Evaluation of linear induction motors with two different topologies by FEM Roberto Andr´e Henrique de Oliveira1 , Tilo Espenhahn2,3 , Dietmar Berger 2 , Ludwig Schultz2,3 , Antˆonio Carlos Ferreira1 and Richard Magdalena Stephan1 2
1 Electrical Engineering Department, Federal University of Rio de Janeiro, Rio de Janeiro, Brazil Institute for Metallic Materials, Leibniz Institute for Solid State and Materials Research Dresden, Dresden, Germany 3 Faculty of Mechanical Science and Engineering, Technical University of Dresden, Dresden, Germany email:
[email protected]
A BSTRACT This paper presents two different topologies for linear induction motors used in superconducting magnetic levitation vehicles. The traction, repulsion and attraction forces of these motors are shown. The propulsion systems are analyzed through FEM computational models and the results compared. 1
I NTRODUCTION
The Federal University of Rio de Janeiro (UFRJ) Brazil - develops a superconducting magnetic levitation vehicle called MagLev-Cobra [1]. A linear induction motor drives the vehicle. This motor has “double-C ” geometry, patented by UFRJ [2], which allows the use of the attraction force between the primary and the secondary to increase the levitation force. The secondary has usual aluminum conductors embedded in an iron core. Another vehicle, also based on the superconducting magnetic levitation method, called SupraTrans, is being developed in Germany by the Leibniz Institute of Solid State and Materials Research Dresden (IFW Dresden). The SupraTrans II is driven by a linear induction motor with the primary positioned above the secondary, as usual, but the secondary consists in a continuous copper plate over a back iron. In this project, there is a repulsion force between the primary and secondary harnessed to increase the levitation force. This article presents the characteristics of these linear motors. A comparison regarding the levitation and traction forces will be carried out using the finite element method (FEM). 2
low input frequency; high value of the normal component Bmy of the airgap magnetic flux density; low slip. Acs is the active surface of the primary core and Bmy is the peak value of the normal component of magnetic flux density in the airgap given by equation 2, where: E1 = voltage induced; Li = effective width of the primary core; αi = ratio average-to-peak value of the normal component of the airgap magnetic flux density; kw1 = primary winding factor for the fundamental space harmonic; σf = form factor of the primary electromotive force (EMF).
Figure 1: Illustration Linear Induction Motor “Double-C ” Topology.
Figure 2: Linear Induction Motor - MagLev-Cobra
L INEAR I NDUCTION M OTOR “D OUBLE -C ” T OPOLOGY
Figure 1 shows the linear induction motor (LIM) “double-C ” topology. The primary is 1.27 m long, consisting of 54 coils, with 13 turns per coil. The LIM has 6 poles and 3 phases. Phase groups are connected in series and the phases are connected in Y. The secondary has a squirrel-cage construction type, with laminated core and short-circuited sidebars. Figure 2 shows the LIM. The long secondary is made of 1.51 -meter length sections connected in series. The motor nameplate data with the primary and secondary characteristics as given in the manufacturer’s data sheet [3]. The motor has a geometry, “double-C ”, developed with the aim of contributing to the levitation force. The attraction force is given by Eq.(1). According to the electromagnetic and machines theory, the attraction force can be increased with [4]: small airgap;
2.1
Fya
=
Bmy
=
2 Bmy Acs 4µ0 E1 4σf f N1 kw1 αi τ Li
(1) (2)
FEM - LIM “Double-C” Topology
To evaluate the traction and attraction forces developed by a linear induction motor with secondary squirrel cage (or ladder) computer simulations using finite element methods were performed. The input voltage (420 V), frequency (25 Hz) and squirrel cage conductor material (aluminum or copper) were used. The traction force presents maximum values according to Figure 3. The attraction force of the motor with aluminum cage is increased compared to the copper cage according to Figure 4. There is
magnetic saturation in some regions of the primary, but the magnetic flux density reaches 1.6 T-1.7 T (Figure 5) similar to the measurement of the bench tests [3].
Propulsion Force (N)
2500
3000
Traction Force (N)
2500
2000 GAP = 08mm
1500
GAP = 12mm
1000
GAP = 16mm GAP = 20mm
500 GAP = 24mm
2000 0
1500
0
5
Fx Al 1000
Fx Cu
10 15 Frequency (Hz)
20
25
(a) Traction Force with Aluminum Cage
500 0 0.2
3000
0.4
0.6
0.8
1.0 Time (s)
1.2
1.4
1.6
1.8 2500 Attraction Force (N)
Figure 3: Traction Force - V = 420Vac−rms @f = 25Hz. 5000
Attraction Force (N)
4000
2000
1500
3000 1000
2000
2
3
1000
0 0.2
Fy Cu
0.6
1.0 Time (s)
4
5
Frequency (Hz)
Fy Al
(b) Attraction Force airgap = 8mm 1.4
Figure 6: Experimental Results Forces - LIM MagLev-Cobra
1.8
Figure 4: Attraction Force - V = 420Vac−rms @f = 25Hz. Table 1: Results Compiled - LIM “Double-C” Topology
Simulation 420V @25Hz Traction Force (N) Attraction Force (N) Experimental Traction Force (N) Attraction Force 1
Figure 5: Magnetic Flux Density.
Figure 6 shows the traction and attraction force developed by the linear motor with “double-C ” topology. The test was performed by applying varied voltage and frequencies but keeping V /f = 16.5. The airgap maintaned at 8 mm for attraction force tests and was varied on the traction force tests. We note that the motor of the MagLev-Cobra develops greater traction force with a aluminum squirrel cage, although the resistivity of copper is less than the resistivity of aluminum (Table 1). The difference of the force between the two types of cage is very small and does not recommend to build a secondary with copper, due to the high cost this material compared to aluminum. The experimental result of traction force with the same cage is 3.6% lower than the simulated result. The attraction force becomes larger when the secondary is constructed with a squirrel cage of the aluminum. The relationship cost benefit makes aluminum the best choice for R secondary construction. The software Maxwell provides the total attraction force, in this case the attraction experimental force was 0.33% higher than the simulated results.
3
CageAl 2489.70 4277.20 CageAl 2403.00 2998.001
CageCu 2250.40 3046.40 CageCu -
Net Force= Fy − Fgrav
L INEAR I NDUCTION M OTOR BACK I RON T OPOLOGY
The current version of the SupraTrans project, the SupraTrans II (ST2) [5] contains an inverter fed short stator asynchronous linear motor. This LIM shares many characteristics with the LIM of MagLev-Cobra. It’s also a three phase machine, consisting of 57 coils, forming 20 poles, due to the indoor application (Figure 7). Beside this the ST2 LIM uses cooper sheets on top of an iron yoke for the secondary. These secondary parts are arranged along the driveway. The overall machine setup is sandwich like: primary, air gap and secondary. The repulsion force is given by Eq.(3). According to the electromagnetic and machines theory repulsion force can be increased with [4]: high-conductivity nonmagnetic layer (copper is better than aluminum); cage type secondary winding; long and thick nonmagnetic cap overhangs and the primary stack wider than the secondary back iron; high value of the tangential component Bmx of the airgap magnetic flux density.
tal results of traction force with concentred windings were 5.8% higher than the simulated results, but the repulsion force was 23.34% lower than the simulated results. However simulations show that the concentrated winding and a 10 mm thick copper layer is higher compared with lower copper layers, shown in Table 2.
800 Fx Wc Cu=5mm
750 700 Traction Force (N)
Figure 7: Linear Induction Motor Back Iron Topology.
Fx Wc Cu=10mm
650 600 550 500
Fx Wd Cu=5mm
450 Fx Wd Cu=10mm
400 350 0
0.2
0.4
0.6
Figure 8: Illustration LIM Back Iron Topology.
Fyr
Bmx = (Fx + ∆Fm ) Bmy
(3)
3.1
FEM - LIM Back Iron Topology
The generated repulsion force of the LIM, with secondary back iron, was calculated via finite element method (FEM) computer simulations. Voltage, frequency and the type of winding used in the primary were changed between two simulations. The characteristics of the simulations is 380V @50Hz, the copper layer thickness (Cu = 5mm; 10mm) and the iron layer thickness was maintained at F e = 5mm. It was considered that the motor is operating with narrowed 6 mm airgap and a locked primary. Figure 9 shows the traction force developed by linear motor with a back iron secondary and a primary with distributed and concentrated windings. The traction force is higher for concentrated windings and a small layer of copper (Cu=5 mm), according to the machine design. The repulsion force is bigger in primary with concentrated windings with 10 mm copper layer. Figure 10 shows repulsion force. Figure 12(a) and Figure 12(b) shows, respectively, the experimental traction force with variation of the airgap (g = 4mm; 6mm; 8mm) and the calculated repulsion force with the g = 6mm. In both cases the voltage and frequency were 380V @50Hz. The motor used in the SupraTrans has traction force with higher amplitudes if primary is constructed with concentrated winding and the copper layer is 5 mm thick. The experimen-
1 1.2 Time (s)
1.4
1.6
1.8
Figure 9: Traction Force - (V = 380Vac−rms @f = 50Hz, Sheet Copper: 5mm-10mm, Wd =Distributed Windings, Wc =Concentrated Windings). 1600
Fy Wc Cu=10mm
1400 Repulsion Force (N)
Generally, electrical machines use distributed windings instead of concentrated windings. The advantage is that the MMF no longer has a rectangular spatial distribution and is replaced by a staggered distribution, in steps form and with less harmonic because there are more coils spatially displaced from each other. The spatial displacement between the MMF of the coils results in a reduction of the MMF resultant amplitude. The use of a distributed winding produces an equivalent effect to reducing the number of coils in series per phase.
0.8
1200 Fy Wc Cu=5mm
1000 800 600
Fy Wd Cu=10mm 400 Fy Wd Cu=5mm
200 0 0
0.2
0.4
0.6
0.8 1 Time (s)
1.2
1.4
1.6
1.8
Figure 10: Repulsion Force - (V = 380Vac−rms @f = 50Hz, Sheet Copper: 5mm-10mm, Wd =Distributed Windings, Wc =Concentrated Windings).
(a) 50Hz − 380Vac−rms , Cu=5mm, Wc
(b) 50Hz − 380Vac−rms , Cu=5mm, Wd Figure 11: Magnetic Flux Density - 50Hz
Table 3: Comparison - LIM’s
1000
gap=4mm gap=6mm
Traction Force (N)
800
gap=8mm
600
400
200
0 0
10
20
30 40 50 Frequency (Hz)
60
70
80
(a) Experimental Result of the Traction Force with Wc . 2500
Repulsion Force (N)
2000 gap=6mm 1500
1000
500
0 0
0.2
0.4
0.6
0.8
1
Slip
(b) Calculated Result of the Repulsion Force with Wc . Figure 12: Results Forces - LIM SupraTrans II Table 2: Results Compiled - LIM Back Iron Topology with g = 6mm
Simulation Traction Force (N) Repulsion Force (N) Traction Force (N) Repulsion Force (N) Experimental Traction Force (N) Repulsion Force
Wdistributed 461.501 95.421 429.192 391.002 Wdistributed -
Wconcentred 746.201 932.501 639.102 1435.002 Wconcentred 790.001 1100.001
1 2
Vin = 380Vrms @50Hz / Thickness layer: Cu=5 mm Vin = 380Vrms @50Hz / Thickness layer: Cu=10 mm
4
C OMPARISON AND C ONCLUSION
The motors have important differences. Table 3 presents the main characteristics. The MagLev-Cobra and the SupraTrans II linear motors have distributed and concentrated winding, respectively. The traction force on concentrated windings is bigger than distributed windings, due to spatial lag between the MMF on distributed windings. These characteristic produces the reduction on the amplitude of the resulting MMF [6]. The harmonics generated by concentrated windings can cause the following problems [7]: increased heating due to increased losses in copper and iron; low efficiency and the available torque; possible increase in noise; problems for the control. The contribution to the levitation force shown in both topologies are considered to be excellent. The choice of secondary is fundamental to the electromagnetic forces developed by the machines but does not affect the performance of the electromagnetic levitation system.
Parameters Voltage Current Frequency Power Number of the Poles Pole Pitch, τ Air Gap Primary Length Height Yoke Width Winding Width Index of Protection Weight Secondary Length Height Width Weight Force Traction Repulsion Attraction Density Fx 1
MagLev-Cobra
SupraTrans II
420V − (Y ) 53A 25Hz 10HP 6 156.0mm 8mm
380V − (Y ) 45A 50Hz 7.2HP 20 57.5mm 6mm
MagLev-Cobra
SupraTrans II
1270mm 106mm 166mm 340mm IP − 23 132kg
1150mm 35mm 140mm 220mm IP − 54 46kg
MagLev-Cobra
SupraTrans II
1510mm 53mm 231mm 53.98kg/m
1190mm 10mm 250mm 11.26kg/m
MagLev-Cobra
SupraTrans II
2403N 1 − 2998N 1
910N 1 1100N 2 −
52.5 × 103 N/m3
102.7 × 103 N/m3
2
Experimental Results Calculted Result
ACKNOWLEDGEMENT This work was supported in part by CAPES, BNDES, CNPq and FAPERJ. R EFERENCES [1] R. M. Stephan, “Maglev-cobra: An urban transportation solution using hts-superconductors and permanent magnets,” Proc. of Int. Conf. on Magnetically Levitated System and Linear Drives 2008, San Diego, pp. 1–4, 2008. [2] UFRJ, “Motor linear aplicado a ve´ıculos de transporte por levitac¸a˜ o magn´etica,” Tech. Rep. PI 1103525-0, Universidade Federal do Rio de Janeiro, July 2011. [3] I. E. Chabu and D. R. Gomes, Relat´orio T´ecnico FAPERJ PI 56.146. 2009. [4] J. F. Gieras, Linear Induction Drives. No. 30, Oxford University Press, 1994. [5] L. K¨uhn, O. de Haas, D. Berger, L. Schultz, H. Olsen, and S. R¨ohlig, “Supratrans 2 - test drive facility for a superconductor-based maglev train,” Elektrische Bahnen, pp. 461–469, 8-9 2012. [6] J. Pyrh¨onen, T. Jokinen, and V. Hrabovcov´a, Design of Rotating Electrical Machines. John Wiley & Sons, Ltd, 2008. [7] “Recommended practices and requirements for harmonic control in electrical power systems,” IEEE Std 519-1992, pp. 1–112, April 1993.
