## 4 Analysis Results and Discussion of Coupled Multi-Body Dynamics
### Analysis of Thermo-Solid Coupling Characteristics during Braking
#### 4.1.3 Surface Deformation Distribution Results of the High-Speed Train Brake Disc  
The thermal deformation of the brake disc is a manifestation of the thermo-solid coupling effect in the process of the brake disc. The brake disc warps to varying degrees during the whole braking process. To further clarify the warping deformation of the brake disc during the braking process, the deformation contours of the brake disc were extracted at the initial braking time \(t=0.5\) s, the maximum deformation time \(t=30\) s, and the braking end time \(t=56.6\) s. The result is shown in Figure 9.  
The thermal warpage deformation of the brake disc follows the same general trend as changes in temperature, which is an increase followed by a decrease. The temperature change and the overall trend is to increase first and then decrease. In the brake to 30 s, the brake disc temperature reached the maximum when its warpage deformation also reached the maximum (0.44 mm). This shows that the deformation of the brake disc is affected by its temperature change. The warping deformation area of the brake disc was mainly concentrated close to the friction radius, and the radial deformation distribution was quite different. The deformation at the friction radius of the brake disc was quite greater than the deformation at both sides. The frictional contact surface of the brake disc lost its flatness due to variations in the degree of deformation at different locations. The above changes were mainly due to the circular distribution of the surface temperature of the brake disc friction disc and the large temperature gradient in the radial direction, resulting in large  
Figure 8: The stress field distribution of the brake disc at different braking moments: (**a**) \(t=0.5\) s; (**b**) \(t=10\) s; (**c**) \(t=22.8\) s; (**d**) \(t=56.6\) s.  
internal thermal stress. Uneven distribution of temperature and stress is the main cause of thermal warpage deformation of the brake disc.  
Figure 10 shows the results at the time of maximum deformation, \(t=30\) s, obtained by extracting the deformation contours of the brake disc's friction surface and then enlarging its axial scale factor to 500 times. This allows for a more intuitive observation of the thermal deformation distribution of the friction surface of the brake disc.  
The temperature rise of the brake disc during the braking process causes it to warp and deform, and the entire friction disc surface loses its flatness during the braking process. As shown in Figure 10, the overall axial deformation of the brake disc surface was in the same direction. The frictional contact area had different degrees of warping deformation under the influence of uneven temperature distribution. The phenomenon of \"annular protrusion\" appeared, and the entire friction surface was distributed in a drum shape. Changes in temperature cause deformation of the brake disc and affect its contact area. In the case of heating, the occurrence of thermal warping deformation of the brake disc will cause the action point of the contact pressure of the friction pair to move. The brake disc and brake pad cannot form good contact with each other, the contact state of the friction pair changes. There is a local contact behavior between the two, and their effective contact area is constantly changing and much smaller than the nominal contact area. Therefore, the middle part of the brake disc will be continuously squeezed and impacted by the brake pads during the braking process, causing an uneven distribution of contact pressure between the braking interfaces, which results in vibration during the braking process.