## 2 Construction of FEM of a Rotating Tire
Figure 2: Tire FEM: (**a**) 3D FEM of tire; (**b**) Tire model coupling with acoustic medium. wear, and the type of road are very important, these factors are not the research goal and core content of this paper, so these factors are not considered. In the rolling tire test, the automobile tire is loaded against the roller drum through a hydraulic actuation system and a rail. The roller drum drives the tire-wheel assembly to rotate, so that the correlative load is able to be measured. Besides, the air in the cavity rotates clockwise with the tire-wheel assembly. In order to accurately simulate the effect of tire rotation on the TACRN, the tire needs to be driven to rotate. However, the simulation in the software cannot be performed because of the non-convergence of the simulation calculation arising from the acoustic mesh element of the air not rotating with the automobile tire. In order to simulate the sound field of TACRN, some equivalent processes are required. For example, the acoustic element in the air cavity and tire-wheel assembly are assumed to be non-rotational, but the roller drum is assumed to rotate anticlockwise around the center axis of the spindle axle of the tire-wheel assembly to demonstrate the interaction between the tire and roller drum. The stimulation excitation in the simulation comes from the extrusion deformation and the fold bending between the roller drum and the tire. To model the rotating tire coupled with inside acoustic medium and simulate the sound field of TACRN, three simulation steps are required and shown as follows. The first step is to fix the tire-wheel assembly and inflate the tire. The second step is to impose radial force to the surface of the tire by changing the contact displacement between the drum and the tire to simulate the load. Finally, the third step is that the drum rotates anticlockwise around the center axis of the spindle axle of the tire-wheel assembly, and the simulated rotation duration is set to be 2 s at a constant rotational speed. Figure 4 is a schematic diagram of simulated rotational tire, and the rotational roller drum in the anticlockwise direction around the center axis of the spindle axle of the tire-wheel assembly. In the experiment, the vehicle speeds are set as 40, 50 and 60 km/h respectively, while the rotational angular speeds of the roller drum are set as the equivalent ones and the tire remains to be stationary. This process can ensure the same contact relation between the tire and drum as the real experiment for setting the static tire and the static air acoustic element of tire cavity. Figure 4: Schematic diagram of simulated rotational tire. Figure 3: FEM of a rotating tire and driving drum. The simulation is implemented by explicit algorithm in Abaqus. The operational conditions of the tire and drum are shown in Table 2. The angular speed of the roller drum corresponding to the vehicle speed is also shown in Table 2. The operational conditions in the simulation are the combination of different tire inflation pressures, vehicle speeds and loads in Table 2.  
Simulation Analysis and Experimental Validation of Sound Pressure Distribution in the Acoustic Cavity of a Rotating Tire  
In the experiment, the tire-wheel assembly is pushed to the drum of the tire-testing machine by a controllable oil cylinder through rail and is driven to revolve by the drum, so its angular velocity and the load on the tire can be determined. The wireless telemetering device collects the sound pressure signal in the tire acoustic cavity real-timely. For each experiment, the tire rotates clockwise, and the customized sound pressure sensor starts from the farthest away from the contact surface of the tire with the drum of the tire-testing machine. Ultimately, the sound pressure distributions in different conditions of the tire are obtained by changing the tire inflation pressure, the angular velocity and the load on the tire respectively. Figure 5a is a position diagram of the particular sensor that is attached to the internal face of the automobile tire.