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Proceedings of the 2008 International Conference on Electrical Machines Paper ID 1083
978-1-4244-1736-0/08/$25.00 ©2008 IEEE 1
Linear Eddy Current Brake for Railway Vehicles Using Dynamic Braking
*Yasuaki Sakamoto, *Takayuki Kashiwagi, *Takashi Sasakawa, **Nobuo Fujii, Member IEEE
*Electromagnetic Applications Laboratory, Railway Technical Research Institute
2-8-38, Hikari-cho, Kokubunji, Tokyo, 185-8540, Japan Tel: (+81)-42-573-7299, Fax: (+81)-42-573-7300, e-mail: [email protected]
** Dept. of Electrical and Electronic Systems Engineering, Kyushu University
744, Motooka, Nishi-ku, Fukuoka, 819-0395, Japan Tel: (+81)-92-802-3694, Fax: (+81)-92-802-3694, e-mail: [email protected]
Abstract-One type of braking system for railway vehicles is the
eddy current brake. Because this type of brake has the problem of rail heating, it has not been put to practical use in Japan. Therefore we proposed using a linear induction motor (LIM) for dynamic braking in eddy current brake systems. It reduces rail heating and uses an inverter for the self-excitation function. In this paper, we estimated the performance of an LIM from experimental results of a fundamental test machine and confirmed that the LIM under constant current excitation has an approximately constant braking force regardless of frequency for relatively low frequencies, and the reduction ratio of rail heating is approximately proportional to the frequency. These characteristics are convenient for the realization of the LIM rail brake system.
I. INTRODUCTION
One type of braking system for railway vehicles is the eddy current brake. It generates braking force by inducing eddy current in the rails while the vehicle runs. Using the electromagnetic force between the bogie and rails, the eddy current brake has the advantage of stable braking force that does not depend on the adhesion between the wheels and rails. But the eddy current brake cannot avoid rail heating because the braking principle is based on converting the kinetic energy of the vehicles into eddy current loss in the rails. The possibility of rail temperature rise affecting buckling stability is one of the reasons why eddy current brakes have not been put to practical use in Japan.
Therefore we proposed a method that reduces rail heating and are investigating it [1]. The technique of reducing rail heating converts a portion of the kinetic energy, which should be consumed while braking, into electric power, using dynamic braking by applying a linear induction motor (LIM) to the excitation poles of the eddy current brake. There are some references on such a LIM with a rail as the secondary (for example [2]), but there are no thorough investigations that focused on dynamic braking. This paper reports on characteristics of the LIM rail brake.
II. CONCEPT
The proposed LIM rail brake is mounted on to the bogie as shown in Fig. 1. To install the armature in the limited space
between the wheels similar to a conventional eddy current brake, it is assumed that the armature length is about 1.2 m in the narrow gauge lines of Japan. The overhang of the armature coil in the lateral direction must be within the limits of the rolling stock gauge of the vehicles.
The advantages of applying the LIM using dynamic braking to the eddy current brake system are:
1) For the same braking force, the LIM rail brake does not raise the rail temperature as much as a conventional eddy current brake.
2) Since the generated electric power can be allotted to the armature copper loss, an on-board energy source becomes unnecessary to maintain excitation of the LIM. The former is a clear solution to a problem with the conventional eddy current brake, and the latter is an advantage to the eddy current brake system itself. Since the LIM with a rail as the secondary is low in efficiency, it is accompanied by a large excitation loss to generate the prescribed braking force. However, because the generated electric power which should be consumed for vehicle braking can be allotted to the armature copper loss, excitation power of the LIM is not serious problem for use in braking. Moreover, the generated electric power can serve as an independent power supply system for the LIM, which is not related to the malfunctioning of the feeder and main circuit for the traction.
Fig. 2 shows an example of the composition of the power
Fig. 1. Image of LIM rail brake.
Proceedings of the 2008 International Conference on Electrical Machines
2
supply system. By using an on-board auxiliary power supply as an initiating excitation power source for the LIM drive, the power supply system for the LIM can be completely independent of the main circuit systems. Such a composition can improve the redundancy of the entire braking system. Incidentally, when the reduction ratio of rail heating is not set to a high value, a composition without a braking resistor and DC chopper can also be selected.
III. FUNDAMENTAL TEST MACHINE
To investigate dynamic braking characteristics of the LIM with a rail as the secondary, we fabricated a fundamental test machine with a solid steel rotor of narrow width by remodeling a conventional squirrel cage induction motor.
Fig. 3 shows the axial sectional view of the test machine, Fig. 4 the photograph of a solid steel rotor of narrow width, and Table I the main specifications. Since the test machine has a pole pitch and rotor width similar to that of a LIM rail brake, the influence of the transverse edge effect can be evaluated but the longitudinal end effect cannot. As shown in [3], the transverse edge effect in the eddy current brake is more significant than the longitudinal end effect.
Fig. 5 shows the experimental apparatus for the fundamental test machine. An arbitrary rotational speed is able to be set as a test condition by using a directly connected drive motor.
A. Slip characteristics The slip characteristic of the test machine under constant
current excitation at 33.4 Hz, corresponding to a synchronous speed of 50 km/h, is shown in Fig. 6. The calculated values were computed by a theoretical analysis method which uses Fourier series [4]. Though a two dimensional analysis model was used, a method that considers transverse edge effects [5] was applied, with the rail (rotor) lateral surfaces considered to be an overhang of the secondary conductor. As for magnetic saturation, a multilayer theory [6] was applied to the modeling of the secondary.
Fig. 6(a) shows that a slip larger than s = -0.4 is required to generate sufficient braking torque, because the secondary resistance of solid steel is large. The braking torque does not change very much for large changes in the slip, in the large
Fig. 3. Fundamental test machine (rotary type). Fig. 4. Solid steel rotor of narrow width Fig. 5. Experimental apparatus for the fundamental test machine.
slip range. The reduction ratio of rail heating is expressed as the ratio of the energy which is not converted into the rail heating to the kinetic energy consumed while braking, and the peak ratio is 55%. Since the secondary material is solid steel, the power factor is very low. In the range excluding small slip, the calculated values agree moderately with measured values.
Fig. 2. Example of a power supply system for a LIM.
TABLE I SPECIFICATIONS OF FUNDAMENTAL TEST MACHINE
Number of poles 4
Rated output 255 kW (before remodeling)
Inner diameter of stator 270 mm
Mechanical clearance 5.0 mm Rotor width 65 mm
Fundamental test machineDrive motor
Torque meter
Clutch
Armature
Rotor(Solid steel: SS400)
Proceedings of the 2008 International Conference on Electrical Machines
3
(a)
(b)
(c)
(d)
(e) Fig. 6. Slip characteristics of the fundamental test machine under constant current excitation at 33.4 Hz. (a) Braking torque. (b) Reduction ratio of rail heating. (c) Power factor. (d) Generated power. (e) Apparent power.
B. Equivalent circuit The parameters of the equivalent circuit of the test machine
(Fig. 7) were ascertained by experiments. The circuit constants depend on the secondary frequency because the skin effect is large. Therefore, the circuit constants can be expressed by approximate curves with parameters of the frequency f and the slip s. The concrete calculation method for the parameters is described below.
At each frequency f, a synchronous operation test was performed with the drive motor. The phase voltage V1, current I1, and power factor cosφ of the test machine were measured. The impedance Zm of the excitation circuit can be calculated as follows:
a1m ΖΖΖ −= (1)
⎟⎠⎞⎜
⎝⎛ −+= φφ 2
1
11 cos1cos j
IVΖ (2)
11a ljr ω+=Ζ (3) where r1 is the armature resistance, l1 is the primary leakage inductance, and ω is the angular frequency. The resistance rm and excitation inductance lm are expressed as follows:
⎥⎦
⎤⎢⎣
⎡= −
m
1m
1ReZ
r (4)
⎥⎦
⎤⎢⎣
⎡⋅= −
m
1m
1Im1Zω
l (5)
where Re-1 and Im-1 express the reciprocal of the real and imaginary parts, respectively.
Then, the load test of slip s was performed at each frequency f. The secondary voltage V2 can be calculated as,
1a2
12 cos1cos IjV ΖV −⎟⎠⎞⎜
⎝⎛ −+⋅= φφ . (6)
The secondary current I2 can be derived with the resistance rm and excitation inductance lm corresponding to each frequency as,
2mm
mm1
m
212 V
ZVΙ
lrjrlII
ωω −−=−= . (7)
The secondary resistance r2/s and secondary leakage inductance l2 are given as follows:
⎥⎦
⎤⎢⎣
⎡=
2
22 ReIV
sr (8)
⎥⎦
⎤⎢⎣
⎡⋅=
2
22 Im1
IV
ωl . (9)
Fig. 8 shows the equivalent circuit constants of the test
machine which were obtained by the calculations shown above.
-1 -0.8 -0.6 -0.4 -0.2 00
20
40
60
80
100
Slip s
Red
uctio
n ra
tio o
f ra
il he
atin
g ηr (
%)
-1 -0.8 -0.6 -0.4 -0.2 00
0.2
0.4
0.6
Slip s
Pow
er fa
ctor
cosφ
-1 -0.8 -0.6 -0.4 -0.2 00
1
2
3
Slip s
Gen
erat
ed p
ower
Pou
t (kW
)
-1 -0.8 -0.6 -0.4 -0.2 00
5
10
15
Slip s
App
aren
t pow
er P
a (kV
A)
-1 -0.8 -0.6 -0.4 -0.2 00
10
20
30
Slip s
Bra
king
torq
ue
T (N
・m
)
MeasuredCalculated
I1 = 48 A
Proceedings of the 2008 International Conference on Electrical Machines
4
Fig. 7. Equivalent circuit of the test machine. V1 : Terminal voltage. I1 : Primary current. V2 : Secondary voltage. I2 : Secondary current. I0 : Excitation current. r1 : Armature resistance. l1 : Primary leakage inductance. x1 : Primary leakage reactance. r2 : Secondary resistance. l2 : Secondary leakage inductance. x2 : Secondary leakage reactance. rm : Resistance. lm : Exciting inductance. xm : Exciting reactance. ω : Angular frequency. s : Slip. The secondary resistance r2 and secondary leakage inductance l2 greatly depend on the slip frequency, and the influence of the skin effect can be confirmed. These circuit constants can be expressed by approximate curves with parameters of the frequency f and slip s as follows:
( ) )(log90.630.9m Ω×+−= fr (10) )mH(47.6m =l (11)
)(0108.0566.02 Ω×+= fsr (12) ( ) )mH(6.22 491.0
2−×= fsl . (13)
Next, the excitation impedance Zm, the secondary
impedance Z2, and the equivalent secondary impedance Z2e can be expressed recursively as follows:
mm
mmm ljr
lrjω
ω+
=Z (14)
22
2 ljsr ω+=Z (15)
2m
2me2 ZZ
ZZZ+⋅= . (16)
Although these impedances are of the test machine, they
have the fundamental characteristic of an induction motor with a rail as the secondary.
To confirm the validity of the obtained circuit constants (10)-(16), the calculated value of the power was compared with the measured value with a prescribed voltage impressed into the equivalent circuit (Fig. 9). The validity of the equivalent circuit was confirmed.
IV. PERFORMANCE OF THE LIM RAIL BRAKE
The performance of the LIM rail brake was estimated by using the equivalent circuit derived by virtually opening and unrolling the fundamental test machine into a linear motor. Since the circumference of the air gap of the test machine and the length of the LIM are different, the estimated circuit constants of the LIM were calculated by adding components of the test machine circuit in series. That is, the impedance of the LIM was
(a)
(b)
(c)
(d)
Fig. 8. Equivalent circuit constants of the test machine. (a) Resistance. (b) Exciting inductance. (c) Secondary resistance. (d) Secondary leakage inductance.
Fig. 9. Comparison of the equivalent circuit and test machine. The frequency f is 33.4 Hz. The primary current I1 is 48 A.
I1
r1 x1 (=ωl1) x2 (=ωl2) r2
xm(=ωlm)
s
rm
V1 I2V2I0I1
r1 x1 (=ωl1) x2 (=ωl2) r2
xm(=ωlm)
s
rm
V1 I2V2I0
-1 -0.8 -0.6 -0.4 -0.2 00
2
4
6
Slip s
Pow
er (
kW) Mechanical input (measured)
Mechanical input (calculated)Electrical output (measured)Electrical output (calculated)
20 40 60
10
20
30
0Frequency f (Hz)
Res
ista
nce
r m (Ω
)
Approximate curve
20 40 60
5
10
0Frequency f (Hz)
Exci
tatio
n in
duct
ance
l m (m
H)
10 20 30 40 50 60
0.5
1
1.5
0Slip frequency sf (Hz)
Seco
ndar
y re
sist
ance
r 2 (Ω
)
10 20 30 40 50 60
5
10
0Slip frequency sf (Hz)Se
cond
ary
leak
age
indu
ctan
cel 2
(mH
)
Proceedings of the 2008 International Conference on Electrical Machines
5
derived by multiplying the impedance of the test machine by a coefficient according to the armature length ratio. However, the longitudinal end effect is not considered in this calculation. As shown in the result of analyses [1], the longitudinal end effect reduces braking force by about 10% in the large slip range.
When the coefficient of the armature length ratio is k, the impedances of the LIM are assumed as follows:
22 ZZ k=′ (17)
e2e2 ZZ k=′ . (18)
The braking force Fx, the reduction ratio of rail heating ηr , the power factor of the equivalent secondary circuit cosφ2 , the generated power (electrical output) Pout , and the apparent power of the equivalent secondary circuit of the LIM can be calculated as follows:
( ) 2
2
2e2
12x
13ZZ
′′
⋅−⋅=vs
IrksF (19)
( )[ ] 2
2e
2
2
e2r
Re1 Z
ZZ′′
⋅′
⋅−
=rs
sη (20)
[ ]2e
e22
RecosZ
Z′
′=ϕ (21)
[ ]( )e212
1out Re3 Z′+−= rkIP (22) 2
1e2a2 3 IP Z′⋅= (23) where v is the velocity of the vehicle using the LIM rail brake.
Fig. 10 shows the estimated performance of the LIM rail brake with an armature length of 1.2 m. The primary current I1 is set to be 250 A, which corresponds to the electric loading of 1,490 A/cm. It is assumed that the LIM is used in a relatively low frequency range in consideration of the inverter capacity. In the low frequency range, a constant braking force (of about 5.4 kN) is generated, which does not depend on the velocity. On the other hand, the reduction ratio of rail heating is approximately proportional to the frequency up to a threshold frequency, and the peak value is 60%. It is characteristic that the plot of the generated power follows a line which depends only on the frequency and is independent of the velocity for frequencies lower than the threshold frequency.
The power factor is relatively low (about 0.4-0.5) in the low frequency range, because the secondary current I2 is small in comparison with the excitation current I0 (shown in Fig. 11).
The generated power is balanced with the armature copper loss at about 10 Hz. In this balanced state, the apparent power is relatively small (about 50 kVA) and no braking resistor is necessary in the power supply system for the LIM. However, the reduction ratio of rail heating is not high. There is a trade-off between the reduction ratio of rail heating and the magnitude of apparent power.
Fig. 12 shows characteristics of the LIM under the condition of constant apparent power operation and Fig. 13 shows
(a)
(b)
(c)
(d)
(e) Fig. 10. Estimated performance of the LIM rail brake with an armature length of 1.2 m, electric loading 1,490 A/cm, air gap 5 mm, and longitudinal end effect not considered. (a) Braking torque. (b) Reduction ratio of rail heating. (c) Power factor. (d) Generated power. (e) Apparent power.
20 40 60 80 100
20
40
60
80
0
Red
uctio
n ra
tio o
fra
il he
atin
g η
r (%
)
Frequency (Hz)
20 40 60 80 100
0.2
0.4
0.6
0.8
0
Pow
er fa
ctor
cosφ
2
Frequency (Hz)
20 40 60 80 100
50
100
150
200
0Gen
erat
ed p
ower
Pou
t (kW
)
Frequency (Hz)
20 40 60 80 100
200
400
600
800
0App
aren
t pow
er P
a2 (k
VA
)
Frequency (Hz)
20 40 60 80 100
2
4
6
8
0
v = 160 km/h 130 km/h 100 km/h 70 km/h
Electric loading 1,490 A/cm
Bra
king
forc
e F
x (k
N)
Frequency (Hz)
Proceedings of the 2008 International Conference on Electrical Machines
6
Fig. 11. Ratio of the excitation current I0 and secondary current I2.
(a)
(b) Fig. 12. Velocity characteristic curves of the LIM rail brake under the condition of constant current and constant apparent power operation of 75 kVA, without considering the longitudinal end effect. (a) Frequency and braking torque. (b) Reduction ratio of rail heating and generated power. characteristics of constant power generation. The calculations confirm that the frequency needs to be varied accordingly with the velocity for constant apparent power operation, while the frequency virtually does not need to be varied for constant power generation. And the calculations also confirm that the braking force almost becomes a constant value at any velocity, just by setting the electric loading constant.
V. CONCLUSIONS
We estimated the performance of the eddy current brake using an LIM for dynamic braking from experimental results of a fundamental test machine. We confirmed that the LIM under constant current excitation has an approximately constant braking force regardless of both the velocity and frequency, for
(a)
(b)
Fig. 13. Velocity characteristic curves of the LIM rail brake under the condition of constant current and constant power generation of 11 kW, without considering the longitudinal end effect. (a) Frequency and braking torque. (b) Reduction ratio of rail heating and apparent power. relatively low frequencies. The LIM generates electric power which is determined by only the frequency. The peak value of the reduction ratio of rail heating is 60%. These characteristics are convenient for designing a controller for the LIM rail brake system.
However, there is a trade-off between the reduction ratio of rail heating and the magnitude of apparent power. Therefore, careful studies are necessary for the arrangement of the inverter capacity and the operation frequency of the LIM.
ACKNOWLEDGMENT
The authors would like to acknowledge Mr. Erimitsu Suzuki of Railway Technical Research Institute for his extremely helpful suggestions.
REFERENCES [1] Y. Sakamoto, T. Murai, and T. Sasakawa, “The Basic Study of A.C.
Excited Eddy-Current Rail Brake,” The papers of Technical Meetings on Linear Drives, IEE Japan, LD-04-34, July 2004 (in Japanese)
[2] M. Hofmann, Th. Werle, A. Binder, R. Pfeiffer, “Asynchronous Linear Machine for Railway Systems,” Conference Proceedings of the ICEM 2000, pp. 223-227, 28-30 August 2000, Espoo, Finland
[3] M. Hofmann, Th. Werle, R. Pfeiffer, and A. Binder, “2D and 3D Numerical Field Computation of Eddy-Current Brakes for Traction,” IEEE Trans. on Magnetics, Vol. 36, No. 4, pp. 1758-1763, April 2000
[4] S. Nonaka and N. Fujii, “Three-Dimensional Analysis of High-Speed Linear Induction Motor with Primary Iron Core of Finite Dimension,” Electrical Eng. In Japan, Vol. 100-B, pp. 413-420, July 1980 (in Japanese)
[5] R. L. Russell and K. H. Norsworthy, “Eddy Current and Wall Losses in Screened-rotor Induction Motors,” Proc. IEE, Vol. 105A, pp. 163-175, 1958
[6] I. Boldea, M. Babescu, “Multilayer Theory of D. C. Linear Brakes with Solid-Iron Secondary,” Proc. IEE, Vol. 123, pp. 220-222, March 1976
50 100 150
10
20
30
40
50
0
Red
uctio
n ra
tio o
f rai
l hea
ting
ηr (
%)
Gen
erat
ed p
ower
Pou
t (kW
)
Pout
ηr
Velocity v (km/h)
50 100 150
20
40
60
80
100
0
Red
uctio
n ra
tio o
f rai
l hea
ting
ηr (
%)
App
aren
t pow
er P
a2 (k
VA
)
Velocity v (km/h)
ηr
Pa2
20 40 60 80 100
1
2
0
I 2 /
I 0
Frequency (Hz)
v = 160 km/h 130 km/h 100 km/h 70 km/h
50 100 150
5
10
15
20
0
Freq
uenc
y f
(Hz)
Bra
king
forc
e F
x (kN
) Electric loading 1,489 A/cmPa2 = 75 kVA
f
Fx
Velocity v (km/h)
50 100 150
5
10
15
20
0
Electric loading 1,489 A/cmPout = 11 kW
Freq
uenc
y f
(Hz)
Bra
king
forc
e F
x (kN
)
Velocity v (km/h)
f
Fx
