# Insertion Performance Study of an Inductive Weft Insertion System for Wide Weaving Machines
## 4 Results Analysis and Validation  
### Simulation Verification  
In the design process of the warp insertion system, the core task is the study of the traction force of the warp insertion guideway. To verify the correctness of the formula for calculating the traction force of the warp insertion guideway, the structural parameters of the warp insertion guideway were calculated based on the formula for the linear motor structure [15]. We established a transient magnetic field 3D simulation model for the warp insertion system, as shown in Figure 4.  
In Figure 4, the three-phase coils are wound around the core of the warp insertion system using a short-distance double-layer winding method, and the coil connection is the same as shown in Figure 1. The conductive plate of the shuttle is located above the warp insertion system. The excitation source for the three-phase coils is assumed to be a three-phase voltage source, and the voltage expression is given by Equation (19). The simulation model has the remaining parameters listed in Table 1.  
\[\left\{ \begin{array}{l}V_{A}(t)=180\sin(2\pi ft)\\ V_{b}(t)=180\sin(2\pi ft+\frac{2\pi}{3})\\ V_{b}(t)=180\sin(2\pi ft+\frac{4\pi}{3})\end{array} \right. \tag{19}\]  
Figure 4: Weft insertion guideway–conductive plate simulation model. After setting up the simulation parameters, with a simulation duration of 100 ms and a step size of 1 ms, Figure 5 shows the magnetic field contour of the cross-section of the warp insertion guideway and the distribution of the induced magnetic field strength on the conductor plate when the power supply frequency is 50 Hz. From left to right, the subfigures depict the magnetic field characteristics at simulation times of 60 ms, 65 ms, and 70 ms, respectively. In each subfigure, the lower part illustrates the magnetic field generated by the weft insertion guideway, including the magnetic flux distribution, while the upper part displays the distribution of induced magnetic field intensity and direction in the conducting plate. From Figure 5, it can be observed that after applying three-phase voltage, the warp insertion guideway generates a rapidly moving wave magnetic field to the right, inducing an eddy current magnetic field in the conductor plate. Under the interaction of these two magnetic fields, the warp insertion guideway generates a continuous traction force on the shuttle, causing the shuttle to move to the right and achieve warp insertion. By using a variable frequency drive to provide three-phase voltage with the opposite phase sequence, the direction of the traction force can be changed. To further investigate the impact of various parameters on the traction force of the drafting guideway, simulations were conducted to separately analyze the variation in the traction force with parameters such as the thickness of the conductive plate, drafting guideway slip rate, and power frequency. Subsequently, the simulation results of the latter two parameters were compared and analyzed with the theoretical values calculated. Figure 6 shows the variation curve of the traction force as a function of the thickness of the conductive plate when the slip rate is 1 (shuttle at rest) and the power frequency is 50 Hz. In Figure 6, it can be observed that at gap thicknesses of 6 mm, 8 mm, and 10 mm, the traction force reaches its maximum when the thickness of the conductive plate is 3 mm, 4 mm, and 5 mm, respectively. This is roughly consistent with the relationship between the conductive plate and gap thickness in Equation (12), with an error of 2.67%. To ensure that the shuttle is not affected by the warp during the drawing-in process and to leave a margin in the suspension height, the initial suspension height of the shuttle should be around 10 mm. Therefore, when using the conductive plate as the driving force for the shuttle, in order to obtain greater starting traction force and reduce the starting distance, the optimal thickness of the conductive plate is 5 mm.