Development of a Halbach Array Magnetic Levitation System Outline Outline Cont. Introduction Previous Work

Development of a Halbach Array Magnetic Levitation System Outline Outline Cont. Introduction Previous Work www.phwiki.com

Development of a Halbach Array Magnetic Levitation System Outline Outline Cont. Introduction Previous Work

Johnston, Betty, Freelance Columnist has reference to this Academic Journal, PHwiki organized this Journal Development of a Halbach Array Magnetic Levitation System By: Dirk DeDecker Jesse VanIseghem 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 in addition to Simulations Outline Cont. Equipment List Lab work Problems in addition to Solutions Results Future Projects Patents References Acknowledgements

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Introduction Magnetic levitation technology can be used in high speed train applications Maglev suspension allows trains to accelerate to over 300 mph in addition to reduces maintenance by almost eliminating all moving parts Previous Work Dr. Sam Gurol in addition to 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: B0=Br(1-e-kd)sin(/M)/( /M) Tesla k = 2/, M = of magnets, Br = magnet strength, d = thickness of each magnet = Halbach array wavelength Physics of the Inductrack Halbach array moving at velocity v m/sec over inductrack generates flux 0sin(t), 0 Tesla-m2, linking the circuit = (2/)v rad/sec Voltage induced in inductrack circuit: V(t) = 0cos(t) Inductrack R-L circuit current equation: V(t) = Ldi(t)/dt + Ri(t) Physics of the Inductrack Cont Close-packed conductors, made utilizing thin aluminum or copper sheets Allows as long as 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 in addition to magnetic field to derive Lift as long as ce: = Bo2w2/2kL1/1+(R/L)2e-ky1 Drag as long as ce: = Bo2w2/2kL (R/L) /1+(R/L)2e-ky1 Where y1 is the levitation height in meters Physics of the Inductrack Cont. Phase shift relates to drag in addition to levitation as long as ces Lift/Drag = L/R L = 0 w/(2kdc) , where dc is the center to center spacing of conducting strips in addition to w is the track width Physics of the Maglev System Force needed to levitate: F = m9.81 Newtons m=.465 kg F = 4.56 N Breakpoint velocity: By solving Lift/Drag as long as v, vb=/(2) m/sec

Simulation with Matlab GUI Equipment List 9” radius polyethylene wheel, with a width of 2” 57”x2”x1/4” copper sheet of thin conducting strips 125 – 6mm cube neodymium magnets Balsa wood structure to house the 5×25 Halbach array Metal in addition to hardware as long as motor st in addition to Dayton permanent magnet DC motor Digital Force Gauge Model: 475040 Displacement Transducer Model: MLT002N3000B5C Lab Work – Design Designed wheel in addition to copper track to be built Wheel in addition to track were machined by Tri-City Machining

Lab Work – Design Cont. Decided to switch from aluminum track to copper Lower resistivity of copper(Cu = 1.68×10-8 m, Al = 2.82×10-8 m) R = PcRc/(NtcNs) , where Rc is the resistivity Lift/Drag – 2v/(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 in addition to epoxy Aluminum covering built to ensure magnets do not eject from balsa wood Lab Work – Halbach Array Device Array is 5×25 magnets = 28 mm Makes our arc length approximately 8”, with an angle of 25 degrees to either side cos(25) = .9063 Arc length s = 90.436 = 3.93 This arc length keeps 90% of the as long as ce in the vertical direction Fv = Ficos() Fi Force Diagram

Lab Work – Set up Motor st in addition to designed in addition to built to hold motor, wheel, in addition to balsa wood device Holes drilled in copper track in addition to 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 as long as changes in displacement

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Problems in addition to 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 as long as shield are ordered in addition to 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 in addition to Tri-City Machining Mr. Darren DeDecker in addition to Caterpillar Inc. Mrs. Sue DeDecker Mr. Dave Miller

Results – Backup Table 1: Displacement Sensor Calibration Measurements Table 2: Force Sensor Measurement Results – Backup Table 3: Displacement Sensor Measurements Results – Backup

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