# Research on Propagation Characteristics of Tire Cavity Resonance Noise in the Automobile Suspension
## 4 Power Flow Analysis of Tire Cavity Resonance Noise Propagation in a Suspension System

Table 3: Finite element calculation results of input and output sectional power flow. Figure 7: Power flow contour of aluminum alloy wheel and suspension system. It can be seen from Table 3 that for the suspension system under 4000 N load, the output power flow of the front bushing of the lower swing arm was the largest and that of the rear bushing was the smallest. Therefore, special attention should be paid to the front bushing of the lower swing arm in order to suppress the transmission of the resonant noise energy of the tire cavity into the vehicle. For different vehicle speeds and load conditions, the sound pressure amplitude function of the tire cavity resonance noise experienced by the wheels is shown in Table 4.  
Figure 8: Distribution of the sound intensity vector of a suspension system in different planes and with partial enlargement. (a) XZ plane sound intensity vector distribution diagram and partial enlargement. (b) XY plane sound intensity vector distribution diagram and partial enlargement. (c) YZ plane sound intensity vector distribution diagram and partial enlargement. According to the amplitude distribution of resonant sound pressure in the tire cavity under different load conditions at 0.22 MPa inflation pressure and 60 km/h speed, as shown in Table 4 (the meanings of symbols in the function are the same as before), the model of a Y-spoke aluminum alloy wheel and suspension system after loading is shown in Figure 9.  
The above five suspension system models under different loads were analyzed using the finite element method, and the response of an aluminum alloy wheel under the action of tire cavity resonance noise was calculated. The stress contour of the aluminum alloy wheel and suspension system under different loads is shown in Figure 10, and the corresponding strain contour is shown in Figure 11. The unit of stress is MPa. \begin{table}
\begin{tabular}{c c c} \hline
**Tire Working Condition** & \multicolumn{2}{c}{**Sound Pressure Amplitude Function**} \\ \hline  & 2500 N & \(P(\theta,t)=(43-18\cos\theta+19\sin\theta+12\cos 2\theta-5\sin 2\theta-\cos 3 \theta-4\sin 3\theta)\cos(2\pi ft)\) \\  & 3000 N & \(P(\theta,t)=(55-9\cos\theta+45\sin\theta-2\cos 2\theta-27\sin 2\theta+8\cos 3 \theta+\sin 3\theta)\cos(2\pi ft)\) \\
0.22 MPa & 3500 N & \(P(\theta,t)=(88-34\cos\theta+6\sin\theta+18\cos 2\theta-6\sin 2\theta)\cos(2\pi ft)\) \\
60 km/h & 4000 N & \(P(\theta,t)=(80-30\cos\theta+30\sin\theta+32\cos 2\theta-24\sin 2\theta+3 \cos 3\theta+14\sin 3\theta)\cos(2\pi ft)\) \\  & 4500 N & \(P(\theta,t)=(92-37\cos\theta+34\sin\theta+29\cos 2\theta-35\sin 2\theta) \cos(2\pi ft)\) \\ \hline  & 0.16 MPa & \(P(\theta,t)=(33-8\cos\theta+7\sin\theta+13\cos 2\theta-11\sin 2\theta+\cos 3 \theta+6\sin 3\theta)\cos(2\pi ft)\) \\
3500 N & 0.19 MPa & \(P(\theta,t)=(53-11\cos\theta+7\sin\theta+5\cos 2\theta-11\sin 2\theta+\cos 3 \theta-6\sin 3\theta)\cos(2\pi ft)\) \\
50 km/h & 0.22 MPa & \(P(\theta,t)=(49-20\cos\theta+6\sin\theta+8\cos 2\theta-8\sin 2\theta)\cos(2\pi ft)\) \\  & 0.25 MPa & \(P(\theta,t)=(39-\cos\theta+11\sin\theta+12\cos 2\theta-14\sin 2\theta-0.1 \cos 3\theta+7\sin 3\theta)\cos(2\pi ft)\) \\  & 0.28 MPa & \(P(\theta,t)=(45-12\cos\theta+5\sin\theta+9\cos 2\theta-11\sin 2\theta-\cos 3 \theta-5\sin 3\theta)\cos(2\pi ft)\) \\ \hline  & 20 km/h & \(P(\theta,t)=(28+5\cos\theta+11\sin\theta+2\cos 2\theta-12\sin 2\theta)\cos(2\pi ft)\) \\
0.22 MPa & 30 km/h & \(P(\theta,t)=(39+2\cos\theta+12\sin\theta+3\cos 2\theta-13\sin 2\theta)\cos(2\pi ft)\) \\
3000 N & 40 km/h & \(P(\theta,t)=(48+\cos\theta+13\sin\theta+2\cos 2\theta-12\sin 2\theta)\cos(2\pi ft)\) \\
3000 N & 50 km/h & \(P(\theta,t)=(48-9\cos\theta+14\sin\theta+2\cos 2\theta-10\sin 2\theta)\cos(2\pi ft)\) \\  & 60 km/h & \(P(\theta,t)=(55-9\cos\theta+45\sin\theta-2\cos 2\theta-27\sin 2\theta+8\cos 3 \theta+\sin 3\theta)\cos(2\pi ft)\) \\ \hline \end{tabular}
\end{table} 
Table 4: Sound pressure amplitude function of wheels under various working conditions. Figure 10: _Cont_. Figure 9: Loading state of a suspension system under different loads.