## 5 Experimental Research of the Planet Tooth Breakage  
In order to check the validity of the simulation results in the previous section and investigate the fault characteristics, experiments for planetary gears with planet gear tooth breakage fault are performed. Figure 10 shows the structure of the test rig. The test rig mainly consists of a wind rotor, a planetary gearbox, an electrical motor, a variable-frequency drive, shafts and bearings. The electrical motor provides the driving power, and the rotor provides load. The planetary gearbox is single stage and has three planetary gears. The overall structure of the gearbox used in experiments and the gearbox used in simulations are the same as shown in Figure 1, but their detailed parameters are different. For the experimental gearbox, the tooth number of the sun gear \(z_{s}=26\), the tooth number of the planet gear \(z_{p}=20\), the tooth number of the ring gear \(z_{r}=67\) and the transmission ratio is about 3.577. There are seven sensors installed shown in Figure 10a, while only the gearbox vertical acceleration signal is analyzed in this paper. Figure 8: Spectrum of the simulated ring acceleration of the (**a**) healthy gear \(p=0\), (**b**) half tooth breakage fault gear \(p=0.2\) and (**c**) the whole tooth breakage fault \(p=1\). Figure 9: Envelope spectrum of the simulated ring acceleration of the (**a**) healthy gear \(p=0\), (**b**) half tooth breakage fault gear \(p=0.2\) and (**c**) the whole tooth breakage fault \(p=1\). Three sets of experiments with a health planetary gear and two fault gears are carried out. As shown in Figure 11, the two fault gears are a half tooth breakage fault gear and a whole tooth breakage fault gear, in which the broken tooth is located at the planet gear at right side. Same as the simulation, each experiment is carried out at seven different rotational speed conditions listed in Table 4, in which the symbols have the same meaning as the symbols in Table 3. Five groups of data are collected under each condition. The sampling rate is 25 kHz, and the time length of each sample is four seconds. Figure 12 shows the average RMS of the ring vertical acceleration varying with rotational speed in three experiments. An obviously rising trend can be found for all of the RMSs. Moreover, under the same rotational speed condition, the RMSs of both fault gears are greater than the RMS of the healthy gear. The simulation results in Figure 6b agree well with these experimental results. Take the gearbox vertical acceleration signals at the rotational speed of 237 rpm for further analysis. According to Table 4, the rotational frequency of the carrier is about 4 Hz; the fault characteristic frequency of the gearbox is about 13.2 Hz; the rotational frequency of sun gear is about 14.1 Hz; and the mesh frequency is about 265 Hz. Figure 13 shows the waveform of the three signals corresponding to the simulation results in Figure 7. From Figure 13a, one can find that periodic impulse components exist in the vibration of the healthy gear; they were caused by the gear meshing and slight shaft misalignment in the test rig. From Figure 13b, it can be found that the vibration waveform of the half tooth breakage fault gear is similar to that of the healthy gear, and the peak-to-peak value has a very small increase. For the whole tooth breakage fault gear in Figure 13c, strong impacts can be observed, and the peak-to-peak value increases significantly. These phenomena validate the simulation results in Figure 7c. Figure 9 shows the spectrum of these three signals. From the spectrum of the healthy gear in Figure 14a, an outstanding component at about 528 Hz can be found, which equals \(2f_{m}\). This phenomenon is very similar to the harmonic resonance at 2632 Hz in Figure 8a; thus, one can infer that the test rig has an natural frequency of around 528 Hz. For the half tooth breakage fault gear in Figure 14b, the sidebands around 3657.8 Hz become obvious. For the whole tooth breakage fault, the sidebands around 2100 Hz become more obvious and dominant.