## 3 Analysis and Results
### Effect of Wear Ring Structure Size on Sealing Performance  
The shape of the cross-section of a wear ring will affect the distribution of contact stress on the sealing surface and directly affect the magnitude of the friction force. The influence of the chamfer R, thickness H, and width L of the wear ring on the sealing performance was analyzed. The working pressure was 25 MPa and the compression rate was 22.5%. \begin{table}
\begin{tabular}{l l l l l l} \hline
**Compression Ratio** & **15\%** & **17.5\%** & **20\%** & **22.5\%** & **25\%** \\ \hline Von-mises stress (Mpa) & 43.288 & 47.978 & 47.066 & 36.262 & 42.782 \\ Contact stress at I (Mpa) & 21.501 & 20.929 & 20.612 & 20.574 & 20.004 \\ Contact stress at II (Mpa) & 25.752 & 26.685 & 26.929 & 27.543 & 28.008 \\ Contact stress at III (Mpa) & 17.974 & 19.5 & 20.184 & 20.77 & 21.716 \\ \hline \end{tabular}
\end{table} 
Table 4: Contact stress and compression ratio (working pressure 20 MPa). \begin{table}
\begin{tabular}{l l l l l l} \hline
**Compression Ratio** & **15\%** & **17.5\%** & **20\%** & **22.5\%** & **25\%** \\ \hline Von-mises stress (Mpa) & 43.288 & 47.978 & 47.066 & 36.262 & 42.782 \\ Contact stress at I (Mpa) & 21.501 & 20.929 & 20.612 & 20.574 & 20.004 \\ Contact stress at II (Mpa) & 25.752 & 26.685 & 26.929 & 27.543 & 28.008 \\ Contact stress at III (Mpa) & 17.974 & 19.5 & 20.184 & 20.77 & 21.716 \\ \hline \end{tabular}
\end{table} 
Table 5: Contact stress and compression ratio (working pressure 25 MPa). For the influence of chamfer R, we took the thickness of the wear ring H as 2.5 mm and the width L as 3.5 mm, while the value range of chamfer R was defined as 0.3 mm to 1.3 mm. The size of each increment was 0.2 mm. The contact stress of three sealing surfaces I, II, and III and the maximum Von Mises stress of the combined ring were analyzed. Figure 6 shows the distribution of contact stress at I under different chamfer R. From the figure, it can be seen that the chamfer R increases continuously, the contact length decreases, and the overall contact stress at I tends to increase. It can be seen that under the same working pressure, although the maximum contact stress at I increases with the increase in the chamfer R size, compared with R = 0.3 mm and R = 0.5 mm, the contact pressure F decreases by 8.04%. For the influence of the thickness H of the wear ring, we took the chamfer R as 0.3 mm and width L as 3.5 mm, and defined the thickness H in the range of 1.5 mm to 2.5 mm. The size of each increment was 0.25 mm. The contact stress of I, II, and III sealing surfaces and the maximum Von Mises stress of the combined ring were analyzed. As can be seen from Figure 7, with the increase in the thickness H, the contact width, maximum contact stress, and position where the maximum stress appeared did not change much. Figure 6: Distribution of the contact stress along contact path I at different chamfer R (mm). Figure 7: Distribution of contact stress along contact path at I at different thicknesses H (mm). It can be seen that, under the same working pressure, the thickness of the wear ring H has no obvious influence on the contact stress of the three sealing surfaces I, II, and III. The contact pressure F decreased slowly with the increase in thickness H. Compared with H at 2 mm and H at 2.5 mm, the contact pressure decreased by 3.93%. For the influence of the wear ring width L, we took R as 0.3 mm and H as 2.5 mm and defined the range of width L as 3.0 mm to 4.0 mm. The size of each increment was 0.25 mm. The contact stress of the three sealing surfaces I stress of the combined ring were analyzed. As can be seen from Figure 8, with the increase in width L, the maximum contact stress first increased and then decreased, with the peak of the maximum stress shifting toward the charging side.