## 4 Experimental Analysis
### Experimental Setup Construction  
The experimental setup mainly consists of the unwinding wheel, winding wheel, braking system, guide rail sliding block mechanism, sliding friction platform, PLC, tension sensor, and upper computer as shown in Figure 6. The braking system is used to provide the strand tension \(T_{i}\) at the end of the cylinder, and the sliding friction platform applies friction force to the strand. The guide rail sliding block is used to change the direction of the centrifugal force on the strand during the twisting process. The tension sensor senses the change of the strand tension in real time through the PLC, and the PLC-Recorder converts and stores the strand tension data in real time. To simulate different twisting paths of each strand at the distribution reel, the relative position between the winding wheel and the sensor was changed in the experimental setup. As shown in Figure 7, a three-dimensional co-ordinate system was established at tension sensor, and the distance between the wheel and the sensor was changed. Simulated experiments were carried out for each of the eight strands at speeds of 200 r/min and 300 r/min. The initial brake tension \(T_{0}\) was set to 2 N, and the initial test conditions are shown in Table 3. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Strand Number**} & **Rotation Speed** & **200 r/min** & **400 r/min** & **800 r/min** & **200 r/min** & **400 r/min** & **800 r/min** \\ \cline{2-7}  & **Radius/M** & & & **Tension \(T_{sum}\)/N** & & & **Frictional Force \(F_{fl}\)/N** \\ \hline \#1 & 0.355 & 5.3 + \(T_{0}\) & 21.2 + \(T_{0}\) & 85.0 + \(T_{0}\) & x \({}^{1}T_{0}\) + 1.6 & x \({}^{1}T_{0}\) + 6.5 & x \({}^{1}T_{0}\) + 26.1 \\ \#2 & 0.28 & 4.3 + \(T_{0}\) & 17.3 + \(T_{0}\) & 69.2 + \(T_{0}\) & y \({}^{2}T_{0}\) + 0.2 & y \({}^{2}T_{0}\) + 0.6 & y \({}^{2}T_{0}\) + 2.5 \\ \#3 & 0.50 & 4.0 + \(T_{0}\) & 16.1 + \(T_{0}\) & 64.2 + \(T_{0}\) & z \({}^{3}T_{0}\) + 2.2 & z \({}^{3}T_{0}\) + 8.7 & z \({}^{3}T_{0}\) + 34.1 \\ \#4 & 0.28 & 3.1 + \(T_{0}\) & 12.5 + \(T_{0}\) & 50.0 + \(T_{0}\) & u \({}^{4}T_{0}\) + 0.2 & u \({}^{4}T_{0}\) + 0.7 & u \({}^{4}T_{0}\) + 2.9 \\ \#5 & 0.30 & 2.2 + \(T_{0}\) & 8.9 + \(T_{0}\) & 35.5 + \(T_{0}\) & 0.03 & 0.12 & 0.46 \\ \#6 & 0.50 & 1.9 + \(T_{0}\) & 7.6 + \(T_{0}\) & 30.6 + \(T_{0}\) & v \({}^{5}T_{0}\) + 0.9 & v \({}^{5}T_{0}\) + 4.0 & v \({}^{5}T_{0}\) + 16.2 \\ \#7 & 0.50 & 1.3 + \(T_{0}\) & 5.2 + \(T_{0}\) & 21.0 + \(T_{0}\) & n \({}^{6}T_{0}\) + 0.7 & n \({}^{6}T_{0}\) + 2.8 & n \({}^{6}T_{0}\) + 11.4 \\ \#8 & 0.44 & 0.6 + \(T_{0}\) & 2.5 + \(T_{0}\) & 10.0 + \(T_{0}\) & k \({}^{7}T_{0}\) + 0.3 & k \({}^{7}T_{0}\) + 1.2 & k \({}^{7}T_{0}\) + 4.9 \\ \hline \hline \end{tabular}  
* \({}^{1}\) x = 0.3; \({}^{2}\) y = 0.03; \({}^{3}\) z = 0.53; \({}^{4}\) u = 0.05; \({}^{5}\) z = 0.5; \({}^{6}\) z = 0.5; and \({}^{7}\) z = 0.4.  
\end{table} 
Table 2: Values of radius of gyration, tension, and frictional force for each strand at different speeds. Figure 6: Simulation and experimental apparatus for strand movement. The range of tension fluctuation of each strand at 200 r/min and 300 r/min is presented in box plots in Figure 9. As the speed increased, the range of the tension fluctuation and the average tension of each strand increased. For the same speed, when the strand had a significant deviation at the distribution reel, the average tension increased, indicating an increase in the overall force on the strand. When the deviation of the strand at the distribution reel was small, the range of the tension fluctuation obviously decreased. It is evident that the change of the strand twisting-deviation path affects the range of the tension fluctuation. It can be seen that there is a certain deviation in the tension between each strand based on the analysis and experiments of the various influencing factors.