Development of a Halbach Array Magnetic Levitation System

Development of a Halbach Array Magnetic Levitation System By: Dirk De. Decker Jesse Van. Iseghem Advised by: Mr. Steven Gutschlag Dr. Winfred Anakwa

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

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

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

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

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.

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

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

Changes to Original Proposal • Focused on demonstration of levitation of the magnet device • Changed closed loop system to open loop

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: B 0=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

Physics of the Inductrack • Halbach array moving at velocity v m/sec over inductrack generates flux φ0 sin(ωt), φ0 Tesla-m 2, linking the circuit ω = (2π/λ)v rad/sec • Voltage induced in inductrack circuit: V(t) = ω φ0 cos(ωt) • Inductrack R-L circuit current equation: V(t) = L*di(t)/dt + R*i(t)

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

Physics of the Inductrack Cont. • Dr. Post used the induced current and magnetic field to derive – Lift force: • <Fy> = Bo 2 w 2/2 k. L*1/1+(R/ωL)2*e-ky 1 – Drag force: • <Fx> = Bo 2 w 2/2 k. L* (R/ωL) /1+(R/ωL)2*e-ky 1 Where y 1 is the levitation height in meters

Physics of the Inductrack Cont. • Phase shift relates to drag and levitation forces • Lift/Drag = ω*L/R • L = μ 0 w/(2 kdc) , where dc is the center to center spacing of conducting strips and w is the track width

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

Simulation with Matlab GUI

Equipment List • 9” radius polyethylene wheel, with a width of 2” • 57”x 2”x 1/4” copper sheet of thin conducting • • • strips 125 - 6 mm cube neodymium magnets Balsa wood structure to house the 5 x 25 Halbach array Metal and hardware for motor stand Dayton permanent magnet DC motor Digital Force Gauge Model: 475040 Displacement Transducer Model: MLT 002 N 3000 B 5 C

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

Lab Work - Design Cont. • Decided to switch from aluminum track to copper – Lower resistivity of copper(Cu = 1. 68 x 10 -8 Ω*m, Al = 2. 82 x 10 -8 Ω*m) • R = Pc. Rc/(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

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

Lab Work – Halbach Array Device • Array is 5 x 25 magnets • λ = 28 mm • Makes our arc length approximately 8”, with an angle of 25 degrees to either side Fv = Fi*cos(Θ) Fi Θ – cos(25) =. 9063 – Arc length s = 9*0. 436 = 3. 93 • This arc length keeps 90% of the force in the vertical direction Force Diagram

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

Lab Work – Set up

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

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

Results – Force Measurements

Results – Displacement Measurements

Results • Successful levitation of 0. 365 cm at 843 RPM, corresponding to a tangential velocity of 10. 0 m/s • Materials for shield are ordered and will be built

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

Acknowledgements • Dr. Winfred Anakwa • Mr. Steven Gutschlag • Mr. Joe Richey and Tri-City Machining • Mr. Darren De. Decker and Caterpillar Inc. • Mrs. Sue De. Decker • Mr. Dave Miller

Applicable Patents • Richard F. Post Magnetic Levitation System for Moving Objects U. S. Patent 5, 722, 326 March 3, 1998 • Richard F. Post Inductrack Magnet Configuration U. S. Patent 6, 633, 217 B 2 October 14, 2003 • Richard F. Post Inductrack Configuration U. S. Patent 629, 503 B 2 October 7, 2003 • Richard F. Post Laminated Track Design for Inductrack Maglev System U. S. Patent Pending US 2003/0112105 A 1 June 19, 2003 • Coffey; Howard T. Propulsion and stabilization for magnetically levitated vehicles U. S. Patent 5, 222, 436 June 29, 2003 • Coffey; Howard T. 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

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. E-mail (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.

Questions?

Results – Backup Table 1: Displacement Sensor Calibration Measurements 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

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

Results – Backup Table 3: Displacement Sensor Measurements Motor Voltage [V] Motor Current [A] RPM Velocity [m/s] Sensor Output [V] Change in Displacement [cm] 0 0 5. 320 0 15 3. 0 140 1. 676 5. 310 0. 010196 25 3. 7 277 3. 316 5. 222 0. 099919 30 4. 0 347 4. 153 5. 213 0. 109095 35 4. 4 417 4. 991 5. 203 0. 11929 40 3. 9 505 6. 045 5. 138 0. 175367 45 3. 6 591 7. 074 5. 080 0. 244698 50 3. 5 678 8. 115 5. 045 0. 280384 55 3. 3 756 9. 049 5. 012 0. 31403 60 3. 1 843 10. 090 4. 962 0. 365008