fundamental electrophysics and engineering design of...
TRANSCRIPT
J. Hoburg 1
Fundamental electrophysics and engineering design of MAGLEV vehicles
Prof. Jim HoburgDepartment of Electrical & Computer Engineering
Carnegie Mellon University
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Gravity
Mass
Gravity field
Force on another mass
gmf =
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+
Electricity
Charge
Electric field
Force on another charge
Eqf =
_
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Magnetism
Current
Magnetic field
Force on anotherCurrent segment
BXi/f =l
X
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Magnetism (microscopic)
Microscopiccurrent loops
Magnetic field
Force on otherMicroscopiccurrent loops
NS NS
Macroscopic description ofassembly of microscopic forces:
Net force: opposite poles attract,same poles repel.
Torque: aligns to imposed field.
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Sources −> Fields
Charge −> Electric field
Current −> Magnetic field
)0
(μBcurlJ =
)0( Ediv ερ =
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Sources −> Fields(the whole story, including time varying fields as sources of fields)
Maxwell’s Equations
)0( Ediv ερ = )0
(0 με Bcurl
tEJ =∂∂+
)(EcurltB =∂∂−)(0 Bdiv=
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Electromagnetic Waves
Even in a vacuum, where and :0=J0=ρ
)(0 Bdiv=
)0(0 Ediv ε= )0
(0 με Bcurl
tE =∂∂
)(EcurltB =∂∂−
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Electromagnetic Waves(continued)
)0
(0 με Bcurl
tE =∂∂
)(EcurltB =∂∂−
mFarad1210X854.80
−=ε
mHenry610X257.10
−=μ
⎟⎠⎞⎜
⎝⎛ → Eρ
⎟⎠⎞
⎜⎝⎛ → BJ
vacuuminlightofspeedcm/s810X00.300
1===
εμ
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What does this have to do with MAGLEV?
Same fundamental physics describes:
• Light, lasers, X-rays, … (electromagnetic spectrum, why is the sky blue?)• Wireless communications (radio, TV, cell phones, wireless computers, …)• Integrated circuits (computer chips)• Lightning• Electrostatic precipitation• Electrophotography & laser printers• Microelectromechanical systems (MEMS)• Magnetic memory (tapes, disks, MRAM, magnetic stripes, …)• Rotating electrical machinery (generators & motors)• Linear synchronous motor (LSM)• Magnetic confinement for nuclear fusion• MAGLEV
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Attractive magnetic levitation:“Electromagnetic levitation”
N
S
N
S
N
S
ferromagnetic material,e.g. steel:
induced magnetization
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Attractive magnetic levitation:
z
z
f
gravitational magnetic
total
unstableequilibriumf
(inherently unstable)
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Attractive magnetic levitation:requires feedback control system to stabilize
equilibriumexcitation
vehicleverticalposition
feedbackexcitation
Σ+
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Repulsive magnetic levitation:“Electrodynamic levitation”
N
S
“track” of electrically conducting material,e.g. copper or aluminum:
induced current
A.C. coilon vehicle
v
permanent magneton moving vehicle
X X
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Repulsive magnetic levitation:This interaction involves an induced electric field in the conducting material, caused by a
time-varying imposed magnetic field.
N
S
v)(Ecurl
tB =∂∂−
EJ σ=X
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Repulsive magnetic levitation:
z
f
gravitational
magnetic
total
stableequilibrium
N
S
v
f
(inherently stable:no feedback control system needed)
X
z
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Either mechanism can be used to levitate a vehicle
• Attractive levitation • Repulsive levitation
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High speed (~ 450 km/hr) MAGLEV systems:
• German Transrapid:Attractive (“electromagnetic”) levitation via conventional electromagnetsLSM propulsion
• Japanese MLX:Repulsive (“electrodynamic”) levitation via superconducting magnets (on-board cryogenics)LSM propulsion
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Transrapid Test Vehicle TR-08
Germany, 1999
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Null Flux Suspension Vehicle MLX01
Japan, 1997 (Yamanashi test facility)
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Low speedurban MAGLEV concept:
• Permanent (NdFeB) magnet arrays on vehicle:
Repulsive (“electrodynamic”) levitation via induced currentsin track coils
LSM propulsion
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Halbachpermanent magnet arrays
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(Envisioned) Pittsburgh Urban Maglev vehicle
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Vehicle on Guideway
Linear Synchronous Motor
Suspension Track
Double Sided Magnet Array
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Magnetic fields from known sources:
computing passenger compartment field levels
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Halbach array fields: basic structure via magnetization charge description:
• propulsion magnet near fields (0.1 m above & below):
components & magnitude above components & magnitude below
-2 -1 0 1 2 3 4 5-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.2
By (red)
Bz (green)
|B| (blue)
y (m)
B in
T
By, Bz and |B| in T from propulsion magnets 0.1 m above
-2 -1 0 1 2 3 4 5-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.2
By (red)Bz (green)
|B| (blue)
y (m)
B in
T
By, Bz and |B| in T from propulsion magnets 0.1 m below
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Halbach array fields: basic structure via magnetization charge description:
• propulsion magnet far fields (0.5 m above & below):
components & magnitude above components & magnitude below
-2 -1 0 1 2 3 4 5-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1x 10-3
By (red)
Bz (green)
|B| (blue)
y (m)
B in
T
By, Bz and |B| in T from propulsion magnets 0.5 m above
-2 -1 0 1 2 3 4 5-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1x 10-3
By (red)
Bz (green)
|B| (blue)
y (m)
B in
T
By, Bz and |B| in T from propulsion magnets 0.5 m below
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Halbach array fields: basic structure via magnetization charge description:
• propulsion magnet very far fields (2.0 m above & below):
components & magnitude above components & magnitude below
-2 -1 0 1 2 3 4 5-2
-1
0
1
2x 10
-5
By (red)
Bz (green)
|B| (blue)
y (m)
B in
T
By, Bz and |B| in T from propulsion magnets 2.0 m above
-2 -1 0 1 2 3 4 5-2
-1
0
1
2x 10-5
By (red)
Bz (green)
|B| (blue)
y (m)
B in
T
By, Bz and |B| in T from propulsion magnets 2.0 m below
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Fields in passenger compartmentmagnetization charge description:
floor level contour plot seat level contour plot head level contour plot
-1 0 1-2
-1
0
1
2
3
4
5
0.00035
0.00020.0001
x (m)
y (m
)
|B| in T at floor: all magnets
-1 0 1-2
-1
0
1
2
3
4
5
0.00011
9e-0057e-005
6e-005
x (m)
y (m
)
|B| in T at seat: all magnets
-1 0 1-2
-1
0
1
2
3
4
5
3.5e-005
2.5e-005
2e-005
x (m)
y (m
)
|B| in T at head: all magnets
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Fields in passenger compartmentmagnetization charge description:
line plots at floor, seat and head levels
-2 -1 0 1 2 3 4 50
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5x 10-4
floor above magnets (red)
floor along center line (green)
seat above magnets (blue) seat along center line (cyan)
head above magnets (magenta)head along center line (yellow)
y (m)
|B| i
n T
|B| in T along lines: all magnets
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Electromechanics: computing lift & drag versus velocity
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∫∫ •−=•SC
danHdtddlE 0μ
Δ=σ
xx
KE
λπω v2=
πλσμ
τ4
0 Δ=m
Faraday’s Law for rectangular contours in lamination planes:
Electric field related to surface currents in lamination planes:
Driving frequency based upon vehicle velocity:
Time constant for induced currents:
( )[ ]∑ ∑Λ+Λ+Λ+Λ+Λ−= abselfBAx pjE ˆˆˆˆˆˆ2 ωl
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( )⎭⎬⎫
⎩⎨⎧
⎥⎦⎤
⎢⎣⎡ −= yvtjKiK x λ
π2expˆRe
[ ] kzjkyzya eeijiKzyH −−+−= )(
2
ˆ),(ˆ
[ ] kzjkyzyb eeijiKzyH +−++= )(
2
ˆ),(ˆ
All induced currents in laminations take the forms:
Resultant fields (above and below) any one lamination are:
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Simultaneous equations governing induced currents in laminations:
( ) ( )
( ) ( )
( ) ( )⎥⎥⎥⎥⎥⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢⎢⎢⎢⎢⎢
⎣
⎡
•••
≡
⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢
⎣
⎡
•••
+
+
+
=
⎥⎥⎥⎥⎥⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢⎢⎢⎢⎢⎢
⎣
⎡
•••
⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢
⎣
⎡
••••••••••••
•••⎟⎟⎠
⎞⎜⎜⎝
⎛+
•••⎟⎟⎠
⎞⎜⎜⎝
⎛+
•••⎟⎟⎠
⎞⎜⎜⎝
⎛+
∫∫
∫∫
∫∫
−−
−−
−−
−−
−−
−−
3
2
1
3
2/
2/3
2/
2/
2
2/
2/2
2/
2/
1
2/
2/1
2/
2/
3
2
1
ˆ
ˆ
ˆ
2
,ˆ,ˆ
,ˆ,ˆ
,ˆ,ˆ
2
ˆ
ˆ
ˆ
11
11
11
2313
2312
1312
z
z
z
BBzA
Az
BBzA
Az
BBzA
Az
m
kdkd
kd
m
kd
kdkd
m
I
I
I
pj
dxzxHdxzxH
dxzxHdxzxH
dxzxHdxzxH
pj
K
K
K
pjee
epj
e
eepj
lll
l
l
l
l
l
l
l
l
l
l
l
τω
τω
τω
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Time-averaged lift and drag forces (per wavelength) on vehicle:
[ ] { }iyi
iBi
ByAi
Ayi
iIK
pdxzxHzxHK
pL ˆˆRe
2),(ˆ),(ˆˆRe
2*0
2/
2/
*0 ∑∫∑ −≡⎭⎬⎫
⎩⎨⎧
+−=−
λμλμλ
l
l
[ ] { }izii
BiBzAi
Azi
iIK
pdxzxHzxHK
pD ˆˆRe
2),(ˆ),(ˆˆRe
2*0
2/
2/
*0 ∑∫∑ −≡⎭⎬⎫
⎩⎨⎧
+−=−
λμλμλ
l
l
Horizontal (y) and vertical (z) field components are based upon 3-D magnetization charge description.
Complex amplitudes are based upon first Fourier components of y dependences at each value of x.
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Double (5 above X 3 below) arrayFull 3-D magnetization charge fields:
Double (5 above X 3 below) arrayFirst Fourier component approximations:
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Comparison with Dick Post’s model for LLNL test rig
Post: Hoburg:
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Comparison with Dick Post’s model for LLNL test rig
Post: Hoburg:
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