Development of a Halbach
Array Magnetic Levitation
System
By:
Dirk DeDecker
Jesse VanIseghem
Advised by: Mr. Steven Gutschlag
Dr. Winfred Anakwa
Outline
• Introduction
• Previous Work
• Project Summary
• Changes to Original Proposal
• Physics of Halbach Array Magnets
• Preliminary Calculations and Simulations
Outline Cont.
• Equipment List
• Lab work
• Problems and Solutions
• Results
• Future Projects
• Patents
• References
• Acknowledgements
Introduction
• Magnetic levitation
•
technology can be
used in high speed
train applications
Maglev suspension
allows trains to
accelerate to over 300
mph and reduces
maintenance by
almost eliminating all
moving parts
Previous Work
• Dr. Sam Gurol and Dr.
Richard Post have
worked on “The
General Atomics Low
Speed Urban Maglev
Technology
Development
Program” utilizing the
rotary track method
Previous Work Cont.
• Work by Paul Friend in 2004
– Levitation Equations
– Matlab GUI
• Work by Glenn Zomchek in 2007
– Design of system using Inductrack method
– Successful levitation to .45 mm.
Previous Work - Results
•Inductrack results from Glenn Zomchek’s
project (2007)
Project Summary
• The goals of our project are:
– Develop an improved Halbach array magnetic
levitation system to achieve 0.5 cm at a track
speed of 10 m/s
– Demonstrate successful levitation
Changes to Original Proposal
• Focused on demonstration of levitation of
the magnet device
• Changed closed loop system to open loop
Physics of Halbach Array Magnets
• Designed by Klaus Halbach
• Creates a strong, enhanced magnetic field on one side, while almost
•
cancelling the field on the opposite side
Peak strength of the array:
B0=Br(1-e-kd)sin(π/M)/(π /M) Tesla
k = 2π/λ, M = # of magnets,
Br = magnet strength, d = thickness of each magnet
λ = Halbach array wavelength
Physics of the Inductrack
• Halbach array moving at velocity v m/sec
over inductrack generates flux
φ0sin(ωt), φ0 Tesla-m2, linking the circuit
ω = (2π/λ)v rad/sec
• Voltage induced in inductrack circuit:
V(t) = ω φ0cos(ωt)
• Inductrack R-L circuit current equation:
V(t) = L*di(t)/dt + R*i(t)
Physics of the Inductrack Cont
• Close-packed conductors,
R1
V1
L1
•
•
•
made utilizing thin
aluminum or copper
sheets
Allows for levitation at
low speeds
Can be modeled as an RL
circuit
Transfer function has
pole at -R/L
Physics of the Inductrack Cont.
• Dr. Post used the induced current and
magnetic field to derive
– Lift force:
• <Fy> = Bo2w2/2kL*1/1+(R/ωL)2*e-ky1
– Drag force:
• <Fx> = Bo2w2/2kL* (R/ωL) /1+(R/ωL)2*e-ky1
Where y1 is the levitation height in meters
Physics of the Inductrack Cont.
• Phase shift relates to drag and levitation
forces
• Lift/Drag = ω*L/R
• L = μ0 w/(2kdc) , where dc is the center to
center spacing of conducting strips and w
is the track width
Physics of the Maglev System
• Force needed to levitate:
F = m*9.81 Newtons
m=.465 kg
F = 4.56 N
• Breakpoint velocity:
– By solving Lift/Drag for v,
vb=λω/(2π) m/sec
Simulation with Matlab GUI
Equipment List
• 9” radius polyethylene wheel, with a width of 2”
• 57”x2”x1/4” copper sheet of thin conducting
•
•
•
•
•
•
strips
125 - 6mm cube neodymium magnets
Balsa wood structure to house the 5x25 Halbach
array
Metal and hardware for motor stand
Dayton permanent magnet DC motor
Digital Force Gauge Model: 475040
Displacement Transducer Model:
MLT002N3000B5C
Lab Work - Design
• Designed wheel and copper track to be
built
• Wheel and track were machined by TriCity Machining
Lab Work - Design Cont.
• Decided to switch from aluminum track to
copper
– Lower resistivity of copper(Cu = 1.68x10-8
Ω*m, Al = 2.82x10-8 Ω*m)
• R = PcRc/(Nt*c*Ns) , where Rc is the resistivity
• Lift/Drag – 2*π*v/λ*(L/R)
• Aluminum Lift/Drag ratio = 0.102
• Copper Lift/Drag ratio = 0.171
Lab Work – Halbach Array Device
• Balsa wood structure built
• Magnets glued into balsa wood
– Used shrink wrap and epoxy
• Aluminum covering built to ensure
magnets do not eject from balsa wood
Lab Work – Halbach Array Device
• Array is 5x25 magnets
• λ = 28 mm
• Makes our arc length
approximately 8”, with an
angle of 25 degrees to either
side
Fv = Fi*cos(Θ)
Fi
Θ
– cos(25) = .9063
– Arc length s = 9*0.436 = 3.93
• This arc length keeps 90% of
the force in the vertical
direction
Force Diagram
Lab Work – Set up
• Motor stand designed and built to hold
motor, wheel, and balsa wood device
• Holes drilled in copper track and track
connected to wheel
• All pieces assembled into the complete
system
Lab Work – Set up
Lab Work – Displacement Sensor
• Displacement sensor outputs linear
voltage change for changes in
displacement
Problems and Solutions
• Copper track too short
• Once holes drilled in copper, track became
weak
• Magnets were very difficult to glue in
direction they had to be
Results – Force Measurements
Levit at ion For ce M easur ement s
15
Force [ N]
10
5
0
0
2
4
6
8
Tangent i al V el o ci t y [ m/ s]
10
Results – Displacement
Measurements
Lev i t at i on H ei ght M easur ement s
0.4
0.35
Displacement [ cm]
0.3
0.25
0.2
0.15
0.1
0.05
0
0
2
4
6
8
Tangent i al V el o ci t y [ m/ s]
10
12
Results
• Successful levitation of 0.365 cm at 843
RPM, corresponding to a tangential
velocity of 10.0 m/s
• Materials for shield are ordered and will be
built
Future Projects
• Closed-loop control of levitation height
• Dynamically balance wheel
• More dampening of vibration
Acknowledgements
• Dr. Winfred Anakwa
• Mr. Steven Gutschlag
• Mr. Joe Richey and Tri-City Machining
• Mr. Darren DeDecker and Caterpillar Inc.
• Mrs. Sue DeDecker
• Mr. Dave Miller
Applicable Patents
•
Richard F. Post
Magnetic Levitation System for Moving
Objects
U.S. Patent 5,722,326
March 3, 1998
•
Richard F. Post
Inductrack Magnet Configuration
U.S. Patent 6,633,217 B2
October 14, 2003
•
Richard F. Post
Inductrack Configuration
U.S. Patent 629,503 B2
October 7, 2003
•
Richard F. Post
Laminated Track Design for Inductrack
Maglev System
U.S. Patent Pending US 2003/0112105 A1
June 19, 2003
•
Coffey; Howard T.
Propulsion and stabilization for magnetically
levitated vehicles
U.S. Patent 5,222,436
June 29, 2003
•
Coffey; Howard T.
Magnetic Levitation configuration
incorporating levitation,
guidance and linear synchronous motor
U.S. Patent 5,253,592
October 19, 1993
•
Levi;Enrico; Zabar;Zivan
Air cored, linear induction motor for
magnetically levitated
systems
U.S. Patent 5,270,593
November 10, 1992
•
Lamb; Karl J. ; Merrill; Toby ; Gossage;
Scott D. ; Sparks;
Michael T. ;Barrett; Michael S.
U.S. Patent 6,510,799
January 28, 2003
Works Consulted
• Glenn Zomchek. Senior Project. “Redesign of a Rotary Inductrack for Magnetic
Levitation Train Demonstration.” Final Report, 2007.
• Paul Friend. Senior Project. Magnetic Levitation Technology 1. Final Report, 2004.
• Gurol, Sam. E-mail (Private Conversation)
• Post, Richard F., Ryutov, Dmitri D., “The Inductrack Approach to Magnetic
Levitation,” Lawrence Livermore National Laboratory.
• Post, Richard F., Ryutov, Dmitri D., “The Inductrack: A Simpler Approach to Magnetic
Levitaiton,” Lawrence Livermore National Laboratory.
• Post, Richard F., Sam Gurol, and Bob Baldi. "The General Atomics Low Speed Urban
Maglev Technology Development Program." Lawrence Livermore National Laboratory
and General Atomics.
Questions?
Results – Backup
Table 1: Displacement Sensor Calibration Measurements
Input Voltage [V]
Displacement [in]
Output Voltage
[V]
5.323
0.0
0.23
5.323
0.4
0.963
5.323
0.9
2.302
5.323
1.2
3.0432
5.323
1.5
3.877
5.323
1.7
4.398
5.323
2.1
5.327
Results – Backup
Table 2: Force Sensor Measurement
Motor
Voltage [V]
Motor
Current [A]
RPM
Velocity
[m/s]
Force [N]
15
2.8
140
1.676
1.1
25
4.3
260
3.112
3.6
35
5.4
390
4.668
7.6
45
6.0
533
6.379
11.0
50
6.2
609
7.289
12.3
55
679
8.127
14.2
59
741
8.869
14.9
Results – Backup
Table 3: Displacement Sensor Measurements
Motor
Voltage
[V]
Motor
Current
[A]
RPM
Velocity
[m/s]
Sensor
Output
[V]
Change in
Displacement
[cm]
0
0
0
0
5.320
0
15
3.0
140
1.676
5.310
0.010196
25
3.7
277
3.316
5.222
0.099919
30
4.0
347
4.153
5.213
0.109095
35
4.4
417
4.991
5.203
0.11929
40
3.9
505
6.045
5.138
0.175367
45
3.6
591
7.074
5.080
0.244698
50
3.5
678
8.115
5.045
0.280384
55
3.3
756
9.049
5.012
0.31403
60
3.1
843
10.090
4.962
0.365008