## 4 Novel Proposed Method Application for Naturally-Developed Fault Diagnosis
Figure 10: Low speed (LS) left bearing faults: (**a**) inner race fault; (**b**) ball fault. Figure 9: HS right bearing faults: (**a**) inner race fault; (**b**) ball fault. meshing frequency (GMF) can be calculated by the following formula: GMF = \(N\times Z\), where \(N\) means the rotating speed of the test gear and \(Z\) represents the number of the test teeth. According to this, the GMF of the HS and IS shaft gears is determined as 700 Hz, and the GMF of the IS and LS shaft gears is determined as 196.93 Hz. First, in order to ensure stable signal, the data acquisition system is adjusted to use the data sample rate based on the tachometer signal. The adjusted sampling rate is a synchronous sampling rate and donates the resampled vibration signal. During the experiment, the load of 199 Nm was applied to the output shaft (LS shaft), and the resampled signal is used. An accelerometer was mounted on the top of the gearbox casing (as shown in Figure 7), and the vibration signals were collected from the accelerometer at position S2. Figure 12a illustrates the correlation coefficient variation vs. the iteration number of DC offset cancellation, while Figure 12b illustrates the CK value variation vs. the iteration number of DC offset cancellation. Figure 12c illustrates the squared envelope signal after the 100 th iteration. It can be seen that both the correlation coefficient and CK cannot be used to determine the optimal iteration number for DC offset cancellation in the multi-fault mode case. Especially for the weak PIS, CK will not work. However, as mentioned in Section 2.1, one DC offset cancellation operation can subtract one harmonic deterministic component. In this case, HS shaft gear mesh frequency and its harmonics dominate the frequency spectrum, as shown in Figure 13. It can be seen that there are mainly five harmonics of the gear mesh frequency. Therefore, theoretically, only five-times DC offset cancellation can suppress the deterministic component of the original signal. Therefore, we conduct five iteration DC offset cancellation for the time synchronous signal. The squared envelope spectrum and its time-frequency contour are illustrated in Figure 14. After checking the squared envelope spectrum carefully, it is very hard to find the bearing fault frequencies. Instead of the bearing fault frequencies, the squared envelope spectrum is dominated by the HS and IS shaft rate and its harmonics because of the gear chip fault and wear fault. However, in the time-frequency contour of the squared envelope signal, weak BPFO, BPFI and BSF information can be seen. On the contrary, no bearing fault information from the envelope spectrum and time-frequency contour of the original signal shown in Figure 15 can be seen. Similarly, the envelope spectrum of the original signal is also dominated by the HS and IS shaft rate and its harmonics. Figure 11: (**a**) HS shaft gear tooth wear; (**b**) intermediate speed (IS) shaft gears, tooth chip and wear. Figure 12: (**a**) Correlation coefficient vs. iteration number; (**b**) CK value vs. iteration number; (**c**) Squared envelope signal after the 100 th DC offset cancellation. Figure 13: Frequency spectrum of the time synchronous signal; GMF, gear meshing frequency. Second, in order to ensure a stable signal, the data acquisition system is adjusted to use the data sample rate based on the tachometer signal. The adjusted sampling rate is a synchronous sampling rate and donates the resampled vibration signal. During the experiment, the load of 405 Nm was applied to the output shaft (LS shaft), and resampled signal is used. An accelerometer was mounted on the top of the gearbox casing (as shown in Figure 7), and the vibration signals were collected from the accelerometer at position S2. Figure 16 illustrates the frequency spectrum of the time synchronous signal with the dominant six harmonics of the HS-IS GMF. Therefore, for the DC offset cancellation operation, we can repeat six times to delete the deterministic component.