## 3 Results  
In this study, after the finite element analysis, the reaction force as well as the corresponding stress distribution on the vacuum extractor and fetal skull with the neck of fetal head as the fixed end were obtained. Figure 5 shows the numerical magnitude and stress direction of the reaction force on the fetal head with different materials of vacuum extractors and under different vacuum pressures. Table 2 shows the magnitude of the reaction force and its components in each axis. With the increase in vacuum pressure, the magnitude of the reaction force increased slightly. In addition, when using vacuum extractors fabricated from different materials, the numerical values of reaction force differed significantly. On the whole, when silicone rubber was used as the material of vacuum extractor (12.229-15.064 N), the reaction force was smaller, compared with using stainless steel (358.04-361.37 N). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & & **500-cm H\({}_{2}\)O** & **600-cm H\({}_{2}\)O** & **700-cm H\({}_{2}\)O** & **800-cm H\({}_{2}\)O** \\ \hline \multirow{4}{*}{**Silicone Rubber**} & X Axis & \(9.4194\times 10^{-5}\) N & \(1.1303\times 10^{-4}\) N & \(1.3187\times 10^{-4}\) N & \(1.5071\times 10^{-4}\) N \\  & Y Axis & \(-12.229\) N & \(-13.174\) N & \(-14.119\) N & \(-15.064\) N \\  & Z Axis & \(9.1197\times 10^{-5}\) N & \(1.0944\times 10^{-4}\) N & \(1.2768\times 10^{-4}\) N & \(1.4592\times 10^{-4}\) N \\ \cline{2-6}  & Total & \(12.229\) N & \(13.174\) N & \(14.119\) N & \(15.064\) N \\ \hline \multirow{4}{*}{**Stainless Steel**} & X Axis & \(9.4307\times 10^{-5}\) N & \(1.1315\times 10^{-4}\) N & \(1.3199\times 10^{-4}\) N & \(1.5082\times 10^{-4}\) N \\  & Y Axis & \(-358.04\) N & \(-359.15\) N & \(-360.26\) N & \(-361.37\) N \\ \cline{2-6}  & Z Axis & \(9.1211\times 10^{-5}\) N & \(1.0945\times 10^{-4}\) N & \(1.2769\times 10^{-4}\) N & \(1.4593\times 10^{-4}\) N \\ \cline{2-6}  & Total & \(358.04\) N & \(359.15\) N & \(360.26\) N & \(361.37\) N \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Magnitudes and components of reaction force. Figure 5: Direction of reaction force on the fetal head. Figure 6 mainly exhibits the distribution of von Mises stress on vacuum extractors with different materials of vacuum extractors and under different vacuum pressures. The results showed that the greater the vacuum pressure applied, the greater the von Mises stress on the vacuum extractor. In addition, when different materials were used for the vacuum extractor, the magnitude of von Mises stress on the vacuum extractor differed significantly. When the material used for the vacuum extractor was silicone rubber (0.5858-0.9510 MPa), the von Mises stress on the vacuum extractor was smaller, compared with using stainless steel. Figure 7 reveals the von Mises stress distribution on the fetal head skull measured under different vacuum extractor materials and pressures at different times (t = 0.25 s, t = 0.5 s, t = 0.75 s and t = 1 s). As the pictures show, the effects of pressures at the time from 0 to 0.5 s mainly indicate the vacuum pressure within the suction device, and the effects of pressures at the time from 0.5 to 1 s principally imply the extraction process of the vacuum extractor on the fetal head caused by pulling out. When the time t = 1 s, the results show that the von Mises stress in the area on the fetal head skull extracted by the vacuum extractor showed relatively greater stress with the increasing vacuum pressure when silicone rubber was used as the material of the vacuum extractor. Furthermore, the maximum stress occurred near the center of the sphere part on the vacuum extractor. In addition, when stainless steel was used as the material of the vacuum extractor, the von Mises stress on the vacuum head skull increased slightly with the increase in the vacuum pressure; moreover, there was high stress distribution on the vacuum head skull in the outer area of the vacuum extractor.