Development of a Development of a Halbach Array Magnetic Halbach Array Magnetic

Levitation SystemLevitation System

By: By: Dirk DeDeckerDirk DeDeckerJesse VanIseghemJesse VanIseghem

Advised by: Advised by: Mr. Steven Gutschlag Mr. Steven Gutschlag Dr. Winfred AnakwaDr. Winfred Anakwa

OutlineOutline• IntroductionIntroduction

• Previous WorkPrevious Work

• Project SummaryProject Summary

• Changes to Original ProposalChanges to Original Proposal

• Physics of Halbach Array MagnetsPhysics of Halbach Array Magnets

• Preliminary Calculations and Preliminary Calculations and SimulationsSimulations

Outline Cont.• Equipment ListEquipment List

• Lab workLab work

• Problems and SolutionsProblems and Solutions

• ResultsResults

• Future ProjectsFuture Projects

• PatentsPatents

• ReferencesReferences

• AcknowledgementsAcknowledgements

IntroductionIntroduction• Magnetic levitation Magnetic levitation

technology can be technology can be used in high speed used in high speed train applicationstrain applications

• Maglev suspension Maglev suspension allows trains to allows trains to accelerate to over accelerate to over 300 mph and 300 mph and reduces reduces maintenance by maintenance by almost eliminating almost eliminating all moving partsall moving parts

Previous WorkPrevious Work

• Dr. Sam Gurol and Dr. Sam Gurol and Dr. Richard Post Dr. Richard Post have worked on “The have worked on “The General Atomics Low General Atomics Low Speed Urban Maglev Speed Urban Maglev Technology Technology Development Development Program” utilizing Program” utilizing the rotary track the rotary track methodmethod

Previous Work Cont.Previous Work Cont.

• Work by Paul Friend in 2004Work by Paul Friend in 2004– Levitation EquationsLevitation Equations– Matlab GUIMatlab GUI

• Work by Glenn Zomchek in 2007Work by Glenn Zomchek in 2007– Design of system using Inductrack Design of system using Inductrack

methodmethod– Successful levitation to .45 mm.Successful levitation to .45 mm.

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

Project SummaryProject Summary

• The goals of our project are:The goals of our project are:– Develop an improved Halbach array Develop an improved Halbach array

magnetic levitation system to achieve magnetic levitation system to achieve 0.5 cm at a track speed of 10 m/s 0.5 cm at a track speed of 10 m/s

– Demonstrate successful levitationDemonstrate successful levitation

Changes to Original Changes to Original ProposalProposal

• Focused on demonstration of Focused on demonstration of levitation of the magnet devicelevitation of the magnet device

• Changed closed loop system to open Changed closed loop system to open looploop

Physics of Halbach Array Physics of Halbach Array MagnetsMagnets

• Designed by Klaus HalbachDesigned by Klaus Halbach• Creates a strong, enhanced magnetic field on one side, while Creates a strong, enhanced magnetic field on one side, while

almost cancelling the field on the opposite sidealmost cancelling the field on the opposite side• Peak strength of the array: Peak strength of the array:

BB00=B=Brr(1-e(1-e-kd-kd)sin()sin(ππ/M)/(/M)/(ππ /M) Tesla /M) Teslak = 2k = 2ππ//λλ, M = # of magnets, , M = # of magnets, Br = magnet strength, d = thickness of each Br = magnet strength, d = thickness of each

magnetmagnetλλ = Halbach array wavelength = Halbach array wavelength

Physics of the InductrackPhysics of the Inductrack

• Halbach array moving at velocity v Halbach array moving at velocity v m/sec over inductrack generates fluxm/sec over inductrack generates flux

φφ00sin(sin(ωωt), t), φφ00 Tesla-m Tesla-m22, linking the circuit, linking the circuit

ωω = (2 = (2ππ//λλ)v rad/sec)v rad/sec

• Voltage induced in inductrack circuit:Voltage induced in inductrack circuit: V(t) = V(t) = ω φω φ00cos(cos(ωωt)t)

• Inductrack R-L circuit current equation:Inductrack R-L circuit current equation:

V(t) = L*di(t)/dt + R*i(t)V(t) = L*di(t)/dt + R*i(t)

Physics of the Inductrack Physics of the Inductrack ContCont

• Close-packed Close-packed conductors, made conductors, made utilizing thin aluminum utilizing thin aluminum or copper sheetsor copper sheets

• Allows for levitation at Allows for levitation at low speedslow speeds

• Can be modeled as an Can be modeled as an RL circuitRL circuit

• Transfer function has Transfer function has pole at -R/Lpole at -R/L

R1

V1 L1

Physics of the Inductrack Physics of the Inductrack Cont.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> = Bo

2w2/2kL* (R/ωL) /1+(R/ωL)2*e-ky1

Where y1 is the levitation height in meters

Physics of the Inductrack Physics of the Inductrack Cont.Cont.• Phase shift relates to drag and Phase shift relates to drag and

levitation forceslevitation forces• Lift/Drag = Lift/Drag = ωω*L/R*L/R• L = L = μμ0 0 w/(2kdw/(2kdcc) , where d) , where dcc is the is the

center to center spacing of center to center spacing of conducting strips and w is the track conducting strips and w is the track width width

Physics of the Maglev Physics of the Maglev SystemSystem

• Force needed to levitate:Force needed to levitate:F = m*9.81 NewtonsF = m*9.81 Newtons

m=.465 kgm=.465 kg

F = 4.56 NF = 4.56 N

• Breakpoint velocity:Breakpoint velocity:– By solving Lift/Drag for v,By solving Lift/Drag for v,

vvbb==λωλω/(2/(2ππ) m/sec) m/sec

Simulation with Matlab GUISimulation with Matlab GUI

Equipment ListEquipment List

• 9” radius polyethylene wheel, with a width 9” radius polyethylene wheel, with a width of 2”of 2”

• 57”x2”x1/4” copper sheet of thin 57”x2”x1/4” copper sheet of thin conducting stripsconducting strips

• 125 - 6mm cube neodymium magnets125 - 6mm cube neodymium magnets• Balsa wood structure to house the 5x25 Balsa wood structure to house the 5x25

Halbach arrayHalbach array• Metal and hardware for motor standMetal and hardware for motor stand• Dayton permanent magnet DC motorDayton permanent magnet DC motor• Digital Force Gauge Model: 475040 Digital Force Gauge Model: 475040 • Displacement Transducer Model: Displacement Transducer Model:

MLT002N3000B5CMLT002N3000B5C

Lab Work - DesignLab Work - Design

• Designed wheel and copper track to Designed wheel and copper track to be builtbe built

• Wheel and track were machined by Wheel and track were machined by Tri-City MachiningTri-City Machining

Lab Work - Design Cont.Lab Work - Design Cont.• Decided to switch from aluminum Decided to switch from aluminum

track to coppertrack to copper– Lower resistivity of copper(Cu = Lower resistivity of copper(Cu =

1.68x101.68x10-8-8 ΩΩ*m, Al = 2.82x10*m, Al = 2.82x10-8-8 ΩΩ*m)*m)•R = PcRc/(Nt*c*Ns) , where Rc is the R = PcRc/(Nt*c*Ns) , where Rc is the

resistivityresistivity

•Lift/Drag – 2*Lift/Drag – 2*ππ*v/*v/λλ*(L/R)*(L/R)

•Aluminum Lift/Drag ratio = 0.102Aluminum Lift/Drag ratio = 0.102

•Copper Lift/Drag ratio = 0.171Copper Lift/Drag ratio = 0.171

Lab Work – Halbach Array Lab Work – Halbach Array DeviceDevice• Balsa wood structure builtBalsa wood structure built

• Magnets glued into balsa woodMagnets glued into balsa wood– Used shrink wrap and epoxyUsed shrink wrap and epoxy

• Aluminum covering built to ensure Aluminum covering built to ensure magnets do not eject from balsa magnets do not eject from balsa woodwood

Lab Work – Halbach Array Lab Work – Halbach Array DeviceDevice• Array is 5x25 magnetsArray is 5x25 magnets• λλ = 28 mm = 28 mm• Makes our arc length Makes our arc length

approximately 8”, with an angle approximately 8”, with an angle of 25 degrees to either sideof 25 degrees to either side– cos(25) = .9063cos(25) = .9063– Arc length s = 9*0.436 = 3.93Arc length s = 9*0.436 = 3.93

• This arc length keeps 90% of This arc length keeps 90% of the force in the vertical the force in the vertical directiondirection

Fv = Fi*cos(Θ)

Fi

Θ

Force Diagram

Lab Work – Set upLab Work – Set up• Motor stand designed and built to Motor stand designed and built to

hold motor, wheel, and balsa wood hold motor, wheel, and balsa wood devicedevice

• Holes drilled in copper track and Holes drilled in copper track and track connected to wheeltrack connected to wheel

• All pieces assembled into the All pieces assembled into the complete systemcomplete system

Lab Work – Set up

Lab Work – Displacement Lab Work – Displacement SensorSensor

• Displacement sensor outputs linear Displacement sensor outputs linear voltage change for changes in voltage change for changes in displacementdisplacement

Problems and SolutionsProblems and Solutions

• Copper track too shortCopper track too short

• Once holes drilled in copper, track Once holes drilled in copper, track became weakbecame weak

• Magnets were very difficult to glue in Magnets were very difficult to glue in direction they had to bedirection they had to be

Results – Force Results – Force MeasurementsMeasurements

0 2 4 6 8 100

5

10

15

Force [N

]

Tangential Velocity [m/ s]

Levitation Force Measurements

Results – Displacement Results – Displacement MeasurementsMeasurements

0 2 4 6 8 10 120

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

Dis

pla

cem

ent [cm

]

Tangential Velocity [m/ s]

Levitation Height Measurements

ResultsResults

• Successful levitation of 0.365 cm at Successful levitation of 0.365 cm at 843 RPM, corresponding to a 843 RPM, corresponding to a tangential velocity of 10.0 m/stangential velocity of 10.0 m/s

• Materials for shield are ordered and Materials for shield are ordered and will be builtwill be built

Future ProjectsFuture Projects

• Closed-loop control of levitation Closed-loop control of levitation heightheight

• Dynamically balance wheelDynamically balance wheel

• More dampening of vibrationMore 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 PatentsApplicable Patents• Richard F. PostRichard F. Post

Magnetic Levitation System for Moving Magnetic Levitation System for Moving ObjectsObjectsU.S. Patent 5,722,326U.S. Patent 5,722,326March 3, 1998March 3, 1998

• Richard F. PostRichard F. PostInductrack Magnet ConfigurationInductrack Magnet ConfigurationU.S. Patent 6,633,217 B2U.S. Patent 6,633,217 B2October 14, 2003October 14, 2003

• Richard F. PostRichard F. PostInductrack ConfigurationInductrack ConfigurationU.S. Patent 629,503 B2U.S. Patent 629,503 B2October 7, 2003October 7, 2003

• Richard F. PostRichard F. PostLaminated Track Design for Inductrack Laminated Track Design for Inductrack Maglev SystemMaglev SystemU.S. Patent Pending US 2003/0112105 U.S. Patent Pending US 2003/0112105 A1A1June 19, 2003June 19, 2003

• Coffey; Howard T.Coffey; Howard T.Propulsion and stabilization for magnetically Propulsion and stabilization for magnetically levitated vehicleslevitated vehiclesU.S. Patent 5,222,436U.S. Patent 5,222,436June 29, 2003June 29, 2003

• Coffey; Howard T.Coffey; Howard T.Magnetic Levitation configuration Magnetic Levitation configuration incorporating levitation,incorporating levitation,guidance and linear synchronous motorguidance and linear synchronous motorU.S. Patent 5,253,592U.S. Patent 5,253,592October 19, 1993October 19, 1993

• Levi;Enrico; Zabar;ZivanLevi;Enrico; Zabar;ZivanAir cored, linear induction motor for Air cored, linear induction motor for magnetically levitatedmagnetically levitatedsystemssystemsU.S. Patent 5,270,593U.S. Patent 5,270,593November 10, 1992November 10, 1992

• Lamb; Karl J. ; Merrill; Toby ; Gossage; Scott Lamb; Karl J. ; Merrill; Toby ; Gossage; Scott D. ; Sparks;D. ; Sparks;Michael T. ;Barrett; Michael S.Michael T. ;Barrett; Michael S.U.S. Patent 6,510,799U.S. Patent 6,510,799January 28, 2003January 28, 2003

Works ConsultedWorks Consulted

• Glenn Zomchek. Senior Project. “Redesign of a Rotary Inductrack for Glenn Zomchek. Senior Project. “Redesign of a Rotary Inductrack for Magnetic Levitation Train Demonstration.” Final Report, 2007.Magnetic Levitation Train Demonstration.” Final Report, 2007.

• Paul Friend. Senior Project. Magnetic Levitation Technology 1. Final Report, Paul Friend. Senior Project. Magnetic Levitation Technology 1. Final Report, 2004.2004.

• Gurol, Sam. E-mail (Private Conversation)Gurol, Sam. E-mail (Private Conversation)

• Post, Richard F., Ryutov, Dmitri D., “The Inductrack Approach to Magnetic Post, Richard F., Ryutov, Dmitri D., “The Inductrack Approach to Magnetic Levitation,” Lawrence Livermore National Laboratory.Levitation,” Lawrence Livermore National Laboratory.

• Post, Richard F., Ryutov, Dmitri D., “The Inductrack: A Simpler Approach to Post, Richard F., Ryutov, Dmitri D., “The Inductrack: A Simpler Approach to Magnetic Levitaiton,” Lawrence Livermore National Laboratory.Magnetic Levitaiton,” Lawrence Livermore National Laboratory.

• Post, Richard F., Sam Gurol, and Bob Baldi. "The General Atomics Low Speed Post, Richard F., Sam Gurol, and Bob Baldi. "The General Atomics Low Speed Urban Maglev Technology Development Program." Lawrence Livermore Urban Maglev Technology Development Program." Lawrence Livermore National Laboratory and General Atomics.National Laboratory and General Atomics.

Questions?

Results – Backup Results – Backup

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

Table 1: Displacement Sensor Calibration Measurements

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

Table 2: Force Sensor Measurement

Results – Backup Results – Backup

Motor Voltage

[V]

Motor Current

[A]

RPM Velocity [m/s]

Sensor Output

[V]

Change inDisplacement

[cm]

0 0 0 0 5.320 015 3.0 140 1.676 5.310 0.01019625 3.7 277 3.316 5.222 0.09991930 4.0 347 4.153 5.213 0.10909535 4.4 417 4.991 5.203 0.1192940 3.9 505 6.045 5.138 0.17536745 3.6 591 7.074 5.080 0.24469850 3.5 678 8.115 5.045 0.28038455 3.3 756 9.049 5.012 0.3140360 3.1 843 10.090 4.962 0.365008

Table 3: Displacement Sensor Measurements

Results – Backup Results – Backup