Download Analytical Model of Airgap Flux of Moving Coil Linear Generator

International Journal of Electrical Energy, Vol.1, No.1, March 2013
Analytical Model of Airgap Flux of Moving Coil
Linear Generator
Imran Fazal
Electronics Engineering, Yanbu Industrial College
Email: [email protected]
Mohammad Noh Karsitti
Electrical Engineering, Universiti Teknologi PETRONAS
Abstract—The modeling of airgap flux is one of essential for
analysis and design of permanent magnet machine. This
paper presents the analytical model of airgap flux of moving
coil linear generator. The analytical model is based on the
resolution of Laplace’s equation (by variable separation
techniques) for airgap. The solution is obtained using
boundary condition. The model data is compared with
Finite element method data. The analytical model is used to
the estimate the thrust force, eddy current losses and
magnetic saturation. 
permanent-magnet linear generators have drawbacks
which include thermal and impact force demagnetization
of magnets in the translator. Thermal insulation of the
moving part is a complex task due to weight limitation of
the translator [3]. In a moving-coil machine, there is no
magnet in the mover thus there is no thermal or impact
force demagnetization [4].The moving coil and Iron linear
generators are adopted. The moving iron linear generator
(MILG) is rugged and low cost for production therefore is
favorable for the application [5].
Index Terms—linear generator, FEM, airgap flux and flux
density
II. PROBLEM STATEMENT
The moving-magnet linear generator (MMLG) requires
complex control strategies. A limit switch is required to
sense the end of stroke. A moving-coil linear generator
with commutators can solve the problem by applying
current at the end of commutator segment [4] and [6]. In a
linear motion actuator, current is supplied in the direction
that assists the movement of the translator with the help of
force of attraction between the coils and permanent
magnets. In the case of starting a free-piston
moving-magnet linear generator, the position of the
translator is important for motoring during the starting
process [7]. Sensing the position of the translator is a
complex task. Therefore MILG and MMLG is having this
drawback while in contrast, starting a moving-coil linear
generator with commutators does not require knowledge
of translator position. The coil is energized via the
commutator in the same way as in rotary DC commutator.
EMF generated by a moving-magnet generator requires an
additional converter stage to convert the distorted AC to
DC. Instead, the conversion of AC to DC in a moving-coil
linear generator with commutator is performed by the
usual commutator segments.
I. INTRODUCTION
The linear machines are used in numerous applications
over its counterpart rotary permanent magnet machines.
One of the application internal combustion engine
generators it replaced its counterpart is called free piston
linear generator. The linear generator is the integral part of
the piston. In this type of engine the crank shaft is removed
from it. The fuel efficiency of the engine is increased. The
figure shows the free piston linear generator [1] and [2].
Figure 1. Free piston linear engine generator Set[2].
Linear generator is of classified in three type’s namely
moving magnet, moving coil and moving iron. The
moving magnet generator the magnets are placed on the
translator and coil is placed on stator. The moving coil
generator is a type in which coil is placed on translator and
magnets are place on stator. The moving iron type
generator consists of reluctance variable translator and
magnet and coil is placed at stator [1] and [2].
The research is focused on moving coil linear generator
due to the advantages of over other types. Moving
III. FEM SETUP
Simulation software Maxwell ™ 13.0 is used as a tool
for the finite element method (FEM) analysis. The FEM
analysis is performed on moving-coil linear generators.
Fig. 2. The magnets are arranged in a way that most of the
flux passes through the central air gap. The translator is
placed in the central air gap. The translator is moved with a
step of 1 mm and data is recorded with respect to distance
for the distance. The setup specification is shown in
TABLE I.
Manuscript received November 1, 2012; revised December 29, 2012.
©2013 Engineering and Technology Publishing
doi: 10.12720/ijoee.1.1.34-36
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International Journal of Electrical Energy, Vol.1, No.1, March 2013
TABLE I: SPECIFICATION OF MOVING COIL MACHINES
Machine
2-pole MCLG
Axial Length
26 mm
Outer stator diameter
30 mm
Inner stator diameter
10 mm
Height of magnets
10 mm
V. ANALYTICAL MODEL
The magnetic field analysis is confined to the
airgap/winding region. In airgap the permeability is µ0.
The flux density of the whole machine is given in (1) [8].
0 H

B
 0  r H   0 M
Airgap / Winding 
.
Magnet

(1)
Where µr is relative recoil permeability of the magnet and
M is the remanent magnetization. For permanent magnet
having linear magnetization M is related to Brem by (2).
M 
Brem
.
0
(2)
The airgap can be represented by (3) [8] and [9].
2 A  0 .
(3)
Where A is magnetic vector potential and it is represented
in terms of flux density in (4).
Figure 2. FEM model of moving coil linear generator.
 A  B.
IV. FEM MODEL RESULTS
The flux lines of the machines is plotted and shown in
Fig. 3. Most of the flux is passing through the air gap and
leakage flux is passing through the spacers. The magnets
at the left side are magnetized in radically downward
direction. The right side magnets are magnetized in
radially upward direction. Flux density distribution in
airgap is shown in Fig. 4.
(4)
Where as in this modeling the flux density components are
deduced from z-axis component of A therefore the (3) and
(4) will take the form of (5) and (6) respectively.
2 A 2 A
 0.

2x 2 y
Bi  Bj 
(5)
A
A
i.
j
y
x
(6)
Therefore
Bx 
A
A
; By 
.
x
y
Solving (5) by variable sepration method and with
following boundary conditions.
Figure 3. Flux lines of moving coil linear generator.
XY Plot 3
Maxwell2DDesign1
ANSOFT
By( x , Hm )  B
Bx( x , 0)  0
Bx( 0, y )  0
Bx(Tp , y )  0
3.00E-011
Where as
2.00E-011
B  0  r H  0 M and 0 M  Brem
1.00E-011
Flux Density(Tesla)
The magnetic vector will take the form as shown in (7).
0.00E+000
A
-1.00E-011
-2.00E-011
y
x
( H  Brem )(Tp)(cos(Tp
))(sinh( Tp
))
Hm
 (cosh( Tp
))
. (7)
Putting the value of magnetic vector potential in (6) the
flux density components are calculated by (8) and (9).
-3.00E-011
0.00
5.00
10.00
15.00
20.00
Distance(mm) [mm]
25.00
30.00
35.00
Figure 4. Flux density of moving coil linear generator.
©2013 Engineering and Technology Publishing
By 
35
y
x
( H  Brem )(Tp)(sin( Tp
))(sinh( Tp
))
Hm
 (cosh( Tp
))
. (8)
International Journal of Electrical Energy, Vol.1, No.1, March 2013
Bx 
y
x
( H  Brem )(Tp)(cos(Tp
))(cosh( Tp
))
Hm
))
 (cosh( Tp
[7]
. (9)
[8]
The Tp is the pole pitch of the machine Brem is the
remenance of the magnet H is the magnetization of the
magnet and Hm is the height of the magnets.
[9]
V. DISCUSSION
The flux density from the model is compared with FEM
data. All the components plug in to the flux density model
is from FEM model.
Imran Fazal is lecturer in Electronics and
Instrumentation Department of Yanbu Industrial
College, He did his master by research from
Universiti Teknologi Petronas Malaysia, Currently
He is working on his PhD Project that is Design of
moving coil linear generator, His areas of interests
are Haptic Feedback, Robotics, Linear Generators, Alternative Energy.
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©2013 Engineering and Technology Publishing
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Mohd Noh Bin Karsiti is Associate Professor in
Electrical and Electronics Engineering department of
Universiti Teknologi Petronas, Malaysia; He did
Doctor of Philosopy in Engineering, University of
Califonia and Masters of Science in Electrical
Engineering, Califonia State University, Long Beach
Bachelor of Science in Electrical Engineering,
Califonia State University, Long Beach. His area specialization is control
systems,robotic, artificial intelligence. He supervised numerous research
projects and students.
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