1. Department of Electrical and Computer Engineering
BRADLEY UNIVERSITY
Department of Electrical and Computer Engineering
Sr. Capstone Project
Student:
Paul Friend
Advisor:
Dr. Anakwa

2. Overview: Background Information Project Summary System Block Diagram
Inductrack Theory
Halbach Array Analysis
Inductrack Analysis
Design Equations
Physical Design
Testing
Results
Comparison
Conclusion

3. Background Information
Choice - Inductrack:
Newest method for Maglev trains
Does not require high power for operation
Does not require complex controls for stability

4. Background Information
Inductrack:
Created by Dr. Richard F. Post in the late 1990’s at Lawrence Livermore National Laboratory
20 meter test track
Burst Propulsion
“Inductrack Demonstration Model, R. F. Post (UCRL-ID )

5. Background Information
Inductrack:
Contracted by NASA for Satellite Launcher
Low-Speed Urban Maglev Program
“Maglev on the Development Track for Urban Transportation, LLNL

6. Project Summary Determine and Understand the Inductrack Theory
Design and Simulate a levitating train utilizing the Inductrack Theory
Build a levitating train and track
Test the Inductrack parameters
If time allows, design and test a propulsion system

7. System Block Diagram High Level: Train Velocity Maglev System
Desired Velocity
Train Velocity
Levitation

8. System Block Diagram Low Level: Controller Desired Velocity Propulsion
Method
Train Velocity
Sensor
Constant
Induced Current
Induced
Magnetism
Train
Levitation

9. Magnets (Induced Current)
Permanent magnet moving at a slow velocity across a closed circuit inductor. Induced current phase = 0 o
Repulsion Drag force
Attraction Drag Force

10. Magnets (Induced Current)
Permanent magnet moving at a fast velocity across a closed circuit inductor. Induced current phase = -90 o
Attraction Force ?
Repulsion Levitation Force

11. Halbach Array Created by Klaus Halbach
Creates a strong, nearly one-sided magnet with a sinusoidal field by directing the magnetic fields.

12. Inductrack Theory Halbach Arrays reacting with track of inductors.
Direction of Movement
Track (Inductor)

13. Inductrack Inductor Physics Lenz’s Law Discovered in 1834
Eddy currents created due to moving magnetic field
(Not guided)

14. Inductrack Basic Methods of Inductors: Array of Inductors
Stranded Rungs
Laminated Aluminum or Copper

15. Inductrack Array of Inductors Used in 1st Inductrack
Insulated Litz-wire

16. Inductrack Stranded Rungs Square Litz-wire bulks
Used for Low-Speed Urban Maglev Program

17. Inductrack Laminated Copper & Aluminum Thin Sheets
Slots cut to guide eddy currents
Slots terminated at ends for “shorts”

18. Stopped/Low Velocities
Basic Operation
Wheels - Supports and guides until levitation occurs
Top Halbach Arrays - Levitation
Side Halbach Arrays - Guidance
Bottom Halbach Arrays - Stability for sharp turns
Fast Velocities
Stopped/Low Velocities

19. Halbach Array Design Halbach Array formation used for Maglev Train 1
Uses least amount of
magnets for most amount
of induced current.

20. Inductrack Simulations
Stopped

21. Inductrack Simulations
0° Induced Current Phase
Drag
Drag

22. Inductrack Simulations
-45° Induced Current Phase
Drag
Lift

23. Inductrack Simulations
-90° Induced Current Phase
No Drag
Lift

24. Circuit Theory I(s) = (V/L)/(R/L + s) Pole at R/L Note:
V increases with velocity

25. Design Equations (Magnetic Fields)
B0 = Br (1 – e-2πd/λ)[(sin(π/M))/( π/M)] [Tesla]
B0 = (1/2” Gr. 38 NdFeB Cube Magnets)
Bx = B0 sin((2π/λ)x) e-(2π/λ) (y1 – y) [Tesla]
By = B0 cos((2π/λ)x) e-(2π/λ) (y1 – y) [Tesla]

26. Design Equations Circuit Equation: V = L dI/dT + RI = ωφ0 cos(ωt) [V]
Magnetic Flux:
φ = wBo/(2π/λ) e (-2πy/λ) sin(2πx/λ) [1 – e (-2πy/λ)]
Current:
I(t) = (φ/L) [1/(1 + (R/ωL)2)] [sin(ωt) + (R/ωL)cos(ωt)] Amps/Circuit
Forces:
Fy = Iz Bx w Newtons/Circuit
Fx = Iz By w Newtons/Circuit
F = Iz w (Bx + By) Newtons/Circuit

27. Design Equations Forces:
Levitation Force:
Fy(ω) = levs[Bo2 w/(4πL dc/λ)] [ 1/(1 + (R/ωL)2)]A e (-4π y/λ) Newtons
Fy(s) = levs[Bo2 w/(4πL dc/λ)] {(L2 s2)/[(s - R/L) (s + R/L)]} A e (-4π y/λ) Newtons
Drag Force:
Fx(ω) = levs[Bo2 w/(4πL dc/λ)] [ (R/ωL)/(1 + (R/ωL)2)]A e (-4π y/λ) Newtons
Fx (s) = levs[Bo2 w/(4πL dc/λ)] {(RL s)/[(s - R/L) (s + R/L)]} A e (-4π y/λ) Newtons
F (ω) = Fy(ω) + Fx(ω) Newtons
F(s) = levs[Bo2 w/(4πL dc/λ)] [(L2s)/(s + R/L)] A e (-4π y/λ) Newtons
Lift/Drag = <Fy>/<Fx> = ω L/R

28. Design Equations: MATLAB GUI

29. Design Equation Output Parameters
Standard:
L = nH
R = mΩ
R/L pole = rad/sec
ωosc = rad/sec
Breakpoint Analysis:
vb = meters/sec
sb = miles/hour
ωb = rad/sec
Fxb = Newtons
Lift/Drag =
Transition Analysis:
vt = meters/sec
st = miles/hour
ωt = rad/sec
Lht = cm
Fxyt = Newtons
Lift/Drag = 1

30. Calculated Forces Locked Levitation Transition Velocity
Unlocked Levitation
Locked Drag
Unlocked Drag

31. Calculated Forces (Zoomed)
Locked Drag
Locked Levitation
Unlocked Levitation
Unlocked Drag
Breakpoint Velocity

32. Calculated Forces (Bode)
Total Force
Drag Force
Total Phase
Levitation Force

33. Calculated Levitation Height

34. Optimum Magnet Thickness
Number of magnets per wavelength
Thickness as a percent of the wavelength
Ideal Magnet Thickness λ (BU)
4 Magnets per wavelength

35. Physical Design
Materials
Wood and 1/16” Aluminum

36. Testing Inductrack Testing Use of a horizontal or lateral wheel
Utilized by Post
“The General Atomics Low Speed Urban Maglev Technology Development Program,” Gurol & Baldi (GA)

37. Test Wheel

38. Test Wheel

39. Induced Current

40. Frequency Response of Track

41. Levitation and Drag Forces

42. Maglev Train 1 & 2 Comparisons
Maglev Train 1 Maglev Train 2
Track Type:
Laminated Sheets Array of Inductors
Breakpoint Velocity:
meters/sec meters/sec
Breakpoint Drag Force to Overcome:
Newtons Newtons
Transition Velocity:
meters/sec meters/sec
Levitation Height at Transition & (Max):
cm cm
( cm) ( cm)

43. Maglev Train 1 & 2 Comparisons
Maglev Train Maglev Train 2
(Using 5mm Fixed Height)

44. Conclusions Wire wrung method best for laboratory setting Tradeoffs -
Levitation Force vs. Efficiency
Levitation Force vs. Levitation Velocity
Applications -
Maglev Trains
Frictionless Bearings
Motors and Generators

45. Tasks Completed and Troubles
The Inductrack theory has been understood
Magnetic simulations
Train has been built
Laminated copper track has been built*
Testing has occurred*
Conclusions have been made
(* - trouble)

46. Parts and Equipment 40 - 1/2” NdFeB, Grade 38 Cubes $90.00
2 -1/2 Alloy 110 Copper Sheets $134.10
Litz-wire Bulks, Copper Sheets, Aluminum Sheets, Wheels, Conductive balls, and Electromagnets
Cart/Train non inductive materials and CNC router machine time provided by Midwestern Wood Products Co.

47. Resources Many Documents by Post & Ryutov (LLNL)
General Conversation with Richard F. Post (LLNL)
General Conversation with Phil Jeter (General Atomics)
General Conversation with Hal Marker (Litz-wire)
General Conversation with Dr. Irwin (BU)
General Conversation with Dr. Schertz (BU)
Dave Miller (BU ME Department)

48. Department of Electrical and Computer Engineering
BRADLEY UNIVERSITY
Department of Electrical and Computer Engineering
Sr. Capstone Project
Advisor:
Dr. Anakwa
Student:
Paul Friend

49. Propulsion Types: Linear Synchronous Motor (LSM)
Linear Induction Motor (LIM)

50. Propulsion Linear Synchronous Motor (LSM)
Used for Low-Speed Urban Maglev Program
Allows for large air gap ~ 25 mm
Varied 3-phase frequency and current for contols
Solid copper cables and laminated iron rails
Works with Halbach array

51. Propulsion Linear Induction Motor (LIM) Synchronized electromagnets
Precision sensing required
Controled via the current
PWM
Current Level

52. Design Equations: (Less Clearance)

53. Design Equations: (Maglev Train 2)