# Bearing Fault Diagnosis Based on Vibration Envelope Spectral Characteristics
## 2 Diagnosis Mechanism and Frequency Characteristics of Bearing Faults  
Rolling bearings generally consist of inner rings, outer rings, balls, and retainers. During the operation of mechanical equipment, assembly errors, component failures of inner and outer ring balls, and localized deterioration can all lead to vibrations in the bearings.  
The failure modes of rolling bearings can be classified into two categories: surface damage and local wear. The latter is a progressive failure, which is far less harmful than surface damage. Therefore, the focus of bearing failure diagnosis is on surface damage. The types of surface damage failure of rolling bearings mainly include outer race fault (ORF), inner race fault (IRF), and ball fault (BF).  
Excluding the influence of structural and environmental factors, there are two main reasons for generating vibration in rolling bearings. The first is due to the high-frequency inherent vibration frequency caused by the elastic factor of the bearing itself [20]. The second is due to faults or damage inherent in the bearing components, manifested as impact vibration, with the frequency referred to as the bearing's intrinsic frequency [21]. It should be noted that the first form of vibration will inevitably occur during the bearing operation. In contrast, the second form of vibration only appears after a fault occurs, with each fault exhibiting different vibration characteristics.  
The actual vibration is a nonlinear superposition of vibrations from the bearing and surrounding components, making the vibration characteristics much more complex than the analysis above. Electromagnetic interference from sensors and measurement circuits in the signal acquisition system can also affect the measured vibration signal, resulting from the complex interaction of multiple factors. Figure 1a-d shows vibration signals of different operating states for a fault diameter of 0.007 inches under 0 hp at a speed of 1797 rpm in the CWRU Dataset.  
From Figure 1a-d, it can be seen that the vibration signal of the rolling bearing exhibits periodic variations and significant non-stationary characteristics. In the normal state, the bearing mainly shows a combination of inherent and mechanical system vibration, with small signal amplitudes and a characteristic of periodic decay. When a fault occurs in the bearing, the rolling elements generate impact excitation as they pass through the defective area, resulting in distinct impact modulation characteristics in the vibration signal, with the interval between impacts being related to the type of fault. Furthermore, the peak values of vibration signals for different fault types vary due to differences in the energy of impact excitation and the paths through which the energy reaches the sensor. As a result, the vibration characteristics produced at the sensor location are also different.  
Figure 1a-d illustrates vibration signals from different conditions. It can be observed that the pulse nature of the ball fault signal in Figure 1b is lower compared to other faults and resembles the signal of the healthy state depicted in Figure 1a. Although the amplitudes of the inner race fault signal in Figure 1c and the outer race fault signal in Figure 1d are higher than that of the healthy state, these two signals are similar. This complicates direct fault diagnosis through vibration signal analysis.