This paper analyzes the stator vibration response under static air-gap eccentricity and rotor inter-turn short circuit composite faults (SAERISC). The detailed formula of the magnetic force on stator is firstly deduced. Then the finite element simulations and practical experiments are taken to investigate the stator vibration response. It’s shown that, 1st to 4th stator vibrations will be produced. The development of the short circuit will decrease the 2nd vibration but increase the 4th vibration, while the increment of the eccentricity will increase the 1st to 4th vibrations at the same time

Fa-Lin Wang

Gui-Ji Tang

Meng-Qiang Ke

Yu-Ling He

English

Vibroengineering PROCEDIA

  © JVE INTERNATIONAL LTD. VIBROENGINEERING PROCEDIA. SEP 2015, VOLUME 5. ISSN 2345-0533 181 
Stator vibration of generator under SAERISC faults 
Meng-Qiang Ke1, Yu-Ling He2, Gui-Ji Tang3, Fa-Lin Wang4 
Department of Mechanical Engineering, North China Electric Power University, Baoding, China 
2Corresponding author 
E-mail: 1kemengqiang@163.com, 2heyuling1@163.com, 3tanggjlk@ncepubd.edu.cn, 4falinwang@163.com 
(Accepted 21 August 2015) 
Abstract. This paper analyzes the stator vibration response under static air-gap eccentricity and 
rotor inter-turn short circuit composite faults (SAERISC). The detailed formula of the magnetic 
force on stator is firstly deduced. Then the finite element simulations and practical experiments 
are taken to investigate the stator vibration response. It’s shown that, 1st to 4th stator vibrations 
will be produced. The development of the short circuit will decrease the 2nd vibration but increase 
the 4th vibration, while the increment of the eccentricity will increase the 1st to 4th vibrations at 
the same time. 
Keywords: generator, static air-gap eccentricity (SAGE), rotor inter-turn short circuit (RITSC), 
magnetic pull, stator vibration. 
1. Introduction 
SAGE and RITSC are common faults in generator. When the eccentricity is more than 10 %, 
intense vibrations, winding damages will be caused [1]. Similarly, RITSC will increase the 
excitation current, and even lead to an earth fault [2]. Scholars have studied much about these two 
faults, such as the circulating current inside parallel branches (CCPB) [3], and the unbalanced 
magnetic pull (UMP) [4, 5] under SAGE, and also the UMP features and vibration characters [6, 7] 
under RITSC. 
However, most of the studies only focused on either of these two faults, while few of them 
have considered these two occurring together. As an improvement, this paper investigates the 
composite fault composed by these two faults, focusing on the stator vibration. 
2. Theoretical analysis 
The magnetic flux density (MFD) is indicated in Eq. (1) [8]: 
ቐ
ܤே(ߙ௠, ݐ) = ܨଵΛ଴cos(߱ݐ − ߙ௠ − ߚ);
ܤி(ߙ௠, ݐ) = ܨ஼(Λ଴ + Λ௦cosߙ௠) cos(߱ݐ − ߙ௠ − ߚଵ)
        −ܨௗଶ(Λ଴ + Λ௦cosߙ௠)cos2(߱ݐ − ߙ௠ − ߮ଶ),
(1)
where ܤே and ܤி are MFD in normal condition and composite fault, respectively, ܨଵ, ܨ஼ are the 
fundamental frequency of magnetomotive force (MMF) under normal condition and the composite 
fault (ܨ஼ < ܨଵ), respectively, ܨௗଶ is the 2nd harmonic component of the reverse MMFs produced 
by RITSC. 
The MPPUA on the stator under normal condition and composite fault is shown in Eq. (2), and 
their amplitudes are shown in Table 1. The subscript ܰ  in the equations stands for normal 
condition, while ܨ stands for the composite fault. 
Table 1. Amplitudes of MPPUA on stator under SAERISC 
Component Amplitude of MPPUA 
0 Hz (ܨ஼ଶ + ܨௗଶమ)(Λ଴ + Λ௦)ଶ/4݅଴ 
50 Hz (ܨ஼ + ܨௗଶ)(Λ଴ + Λ௦)ଶ/2݅଴
100 Hz ܨ஼మ(Λ଴ + Λ௦)ଶ/4݅଴ 
150 Hz ܨ஼ܨௗଶ(Λ଴ + Λ௦)ଶ/2݅଴
2000 Hz ܨௗଶమ(Λ଴ + Λ௦)ଶ/4݅଴ 
 
STATOR VIBRATION OF GENERATOR UNDER SAERISC FAULTS.  
MENG-QIANG KE, YU-LING HE, GUI-JI TANG, FA-LIN WANG 
182 © JVE INTERNATIONAL LTD. VIBROENGINEERING PROCEDIA. SEP 2015, VOLUME 5. ISSN 2345-0533  
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ۓݍே(ߙ௠, ݐ) =
[ܤே(ߙ௠, ݐ)]ଶ
2ߤ଴ =
ܨଵଶ[2Λ଴ଶ + 2Λ଴ଶ cos(2߱ݐ − 2ߙ௠ − 2ߚ)]
8ߤ଴ ,
ݍி(ߙ௠, ݐ) = ቈ
ܤே(ߙ௠, ݐ)]ଶ
2ߤ଴ = ൬
1
8ߤ଴൰ ሼ[(ܨ஼
ଶ + ܨௗଶଶ )(2Λ଴ଶ + Λ௦ଶ) + 4(ܨ஼ଶ + ܨௗଶଶ )Λ଴Λ௦cosߙ௠
      +(ܨ஼ଶ + ܨௗଶଶ )Λ௦ଶcos2ߙ௠] + [−4ܨ஼ܨௗଶΛ଴Λ௦cos(߱ݐ + ߚଵ − 2߮ଶ)
      −2ܨ஼ܨௗଶ(2Λ଴ଶ + Λ௦ଶ)cos(߱ݐ − ߙ௠ + ߚଵ − 2߮ଶ) − ܨ஼ܨௗଶΛ௦ଶcos(߱ݐ + ߙ௠ + ߚଵ − 2߮ଶ)
      −4ܨ஼ܨௗଶΛ଴Λ௦cos(߱ݐ − 2ߙ௠ + ߚଵ − 2߮ଶ) − ܨ஼ܨௗଶΛ௦ଶcos(߱ݐ − 3ߙ௠ + ߚଵ − 2߮ଶ)]
      +[0.5ܨ஼ଶΛ௦ଶcos(2߱ݐ − 2ߚଵ) + 2ܨ஼ଶΛ଴Λ௦cos(2߱ݐ − ߙ௠ − 2ߚଵ)
      +ܨ஼ଶ(2Λ଴ଶ + Λ௦ଶ)cos(2߱ݐ − 2ߙ௠ − 2ߚଵ) + 2ܨ஼ଶΛ଴Λ௦cos(2߱ݐ − 3ߙ௠ − 2ߚଵ)
      +0.5ܨ஼ଶΛ௦ଶcos(2߱ݐ − 4ߙ௠ − 2ߚଵ)] + [−ܨ஼ܨௗଶΛ௦ଶcos(3߱ݐ − ߙ௠ − ߚଵ − 2߮ଶ)
      −4ܨ஼ܨௗଶΛ଴Λ௦cos(3߱ݐ − 2ߙ௠ − ߚଵ − 2߮ଶ)
      −2ܨ஼ܨௗଶ(2Λ଴ଶ + Λ௦ଶ)cos(3߱ݐ − 3ߙ௠ − ߚଵ − 2߮ଶ)
      −4ܨ஼ܨௗଶΛ଴Λ௦cos(3߱ݐ − 4ߙ௠ − ߚଵ − 2߮ଶ)
−ܨ஼ܨௗଶΛ௦ଶcos(3߱ݐ − 5ߙ௠ − ߚଵ − 2߮ଶ)] + [0.5ܨௗଶଶ Λ௦ଶcos(4߱ݐ − 2ߙ௠ − 4߮ଶ)
+2ܨௗଶଶ Λ଴Λ௦cos(4߱ݐ − 3ߙ௠ − 4߮ଶ) + ܨௗଶଶ (2Λ଴ଶ + Λ௦ଶ)cos(4߱ݐ − 4ߙ௠ − 4߮ଶ)
+2ܨௗଶଶ Λ଴Λ௦cos(4߱ݐ − 5ߙ௠ − 4߮ଶ) + 0.5ܨௗଶଶ Λ௦ଶcos(4߱ݐ − 6ߙ௠ − 4߮ଶ)]}.
 (2)
As indicated in Eq. (2) and Table 1, normally, the stator is affording a constant force and a 
pulsating force at 2݂, of which the constant one will not generate vibrations. When the composite 
fault occurs, MPPUA has a constant force and 1st-4th harmonics. Keeping SAGE constantly, the 
2nd harmonic will be decreased as the RITSC develops, but the 4th harmonic will be increased. 
However, with the increment of SAGE, the DC component and the 1st-4th harmonics will be all 
increased. 
3. Study on simulation and experiment  
3.1. Object and methods 
The digital simulation with Ansoft Maxwell is taken together with the experiment for the 
object of SDF-9 type fault simulating generator, as indicated in Fig. 1(a). The rotor is kept to the 
underframe by the bearing pedestal, while the stator can be moved along the horizontally radial 
direction by adjusting the screws so that different faulty degrees of SAGE can be simulated, as 
shown in Fig. 1(b). Meanwhile, there are several short circuit taps of the excitation winding on 
the generator which can be connected to simulate different degrees of RITSC. The stator vibration 
is sampled and collected by a CD-21C velocity sensor and a U60116C collector. More details 
about the corresponding parameters of the generator are shown in Table 2. 
The simulation model is shown in Fig. 1(c), where SAGE is modeled by shifting the rotor of 
12.5 %, 25 %, and 37.5 % degree, respectively, which have also been set in the experiment. The 
short circuit is set to 10 % degree, 20 % degree and 30 % degree, respectively. 
Table 2. Primary parameters of study object 
Parameters Values Parameters Values 
Rated capacity 7.5 kVa Radial air-gap length ܩ = 0.8 mm 
Rated exciting current 1.5 A Number of exciting slots per pole 6 
Rated rotation speed 3000 r/min Number of exciting turns peer pole 480 
Number of pole pairs ܲ = 1 Number of stator slots 24 
Polar distance ෠ܱ = 252 mm Power factor 0.8 
 
STATOR VIBRATION OF GENERATOR UNDER SAERISC FAULTS.  
MENG-QIANG KE, YU-LING HE, GUI-JI TANG, FA-LIN WANG 
 © JVE INTERNATIONAL LTD. VIBROENGINEERING PROCEDIA. SEP 2015, VOLUME 5. ISSN 2345-0533 183 
 
a) 
 
b) 
 
c) 
Fig. 1. Study object: a) generator outlook, b) method to set static eccentricity, c) simulation model 
3.2. Results and discussion 
3.2.1. Different RITSC degrees with constant SAGE  
According to the simulation results, as shown in Fig. 2(a)-(d) and Table 3, with the increment 
of RITSC, the 2nd harmonic of MPPUA decreases while the 4th harmonic increases. Compared 
with the faulty condition composed by 12.5 % SAGE and 0 % RITSC, as RITSC is increased to 
10 %, 20 %, 30 %, respectively, the 2nd harmonic of MPPUA decreased by 25.0 %, 40.0 %, and 
50.9 %, while the 4th harmonic increased by 11.3 %, 98.0 %, and 185.7 %. 
a) 
 
b) c) 
 
d) 
e) f) g) h) 
Fig. 2. Spectra of MPPUA and vibration: a)-d) MPPUA under normal condition, 12.5 % SAGE and 10 % 
RITSC, 12.5 % SAGE and 20 % RITSC, and 12.5 % SAGE and 20 % RITSC, respectively,  
e)-h) stator vibrations under normal condition, 12.5 % SAGE and 3 % RITSC, 12.5 % SAGE  
and 6 % RITSC, and 12.5 % SAGE and 12 % RITSC, respectively 
STATOR VIBRATION OF GENERATOR UNDER SAERISC FAULTS.  
MENG-QIANG KE, YU-LING HE, GUI-JI TANG, FA-LIN WANG 
184 © JVE INTERNATIONAL LTD. VIBROENGINEERING PROCEDIA. SEP 2015, VOLUME 5. ISSN 2345-0533  
As indicated in Fig. 2(e)-(h) and Table 4, it is shown that, keeping SAGE at 12 %, the 
corresponding decease rates from no RITSC to 12 % RITSC for the 2nd harmonic are 60.8%, 
74.5 %, and 82.4 %, respectively, while the rise rates for the 4th harmonic are 230 %, 400 %, and 
800 %. In addition, there is also stator vibration at fundamental frequency due to the rotor vibration 
transmission and the asymmetry inside the generator. Combined with the foregoing, the simulation 
analysis and the experimental study are generally consistent with the theoretical analysis. 
Table 3. Amplitude of MPPUA obtained from simulation under different conditions (N/m2) 
Working conditions 50 Hz 100 Hz 150 Hz 200 Hz 
Normal 259.28 20390.91 162.47 2241.02 
SAGE = 12.5 % RITSC = 0 % 284.94 22997.80 187.89 2501.83 
SAGE = 12.5 % RITSC = 10 % 3586.37 17236.60 4096.76 2784.37 
SAGE = 12.5 % RITSC = 20 % 4567.48 13773.13 6865.25 4953.71 
SAGE = 12.5 % RITSC = 30 % 4811.77 11287.57 9083.76 7148.95 
Table 4. Amplitude of stator vibration under different conditions (mm/s) 
Working conditions 50 Hz 100 Hz 150 Hz 200 Hz 
Normal 2.95 2.7 0.3 0.1 
SAGE = 12.5 % RITSC = 0 % 2.30 3.7 0.3 0.1 
SAGE = 12.5 % RITSC = 3 % 3 1.45 0.55 0.33 
SAGE = 12.5 % RITSC = 6 % 3.1 0.94 0.35 0.5 
SAGE = 12.5 % RITSC = 12 % 2.79 0.65 0.47 0.9 
3.2.2. Different degrees of SAGE with constant RITSC 
In faulty conditions, the DC component and the 1st-4th harmonics of the MPPUA increase 
with the increment of SAGE, as illustrated in Fig. 3(a)-(d) and Table 5. When the degree of SAGE 
varies from 0 % to 37.5 % but meanwhile keeping RITSC at 10 %, the amplitude of the 
fundamental frequency component is increased by 42.6 %, 111.9 % and 227 %, respectively, while 
the 2nd harmonic is increased by 11.1 %, 25.6 %, and 45.8 %. Moreover, the 3rd harmonic is 
increased by 26.1 %, 61.8 %, and 113.4 %, and the 4th harmonic increased by 28.1 %, 67.1 %, 
and 124.0 %.  
a) b) c) 
 
d) 
e) f) g) 
 
h) 
Fig. 3. Spectra of MPPUA and vibration: a)-d) MPPUA under normal condition, 12.5 % SAGE and 10 % 
RITSC, 25.0 % SAGE and 10 % RITSC, and 37.5 % SAGE and 10 % RITSC, respectively, while e)-h) 
stator vibrations under normal condition, 12.5 % SAGE and 3 % RITSC, 25.0 % SAGE  
and 3 % RITSC, and 37.5 % SAGE and 3 % RITSC, respectively 
STATOR VIBRATION OF GENERATOR UNDER SAERISC FAULTS.  
MENG-QIANG KE, YU-LING HE, GUI-JI TANG, FA-LIN WANG 
 © JVE INTERNATIONAL LTD. VIBROENGINEERING PROCEDIA. SEP 2015, VOLUME 5. ISSN 2345-0533 185 
The experimental results are shown in Fig. 3(e)-(f) and Table 6. The 1st-4th harmonics will be 
increased with the development of SAGE, keeping the RITSC degree unchanged. As illustrated 
in Table 6, compared with the faulty condition of 0 % SAGE and 3 % RITSC, when the faulty 
degree of SAGE is 12.5 %, 25.0 %, and 37.5 %, respectively, the amplitude of the fundamental 
frequency component is increased by 0.7 %, 10.1 %, and 17.4 %, while the 2nd harmonic is 
increased by 20.8 %, 33.3 %, and 312.5 %. At the mean time, the 3rd harmonic is increased by 
37.5 %, 100.0 %, and 166.7 %, while the 4th harmonic is increased by 120 %, 366.7 %, and 
466.7 %. This shows that the simulation and the experiment results match the previously 
theoretical deduction well. 
Table 5. Amplitude of MPPUA obtained from simulation under different conditions (N/m2) 
Working conditions 50 Hz 100 Hz 150 Hz 200 Hz 
Normal 259.28 20390.91 162.47 2241.02 
SAGE = 0 % RITSC = 10 % 2514.23 15512.35 3249.70 2174.91 
SAGE = 12.5 % RITSC = 10 % 3586.37 17236.60 4096.76 2784.37 
SAGE = 20.0 % RITSC = 10 % 5327.31 19507.83 5257.61 3632.51 
SAGE = 37.5 % RITSC = 10 % 8222.78 22623.08 6933.53 4870.86 
Table 6. The amplitude of stator vibration under different conditions (mm/s) 
Working conditions 50 Hz 100 Hz 150 Hz 200 Hz 
Normal 2.95 2.70 0.30 0.10 
SAGE = 0 % RITSC = 3 % 2.98 1.20 0.40 0.15 
SAGE = 12.5 % RITSC = 3 % 3.00 1.45 0.55 0.33 
SAGE = 20.0 % RITSC = 3 % 3.28 1.60 0.80 0.70 
SAGE = 37.5 % RITSC = 3 % 3.50 4.95 1.15 0.85 
4. Conclusions 
This paper investigates the stator vibration response under the normal condition and the 
composite fault composed by SAGE and RITSC. According to the results, primary conclusions 
can be drawn up as follows. 
1) The spectrums of both MPPUA and stator vibration consist of 2nd harmonic in normal 
condition while composed by 1st-4th harmonics under composite fault. 
2) With the development of RITSC while SAGE remains unchanged, the amplitudes of 2nd 
harmonic of MPPUA and stator vibration decrease and 4th harmonic increase. 
3) The spectrums of MPPUA and stator vibration are composed by 1st-4th harmonics which 
increase with the development of SAGE though the degree of RITSC unchanged. 
Acknowledgements 
This work is in part supported by National Natural Science Foundation of China (51307058), 
Natural Science Foundation of Hebei Province, China (E2014502052, E2015502013), and 
Chinese Fundamental Research Funds for the Central Universities (2015ZD27). 
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STATOR VIBRATION OF GENERATOR UNDER SAERISC FAULTS.  
MENG-QIANG KE, YU-LING HE, GUI-JI TANG, FA-LIN WANG 
186 © JVE INTERNATIONAL LTD. VIBROENGINEERING PROCEDIA. SEP 2015, VOLUME 5. ISSN 2345-0533  
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Stator vibration of generator under SAERISC faults

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Stator vibration of generator under SAERISC faults

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