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

J. Hoburg 35

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.

J. Hoburg 36

Double (5 above X 3 below) arrayFull 3-D magnetization charge fields:

Double (5 above X 3 below) arrayFirst Fourier component approximations:

J. Hoburg 37

Comparison with Dick Post’s model for LLNL test rig

Post: Hoburg:

J. Hoburg 38

Comparison with Dick Post’s model for LLNL test rig

Post: Hoburg:

J. Hoburg 39