# Fault Diagnosis of Rolling Bearings Based on Acoustic Signals in Strong Noise Environments
## 4 Simulation Verification Analysis
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Geometric Dimensions** & **Size** & **Unit** \\ \hline Outer raceway diameter, _do_ & 52 & mm \\ Inner raceway diameter, \(d_{i}\) & 25 & mm \\ Rolling element diameter, \(d\) & 7.938 & mm \\ Number of rolling elements, \(z\) & 13 & pieces \\ Pitch circle diameter, \(D\) & 38.5 & mm \\ Contact angle, \(\theta\) & 40\({}^{\circ}\) & (\({}^{\circ}\)) \\ Spindle rotation frequency, \(f_{5}/\mathrm{Hz}\) & 200 & Hz \\ \hline Fault characteristic frequency & Value & Unit \\ Inner raceway fault characteristic frequency, \(f_{i}\) & 1505 & Hz \\ Outer raceway fault characteristic frequency, \(f_{o}\) & 1094 & Hz \\ Rolling element failure characteristic frequency, \(f_{b}\) & 945 & Hz \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The geometry and the fault characteristic frequencies of bearing 7205. Figure 21: Bearing 7205. In this experiment, the relationship between the placement of the sensor and the bearing under test significantly impacts the fault detection results. As illustrated in the structural diagram of the test bench in Figure 25, the test bearings are symmetrically distributed on either side of the support bearings. The dimensions of the tested bearings are as follows: the outer raceway diameter (_do_) is equal to 52 mm, the inner raceway diameter (_d_) is equal to 25 mm, the rolling element diameter (_d_) is equal to 7.938 mm, the number of rolling elements (_z_) is equal to 13, the pitch circle diameter (_D_) is equal to 38.5 mm, and the contact angle (_th_) is equal to 40\({}^{\circ}\). In this paper, a disc spring is used for loading, with an axial load of 5 KN and a radial load of 2 KN. The drive mechanism is belt-driven. Bearings located near the belt side experience relatively large radial loads, and the fault characteristic signals are more pronounced in these locations. Consequently, the sound sensor is positioned at the bearing near the belt end to collect radial data, thereby enhancing the accuracy of fault characteristic signal capture. However, the experimental environment is characterized by considerable noise interference, which can lead to rapid attenuation of the sound signal during propagation. If the sound sensor is positioned too far from the test bench, the signal strength may be significantly diminished, and crucial fault information from the bearing may be obscured by noise, thereby compromising the accuracy of fault diagnosis. Conversely, if the sensor is placed too close, the vibrations and shaking of the bench during operation could potentially damage the front end of the contacting sound sensor, adversely affecting both the performance of the sensor and the stability of signal collection. Figure 23: Sound sensor location. Figure 22: Rig of bearing 7205. To effectively address these challenges, extensive trials and experiments led to the conclusion that the sound sensor should be positioned as close as possible to the radial end of the bench's belt (as shown in Figure 26). This placement minimizes the signal propagation path and reduces noise interference. Additionally, 3D printing technology was employed to create a specialized shell (as shown in Figure 27) to secure the sound sensor, ensuring its stability throughout the experiment and preventing displacement or damage caused by bench vibrations. The shell shown in Figure 27 is made of polyamide (nylon). The principal dimensions of the shell are as follows: the total height is 36 mm, the inlet diameter is 16 mm, and the outlet diameter is 52 mm. Additionally, the cylindrical portion of the shell has a length of 20 mm and a wall thickness of 2 mm. The interior of the shell is filled with efficient noise-absorbing material for sealing, while the exterior is further reinforced with clay, providing dual protection. This design effectively diminishes external noise interference with sound signals, thereby ensuring the integrity and stability of sound signal transmission.