## 4 Experiment Analysis
### Influence of Ambient Temperature and Air Content on the Support Height of Support Cylinder
To determine the compensation ability of the pressure transmitter under temperature changes, the electronic pressure transmitter and mechanical pressure gauge are connected to the pipeline to measure the system pressure. It can be seen from Figure 10 that the pressure measured by the two sensors was roughly the same, and the resulting pressure deviation was a reading error. It can be concluded that the value measured by the pressure transmitter was accurate, and this data value was used as the measured data in the subsequent analysis process. During the experiment, the temperature in the laboratory fluctuated from 24 \({}^{\circ}\)C to 27 \({}^{\circ}\)C, and the experiment lasted for 1640 min. It can be seen from the collected pressure error of the upper and lower chambers of the FSS, after 900 min that, even if the temperature in the laboratory rises, the pressure error of the upper and lower chambers of the FSS is always negative and the deviation increases progressively. This phenomenon may be caused by leakage in the FSS, which leads to the loss of the working medium in the upper and lower chambers. Therefore, when analyzing the experimental data, the data collected before 900 min should be used for the analysis. The data collected in the first 900 min are shown in Figures 11 and 12, respectively. Figure 9: Support height error when injecting hydraulic oil with filtered air. Figure 11: Pressure error of the upper and lower chambers when injecting unfiltered air. Figure 10: Data measured by electronic pressure transmitter and mechanical pressure gauge. The pressure changes in the upper and lower chambers with changes in the ambient temperature when the hydraulic oil with unfiltered air and filtered air was injected into the FSS are shown in Figures 11 and 12. It can be seen from the data that the pressure error of the upper chamber is generally higher than that of the lower chamber. This is because, under the influence of gravity of the internal piston, external piston, support shaft, and lock nut of the support cylinder, the support piston will produce a downward displacement, resulting in the volume of the upper chamber being larger than the volume of the lower chamber. As a result, the pressure error in the upper chamber is always greater than the error generated by the lower chamber during ambient temperature change. It can be seen from the scatter plot that when the ambient temperature changed from 24.2 \({}^{\circ}\)C to 27 \({}^{\circ}\)C and the working medium with unfiltered air was injected, the pressure error of the upper and lower chambers varied from \(-\)0.011 MPa to 0.01 MPa. When injecting the working medium with filtered air, the pressure error of the upper and lower chambers varied between \(-\)0.0045 MPa and 0.005 MPa. After the air was filtered, the pressure error in the support cylinder reduced significantly with the ambient temperature change, and the experimental results are roughly the same as the results of the simulation in Section 3.3, which further verifies the validity of the established mathematical model. Influence of Different Ambient Temperatures and Air Contents on the Support Stiffness of Support Cylinder  
Through the support pressure and support height errors collected as described in Sections 4.1 and 4.2, combined with Equations (23) and (24), the error of the support stiffness of the support cylinder can be obtained. The unfiltered air support stiffness error is shown in Figure 13. The support stiffness error of most test points is from \(-\)280 N/mm to 400 N/mm, and individual test points outside the interval may be caused by objective factors. The stiffness error of the filtered air support is shown in Figure 14. The support stiffness error of most test points in this case was between \(-\)100 N/mm and 190 N/mm. Compared with the unfiltered air working medium, the support stiffness error is greatly reduced, but it still varies randomly within the interval. This is due to the following systematic errors or random errors during the experiment.