# Noise Identification for an Automotive Wheel Bearing
## 4 Excitation Source for Noise  
In this section, the excitation source that induces noise and vibration of the assembled wheel bearing is analyzed. In an assembled wheel bearing, the knuckle and dust shield are stationary, whereas only the wheel bearing rotates with the driving shaft. It can be inferred that an excitation force is generated inside the wheel bearing, and this force is transmitted to the knuckle and dust shield. Therefore, the vibration of the wheel bearing in the outer ring obtained in the previous section was analyzed in more detail.  
Figure 9 is an enlarged figure, showing frequencies below 100 Hz, to clearly denote the low-frequency components of Figure 5. As shown in Figure 9, the rotational frequencies of 1\(X\), 2\(X\), 3\(X\), 4\(X\), 5\(X\), 6\(X\), and 6.79\(X\) are observed, where \(X\) denotes the rotating frequency. If the rotation speed is 300 rpm, the rotating frequency \(X\) becomes 5 Hz. Specifically, frequency of 22.63 Hz, which is largely observed in Figure 4, corresponds to 6.79\(X\). In general, the magnitude of the rotational frequency tends to increase gradually because the centrifugal force increases as the rotational speed increases. However, the frequency corresponding to 6.79\(X\) in Figure 9 has a large magnitude even at a low rotational speed regardless of the rotational speed. This implies that another force, which causes 6.79\(X\), along with the centrifugal force exists. Given that no additional external force was applied  
Figure 8: Mode shapes of the dust shield corresponding to natural frequencies of (**a**) 888 Hz, (**b**) 940 Hz, (**c**) 998 Hz, (**d**) 1120 Hz, (**e**) 1200 Hz, and (**f**) 1300 Hz.  
to the wheel bearing, it can be considered that the previously mentioned force was due to defects inside the wheel bearing.  
To verify the cause for 6.79\(X\), the characteristic frequencies (often called the defect frequencies) of the bearing were investigated. The characteristic frequencies include fundamental train frequency (\(f_{\text{FTF}}\)), ball pass frequency outer ring (\(f_{\text{BPFO}}\)), ball pass frequency inner ring (\(f_{\text{BPFI}}\)), and ball spin frequency (\(f_{\text{BSF}}\)), which are obtained by the following equations [22,23]:  
\[f_{\text{FTF}} =(1/2)[1-(B_{d}/P_{d})\cos\theta]X \tag{1}\] \[f_{\text{BPFO}} =(N/2)[1-(B_{d}/P_{d})\cos\theta]X\] (2) \[f_{\text{BPFI}} =(N/2)[1+(B_{d}/P_{d})\cos\theta]X\] (3) \[f_{\text{BSF}} =(P_{d}/2B_{d})\Big{\{}1-[(B_{d}/P_{d})\cos\theta]^{2}\Big{\}}X \tag{4}\]  
where, as mentioned before, \(X\) is the rotating frequency, \(N\) is the number of balls, \(B_{d}\) is the ball diameter, \(P_{d}\) is the pitch diameter, and \(\theta\) is the contact angle. The characteristic frequencies are obtained by substituting the design specifications in Table 1 into Equations (1)-(4), and the results are listed in Table 3. As shown in Table 3, \(f_{\text{FTF}}\), \(f_{\text{BPFO}}\), \(f_{\text{BPFI}}\), and \(f_{\text{BSF}}\) of the inboard row are 0.42X, 6.29\(X\), 8.71\(X\), and 2.47\(X\), respectively, whereas \(f_{\text{FTF}}\), \(f_{\text{BPFO}}\), \(f_{\text{BPFI}}\), and \(f_{\text{BSF}}\) of the outboard row are 0.42\(X\), 6.79\(X\), 9.21\(X\), and 2.65\(X\), respectively. Consequently, the value observed for 6.79\(X\) in Figure 9 is consistent with \(f_{\text{BPFO}}\) of the outboard row. This implies that a defect on the outer ring of the outboard row was detected in the vibration of the wheel bearing. Thus, the excitation force that induces the noise and vibration of the assembled wheel bearing is generated by the outer-ring defect of the wheel-bearing outboard row.