1. Development of a Halbach Array Magnetic Levitation System
By: Dirk DeDecker
Jesse VanIseghem
Advised by: Mr. Steven Gutschlag
Dr. Winfred Anakwa

2. Outline Introduction Previous Work Project Summary
Changes to Original Proposal
Physics of Halbach Array Magnets
Preliminary Calculations and Simulations

3. Outline Cont. Equipment List Lab work Problems and Solutions Results
Future Projects
Patents
References
Acknowledgements

4. 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

5. 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
Dr. Richard Post was the head scientist for the magnetic levitation program at Lawrence Livermore National Laboratory
Pioneered the Inductrack method of magnetic levitation in the 1990’s
Inductrack method has been researched by NASA as a means to launch rockets

6. 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.

7. Previous Work - Results
Inductrack results from Glenn Zomchek’s project (2007)

8. 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

9. Changes to Original Proposal
Focused on demonstration of levitation of the magnet device
Changed closed loop system to open loop
Not enough time this year to order new controller and model the controller and system
Working through equations and getting parts manufactured to test levitation took longer than expected

10. 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

11. 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)

12. Physics of the Inductrack Cont
Close-packed conductors, 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

13. 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

14. 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
To maximize lift, a large amount of inductance and low resistance is desired
Equation shows that we want the narrow transverse slots on the track as wide and close together as possible to maximize L

15. 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

16. Simulation with Matlab GUI

17. Equipment List 9” radius polyethylene wheel, with a width of 2”
57”x2”x1/4” copper sheet of thin conducting strips
mm 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:
Displacement Transducer Model: MLT002N3000B5C

18. Lab Work - Design Designed wheel and copper track to be built
Wheel and track were machined by Tri-City Machining

19. 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
Resistance decreases, lift/drag increases
Allows for levitation at lower rotational speeds

20. 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

21. 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
cos(25) = .9063
Arc length s = 9*0.436 = 3.93
This arc length keeps 90% of the force in the vertical direction
Fv = Fi*cos(Θ) Fi Θ
Force Diagram

22. 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

23. Lab Work – Set up

24. Lab Work – Displacement Sensor
Displacement sensor outputs linear voltage change for changes in displacement

25. 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

26. Results – Force Measurements

27. Results – Displacement Measurements

28. Results
Successful levitation of cm at 843 RPM, corresponding to a tangential velocity of 10.0 m/s
Materials for shield are ordered and will be built

29. Future Projects Closed-loop control of levitation height
Dynamically balance wheel
More dampening of vibration

30. 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

31. Applicable Patents Coffey; Howard T. Richard F. Post
Propulsion and stabilization for magnetically levitated vehicles
U.S. Patent 5,222,436
June 29, 2003
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
Richard F. Post
Magnetic Levitation System for Moving Objects
U.S. Patent 5,722,326
March 3, 1998
Inductrack Magnet Configuration
U.S. Patent 6,633,217 B2
October 14, 2003
Inductrack Configuration
U.S. Patent 629,503 B2
October 7, 2003
Laminated Track Design for Inductrack Maglev System
U.S. Patent Pending US 2003/ A1
June 19, 2003

32. 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. (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.

33. Questions?

34. Results – Backup Table 1: Displacement Sensor Calibration Measurements
Input Voltage [V]
Displacement [in]
Output Voltage [V]
5.323
0.0
0.23
0.4
0.963
0.9
2.302
1.2
3.0432
1.5
3.877
1.7
4.398
2.1
5.327

35. 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

36. Results – Backup Table 3: Displacement Sensor Measurements
Motor Voltage [V]
Motor Current [A]
RPM
Velocity [m/s]
Sensor Output [V]
Change in
Displacement [cm]
5.320 15
3.0
140
1.676
5.310 25
3.7
277
3.316
5.222 30
4.0
347
4.153
5.213 35
4.4
417
4.991
5.203 40
3.9
505
6.045
5.138 45
3.6
591
7.074
5.080 50
3.5
678
8.115
5.045 55
3.3
756
9.049
5.012 60
3.1
843
10.090
4.962