Analytical Model of Airgap Flux of Moving Coil

Linear Generator

Imran Fazal Electronics Engineering, Yanbu Industrial College

Email: imranf79pk@yahoo.com

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.

Index Terms—linear generator, FEM, airgap flux and flux

density

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

Manuscript received November 1, 2012; revised December 29, 2012.

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].

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.

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.

International Journal of Electrical Energy, Vol.1, No.1, March 2013

34©2013 Engineering and Technology Publishing doi: 10.12720/ijoee.1.1.34-36

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

Figure 2. FEM model of moving coil linear generator.

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.

Figure 3. Flux lines of moving coil linear generator.

0.00 5.00 10.00 15.00 20.00 25.00 30.00 35.00Distance(mm) [mm]

-3.00E-011

-2.00E-011

-1.00E-011

0.00E+000

1.00E-011

2.00E-011

3.00E-011

Flu

x D

en

sity(T

esla

)

Maxwell2DDesign1XY Plot 3 ANSOFT

Figure 4. Flux density of moving coil linear generator.

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].

MagnetMH

WindingAirgapHB

r 00

0 /

. (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).

0

remBM . (2)

The airgap can be represented by (3) [8] and [9].

02 A . (3)

Where A is magnetic vector potential and it is represented

in terms of flux density in (4).

BA . (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.

02

2

2

2

y

A

x

A. (5)

iy

Aj

x

ABjBi

. (6)

Therefore

x

ABy

y

ABx

; .

Solving (5) by variable sepration method and with

following boundary conditions.

00

0

),(),0(

)0,(),(

yTpy

xHmx

BxBx

BxBBy

Where as

MHB r 00 and remBM 0

The magnetic vector will take the form as shown in (7).

))(cosh(

))))(sinh()(cos()((

TpHm

Tp

y

Tpx

rem TpBHA

. (7)

Putting the value of magnetic vector potential in (6) the

flux density components are calculated by (8) and (9).

))(cosh(

))))(sinh()(sin()((

TpHm

Tp

y

Tpx

rem TpBHBy

. (8)

International Journal of Electrical Energy, Vol.1, No.1, March 2013

35©2013 Engineering and Technology Publishing

))(cosh(

))))(cosh()(cos()((

TpHm

Tp

y

Tpx

rem TpBHBx

. (9)

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.

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.

REFERENCES

[1] I. Boldea and S. A. Nasar, “Linear electric actuators and

generators,” Cambridge University Press, New York, 1997.

[2] W. M. Arshad, “A low-leakage linear transverse-flux machine for a

free-piston generator,” Ph.D. dissertation, ISBN 91-7283-535-4,

Royal Institute of Technology, Stockholm, 2003.

[3] W. M. Arshad, T. Bäckström, P. Thelin, and C. Sadarangani

“Integrated free-piston generators: An overview,” IEEE

NORPIE-2, Stockholm, 2002.

[4] P. X. Zhao and S. Q. Chang, “Improved moving-coil electric

machine for internal combustion linear generator,” IEEE Trans.

On Energy Conversion, vol. 25, issue 2, pp. 281-286, June 2010.

[5] D. Rerkpreedapong, “Field analysis and design of a moving iron

linear alternator for use with linear engine,” Master Thesis,

College of Engineering and Mineral Resources, West Virginia

University, West Virginia, 1999.

[6] I. Boldea, “Variable speed generator,” CRC Taylor & Francis

Group Press, New York, 2006.

[7] S. A. Zulkifli, “Modeling, simulation and implementation of

rectangular commutation for starting of free-piston linear

generator,” M.Sc. Thesis, Universiti Teknologi PETRONAS,

Malaysia, 2007.

[8] J. Wang, G. W. Jewell, and D. Howe, “A general framework for the

analysis and design of tubular linear permanent magnet achiness,”

IEEE Trans. On Magnetic, vol. 35, issue. 3, pp. 1986-2000, May

1999.

[9] I. Boldea, S. A. Nasar, and Z. X. Fu, “Fileds, forces and

performance equation of aircore linear self-synchronous motor

with rectangular current control,” IEEE Trans. On Magnetics, vol.

24, issue 5, pp. 2194-2203, Sep. 1988.

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.

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.

International Journal of Electrical Energy, Vol.1, No.1, March 2013

36©2013 Engineering and Technology Publishing