## 4 Analysis Results and Discussion of Coupled Multi-Body Dynamics
### Influence of Braking Parameters on the Vibration Characteristics of the Brake Disc  
#### 4.3.1 Influence of Brake Pressure Changes on the Vibration Characteristics of the Brake Disc  
To study the influence of brake pressure changes on the vibration characteristics of the brake disc, under the premise that the initial braking speed remains constant at 200 km/h, multi-physical field coupling simulations were run on the brake finite element model at brake pressures of 0.23 MPa, 0.36 MPa, and 0.49 MPa, respectively. After the overall axial vibration displacement range and root mean square value of vibration velocity were extracted, the change results of the brake disc vibration characteristics under the change of brake pressure were obtained, as shown in Figure 12.  
Figure 11: Axial vibration acceleration of brake disc: (**a**) thermo-solid coupling was not considered; (**b**) considering the thermo-solid coupling effect.  
Figure 12a-c are, respectively, the brake disc vibration displacement-time curve, axial vibration displacement range-brake pressure bar graph, and axial vibration velocity RMS value-brake pressure graph. Figure 12a illustrates that the variation range of the axial vibration displacement amplitude of the brake disc gradually increased with the increase of the brake pressure. Figure 12b shows that when the brake pressure was 0.23 MPa, 0.36 MPa, and 0.49 MPa, the difference between the maximum value and the minimum value of the axial vibration displacement of the brake disc was \(3.8\times 10^{-5}\) m, \(5.04\times 10^{-5}\) m, and \(8.82\times 10^{-5}\) m, respectively. Its value exhibited an increasing trend as the brake pressure was increased. It can be seen from Figure 12c that the axial vibration intensity, that is, the effective value of the axial vibration velocity, increased gradually with the increase of the brake pressure. From Figure 12a-c, it can be concluded that when the brake pressure increased, the brake disc axial vibration amplitude increased at the same time, and vibration speed was faster, that is, the brake disc axial vibration intensity was increasing. The main reasons leading to the above phenomenon are as follows: When the brake pressure on the brake pad increases, the friction force on the brake disc also increases, and the mechanical friction between the brake disc and the brake pad raises the friction pairs product heat. The increase in the temperature of the brake disc leads to greater thermal stress and thermal deformation. The reduction of the contact area of the friction pair affects its contact state. The brake disc and the brake pad cannot form a good and effective contact, causing a phenomenon of contact separation, which leads to aggravated vibration. At the same time, to overcome the effect of the increased frictional force on its movement, the brake disc resists this increasingly strong obstruction. In addition, the increase in the brake pressure will have a stronger impact on the brake disc, resulting in a more unstable vibration characteristic and aggravated axial vibration.  
Figure 12: Vibration characteristics of brake disc under changing brake pressure: (**a**) vibration displacement; (**b**) extreme difference in vibration displacement; (**c**) vibration intensity.