## 5 Conclusions  
This paper establishes a multi-body dynamics model of high-speed train disc brake thermo-solid coupling, obtains the disc surface temperature through a scaled inertia braking experiment, and compares it with the model temperature to verify the accuracy of the model. The changing rules of temperature, stress, and strain of the brake disc under the influence of vibration are obtained through the mode. Comparing the results with and without considering the thermal coupling effect, the influence of the thermo-solid coupling effect of the brake on its vibration characteristics is discussed. In addition, by extracting the vibration displacement range and root mean square value of vibration velocity at different rotating speeds and pressures, the change regulation of the vibration characteristics of the brake disc under the change of the braking speed and braking pressure is analyzed. However, due to the complexity of multi-physical field coupling analysis and the difficulty in convergence of calculations, this study does not consider the impact of wind load on vibration in the flow field during the braking process, and the impact of friction and wear on vibration during braking is not discussed. Therefore, subsequent research can be carried out from these perspectives. Key findings include the establishment of a multi-body dynamics analysis model for the thermo-solid coupling of high-speed train disc brakes, which effectively analyzed vibration characteristics considering thermo-solid coupling effects. During the braking process, the surface temperature and stress of the brake disc were in a dynamic change process, and there was stress concentration and obvious high-temperature concentration in the friction area. When the braking initial velocity was 200 km/h and the braking pressure was 0.36 MPa, the maximum temperature and stress of the brake disc reached 226 \({}^{\circ}\)C and 198 MPa, respectively. The temperature and stress concentration will aggravate the local warping deformation of the friction interface. The brake disc underwent different degrees of elastic warping deformation during the braking process, and its maximum deformation reached 0.44 mm. The warping deformation caused the frictional contact surface of the brake disc to lose its flatness, resulting in uneven contact between the brake disc and the brake pad. This affected their contact state and led to the occurrence of brake vibration. Furthermore, the thermo-solid coupling effect during the braking process significantly influenced the vibration characteristics of the disc brake. When the model considered the thermo-solid coupling effect, part of the brake disc's energy was released into the air in the form of heat energy, which reduced the severity of the vibration of the brake disc. With the increase of the initial braking speed and braking pressure, the axial vibration displacement of the brake disc increased, and the vibration velocity increased at the same time, that is, the axial vibration of the brake disc intensified. J.Y. and Q.Z. : conceptualization, methodology; Q.Z. and J.Y. conducted the simulation; data curation; Q.Z. : original draft preparation, X.F. : review and editing, Z.S. and Y.L. : supervision, funding acquisition; Z.L. and S.Z. : project administration. All authors have read and agreed to the published version of the manuscript. This research was funded by National Natural Science Foundation of China (52375169), Liaoning Provincial Science and Technology Program (No. 2022 JHZ/101300228), Liaoning Provincial Doctoral Research Foundation Project (No. 2022-BS-260), Liaoning Provincial Department of Education Scientific Research Project (IJKZ0479) and Liaoning Provincial Department of Transport Research Project (No. 202148). Not applicable. Data Availability Statement: The data used to support the findings of this study are available from the corresponding author upon request. The data are not publicly available due to privacy.