- Email: [email protected]
Theoretical and FEM analysis of suspension and propulsion system with HTS hybrid electromagnets in an EMS Maglev model
Physica C 471 (2011) 1487–1491
Contents lists available at ScienceDirect
Physica C journal homepage: www.elsevier.com/locate/physc
Theoretical and FEM analysis of suspension and propulsion system with HTS hybrid electromagnets in an EMS Maglev model Y.D. Chung a,⇑, C.Y. Lee b, J.Y. Jang c, Y.S. Yoon d, T.K. Ko c a
Department of Electrical Engineering, Suwon University, Bongdang Eup, Hwaseong Si 445-743, Republic of Korea Korea Railroad Research Institute, Woram Dong, Uiwang Si 437-757, Republic of Korea c Department of Electrical Engineering, Ansan College of Technology, Choji-Dong, Ansan Si 425-792, Republic of Korea d Department of Electrical and Electronic Engineering, Yonsei University, Sinchon-dong, Seoul 120-749, Republic of Korea b
a r t i c l e
i n f o
Article history: Available online 13 May 2011 Keywords: EMS-based hybrid electromagnet Propulsion stator coils Suspension force 3D FEM analysis
a b s t r a c t We have been constructed a proto-type electromagnetic suspension (EMS) based maglev vehicle system. The maglev concept utilizes magnetic forces for noncontact suspension, guidance and propulsion. The suspension system with high temperature superconducting (HTS) hybrid electromagnet (EM) is composed of HTS coils and normal coils, which consume little power to keep large suspension gap. The magnetic forces realize to guide the vehicle, propel the vehicle along the guide-way and assist in braking action. The proto-type EMS-based Maglev model is designed to keep the suspension gap of 20 mm. This paper presents the theoretical analysis of the maglev vehicle based on the EMS model to obtain the designing parameters for levitation and propulsion forces. The magnetic field distributions of the electromagnetic forces with hybrid EM and propulsion stator coils are analyzed based on three dimension (3D) finite element method (FEM) analysis. From the simulation results, appropriately design parameters of the suspension, guidance and propulsion were obtained. Ó 2011 Elsevier B.V. All rights reserved.
1. Introduction Nowadays, research of high-speed transportation in Germany and Japan shows that vehicles suspended magnetically and propelled by linear motors are the optimum solution to modern transport problems. A magnetic levitation (Maglev) can provide a super high-speed ground transport with a non-adhesive drive system that is independent of frictional forces between the guide-way track and vehicle bodies. Maglev trains, which are a combination of contactless magnetic suspension and linear motor technology, realize super high speed running, safety, reliability, low environmental impact and minimum maintenance [1,2]. The maglev concept utilizes magnetic forces for noncontact suspension, guidance and propulsion. The electromagnetic suspension system in maglev system is classified as electromagnetic suspension (EMS) and electrodynamic suspension (EDS). The German Maglev of Transrapid, which is representative of EMS technology with normal conducting EM, is in the commercial operation in Shanghai. The narrow gap of the maglev in Shanghai caused in high construction costs of guide-way system, which has been one of major obstacles in extending service [3].
⇑ Corresponding author. Tel.: +82 31 229 8169, +82 10 5094 5406; fax: +82 31 220 2667. E-mail address: [email protected] (Y.D. Chung). 0921-4534/$ - see front matter Ó 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.physc.2011.05.222
From this point of view, a superconducting EM has been considered as a reasonable solution in order to keep a larger gap with smaller energy consumption; the first EMS using low temperature superconducting (LTS) coils was studied by Northrop Grumman Co. Ltd. in 1995 [4]. To reduce the cost in cryogenic requirement, a feasibility research of EMS using HTS coils has been progressed in China. As HTS magnets are used in the maglev high-speed mass transportation, it is possible to achieve lightweight of the vehicle and low construction cost compared with LTS magnets [5,6]. Our study focuses on the design and fabrication of a prototype HTS– EM model which will be consistent with the German Transrapid. This EMS model is composed of a guide-way wound 3-phase armature coils, an HTS coil, a pair of DC-control coils and a U-shaped iron core. The HTS EM actively generates vertical suspension force. Two control normal coils play a role to maintain the stable gap distance. That is, the hybrid EM using HTS and normal coils are needed to keep the constant suspension force. The magnetomotive forces (MMF) of the hybrid EM and 3-phase armature current in the guide-way are dependent on the propulsion force and speed of the maglev vehicle. Our former studies concentrated on a conceptual profile of the hybrid EM using HTS wire, and a control method using magnetic interface in the hybrid EM [7,8]. In this paper, in order to calculate optimal parameters of the structural maglev system, the theoretical and numerical analyses of the levitation and propulsion forces were introduced. As well as, the magnetic distributions and intensities of
1488
Y.D. Chung et al. / Physica C 471 (2011) 1487–1491
the levitation and propulsion forces, which are generated by the MMF of hybrid EM and armature current in the guide-way, were calculated based on 3D finite element method (FEM). 2. Prototype hybrid electromagnets in EMS model 2.1. Structure of hybrid electromagnets The configurations of the proposed hybrid EM for high speed EMS Maglev are illustrated in Fig. 1. The slot of 3-phase armature coils in the laminated iron guide-way is wound like as linear synchronous motor. The dimension parameters of the EMS maglev system are shown in Table 1. A short pitch with double-layer method is introduced for 3-phase armature winding which produces a traveling magnetic field in the air gap. The main levitation force is generated by the magneto motive force (MMF) of HTS coils and enforced by the three phase armature current in the guideway. A pair of DC control copper coils is installed to maintain the fixed gap distance. The gap sensor that is installed in the air gap detects the variations of the gap distance. In this work, the target levitation gap is 20 mm, which is about four times wider than that of the German Transrapid. The maximum DC current source supplied to HTS coil was assumed to be 100 A. The specifications of superconducting HTS coils are shown in Table 2. 2.2. Calculation of levitation and propulsion force In order to analyze levitation and propulsion forces between guide-way and EM poles, the EM suspension and propulsion system can be simplified into several magnet parts as shown in Fig. 1 and assumed as follows; (a) (b) (c) (d)
Leakage flux paths are neglected. Nonlinearities are neglected. All the field energy is stored in the air gap (l0lr l0). Armature currents flow only in the direction perpendicular to the xz plane in the y direction.
Nn/2, Ns, In, Is, S and z represent the number of turns of DC coils, the number of turns of HTS coil, the current of copper coils, the current of HTS coils, the cross section area of the magnetic pole and the interval of air gap, respectively. The average magnetic flux density at the air gap between guide-way and EM is expressed as
Table 1 Specifications of prototype HTS-EM model. Dimensional parameters
Dimension
Guideway (thickness hight width) Slot for LSM cable Pole face Pole distance (P1) Pole height (P2) Diameter of back leg of iron core (P3) Max. levitation gap
91.5 mm 95 mm 520 mm 30 mm 28 mm 129 mm 129 mm 129 mm 129 mm 90 mm 100 mm 20 mm
Table 2 Specifications of HTS coils. Parameter
Value
HTS wire
AMSC Co. Bi-2223/Ag Ic = 145 A @ 77 K, self-field Average thickness: 0.27 mm Width: 4.4 mm 360 turns 4 DP 90 turn 120 mm 170 mm 43 mm
Total coil turns Number of DP Coil turns of DP Inner diameter of coil Outer diameter of coil Length of coil
Bg ¼
Uðz; iÞ S
¼
l0 ðNn in þ Ns is Þ 2z
ð1Þ
The stored field energy per the volume of the air gap is expressed as
u¼
2 W 1 1 Bg ¼ Bg H ¼ ½J=m3 Sz 2 2 l0
ð2Þ
where W is stored energy in the magnetic field. With the displacement dz of the new air gap, change in stored energy is
dW ¼
B2g
l0
Sdz
ð3Þ
Thus, the levitation force F in the air gap by the hybrid EM is expressed as
Fðz; iÞ ¼
2 2 dW Bg S Nn in þ Ns is ¼ ¼ l0 S dz l0 2z
ð4Þ
Also, in order to calculate propulsive force, the currents in the armature winding are simplified to the perpendicular to the laminations (y direction), and magnetic flux density has only two components i.e., tangential component Bx and normal component Bz. The excitation winding can be described by the following space time distribution of the complex line current density is expressed as
In
Nn 2
Nn 2
Ns Is
Fig. 1. Illustrations of the structure of electromagnetic suspension maglev model with hybrid electromagnets.
Af ðx; tÞ ¼ Amf ejðxtbxeÞ ;
2Nf kwf If Amf ¼ ps
ð5Þ
The Amf means the field excitation by DC current. The angular frequency is x ¼ 2pf and the value b is defined by ps. The force angle e represents the angle between phasors of the excitation flux in the d-axis and the armature current. The symbols of Nf, kwf, If, p and s represent the number of field series turns, the armature winding factor, the armature current, the number of pole and pole pitch, respectively. The two dimensional distribution of the magnetic vector potential of the field excitation by the armature current is described by Laplace’s equation as follows
@ 2 Afy @ 2 Afy þ ¼0 @x2 @z2
ð6Þ
1489
Y.D. Chung et al. / Physica C 471 (2011) 1487–1491
On the basis of the definition of the magnetic vector potential, there are only two components of the magnetic flux density of the field excitation by the armature current, i.e.,
Bfx ¼
@Afy ; @z
Bfz ¼
@Afy @x
ð7Þ
The general solution of Eq. (6) for the air gap of z direction is as follows
Ay ðx; zÞ ¼
l0 2b
Am e
jðxtbxÞ bðgzÞ
e
ð8Þ
The symbols of Am and g mean field excitation by armature current and air gap distance. Based on the Lorentz equation, the force in the x and z direction per unit area can be found such as
fdx ¼
1 1 Re½Aðx; tÞBfz ¼ l0 Am Amf ebg sin e½N=m2 2 4
ð9aÞ
fdz ¼
i 1 h 1 Re Aðx; tÞBfx ¼ l0 Am Amf ebg cos e½N=m2 2 4
ð9bÞ
Thus, the normal propulsion force by the hybrid EM and armature current is expressed as
F dx ¼ F max sin e
3. Numerical analysis and FEM results 3.1. Numerical analysis method Since the properties of the nonlinear superconductors are typically characterized as current density J, vs. electric field E, (J–E) constitutive relation, the following power law expression is usually utilized for convenience.
E ¼ Ec
jJj J c ðl0 jHjÞ
n
J jJj
ð13Þ
where the parameter n is the power-law index and denotes the sharpness of the take-off of the J–E curve. In other words, n shows the nonlinearity of the superconducting properties. The parameter Ec means the electric field criterion for the definition of the critical current density Jc, which is varied as a function of l0H. As can be seen in Eq. (13), it is assumed that the direction of E is always parallel to that of J. Thus, the equivalent electric conductivity rs is given as [10]
rs ¼
n1 jJj J c ðl0 jHjÞ J c ðl0 jHjÞ ¼ jEj Ec jJj
ð14Þ
3.2. FEM analysis results
ð10Þ
Also, total levitation force by hybrid EM and armature current is expressed as
F dz ¼ F max cos e
ð11Þ
where the peak force of the EM thrust
pffiffiffi Li F max ¼ 4l0 m1 p 2N1p kw1 Nfp kwf Ia If ebg
s
ð12Þ
where Ia: the phasor of armature current, m1: the number of coils per phase, N1p: the number of series turns per phase, kw1: the armature winding factor for fundamental space harmonic v = 1, Nfp: the number of field turns per pole, kwf: the form factor of the armature winding, Li; the effective length of the stator core, If: armature current [9].
We already obtained the profiles of the HTS design of the EMS based Maglev vehicle in the previous study. In this work, the levitation and propulsion forces by the superconducting electromagnet and armature current were investigated based on FEM analysis. The numerical analysis is carried out by the commercial simulation program: COMSOLÒ. Fig. 2 shows contour plots of magnetic field distribution of the EMS model with the MMF of HTS EM of 40 [kA-Turn] and armature coils of 1.2 [kA-Turn] and the maximum magnetic flux density of the model is 1.59T. Fig. 3 shows the distributions of the magnetic field density at the air gap of 10 mm in the case of the MMF of the HTS EM, and the MMF of the HTS EM added armature current, respectively. Compared with the levitation force by the HTS EM, the maximum levitation value by HTS EM and AC current is increased about 30%.
Max: 1.59 T 520 mm
Guideway
3-phase coil
1.4
1.2
1.0
0.8
Analysis position
DC coil U-core
0.6
0.4
0.2
HTS coil
0.1
Min: 4.22e-7 Fig. 2. Contour plots of magnetic flux density of HTS EMS maglev model.
1490
Y.D. Chung et al. / Physica C 471 (2011) 1487–1491
Fig. 3. Simulation results of distributions of magnetic flux density in the air gap with HTS current at 40 [kA-Turn] and AC armature current at 1.2 [kA-Turn], and with only HTS current at 40 [kA-Turn], respectively.
Fig. 6. Simulation results of levitation force in the air gap from increase in the MMF of armature current and fixed MMF HTS EM at 40 [kA-Turn].
Fig. 7. Simulation results of propulsion force in the air gap from increase in MMF of armature current and fixed MMF of HTS EM at 40 [kA-Turn]. Fig. 4. Simulation results of levitation force in the air gap from increase in MMF of HTS electromagnet.
Fig. 5. Simulation results of levitation force in the air gap from increase in MMF of HTS electromagnet and fixed MMF of armature current at 1.2 [kA-Turn].
The levitation force by the increase in the perpendicular magnetic field of HTS EM is estimated and the levitation force of z direction is calculated based on simulation method and theoretical Eq. (4). The values of magnetic flux density at different levitation gaps for MMF increases are obtained as shown in Fig. 4. In Fig. 5, the levitation force is numerically calculated by the increase current in HTS coils and the fixed MMF value of the armature current. The MMF range of HTS magnet is from 5 to 55 [kA-
Turn]. The MMF value of the armature current in the guide-way is fixed at 1.2 [kA-Turn]. As shown in Figs. 4 and 5, we investigated that levitation force by together MMF of HTS EM and AC armature current is larger over 30% than that of only HTS EM. The levitation force by the increase in MMF of armature coils and fixed MMF of HTS EM is numerically calculated. The MMF range of armature current in the guide-way is from 1.0 to 1.9 [kA-Turn]. The MMF value of the HTS EM is fixed at 40 [kA-Turn]. Compared with Figs. 5 and 6, it is confirmed that the levitation force is independent with increase in the perpendicular magnetic field of HTS magnet while the MMF of the armature current in the guide-way is operated as shown in Fig. 5. On the other hands, the levitation force is dependent on the increase in MMF of AC current while the MMF of HTS EM is operated as shown in Fig. 6. We calculated the propulsion force with increase in MMF of armature current and fixed MMF of HTS EM as shown in Fig. 7. The MMF range of armature current of 60 Hz is from 1.0 to 1.9 [kA-Turn] while the MMF of HTS EM is fixed at 40 [kA-Turn]. Compared with the propulsion force (x direction) and levitation force (z direction) in the same conditions in Figs. 6 and 7, the levitation force is about 15% larger than the propulsion force. 4. Conclusions This work presented the operating principle of the proposed proto-type HTS EM EMS based Maglev, also proper parameters of MMF by HTS EM and AC current for levitation and propulsion force. Especially, we confirmed that the levitation force is separately dependent on AC current and HTS EM, respectively. As well as, in
Y.D. Chung et al. / Physica C 471 (2011) 1487–1491
the case of the fixed AC current, the levitation force is almost independent on the MMF by the HTS EM. In addition, the levitation force is larger than propulsion force over 15% in the case of 60 Hz of AC current. The simulated and theoretical results presented here are being considered the next study which addresses the design and fabrication of EMS Maglev using the HTS–EM.
References [1] G. Bohn, G. Steinmetz, IEEE Trans. Magn. Mag 20 (1984) 1666. [2] R.M. Goodall, C.J. MacLeod, A.A. El-Abbar, A.M. Campbell, H. Jones, R.G. Jenkins, IEEE Trans. Appl. Supercond. (1995) 650.
1491
[3] S.A. Nasar, I. Boldea, Linear Motion Electric Machines, John Wiley &Sons Publication, New York, 1975. pp. 75–106. [4] G. Zhang, Y. Fang, F. Song, G. Zhu, Z. Wang, IEEE Trans. Appl. Supercond. (2004) 1850. [5] S. Kalsi, M. Proise, T. Schultheiss, B. Dawkins, IEEE Trans. Appl. Supercond. (1995) 964. [6] C. Gu, M. Liu, H. Xing, T. Zhou, W. Yin, J. Zong, Z. Han, Physica C 423 (2005) 37. [7] C.Y. Lee, J.M. Jo, B.B. Kang, Y.J. Han, D.K. Bae, Y.S. Yoon, Y.D. Chung, S.Y. Joo, Y.J. Whang, T.K. Ko, Proc. Appl. Supercond. Conf. (2010). 4LPE-09. [8] J.Y. Jang, Y.J. Kim, K.S. Chang, Y.D. Chung, C.Y. Lee, T.K. Ko, Proc. Appl. Supercond. Conf. (2010). 4LPA-03. [9] J.F. Gieras, Z.J. Piech, Linear Synchronous Motors, CRC Press, New York, 2000. pp. 134–159. [10] Y. Iwasa, Case studies in Superconducting Magnets Design and Operational Issues, Plenum Press, New York, 1994. pp. 306–308.
Contents lists available at ScienceDirect
Physica C journal homepage: www.elsevier.com/locate/physc
Theoretical and FEM analysis of suspension and propulsion system with HTS hybrid electromagnets in an EMS Maglev model Y.D. Chung a,⇑, C.Y. Lee b, J.Y. Jang c, Y.S. Yoon d, T.K. Ko c a
Department of Electrical Engineering, Suwon University, Bongdang Eup, Hwaseong Si 445-743, Republic of Korea Korea Railroad Research Institute, Woram Dong, Uiwang Si 437-757, Republic of Korea c Department of Electrical Engineering, Ansan College of Technology, Choji-Dong, Ansan Si 425-792, Republic of Korea d Department of Electrical and Electronic Engineering, Yonsei University, Sinchon-dong, Seoul 120-749, Republic of Korea b
a r t i c l e
i n f o
Article history: Available online 13 May 2011 Keywords: EMS-based hybrid electromagnet Propulsion stator coils Suspension force 3D FEM analysis
a b s t r a c t We have been constructed a proto-type electromagnetic suspension (EMS) based maglev vehicle system. The maglev concept utilizes magnetic forces for noncontact suspension, guidance and propulsion. The suspension system with high temperature superconducting (HTS) hybrid electromagnet (EM) is composed of HTS coils and normal coils, which consume little power to keep large suspension gap. The magnetic forces realize to guide the vehicle, propel the vehicle along the guide-way and assist in braking action. The proto-type EMS-based Maglev model is designed to keep the suspension gap of 20 mm. This paper presents the theoretical analysis of the maglev vehicle based on the EMS model to obtain the designing parameters for levitation and propulsion forces. The magnetic field distributions of the electromagnetic forces with hybrid EM and propulsion stator coils are analyzed based on three dimension (3D) finite element method (FEM) analysis. From the simulation results, appropriately design parameters of the suspension, guidance and propulsion were obtained. Ó 2011 Elsevier B.V. All rights reserved.
1. Introduction Nowadays, research of high-speed transportation in Germany and Japan shows that vehicles suspended magnetically and propelled by linear motors are the optimum solution to modern transport problems. A magnetic levitation (Maglev) can provide a super high-speed ground transport with a non-adhesive drive system that is independent of frictional forces between the guide-way track and vehicle bodies. Maglev trains, which are a combination of contactless magnetic suspension and linear motor technology, realize super high speed running, safety, reliability, low environmental impact and minimum maintenance [1,2]. The maglev concept utilizes magnetic forces for noncontact suspension, guidance and propulsion. The electromagnetic suspension system in maglev system is classified as electromagnetic suspension (EMS) and electrodynamic suspension (EDS). The German Maglev of Transrapid, which is representative of EMS technology with normal conducting EM, is in the commercial operation in Shanghai. The narrow gap of the maglev in Shanghai caused in high construction costs of guide-way system, which has been one of major obstacles in extending service [3].
⇑ Corresponding author. Tel.: +82 31 229 8169, +82 10 5094 5406; fax: +82 31 220 2667. E-mail address: [email protected] (Y.D. Chung). 0921-4534/$ - see front matter Ó 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.physc.2011.05.222
From this point of view, a superconducting EM has been considered as a reasonable solution in order to keep a larger gap with smaller energy consumption; the first EMS using low temperature superconducting (LTS) coils was studied by Northrop Grumman Co. Ltd. in 1995 [4]. To reduce the cost in cryogenic requirement, a feasibility research of EMS using HTS coils has been progressed in China. As HTS magnets are used in the maglev high-speed mass transportation, it is possible to achieve lightweight of the vehicle and low construction cost compared with LTS magnets [5,6]. Our study focuses on the design and fabrication of a prototype HTS– EM model which will be consistent with the German Transrapid. This EMS model is composed of a guide-way wound 3-phase armature coils, an HTS coil, a pair of DC-control coils and a U-shaped iron core. The HTS EM actively generates vertical suspension force. Two control normal coils play a role to maintain the stable gap distance. That is, the hybrid EM using HTS and normal coils are needed to keep the constant suspension force. The magnetomotive forces (MMF) of the hybrid EM and 3-phase armature current in the guide-way are dependent on the propulsion force and speed of the maglev vehicle. Our former studies concentrated on a conceptual profile of the hybrid EM using HTS wire, and a control method using magnetic interface in the hybrid EM [7,8]. In this paper, in order to calculate optimal parameters of the structural maglev system, the theoretical and numerical analyses of the levitation and propulsion forces were introduced. As well as, the magnetic distributions and intensities of
1488
Y.D. Chung et al. / Physica C 471 (2011) 1487–1491
the levitation and propulsion forces, which are generated by the MMF of hybrid EM and armature current in the guide-way, were calculated based on 3D finite element method (FEM). 2. Prototype hybrid electromagnets in EMS model 2.1. Structure of hybrid electromagnets The configurations of the proposed hybrid EM for high speed EMS Maglev are illustrated in Fig. 1. The slot of 3-phase armature coils in the laminated iron guide-way is wound like as linear synchronous motor. The dimension parameters of the EMS maglev system are shown in Table 1. A short pitch with double-layer method is introduced for 3-phase armature winding which produces a traveling magnetic field in the air gap. The main levitation force is generated by the magneto motive force (MMF) of HTS coils and enforced by the three phase armature current in the guideway. A pair of DC control copper coils is installed to maintain the fixed gap distance. The gap sensor that is installed in the air gap detects the variations of the gap distance. In this work, the target levitation gap is 20 mm, which is about four times wider than that of the German Transrapid. The maximum DC current source supplied to HTS coil was assumed to be 100 A. The specifications of superconducting HTS coils are shown in Table 2. 2.2. Calculation of levitation and propulsion force In order to analyze levitation and propulsion forces between guide-way and EM poles, the EM suspension and propulsion system can be simplified into several magnet parts as shown in Fig. 1 and assumed as follows; (a) (b) (c) (d)
Leakage flux paths are neglected. Nonlinearities are neglected. All the field energy is stored in the air gap (l0lr l0). Armature currents flow only in the direction perpendicular to the xz plane in the y direction.
Nn/2, Ns, In, Is, S and z represent the number of turns of DC coils, the number of turns of HTS coil, the current of copper coils, the current of HTS coils, the cross section area of the magnetic pole and the interval of air gap, respectively. The average magnetic flux density at the air gap between guide-way and EM is expressed as
Table 1 Specifications of prototype HTS-EM model. Dimensional parameters
Dimension
Guideway (thickness hight width) Slot for LSM cable Pole face Pole distance (P1) Pole height (P2) Diameter of back leg of iron core (P3) Max. levitation gap
91.5 mm 95 mm 520 mm 30 mm 28 mm 129 mm 129 mm 129 mm 129 mm 90 mm 100 mm 20 mm
Table 2 Specifications of HTS coils. Parameter
Value
HTS wire
AMSC Co. Bi-2223/Ag Ic = 145 A @ 77 K, self-field Average thickness: 0.27 mm Width: 4.4 mm 360 turns 4 DP 90 turn 120 mm 170 mm 43 mm
Total coil turns Number of DP Coil turns of DP Inner diameter of coil Outer diameter of coil Length of coil
Bg ¼
Uðz; iÞ S
¼
l0 ðNn in þ Ns is Þ 2z
ð1Þ
The stored field energy per the volume of the air gap is expressed as
u¼
2 W 1 1 Bg ¼ Bg H ¼ ½J=m3 Sz 2 2 l0
ð2Þ
where W is stored energy in the magnetic field. With the displacement dz of the new air gap, change in stored energy is
dW ¼
B2g
l0
Sdz
ð3Þ
Thus, the levitation force F in the air gap by the hybrid EM is expressed as
Fðz; iÞ ¼
2 2 dW Bg S Nn in þ Ns is ¼ ¼ l0 S dz l0 2z
ð4Þ
Also, in order to calculate propulsive force, the currents in the armature winding are simplified to the perpendicular to the laminations (y direction), and magnetic flux density has only two components i.e., tangential component Bx and normal component Bz. The excitation winding can be described by the following space time distribution of the complex line current density is expressed as
In
Nn 2
Nn 2
Ns Is
Fig. 1. Illustrations of the structure of electromagnetic suspension maglev model with hybrid electromagnets.
Af ðx; tÞ ¼ Amf ejðxtbxeÞ ;
2Nf kwf If Amf ¼ ps
ð5Þ
The Amf means the field excitation by DC current. The angular frequency is x ¼ 2pf and the value b is defined by ps. The force angle e represents the angle between phasors of the excitation flux in the d-axis and the armature current. The symbols of Nf, kwf, If, p and s represent the number of field series turns, the armature winding factor, the armature current, the number of pole and pole pitch, respectively. The two dimensional distribution of the magnetic vector potential of the field excitation by the armature current is described by Laplace’s equation as follows
@ 2 Afy @ 2 Afy þ ¼0 @x2 @z2
ð6Þ
1489
Y.D. Chung et al. / Physica C 471 (2011) 1487–1491
On the basis of the definition of the magnetic vector potential, there are only two components of the magnetic flux density of the field excitation by the armature current, i.e.,
Bfx ¼
@Afy ; @z
Bfz ¼
@Afy @x
ð7Þ
The general solution of Eq. (6) for the air gap of z direction is as follows
Ay ðx; zÞ ¼
l0 2b
Am e
jðxtbxÞ bðgzÞ
e
ð8Þ
The symbols of Am and g mean field excitation by armature current and air gap distance. Based on the Lorentz equation, the force in the x and z direction per unit area can be found such as
fdx ¼
1 1 Re½Aðx; tÞBfz ¼ l0 Am Amf ebg sin e½N=m2 2 4
ð9aÞ
fdz ¼
i 1 h 1 Re Aðx; tÞBfx ¼ l0 Am Amf ebg cos e½N=m2 2 4
ð9bÞ
Thus, the normal propulsion force by the hybrid EM and armature current is expressed as
F dx ¼ F max sin e
3. Numerical analysis and FEM results 3.1. Numerical analysis method Since the properties of the nonlinear superconductors are typically characterized as current density J, vs. electric field E, (J–E) constitutive relation, the following power law expression is usually utilized for convenience.
E ¼ Ec
jJj J c ðl0 jHjÞ
n
J jJj
ð13Þ
where the parameter n is the power-law index and denotes the sharpness of the take-off of the J–E curve. In other words, n shows the nonlinearity of the superconducting properties. The parameter Ec means the electric field criterion for the definition of the critical current density Jc, which is varied as a function of l0H. As can be seen in Eq. (13), it is assumed that the direction of E is always parallel to that of J. Thus, the equivalent electric conductivity rs is given as [10]
rs ¼
n1 jJj J c ðl0 jHjÞ J c ðl0 jHjÞ ¼ jEj Ec jJj
ð14Þ
3.2. FEM analysis results
ð10Þ
Also, total levitation force by hybrid EM and armature current is expressed as
F dz ¼ F max cos e
ð11Þ
where the peak force of the EM thrust
pffiffiffi Li F max ¼ 4l0 m1 p 2N1p kw1 Nfp kwf Ia If ebg
s
ð12Þ
where Ia: the phasor of armature current, m1: the number of coils per phase, N1p: the number of series turns per phase, kw1: the armature winding factor for fundamental space harmonic v = 1, Nfp: the number of field turns per pole, kwf: the form factor of the armature winding, Li; the effective length of the stator core, If: armature current [9].
We already obtained the profiles of the HTS design of the EMS based Maglev vehicle in the previous study. In this work, the levitation and propulsion forces by the superconducting electromagnet and armature current were investigated based on FEM analysis. The numerical analysis is carried out by the commercial simulation program: COMSOLÒ. Fig. 2 shows contour plots of magnetic field distribution of the EMS model with the MMF of HTS EM of 40 [kA-Turn] and armature coils of 1.2 [kA-Turn] and the maximum magnetic flux density of the model is 1.59T. Fig. 3 shows the distributions of the magnetic field density at the air gap of 10 mm in the case of the MMF of the HTS EM, and the MMF of the HTS EM added armature current, respectively. Compared with the levitation force by the HTS EM, the maximum levitation value by HTS EM and AC current is increased about 30%.
Max: 1.59 T 520 mm
Guideway
3-phase coil
1.4
1.2
1.0
0.8
Analysis position
DC coil U-core
0.6
0.4
0.2
HTS coil
0.1
Min: 4.22e-7 Fig. 2. Contour plots of magnetic flux density of HTS EMS maglev model.
1490
Y.D. Chung et al. / Physica C 471 (2011) 1487–1491
Fig. 3. Simulation results of distributions of magnetic flux density in the air gap with HTS current at 40 [kA-Turn] and AC armature current at 1.2 [kA-Turn], and with only HTS current at 40 [kA-Turn], respectively.
Fig. 6. Simulation results of levitation force in the air gap from increase in the MMF of armature current and fixed MMF HTS EM at 40 [kA-Turn].
Fig. 7. Simulation results of propulsion force in the air gap from increase in MMF of armature current and fixed MMF of HTS EM at 40 [kA-Turn]. Fig. 4. Simulation results of levitation force in the air gap from increase in MMF of HTS electromagnet.
Fig. 5. Simulation results of levitation force in the air gap from increase in MMF of HTS electromagnet and fixed MMF of armature current at 1.2 [kA-Turn].
The levitation force by the increase in the perpendicular magnetic field of HTS EM is estimated and the levitation force of z direction is calculated based on simulation method and theoretical Eq. (4). The values of magnetic flux density at different levitation gaps for MMF increases are obtained as shown in Fig. 4. In Fig. 5, the levitation force is numerically calculated by the increase current in HTS coils and the fixed MMF value of the armature current. The MMF range of HTS magnet is from 5 to 55 [kA-
Turn]. The MMF value of the armature current in the guide-way is fixed at 1.2 [kA-Turn]. As shown in Figs. 4 and 5, we investigated that levitation force by together MMF of HTS EM and AC armature current is larger over 30% than that of only HTS EM. The levitation force by the increase in MMF of armature coils and fixed MMF of HTS EM is numerically calculated. The MMF range of armature current in the guide-way is from 1.0 to 1.9 [kA-Turn]. The MMF value of the HTS EM is fixed at 40 [kA-Turn]. Compared with Figs. 5 and 6, it is confirmed that the levitation force is independent with increase in the perpendicular magnetic field of HTS magnet while the MMF of the armature current in the guide-way is operated as shown in Fig. 5. On the other hands, the levitation force is dependent on the increase in MMF of AC current while the MMF of HTS EM is operated as shown in Fig. 6. We calculated the propulsion force with increase in MMF of armature current and fixed MMF of HTS EM as shown in Fig. 7. The MMF range of armature current of 60 Hz is from 1.0 to 1.9 [kA-Turn] while the MMF of HTS EM is fixed at 40 [kA-Turn]. Compared with the propulsion force (x direction) and levitation force (z direction) in the same conditions in Figs. 6 and 7, the levitation force is about 15% larger than the propulsion force. 4. Conclusions This work presented the operating principle of the proposed proto-type HTS EM EMS based Maglev, also proper parameters of MMF by HTS EM and AC current for levitation and propulsion force. Especially, we confirmed that the levitation force is separately dependent on AC current and HTS EM, respectively. As well as, in
Y.D. Chung et al. / Physica C 471 (2011) 1487–1491
the case of the fixed AC current, the levitation force is almost independent on the MMF by the HTS EM. In addition, the levitation force is larger than propulsion force over 15% in the case of 60 Hz of AC current. The simulated and theoretical results presented here are being considered the next study which addresses the design and fabrication of EMS Maglev using the HTS–EM.
References [1] G. Bohn, G. Steinmetz, IEEE Trans. Magn. Mag 20 (1984) 1666. [2] R.M. Goodall, C.J. MacLeod, A.A. El-Abbar, A.M. Campbell, H. Jones, R.G. Jenkins, IEEE Trans. Appl. Supercond. (1995) 650.
1491
[3] S.A. Nasar, I. Boldea, Linear Motion Electric Machines, John Wiley &Sons Publication, New York, 1975. pp. 75–106. [4] G. Zhang, Y. Fang, F. Song, G. Zhu, Z. Wang, IEEE Trans. Appl. Supercond. (2004) 1850. [5] S. Kalsi, M. Proise, T. Schultheiss, B. Dawkins, IEEE Trans. Appl. Supercond. (1995) 964. [6] C. Gu, M. Liu, H. Xing, T. Zhou, W. Yin, J. Zong, Z. Han, Physica C 423 (2005) 37. [7] C.Y. Lee, J.M. Jo, B.B. Kang, Y.J. Han, D.K. Bae, Y.S. Yoon, Y.D. Chung, S.Y. Joo, Y.J. Whang, T.K. Ko, Proc. Appl. Supercond. Conf. (2010). 4LPE-09. [8] J.Y. Jang, Y.J. Kim, K.S. Chang, Y.D. Chung, C.Y. Lee, T.K. Ko, Proc. Appl. Supercond. Conf. (2010). 4LPA-03. [9] J.F. Gieras, Z.J. Piech, Linear Synchronous Motors, CRC Press, New York, 2000. pp. 134–159. [10] Y. Iwasa, Case studies in Superconducting Magnets Design and Operational Issues, Plenum Press, New York, 1994. pp. 306–308.