# Interior Sound Quality Prediction of Pure Electric Vehicles Based on Transfer Path Synthesis
## 3 Measurements
### Transfer Function Measurements
#### 3.1.1 Airborne Noise Transfer Function Measurements  
The noise transfer function of the electric drive system was measured using the airborne source quantification (ASQ) technique. The ASQ technique quantifies airborne noise sources by determining the contribution level of each noise transfer path. To this end, it considers the transfer path between each noise source and the response at the target point [27]. ASQ can accurately measure the contributions of surface-plate noise sources to the total noise [28]. The noise source excitation characteristics are described in terms of volume acceleration or volume velocity, and the response at the target point is indicated by the sound pressure measured by a microphone [29]. As the electric drive system cannot be treated as a single sound source, its surface was divided into several equal-area meshes. Each grid was considered equivalent to a point source, and its intensity was determined as the acceleration at the center point of the mesh multiplied by the surface area of the mesh. In the general meshing principle, the spacing between the mesh centers is less than half the wavelength of sound waves with the corresponding frequency. However, even when the mesh density does not meet these requirements, ASQ is more accurate than traditional measurements of the airborne noise transfer function (in which volume source measurements are separately collected on each surface of the electric drive system). In this measurement, the electric drive system was divided into 61 squares of side length 8.5 cm, as shown in Figure 4.  
The airborne noise transfer path function of the tires was measured using the reciprocity method. Airborne noise transfer functions should be measured in the semi-anechoic chamber of the whole vehicle, and the background noise should be below 25 dB (A). Airborne noise transfer function measurement equipment is shown in Table 1. In these measurements, we employed a medium- and high-frequency tubular volume sound source with a high signal-to-noise ratio. The nozzle of the volume sound source was positioned at each location of the noise source. The target point in the vehicle (where the microphone was placed) was the position of the driver's right ear. The left and right panels of Figure 5 show the measurement positions of the noise transfer path functions of the left front tire and microphone, respectively. The volume sound source was arranged at each test point to generate white noise, and its sound signal and the signal at the target point in the vehicle were recorded with the microphone. The airborne noise transfer function of each path was then estimated by Equation (6). Figure 4: Mesh division of the electric drive system. Figure 6 displays the spectra of the airborne noise transfer functions from Points 1, 2, and 3 on the motor surface to the target point. Since the amplitude of FRF varies greatly, the \(Y\)-axis values are displayed on the dB scale. The dB scale can clearly express the huge changes of amplitude. At the different surface measurement points, the airborne noise transfer functions showed almost the same trends, with a gradually decreasing sensitivity as the frequency ranged from low to high. The peak frequencies of the noise transfer functions differed among the measurement points, but the differences were ignorable. Figure 7 shows the airborne transfer function spectra of the four tires to the target point. \begin{table}
\begin{tabular}{c c c} \hline
**No.** & **Equipment** & **Type** \\ \hline
1 & Microphone & B\&K 4189-A-021 \\ \hline
2 & Acoustic calibrator & B\&K 4231 \\ \hline
3 & Data collector & LMS SC316W \\ \hline
4 & Medium-high frequency volume source & LMS SN5114 \\ \hline
5 & Laptop & Dell 5511 \\ \hline \end{tabular}
\end{table} 
Table 1: Airborne noise transfer function measurement equipment. Figure 5: Measurement position of noise transfer path function of the left front tire: Layouts of (**a**) the microphone and volume sound source at the left front tire and (**b**) the microphone placed at the driver’s right ear.