## 3 Experiment and Result Analysis
### Variation Law of Twisting Yarn Tension under Different Yarn Finteness  
In order to investigate the effect of yarn fineness on the twisting tension, in the experiment, the twisting tension was measured for yarns of different fineness. The polynomial fitting method was used for fitting, and the fitting equations of the relationship between  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \begin{tabular}{c} **Experimental** \\ **Item** \\ \end{tabular} & \begin{tabular}{c} **Spiable Angular** \\ **Velocity, r/Min** \\ **(rad/s)** \\ \end{tabular} & \begin{tabular}{c} **The Measurement** \\ **of Twisting Tension** \\ **(cN)** \\ \end{tabular} & \begin{tabular}{c} **The Mean of** \\ **Twisting Tension** \\ **(cN)** \\ \end{tabular} & \
\begin{tabular}{c} **Standard** \\ **Deviation (cN)** \\ \end{tabular} &
\begin{tabular}{c} **Coefficient of** \\ **Overall Standard** \\ **Deviation** \\ \end{tabular} \\ \hline \multirow{4}{*}{1} & & \(1341.2\) & & & \\  & & \(1346.7\) & & & \\  & & \(1339.8\) & & & \\  & & \(1347\) & & & \\  & & \(1349.3\) & & & \\ \hline \multirow{4}{*}{2} & & \(1421\) & & & & \\  & & \(1413.9\) & & & \\  & & \(1423\) & & \(1417.6\) & & \(3.72\) & \(0.26\%\) \\  & & \(1416\) & & & \\  & & \(1414.1\) & & & & \\ \hline \multirow{4}{*}{3} & & \(1519\) & & & & \\  & & \(8000\) & \(1515.4\) & \(1520.6\) & \(3.27\) & \(0.22\%\) \\  & & \(1524.8\) & & & \\  & & \(1520.7\) & & & & \\ \hline \multirow{4}{*}{4} & & \(1634\) & & & & \\  & & \(1629.2\) & & & & \\  & & \(1627.8\) & & & & \\  & & \(1635.9\) & & & & \\  & & \(1624.1\) & & & & \\ \hline \multirow{4}{*}{5} & & \(1794.4\) & & & & \\  & & \(1785.3\) & & & & \\  & & \(1783.5\) & & & & \\  & & \(1783.5\) & & & & \\  & & \(1783.5\) & & & & \\  & & \(1796.1\) & & & & \\  & & \(1787.7\) & & & & \\ \hline \hline \end{tabular}
\end{table}
Table 1: Tension measurement results and standard deviation analysis of different spindle angular velocity.  
Figure 6: Tension–spindle angular velocity fitting curve for 1440 dtex.  
twisting tension and spindle angular velocity under different fineness were obtained, as shown in Table 2, and the fitting curve is shown in Figure 7. \(P_{\omega 1}\), \(P_{\omega 2}\), \(P_{\omega 3}\), \(P_{\omega 4}\), and \(P_{\omega 5}\) represent the fitting values of twisting tension obtained under different fineness, the unit of \(P_{\omega 1}\)-\(P_{\omega 5}\) is cN. \(R^{2}\) represents the coefficient of determination.  
The experimental conditions: industrial yarn fineness were: 930 dtex, 1100 dtex, 1440 dtex, 1670 dtex, 2200 dtex, the diameter of twisting tray was 220 mm, the diameter of yarn storage tray was 120 mm, and the diameter of spindle can was 266 mm.  
It can be analyzed from the measurement results and the fitting curve that when the angular velocity of the spindle increased from 680.68 rad/s (6500 r/min) to 994.84 rad/s (9500 r/min), the twisting tension gradually increased. At the same angular velocity, the twisting tension increased in turn with the increase in yarn fineness. Yarn with a fineness of 2200 dtex had the highest twisting tension, and the yarn with a fineness of 930 dtex has the lowest twisting tension.