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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

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slide1

BRADLEY UNIVERSITY

Department of Electrical and Computer Engineering

Sr. Capstone Project

Student:

Paul Friend

Advisor:

Dr. Anakwa

slide2

Overview:

  • Background Information
  • Project Summary
  • System Block Diagram
  • Inductrack Theory
  • Halbach Array Analysis
  • Inductrack Analysis
  • Design Equations
  • Physical Design
  • Testing
  • Results
  • Comparison
  • Conclusion
slide3

Background Information

  • Choice - Inductrack:
  • Newest method for Maglev trains
  • Does not require high power for operation
  • Does not require complex controls for stability
slide4

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)

slide5

Background Information

  • Inductrack:
  • Contracted by NASA for Satellite Launcher
  • Low-Speed Urban Maglev Program

“Maglev on the Development Track for Urban Transportation, LLNL

slide6

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
slide7

Maglev

System

Train Velocity

Desired Velocity

Levitation

System Block Diagram

High Level:

slide8

Desired Velocity

Controller

Propulsion

Method

Train Velocity

Sensor

Constant

Induced Current

Induced

Magnetism

Train

Levitation

Levitation

Constant

System Block Diagram

Low Level:

slide9

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

slide10

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

slide11

Halbach Array

  • Created by Klaus Halbach
  • Creates a strong, nearly one-sided magnet with a sinusoidal field by directing the magnetic fields.
slide12

Inductrack Theory

Halbach Arrays reacting with track of inductors.

Direction of Movement

Track (Inductor)

slide13

Inductrack

  • Inductor Physics
  • Lenz’s Law
  • Discovered in 1834
  • Eddy currents created due to moving magnetic field
  • (Not guided)
slide14

Inductrack

  • Basic Methods of Inductors:
  • Array of Inductors
  • Stranded Rungs
  • Laminated Aluminum or Copper
slide15

Inductrack

  • Array of Inductors
  • Used in 1st Inductrack
  • Insulated Litz-wire
slide16

Inductrack

  • Stranded Rungs
  • Square Litz-wire bulks
  • Used for Low-Speed Urban Maglev Program
slide17

Inductrack

  • Laminated Copper & Aluminum
  • Thin Sheets
  • Slots cut to guide eddy currents
  • Slots terminated at ends for “shorts”
slide18

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

slide19

Halbach Array Design

Halbach Array formation

used for Maglev Train 1

Uses least amount of

magnets for most amount

of induced current.

slide21

Inductrack Simulations

0° Induced Current Phase

Drag

Drag

slide22

Inductrack Simulations

-45° Induced Current Phase

Drag

Lift

slide23

Inductrack Simulations

-90° Induced Current Phase

No Drag

Lift

slide24

Circuit Theory

I(s) = (V/L)/(R/L + s)

Pole at R/L

Note:

V increases with velocity

slide25

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]

slide26

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

slide27

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

Levitation Force:

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

slide29

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

slide30

Locked Levitation

Transition Velocity

Unlocked Levitation

Locked Drag

Unlocked Drag

Calculated Forces

slide31

Locked Drag

Locked Levitation

Unlocked Levitation

Unlocked Drag

Breakpoint Velocity

Calculated Forces (Zoomed)

slide32

Total Force

Drag Force

Total Phase

Levitation Force

Calculated Forces (Bode)

slide34

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
slide35

Physical Design

Materials

Wood and 1/16” Aluminum

slide36

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)

slide42

Maglev Train 1 & 2 Comparisons

Maglev Train 1Maglev 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)

slide43

Maglev Train 1 & 2 Comparisons

Maglev Train 1Maglev Train 2

(Using 5mm Fixed Height)

slide44

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

slide45

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)

slide46

Parts and Equipment

40 - 1/2” NdFeB, Grade 38 Cubes $90.00

40 - 1/4” NdFeB, Grade 38 Cubes $14.40

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.

slide47

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)
slide48

BRADLEY UNIVERSITY

Department of Electrical and Computer Engineering

Sr. Capstone Project

Advisor:

Dr. Anakwa

Student:

Paul Friend

slide49

Propulsion

  • Types:
  • Linear Synchronous Motor (LSM)
  • Linear Induction Motor (LIM)
slide50

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
slide51

Propulsion

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