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

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

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

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-129664)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Inductrack Simulations Stopped

Inductrack Simulations 0° Induced Current Phase Drag Drag

Inductrack Simulations -45° Induced Current Phase Drag Lift

Inductrack Simulations -90° Induced Current Phase No Drag Lift

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

Design Equations (Magnetic Fields) B0 = Br (1 – e-2πd/λ)[(sin(π/M))/( π/M)] [Tesla] B0 = 0.82843 (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]

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

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

Design Equations: MATLAB GUI

Design Equation Output Parameters Standard: L = 57.619 nH R = 0.70652 mΩ R/L pole = 12261 rad/sec ωosc = 47.343 rad/sec Breakpoint Analysis: vb = 23.2038 meters/sec sb = 51.9054 miles/hour ωb = 2650.80 rad/sec Fxb = 17.02 Newtons Lift/Drag = 0.21618 Transition Analysis: vt = 107.34 meters/sec st = 240.10 miles/hour ωt = 12261.99 rad/sec Lht = 2.057 cm Fxyt = 41.198 Newtons Lift/Drag = 1

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

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

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

Calculated Levitation Height

Optimum Magnet Thickness Number of magnets per wavelength Thickness as a percent of the wavelength Ideal Magnet Thickness 0.245 λ (BU) 4 Magnets per wavelength

Physical Design Materials Wood and 1/16” Aluminum

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)

Test Wheel

Test Wheel

Induced Current

Frequency Response of Track

Levitation and Drag Forces

Maglev Train 1 & 2 Comparisons Maglev Train 1 Maglev Train 2 Track Type: Laminated Sheets Array of Inductors Breakpoint Velocity: 23.2038 meters/sec 5.8401 meters/sec Breakpoint Drag Force to Overcome: 17.0171 Newtons 41.7156 Newtons Transition Velocity: 107.3356 meters/sec 9.6872 meters/sec Levitation Height at Transition & (Max): 2.0573 cm 0.88541 cm (2.3607 cm) (1.3101 cm)

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

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

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)

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.

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)

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

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

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

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

Design Equations: (Less Clearance)

Design Equations: (Maglev Train 2)