## 2 Working Principle and Modeling
### Diaphrag Mechanical Model
Similar to the RD simulations, the sleeve and flange 2 were set as fixed constraints, and the contact surfaces of the different components were set as contact pairs. In the simulations, the magnitudes of the acting forces were changed, and the displacements of the shafts were recorded. Considering the complex shapes of the models, the grids of the models were divided by the free triangle mesh function of the COMSOL Multiphysics 6.2 software, as shown in Figure 8,d. To ensure the accuracy of the results, grid independence tests were carried out. The specific test process was as follows: First, the mesh size parameter was set to four \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Definition** & **Parameter** & **Value** & **Unit** \\ \hline Shore hardness & \(s\) & 70 & HA \\ Density & \(\rho\) & 1.3 & g/cm\({}^{3}\) \\ Mechanical characteristic coefficient of the constitutive model & \(k_{\mathrm{r}}\) & 0.25 & - \\ Model parameter & C\({}_{10}\) & 0.7388 & MPa \\ Model parameter & C\({}_{01}\) & 0.1847 & MPa \\ Elastic modulus & \(E\) & 5.545 & MPa \\ Poisson’s ratio & \(\mu\) & 0.5 & - \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Rubber material parameters. Figure 8: Solid model and grid model of finite element simulations: (**a**) solid model of RD; (**b**) solid model of CD; (**c**) grid model of RD; and (**d**) grid model of CD. different levels in COMSOL, and the corresponding grids of the RD and CD part models were divided. Second, the test condition was randomly selected, in which the acting forces of the RD and CD parts were 8.7 N and 1.35 N, respectively. Finally, the deformation states of the RD and CD parts under the specified loads were simulated by using the four grids of different sizes mentioned above. Taking the RD part of the No. 3 level grid as an example, the simulation results are shown in Figure 9. The displacements of shafts were measured and used as the criteria to judge the grid independence, and the results are shown in Table 2. Generally, in grid independence tests, when the grid deviation rate is below 2%, it is considered the simulation result error is within the acceptable range [24]. Considering the efficiency and the accuracy of the simulation calculation, No. 3 and No. 7 were selected as the research grids. To judge the influence of the mesh type on simulation accuracy, a quadrilateral grid of the RD part was divided using the same mesh size parameter as No. 3, as shown in Figure 10. The number of quadrilateral grids was 5857 domain units and 816 edge units. The simulation of the RD part model was conducted under the same 8.7 N load force, and the results are shown in Figure 11. The displacement of RD part shaft is 4.072 mm, and the deviation from the free triangle grid is only 0.07 mm. It can be seen that the mesh type has no obvious influence in the research, and the free triangle grids are used uniformly in the following research. The axial displacement of the RD ranges from \(-\)1 mm to 6 mm, while the axial displacement of the CD ranges from \(-\)0.12 mm to 1.2 mm. A finite element parametric scanning tool was used to analyze the state of the diaphragm under different forces and pressures. The tensile strength of the HNBR with 70 HA hardness is 18.2 MPa. The safety factor was set to 3 times. The displacement and stress cloud diagrams of the diaphragms are shown in Figure 12. When the displacement of the RD is 6 mm, the maximum stress is