil appears near 20 mm, which is equivalent to the peak of the 3-level combined coil appearing near 80 mm; the peak of the electromagnetic force of the 45 mm combined coil appears near 40 mm, which is equivalent to the peak of the 2-level combined coil near 85 mm. Figure 15 shows that the electromagnetic force fluctuation range and peak size in the transient state are consistent with the steady state. The difference lies in the acceleration time and the number of accelerations (coil stages). Similarly, speeding up to 125 m/s  
Figure 14: Comparison of steady state electromagnetic forces of combined coils with different lengths. Figure 13: The electromagnetic force of 15 mm continuous acceleration coil. required for export express delivery requires 9 levels for the combined coil with a length of 45 mm; 30 mm is 2 levels more than 45 mm; and 15 mm requires 6 levels more than 45 mm. Because the stepwise-combined acceleration is repeatedly accelerated by the highest level of the electromagnetic force of the superimposed magnetic field--despite the electromagnetic force remaining at the highest band its working distance is relatively short --the shorter the coil length, the more levels required. As shown in Table 3, in terms of total coil length, segmented combined coils are shorter. Among them, the thickness of the combined coil yoke is 1 mm, two sections, and the total yoke thickness is 2 mm. The peak electromagnetic force of the combined coils of different lengths fluctuates by several hundred Newtons, which is mainly due to the influence of the coil yoke. The combined coil yoke is made of pure iron, and the thickness of the yoke cannot be ignored when the combined coil length is small enough. The magnetized internal yoke further increases the electromagnetic force as the iron core is added to the energized coil. Another difference is the total acceleration time of the combined coil. Combining Figures 15 and 16, we can see that the shortest time spent by the 15 mm combined coil is about 4.3 ms, the 30 mm combined coil has an acceleration time of about 4.5 ms, and the 45 mm combined coil has the longest time, about 6.3 ms. It can also be seen from the speed-time curve that the slope of the curve--that is, the speed ratio increase coefficient of 15 mm--is the largest, followed by 30 mm. Meanwhile, 45 mm is the smallest, indicating that the acceleration and magnetic force of 15 mm is the largest. From the perspective of acceleration time and processing technology, the 30 mm combined coil is a better choice. From the perspective of the acceleration effect and the acceleration time, it is not particularly different to the 15 mm combined coil.