# Research on the Reciprocating Friction and Installation Force of Seals in Deep-Sea Samplers
## 2 Methods
### Experimental Study
#### 2.2.2 Experiment Under High Pressure and Low Temperature  
A test rig, as illustrated in Figure 5a, was designed to measure the seal installation force and reciprocation friction under high-pressure, low-temperature conditions. Table 4 presents the dimensional parameters of the key parts of the test module. The pressure vessel was fabricated from 316 stainless steel and includes a centrally machined through-hole with a diameter of 24 mm. The two pistons and the connecting rod were made from precipitation-hardening stainless steel 17-4 PH. Both the pistons and connecting rods were machined with housing for an O-ring. Additionally, two threaded holes were located on the lateral side of the pressure vessel for connecting the pressure sensor (Tuopu Electronic Instrument Co., Dongguan, China, PT124) and the booster pump (Jinran Co., Shanghai, China, 4 DSY-120). The piston was connected to the force transducer via a double-end stud, and the force transducer (Dayang Co., Bengbu, China, DYLY-108) was connected to the linear actuator (Zhengyuan Co., Shenzhen, China, AM-BD45100 AN) through a stainless-steel shaft. The friction measurement module was placed within a water bath environment inside an insulated box to facilitate testing at a specific temperature. A water chiller (Jiale heating engineering Co., Hefei, China LS27-1000) was used to circulate the water in the insulated box, ensuring a constant temperature. The assembled test rig is shown in Figure 5b.  
Figure 5: _Cont._  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**No.** & **Chamfer Angle (\({}^{\circ}\))** & **Chamfer Length (mm)** & **Roughness of the Contact Surface (\(\upmu\)m)** \\ \hline
1 & 20 & 2, 3 & 1.6 \\
2 & 25 & 2, 3 & 1.6 \\
3 & 15 & 1, 2 & 0.8 \\ \hline \hline \end{tabular}
**Note:** Ra was used in this study to describe the surface roughness. Ra represents the arithmetic mean of the absolute values of the contour deviations within a specified sampling length.  
\end{table}
Table 3: Parameters of cylinders used in the experiment.  
As shown in Figure 5a, State (1) represents the initial position of the assemblies. At this stage, the motor drives the piston to perform an upward stroke. The output of the sensor (\(F_{O1}\)) is the sum of \(f_{1}\) and \(f_{3}\) (the friction between the O-ring and the inner wall of the pressure vessel), as well as the gravity \(m\) (18.2 N) of the two pistons, the connecting rod, and the two limit plates (Equation (2)).  
\[F_{O1}=f_{1}+f_{3}+m \tag{2}\]  
In State (2) and State (3), O-ring 2 makes contact with the inner wall of the step. As a result, the installation and friction force of O-ring 2 (\(f_{2}\)) is incorporated into the output of the sensor (\(F_{O2}\)), as shown in Equation (3).  
\[F_{O2}=f_{1}+f_{2}+f_{3}+m \tag{3}\]  
As the forward stroke progresses, O-ring 2 detaches from the step until it reaches State (4), at which point the sensor's output equals \(F_{O1}\). In this case,\(f_{1}\) is equal to \(f_{3}\), and both \(f_{1}\) and \(f_{2}\) can be expressed in Equations (4) and (5).  
\[f_{1}=\frac{F_{O1}-m}{2} \tag{4}\]  
\[f_{2}=F_{O2}-F_{O1} \tag{5}\]  
\begin{table}
\begin{tabular}{c c} \hline
**Part Name** & **Design Parameters** \\ \hline Pressure vessel & 40 mm in ID, 90 mm in OD, and 170 mm in length \\ Piston & 40 mm in diameter, 80 mm in length, and weighs 0.634 kg \\ Connecting rod & 24 mm in diameter, 110 mm in length, and weighs 0.291 kg \\ Limit plate & 70 mm in diameter, 5 mm in height, and weighs 0.129 kg \\ O-ring & 33.5 mm in ID, 3.55 mm in cross-section diameter \\ \hline \end{tabular}
\end{table}
Table 4: Design parameters of key parts of the test module.  
Figure 5: The experiment setup. (**a**) Details of the test module. (**b**) Experimental setup.