**Appendix A**

(C1) The vibration generated by the generator is caused by an uneven magnetic force acting on the rotor or the stator. In the case of vibration caused by the impulse torque, the induction motor essentially generates a pulsed torque and causes vibration, and impulse torque is thus generated. It is the result of rotating the magnetic field to actuate the poles of the stator. Since each stator pole is actuated twice when the AC power source completes a cycle, the resulting vibration frequency is twice that of the AC power source. That is if the frequency of the AC power used is 60 Hz, the vibration frequency of the impulse torque is 120 Hz. This type of vibration due to pulsed torque is often not significant unless the motor needs to operate in a relatively low vibration environment or because the pulsed torque vibration frequency matches the tower's natural frequency or blade body frame. When an abnormal phenomenon occurs, however, it must be dealt with. The magnitude of the vibration caused by the impulse torque depends on the evenness of the rotor winding. The more uniform the rotor winding, the lower the vibration value of the impulse torque. Therefore, for more demanding applications, good uniformity of windings should be required during a motor's manufacturing. Moreover, when the rotor winding rod is loose, or the stator winding is open, it will generate 2×, 3×, or even a higher multiple of the vibration frequency at the pulse torque frequency, i.e., 120 Hz and 180 Hz will be generated in the frequency spectrum analysis.

(C2) Vibrations generated by the generator or vibrations caused by an abnormal rotor or rotor coils. The causes of faults within the generator related to the rotor coil can consist of issues such as a rotor winding bar break, a rotor winding open or short circuit, rotor deflection, rotor eccentricity, and so on. The vibrations caused by the causes mentioned above of the fault will all be unstable. In other words, if the amplitude is measured with a vibrating instrument, the pointer or digit on the instrument will oscillate continuously. It will be a single-frequency vibration due to the causes of malfunction; the amplitude will be modulated. This modulation phenomenon is based on the reasons mentioned above of failure, which causes the imbalance of the magnetic forces between the upper and lower magnetic poles and between the rotor coil and the permanent magnet. Suppose a two-pole induction rotor is winding breaks when the generator's stator winding is actuated by AC power to generate a magnetic field. In that case, the broken part of it will be precisely aligned with the magnetic pole in a specific direction. At this moment, the current will reach a maximum value. That is, the magnetic force of the magnetic pole will be at its maximum; the magnetic pole of the other pole of the stator will act on the rotor with the maximum magnetic force. However, due to the induced magnetic poles, the rotor corresponding to one pole will be intact. The rotor corresponding to the other bar will be fractured, so the two poles' magnetic force will not be equal, resulting in an unbalanced force being generated between the rotor and the stator. Meanwhile, the broken wire rod gradually moves away from the magnetic field, which no longer precisely aligns with the magnetic pole in either direction. Then, the magnetic force difference between the two pole-operated rotors will be reduced, and the vibration force will be reduced. As a result of this cyclic operation, the vibration amplitude generated by the rotor will form a periodic vibration, and the vibration frequency will be the rotational frequency of the magnetic field, not the rotational frequency of the rotor.

(C3) Vibrations generated by the generator or vibrations caused by an abnormal stator or stator coils. If the motor problem occurs in the winding of the stator of the generator, the frequency of the vibration generated by the generator will be the frequency of the magnetic field, but its amplitude will not be. In other words, there is a modulation phenomenon. However, abnormal vibrations appearing on a stator or stator coils often have pulsating amplitudes. This pulsation is not the result of amplitude modulation, but rather the result of a slap phenomenon caused by two very similar vibration waveforms. The stator-related faults are usually caused by stator windings or short circuits, gaps of different sizes, and phase imbalances. If the vibration problem associated with the stator produces a pulsation amplitude, it needs two vibration amplitudes near each other in their frequency spectrum. One of the vibrations of the two near-frequency frequencies may be the vibration of the rotation shaft frequency caused by an imbalance of the shaft or poor centring of the post, while the motor factor will cause the pulse of the other frequency. Since the frequency of the shaft factor is very close to the electrical equipment's frequency, the two's vibration amplitude will be alternately added or subtracted at the rate of the difference between the two frequencies. It causes the motor to produce a significant slap phenomenon. As a result, amplitude ripples are formed. Suppose you want to determine the pulsation amplitude. In that case, regulated by the amplitude of a single frequency or by the result of adding two very similar vibration frequencies, you can use the internal key amplification function of the frequency analyser. First, amplify the frequency coordinate axis. Then, analyse the frequency spectrum near the shaft rotation frequency. If the frequency-axis amplification analysis shows that there are two closely related vibration frequencies stacked together, the cause of the pulsation in the amplitude can be determined to be caused by a slap phenomenon. If the frequency is amplified, there is still only a single frequency. A significant up-and-down variation in the spectrum analyser's amplitude causes the pulsation amplitude, which is the result of the modulation.

(C4) Unbalanced weight of the shaft of the driveshaft. When the shaft quality is not uniform due to the centrifugal force after the rotation, the wind turbine drive mechanism generates vibration. This unbalanced phenomenon is caused by factors such as non-uniformity in the structure of the shaft during the manufacturing process or shape asymmetry during the processing. Because of the unbalanced vibrations, radial vibrations occur. Therefore, the amount of vibration in each direction is measured. The amplitude ratio in the horizontal, vertical, and axial directions is 5:4:1, and the amplitude is proportional to the unbalanced mass. The vibration frequency based on the imbalance is one time the rotating frequency of the rotating shaft. Therefore, for the frequency spectrum analysis, the primary vibration frequency and speed are the same for determining the unbalanced force's vibration. However, in addition to the imbalance, many vibration frequencies are the same as the vibration speed. Therefore, pure spectrum analysis often cannot determine the vibration of this one-time rotational speed, which is purely due to the imbalance phenomenon. If supplemented by phase analysis, however, the imbalance phenomenon is apparent. When the phase analysis is applied, the radial phase on the bearing seats at both ends of the shaft can be measured. The vibration value and phase can be measured at a position separated by 90◦, and the results of corresponding measurements of the two bearing blocks can be compared. If the stage measured by the 90◦ position is different by about 90◦ and the vibration amount calculated by the two bearing housings is a ratio, it can be determined that this vibration frequency is generated by the unbalanced force.

(C5) The shaft of the driveshaft is bent. Due to a lack of precision in its manufacturing or external force being applied during transportation and installation, the transmission shaft may cause the shaft to bend. This bending may occur at the midpoint of the distance between the two bearings or at one of the paths. This will cause the shaft to have higher vibration in the axial direction. If the beam's bending occurs at the centre of the distance between the two bearing seats, the axial vibrations derived from it will arise in both the free end and the bearing's load end. If the shaft's bending occurs at the load end of the post passing through the path, the load end's bearing will measure higher axial vibration than the free end. The spectrum analyser's pulse is generated by the beam bending phenomenon to find that the primary vibration frequency is double the rotation speed. Sometimes, it is accompanied by a slight dual rotation frequency. If we want to perform further analysis, we need to supplement the above analysis with a phase analysis to confirm its results. In general, when the shaft bending position is at the centre of the two bearings, the corresponding axial phases measured by both approaches are 180◦ out of step with each other, and the shaft is twisted so that it is measured at different positions on the bearing housing. The phases are different. When the shaft bending position is at the bearing or the bearing's outer end, the stage measured by the direction at the load end is different from the degrees measured in other paths, but the step is measured at the free end is the same at each position.

(C6) Improper installation of the shaft of the driveshaft. Poor installation of the shaft can be attributed to material-processing factors and installation techniques. When the rotary shaft is processed, the journal's roundness may be unsatisfactory due to a lack of precision, and ellipses or triangles may be generated, resulting in a subpar installation. The vibration caused by such a lack of roundness mainly occurs in the radial direction, horizontal or vertical. For an elliptical journal, measuring its phase angle will produce a phase difference of 180◦ between the horizontal and vertical directions. Still, below the vertical direction, the phase of the measured phase and the other directions will be 180◦ out of phase. If the frequency spectrum analyses the vibration frequency, it will be found that the main vibration frequency at the elliptical ellipse is twice the rotational frequency. The primary vibration frequency when the journal is triangular will be triple the rotational frequency. When the shaft is installed, if the shaft's centreline cannot be installed parallel to the centreline of the two bearing seats, it will result in poor centring. When the post has a poor centring, it will produce a higher vibration in the axial direction. When the axial vibration is more generous than 1/2 of the radial (horizontal or vertical) vibration, various problems may result. If a spectrum analysis is performed, it can be found that the vibration frequency of the shaft centre is poor. In addition to indicating 1.0 times the speed, there will be 2.0 times or 3.0 times the rotation frequency, and the phases of the two bearings' corresponding points will be 180◦ out of phase. For the bearing measurement horizontal and vertical phases, the phase angles will also have a difference of 180◦.

(C7) When the transmission shaft is misaligned with the coupling connecting the machine during installation, it will cause the machine to vibrate violently. Generally, there are two types of misalignment: misaligned misalignment and low centripetal misalignment. Decentralization and angling do not occur at the same time. When a machine has a poor centring, it will produce high axial vibration values, and the frequency spectrum shown in the analysis of the vibration frequency will, in addition to being double the speed, have twice or three times the speed frequency. If the form of the poor centring is poor, the phase angle of the corresponding point of the bearing on both sides of the coupling is measured at the phase angle, and the horizontal phase is 180◦ out of phase. If the bad machine core part's pattern is a purely eccentric type, the vertical phase of the corresponding point will also differ by 180◦. When the axial vibration is more than half the horizontal vibration, it is necessary to pay attention to whether the image's adverse effect is bad or the coupling is damaged. When the coupling is damaged, loosening occurs in the coupling portion due to the excessive clearance, and in the frequency spectrum analysis, there will be an abnormal vibration at a multiple of the rotational speed frequency that is the same as the number of coupling claws. If the cause of the diagnosis's vibration is caused by poor coring, the axis centring correction must be done appropriately. If the coupling is damaged, the coupling needs to be replaced.

(C8) When the bearing is installed, the shaft diameter may be too small, resulting in the bearing's relative movement and the inner ring of the bearing. The bearing seat's diameter may be too little, causing the path to slip during operation. When this phenomenon occurs, the horizontal and vertical directions will produce more severe vibrations. For spectrum analysis, harmonic vibration frequencies with an integer multiple speeds will be generated in the low-frequency range. This harmonic frequency is based on the mains frequency or the pulsed torque frequency. The resulting harmonic vibration of the magnetic field frequency is caused by the air gap.

(C9) When the bearing is installed, the shoulder's angle may not be good, resulting in the centre of the inner and outer rings no longer being on the same straight line. Rotating causes the motor-transmission mechanism to generate a large axial force due to this twisting. A significantly higher level of noise will accompany the amount of vibration during operation. When spectrum analysis is performed, it will show that the vibration amplitude of the spindle-rotation speed is increased. If a phase analysis is performed, the axial phase will be 90◦ apart every 90◦.

(C10) When the bearing is mounted, the ball bearing can cause temperature rise and vibration due to insufficient lubrication or improper lubrication viscosity. In the diagnostic analysis, if the fan temperature is found to be above 30 ◦C above the ambient temperature, it suggests that there is poor lubrication. Sleeve bearings, on the other hand, tend to wear with the shaft and cause loosening. This loosening phenomenon will cause the wind turbine to produce eccentricity and poor centring, and different vibration patterns. Frequency spectrum analysis of the vibration frequency will be accompanied by a harmonic frequency of twice or a high multiple of its radial and axis, in addition to a doubling of the number of revolutions. There will also be no relation to the phase. As for gasification bearings, abnormal vibration may occur due to the intrusion of foreign matter. Since a magnetic field's action forms the rotation of a gasification bearing, if foreign matter invades, the rotation speed of the wind turbine will be unstable, and it may even stop due to failure. In the spectrum analysis, it can be found that its central frequency will be intricate and cluttered, such that it is almost impossible to stabilise. Moreover, if the

average signal function is applied, noise cannot be eliminated. This phenomenon is caused by the intrusion of foreign material into the gasification bearing, which results in varying rotation speed.

(C11) Gearbox. The wind turbine drives the rotating shaft by rotating the blades through the winds provided by nature. The initial low speed accelerates the rotating shaft via the speed-change gearbox, and the output is driven by the high-speed rotating shaft to drive the generator. Gearboxes play an essential role in wind power transmission systems, usually using a third-order parallel shaft gear drive. They also have a transmission mechanism designed as a hybrid of a third-order planetary gear and a helical gear. A wind turbine generator gearbox is affected by wind power generation and is subjected to extreme loads. It is also deployed in harsh environments. Its frequent faults and breakdowns are time-consuming to repair, resulting in a heavy operational burden. In general, wind turbine gearbox failures, the causes of which are complex, will not damage a single part, but rather a chain effect of damage across multiple parts. For example, when the gearbox's oil fails, its bearings will be damaged by wear and tear, which will gradually affect the gear, causing it to crack, eventually leading to gearbox failure. The gearbox structure and components are large and complex, easily causing the deformation of the gearbox housing and the main driveshaft. When starting up, it is easy to cause wear on the gearbox bearings and cause the post's eccentricity to run in an unbalanced manner, causing excessive vibration and noise.

The vibration frequency caused by gearbox meshing during transmission is much higher than the vibration frequency generated by an unbalanced shaft and poor centring of the gear. When the gearbox fault causes vibration or noise, the analysis of its frequency occurs at the spindle speed and is based on the shaft's number of teeth. Besides, when the two corresponding motion gears mesh, the contact point collision is rigid and rapid, and it efficiently induces the gear vibration's harmonic frequency. Measuring the vibration signal of the gearbox requires two sets of probe sensors. One set of probes is mounted on the bearing to measure the gear transmission shaft's vibration signal and the bearing, and the other set of probes is fixed on the gear section near the gear mesh. The meshing frequency is the number of teeth multiplied by the number of revolutions. Usually, the gears' meshing frequency is not much larger than the frequency of one frequency, and a large amount of vibration often occurs at twice the frequency. When the gear is engaged, the clearance between the two teeth is too large, or the rotating shaft is too loose in the bearing, there will be a loosening phenomenon during the transmission. Under these circumstances, the vibration frequency will be 0.5 times the meshing frequency. Analysing the spectrum of the complicated gearbox and studying the damage and cracking of gears, inverse Fourier analysis can be used to invert the Fourier function of the frequency domain into the time domain to calculate the defect position. The weight of a wind turbine's gearbox can be as much as 15 tons. If the structure is deformed during installation, the base vibration will cause the gearbox to cause abnormal wear, gear eccentricity, and shaft bending. The cause of vibration due to gear deterioration is typically improper lubrication or insufficient lubrication or even the oil's infiltration of metal impurities, all of which will allow the gearbox is operating temperature to increase, causing tooth surface wear or the intrusion of foreign matter or dust particles in gear. Relatedly, the excessive, long-term intrusion of salt into the gearbox will cause pitting on the tooth surface and even cracking of the teeth.

(C12) Bearing damage. The bearings mounted on a wind turbine drive mechanism consist of ball bearings, sleeve bearings, and gasification bearings. These bearings are often inaccessible due to handling, installation, or miscellaneous infiltration. They operate at high temperatures or high loads for a long time and have insufficient lubrication or wear. The resulting flaws can cause other defects to appear on the inner and outer ring raceways or rolling elements and retainers in ball bearings. According to the relative speed calculation, when any kind of bearing assembly is damaged, there is a specific rate. This particular frequency is the frequency at which the ball rolls over the inner and outer rings. This relative rolling frequency often occurs when the bearing is subjected to a local load. Therefore, in a frequency spectrum analysis, the passing frequency of the low frequency is often filtered out, and the frequency band of the high frequency generated by the crucible is used. Then the absolute value and envelope processing are applied. In other words, when there is a ball-rolling frequency through the frequency spectrum, it means that the bearing has a high-frequency vibration due to impact, and the specific frequency generated when the ball bearing components are damaged.
