# A Novel Structure of Rubber Ring for Hydraulic Buffer Seal Based on Numerical Simulation
## 3 Modeling
### Finite Element Model  
According to the rubber ring of hydraulic buffer used in articulated landing gear, considered the axisymmetric characteristic of geometry and load condition [22; 23], the axisymmetric model of rubber O-ring is established with section diameter 7 mm as shown in Figure 2a. Specific geometry size of groove and piston rod are set according to the part 1 of ISO 3601 standard.  
HyperMesh v.14.0 program is used to mesh the structure, because the mesh size has a direct impact on the numerical results. Therefore, by reducing the mesh size from 0.4 to 0.05, the mesh convergence is studied in 0.05 steps. When the mesh size is less than 0.2, the numerical results have no obvious change. Therefore, the mesh size is 0.2, the number  
Figure 1: Schematic of seals for articulated landing gear. The hydraulic buffer is a key structure of load-bearing in the articulated landing gear. And the hydraulic buffer of articulated landing gear is composed of buffer tube, groove, seals, and piston rod. To prevent the leakage of hydraulic fluid, the rubber O-rings are used as the inner seal and outer seal.  
of meshes for O-ring sealing structures are 4985, and the number of meshes for Butterfly-ring sealing structures are 7529. The APDL statement of ANSYS v.16.2 program is used to complete the parameter definition and solution. In the 2D axisymmetric analysis, plane 182 element is used. The material model of seal ring is the Mooney-Rivlin Hyperelastic with two parameters, and the material parameters are 1.84 and 0.47, which have been discussed in Section 2.1. The material of piston rod and groove is STS 430 steel (Elastic modulus 210 GPa, Poisson ratio 0.3). Loads applied and boundary conditions are the variable in this study, in which the pre-compression ratio is in the range of 8% to 16%, and the hydraulic pressure is in the range of 0 to 20 MPa. The contact pressure of groove side is the major cause of hydraulic leakage during assemble process, in order to enhance the contact peak pressure, the butterfly-ring is designed to elevate the contact pressure of groove side as Figure 2b shown. The maximum section diameter of butterfly-ring is the same as that of O-ring, which is 7 mm. Specific parameters are illustrated in the Appendices A-C.  
The contact pair, which is adopted to simulate the contact nonlinear behavior [24; 25; 26], is defined at the squeeze area during the installation mode and working mode, as shown in Figure 3. And the element type of TARGE169 and CONTA171 are adopted to simulate the contact behavior. The rubber ring is set as contact surface [27], due to its stiffness being softer than the material of piston rod and groove (Elastic modulus 210 GPa). Augmented Lagrange method, which could lead to better conditioning than the pure penalty method, is adopted to solve the contact problem of stiffness hardening for large displacement and deformation [28; 29]. The material of the groove and piston rod is STS 430 steel, the surface roughness of the piston rod is 0.05 to 0.1 \(\upmu\)m, and the surface roughness of the groove is 0.2 to 0.3 \(\upmu\)m. Considering that the surface roughness of piston rod is less than that of groove surface, the friction coefficient between piston rod and sealing ring is set as 0.1, and the friction coefficient between groove and sealing ring is set as 0.2.  
Figure 3: Modeling of contact pair. Three contact pairs are modeled, contact pair 1 is between piston rod and rubber ring, contact pair 2 is between groove side and rubber ring, contact pair 3 is between groove bottom and rubber ring.  
Figure 2: Finite element model. The original structure of seal is O-ring in **(a)**, and the proposed structure of seal is butterfly-ring in **(b)**, with the same maximum diameter as the O-ring. Both are assembled with groove in green mesh and piston rod in yellow mesh.