# Noise Identification for an Automotive Wheel Bearing
## 2 Noise and Vibration of Assembled Wheel Bearing
The vibration of the dust shield was approximately four times higher than that of the outer ring. Conversely, periodic peaks with an interval of 0.31 s were observed in the noise and vibration responses of Figure 3a-c. The periodic oscillation was converted to a frequency of 3.23 Hz. This frequency is similar to the rotational frequency (3.33 Hz, 1X) of a system rotating at 200 rpm. It is well known that 1X in a rotating system is due to the eccentricity between the rotation axis and center of gravity of the system. Thus, it can be stated that the periodic vibration of 3.23 Hz in Figure 3a-c corresponds to the rotational frequency of 1X, which is due to the eccentricity between the rotation axis of driving shaft and center of gravity of assembled wheel bearing. However, 1X was not considered in further analysis because it does not affect bearing defects or structural problems. Moreover, in Figure 3c, periodic peaks at 0.044 s are observed in addition to the periodic peaks at 0.31 s.  
Figure 2: Experimental setup for measuring the noise and vibration of an assembled wheel bearing. Frequency spectra are obtained by applying a Fourier transform (FFT) to the time responses shown in Figure 3, and the results are illustrated in Figure 4. As shown in Figure 4a, the peak frequencies for the noise were predominantly observed at 896, 940, 1000, 1125, 1206, and 1306 Hz. This implies the noise of the assembled wheel bearing exhibits a high-frequency range of approximately 800-1300 Hz. In Figure 4b, the peak frequencies for the vibration of the dust shield are observed at several frequencies, including at 940 Hz, 1000 Hz, 1125 Hz, 1206 Hz, and 1306 Hz, which coincide with the peak noise frequencies. Conversely, in Figure 4c, the peak frequencies for the vibration of the outer ring were observed at low frequencies below 100 Hz. Specifically, it was significantly observed at 22.63 Hz. This peak frequency corresponds to periodic oscillation with an interval of 0.044 s in the time response shown in Figure 3c. Figure 3: Time responses for the noise and vibration of the assembled wheel bearing: (**a**) noise, (**b**) vibration of the dust shield, and (**c**) vibration of the outer ring. Next, the noise and vibration of the assembled wheel bearing were measured while increasing the rotational speed from 100 rpm to 400 rpm at intervals of 20 rpm. The measured results are plotted as a waterfall plot that expresses the frequency spectrum in three dimensions as shown in Figure 5. The previously analyzed frequency spectrum at 200 rpm is indicated in red in Figure 5. As shown in Figure 5a, the peak noise frequencies are always observed at 896, 940, 1000, 1125, 1206, and 1306 Hz regardless of the rotational speed. Furthermore, in Figure 5b, the peak vibration frequencies for the dust shield are same as those for all rotational speeds, and these peak frequencies coincide with the frequencies observed in Figure 4b. Among the frequencies, 940, 1000, 1125, 1206, and 1306 Hz always coincided with the peak noise frequencies regardless of the rotational speed. The peak vibration frequencies for the outer ring in Figure 5c are observed at low frequencies and are independent of the peak noise frequencies in Figure 5a. Therefore, it was observed that the noise for assembled wheel bearing is not affected by the rotational speed, and it is closely related to the vibration of dust shield. Figure 4: Frequency spectra for the noise and vibration of the assembled wheel bearing: (**a**) noise, (**b**) vibration of the dust shield, and (**c**) vibration of the outer ring.