close

Вход

Забыли?

вход по аккаунту

?

ICONE25-66807

код для вставкиСкачать
Proceedings of the 2017 25th International Conference on Nuclear Engineering
ICONE25
July 2-6, 2017, Shanghai, China
ICONE25-66807
STUDY ON VIBRATION CHARACTERISTICS OF INDUCTION MOTOR UNDER LOAD CONSIDERING
SATURATION OF MAGNETIC CIRCUIT
Pu Zhou
Shanghai Marine Equipment
Research Institute
Shanghai, China
Zhen Zhen
Micropowers Ltd.
Shanghai, China
Yue Zhang
Shanghai Marine Equipment
Research Institute
Shanghai, China
Qiang Wang
Shanghai Marine Equipment
Research Institute
Shanghai, China
Hai-jun Feng
Shanghai Marine Equipment
Research Institute
Shanghai, China
abroad, the research of induction motors about the influence of
the magnetic field saturation often concentrated in the motor
performance and the saturation inductance caused by
harmonic parameters are always calculated to analyze the
performance of the motor changes [2]. For example, Julio C.
and T. A. Lipo et al. developed a harmonic equivalent circuit
model and introduced the third harmonic of the air-gap
magnetic potential into the equivalent rotor circuit to calculate
the torque and loss due to saturation harmonics [3]. Liang X,
Luy Y researched the saturated harmonics of induction motors
and the influence of harmonics on motor current and torque
was calculated by adjusting the inductance of rotor side in
equivalent circuit [4].
In the design of low-noise motor, in addition to the motor
performance, more attention should be paid to the vibration
and noise characteristics of the motor. Due to the influence of
load characteristics and environmental factors, the saturation
coefficient of the magnetic circuit will fluctuate and affect the
vibration characteristics of the motor.
Based on the principle of T-equivalent circuit, the law of
flux density change under the saturated state was analyzed in
this paper. Through finite element simulation and bench test, a
small induction motor is studied and the vibration
characteristics of this motor under saturated magnetic circuit
were researched to find the relationship between magnetic
saturation and motor vibration.
ABSTRACT
The variation law of motor vibration with load under
saturation of magnetic circuit is one of the focus of motor
vibration research. T-type equivalent circuit method is shown
to be a suitable engineering analysis way. In this paper, the
variation of magnetic flux density under saturation state was
analyzed by using a small induction motor, and a physical
model of magnetic saturation and motor vibration was
established by the way of T-shaped equivalent circuit. Based
on the physical model, the vibration mechanism of the motor
under the saturated magnetic circuit was analyzed and the
motor vibration simulation with different load conditions was
carried out by the finite element method. Finally, a vibration
test rig for motor under load was built and the simulation
results were verified by experiments. The results show that
when the motor load is less than the rated load, the amplitudes
of the electromagnetic force in the middle and high frequency
band change little. When the load is close to or higher than the
rated value, the harmonic components of electromagnetic
force in the middle and high frequency bands increase, and the
amplitudes gradually increases due to the saturation of the
magnetic circuit. Therefore, in the low-noise motor design,
motor torque performance and vibration noise performance
should be considered to optimize the saturation control of the
magnetic circuit.
KEY WORDS: Induction motor; Magnetic circuit saturation;
Vibration under load; Electromagnetic force
T-SHAPED EQUIVALENT CIRCUIT THEORY
The motor system T-shaped equivalent circuit is shown in
Fig.1, where R1 is the stator resistance, R2' is the rotor
resistance, X 1 is the stator reactance , X 2' is the rotor
reactance, Rm is the magnetic path loss resistance, X m is the
magnetic path reactance, and s is the slip ratio.
INTRODUCTION
Induction motor is often designed to have a certain
degree of magnetic saturation in some special applications in
order to improve the electromagnetic torque [1]. At home and
1
Copyright © 2017 ASME
Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 10/25/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use
By
defining
Z1 = R1 + jX 1
,
Z m = Rm + jX m
increase and Fδ will decrease, eventually leading to the
increase of the saturation coefficient K s of the magnetic
circuit.
In addition, K s is related to the magnetic resistance of
the magnetic circuit. Fig.2 shows the two most typical relative
positions of stator and rotor when the motor is running. When
the motor is in position a, due to the stator tooth surface is
opposite to the rotor tooth surface, the magnetic reluctance of
tooth and yoke is small, as well as K s .When the motor is in
position b, because the rotor tooth tip is opposite to the stator
tooth surface, K s is obviously larger than the K s in position
a. According to the exponential change of the saturation
coefficient, the increment of K s in position b is greater than it
in position a when the motor load increases. Especially when
the motor load exceeds the rated load, the saturation
coefficient in position b largely increases. As the motor
rotating, the relative position of the rotor keeps changing and
experiences a, b, a, b, a, b ... ..., so the motor saturation
coefficient volatility increases.
,
1 '
R2 + jX 2' , we have
s
Z2 =
.
.
I1 =U1
.
.
1
1
=U1
Z2Zm
Zm
Z1 +
Z1 +
Z
Z2 + Zm
1+ m
Z2
Z2Zm
Z2 + Zm
.
I 2 =U1
.
=U1
(1)

Z Z
 Z1 + 2 m
Z
2 + Zm


 Z 2

Zm
(Z1 + Z m )Z 2 + Z1Z m
(2)
Z2Zm
Z2 + Zm
I m = U1

Z Z 
 Z1 + 2 m  Z m
Z
2 + Zm 

.
.
.
=U1
1
Z1 Z m
Z1 +
+ Zm
Z2
(3)
When the load increases, the motor slip ratio s will
increase, leading to the decrease of Z2. From eqns.3, it can be
seen that if the excitation current of the motor Im decreases, the
synthetic magnetic potential of the fundamental wave in the
air gap space will decrease. Similarly, eqns.1 and eqns.2 show
.
that when the load increases, the stator current I1 and rotor
.
current I 2' increase.
.
R1
I1
.
I 2'
X1
R2'
(a)
(b)
Fig.2 typical relative positions of stator and rotor
To sum up, when the motor load increases, the excitation
current decreases, while the magnetic saturation coefficient
and its fluctuation increase. As the excitation current is
proportional to the amplitude of the magnetic flux density and
the fluctuation of the saturation coefficient has great influence
on the harmonic component of the flux density, the amplitude
of the fundamental flux density will ultimately decrease and
the harmonic amplitude will increase if the motor load
increases.
X 2'
.
Im
Rm
1− s  '

 R2
 s 
.
U1
Xm
SIMULATION OF ELECTROMAGNETIC FORCE
UNDER DIFFERENT LOAD
When the motor is used, the load will change in a certain
range, which is often affected by the environment and will
cause the change of the rotor winding current, motor speed
and other characteristics. These will finally affect the motor's
internal radial electromagnetic force.
The finite element model of the motor was built and a
constant torque load was added in the model, as shown in
Fig.3. According to the preliminary calculation result of the
motor, the starting torque is about 3.5 Nm. As a result, the
load step was taken 0.5 Nm and 8 conditions were calculated
ranging in 0 ~ 3.5Nm.
Fig.1 T-shaped equivalent circuit
The magnetic saturation coefficient [5] is expressed by
Ks =
Fδ + F j1 + Fi ,
Fδ
(4)
where Fδ , Fi and F j1 are the magnetic drop of air gap,
stator
tooth,
and stator yoke, and are positively correlated
to
.
.
.
.
.
I1 , I 2' , I m , respectively. When the load increases, I1 , I 2'
.
will increase while I m will decrease. Therefore, Fi , F j1 will
2
Copyright © 2017 ASME
Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 10/25/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use
5
0
5
0
Order
2000
-5 0
1000
Frequency (Hz)
Force Amplitude (Pa)
Force Amplitude (Pa)
4
x 10
4
x 10
4
2
0
5
(a)
(b)
Fig.3 Motor section and finite elements division
The time-domain results of the air-gap flux density (one
point) at different loads are shown in Fig.4. It can be clearly
seen from the figure that the radial flux density of the
fundamental wave decreases while the load increases, and the
fluctuation of the harmonic wave does not change obviously at
first, but sharply increases later.
4
2
0
Order
-5 0
2000
1000
Frequency (Hz)
x 10
4
2
0
5
(c)1 Nm torque
0
Order
4
2
2000
-5 0
1000
Frequency (Hz)
x 10
4
2
0
5
(e)2 Nm torque
1
-5 0
2000
1000
Frequency (Hz)
Force Amplitude (Pa)
Force Amplitude (Pa)
-5 0
2000
1000
Frequency (Hz)
4
2
0
Order
0
Order
(f)2.5 Nm torque
4
x 10
0
5
2000
1000
Frequency (Hz)
4
Force Amplitude (Pa)
Force Amplitude (Pa)
4
0
Order
-5 0
(d)1.5 Nm torque
x 10
0
5
2000
1000
Frequency (Hz)
4
4
x 10
0
5
-5 0
(b)0.5 Nm torque
Force Amplitude (Pa)
Force Amplitude (Pa)
(a)0 Nm torque
0
Order
x 10
2
1
0
5
0
Order
-5 0
2000
1000
Frequency (Hz)
(g)3 Nm torque
(h)3.5Nm Nm torque
Fig.5 Radial electromagnetic force of motor under different loads
Fig.4 Time - domain result of radial flux density under different loads
As the magnitude of the electromagnetic force is
proportional to the square of the magnetic flux density, this
eventually results in the decrease of the double frequency
electromagnetic force of the power supply generated by the
fundamental field when the load increases. However, the
electromagnetic forces generated by the harmonic magnetic
field in the middle and high frequency bands increase. When
the load is less than the rated load (~ 2 Nm), the saturation
coefficient of stator and rotor is small, so the increment of
harmonic forces is not obvious. If the load exceeds the rated
value, the harmonic forces increase rapidly.
Based on the Maxwell stress tensor method, the magnetic
flux density was transformed into the radial electromagnetic
force, and then the two-dimensional Fourier transform was
performed. The results are shown in Fig.5.
In Fig.5, the highest point of electromagnetic force is the
second order 50 Hz force generated by the fundamental wave
on different conditions, and the magnitude of the force wave
decreases with the load increasing. On the other hand, the
components of the force in the low frequency band of 0 Hz ~
300 Hz in each order become complicated with the load
increasing, and the amplitudes of the most force increase in
different degrees.
From the magnetic circuit theory, the amplitude of the
flux density is related to magnetic potential and permeability.
The magnetic potential is proportional to the excitation
current, and the permeability is inversely proportional to the
saturation coefficient of the magnetic circuit. As the material
magnetization curve is nonlinear, the saturation coefficient
changes exponentially with the motor stator current and rotor
current changing.
VIBRATION TEST OF THE MOTOR UNDER
DIFFERENT LOAD
In order to validate the correctness of the simulation
conclusion, a vibration test rig for motor under loads was
built.
When the motor is running, there will be some
fluctuation of the speed due to the tangential electromagnetic
force. When the motor is under load, the load fluctuation will
also affect the running speed. In order to minimize the impact
of the load fluctuation on the vibration of the motor, a
vibration test rig was built shown as Fig.6. From left to right
are the magnetic brake load, plum flexible coupling, torque
and speed measurement sensors, flange coupling and the
measured motor. The tri-direction-force transducers were
installed at the motor feet.
3
Copyright © 2017 ASME
Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 10/25/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use
Tab.2 Summary of the main transmission force under different
conditions (N)
Hz
50
400
In addition, the acceleration sensors were arranged
around the front bearing, rear bearing and the upper part of the
four force sensors (i.e., the four mounting feet of the motor) to
measure the vibration acceleration response of the motor.
1
1.5
2
2.5
3
3.5
4.0
0.2
2.6
0.1
2.4
0.2
2.3
0.4
2.1
0.7
1.6
1.3
0.9
2.9
0.7
7.6
SATURATION CONDITION
In addition to the electromagnetic force, the induction
motor vibration excitation includes the mechanical force of the
rotor and the fluid force of the fan. Therefore, the increase of
the load does not necessarily make the overall motor vibration
increase.
In order to study the effect of load on the overall motor
vibration with the saturated condition, the vertical vibration
response of each measuring point of the motor under different
loads were measured. In addition, the same motor was used to
drive the measured motor to obtain non-electromagnetic
response under the different loads. The vibration responses of
each measuring point are shown in Fig. 7 to Fig.9.
UNDER SATURATION CONDITION
Through a series of load tests, the mechanical
characteristics curve of the motor was gotten. Table 1 shows
the comparison of results between experiments and
simulation. The simulation results of each load case are very
close to the actual test results, so the measured forces can be
used to verify the conclusions of the simulation.
Tab. 1 Comparison of simulation and the measured speed
0
0.5
1
1.5
2
2.5
3
3.5
0.5
INFLUENCE OF LOAD ON MOTOR VIBRATION UNDER
INFLUENCE OF LOAD ON MOTOR VIBRATION FORCE
Speed (r/min)
Simulation
measured
1491
1490
1468
1474
1453
1448
1424
1425
1346
1394
1346
1355
1286
1309
1131
1237
0
The results in Table 2 are almost the same as the
simulation results, that is, when the load increases, the 50 Hz
electromagnetic force (i.e., the double frequency
electromagnetic force of the power supply) generated by the
fundamental magnetic field is reduced, while the 400 Hz
electromagnetic force generated by the harmonic magnetic
field increases. This verifies the correctness of the simulation
conclusion.
Fig.6 The vibration test rig for motor under loads
Load (Nm)
Nm
Error (%)
0.07
-0.41
0.35
-0.07
3.44
-0.66
-1.76
-8.57
Through a series of vibration tests under variable load,
each transmission force of the motor foot and the vibration
response of the measuring points were gotten. As the motor
slip will change the frequency of transmission force, each
frequency was conversed in order to facilitate comparison.
When the slip is small, it is provided that
ft ,
(5)
f =
(1 − s )
where f t is the measured frequency, and s is the measured
slip ratio.
The main transmission forces of each motor feet after the
frequency conversion are shown in Table 2.
Fig.7 Comparison of vibration responses of motor's front bearing
Fig.8 Comparison of vibration responses of motor's rear bearing
4
Copyright © 2017 ASME
Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 10/25/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use
Fig.9 Comparison of vibration response of motor's feet
Fig.12 The response curves of motor's feet at 50 Hz and 400 Hz
From Fig. 7 to Fig. 9, it can be seen that when the
induction motor load increases and the rotation speed
decreases, the vibration of the machine body caused by the
non-electromagnetic force decreases, while the vibration
caused by the integrated force basically keeps the same at first,
and then gradually increases. At the same time, the 50Hz and
400Hz electromagnetic excitation response curves of each
load are shown in Fig. 10 to Fig. 12, the main trend of which
is consistent with the simulation results.
It can be inferred that when the load of the induction
motor is less than the rated load, the overall vibration response
of the motor changes little with the increase of the load. It is
because that the non-electromagnetic force decreases and the
electromagnetic force increases little. When the motor load
exceeds the rated load and continues to increase, the
electromagnetic force in the middle and high frequency bands
increases obviously. It is affected by the saturation of the
magnetic circuit, which gradually takes the leading factor. It
makes the vibration response of the motor become larger.
CONCLUSIONS
In this paper, the T-shaped equivalent circuit was
combined with the induction motor running rule to study the
change mechanism of electromagnetic excitation under
different loads and saturation states. The simulation of
electromagnetic excitation force of induction motor with finite
element method was studied. By building up a motor load test
rig, the correctness of the simulation conclusion was verified
and the influence of the load on the vibration response of the
motor under saturated operating conditions was further
analyzed. Through the above study, the conclusions are as
follows:
1. The excitation current decreases but the fluctuation of
the saturation coefficient increases as the load increases.
Therefore, the electromagnetic force amplitudes of the low
frequency band such as twice the power frequency are reduced
but the electromagnetic force amplitudes of the middle and
high frequency bands are increased.
2. When the load of the induction motor is less than the
rated load, the non-electromagnetic force decreases and the
increment of the electromagnetic force is small as the load
increases, and thus the overall vibration response of the motor
changes little.
3. The high-frequency electromagnetic force amplitude
influenced by the saturation of the magnetic circuit will
increase obviously when the motor load exceeds the rated
load. It continues to increase and will gradually become the
major factor which resulting in motor vibration response
increasing.
Fig.10 The response curves of motor's front bearing at 50 Hz and 400
Hz
Fig.11 The response curves of motor's rear bearing at 50 Hz and 400
Hz
5
Copyright © 2017 ASME
Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 10/25/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use
[3] Moreira J C,Lipo T A. Modeling of Saturated AC Machines
IncludingAir Gap Flux Harmonic Components [J]. Industry
Applications,IEEE Transactions on,1992,28(2): 343-349.
[4] Liang X,Luy Y. Harmonic Analysis for Induction Motors
[C] . Electrical and Computer Engineering , Canadian
Conference on. IEEE,2006: 172-177.
[5] CHEN Shi-kun. Motor Design [M]. Second Edition. Beijing:
Mechanical Industry Press, 2000: 35-39.
.
REFERENCES
[1] DU Xiao-fei,GUO Nong-sheng,ZHOU Yuan-jun. Simulation
Analysis on Magnetic Saturation of Induction Machine [J].
Micromotors, 2014,(47)9: 1-4.
[2] Donescu V , Charette A , Yao Z , et al. Modeling and
Simulation of Saturated Induction Motors in Phase Quantities
[J]. Energy Conversion,IEEE Transactions on,1999,
14(3): 386-393.
.
6
Copyright © 2017 ASME
Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 10/25/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use
Документ
Категория
Без категории
Просмотров
0
Размер файла
1 136 Кб
Теги
icone25, 66807
1/--страниц
Пожаловаться на содержимое документа