## 2 Analysis Model and Experimental Verification
### Construction of Ring-Block Friction Pair Model  
The research object of this article is the friction pair composed of copper ring and rubber block. The size of the copper ring has an outer diameter of 35 mm and a width of 10 mm. The rubber block is assembled from nitrile rubber block and 45 carbon steel block. The rubber is fixed on the steel block through vulcanization, and the clamp clamps the steel block for loading. The rubber block size is 16 mm \(\times\) 6.5 mm \(\times\) 6.5 mm, and the steel block size is 16 mm \(\times\) 6.5 mm \(\times\) 6 mm. In addition, the finite element model is established, as shown in Figure 1.  
**Materials:** The rubber block is mainly under pressure in this experiment, and the stress-strain curve of the rubber is measured using the CMT5305 electronic universal testing machine before the experiment. In the rubber compression test, it is found that the  
Figure 1: Ring–block finite element model.  
rubber is in the linear deformation stage, so the [PERSON]'s modulus of the rubber is directly calculated, which is 13.71 MPa. The parameters of each material are shown in Table 1.  
**Meshing:** The rubber part adopts C3D8H hexahedral elements, and the number of elements for the rubber block is 5408. The metal part adopts C3D8R hexahedral units, with 672 steel block units and 12,000 copper ring units. After 100% mesh refinement, the model has a total of 46,080 meshes, but the difference in results is only 0.032%. An example analysis requires 10 h and 11 min for model with 18,080 meshes but 27 h and 2 min for model with 46,080 meshes, and the computer configuration is shown in Table 2. Therefore, in order to accelerate computing speed, the model with 18,080 meshes is used.  
**Boundary conditions:** In finite element analysis, the accuracy of the obtained results is closely related to the accuracy of the set boundary conditions. In this model, the copper ring is coupled to its center point, with a fixed constraint applied to the center point, and a speed load of 50 rpm is also applied to this point. The upper surface of the steel block is coupled with its center point, and displacement constraints are set at the center point to constrain the five degrees of freedom of the steel block, only allowing vertical movement of the steel block, that is, only x-axis degrees of freedom exist. A vertical load of 50 N is applied to the center point of the surface of the steel block. Tie constraints are used between the upper surface of the rubber block and the lower surface of the steel block. Penalty contact is used between the lower surface of the rubber and the outer surface of the copper ring, and the specific friction coefficient is obtained through experiments in subsequent chapters and written into the model.  
**Analysis step:** The vibration frequency of water-lubricated bearings in existing articles is around 2000 Hz [8]. So the analysis step length is set to 1 s, and the field output and process output are output 6000 times within 1 s, which means the vibration frequency that can be analyzed is 3000 Hz. The process output is the acceleration time curve along the y-axis at the red point in Figure 1, in order to analyze the vibration of the rubber block.