# Gear Wear Process Monitoring Using a Sideband Estimator Based on Modulation Signal Bispectrum
## 4 Results and Discussion
### Gear Wear Monitoring  
It can be seen from Figure 4a that the overall trend of the MSB-SE peak at \(f_{r1}\) increases with the operating time, whereas those at \(f_{r2}\) and \(f_{r3}\) remained almost unchanged. This shows that the driving gear of the first stage has experienced more significant wear process than other gears. Meanwhile, the overall trend of MSB-SE coherence peaks at these shaft rotation frequencies stayed almost constant, showing that the values of their corresponding MSB-SE peaks are reliable. The trends of indicator \(R\) are presented in Figure 4. \(f_{r1},f_{r2}\) and \(f_{r3}\) represent the \(R\) value of gear shaft frequency at corresponding meshing frequency, respectively. The vibration signal measured at the beginning of the test is used as the baseline. It can be clearly seen that there are obvious differences in trend of \(R\) between \(f_{r1},f_{r2}\) and \(f_{r3}\). In Figure 4, \(f_{r1}\) shows an increasing trend in the whole lifetime, whereas \(f_{r2}\) and \(f_{r3}\) stay with a mostly unchanged trend. This shows that the driving gear of the first stage has experienced a more severe wear process than other gears. In particular, in Figure 4a, the \(R\) of \(f_{r1}\) first decreases then increases with wear, reaching its lower level at the 27 th h, beyond which \(f_{r1}\) will increase generally with amplitude. It can be observed that \(f_{r1}\) remains at a lower level between the 27 th and 100 th h, showing that gear wear process is slower and the gear transmission is relatively smoother, which can be viewed as mild wear period because it is usually characterized by slow but steady material removal. From the 100 th to 200 th h, the \(f_{r1}\) increases slowly, showing that the gear wear is growing during this period. During the testing time between 200 th and 570 th h, \(f_{r1}\) reaches higher levels and exhibits higher fluctuation, clearly showing that the gear experiences faster wear. From the 570 th h up to the test termination (the 574 th h), the \(f_{r1}\) increases sharply, showing that severe gear wear is occurring. These changes show that the indicator \(f_{r1}\) can accurately and indicate the wear procedure in a timely fashion. A similar trend can be observed for \(f_{r1}\) in Figure 4b. Between the 200 th and 570 th h, the general trend of \(f_{r1}\) exhibits a more clearly monotonic increase than that in Figure 4a. The explanation for this difference is that the driving gear of the first stage would transmit the strong nonlinear signal directly caused by severely worn surface, while the effects of this severe wear would go through torsional vibration, which is relatively linear [33] and increases with the wear deterioration process, to the second stage. As mentioned before, the effects of wear accumulate over a relatively long period; the tooth surface state will become farther away from the ideal surface with wear, and the sideband will deviate further from its initial value. Although \(R\) will show fluctuations when inspecting its variations over a short period of time, the general trend of parameter \(R\) is still increasing, indicating an increase of wear severity. Therefore, it would be clearer to show the gear wear process and assess wear severity using the indicator \(R\) over a relatively long period of time. Although \(f_{r1}\) exhibits a clear change trend with significant amplitude changes throughout the test period, both \(f_{r2}\) and \(f_{r3}\) exhibit high fluctuations in the first 100 h, and then fluctuate around a constant level in the following period. This means that these gears experience a long period of slow, steady wear throughout the operation course, reflecting the slow deterioration of gear surface condition. Meanwhile, \(f_{r2}\) is a little bit larger than \(f_{r3}\) after 400 h, showing that the gear of the second shaft is worn more than the gear of the third shaft. These results also confirm that the proposed indicator is reliable and sensitive in detecting and evaluating different wear severity occurring at the identified gear.