Fundamental electrophysics and engineering design of MAGLEV vehicles

Transcription

1 Fundamental electrophysics and engineering design of MAGLEV vehicles Prof. Jim Hoburg Department of Electrical & Computer Engineering Carnegie Mellon University J. Hoburg 1

2 Gravity Mass Gravity field f = mg Force on another mass J. Hoburg

3 Electricity Charge Electric field Force on another charge _ f =qe + J. Hoburg 3

4 Magnetism Current Magnetic field X f / l = i X B Force on another Current segment J. Hoburg 4

5 Magnetism (microscopic) Microscopic current loops S N S N Magnetic field Force on other Microscopic current loops Macroscopic description of assembly of microscopic forces: Net force: opposite poles attract, same poles repel. Torque: aligns to imposed field. J. Hoburg 5

6 Sources > Fields Charge > Electric field ρ = div( ε E) Current > Magnetic field J = curl( B ) μ J. Hoburg 6

7 Sources > Fields (the whole story, including time varying fields as sources of fields) Maxwell s Equations ρ = div( ε E) E J + ε = curl( B ) t μ = div( B) B = curl(e) t J. Hoburg 7

8 Electromagnetic Waves Even in a vacuum, where ρ = and J = : = div( ε E) E ε curl( B ) = t μ = div( B) B = curl(e) t J. Hoburg 8

9 Electromagnetic Waves (continued) E ε curl( B ) = t μ B = curl(e) t ε = X1 1 μ = 1.57 X16 Farad m Henry m ρ E J B 1 μ ε = 3. X 1 8 m/s = c = speed of light in vacuum J. Hoburg 9

10 What does this have to do with MAGLEV? Same fundamental physics describes: Light, lasers, X-rays, (electromagnetic spectrum, why is the sky blue?) Wireless communications (radio, TV, cell phones, wireless computers, ) Integrated circuits (computer chips) Lightning Electrostatic precipitation Electrophotography & laser printers Microelectromechanical systems (MEMS) Magnetic memory (tapes, disks, MRAM, magnetic stripes, ) Rotating electrical machinery (generators & motors) Linear synchronous motor (LSM) Magnetic confinement for nuclear fusion MAGLEV J. Hoburg 1

11 Attractive magnetic levitation: Electromagnetic levitation N S N S N S ferromagnetic material, e.g. steel: induced magnetiation J. Hoburg 11

12 Attractive magnetic levitation: gravitational total magnetic f unstable equilibrium f (inherently unstable) J. Hoburg 1

13 Attractive magnetic levitation: requires feedback control system to stabilie equilibrium excitation + Σ vehicle vertical position feedback excitation J. Hoburg 13

14 Repulsive magnetic levitation: Electrodynamic levitation A.C. coil on vehicle permanent magnet on moving vehicle N v S X X track of electrically conducting material, e.g. copper or aluminum: induced current J. Hoburg 14

15 Repulsive magnetic levitation: This interaction involves an induced electric field in the conducting material, caused by a time-varying imposed magnetic field. N S v B = curl(e) t X J = σ E J. Hoburg 15

16 Repulsive magnetic levitation: N f v gravitational magnetic S stable equilibrium X total f (inherently stable: no feedback control system needed) J. Hoburg 16

17 Either mechanism can be used to levitate a vehicle Attractive levitation Repulsive levitation J. Hoburg 17

18 High speed (~ 45 km/hr) MAGLEV systems: German Transrapid: Attractive ( electromagnetic ) levitation via conventional electromagnets LSM propulsion Japanese MLX: Repulsive ( electrodynamic ) levitation via superconducting magnets (on-board cryogenics) LSM propulsion J. Hoburg 18

19 Transrapid Test Vehicle TR-8 Germany, 1999 J. Hoburg 19

20 Null Flux Suspension Vehicle MLX1 Japan, 1997 (Yamanashi test facility) J. Hoburg

21 Low speed urban MAGLEV concept: Permanent(NdFeB) magnet arrays on vehicle: Repulsive ( electrodynamic ) levitation via induced currents in track coils LSM propulsion J. Hoburg 1

22 Halbach permanent magnet arrays J. Hoburg

23 (Envisioned) Pittsburgh Urban Maglev vehicle J. Hoburg 3

24 Vehicle on Guideway Linear Synchronous Motor Suspension Track Double Sided Magnet Array J. Hoburg 4

25 Magnetic fields from known sources: computing passenger compartment field levels J. Hoburg 5

26 Halbach array fields: basic structure via magnetiation charge description: propulsion magnet near fields (.1 m above & below): components & magnitude above components & magnitude below. By, B and B in T from propulsion magnets.1 m above B (blue). By, B and B in T from propulsion magnets.1 m below B (blue) B in T -.5 B in T -.5 By (red) B (green) By (red) B (green) y (m) y (m) J. Hoburg 6

27 Halbach array fields: basic structure via magnetiation charge description: propulsion magnet far fields (.5 m above & below): components & magnitude above components & magnitude below 1 x By, B and B in T from propulsion magnets.5 m above B (blue) 1 x By, B and B in T from propulsion magnets.5 m below B (blue).. B in T -. B in T -. By (red) -.4 B (green) -.4 B (green) By (red) y (m) y (m) J. Hoburg 7

28 Halbach array fields: basic structure via magnetiation charge description: propulsion magnet very far fields (. m above & below): components & magnitude above components & magnitude below x 1-5 By, B and B in T from propulsion magnets. m above x 1-5 By, B and B in T from propulsion magnets. m below B (blue) B (blue) 1 1 B in T B in T By (red) B (green) -1-1 By (red) B (green) y (m) y (m) J. Hoburg 8

29 Fields in passenger compartment magnetiation charge description: floor level contour plot seat level contour plot head level contour plot B in T at floor: all magnets B in T at seat: all magnets B in T at head: all magnets e e e-5 7e-5 3 y (m) 1.1. y (m) 1 6e-5 y (m) e x (m) x (m) x (m) J. Hoburg 9

30 Fields in passenger compartment magnetiation charge description: line plots at floor, seat and head levels 5 x 1-4 B in T along lines: all magnets floor above magnets (red) 3.5 B in T 3.5 floor along center line (green) seat above magnets (blue) seat along center line (cyan).5 head along center line (yellow) head above magnets (magenta) y (m) J. Hoburg 3

31 Electromechanics: computing lift & drag versus velocity J. Hoburg 31

32 Faraday s Law for rectangular contours in lamination planes: [ Λ + Λ + p( Λ + Λ + )] le x = jω A B self b Λ a d dl = dt E μ C S H nda Electric field related to surface currents in lamination planes: E x K x = σ Δ Time constant for induced currents: τ m μ σδλ = 4π Driving frequency based upon vehicle velocity: v ω = π λ J. Hoburg 3

33 J. Hoburg 33 ( ) = y vt j K i K x λ π exp Re [ ] k jky y a e e i j i K y H + = ) ( ), ( [ ] k jky y b e e i j i K y H = ) ( ), ( All induced currents in laminations take the forms: Resultant fields (above and below) any one lamination are:

34 J. Hoburg 34 Simultaneous equations governing induced currents in laminations: ( ) ( ) ( ) ( ) ( ) ( ) = / / 3 / / / / / / 1 / / 1 / / 3 1,,,,,, B B A A B B A A B B A A m kd kd kd m kd kd kd m I I I p j dx x H dx x H dx x H dx x H dx x H dx x H p j K K K p j e e e p j e e e p j l l l l l l l l l l l l l l τ ω τ ω τ ω

35 J. Hoburg 35 Time-averaged lift and drag forces (per wavelength) on vehicle: [ ] { } i y i i Bi B y Ai A y i i I K p dx x H x H K p L Re ), ( ), ( Re * / / * + = λ μ λ μ λ l l [ ] { } i i i Bi B Ai A i i I K p dx x H x H K p D Re ), ( ), ( Re * / / * + = λ μ λ μ λ l l Horiontal (y) and vertical () field components are based upon 3-D magnetiation charge description. Complex amplitudes are based upon first Fourier components of y dependences at each value of x.

36 Double (5 above X 3 below) array Full 3-D magnetiation charge fields: Double (5 above X 3 below) array First Fourier component approximations: J. Hoburg 36

37 Comparison with Dick Post s model for LLNL test rig Post: Hoburg: J. Hoburg 37

38 Comparison with Dick Post s model for LLNL test rig Post: Hoburg: J. Hoburg 38

39 J. Hoburg 39