# Continuous Wavelet Transform and CNN for Fault Detection in a Helical Gearbox
## 3 Test Rig, Gearbox States, and Data Processing
### Test Rig, Gearbox States, and Data Acquisition
The first reducer stage is represented by the 19-tooth pinion P1, which meshes with the associated wheel G1 with 51 teeth. The localized pitting defect belongs to the active flank of one tooth of the pinion P1. In Figure 4b, the defect can be observed approximately 6 mm away from the right side of the pinion P1. The defect is inscribed in a circle of 1 mm, the maximum depth is about 0.2 mm, and the shape of the defect is approximately triangular. When a pair of helical gear teeth begin to engage, the contact gradually starts at one end of the teeth and maintains contact as the gear rotates into full involvement. The loss of material from the engaging teeth flanks due to sliding and rolling motions is called wear on flanks. The wear defect belonging to pinion P1 is 3 mm long along the helical tooth, with a maximum width of 0.9 mm (Figure 4c). This defect involves a transverse change of the profile slope (chamfer) at the addendum of the unhealthy tooth. The resulting effect is a slight shortening of the contact line when the area of the defective pinion tooth is engaged with the wheel G1. Extra information and details about these defects, namely localized pitting and localized wear on helical gears, can be found in [PERSON] et al. [10]. By using the friction brake, the same three distinct load levels--the unloaded condition (L0) and two distinct friction levels (L1, L2)--are imposed for each of the three motor speeds. Each of the four health states that are observed is subjected to these nine combinations. Three rotation speeds (v1, v2, and v3) were chosen for each load level (L0, L1, and L2), yielding nine files (acquisition records) per health state, so a total of 36 files for all four health states. The sampling frequency during signal acquisition is F\({}_{\text{s}}\) = 10 kHz and the duration of one acquisition record is 240 s. The acquisition records with load L2 and speeds v2 and v3 for the defects D2, D3, and D4 have a shorter duration, namely 120 s. In an analyzing record (observation), we propose a number of rotations of the pinion P1, namely 18 rotations, which means about 1.8 rotations at the reducer output shaft, regardless of the motor velocity. Considering the constant acquisition sampling frequency (F\({}_{\text{s}}\)), for a lower input shaft rotation speed (longer time per revolution), a larger number of samples are acquired for a pinion (P1) complete rotation. Thus, the following values were obtained: 444.26 samples/rotation for v1 rotation speed [rps], 436.18 samples/rotation for v2 rotation speed [rps], and 428.39 samples/rotation for v3 rotation speed [rps]. The number of samples in an acquisition record is divided by the number of samples in 18 rotations of pinion P1, resulting in a collection of analyzing records. Each analyzing record (observation) contains three lines, one for each accelerometer axis (\(X\), \(Y\), and \(Z\)), and is saved in a comma-separated values (csv) file. A total of 36 folders (with csv files) associated with four states \(\times\) three loads \(\times\) three velocities were created. The files pertaining to the same state were collected together. The dataset used further in data processing with CWT contains a total of 9913 observations, 2593 for the state D1 and 2440 for each of the other three states.