## 3 Multi-Body Dynamics Analysis Model of Disc Brake Coupling in High-Speed Trains
### Finite Element Model of Disc Brake Braking Process
#### 3.2.2 Establishment of Finite Element Model  
The geometric model of the high-speed train brake disc/brake pad was meshed using COMSOL 5.6 software. There were many connecting parts between the surfaces of the brake disc and the ventilated blades. Direct meshing can lead to uneven mesh distribution, which can have negative effects on calculation accuracy and convergence. In addition, considering the continuity of the mesh nodes, mesh sectioning was used to divide the two. To obtain uniform grid distribution, the brake pads and brake disc friction surfaces were divided into free tetrahedral meshes, and the ventilated blades of the brake disc were hexahedral meshes. In addition, to guarantee calculation accuracy, the mesh was adaptively divided according to extremely fine specifications. After mesh division, the number of meshes in this model was 75,113, and the number of nodes was 28,536. The material of brake disc was comprised of low-alloy steel, and the material of the brake pad was comprised of copper-based powder metallurgy material. The corresponding material parameters are shown in Table 1.  
According to the actual working principle of high-speed train disc brakes, the multi-body dynamics method was used to set motion constraint boundary conditions for high-speed train disc brakes, and the relative motion relationship between the brake disc and the brake pad was transformed. The constraint relationship was added between the components of the brake according to the kinematic pair shown in Table 2. An interference fit was used to assemble the axle and the inner ring of the brake disc. The connecting portion of the inner ring of the brake disc was set as a rigid area to prevent the inner ring part from deforming. The area could act as a constraint for the remaining flexible parts of the brake disc. Using a rotating pair and restricting other degrees of freedom, the brake  
Figure 3: Geometric model of high-speed train brake disc/brake pad. disc could only rotate around the axis, and the initial speed needed for rotation is set at 200 km/h. The brake pad restricted other degrees of freedom through the translation pair while achieving axial movement during the braking process and provided the required braking pressure of 0.36 MPa during the braking process. In addition, the contact type between the brake disc and the brake pad was defined as friction contact through the contact pair, the penalty function method was used for simulation calculation, and the friction coefficient was set to 0.3. The entire simulation process was divided into two steps. The brake disc speed rose to the predetermined value in the first 0.1 s, and the brake started braking after 0.1 s until the brake disc speed drops to 0. The heat generated by the brake disc and the brake pad was loaded on the contact surface of the brake disc and the brake pad in the form of the dissipation rate of friction, and it was used as a friction input heat source for structural heat transfer. The heat transfer between the brake disc and the brake pad was realized through the pair thermal contact, the initial temperature of the brake disc and the brake pad and the ambient temperature was set to 20 \({}^{\circ}\)C, and the convective heat transfer and thermal radiation were set at the contact boundary between the brake surface and the air. When defining the thermal radiation boundary condition of the brake disc surface, the effect of temperature change on the brake surface emissivity was ignored, that is, it was assumed to be a constant. The high-speed train brake disc/brake pad finite element model is shown in Figure 4.