This paper investigates the radial stator vibration characteristics of turbogenerator under the static airgap eccentricity (SAGE) fault, the rotor interturn short circuit (RISC) fault, and the composite faults (CFs) composed of SAGE and RISC, respectively. Firstly, the impact of the faulty types on the magnetic flux density (MFD) is analyzed, based on which the detailed expressions of the magnetic pull per unit area (MPPUA) on the stator under different performing conditions are deduced. Then, numerical FEM simulations based on Ansoft and an experimental study are carried out, taking the SDF9 type fault simulating generator as the study object. It is shown that SAGE will increase the stator vibration at 2
SAGE and RISC are common faults of turbogenerator. When the eccentricity degree is more than 10%, severe vibrations, stator core deformations, and even winding damage will be caused [
By far, scholars have paid much attention to either SAGE or RISC, while few of them studied the CF considering these two faults occurring at the same time. Achievements obtained for SAGE mainly focus on the threephase current or voltage change [
For RISC, the primary monitor performances are taken by means of installing extra search coils inside the generator [
Currently, achievements obtained by scholars have set up a good basis for condition monitoring and diagnosis for these two faults. However, since SAGE exists in almost every generator, there is actually a CF occurring when RISC takes place. Previous studies on this kind of CF found that the failure characteristics are different from those of the single SAGE and RISC faults [
As an improvement, this paper investigates the stator vibration characteristics under SAGE, RISC, and CF composed of SAGE and RISC, respectively, in order to obtain a significant identification criterion for these three faults. The whole work is taken based on the theoretical analysis, the numerical FEM simulation, and the experiment study.
The airgap magnetic flux density (MFD) is composed of the magnetomotive force (MMF) and the permeance per unit area (PPUA) through a multiplying operation. Generally, RISC mainly affects MMF, while SAGE primarily affects PPUA. Thus, MFD will be affected by either of these two faults. Typically, the air gap and MMFs under different conditions are indicated in Figure
Air gap and MMFs of turbogenerator under different conditions.
Normal (
SAGE (
MMF under normal condition and SAGE
MMF under RISC and CF
PPUAs and MMFs for each case can be written as
Correspondingly, MFDs under different conditions are
As indicated in (
However, in the cases of RISC and CF, besides the 1st harmonic components, 2nd harmonic components also exist. As RISC develops, the inverse MMFs of 1st harmonic and 2nd harmonic will both be increased, resulting in the decrease of the 1st MFD but meanwhile the increment of the 2nd MFD (see Figure
The generator stator is made up of the stator core, the windings, the frame, the end covers, and so forth. Stator vibrations are primarily produced by the magnetic forces acting on the stator core. This kind of magnetic force is actually a unit magnetic pull performing on the whole inner surface of the stator core, usually called magnetic pull per unit area (MPPUA), as indicated in Figure
Structure and magnetic force of stator core.
Structure of stator core
MPPUA on stator core
MPPUA mainly acts on the stator core surface, and the composite magnetic pulls can be obtained by integrating MPPUA. Because the stator core is a shell structure that is made up of silicon steel sheets, the radial rigidity is small and the composite magnetic pull is zero (shown in Figure
Therefore, due to the specific structure of the stator core, the essential exciting force for the stator vibration is MPPUA, which can be deduced based on
Substituting (
As indicated in (
Upper amplitude expressions of MPPUA for different conditions.
Component  Performing condition  Amplitude formulas  Influential factors 

DC component  Normal condition 


SAGE 

 
RISC 

 
CF 

 


1st harmonic  Normal condition  —  — 
SAGE  —  —  
RISC 

 
CF 

 


2nd harmonic  Normal condition 


SAGE 

 
RISC 

 
CF 

 


3rd harmonic  Normal condition  —  — 
SAGE  —  —  
RISC 

 
CF 

 


4th harmonic  Normal condition  —  — 
SAGE  —  —  
RISC 

 
CF 


As shown in Table
The numerical FEM simulation and the experiment study are taken for a SDF9 type nonsalient pole fault simulating generator (see Figure
Primary parameters of SDF9 type generator.
Parameter  Value 

Rated capacity  7.5 kVA 
Rated voltage  400 V 
Power factor  0.8 
Rated speed 

Number of pole pairs 

Radial airgap length 

Stator series conductors per phase 

Axial length 

Number of stator slots 

Ratio of pitch to polar distance 

Pitchshortening value 

Distribution coefficient 

Number of parallel branches 

Number of exciting turns for each pole 

Study object of SDF9 type generator.
Physical model of SDF9 type generator
Method to set SAGE
Method to set RISC
Experimental testing system
2D finite element model
Coupling circuit of rotor winding for normal and SAGE cases
Coupling circuit of rotor winding for RISC and CF
Coupling circuit for stator windings
The rotor of the generator is fixed by the bearing block, while the stator can be moved along the horizontally radial direction by adjusting the four screws on the generator to simulate SAGE faults. The movement performance can be controlled by the two dial indicators, as shown in Figure
Objectively, there are some differences to set the velocity sensors in different positions. The general rigidities in the horizontal direction and the vertical direction are different (the vertical direction has a larger rigidity because the foundation is in this direction and therefore sensors here will sample smaller vibration amplitudes). What is more, since the stator is moved along the horizontal direction, the magnetic flux density is larger on one side in this direction but smaller on the other side. So, the MPPUA density is actually larger on the side which has the minimum airgap length but smaller on the opposite side. Consequently, the sensors set on different positions will have varied vibration amplitudes. However, no matter where the sensors are set, the developing tendency of the stator vibration will be the same due to the uniform exciting force indicated in (
The finite element model is built up, setting the performing parameters the same as the experiment, as indicated in Figure
The experiment work and the FEM simulation study are gradually taken by following the four steps.
MPPUA distributions on stator under different performing conditions obtained by FEM calculation are indicated in Figure
MPPUA distribution under different conditions.
Normal condition
0.1 mm SAGE
0.2 mm SAGE
0.3 mm SAGE
3% RISC
6% RISC
12% RISC
0.1 mm SAGE and 3% RISC
0.1 mm SAGE and 6% RISC
0.1 mm SAGE and 12% RISC
0.2 mm SAGE and 3% RISC
0.3 mm SAGE and 3% RISC
However, when RISC takes place, MPPUA will be decreased, as indicated in Figures
Comparing Figure
To show the developing tendency of MPPUA more clearly, the time domain curves for a stable period obtained from FEM calculations for each performing condition are indicated in Figure
Time domain curves of MPPUA under different conditions.
MPPUA under different SAGE conditions
MPPUA under different RISC conditions
MPPUA under CFs with different SAGE values
MPPUA under CFs with different RISC degrees
For the CF cases, the increment of SAGE will increase MPPUA (see Figure
Correspondingly, the stator vibration intensity, which is computed via (
Vibration intensity under different performing conditions.
Vibration intensity under different SAGE conditions
Vibration intensity under different RISC conditions
As indicated in Figure
To further study the impact of different faulty kinds on the stator vibration characteristics, specialfrequency components of MPPUA and vibration, including the 1st, 2nd, 3rd, and 4th harmonic components, are investigated as well. The MPPUA amplitudes for each harmonic component under different performing conditions are indicated in Figure
Spectra of MPPUA under different conditions.
Normal condition
0.1 mm SAGE
0.2 mm SAGE
0.3 mm SAGE
3% RISC
6% RISC
12% RISC
0.1 mm SAGE and 3% RISC
0.1 mm SAGE and 6% RISC
0.1 mm SAGE and 12% RISC
3% RISC and 0.2 mm SAGE
3% RISC and 0.3 mm SAGE
Tested stator vibration spectra under different conditions.
Normal condition
0.1 mm SAGE
0.2 mm SAGE
0.3 mm SAGE
3% RISC
6% RISC
12% RISC
0.1 mm SAGE and 3% RISC
0.1 mm SAGE and 6% RISC
0.1 mm SAGE and 12% RISC
0.2 mm SAGE and 3% RISC
0.3 mm SAGE and 3% RISC
It is suggested from Figure
As illustrated in Figures
Comparing Figure
Taking MPPUA as the exciting force, the stator vibration can be treated as the response. As indicated in Figure
To better show the relation between the input excitation force and the output vibration response, the line charts of MPPUA and the stator vibration at each frequency under different running conditions are illustrated in Figure
Comparison between MPPUA and tested stator vibration for different conditions.
MPPUA when SAGE varies
Vibration when SAGE varies
MPPUA when RISC develops
Vibration when RISC develops
Based on the theoretical analysis, the numerical FEM calculation, and the experiment study, it is found that the stator vibration characteristic varies under different faulty conditions. This can be employed to develop an identification criterion for the single and the composite faults composed of SAGE and RISC. More details can be found in Table
Fault identification criterion based on stator vibration characteristics.
Stator vibration characteristics  Performing condition 

Having only soft 2nd harmonic vibrations  Normal condition 
The vibration at 2 
SAGE exists 
The vibration at 2 
RISC exists 
The vibration at 2 
CF exists 
This paper investigates the stator vibration difference among SAGE, RISC, and the composite faults composed of SAGE and RISC. Based on the proposed theoretical analysis, the numerical FEM calculation, and the experimental study, primary conclusions can be generally drawn as follows:
Normally, stator vibration has only the 2nd harmonic component in theory, while actually it also has the 1st harmonic component which is transferred from the rotor vibration. The occurrence of SAGE will increase the 2nd harmonic component.
As RISC and CF take place in the generator, extra stator vibrations at
In the case of CF, the increment of SAGE will raise the 1st, 2nd, 3rd, and the 4th harmonic components of the stator vibration at the same time, while under the single SAGE fault only the 2nd harmonic component will be increased.
As RISC develops, the stator vibration under CF at
Potentially, these sensitive conclusions can be applied to the practical online monitoring on the generators. Since it is very convenient to test the stator vibration with the industrial velocity sensors, further development of monitoring systems and utilities, which will be beneficial for the fault identification among SAGE, RISC, and the composite fault composed of SAGE and RISC, is probably to be carried out.
The authors declare that they have no competing interests.
This work is supported by the National Natural Science Foundation of China (51307058), the Natural Science Foundation of Hebei Province, China (E2015502013, E2015502008), and the Chinese Fundamental Research Funds for the Central Universities (2015ZD27).