## 4 Applications to Gear and Bearing Fault Classification
### Application to Drivetrain Diagnostics Simulator  
Through simulation researches, the proposed fault classification method based on the smooth local subspace projection and PE can be applied to the Gear signals. Owing to unqualified manufacture or improper manipulation, different kinds of gear faults would occur during the operation process. In the studies of this paper, the collected different fault signals of the Drivetrain Diagnostics Simulator are adopted to verify the effectiveness of the proposed method. The experimental apparatus has a single stage of gear transmission; the small gear is installed on the input shaft which tooth \(z_{1}=20\), the big gear is installed on the output shaft which tooth \(z_{1}=37\). The module of gears is 3. The load is generated by the magnetic powder brake, and the acceleration sensor is installed on the bearing pedestal of the input shaft in a vertical direction. Under different working conditions, several group signals, such as normal gear, broken tooth, wearing and circular pitch error gear vibration signals, were collected. There is a significant crack in the root of the broken tooth, the depth account tooth thickness of 2/5, and there is a distinct wear on the gear surface of the wearing tooth. The specific parameters of test conditions are as follows: The speed of high speed shaft is 363 r/min, and the load is 0 when the apparatus is idle, the sampling frequency and time are  
Figure 28: The permutation entropies of the proposed approach. Figure 27: The permutation entropies of original signals. 2000 Hz and 3s respectively, so each set of data has 6000 sampling points. The experimental apparatus and its schematic diagram are shown in Figure 29. The apparatus contains a variable speed drive, a single stage gear transmission, and a magnetic powder brake. Since this apparatus is small, and has a high rigidity, the collected signals such as normal gear, broken tooth, wearing and circular pitch error signals, are all affected by vibration of the apparatus foundation bolts. The time domain plots of one set of gear signals are shown in Figures 30-33. The spectral analysis of these groups of signals cannot show clear differences between different kinds of faults. The smooth local projection method is applied to denoise 19 groups of signals for 10 times iteration denoising, and PE values of original vibration signals and denoised vibration signals are calculated, so as to conduct fault classification. The PE values of the original vibration signals and denoised vibration signals are shown in Figures 34 and 35, respectively. Figure 34: The permutation entropies of original signals. Figure 32: The time domain plot of wearing gear. Figure 33: The time domain plot of circular pitch error gear. Through the PE values of original signals and denoised signals above, it can show that before the smooth local subspace projection denoising, the PE values of one working condition are not distinguished from another working condition. All the PE values are aliasing, as shown in Figure 34. However, after the gear vibration signals are denoised by the local projection method, the entropies of gear signals of four kinds of working conditions are distinguished very clearly. As shown in Figure 35, the permutation entropies of vibration signals of broken gears are the smallest, ranging from 3.47 to 3.60, and their mean value is 3.54; the permutation entropies of the vibration signals of wearing gear range from 3.71 to 3.84, and their mean value is 3.75; the permutation entropies of vibration signals of normal gear range from 3.78 to 3.90, and their mean value is 3.85; the permutation entropies of circular pitch error gears are the biggest, and range from 3.90 to 4.08, and their mean value is 3.99. The PE values of different fault types have different mean value and range, which can be applied to classify different kinds of mechanical fault signals.