Recent Developments of Electrical Drives - Part 30 docx

II-12. Field-Circuit Finite Elements Models 283
0
0,2
0,4
0,6
0,8
1
1,2
0 0,02 0,04 0,06 0,08 0,1 0,12 0,14
current [A]
calculated A1e
s1t
+ A2e
s2t
A1e
s1t
A2e
s2t
measured
time [s]
Figure 16. Decomposition of measured current curve vs. time into exponential components for DC
voltage 23.82 V.
0
0,2
0,4
0,6
0,8
1
1,2
1,4
1,6

1,8
0 0,04 0,08 0,12 0,16 0,2 0,24
current [A]
calculated A1e
s1t
+ A2e
s2t
A1e
s1t
A2e
s2t
measured
time [s]
Figure 17. Decomposition of measured current curve vs. time into exponential components for DC
voltage 32.49 V.
0
1
2
3
4
5
6
7
8
0 0,03 0,06 0,09 0,12 0,15 0,18
time [s]
measured
polynomial
A2e
s2t

calculated polynomial + A2e
s2t
current [A]
Figure 18. Decomposition of measured current curve vs. time into exponential components for DC
voltage 138 V.
284 Kom
˛
eza et al.
Table 3. Values of solution coefficients obtained from measured curves
DC supply Steady-state
U
s
(V) current (A) A
1
(A) A
1
/U
s
() −s
1
(1/s) A
2
(A) A
2
/U
s
() −s
2
(1/s)
13.41 0.58 0.18 0.0134 18.3 0.4481 0.0334 335.9

23.31 1.01 0.34 0.0146 22.4 0.7883 0.0338 385.3
32.49 1.48 0.515 0.0159 13.3 1.1 0.0339 341.2
138.01 6.18 4.8 0.0348 422.0
In Fig. 21 the relative permeability curves vs. time is shown: a—average for both stator
and rotor core, b—average for one tooth pitch. The average value changes significantly and
the permeability distribution is also different.
The second important reason for the observed effect is a very well known skin effect in
the rotor bars.
As can be expected the current density distribution in the rotor bar changes consider-
ably during the time (Fig. 22). The resulting value of equivalent rotor bar resistance and
inductance changes too (Figs. 23–25).
It should be emphasized that all described changes occur during the initial period when
the stator current is compensated by rotor current. The main flux and magnetizing current
do not grow as they occur in the final period when stator current goes to a constant value
Figure 19. Relative permeability for time 0.005 s.
II-12. Field-Circuit Finite Elements Models 285
Figure 20. Relative permeability for time 0.01 s.
and rotor current disappears. According to these results, it should be clear why constant
parameter equivalent circuits, sometimes used especially by Matlab Simulink users, are
not usable for transient simulation of induction machines. Therefore noticeable growth of
scientific reports according to adjustable parameters can be observed.
0
20000
40000
60000
80000
100000
120000
0 0,002 0,004 0,006 0,008 0,01
time [s]

b
a
relative permeability
Figure 21. The relative permeability curves vs. time. (a) Average for both stator and rotor core. (b)
Average for one tooth pitch.
286 Kom
˛
eza et al.
0,0E+0
4,0E+6
8,0E+6
1,2E+7
1,6E+7
2,0E+7
0 0,002 0,004 0,006 0,008 0,01 0,012
0,01
0,005
0,004
0,003
0,002
0,001
0,0001
current density [A/m
2
]
height [m]
0,0005
Figure 22. Current density distributions vs. bar height at different time instants for DC voltage equal
138 V.
0,0E+0

5,0E-5
1,0E-4
1,5E-4
2,0E-4
2,5E-4
3,0E-4
0 0,002 0,004 0,006 0,008 0,01
resistance [
Ω]
time [s]
Figure 23. Equivalent resistance of the rotor bar vs. time.
0,0E+0
1,0E-7
2,0E-7
3,0E-7
4,0E-7
5,0E-7
6,0E-7
0 0,002 0,004 0,006 0,008 0,01
inductance [H]
time [s]
Figure 24. Equivalent inductance of the rotor bar vs. time.
II-12. Field-Circuit Finite Elements Models 287
0
100
200
300
400
500
600

700
0 0,02 0,04 0,06 0,08
time [s]
bar current [A]
Figure 25. Rotor bar current vs. time for DC supply voltage 138 V.
Starting test with sinusoidal supplying voltages
The examination of the motor characteristics during starting is the most important method
for comparisonofthe field-circuitdynamic model ofthe motor withthe measurements. This
test makes possible to compare all electromechanical quantities with the measurement.
The solution of the mechanical transient equation due to moment of inertia value is not
very sensible to torque higher frequency components. Therefore the speed vs. time curves,
calculated using different methods, are very similar to the measuredone. A similar situation
can be observed for the current because of a significant value of magnetization current and
the stator windings impedance. The most important is of course the torque characteristic
vs. time (Figs. 26–28).
Conclusion
The presented paper has shown methods that can be used to verify the validity of the created
field-circuit model for simulating transients occurring during the starting of the induction
-100
100
300
500
700
900
1100
1300
1500
1700
0 0,02 0,04 0,06 0,08 0,1 0,12
time [s]

measured
calculated
rotor speed [rpm]
Figure 26. Rotor speed vs. time during starting.
288 Kom
˛
eza et al.
-8
-6
-4
-2
0
2
4
6
8
10
0 0,04 0,06 0,08 0,1
0,12
current [A]
time [s]
measured

calculated
0,02
Figure 27. Current vs. time during starting.
-2
0
2
4

6
8
10
12
0
0,02 0,04 0,06 0,08 0,1 0,12
t s
calculated
measured
time [s]
torque [Nm]
Figure 28. Torque vs. time during starting.
motor feed from an inverter. After verification this model can be successfully used for the
analysis and optimization of the induction motor feed from an inverter.
References
[1] M. Dems, K. Kom
˛
eza, “Circuit and Field-Circuit Analysis of Induction Motor with Power
Controller Supply”, International XIII Symposium Microdrives and Servomotors, MIS’2002,
Krasiczyn, Poland, September 15–19, 2002, Tom II, Vol. 2, pp. 453–458.
[2] M. Dems, K. Kom
˛
eza, Electromechanical transient processes of the induction motor with
power controller supply, Electromotion, Vol. 10, No. 1, pp. 19–25, 2003.
[3] M. Dems,K. Kom
˛
eza, “Simulationsof ElectromagneticField Distribution in anInduction Mo-
tor withPower Controller Supply”, Proceedingsof theXXII InternationalAutumn Colloquium
ASIS 2000.
[4] K. Kom

˛
eza, M. Dems, “The Comparison of the Starting Characteristics of an Induction Motor
for Frequency and Soft Starter Starting”, Proceedings of the 8thPortuguese-Spanish Congress
on Electrical Engineering, Portugal, July 3–5, 2003.
II-12. Field-Circuit Finite Elements Models 289
[5] M. Dems, K. Kom
˛
eza, “A Comparison of Circuit and Field-Circuit Models of Electromechan-
ical Transient Processes of the Induction Motor with Power Controller Supply”, Proceedings
COMPUMAG’2001, Lyon-Evian, France, July 2–5, 2001, pp. 206–207.
[6] PC OPERA-2D—version 10.5,Software forElectromagneticDesign from VECTORFIELDS,
2005.
[7] S. Wiak,K. Kom
˛
eza, M. Dems,“Electromagnetic Fieldand Parameters Modelling ofInduction
Motors by Means of FEM”, Proceedings 32 Spring. International Conference MOSIS’98,
Ostrava, Czech Republic, May 5–7, 1998, Vol. 3, pp. 275–281.
[8] M. Dems, K. Kom
˛
eza, Influence of mathematical model simplifications on dynamic calcula-
tions ofinduction motors,Zeszyty Naukowe Politechniki L
 ´odzkiej, Elektryka, wrzesie´n, L ´od´z,
2005.
[9] M. Dems, J. Zadro˙zny, J. Zadro˙zny Jr., “Comparison of Simulation Methods of Small Induc-
tion Motor Electromechanical Transients”, International XII Symposium Micromachines and
Servodrives, MIS’2000, Kamie´n
´
Sl
c
aski, Poland, September, 2000.

[10] K. Kom
˛
eza, M. Dems, S. Wiak, Analysis of the influence of the assumption of equivalent
saturation on starting currents in induction motor, COMPEL Int. J. Comput. Math. Electr.
Electron. Eng., Vol. 19, No. 2, pp. 463–468, 2000.
III-1.1. DESIGN AND MANUFACTURING
OF STEEL-CORED PERMANENT
MAGNET LINEAR SYNCHRONOUS
MOTOR FOR LARGE THRUST
FORCE AND HIGH SPEED
Ho-Yong Choi
1
, Sang-Yong Jung
2
and Hyun-Kyo Jung
1
1
Electromechanics Labratory, School of Electrical Engineering, Seoul National University, Korea
Shillim-Dong, Kwanak-Gu, Seoul, Korea
2
Namyang R&D Center, Hyundai Motor Company, Hwasung-Si, Kyunggi-Do 445-706, Korea

Abstract. Design characteristics of steel-cored PMLSM (Permanent Magnet Linear Synchronous
Motor) are presented. Particularly, dynamic constraints resulted from repeated short-stroke travel are
applied to the design criteria determining the machine specification. In addition, distinctive unde-
sirable feature of detent force in steel-cored PMLSM and its notable minimizing methods based on
manufacturing feasibility are considered. The designed machine is manufactured and tested for the
verification.
Introduction
In thesedays, linearmachine is widely usedin industrial fieldbecause of itsbetter character-

istics,such ashighaccelerationandspeed,largethrustforce,andsoon.Torealizesufficiently
large thrust force and power density, steel-cored permanent magnet linear synchronous mo-
tor is superior to air-cored motor. However, steel-cored motor has some demerits such as
large normal force and force ripples caused by the high detent force. The normal force
problem can be overcome by the LM (Linear-Motion) guide or the bearing system and the
detent force reduction method should be considered during the machine design procedure.
The magnetic saturation from large operation currents for the high speed operation can be
a problem and proper steel-core design is also required [1,2].
Many linear applications require high acceleration and velocity with the short-stroke
movement. In such applications, general design strategies considering the steady-state con-
dition are not agreeable because linear motor operates mostly under the accelerating or
decelerating circumstances on short travel displacements [3]. In addition, since the servo-
capability responding to various motional profiles is recently regarded to be necessary,
new plans considering dynamic constraints under the maximum input voltage and current
should be made for better efficiency in machine sizing. Generally, capability of steel-cored
S. Wiak, M. Dems, K. Kom
˛
eza (eds.), Recent Developments of Electrical Drives, 295–306.
C

2006 Springer.
296 Choi et al.
PMLSM is defined by maximum input voltage and current, which expresses the maximum
thrust force accordingto thespecified mover velocity [4].Thiscapability, directly connected
to a motor size, must be at least larger than the required motional profiles. Accordingly, dy-
namic constraints can be induced from arelation between such different dynamic capability
and required motional profiles under the limited input voltage and current. These dynamic
constraints express the admissible design range from which the design variables meeting
the required trajectory can be obtained after all [5–7].
In this paper, steel-cored permanent magnet linear synchronous motor for large thrust

force and high speed operation is designed and tested. The required maximum thrust force
of the motor is 15,000 N and the maximum speed is 4 m/s. The continuous thrust force is
3,000 N under input voltage of 220 V and maximum peak current of 300 A. Finite element
analysisis appliedin themachine designprocedure andsome optimizationmethod isusedto
minimize the detent force problem. The machine is manufactured and tested forverification
of the designed model’s validity.
Design of steel-cored PMLSM
Steel-cored PMLSM
Fig. 1 shows the moving-coil type steel-cored PMLSM with the magnetic combination of
four poles and three coils which shows better operation in control. Self-bonded wires are
much convenient to be attached to the core simply with a voltage of 5 to 6 V or thermal
heating. Hall-sensors and incremental encoders are used for feedback control system, and
Cable-Veyor, LM guide, and Shock-Absorber must be equipped. In addition, steel-cored
Figure 1. Steel-cored PMLSM (moving coils, four poles + three coils).
III-1.1. Design and Manufacturing of Steel-Cored PMLSM 297
PMLSM has been much advanced from coreless one, and getting widely used mainly due
to its large force productivity.
Capability and required motional profile
PMLSM with limited input voltage (V
max
) and current (I
max
) has dynamic capability as
follows, which is induced with commands as i
d
= 0 (force maximization).
F
e,max
=
3

2
K
e
min

C
1
+
√
C
2
−C
3
R
2
s
+ (π/τ)
2
L
2
s
v
2
, I
max

, (1)
where,
C
1

≡−R
s

K
e
v +

2L
s
3K
e

m
da
dt
+ Ba

,
C
2
≡


π
τ

2
L
2
s

v
2
+ R
2
s

V
2
max
,
C
3
≡

π
τ

2
L
2
s
v
2

K
e
v +

2L
s

3K
e

m
da
dt
+ Ba

2
,
τ :Pole pitch [m], K
e
: EMF constant [V/(m/sec)]
R
s
:Resistance [], L
s
: Synchronous Inductance [H]
Equation (1) indicates the maximum thrust force at specified velocity under the max-
imum input voltage and current, and also includes the time-varying component, such as
acceleration (a) and jerk (J = da/dt), available in dynamic analysis. Proposed dynamic
capability has more meaning in linear machine than the conventional static capability under
the acceleration and jerk set to be zero, which has been conventional approaches to the
design process until now.
In Fig. 2, motional profiles of trapezoidal acceleration mode, most common in actual
operation, andits relevantForce-Speed curveare shown. Force-Speed characteristics, which
are obtained at each time interval, can be summarized as follows.
F
e
(v) =

⎧
⎪
⎪
⎪
⎪
⎨
⎪
⎪
⎪
⎪
⎩
m

2a
max
t
1
v + Bv + F
l
(0 <v≤ v
1
)
ma
max
+ Bv + F
l
(v
1
<v≤ v
2

)
m

2a
max
(v
max
− v)
t
1
+ Bv + F
l
(v
2
<v≤ v
max
)
(2)
where, v
1
= (a
max
/2)t
1
,v
2
= a
max
(t
1

/2 + t
2
)
Figure 2. Motional profiles of trapezoidal acceleration and Force-Speed curve.