Analysis on Mechanism and Characteristic of Vibration Fault on New Large Capacity Synchronous Condenser

Vibration faults are the most common faults in large capacity synchronous condenser. The article proposes 11 common vibration faults of condenser, including imbalance, misalignment, looseness, resonance, oil film oscillation, steam flow excitation, dynamic static friction, rotational stall, gear fault, rolling bearing fault, and other vibration faults. The article also proposes the mechanism, characteristics and case analysis of each type of fault separately. The research results on the mechanisms and characteristics of these faults are the foundation of condenser fault diagnosis, and are crucial for the development of intelligent decision-making systems and platforms. Which can provide the strongest technical support for improving power transmission and safety and stability of the power grid.


Introduction
Vibration is one of the main causes of faults in large capacity synchronous condensers [1][2] (hereinafter referred to as condenser).According to the fault mechanism, vibration is divided into forced vibration and self-excited vibration.Under stable forced vibration conditions, the amplitude and phase of vibration in the fundamental frequency do not change while the operating time and operating conditions change.The stable forced vibration faults mainly caused by mass imbalance.The causes of unstable forced vibration faults include dynamic and static rubbing.While the self-excited vibration is mainly caused by energy feedback links within the system, such as oil film vortex.The frequency of forced vibration is related to the working frequency of the rotor, while the self-excited vibration frequency is related to the critical speed and the natural frequency of the component.
The vibration relationship equation as follow: In the formula: A is the amplitude, P is the excitation force, and Κ is the dynamic stiffness of the component.
The main factors causing the increase of excitation force P include mass imbalance, shaft bending, component detachment, thermal imbalance, scaling, Misalignment, Oil film whirling, steam flow excitation, Rotating stall and surge, Dynamic and static rubbing, etc.The main factors that cause the change of the dynamic stiffness K of components include loose bearing shells, loose connecting bolts, loose pad iron, and loose foundation, Misalignment, dynamic and static rubbing, Changes in oil

Common Vibration Faults of Condenser
There are 11 common vibration faults in condenser [3-10]: imbalance, misalignment, loose, resonance, oil film whirling and oscillation, steam flow vortex and steam flow excitation, dynamic and static rubbing, rotating stall and surge, gear failure, rolling bearing failure, other vibration faults.

Imbalanced Faults
The mechanism of rotor mass imbalance fault is that the line connecting the centroids of each crosssection of the rotor does not coincide with the line connecting the geometric centers of each crosssection, so that when the rotor rotates, the centrifugal force of each cross-section forms a spatial continuous force, and the deflection curve of the rotor is a continuous three-dimensional curve.The centrifugal force in this space and the deflection curve of the rotor rotates at the same speed as the rotor, resulting in power frequency vibration of the rotor.
Disk mass is m, center of mass is C point, the rotating shaft passes through the geometric center point A of the disc, AC=e.The disc and shaft jointly rotate at a uniform angular velocity ω, Κ is the dynamic stiffness of the component as shown in figure 1.
The critical angular velocity is 1) Amplitude.
In the equation, A represents the maximum amplitude of the system, ω is the angular velocity, ωn is the critical angular velocity.
2) Phase difference.In the figure 1, r represents the distance between the disc center and the shaft center.
For an undamped flexible rotor, the phase of the rotor imbalance vector and the vibration vector are the same when speed is below the critical speed.After passing through the critical speed, the phase of the imbalance vector suddenly flips and changes, and the phase difference between the rotor imbalance vector and the vibration vector is 90°.After exceeding the critical speed, the unbalanced vector and the vibration vector have opposite phases, with a phase difference of 180°.And the vibration actually decreases, which is called automatic rotor centering.The process is shown in figure 2.  1) The vibration caused by imbalanced rotor mass and permanent deflection occurs throughout the entire shaft system, and increases significantly when passing through the critical speed, mainly with a first harmonic amplitude.When the speed remains constant, the amplitude and phase is stable.The vibration does not decrease after low speed turning.
2) The waveform is a sine wave.
3) The axis trajectory is a circle or ellipse.
4) The vibration is mainly based on the first harmonic, and the phase difference between horizontal and vertical vibrations is close to 90 °.
5) The radial vibration is relatively large, while the axial vibration is not significant.
6) The amplitude changes significantly with the speed.7) There is a resonance peak when the critical speed is exceeded.

Misalignment Faults
Due to manufacturing and installation deviations or the failure to consider the impact of the coupling during dynamic balancing, it may cause imbalance by the coupling.With the improvement of rotor dynamic balance accuracy, the imbalance problem caused by coupling is more prominent.Rotating machinery is generally composed of multiple rotors, and the rotors are generally connected by rigid or semi flexible couplings.Due to uneven expansion of the support shaft frame, pipeline force, casing expansion, and uneven settlement of the foundation during manufacturing, installation, and operation, rotor misalignment (misalignment of the shaft system) faults are caused.Coupling misalignment can be divided into three situations: parallel misalignment, misalignment, and parallel misalignment, (which is shown in figure 3).The misalignment of the bearing actually reflects the deviation in the bearing coordinate height and the left -right positions.Due to structural reasons, bearings have different stiffness and damping in both horizontal and vertical directions, and the misalignment increases this difference.Although the oil film has both elasticity and damping, it can compensate for the impact of misalignment to a certain extent, excessive misalignment can still change the working conditions of the bearing, can cause additional forces and moments on the rotor, and even potentially cause dynamic and static friction or steam flow excitation.
The misalignment of the bearings causes a change in the balance position of the bearing neck center, which redistributes the load of the shaft system.The oil film of bearings with larger loads exhibits nonlinearity, so high-order harmonic vibration possibly occur under certain conditions.Bearings with lighter loads are prone to cause oil film whirling, which in turn leads to oil film oscillation.Changes in support load also cause changes in the critical speed and vibration mode of the bearing system.
Characteristics of Imbalanced Faults as following: EPES-2023 Journal of Physics: Conference Series 2731 (2024) 012002 The alignment of the shaft system can be effectively monitored through shaking during turning, bearing lifting height, and offset angle.The main features are as follows: 1) Large shaking at low speed.
2) At high constant speed, there is a significant deviation in the displacement and angle of adjacent bearings.
3) At high constant speed, there is a significant deviation between the amplitude and temperature of adjacent bearings.
4) During stable operation, the normal lifting height of the steam turbine is around 200um-300um.If the top clearance ratio and the vibration or temperature of adjacent bearings differ significantly, it is abnormal.
5) The second harmonic vibration is significant.
6) The oil film pressure of adjacent two bearings changes in the opposite direction.7) When the coupling is misaligned, there is significant axial vibration.8) Vibration is sensitive to change in load.

Resonance Faults
1) Due to unavoidable structural design or design defects, there are inherent frequencies of rotating bodies and components within the operating speed range.Due to the decrease in system stiffness, the critical speed decreases, and the natural frequencies of the rotating body and components fall into the resonance zone.
2) Due to design reasons, the vibration rapidly increases when the rotational speed approaches a certain natural frequency, mainly a doubling frequency.
3) Fractional harmonic resonance caused by increased clearance due to bearing design and wear, with a frequency of accurate 1/2, 1/3,... times the rotational speed.
4) Due to insufficient or decreased foundation stiffness, foundation vibration is manifested as large vertical vibration, mainly in the first harmonic generation.

Oil Film Oscillation Fault
When the bearing neck rotates in the bearing, it is subjected to the squeezing force of the oil film, and its tangential component causes the bearing to undergo vortex.This can prove that when the speed is greater than the unstable speed, the bearing neck undergoes vortex with a frequency less than or equal to half of the speed, and increases accordingly with the increase of the speed.When the vortex frequency approaches the first critical speed of the bearing system, resonance occurs, which is called oil film oscillation.The characteristics of oil film oscillation are as follows: 1) The frequency of oil film oscillation is close to the first critical speed of the rotor.Even if the speed increases again, its frequency remains basically unchanged.
2) The vibration phase of the bearings at both ends of the rotor is basically the same.
3) When the oil film oscillates, the axis trajectory is precessing.4) Oil film oscillation is more sensitive to changes in oil temperature.
5) The occurrence and disappearance of oil film oscillation are sudden.

Steam Vortex and Steam Excitation
From the perspective of mechanism, oil film oscillation is similar to steam flow excitation.But due to the poor compressibility of oil and the strong compressibility of gas, the spectrum range of steam flow excitation is relatively wide.Steam flow excitation usually occurs in high-medium pressure rotors, while oil film oscillation usually occurs in low pressure rotors.
1) The vortex frequency is generally 0.5~0.9times the power frequency.
2) When subjected to strong vibration, the first natural frequency of the high-medium pressure rotor is excited, manifested as self-excited vibration with a wide frequency band.
3) There is a threshold for the load, which can cause strong vibration near its value.
4) The reproducibility of vibration is strong.
Solution: Increase bearing elevation, replace bearings, adjust sealing clearance, adjust the opening sequence and degree of high-pressure regulating valves, etc.

Dynamic and Static Rubbing
The dynamic and static clearances (radial and axial) disappear in the system may cause misalignment, imbalance, etc., friction between rotating and stationary components will occur, which has the following effects: 1) Friction adds a torque to the rotor, which may cause speed fluctuations.Due to the intervention of friction, the forward precession of the rotor may be transformed into reverse precession, especially severe full cycle friction.
2) The effect of friction causes the dynamic and static components to collide with each other, which is equivalent to increase the support conditions of the rotor, increase the stiffness of the system, change the critical speed and vibration mode of the rotor.While this additional support is unstable, and may cause unstable and nonlinear vibration.
3) Local rubbing can also generate impact effects, which may cause a complex vibration with superimposed free vibrations under certain conditions.
4) The thermal deformation caused by friction may cause the rotor to bend, increase eccentricity, and increase the vibration amplitude.
The faults caused by friction between dynamic and static components have the following characteristics: 1) Before rotor instability, the frequency spectrum is rich, with waveform distortion and irregular changes in the axis trajectory.After rotor instability, the waveform is severely distorted or clipped, and the axis trajectory diverges.
2) When there is slight friction, the amplitude and phase has a same fluctuation frequency, and the axis trajectory is a small circular ring.When the collision is severe, the amplitude of the pass-band frequency and the first harmonic increase rapidly, and the phase may change rapidly at the same time.
3) The stiffness of the system increases, the critical speed zone widens, and the phase of each order of vibration changes.
4) Due to the thermal bending caused by friction, the amplitude increases significantly when the speed decreases compared to when the speed increases, and the shaking (eccentricity) decreases after turning.
5) When the slight frictional vibration occurs at working speed, its amplitude slowly changes over time and phase rotates in the opposite direction.

Gear Fault
The gear faults in the condenser system can be summarized as follows: 1) Gear pitting and wear.
3) Broken or broken teeth of gears.Under the above fault conditions, the characteristic frequencies are shown in table 1. Where: r is the radius of the rolling element, m，ρ is the material density, kg/m 3 , E is the elastic modulus, N/mm 2 , and the bearing fault frequency is usually a non-integer multiple of the rotational speed frequency.
In addition to the fault frequency and its harmonics, bearing defects are often accompanied by a side frequency of 1X speed frequency.Sum frequency of inner and outer ring fault frequency="Bearing rolling element passing frequency" (number of rolling elements) ×fRPM).

Imbalanced Faults
1) An imbalance fault occurred in the high-medium pressure rotors of a 30Mvar unit.
From the startup bode plot (figure 4) in 1Y direction, it can be seen that there is a significant vibration at around 1740rpm, with a first harmonic amplitude of over 22 wires.The rotor exhibits firstorder imbalance, mostly due to long-term thermal deformation during operation, especially for highmedium pressure rotors.2) An imbalance fault occurred in the exciter rotor of a 250Mvar unit.The generator and exciter of a certain plant are of a three support structure, and the NO.9 bearing is the exciter bearing.As shown in figure 5, during the shutdown process, the vibration amplitude of No. 9 in X direction is relatively large, reaching 160μm at the first critical speed, the vibration of No. 9 in Y direction is not significant, and the first harmonic in the vibration spectrum is larger.

Misalignment Faults
The case of shaft misalignment fault in a 60Mvar unit is shown in figure 6.After the first bearing was lowered by 10 wires and the second bearing was raised by 10 wires, the vibration of the second bearing decreased slightly but remained relatively large, the rotor lifting height was significantly higher, and the rotor load was lighter.Adjust the relative elevation of the first, second, and third bearings at an appropriate time.As shown in figure 7, the vibration of bearing No.5 increases from 18um to 40um during the loadup process of 2800rpm to 3000rpm, mainly in the first harmonic.The bearing vibration is not significant, and manifested as the resonance response of the bearing seat.We can check whether the bolt is loosen, or the pad iron and foundation are loosen.Perform fine dynamic balancing test, and adjust the support stiffness of the bearing seat if necessary.In response to the phenomenon of sudden strong vibration occurring twice in the condenser, the load of the shaft system was readjusted.The elevation of the No. 4 bearing was lowered, and the top clearance of the No. 5 and No. 6 bearing was reduced to increase the load and stability of the generator bearing.After restarting and setting the unit at a constant speed of 3600r/min, there was no oil film oscillation during no-load operation.

Steam Vortex and Steam Excitation
A steam flow induced vibration fault occurred in the high-pressure rotor of a 50Mvar unit.During the start-up process of Unit 2 in a certain factory, there was almost no low-frequency vibration in the high-pressure rotor.From figure 8, it can be seen that low-frequency vibration widely exists within a wide load range, and there are significant changes in the low-frequency vibration spectrum under different loads.After adjusting the elevation of the bearing seat, the steam flow vortex is significantly reduced.

Gear Fault.
The tooth coupling between the motor and the fan is a tooth sleeve connection method with 70 teeth, with a meshing frequency of 70×24.82=1737Hz,twice the meshing frequency is 3474Hz.The high frequency spectrum of the motor drive end bearing shows that the meshing frequency of the gear is the basic frequency.Infinite sideband families interval based on the operating frequency of faulty gears were detected at 1 or 2 times the meshing frequency and its harmonics.After removing the protective cover of the coupling, it was found that there was a crack on the external gear sleeve of the coupling that was 45°to the axis, which had penetrated 1/3 of the axial position of the gear sleeve.After uncovering the gear sleeve of the coupling, it was found that multiple internal teeth had been broken and most of them were corroded.

Rolling Bearing Fault
The following is a case of rolling bearing failure in a certain gearbox.The motor speed of a certain gearbox is 148.5r/min, with a rotational frequency of 2.475Hz.Through calculation, the passing frequencies of the inner ring, outer ring, and rolling element of the bearing are 34.0,27.9, and 30.6 Hz, respectively.In envelope analysis, it can be seen that the fault frequency is 32Hz, which is relatively close to the passing frequency of the inner ring of the bearing, indicating that the inner ring of the bearing has fault.

Conclusion 1)
Eleven common vibration faults of the condenser were proposed, including imbalance, misalignment, looseness, resonance, oil film vortex/oil film oscillation, steam flow vortex/steam flow excitation, dynamic static friction, rotating stall, gear fault, rolling bearing fault, and other vibration faults.
2) The mechanism, characteristics, and case analysis of each type of fault were provided separately.The research results on the mechanisms and characteristics of these faults are the foundation of condenser fault diagnosis, and are crucial for the development of intelligent decision-making systems and platforms.

Figure 1 .
Figure 1.The disc and shaft rotate at a uniform angular velocity.

Figure 2 .
Figure 2. Schematic diagram of rotor phase change.

Figure 6 .
Figure 6.Case study of bearing misalignment fault in a 60Mvar unit.4.3.Resonance Faults 1) Resonance fault of bearing seat No.5 of a 30Mvar unit.As shown in figure7, the vibration of bearing No.5 increases from 18um to 40um during the loadup process of 2800rpm to 3000rpm, mainly in the first harmonic.The bearing vibration is not significant, and manifested as the resonance response of the bearing seat.We can check whether the bolt is loosen, or the pad iron and foundation are loosen.Perform fine dynamic balancing test, and adjust the support stiffness of the bearing seat if necessary.

Figure 7 .
Figure 7. Resonance fault of bearing No.5 of a 30Mvar unit.Resonance fault of the bearing seat of a 60Mvar unit generator.One 60Mvar condenser is a single extraction and air cooling unit, with three supports and an air cooling model QFL60-2 for the rotor.The unit was put into operation in 1996, and the axial vibration amplitude of the rotor's No. 4 and No. 5 bearings has always been between 160 to 220 μm.Despite multiple treatments have been executed by personnel from the Electric Power Research Institute, the

Figure 8 .
Figure 8. Waterfall diagram of No.1 X for steam flow induced vibration fault of high-pressure rotor of a 50Mvar unit.

4. 6 .
Dynamic and Static RubbingThe case of high-medium pressure rotor rubbing fault in a 100MVar unit is shown in figure9.During the warm-up process at 1500rpm for Unit 2 of a certain factory, the vibration of the high-medium pressure rotors was relatively small at the beginning.Later, the Y-direction amplitude of bearing No.3 rapidly increased, and the phase changed significantly.Subsequently, the vibration of Bearings No.2 and No.1 increased significantly, leading to trip and shutdown.Based on the changes in amplitude and phase, it can be determined that the increase in vibration is a problem of dynamic static friction, and it EPES-2023 Journal of Physics: Conference Series 2731 (2024) 012002 IOP Publishing doi:10.1088/1742-6596/2731/1/01200210can be ruled out that there is mass imbalance in the high-medium pressure rotors.After more than 4 hours of turning, the engine revved again and successfully passed the critical speed.

Figure 9 .
Figure 9.A case study of high-medium pressure rotors rubbing fault in a 100Mvar unit.

Table 1 .
Characteristic frequencies under different faults.In the table, the bearing frequency fr =N/60, where N represents the bearing speed in rpm.The meshing frequency of the gear fm =Z* fr, where Z is the number of teeth in the gear.Bd is diameter of rolling element, Pd is diameter of bearing pitch circle,α is Contact angle, Z- 7

Table 2 .
Vibration data after maintenance.MARIVELES No. 2 condenser set was first driven to 3600r/min.110 minutes after constant speed, the vibration of No. 5 bearing suddenly increased and tripped, with a maximum amplitude exceeding 500μm.Starting again, about 140 minutes after the unit was set to constant speed, the vibration of the No. 5 bearing suddenly increased again and tripped.The main component in the vibration spectrum is the 15Hz low-frequency component, which is consistent with the first critical speed of the generator rotor.