## 3 Simulation Analysis of FSS  
Under different FSS working pressures, the amount of air contained in the working medium and the change in ambient temperature during the work will have different degrees of influence on the support pressure and support height of the FSS. To study the corresponding relationship between the influencing factors and affected parameters, the effects of ambient temperature change on the volume, support height, and support pressure at different air contents are simulated.  
In the simulation calculation process, the working medium characteristic parameters and disturbance coefficient are shown in Table 1.  
To study the specific influence of the air content in hydraulic oil and the changes in ambient temperature on the performance of the FSS, it is necessary to combine the structural parameter analysis of the support cylinder and rolling diaphragm. The structural parameters of the designed support cylinder are listed in Table 2.  
The structural parameters of rolling diaphragm are shown in Table 3.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Name** & **Value** & **Name** & **Value** \\ \hline Calibration temperature of & \(T_{r1}=20\)\({}^{\circ}\)C & The expansion of hydraulic oil & \(\alpha_{oil}=1.66\times 10^{-4}\) \\ hydraulic oil & \(K=1.66\times 10^{3}\) MPa & The expansion of air & \(\alpha_{air}=3.767\times 10^{-3}\) \\ Density of hydraulic oil & \(\rho_{T1}=900\) kg/m\({}^{3}\) & Density of air at 0 \({}^{\circ}\)C & \(\rho_{T2}=1.29\) kg/m\({}^{3}\) \\ Standard atmosphere & \(P_{r1}=0.101\) MPa & Disturbance coefficient & a, b = 1 \\ The volume compression & \(k=1.17\times 10^{-3}\) & Air content & \(\Delta V=0\)–10\% \\ coefficient of hydraulic oil & & & \\ \hline \hline \end{tabular}
\end{table}
Table 1: The working medium characteristic parameters and disturbance coefficient.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Name** & **Value** & **Name** & **Value** \\ \hline The installation height of small & \(L_{1}=19.8\) mm & The width upper and lower & \(W_{1}=2.6\) mm \\ diaphragm & & chambers & \\ The height of upper and lower & \(L_{2}=2.4\) mm & The clearance between small & \(W_{2}=11.0\) mm \\ chambers at 0 displacement & \(L_{3}=2.4\) mm & piston and cylinder wall & \(W_{3}=2.6\) mm \\ The installation height of large & \(L_{4}=11.8\) mm & Small piston radius & \(W_{4}=6.6\) mm \\ diaphragm & \(L_{5}=1.1\) mm & The length inlet and outlet & \(W_{5}=2.0\) mm \\ The diameter of inlet and outlet & \(L_{6}=15.75\) mm & Total inlet length & \(W_{6}=8.0\) mm \\ The compression height of small & \(L_{7}=14.0\) mm & The compression width small & \(W_{7}=3.0\) mm \\ diaphragm & \(L_{8}=14.0\) mm & diaphragm & \(W_{7}=3.0\) mm \\ \hline \hline \end{tabular}
\end{table}
Table 2: The structural parameters of support cylinder.  
The relationship between the volume of the upper and lower chambers of the support cylinder and the ambient temperature, air content, and support pressure is shown in Figure 4a,b. It can be seen from the figure that the volume of the lower chamber of the support cylinder is still smaller than the volume of the upper chamber, and considering the weight of the internal and external piston parts, will cause the support shaft to move because of the asymmetric structure of the large rolling diaphragm. When the volume fraction of the air in the hydraulic oil and the ambient temperature are higher, the volume of the upper and lower chambers of the support cylinder will be larger. When the support pressure of the support system increases, the volume of the upper and lower chambers will increase, which is caused by the volume reduction of the rolling diaphragm when the pressure increases.