The Inductrack: A Home-Grown Maglev

System for our Nation

Lockheed Martin Palo Alto Colloquium

Presented by: Richard F. Post,

Lawrence Livermore National Laboratory

15 Apr 2004

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There are many reasons why magnetically levitated

trains could be preferred over conventional trains

• Inter-city transportation: Much higher speeds than are possible

with steel-wheeled trains, lower noise, greater passenger

comfort, increased safety against mechanical failures, reduced

maintenance.

• Relative to aircraft: Higher energy efficiency, safer, less

weather-dependent, and would permit in-city departure and

arrival.

• Urban transit systems: Lower noise, much lower maintenance,

greater rider comfort, can climb steeper grades, potentially

higher energy efficiency than buses or rubber-tired urban trains.

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Two different types of Maglev trains have been built and

demonstrated at full scale at speeds up to 500 km/hr

• Magnetic attraction - EMS (Electro-Magnetic Suspension) systems,

using servo-controlled electromagnets on the train car, attracted

upward to a iron-plate rail.

• Magnetic repulsion -EDS (Electro-Dynamic Suspension) systems,

using cryogenically cooled superconducting magnets on the moving

car, repelled by currents induced in coils embedded in “tracks” on each

side of the train.

• Example EMS system: The German Trans-Rapid TR08 demonstration

train and 30 kilometer test track, with operating speeds up to 450

km/hr.

• Example EDS system: The Japanese Yamanashi demonstration train,

with speeds of 500 km/hr on a 18 kilometer test track.

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The German Trans-Rapid maglev train is an EMS

system using electromagnets attracted to an iron “rail”

Gap: 1 cm ± 1 mm

Iron-plate "rail"

Iron magnet yokeTo control amplifier To control amplifier

(on train car)

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The German Trans-Rapid maglev train uses powered

electromagnets attracting upward to an iron rail

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The Japanese Yamanashi demonstration maglev

train uses superconducting magnets on its sides

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At speed superconducting magnet coils on the Japanese

train induce currents in coils in the “tracks” on each side

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An EDS Urban Transit Maglev system test track and

test car has been built and operated in Korea

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The proposed “Swiss-Metro” would link major Swiss

cities by maglev trains running in evacuated tunnels.

Proposed in 1974, and under study since 1989, the Swiss-Metro system would carry

200 passengers in train cars running every 6 minutes. The trains would operate in

tunnels evacuated to 1/10 atmosphere (atmos. pressure at Concorde flying altitude).

Contactless energy

transfer system

Linear electric motor

and guidance system

Magnetic levitation

inductor

Emergency pavementEmergency guidance

And braking system

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The LLNL “Inductrack” maglev system developed as a

spin-off from the Lab’s flywheel energy storage program

• It is an EDS system, but uses only permanent magnets and does not

require cryogenically cooled superconducting coils

• It is a passive system that requires no control circuits to maintain stable

levitation

• Levitation off of the auxiliary wheels occurs as soon as a low “transition

speed” is reached.

• The Inductrack system is”fail safe” in the event of a power failure; the

train car would simply slow down and settle down on its auxiliary

wheels at a low speed.

• The simplicity of the Inductrack should make it substantially less

expensive than the present EDS or EMS maglev trains.

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LLNL Flywheel Technology

and Applications

Integrated System

Composite rotor Lock./11

The Inductrack system optimizes levitation efficiency,

using permanent magnets and a passive “track.”

• Special arrays (Halbach arrays) of permanent

magnets are employed, mounted on “bogies”

underneath the car.

• The periodic magnetic fields from the magnet arrays

on the moving train car induce currents in a close-

packed array of shorted electrical coils in the “track”

to produce levitation (above a low “transition” speed).

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In the 1980’s Klaus Halbach came up with better ways to

employ permanent magnets in focusing particle beams

• The Halbach array makes optimal use of permanent-magnet material by concentrating the field on the front face of the array, while nearly canceling the field on the back face of the array

• The magnetic field on the front face of the array varies sinusoidally with position parallel to the face of the array, and falls off exponentially with distance away from the front face.

• Only permanent-magnet material is employed in Halbach arrays; no “back iron”elements or iron poles are needed.

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Klaus Halbach 1925-2000

Klaus Halbach, good friend

and kind mentor, died on 11 May 2000.

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Fields of the in-between permanent-magnet bars add to

the field of the adjacent bars below and cancel above

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The moving Halbach array magnets induce currents in

the close-packed shorted circuits embedded in the track

End view of Halbach array on moving car

Upper conductors of short ed levitation circuits in track

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One possible configuration of the Inductrack is the

magnetic equivalent of the flanged wheels on a train

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The levitating force becomes effective at very low

vehicle speeds and remains constant at high speeds

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0 5 10 15 20 25 30

0.0

0.2

0.4

0.6

0.8

1.0

Fraction of Maximum Levitation Force vs Speed

Speed (km/hr)

Fra

cti

on

of

Ma

xim

um

Lif

t F

orc

e

Transition speed (1.2 km/hr)

The Lift-to-drag ratio of the Inductrack increases linearly

with speed, and can exceed 200 at maglev train speeds

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0 100 200 300 400 500

0

50

100

150

200

250

300

350

400

450

Lift/Drag Ratio for Inductrack and for Conducting Plate

Speed (km/hr)

Lif

t/D

rag

Conducting plate

Inductrack (L = 0)

Inductrack ( K = 3.0 Newtons/Watt)

(Wav elength of Halbach array = 1.0 m.)

Jet airplane

Conv . rails @ 250 km/hr

(aero. not included)

Our Inductrack model car is launched by

pulses from a series of electronic circuits

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The model Inductrack levitated and traveled down its

track in good agreement with the theoretical design

• Front-view photograph of the cart and the track coil

assembly. The cart is shown in flight approximately 3

centimeters above the track at approximately 10.5 m/s.

•

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Ferrite “tiles” add inductive loading for our model

Inductrack, reducing the transition speed.

Coil

Ferrite "Tile"

Schematic Drawing of Inductrack Model Track

Wood

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The Inductrack maglev concept may help NASA reduce

the cost of launching satellites

• NASA studies project that savings of 30 to 40 percent of the rocket fuel, permitting single-stage-to-orbit missions, should be possible with maglev acceleration and launching up a sloping track at Mach 0.8.

• Under NASA sponsorship, we designed, built, and operated a model Inductrack system to demonstrate the concept, including a pulsed high-acceleration electromagnetic drive system.

• Preliminary estimates indicate that a full-scale Inductrack system for magnetically launching large rockets should be technically feasible.

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Carbon fiber cradle was designed using ANSYS

Locations of each 5-magnet Halbach array(same front and back)

Ribs needed to withstand the repulsive force caused by the magnets andinduced current

65-cm

Cradle weight = 3.5 kg

Magnet weight = 5.5 kg

The cradle is fabricated from high-modulus carbon-fiber

composite to maximize rigidity and minimize weight

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The levitated cradle surrounds the “track” that is

composed of levitation coils and interleaved drive coils

Guide rails to preventmagnets from hittingtrack prior to levitation

One of 6 magnets(3 front, 3 back)that provide levitationand centering forces

Steel box beam

Drive &levitationcoils intrack

C-fibercradlewith ribsto supportmagnetic force

Fiberglass I-beam

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The NASA model track is made up of modules that are

composed of 13 interleaved drive and levitation coils

Drive Coil #6 GA Magnet Wire

4

1

Coil A ssembly: 1 3 Drive and Levit at ion Coils

Lev it at ion Coil #1 0 GA Magnet Wire

Dimensions incm

Tolerance + / - 0.05

5

6 5

1 2 1 5

Support blocks that

attach coils to rail

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An analytical theory exists which can be used to

optimize the design parameters of an Inductrack system

• Lift-to-Drag ratios can be specified by design over a

wide range of parameters

• The ratio of levitated weight to magnet weight can be

optimized for a given application

• Levitation forces approaching the theoretical

maximum can be achieved in practical designs

• Economic factors, such as track conductor costs, can

be analyzed and optimized

• Stability can be assured by the satisfaction of specific

criteria (e.g., geometry, damping factors, etc.)

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The levitation and drag forces of the Inductrack can be

analyzed using circuit theory and Maxwell’s equations

Induced voltage :

V LdI

dtRI 0 cos(t)

Induced current (steady state):

I(t) = 0

L

1

1(R /L)2

sin(t) (R /L)cos(t)

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To analyze the Inductrack we start with the equations

for the magnetic field components of a Halbach array

Bx B0 sin(kx) exp[k(y1 y)]

By B0 cos(kx) exp[k(y1 y)]

B0 Br [1 exp(kd)]sin( / M)

/ M

Br = Remanent field (Tesla), M = no. of magnets/wavelength.

d(meters) = thickness of Halbach array magnets, k = 2π/l

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Integrating Bx in y gives the flux linked by the Inductrack

circuits and yields equations for the Lift and Drag forces

Fy B0

2w2

2kL

1

1 (R /L)2

exp(2ky1)

Fx B0

2w2

2kL

(R /L)

1 (R /L)2exp(2ky1)

w = width of Halbach array, L,R = circuit induct./resistance

Newtons/circuit

Newtons/circuit

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Dividing <Fy > by <Fx > yields an equation for the Lift-to-

Drag ratio as a function of the track circuit parameters.

Lift

Drag

L

R

2v

l

L

R

The Lift/Drag ratio increases linearly with velocity,

and with the L/R ratio of the Inductrack track circuits.

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The levitation efficiency (Newtons/Watt) can be determined

directly from the equation for the Lift/Drag ratio

Since P Fx v, the equation

for the levitation efficiency is:

K Fy

P

2

l

L

R

Newtons/Watt

Typical K values: K=1.0 to 5.0, depending on track design

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Design of the Levitation Track

The track design must fulfill the need for efficient and

cost-effective levitation coil circuits to take full

advantage of the Inductrack maglev configuration.

Two alternative track designs:

Litz-wire cables, encased in stainless steel tubes

Slotted, laminated, conductor sheets, bonded and

mechanically reinforced

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A “ladder track” can be constructed using litz-wire

cables encapsulated in thin-wall stainless-steel tubes

Cable ends soldered

Into shorting bus bars

The use of “braided” litz-wire in the cables assures current

uniformity and minimizes parasitic eddy-current lossesLock./34

The laminated “ladder track” is a high-efficiency, cost-

effective, alternative to the litz-wire ladder track

Laminated stack of slotted thin copper or anodized aluminum sheets

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The feasibility of the laminated track as an alternative

to the litz-wire ladder track is under study at LLNL

A computer code based on the Inductrack theory has been

written to predict the lift and drag performance of the

laminated track.

An instrumented linear “test track” has been built

to provide scalable data for comparison with the code

and for use in the design of full-scale tracks.

The LLNL code has been benchmarked against test-rig

measurements for several Inductrack magnet

configurations.

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Photo of LLNL Laminated-Track Test Rig

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There is good agreement between the LLNL code

predictions and the Inductrack test-rig measurements

The code predictions are shown for zero and plus and minus 1.0 mm displacements

Track: 15 laminations of 0.5 mm thick copper sheet. Slots: 15 cm. long, 0.25 mm. wide.

Conductor strips 2.5 mm wide.

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The Laboratory is a member of a team that is designing an

urban maglev system employing the Inductrack approach.

• The team (which also includes several engineering firms in the Pittsburgh, Penn. area), was organized by General Atomics (San Diego) and is funded by the Federal Transit Administration.

• The advantages of maglev in urban settings (relative to conventional urban rail systems) include: Lower noise, lower maintenance, higher efficiency, higher grade and tighter turn capabilities (allowing operation on elevated tracks that can accommodate to an urban environment without the need for underground-tunnel operation).

• Better to satisfy urban (moderate speed) applications we have developed the Inductrack II configuration, which greatly reduces electromagnetic drag forces at urban speeds (relative to Inductrack I, which is more suitable for high-speed applications).

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The Inductrack II maglev employs dual Halbach arrays,

reducing drag losses and enhancing levitation forces

• A cantilevered ladder track is used, interacting with two facing Halbach

arrays, one above, and one below the track.

• The horizontal component of the magnetic fields from the upper and

lower Halbach arrays are additive, while the vertical field of the lower

array opposes that of the upper array.

• By adjusting the thickness or the width of the magnets of the lower

array relative to the upper array an optimum level of induced levitating

current can be achieved for a given levitated weight and magnet

weight.

• Either a litz-cable “flat track” or slotted, laminated, sheet conductors

with fiber composite reinforcement could be used to construct the

cantilevered track.

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Adjusting the relative height of the Inductrack II Halbach

arrays optimizes the levitation force vs drag power

Vert. field null

Levitation height

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Inductrack II Lift-to-Drag Ratios

• The L/D for Inductrack II systems is much higher than for Inductrack I

Inductrack I Inductrack II

Guideway parameters (both cases): 2.0 cm. laminated copper, p.f. = 0.9

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Vehicle on

Guideway

Linear

Synchronous

Motor

Suspension Track

Double Sided

Magnet Array

The General Atomics urban maglev system employs

The Inductrack II dual-Halbach-array configuration

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A full-scale levitation/propulsion test track is nearing

completion at General Atomics in San Diego

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Summary

• Magnetic levitation (maglev) trains have been under development for many years in Germany and Japan for high-speed rail systems.

• Maglev would offer many advantages as compared to conventional rail systems or inter-city air travel.

• The cost and complexity of presently developed high-speed maglev trains has slowed their deployment.

• The Inductrack maglev system, employing simple arrays of permanent magnets, may offer an economic alternative to existing maglev systems.

• The simplicity of the Inductrack may make it attractive for use in a variety of applications, including urban maglev systems, people movers, and point-to-point shipment of high-value freight

• The Inductrack, employing Halbach arrays, is an example of a practical application of the results of fundamental studies in magnetics and particle-accelerator physics.

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