Optimal-Airgap Control of a Linear Induction Motor for Korean Railway Transit
1
H.-W. Lee, 1C. Park, 2K.-H. Han, 1B. Lee, 1S.-Y. Kwon and 1H.-J. Park
Korea Railroad Research Institute, Uiwang, Korea1; Dongguk University, Seoul, Korea2
Abstract
There have been many researches to develop linear induction motors for railway systems for last
three decades. However, most of them are regarding design of the primary or secondary reaction
plate to increase the performance of the system. Control of the airgap length has been a tough topic
because of lack of technology, expensive construction cost, and so on. In this research, the optimum
airgap length of a linear induction motor used for Korean railway transit has been derived by using an
analytical method and verified by simulations. Moreover, feasibility of the optimum airgap control
which is incorporated with actuators has been done.
Introduction
As demands for cost-effective, less susceptible to weather, and reliable means of public transportation
have increased, Korean government has taken into account the linear railway system since the late
twenty century. The linear railway system is called the non-adhesion drive system, where as
conventional railway system is called the adhesion drive system which gets the propulsion force from
the friction between wheel and rail (wheel-on-rail type). The non-adhesion drive system has lots of
advantages over the adhesion derive system as follows; (1)Excellent acceleration and deceleration,
(2)Capability of climbing steep gradients, (3)Lower construction cost due to the small tunnel crosssection, (4)Enable flexible route planning(travel through sharp curves), (5)Less susceptibility to
weather conditions, (6)Quiet and smooth running(No mechanical couplings), (7)Less maintenance
cost. Consequently, the linear railway transit is already in use in all over the world and continuously
being extended.
Linear railway system gets the propulsion force from a linear motor different from a conventional
rotary motor and it produce thrust force electromagnetically without any contact. Therefore, it does not
use any mechanical coupling for the rectilinear movement. Figure 1 shows the concept of a linear
motor derived from a rotary motor. A linear motor is a conventional rotary motor whose stator, rotor
and windings have been cut open, flattened, and placed on the guideway.
Among many kinds of linear motors, linear induction motor(LIM) is prefer for the urban railway
transportation system because the construction cost is much cheaper than linear synchronous
motor(LSM), even though the efficiency and performance is little bit poor. The operating principle of a
LIM is identical to a rotary induction motor. Space-time variant magnetic fields are generated by the
primary part across the airgap and induce the electromotive force (EMF) in the secondary part, a
conducting sheet. This EMF generates the eddy currents, which interact with the airgap flux and so
produce the thrust force known as Lorenz’s force.
There are two types of LIM as follows; (1) Short primary type (SP): stator coils are on board and
conducting sheets are on the guideway, (2) Long primary type (LP): stator coils are on the guideway
and conducting sheets are on board. For the LP type, construction cost is much higher than SP type
but it does not need any current collector for operation. In high speeds, the LP type is usually used
because transfer of energy using a current collector is difficult. On the other hand, the SP type is very
easy to lay conducting sheets on the guideway and thereby reducing construction costs. However, the
SP type has low energy efficiency because of the drag force and leakage inductance caused from the
end effect. In general, the SP type LIM is applied for the low-medium speed urban lightweight
transit[1]. Figure 2 represents the configuration of a SP type linear induction motor.
Even though the operating principle is exactly the same as a rotary motor, the linear motor has a finite
length of the primary or secondary parts and it causes static and dynamic end-effect which is the
discontinuous airgap flux phenomenon. This end-effect causes the deterioration of the system
performance, especially in high-speed operation. Another problem is that construction tolerance
restricts the minimum airgap in order to prevent a collision between the primary part and the
secondary reaction plate. Moreover, as the airgap length is getting smaller, the attraction force
between the primary and secondary parts is getting larger dramatically and the attraction force would
be another friction against propulsion. Therefore, large airgap is inevitable. However, this large airgap
is one of the biggest problems in the system efficiency.
Figure 1: Concept of a linear motor from a rotary motor [2].
Figure 2: Configuration of a SP type linear induction motor.
Optimum airgap
The large airgap(around 9 ~ 15 mm) increases the reluctance and leakage flux of the magnetic circuit,
and decreases the magnetizing inductance as shown in Fig. 3. Consequently, much more excitation
current is required. The increased excitation current results in significant decrease of power factor and
efficiency. Therefore, it is necessary to figure out the optimum airgap length and develop a control unit
such as a rapid sensing unit, interface algorithm, and an airgap controller in order to control the airgap
length, consequently accomplish the high-efficiency system and energy savings.
Figure 3: Magnetizing inductance according to variation of the airgap length.
Typical variation of the normal force and thrust force of a LIM can be derived as in (1) and (2), based
on [3].
Fnormal ( g ) = 4.52 + 114e
(−
g
)
1.334
Fthrust ( g ) = 9.15 + 109.8e
(−
+ 82e
g
)
5.81
(−
g
)
8.58
+ 14.6e
(−
− 0.45e
g
)
0.163
(−
g
2.18e151
+ 9.66e
(−
)
(1)
g
1.06 e143
)
(2)
Where g is an airgap length.
The novel function H(g) is derived to figure out the optimum airgap length which maximizes the thrust
force and minimizes the normal force.
H (g) =
Fthrust ( g )
Fnormal ( g )
(3)
Figure 4 shows each force and H(g) function according to variation of the airgap length. From the
figure, the thrust force is getting smaller with the airgap increase and the H(g) is small below 5[mm]
that is, the attraction force is relatively big to the thrust force. And above 11[mm], the thrust force is
too small even though the H(g) is little bit increased. Therefore, the optimum airgap length is around
5[mm].
45000
2.0
40000
1.8
1.6
Attraction Force
1.4
30000
1.2
25000
H(g)
Thrust Force
20000
1.0
H(g)
Force [kgf]
35000
0.8
15000
0.6
10000
0.4
5000
0.2
0
0.0
0
1
2
3
4
5
6
7
8
9
10
11
12
13
Airgap [mm]
Figure 4: Each force and H(g) of a SP type linear induction motor.
Simulation results
For simulation of the airgap control, a LIM is designed based on the W-3 full weight of 33[ton] and the
weight of the designed LIM itself is about 700[kg]. Figure 5 shows the model for the airgap control and
Figure 6 shows the currents in each case of airgap 5[mm] and 12[mm]. In the same load condition,
the shorter airgap length, the smaller transient and steady state currents. In addition, the time
required to reach the steady state is also short in case of 5[mm].
Figure 5: Simulation model for the airgap control.
Figure 6: Currents in both 5[mm] and 12[mm] of airgap length.
Figure 7 shows simulation results of the airgap control. In the simulation, spring coefficient and
damping coefficient are set to be 30[N/mm] and 1[N/mm/sec]. In an urban train, the actuator must
operate for 3[mm] within 0.1[sec] after sensing the airgap length and the result shows that the airgap
control works well.
Figure 7: Actuator force of 300[N] and airgap variation from 591[mm] to 594[mm].
Conlcusion
This paper has presented the characteristic of an airgap control for linear induction motor used for
Korean urban railway propulsion system. The airgap between the primary and secondary reaction
plate is very important and should be optimized for high-performance. Therefore, the optimum airgap
length has been derived by using an analytical method. From the simulation, the effect of the airgap to
the currents and feasibility of the airgap control by using actuators and spring has been verified. The
experimental verification remains as a future work.
References
[1]
[2]
[3]
[4]
Hyung-Woo Lee, Ki-Chan Kim and Ju Lee, ”Review of maglev train technologies”, IEEE Trans.
On Magnetics, Vol. 42, No. 7, pp 1917-1925, (2006).
Korea Railroad Research Institute, ”Linear Electric Railway System”, pp 1-8, (2007).
I. Boldea and S. A. Nasar, ”Linear motion electromagnetic devices”, New York: Taylor & Francis,
(2001).
Sakae Yamamura, ”Theory of linear induction motors”, Tokyo: University of Tokyo Press, (1978).