1. Dynamic Modeling of an Eddy-Current
Device: an Application to Maglev
By
Nirmal Paudel
Laboratory for Electromechanical Energy Conversion and Control (LEECC)
Department of Electrical and Computer Engineering
University of North Carolina at Charlotte (UNCC)
Charlotte, North Carolina, USA
Date: May 29, 2012
PhD Dissertation

2. 2
8/27/2016
 Magnetic levitation (Maglev) technology types
 Electrodynamic wheel (EDW)
 Steady-state analytic modeling and validation
 Transient analytic modeling and validation
 Electromechanical dynamic behavior
 Experimental validation using 1-DOF pendulum setup
 Experimental setup using 4-wheeled EDWs Maglev
 Conclusion and future works
Presentation Outline

3. 3
 Lift and guidance forces are provided by
electromagnets
 Propulsion forces are created by dual linear
synchronous motors on the guideway
 Operates with an 8-12mm air-gap
 Laminated iron stator packs along the track to
mitigate the eddy current loss
 Commercially operating in Shanghai, China
(at 431km/h)
Electromagnetic Suspension (EMS)- Transrapid technology
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Types of Magnetic Levitation (1)

4. 4
Uses electrodynamic suspension (with NdFeB magnets) to create lift forces and a
linear synchronous motor on the track to create the thrust forces
Test Chassis
Double Halbach Array Magnet Configuration try’s to cancel
out drag force
Electrodynamic Suspension (EDS)- General Atomic Inductrack
0
500
1000
1500
2000
2500
0 2.5 5 7.5 10 12.5 15 17.5 20 22.5
Translational velocity [m/s]
Dragforce[N]
0
5
10
15
20
25
Powerloss[kW]
Drag force Guideway power loss
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Types of Magnetic Levitation (2)

5. Electrodynamic Suspension
5
0 50 100 150 200 250 300 350
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Normal Force
Drag Force
xv
L
L
D
F
F
 
NormalizedForce
(scaledtoamaximumof1)
Translational motion of magnetic
source creates lift and a drag forces:
Loss D xP F v
Translational velocity [km/h]
Electrodynamic suspension first
proposed by Bachelet in 1912, and later
by Powell and Danby using
superconducting magnets
LF
DF
a
a. Stationary b. Moderate Speed
b
c. High Speed
xv
xB zJ
yB
zJ
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c
c

6.  The drag force in EDS and EMS can be converted into a thrust by rotating the
source over a conductive passive guideway.
 Propulsion/braking depends on the relative velocity of rotor compared to the
travelling velocity.
 Guideway cost should be comparable with high speed rail
 Power supply must on board or transferred to vehicle
Electrodynamic Wheel (EDW)
4 pole-pair NdFeB
Halbach Rotor
Add fig
6
m o x
e m
Slip r v
P

 
 

8/27/2016
Fig. 1: EDW and guideway
Fig. 2: EDW forces
-30 -20 -10 0 10 20 30
-200
-100
0
100
200
300
Slip (ms-1
)
Forces(N)
vx
= 0 ms-1
vx
= 30 ms-1
Thrust/Drag Force
Lift Force

7. 2D Steady-State Modeling of EDW
 The combination of vector potential, Az
and scalar potential, ø
 Conducting region-vector potential, Az
 Non-conducting region-scalar potential, ø
 Rotor field only needs to be included on
the connecting boundaries
 Therefore, the modified problem region is
Fig. 1: JMAG finite element model of EDW in 2D
Guideway
Halbach Rotor
(4 Pole-pairs)
7
1
2
3
12
23
1
2
3
x
y
b
nnc
2
(0,0)(-L,0) (L,0)
Fig. 2: Analytical based problem region
Air region
Air region
Conducting region
8/27/2016

8.  The external Halbach rotor magnetic field is
approximately modeled by using a current
sheet using only the fundamental component
Halbach Rotor Magnetic Field
ro = outer radius of the rotor
P = rotor pole-pairs
ωe = rotor angular electrical velocity
Br = remanence of the magnet
μr = relative permeability of the magnet
where,
1( )
( , ) ej t Ps
z P
C
A r e
Pr
 
 

2 1 1
2 2 2 2
(1 ) ( )2
1 (1 ) (1 )
P P P
r o o ir
P P
r i r o
r r rB P
C
P r r

 
 
  
      
Fig. 2: Contour plot of the vector potential
of the 4 pole pairs Halbach rotor
8/27/2016
Fig. 1: Equivalent current sheet of
the 4 pole pairs Halbach rotor
(1)
(2)
 The Halbach rotor analytical field equation as
derived in [Xia 2004]

9. Rotor
Outer radius, ro 70 mm
Inner radius, ri 47.88 mm
Magnet (NdFeB), Br 1.42T
Pole-pairs, P 4
Conductive
guideway
Conductivity, σ
(Al)
2.459107 Sm-1
Thickness, b 10 mm
Air-gap between
rotor and
conducting plate, g
10 mm
Guideway length
(±L)
0.8m
9
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-30 -20 -10 0 10 20 30
0
20
40
60
80
100
Slip (ms-1
)
PowerLoss(KW/m)
Analytical Method
FEA Method0 ms-1
15 ms-1
30 ms-1
Fig. Power loss in the conducting plate as a function
of slip and translational velocity.
Simulation Parameters
Results Comparison: Single Halbach Rotor (1)

10. 10
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-30 -20 -10 0 10 20 30
-0
2
4
6
8
Slip (ms-1
)
LiftForce(KN/m)
Analytical Method
FEA Method
30 ms-1
0 ms-1
15 ms-1
-30 -20 -10 0 10 20 30
-5
-2.5
0
2.5
5
Slip (ms-1
)
ThrustForce(KN/m)
Analytical Method
FEA Method
30 ms-1
0 ms-1
15 ms-1
-30 -20 -10 0 10 20 30
-1
-0.5
0
0.5
1
ThrustError(%) 0 ms-1
30 ms-1
-30 -20 -10 0 10 20 30
-1
-0.5
0
0.5
LiftError(%)
Slip (ms-1
)
0 ms-1
30 ms-1
Results Comparison: Single Halbach Rotor (2)

11. 11
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References:
[1] N. Paudel and J. Bird, "2D Analytical Based Model of a Rotor Moving Over a Conductive Guideway," presented at the IEEE
Conf. on Elec. Field Comp., Chicago, IL, 2010.
[2] N. Paudel and J. Bird, "General 2D Steady-State Force and Power Equations for a Traveling Time-Varying Magnetic Source
Above a Conductive Plate," Magnetics, IEEE Transactions on, vol. 48, pp. 95-100, 2012.
-30 -20 -10 0 10 20 30
-4
-2
0
2
4
6
8
10
Slip (ms-1
)
LiftForce(KN)
Analytical Method
FEA Method
vy
=-2ms-1
vy
=2ms-1
vy
=0ms-1
-30 -20 -10 0 10 20 30
-6
-4
-2
0
2
4
6
Slip (ms-1
)
ThrustForce(KN/m)
Analytical Method
FEA Method
vy
=0ms-1 vy
=-2ms-1
vy
=2ms-1
@
vx=20m/s
Slip=30m/s
g=10mm
Results Comparison: Single Halbach Rotor (3)

12. Results Comparison (Halbach Rotors in Series)
12
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1
( )
0
2
( , ) ( ) u( )
!
o o
n
g r j kxs P P
x
k
B b j C e e
P
 
  

  

  
1
( )1
0
2
( , ) ( ) u( )
!
o o
n
g r j kxs P P
y
k
B b j C e e
P
 
  

  

  

13. 2D Transient Modeling of EDW
 The combination of vector potential, Az
and scalar potential, ø
 Conducting region-vector potential, Az
 Non-conducting region-scalar potential, ø
 Rotor field only needs to be included on
the connecting boundaries
1
2
3
12
23
1
2
3
x
y
b
nnc
2
(0,0)(-L,0) (L,0)
Fig. 2: Analytical based problem region
Fig. 1: Magsoft FEA transient 2D model
Guideway
Halbach Rotor
(4 Pole-pairs)
13
Air region
Air region
Conducting region
8/27/2016
ωm

14. Force Calculations and Results
 Forces directly calculated using Maxwell’s stress tensor in the Fourier domain
using Parseval’s theorem
14
 Numerical integration was performed in Matlab to calculate the forces
0 5 10 15 20 25 30
0
50
100
150
200
250
Time (ms)
Forces(N)
Analytical Model
FEA Model
Thrust Force
Lift Force
ωm=0 RPM to 3000 RPM
vx= 0 m/s @ t = 0 ms
Slip =15.708 m/s
vx = 0 m/s to 10 m/s
ωm = 3000 RPM @ t = 15 ms
Slip =5.708 m/s
0 5 10 15 20 25 30
0
50
100
150
Time (ms)
Forces(N)
Analytical Model
FEA Model
Thrust Force
Lift Force
ωm = 0 RPM to 1000 RPM
vx = 0 m/s @ t = 0 ms
Slip = 5.23 m/s
ωm = 1000 to 2000 RPM
vx = 0 m/s @ t = 15 ms
Slip = 10.47 m/s
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*
0
1
( ) Re
4
x x yF t B B d w



 
  
 

* *
0
1
( ) Re ( )
8
y y y x xF t B B B B d w



 
  
 
(1) (2)

15. Simulation Parameters
Rotor
Outer radius, ro 50 mm
Inner radius, ri 34.2 mm
Magnet (NdFeB), Br 1.42
Pole-pairs, P 4
Rotor width, w 100mm
Conductive
guideway
Conductivity, σ (Al) 2.459107 Sm-1
Thickness, b 10 mm
Air-gap between rotor
and conducting plate, g
10 mm
Guideway length (±L) 0.3m
15
8/27/2016
References:
[1] N. Paudel, J. Bird, S. Paul and D. Bobba, "A Transient 2D Model of an Electrodynamic Wheel Moving Above a Conductive
Guideway" on IEEE International Electric Machines and Drives Conference May 15-18, 2011, Niagara Falls, Canada.
[2] N. Paudel, J. Bird, S. Paul and D. Bobba, "General 2D Transient Force and Power Equations for a Traveling Time-Varying
Magnetic Source above a Conductive Plate", submitted to IEEE Transactions on Magnetics.
For vx=0 to 10ms at 1ms, 0RPM, g=10mm
For vx=0 to 10ms at 5ms, 0RPM, g=10mm

16. 16
8/27/2016
Transient 2D Model FEA Model Using Magsoft
0 5 10 15 20 25 30
0
50
100
150
200
250
Lift Force
Time (s)
LiftForce(N)
Magsoft 16-Segment
Magsoft 32-Segment
Magsoft 64-Segment
Analytic Model
Comsol Model
0 5 10 15 20 25 30
0
50
100
150
200
Thrust Force
Time (s)
ThrustForce(N)
Magsoft 16-Segment
Magsoft 32-Segment
Magsoft 64-Segment
Analytic Model
Comsol Model
0 5 10 15 20 25 30
0
500
1000
1500
2000
2500
3000
3500
Power Loss
Time (ms)
PowerLoss(W)
Magsoft 16-Segment
Magsoft 32-Segment
Magsoft 64-Segment
Analytic Model
Comsol Model
Fig. 1: 16-segment Magsoft FEA Model
Fig. 2: Meshplot of Magsoft FEA Model

17.  The nonlinear electro-mechanical mass spring system
 The steady-state and transient analytical based model are validated using
the electromechanical dynamic simulation
 FEA is very time intensive: 14 days in Dell Precision T7400
17
8/27/2016
Electromechanical Dynamic Simulation
Fig. 2: The comparison of Lift, Thrust and Airgap of 2D transient analytical model with FEA transient model in the electro-
mechanical dynamic simulation.
vxo = 10m/s.
𝜔mo = 400rad/s.
go = 10mm.
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45
0
200
400
600
Time (s)
Lift(N)
Transient Model FEA ModelAnalytic Model
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45
0
100
200
300
400
500
Time (s)
Thrust(N)
Transient Model FEA ModelAnalytic Model
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45
0
10
20
30
Time (s)
Airgap(mm)
Analytical Model FEA ModelAnalytic Model
2
2
( )
( )y g
d g t
m F t F
dt
  2
0.5d d xF C Av
2
2
( )
( )x d
d x t
m F t F
dt
 (1) (2) (3)
Fig. 1: Block diagram for electromechanical dynamic simulation.

18. 18
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Dynamic Simulations (1)
 Step Change in Angular Velocity:
0 1 2 3 4 5 6
20
30
40
0 1 2 3 4 5 6
-30
-20
-10
SS Model Transient Model
0 1 2 3 4 5 6
-30
-25
-20
-15
-10
Drag
vx
Velocity(m/s)
Drag(N)
Time (s)
0 1 2 3 4 5 6
400
500
600
Time (s)
mrad/sωmrad/s
0 1 2 3 4 5 6
100
200
300
Time (s)
Lift(N)
Transient Model
SS Model
LiftForce(N)
0 1 2 3 4 5 6
400
500
600
Time (s)
mrad/s
0 1 2 3 4 5 6
5
10
15
20
25
Time (s)
Airgap(mm)
Transient Model
SS Model
Air-gap(mm)
0 1 2 3 4 5 6
400
500
600
Time (s)
mrad/s
0 1 2 3 4 5 6
0
100
200
Time (s)
Thrust(N)
Transient Model
SS Model
ThrustForce(N)
0 1 2 3 4 5 6
400
500
600
Time (s)
mrad/s
0 1 2 3 4 5 6
-0.2
0
0.2
Time (s)
Velocity:vy(ms
-1
)
Transient Model
SS Model
vy(m/s)
0 1 2 3 4 5 6
400
500
600
Time (s)
mrad/s
Fig. Airgap percentage error between steady state and
transient for step change in ωm
Time (s)
0 1 2 3 4 5 6
-5
0
5
Error(%)
Step Change

19. 19
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Dynamic Simulations (2)
Fig. 1: Airgap percentage error between steady state and transient for
step change in weight of the vehicle.
Time (s)
Fig. 4: Lift Force using the transient model (N) Fig. 4: Lift Force using the steady-state model (N)
Fig. 2: Airgap for transient model (mm) Fig. 3: Airgap for steady-state model (mm)
0 1 2 3 4 5 6 7 8
-10
-5
0
5
10
0 1 2 3 4 5 6 7 8
5
10
15
20
25
Time (s)
Airgap(mm)
0 1 2 3 4 5 6 7 8
5
10
15
20
25
Time (s)
Airgap(mm)
0 1 2 3 4 5 6 7 8
0
200
400
Time (s)
Lift(N)
0 1 2 3 4 5 6 7 8
0
200
400
Time (s)
Lift(N)
 Step Change in the weight of the vehicle.
LiftForce(N)
LiftForce(N)
Air-gap(mm)
Air-gap(mm)
Time (s)
Time (s) Time (s)
Time (s)
Time (s)
Time (s)
0 1 2 3 4 5 6 7 8
200
250
Time (s)
Weight(N)Weight(N)
Error(%)
Step Change
ωm0=400rad/s, sl=10ms-1.
go=10mm, vxo =10m/s

20. 20
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Dynamic Simulations (3)
Fig. 1: The translational velocity and aero-drag for transient and
steady-state models.
Time (s)
Fig. 2: Thrust Force using transient model (N) Fig. 3: Thrust Force using steady-state model (N)
Fig. 4: Heave velocity for transient model (m/s) Fig. 5: Heave velocity for steady state model (m/s)
0 1 2 3 4 5 6 7 8
0
100
200
Time (s)
Thrust(N)
0 1 2 3 4 5 6 7 8
0
100
200
Time (s)
Thrust(N)0 1 2 3 4 5 6 7 8
-0.2
0
0.2
Time (s)
vy(ms
-1
)
0 1 2 3 4 5 6 7 8
-0.2
0
0.2
Time (s)
vy(ms
-1
)
0 1 2 3 4 5 6 7 8
10
20
25
0 1 2 3 4 5 6 7 8
-15
-10
-5
0
SS Model Transient Model
0 1 2 3 4 5 6 7 8
-15
-10
-5
0
vx
Drag
 Step Change in the weight of the vehicle (cntd.)
References:
[1] N. Paudel, J. Bird, S. Paul and D. Bobba, "Modeling the Dynamic Suspension Behavior of an Eddy Current Device", IEEE
Energy Conversion Congress & Expo, September 17-22, 2011, Arizona, USA
Time (s)
0 1 2 3 4 5 6 7 8
200
250
Time (s)
Weight(N)Weight(N)
ThrustForce(N)
ThrustForce(N)
Time (s)
Time (s)
Time (s)
Velocity(m/s)
Drag(N)
Time (s)
vy(m/s)
vy(m/s)
Step Change

21.  EDW Pendulum model setup
 Investigate the dynamic behavior of EDW
 Matlab: Real Time Windows has been used
21
8/27/2016
Fig. 1: Pendulum model of EDW experimental setup
Fig.2: EDW with drive motors and controllers
EDW Pendulum Setup
Guideway speed : Rotary encoder
EDW speed : Hall effect sensor
Airgap : Laser displacement sensor

22. 22
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Fig.1: A sample plot of air-gap as a function of time from a free oscillation test
Viscous damping:
Equation of motion with EDWs rotating is solved using ode45
Air & Friction Stiffness and Damping
0 5 10 15 20 25 30 35 40 45 50
-20
-10
0
10
20
Airgap (mm)
Time (s)
Airgap(mm)
Experimental Data
Estimated Data
2
2
( ) ( )
( ) 0
d y t dy t
m c ky t
dt dt
  
2
2
( ) ( )
sgn ( ) 0
d y t dy t
m mG ky t
dt dt

 
   
 
2
2
( ) ( ) ( )
sgn ( ) 0
d y t dy t dy t
m c mG ky t
dt dt dt

 
    
 
2
2
( ) ( ) ( )
' sgn ' ( ) ( , , , )EDW
y x y m
d y t dy t dy t
m c m G ky t F y v v
dt dt dt
 
 
    
 
Sliding friction damping:
Where,
m = mass of pendulum
c = viscous damping
k = stiffness constant
= sliding friction coefficient
G = acceleration due to gravity
𝜇
1
' EDW
xm m F
G
 
(1)
(2)
(3)
(5)
(4)
guideway
Fx
Fy

23. 23
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Test Results: Test-A
Guideway
Pendulum
geq=11.95mm
Initial Conditions:
g0=11.95mm
vx=0m/s
ωm=0rad/s
vy=0m/s
sl=0m/s
2
2
( ) ( ) ( )
' sgn ' ( ) ( , , , )EDW
y x y m
d y t dy t dy t
m c m G ky t F y v v
dt dt dt
 
 
    
 
Fig. 2: Measured RPM and vy
Fig. 1: Measured and calculated air-gap values
Fig. 3: Calculate lift and thrust forces
Note: Guideway is fixed in this test.

24. 24
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Test Results: Test-B
Initial Conditions:
g0=26.15mm geq=11.95mm vx=2.46m/s
ωm=94.7rad/s vy=0m/s sl=2.275m/s
2
2
( ) ( ) ( )
' sgn ' ( ) ( , , , )EDW
y x y m
d y t dy t dy t
m c m G ky t F y v v
dt dt dt
 
 
    
 
Fig. 1: Measured RPM , vx and vy
Fig. 2: Measured and calculated air-gap values
Fig. 3: Calculate lift and thrust forces

25. 25
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Test Results: Test-C
Guideway
Pendulum
geq=21.5mm
Initial Conditions:
g0=21.5mm
vx=0m/s
ωm=0rad/s
vy=0m/s
sl=0m/s
2
2
( ) ( ) ( )
' sgn ' ( ) ( , , , )EDW
y x y m
d y t dy t dy t
m c m G ky t F y v v
dt dt dt
 
 
    
 
Fig. 2: Measured RPM and vy
Fig. 1: Measured and calculated air-gap values
Fig. 3: Calculate lift and thrust forces
Note: Guideway is fixed in this test.

26. 26
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Test Results: Test-D
Initial Conditions:
g0 =26.79mm geq=21.5mm
vx=3.5m/s ωm=77.21rad/s
vy=0m/s sl=0.3605m/s
2
2
( ) ( ) ( )
' sgn ' ( ) ( , , , )EDW
y x y m
d y t dy t dy t
m c m G ky t F y v v
dt dt dt
 
 
    
 
Fig. 1: Measured RPM and vy
Fig. 2: Measured and calculated air-gap values
Fig. 3: Calculate lift and thrust forces

27. 27
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Test Results: Test-E
2
2
( ) ( ) ( )
' sgn ' ( ) ( , , , )EDW
y x y m
d y t dy t dy t
m c m G ky t F y v v
dt dt dt
 
 
    
 
Fig. 1: Measured RPM, vy and vx
Fig. 2: Measured and calculated air-gap values
Fig. 3: Calculate lift and thrust forces
Initial Conditions:
g0 =22.10mm geq=21.5mm
vx=1.55m/s ωm=10.62rad/s
vy=0m/s sl=-1.019m/s

28. 28
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Fig. 1: Multiple EDW vehicle experimental setup
EDW Maglev Vehicle Setup
Guideway
Guideway
DC Motor
EDW Maglev
vehicle
Fig. 3: EDW vehicle.
Fig. 2: EDW vehicle with cooling fans and
adjustable height mechanism.
Weight of Maglev vehicle = 11.3kg

29. 29
8/27/2016
Fig. 2: EDW vehicle bottom view in Autocad.
EDW Maglev Vehicle Setup
Fig. 4: Guideway and EDW configuration.
Fig. 3: EDW Maglev top view.Fig. 1: EDW Maglev bottom view.
z
y

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Fig. 2: Rotor assembly setup and rotor
EDW Magnetic Fields Measurements
Front Right
Rear Right
Front Left
Rear Left
Fig. 3: Rotor magnetization and length
Fig. 1: Halbach rotor By field measured at 7.8mm away from rotor surface.

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Fig. 3: Lift and thrust force vs RPM of the experimental EDW.
Maglev in Simulink/SimMechanics (1)
Fig. 2: SimMechanics Maglev (Convex hull)
Fig. 4: Force and angle direction of Maglev.
0 1000 2000 3000 4000 5000 6000 7000
-100
-50
0
50
100
Slip speed
ThrustForce(N)
vx
=0ms-1
vx
=5ms-1
vx
=10ms-1
@ g=5mm, z-offset =0mm
RPM
0 1000 2000 3000 4000 5000 6000 7000
0
50
100
150
Slip speed
LiftForce(N)
vx
=0ms-1
vx
=5ms-1
vx
=10ms-1
@g=5mm, z-offset = 0mm
RPM
Fig. 1: Lateral force vs z-offset .
-0.06 -0.04 -0.02 0 0.02 0.04 0.06
-20
-10
0
10
20
z-offset
LateralForce(N)
vx
=0ms-1
vx
=5ms-1
vx
=10ms-1
@4000RPM, g=5mm
z-offset (m)

32. 0 0.5 1 1.5 2
-2
0
2
4
6
x 10
-4
RollAngle(deg)
Time (s)
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Fig. Pitch, roll and yaw angle of Maglev.
Maglev in Simulink/SimMechanics (2)
0 0.5 1 1.5 2 2.5
0
10
20
30
40
Airgap(mm)
Airgap of 4-EDWs [mm]
Time (s)
Front Right
Front Left
Rear Right
Rear Left
0 0.5 1 1.5 2 2.5
-1
-0.5
0
0.5
Velocity:vy
(m/s)
Heave velocity (vy
) of 4 EDWs
Time (s)
Front Right
Front Left
Rear Right
Rear Left
0 0.5 1 1.5 2
-2
0
2
4
6
PitchAngle(deg)
Time (s)
0 0.5 1 1.5 2
-20
-15
-10
-5
0
5
x 10
-4
YawAngle(deg)
Time (s)
Maglev pitch angle
Maglev roll angle
Maglev yaw angle

33. 0 0.5 1 1.5 2
0
5
10
15
20
25
30
Airgap(mm)
Time (s)
Maglev airgap
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Maglev in Simulink/SimMechanics (3)
0 0.5 1 1.5 2 2.5
-5
0
5
10
15
LateralForce(N)
Lateral Forces of 4 EDWs
Time (s)
Front Right
Front Left
Rear Right
Rear Left
0 0.5 1 1.5 2 2.5
-20
0
20
40
60
80
100
LiftForce(N)
Lift Forces of 4 EDWs
Time (s)
Front Right
Front Left
Rear Right
Rear Left
0 0.5 1 1.5 2 2.5
-20
0
20
40
60
80
100
ThrustForce(N)
Thrust Forces of 4 EDWs
Time (s)
Front Right
Front Left
Rear Right
Rear Left
0 0.5 1 1.5 2 2.5
0
5
10
15
Velocity:vx(m/s)
Translational velocity (vx
) of 4 EDWs
Time (s)
Front Right
Front Left
Rear Right
Rear Left
0 0.5 1 1.5 2 2.5
-0.02
0
0.02
0.04
0.06
0.08
zoffset(m)
zoffset of 4-EDWs [m]
Time (s)
Front Right
Front Left
Rear Right
Rear Left
Initial conditions: g=5mm, ωm=4000RPM, vx=0m/s, vy=0m/s, z-offset=0mm

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Fig. 3: Lift & thrust force at z-offset=31.5mm,
g=5mm and vy=0m/s.
Maglev Stability in z-direction
Fig. 1: EDW and guideway lateral configuration
0 1000 2000 3000 4000 5000 6000 7000
-20
0
20
40
RPM
ThrustForce(N)
v
x
=0ms-1
vx
=5ms-1
v
x
=2ms-1
0 1000 2000 3000 4000 5000 6000 7000
0
20
40
60
RPM
LiftForce(N)
v
x
=0ms-1
v
x
=5ms-1
vx
=2ms-1
Unstable region
-0.06 -0.04 -0.02 0 0.02 0.04 0.06
0
20
40
60
80
100
z-offset
LiftForce(N)
vx
=0ms-1
vx
=5ms-1
vx
=10ms-1
-0.06 -0.04 -0.02 0 0.02 0.04 0.06
0
20
40
60
80
100
z-offset
ThrustForce(N)
vx
=0ms-1
vx
=5ms-1
vx
=10ms-1
Fig. 2: Lateral, lift & thrust force at 4000RPM , g=5mm and vy=0m/s.

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Fig. 3: Guideway and EDW configuration for lateral stability.
EDW Maglev Vehicle with Lateral Stability
Fig. 2: Bottom view of 4-wheeled Maglev setup.
Fig. 1: Maglev setup with lateral stability.

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EDW Maglev Vehicle Setup

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Maglev Experimental Results
0 5 10 15 20
-2
0
2
4
6
8
Time (s)
Airgap(mm)
Front Right
0 5 10 15 20
0
1
2
3
4
5
Time (s)
Airgap(mm)
Rear Right
Rear Left
Front Left
0 5 10 15 20
-0.5
0
0.5
1
1.5
Time (s)
Airgap(mm)
Front Left
0 5 10 15 20
-2
0
2
4
6
Time (s)Airgap(mm)
Rear Left
Rear Right
Front Right
* The initial airgap is about 5mm on all rotors.
* The maximum angular speed of rotor = 5000RPM

38. Summary
 A 2D analytic based steady-state eddy-current model has been developed and verified
using FEA model
 A 2D analytic based transient eddy-current model has been developed for a step change
and continuous input changes and verified using FEA models
 The equations are written in a general form so other magnetic sources can be used.
 Magnetic stiffness and damping constants are evaluated analytically and analyzed for
various input parameters
 The dynamic behavior of EDW Maglev vehicle has been investigated using both steady-
state and transient 2D analytical model with 2-DOF Maglev vehicle
 Experimental set-up of pendulum model EDW has been validated.
 Experimental Maglev vehicle using 4 EDWs has been constructed and tested for lateral
stability.
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39. Thank you !
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