## 6 Analysis of Bearing Fault Signal of Case Western Reserve University  
The bearing fault signals of Case Western Reserve University in the United States are analyzed by this article method. In an experimental device the 1.5 kW 3-phase induction motor is connected to a power meter and a torque sensor through a self-calibrating coupling, and is operated by a driving fan.  
The vibration signal is collected by the acceleration sensor and installed on the bearing seat with a magnetic seat. The sampling frequency is 12,000 Hz, and the number of sampling points is 8192. The rolling bearing is SKF6205-2 RS JEM deep groove ball bearing. Single point fault is found on the surface of inner ring and outer ring respectively by electro discharge machining, which is then run at constant speed for motor loads of 1 horsepower. The size of faults is 0.18 mm in diameter and 0.28 mm in depth. The rotation frequency fr of the shaft is 1772 rpm (29.53 Hz). According to the literature [33], the inner ring fault frequency is 5.415 fr (159.9 Hz), and the outer ring fault frequency is 3.585 fr (105.9 Hz).  
The fault signal of the bearing inner ring and its power spectrum are shown in Figure 19a,b. The AR model is established based on the vibration signal of inner ring, and the model order is 6, as shown in Figure 19c. The model parameters have convergence, respectively 0.9335, \(-\)1.5689, 1.4184, \(-\)1.2555, 0.6631, \(-\)0.4627, as shown in Figure 19d. The signal after the Kalman filter is shown in Figure 19e. The autocorrelation function has tailing, as shown in Figure 19f. The SNR after filtering is 9.1874. An improved autocorrelation envelope power spectrum, 159.7 Hz and 319.3 Hz correspond to the inner ring fault frequency and its multiple frequency, and 29.3 Hz corresponds to the shaft frequency, as shown in Figure 19g. The maximum amplitude extracted by autocorrelation envelope maximum entropy spectrum corresponds to the fault frequency of bearing inner ring, as shown in Figure 19h.  
Figure 19: _Cont._The fault signal of the bearing outer ring is obvious, and the time domain signal and its power spectrum are shown in Figure 20a,b. AR model order is 5, as shown in Figure 20c. Model parameters are \(-0.1491\), \(-1.1965\), \(0.1153\), \(-0.3152\), \(0.1179\), as shown in Figure 20d. The signal after the Kalman filter is shown in Figure 20e. The autocorrelation function has tailing, as shown in Figure 20f. The SNR after filtering is \(16.3518\). Improved autocorrelation envelope power spectrum, \(106.9\) Hz, \(212.4\) Hz, \(319.3\) Hz, \(424.8\) Hz correspond to the outer ring fault frequency and its multiple frequency, and \(29.3\) Hz corresponds to the shaft frequency, as shown in Figure 20g. The maximum amplitude extracted by autocorrelation envelope maximum entropy spectrum corresponds to the fault frequency of the bearing outer ring, as shown in Figure 20h.  
Figure 19: Inner ring fault analysis results: (**a**) bearing inner ring fault signal; (**b**) power spectrum analysis; (**c**) model order; (**d**) model parameters; (**e**) signal after Kalman filter; (**f**) autocorrelation function curve; (**g**) improved autocorrelation envelope power spectrum analysis; and (**h**) autocorrelation envelope maximum entropy spectrum analysis.  
Figure 20: _Cont._