## 2 Fault Detection Method  
### Signals Collection  
The experimental platform for crack fault detection of asymmetric shafting is designed and built based on a ZT-3 platform. The schematic diagram of the experimental platform is shown in Figure 1, and the physical diagram is shown in Figure 2. The platform is composed of an asymmetric shaft body, a drive system and a measurement system. The asymmetric shaft body consists of three rotors. Taking the DC motor end as left, from left to right, respectively, there is a double disk rotor, a single disk rotor and a generator rotor. Bearings 1, 2 and 3 are rolling bearings, and bearing 4 is a sliding bearing. The length of the three rotors is 320 mm. The diameters of the double-disk rotor shaft, the single-disk rotor shaft and the generator rotor shaft are 9.5 mm. The diameter and thickness of the double disk rotor disc are 76 mm and 19 mm, respectively, and the diameter and thickness of the single disk rotor disc are 76 mm and 25 mm, respectively. The drive system consists of a speed governor and a DC motor. The DC motor drives an asymmetric shaft system through a coupling. The measuring system consists of a DC regulated power supply, an eddy current displacement sensor and a data acquisition instrument, as shown in Figure 3. The DC regulated power supply provides voltage  
Figure 1: Schematic diagram of the experimental platform for crack fault detection in asymmetric shafts. Figure 2: Experimental platform for crack fault detection in asymmetric shafts. to the eddy current displacement sensor. When the distance between the rotor and the sensor changes, the dynamic voltage signal generated by the sensor is transmitted to the data collector. The platform contains three eddy current displacement sensors, which are, respectively, used to pick up the vibration displacement signals of the double-disk rotor, the single-disk rotor and the generator rotor near the bearing. The rotors is shown in Figure 4a-c. In order to avoid interference between eddy current displacement sensors, sensors are arranged only in the horizontal direction. Subsequent research shows that the use of only a horizontal displacement signal can also ensure high fault detection accuracy. The data collector uses a DASH8 HF-HS system; the sampling rate is set to 20 kHz. Figure 4: Diagram of asymmetric shaft system; (**a**) dual-disk rotor; (**b**) single disk rotor; (**c**) generator rotor. Figure 3: Measuring system. In order to simulate the crack fault, a crack with a depth of 2.4 mm was machined on the shafts of the double-disk rotor and the single-disk rotor by wire cutting. The ratio of the crack depth to the shaft diameter was about 0.25. The diagrams of a healthy rotor and a cracked rotor are shown in Figure 5. This paper studies cracks in four different locations. The cracks are machined at a location away from the center of the shaft in order to simulate two different locations of the crack by turning the crack shaft upside down left and right during the experiment. According to the above description, the distances between the cracks at four different locations and the left end of the asymmetric shaft system are 100 mm (Case 1), 220 mm (Case 2), 420 mm (Case 3) and 540 mm (Case 4), respectively. The cracks in Case 1 and Case 2 are located on the double disk rotor, while the cracks in Case 3 and Case 4 are located on the single disk rotor. Case 1 and case 2 and Case 3 and Case 4 are centrosymmetric about the double disk rotor and the single disk rotor, respectively. The shaft without cracks is called a healthy rotor, denoted as Case 0. This section collects the vibration signals at three channels when the rotating speed is 2000 rpm, that is, the vibration signals of the double disk rotor, the single disk rotor and the generator rotor along the horizontal direction. There are five working conditions for no crack (Case 0), the double disk rotor left crack (Case 1), the double disk rotor right crack (Case 2), the single disk rotor left crack (Case 3) and the single disk rotor right crack (Case 4).