Download PNIMNiPE_nr63 - Instytut Maszyn, Napędów i Pomiarów

Nr 63
Prace Naukowe Instytutu Maszyn, Napędów i Pomiarów Elektrycznych
Politechniki Wrocławskiej
Nr 63
Studia i Materiały
Nr 29
2009
Terms—FEM calculation, magnetic stress,
natural vibration, synchronous motor
Janusz BIALIK Jan ZAWILAK
VIBRATION MODELING OF THE TWO-SPEED, LARGE
POWER, SYNCHRONOUS MOTOR
In this paper the calculation results of a two –speed synchronous, silent pole, large power motor, are presented. Using the FEM tools, the two dimensional, field circuit model (for electromagnetic calculation) and two- and three-dimensional mechanical models, for the large power motor, type
GAe 1510/12p were examined. The simulations, for load, for both rotational speeds, were conducted.
The target of application of discussed analysis is the vibration behavior of the machine.
1. NOMENCLATURE
Bn(τ) – radial component of the flux density [T]
Bτ(τ) – tangential component of the flux density [T]
Tnn(τ) – radial component of the magnetic stress [Pa]
Tnτ(τ) – tangential component of the magnetic stress [Pa]
μ0 – absolute permeability [H/m]
2. INTRODUCTION
To assure high efficiency and reliability of electrical machines nowadays the use of
modern FEM tools is required. In term to model precisely the different states of work of
rotating machines, the electromagnetic field equation, the circuit equation and the motion equation have to be simultaneously solved [7]. This possibility has the field–circuit
methods together with moving of the rotating elements. These methods can be used in
__________

ALSTOM Power Sp. z o.o. Wrocław, Fabryczna 10, [email protected]
Politechnika Wrocławska, Instytut Maszyn, Napędów i Pomiarów Elektrycznych, 50-372 Wrocław
ul. Smoluchowskiego 19, [email protected]

2
design phase of electrical machines and to analyses phenomenon in existing machines as
well (calculation of magnetic noise, vibration, heating, etc.). Finite element modeling
FEM can be done in 2D or 3D space. More accurate are the three–dimensional models.
But creating the models in 3D space and its calculation takes much time. Such modeling
is very difficult with complicated structures and shapes of modeled devices. Therefore
three–dimensional analysis is used usually to model only a piece of symmetrical machines. In no symmetrical machines more practical are 2D models [1].
Examples of such no symmetrical machines are two speed synchronous large power
motors. These motors were built by replacing the stator and the rotor winding with
switchable windings. By switching the windings, two different numbers of pairs of
magnetic pole are obtained. Thus two rotating speeds are obtained. These types of motors have been successfully worked for several years to drive main fans in coal and copper mines of the exhaust system [2].
In this paper calculation results of the two–speed synchronous motor type
GAe1510/12p are presented. This motor has two different speeds: n=500 rpm (p=12)
and n=600 rpm (p=10) and corresponding nominal powers P= 600kW and 1050 kW.
Determination of magnetic radial forces acting in mentioned motor together with its
natural frequencies is the goal of this paper.
3. MAGNETIC CALCULATION
Rated data of the modeled motor type GAe1510/12p is introduced in Table 1.
Table 1. Rated parameters of the motor
Nominal power
Pn
kW
600/1050
Nominal voltage
Un
V
6000
Phase connection
–
–
Y / YY
Nominal current
In
A
86 / 121
Field voltage
Ufn
V
51 / 70
Field current
Ifn
A
175 / 240
Nominal speed
Power factor
Efficiency
nn
rpm
500 / 600
cosn
–
0,8 lag / 0,9 lead
n
%
80,0 / 94,2
This motor has double layer stator winding placed in 108 slots, field winding and the
damper circuit, allocated in 10 pole shoes.
Field part of the model takes into account non-linear characteristics of the magnetic
part of the motor and the motion of the rotor. Circuit part takes into consideration the
3
electrical parameters of the source, damper circuit and switchable armature and field
windings. In elaborated 2D model an assumption of constant parameters of the end parts
of all windings, which is of stator, rotor and damper circuit is done. Values of the reactance and resistances of the end parts are calculated according to the well-known equations [4, 5]. To change the circular flux of the armature and field windings, which qualify speed variation of the rotating field, the direction of the stator and rotor currents in
right section of the windings must be changed [3].
In term to calculate the electromagnetic forces, the distribution of the radial (normal)
component of the flux density in the air-gap of the motor, is determined. An example of
such distribution, valid for one time moment, is presented in the Fig. 2. To picture clarity the flux distribution is shown only for the half of the machine circumference.
1,2
n=600
Flux density
Bn [T]
n=500
0,8
0,4
0
-0,4
-0,8
-1,2
0
60
120
Angle [deg] 180
Fig. 2. Distribution of the radial component of the
flux density in air-gap for both rotational speeds at
rated load (the half of machine circumference
only)
Fig. 1. Numerical model of analyzed motor (part
with mesh)
Maxell Stress Tensor components in air-gap, in 2D calculations, in cylindrical coordinate system, can be calculated from the well know equations:
1
T   
nn
2

0
T   
B  B  
n

 n
0
1

B 2    B 2  
n

(1)
In the figure 3 are presented instantaneous distribution of the radial component of
magnetic stress in the air gap, valid for the rated load of motor. In addition, in Figure 3
are demonstrated the tangential component of the magnetic stress. The 2D DFT method
is used for the conversion of time-space domain into modal-frequency domain. Results
of such approach are presented in figure 4.
2
a).
b).
800
n=600
Radial
magnetic
stress Tnn
[kPa]
600
400
200
400
0
200
-200
0
0
120 Angle [deg] 180
60
n=600
Tangential
magnetic
stress Tnt
[kPa]
n=500
n=500
-400
0
120 Angle [deg] 180
60
Fig. 3. Distribution of magnetic stress components in the air-gap for both rotational speeds (the half of
machine circumference only), a) radial component at rated load, b) tangential component at rated load
Radial
Radial
stress Tnn
[kPa]
600
stress Tnn
[kPa]
600
400
400
200
200
0
0
0
10
0
20
10
Time order
30
20 40
Space order
0
10
0
20
10
Time order
30
Space order
20 40
Fig. 4. Modal-frequency spectrum of the magnetic stress (radial component) in the air-gap: a) for higher
speed 600 rpm, b) for lower speed 500 rpm
4. NATURAL FREQUENCY ANALYSIS
Natural frequency analysis is done using 2D and 3D models, which are mutually
combined [6]:
2
• the real slotting geometry of the stator iron is analyzed within 2D mechanical
model. Results of such model are the base for determination equivalent cylindrical structure of the stator core,
• that equivalent structure is introduced later into 3D model together with the geometry of the housing.
The two dimensional model of stator take into account the mechanical properties of
the winding. The outline of the 2D mechanical model is presented in Fig. 5. The results
of the 2D model are the input data for the equivalent 3D stator core structure. Such approach is forced by the computer facilities and very complicated motor’s structure. The
2D model has about 70000 DOFs, what is equivalent to the few hours of computation
time. In 3D this numbers of the DOFs of stator core will exceed value 1000000 (450 mm
axial length of the stator iron). Adding about 500000 DOFs of the stator housing one
will give numbers of equation which will be solved more that 24 hours.
a).
b).
Fig. 5. 2D model of the synchronous motor, a) outlook; b) part of the model with the mesh
The criterion of the equivalent cylinder to the real stator core model is the identity of
the natural frequency of such structures.
core (part of model with mesh)
Fig. 6. 2D simplified model of the stator
2
Table 2. Main properties of two 2d
mechanical models of the synchronous
motor
Full model
Outer diameter
Yoke height
mm
mm
1450
150
Young modulus
Poisson ratio
Density
2,1 105
0,29
7850
MPa
kg/m3
2,1 105
0,29
13650
Simplified
model
1450
75
The cylindrical model (Fig. 6) allows reducing numbers of equation more that 10
times. Table 2 shows parameters of the full 2D and simplified 2D model and Table 3
shows the results of the simplified structure (model).
Table 3. Results of the two mechanical models
f [Hz]
Full model
1344
1383
1492
1617
Simplified model
1312
1347
1445
1549
Full model
1702
1891
2001
2099
Simplified model
1677
1808
1970
2142
Comparisons between the space natural forms of both models are shown in Fig. 7.
The simplified model has 1000 DOFs.
a).
b).
Fig. 7. Example of a natural space mode for full 2D model (a) and simplified 2D model (b) for r=6
The full 3D finite element model of a two-speed synchronous motor is made of solid
elements and the total numerical size of the model is about 1000000 DOFs. The Fig. 8
shows the outer view of the model and of finite element mesh.
a).
2
b).
Fig. 8. View (a) and the mesh (b) of the full 3D model of synchronous motor (part of the model is removed to picture clarity)
The longitudinal ribs, screws etc. cause a very rich spectrum of natural frequencies
of a presented structure. Table 4 shows the results of the natural vibration analysis of the
examined synchronous motor. Only first 46 results are shown in this table. This shows
how the structure of the motor is weak.
Table 4. Results of the natural frequency of the full 3D model of the synchronous motor
1
2
3
4
5
6
7
8
9
10
29
33
34
38
39
40
41
42
45
46
f [Hz]
62,4
95,6
129,4
147,8
152,8
205,9
215,4
264,8
302,4
358,2
f [Hz]
841,0
871,1
902,9
913,7
918,9
927,4
932,9
935,0
956,1
969,1
11
12
13
14
15
16
17
20
21
26
f [Hz]
411,9
462,9
568,4
613,7
677,9
684,8
693,7
705,9
760,7
791,2
2
Examples of natural modes of examined motor are shown in the Fig. 9-11. Arrows in
this figures shows the movement of the structure.
5. CONCLUSIONS
Elaborated and described model of the two speed synchronous motor type GAe151012p allows to determine the static and the transient characteristic as well. Presented
model is useful to analyses the electromagnetic and mechanical phenomenon in two
speed synchronous, silent pole motors. The first results of a natural vibration analysis
shows, that the structure of stator frame of examined motor is very sensitive to the stator
iron core vibration – below 1 kHz can be found more that 50 natural modes.
Fig. 9. Example of natural mode (f=62.4 Hz)
Fig. 10. Example of natural mode (f=147.8 Hz)
Fig. 11. Example of natural mode (f=205.9 Hz)
2
REFERENCES
[1] ANTAL L., ZAWILAK J., Torque of the two speed synchronous motors with switchable armature
and field windings, XLI International Symposium on Electrical Machines, SME 2003, Gdańsk Jurata, June 9 11, 2003, pp. 104, (in Polish)
[2] ANTAL L., ZAWILAK J., ZAWILAK T., Testing of a Two-speed Synchronous Motor, XVI International Conference on Electrical Machines ICEM’2004 Cracow, September 5-8, 2004, pp.793-799
[3] BIALIK J., ZAWILAK J., Vibrations and electromagnetic forces in two speed, large power synchronous motors, XLI International Symposium on Electrical Machines, SME 2003, Gdańsk Jurata,
June 9 11, 2003, pp. 10 (in Polish)
[4] DUBICKI B., Electrical machines, part III, Warszawa, PWN, 1964. (in Polish)
[5] SERGEEV P. S., VINOGRADOV N. V., GORJANOV F. A., Projektirovanie Električeskich Mašin,
Energija, Moskva 1969 (in Russish)
[6] WITCZAK P., KACPERSKI M., Vibration modeling of a large power induction motor, Scientific
Papers of Technical University of Lodz, no. 965, 2005
[7] ZHOU P., STANTON R. S., and CENDES Z. J., Dynamic modeling of electrical machines,
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